Finite Group Databasebeta

← #33967923

Subgroups — #33967923

Order 18688.

2104 conjugacy classes of subgroups.

The subgroup lattice has 1782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623547C211yesmaximal, characteristic, complemented
2D4×#11924027C211yesmaximal, characteristic, complemented
3#22622948C211yesmaximal, characteristic, complemented
4#22622853C211yesmaximal, characteristic, complemented
5#22622655C211yesmaximal, characteristic, complemented
6#22622644C211yesmaximal, characteristic, complemented
7#22622373C211yesmaximal, characteristic, complemented
8#22622366C211yesmaximal, characteristic, complemented
9#22622275C211yesmaximal, characteristic, complemented
10#22621952C211yesmaximal, characteristic, complemented
11#22621945C211yesmaximal, characteristic, complemented
12#22621922C211yesmaximal, characteristic, complemented
13#22621915C211yesmaximal, characteristic, complemented
14#22621789C211yesmaximal, characteristic, complemented
15#22621737C211yesmaximal, characteristic, complemented
16SD16×C22⋊D73C211yesmaximal, characteristic, complemented
17#22621420C211yesmaximal, characteristic, complemented
18#22620644C211yesmaximal, characteristic, complemented
19#22620626C211yesmaximal, characteristic, complemented
20#22620624C211yesmaximal, characteristic, complemented
21#22620075C211yesmaximal, characteristic, complemented
22#22620068C211yesmaximal, characteristic, complemented
23#22620064C211yesmaximal, characteristic, complemented
24#22620052C211yesmaximal, characteristic, complemented
25#22620048C211yesmaximal, characteristic, complemented
26#22620025C211yesmaximal, characteristic, complemented
27#22618941C211yesmaximal, characteristic, complemented
28AGL(1,ℤ/8)×Dic73C211yesmaximal, characteristic, complemented
29C2×#17988688C211yesmaximal, characteristic, complemented
30#440×D73C211yesmaximal, characteristic, complemented
31C73×#3265C211yesmaximal, characteristic, complemented
32C22×#11924027—21no—
33C2×SD16×D73C2211yescharacteristic
34#17989313C2211yescharacteristic, complemented
35#17989306—21no—
36#17989306C2211yescharacteristic, complemented
37#17989277—21no—
38#17989277C2211yescharacteristic, complemented
39#17989271—21no—
40#17989271C2211yescharacteristic, complemented
41#17989257C2211yescharacteristic
42D4×Dic146C2211yescharacteristic
43Q8×C22⋊D73C2211yescharacteristic, complemented
44#17989244C2211yescharacteristic, complemented
45#17989243—21no—
46#17989241C2211yescharacteristic
47#17989237—21no—
48#17989237C2211yescharacteristic
49#17989237C2211yescharacteristic
50#17989237C2211yescharacteristic, complemented
51#17989231—21no—
52#17989224—21no—
53#17989224—21no—
54D4×C22⋊D73C2211yescharacteristic
55D4×C22⋊D73C2211yescharacteristic
56#17989139—21no—
57#17989139C2211yescharacteristic, complemented
58#17989135C2211yescharacteristic
59#17989132C2211yescharacteristic
60#17989132C2211yescharacteristic
61#17989118—21no—
62#17989118C2211yescharacteristic, complemented
63#17989116—21no—
64#17989116C2211yescharacteristic, complemented
65#17989097—21no—
66#17989093—21no—
67#17989093—21no—
68#41×Dic73C2211yescharacteristic, complemented
69C4×#11924027—21no—
70C4×#11924027C2211yescharacteristic
71C2×Q8×Dic73C2211yescharacteristic, complemented
72C4×Q8×D73C2211yescharacteristic, complemented
73C2×D4×Dic73C2211yescharacteristic
74C2×D4×Dic73C2211yescharacteristic
75C4×D4×D73C2211yescharacteristic
76#17988996C2211yescharacteristic, complemented
77#17988995C2211yescharacteristic, complemented
78#17988991C2211yescharacteristic, complemented
79#17988975C2211yescharacteristic, complemented
80#17988958C2211yescharacteristic, complemented
81#17988951C2211yescharacteristic, complemented
82#17988950C2211yescharacteristic, complemented
83#17988946C2211yescharacteristic, complemented
84#17988945C2211yescharacteristic, complemented
85#17988936C2211yescharacteristic, complemented
86#17988932C2211yescharacteristic, complemented
87#17988923C2211yescharacteristic, complemented
88#17988920C2211yescharacteristic, complemented
89#17988918C2211yescharacteristic, complemented
90#17988916C2211yescharacteristic, complemented
91#17988912C2211yescharacteristic, complemented
92#17988908C2211yescharacteristic, complemented
93#17988901C2211yescharacteristic, complemented
94#17988899C2211yescharacteristic, complemented
95#17988899C2211yescharacteristic, complemented
96#17988899C2211yescharacteristic, complemented
97#17988898C2211yescharacteristic, complemented
98#17988898C2211yescharacteristic, complemented
99#17988889C2211yescharacteristic
100#17988889C2211yescharacteristic, complemented
101#17988888C2211yescharacteristic, complemented
102#17988887C2211yescharacteristic
103#17988883C2211yescharacteristic, complemented
104#17988882C2211yescharacteristic, complemented
105#17988880C2211yescharacteristic, complemented
106#17988880C2211yescharacteristic, complemented
107#17988870C2211yescharacteristic, complemented
108#17988865C2211yescharacteristic
109#17988865C2211yescharacteristic, complemented
110#17988865C2211yescharacteristic, complemented
111#17988835C2211yescharacteristic, complemented
112#17988833C2211yescharacteristic, complemented
113#17988831C2211yescharacteristic, complemented
114#17988821C2211yescharacteristic, complemented
115#17988820C2211yescharacteristic, complemented
116#17988820C2211yescharacteristic, complemented
117#17988816C2211yescharacteristic, complemented
118#17988814C2211yescharacteristic, complemented
119#17988813C2211yescharacteristic, complemented
120#17988813C2211yescharacteristic, complemented
121#17988800C2211yescharacteristic
122#17988800C2211yescharacteristic, complemented
123#17988799C2211yescharacteristic, complemented
124#17988790C2211yescharacteristic
125#17988790C2211yescharacteristic, complemented
126#17988785C2211yescharacteristic, complemented
127#17988785C2211yescharacteristic, complemented
128#17988785C2211yescharacteristic, complemented
129#17988784C2211yescharacteristic, complemented
130#17988780C2211yescharacteristic, complemented
131#17988738C2211yescharacteristic
132#17988738C2211yescharacteristic
133#17988736C2211yescharacteristic
134#17988732C2211yescharacteristic, complemented
135#17988726C2211yescharacteristic, complemented
136#17988724C2211yescharacteristic, complemented
137#17988724C2211yescharacteristic, complemented
138#17988719C2211yescharacteristic
139#17988716C2211yescharacteristic, complemented
140#17988715C2211yescharacteristic, complemented
141#17988699C2211yescharacteristic
142#17988699C2211yescharacteristic, complemented
143#17988699C2211yescharacteristic, complemented
144#17988696C2211yescharacteristic, complemented
145#17988690C2211yescharacteristic, complemented
146#17988690C2211yescharacteristic, complemented
147#17988689C2211yescharacteristic, complemented
148#17988688C2211yescharacteristic
149#17988688C2211yescharacteristic
150#17988688C2211yescharacteristic
151#17988688C2211yescharacteristic
152#17988688C2211yescharacteristic, complemented
153#17988688C2211yescharacteristic, complemented
154#17988688C2211yescharacteristic, complemented
155#17988688C2211yescharacteristic, complemented
156#17988688C2211yescharacteristic, complemented
157#17988688C2211yescharacteristic, complemented
158#17988687C2211yescharacteristic
159#17988686C2211yescharacteristic, complemented
160#17988685C2211yescharacteristic, complemented
161#17988684C2211yescharacteristic
162#17988684C2211yescharacteristic, complemented
163#17988684C2211yescharacteristic, complemented
164SD16×Dic73C2211yescharacteristic
165SD16×Dic73C2211yescharacteristic, complemented
166D8×Dic73C2211yescharacteristic
167D8×Dic73C2211yescharacteristic, complemented
168#17988661C2211yescharacteristic, complemented
169#17988659C2211yescharacteristic, complemented
170#17988656C2211yescharacteristic, complemented
171C8×C22⋊D73C2211yescharacteristic, complemented
172#17988650C2211yescharacteristic, complemented
173#17988643C2211yescharacteristic, complemented
174#17988641C2211yescharacteristic, complemented
175#17988641C2211yescharacteristic, complemented
176#17988629C2211yescharacteristic, complemented
177C2×#14556525C2211yescharacteristic, complemented
178#107×D73C2211yescharacteristic, complemented
179#17988592C2211yescharacteristic
180#17988588C2211yescharacteristic, complemented
181C2×#14556515C2211yescharacteristic, complemented
182#103×D73C2211yescharacteristic, complemented
183C2×#14556512C2211yescharacteristic
184#102×D73C2211yescharacteristic
185M16×Dic73C2211yescharacteristic, complemented
186C2×#14556501C2211yescharacteristic, complemented
187#97×D73C2211yescharacteristic, complemented
188C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
189C22×SD16×C73C2211yescharacteristic
190#548×C73C2211yescharacteristic, complemented
191D42×C73C2211yescharacteristic
192#496×C73C2211yescharacteristic, complemented
193#468×C73C2211yescharacteristic, complemented
194#466×C73C2211yescharacteristic, complemented
195#463×C73C2211yescharacteristic
196#460×C73C2211yescharacteristic, complemented
197#450×C73C2211yescharacteristic
198#449×C73C2211yescharacteristic, complemented
199#448×C73C2211yescharacteristic, complemented
200#447×C73C2211yescharacteristic
201#440×C73C2211yescharacteristic
202#435×C73C2211yescharacteristic, complemented
203C2×#11924027—21no—
204C2×#11924027—21no—
205C2×#11924027—21no—
206C2×#11924027—21no—
207C2×#11924027—21no—
208C2×#11924027—21no—
209C2×#11924027—21no—
210C2×#11924027—21no—
211C2×#11924027—48no—
212C2×#11924027D411yescharacteristic
213C22×Dic146—21no—
214C2×Q8×D73C2311yescharacteristic
215C22×C22⋊D73—21no—
216C22×C22⋊D73—21no—
217C2×D4×D73C2311yescharacteristic
218C23×Dic73—21no—
219C23×Dic73—21no—
220C22×C4×D73—21no—
221C2×#11924017C2311yescharacteristic
222C2×#11924016C2311yescharacteristic
223C2×#11924016C2311yescharacteristic
224C2×#11924016C2311yescharacteristic
225C2×#11924015C2311yescharacteristic
226C2×#11924015C2311yescharacteristic
227SD16×D73—24no—
228C2×#11924013C2311yescharacteristic
229C2×#11924012C2311yescharacteristic
230C22×#10596831C2311yescharacteristic
231C2×C8×D73C2311yescharacteristic
232C2×C8×D73C2311yescharacteristic
233#14556591C2311yescharacteristic
234#14556590—21no—
235#14556590C2311yescharacteristic
236#14556590C2311yescharacteristic
237#14556590C2311yescharacteristic
238#14556589—21no—
239#14556589C2311yescharacteristic
240#14556587C2311yescharacteristic
241#14556587C2311yescharacteristic
242#14556584—21no—
243#14556584—21no—
244#14556584—21no—
245#14556584—21no—
246#14556584—21no—
247#14556584—21no—
248#14556583—21no—
249#14556583C2311yescharacteristic
250#14556582—21no—
251#14556582C2311yescharacteristic
252#14556581—21no—
253#14556581—21no—
254#14556581—21no—
255#14556578—21no—
256#14556578—21no—
257#14556578C2311yescharacteristic
258#14556577—21no—
259#14556577—21no—
260#14556575—21no—
261#14556575—21no—
262#14556573—21no—
263#14556573—21no—
264#14556573—21no—
265#14556573—21no—
266#14556573—21no—
267#14556572—21no—
268#14556572—21no—
269#14556572—21no—
270#14556572—21no—
271#14556572—21no—
272#14556571—21no—
273#14556570—21no—
274#14556570—21no—
275#14556570—21no—
276#14556570C2311yescharacteristic
277#14556570C2311yescharacteristic
278#14556568—21no—
279#14556568—21no—
280#14556568—21no—
281#14556568—21no—
282#14556568—21no—
283#14556568—21no—
284#14556568—21no—
285#14556567—21no—
286#14556567C2311yescharacteristic
287#14556565C2311yescharacteristic
288#14556565C2311yescharacteristic
289#14556563—21no—
290#14556563—21no—
291#14556563—21no—
292#14556563—21no—
293#14556563—21no—
294#14556563—21no—
295#14556562—21no—
296#14556562—21no—
297#14556562—21no—
298#14556562C2311yescharacteristic
299#14556562C2311yescharacteristic
300#14556562C2311yescharacteristic
301#14556560—21no—
302#14556560—21no—
303#14556559—21no—
304#14556559—21no—
305Q8×Dic73—21no—
306Q8×Dic73—21no—
307Q8×Dic73C2311yescharacteristic
308Q8×Dic73C2311yescharacteristic
309Q8×Dic73C2311yescharacteristic
310Q8×Dic73C2311yescharacteristic
311Q8×Dic73C2311yescharacteristic
312C4×Dic146—21no—
313C4×Dic146—21no—
314C4×Dic146C2311yescharacteristic
315C4×Dic146C2311yescharacteristic
316#14556556—21no—
317#14556556—21no—
318#14556556D411yescharacteristic
319#14556556C2311yescharacteristic
320C4×D292C2311yescharacteristic
321D4×Dic73—21no—
322D4×Dic73—21no—
323D4×Dic73—21no—
324D4×Dic73—21no—
325D4×Dic73—21no—
326D4×Dic73—21no—
327D4×Dic73—21no—
328D4×Dic73—21no—
329D4×Dic73D411yescharacteristic
330D4×Dic73C2311yescharacteristic
331D4×Dic73C2311yescharacteristic
332D4×Dic73C2311yescharacteristic
333D4×Dic73C2311yescharacteristic
334D4×Dic73C2311yescharacteristic
335D4×Dic73C2311yescharacteristic
336D4×Dic73C2311yescharacteristic
337D4×Dic73C2311yescharacteristic
338D4×Dic73C2311yescharacteristic
339#14556553C2311yescharacteristic
340C4×C22⋊D73—21no—
341C4×C22⋊D73—21no—
342C4×C22⋊D73—21no—
343C4×C22⋊D73C2311yescharacteristic
344C4×C22⋊D73C2311yescharacteristic
345#14556551—21no—
346#14556551—21no—
347#14556551—21no—
348#14556551—21no—
349#14556551D411yescharacteristic
350#14556551D411yescharacteristic
351#14556550—21no—
352#14556550C2311yescharacteristic
353#14556549—21no—
354#14556549D411yescharacteristic
355#14556547—21no—
356#14556547—21no—
357#14556547—21no—
358#14556547—21no—
359#14556547—21no—
360#14556547D411yescharacteristic
361#14556547D411yescharacteristic
362C2×C4⋊Dic73—21no—
363C2×C4⋊Dic73C2311yescharacteristic
364C2×C4⋊Dic73C2311yescharacteristic
365C2×C4⋊Dic73C2311yescharacteristic
366C4⋊C4×D73—21no—
367C4⋊C4×D73C2311yescharacteristic
368C4⋊C4×D73C2311yescharacteristic
369C2×C22⋊Dic73—21no—
370C2×C22⋊Dic73—21no—
371C22⋊C4×D73—21no—
372C2×C4×Dic73—21no—
373C2×C4×Dic73—21no—
374C2×C4×Dic73C2311yescharacteristic
375C2×C4×Dic73C2311yescharacteristic
376C42×D73—21no—
377C42×D73C2311yescharacteristic
378#14556525C2311yescharacteristic
379#14556525C2311yescharacteristic
380#14556525C2311yescharacteristic
381#14556525C2311yescharacteristic
382#14556525C2311yescharacteristic
383#14556525C2311yescharacteristic
384#14556524C2311yescharacteristic
385#14556524C2311yescharacteristic
386#14556524C2311yescharacteristic
387#14556524C2311yescharacteristic
388#14556524C2311yescharacteristic
389#14556523C2311yescharacteristic
390#14556523C2311yescharacteristic
391#14556523C2311yescharacteristic
392#14556522C2311yescharacteristic
393C4⋊#10596831C2311yescharacteristic
394#14556520C2311yescharacteristic
395#14556520C2311yescharacteristic
396#14556520C2311yescharacteristic
397#14556520C2311yescharacteristic
398#14556516C2311yescharacteristic
399#14556516C2311yescharacteristic
400#14556516C2311yescharacteristic
401#14556515C2311yescharacteristic
402#14556515C2311yescharacteristic
403#14556515C2311yescharacteristic
404#14556515C2311yescharacteristic
405#14556515C2311yescharacteristic
406#14556515C2311yescharacteristic
407#14556514C2311yescharacteristic
408#14556513C2311yescharacteristic
409#14556513C2311yescharacteristic
410#14556513C2311yescharacteristic
411#14556512C2311yescharacteristic
412#14556512C2311yescharacteristic
413#14556512C2311yescharacteristic
414#14556512C2311yescharacteristic
415#14556512C2311yescharacteristic
416#14556512C2311yescharacteristic
417#14556512C2311yescharacteristic
418#14556512C2311yescharacteristic
419#14556512C2311yescharacteristic
420#14556512C2311yescharacteristic
421#14556512C2311yescharacteristic
422#14556512C2311yescharacteristic
423#14556511C2311yescharacteristic
424C22⋊#10596831C2311yescharacteristic
425C22⋊#10596831C2311yescharacteristic
426#14556503C2311yescharacteristic
427#14556503C2311yescharacteristic
428#14556502C2311yescharacteristic
429#14556501C2311yescharacteristic
430#14556501C2311yescharacteristic
431#14556501C2311yescharacteristic
432#14556501C2311yescharacteristic
433#14556501C2311yescharacteristic
434#14556501C2311yescharacteristic
435C8×Dic73C2311yescharacteristic
436C8×Dic73C2311yescharacteristic
437C2×#41×C73C2311yescharacteristic
438C22×Q8×C73C2311yescharacteristic
439C22×D4×C73—21no—
440C22×D4×C73C2311yescharacteristic
441C22×D4×C73C2311yescharacteristic
442AGL(1,ℤ/8)×C73—24no—
443C2×SD16×C73—24no—
444C2×SD16×C73C2311yescharacteristic
445C2×SD16×C73C2311yescharacteristic
446C2×SD16×C73C2311yescharacteristic
447C2×SD16×C73C2311yescharacteristic
448C2×SD16×C73C2311yescharacteristic
449C2×SD16×C73C2311yescharacteristic
450C2×D8×C73C2311yescharacteristic
451C2×D8×C73C2311yescharacteristic
452C2×D8×C73C2311yescharacteristic
453C2×M16×C73C2311yescharacteristic
454C22×C8×C73C2311yescharacteristic
455#127×C73C2311yescharacteristic
456#124×C73—21no—
457#124×C73C2311yescharacteristic
458C22⋊Q8×C73—21no—
459C22⋊Q8×C73C2311yescharacteristic
460#121×C73—21no—
461#121×C73—21no—
462#121×C73C2311yescharacteristic
463#121×C73C2311yescharacteristic
464#121×C73C2311yescharacteristic
465#120×C73—21no—
466#120×C73—21no—
467C4×Q8×C73C2311yescharacteristic
468C4×D4×C73—21no—
469C4×D4×C73C2311yescharacteristic
470C4×D4×C73C2311yescharacteristic
471#107×C73C2311yescharacteristic
472C4⋊C8×C73C2311yescharacteristic
473#103×C73C2311yescharacteristic
474#103×C73C2311yescharacteristic
475#102×C73C2311yescharacteristic
476#102×C73C2311yescharacteristic
477#102×C73C2311yescharacteristic
478#102×C73C2311yescharacteristic
479C22⋊C8×C73C2311yescharacteristic
480C22⋊C8×C73C2311yescharacteristic
481#97×C73C2311yescharacteristic
482C23×D73—21no—
483#11924027—24no—
484#11924027—44no—
485#11924027—44no—
486#11924027—44no—
487#11924027—44no—
488#11924027—44no—
489#11924027—44no—
490#11924027—44no—
491#11924027—44no—
492C2×Dic146—21no—
493C2×Dic146—21no—
494C2×Dic146—21no—
495C2×Dic146—21no—
496C2×Dic146—21no—
497C2×Dic146—44no—
498C2×Dic146C2×D411yescharacteristic
499C2×Dic146C2411yescharacteristic
500Q8×D73—22no—
501Q8×D73—41no—
502C2×D292C2411yescharacteristic
503C2×C22⋊D73—21no—
504C2×C22⋊D73—21no—
505C2×C22⋊D73—21no—
506C2×C22⋊D73—21no—
507C2×C22⋊D73—21no—
508C2×C22⋊D73—21no—
509C2×C22⋊D73—21no—
510C2×C22⋊D73—21no—
511C2×C22⋊D73—21no—
512C2×C22⋊D73—21no—
513C2×C22⋊D73—44no—
514C2×C22⋊D73—44no—
515C2×C22⋊D73C2×D411yescharacteristic
516C2×C22⋊D73C2×D411yescharacteristic
517D4×D73—22no—
518D4×D73—41no—
519C22×Dic73—21no—
520C22×Dic73—21no—
521C22×Dic73—21no—
522C22×Dic73—21no—
523C22×Dic73—21no—
524C22×Dic73—21no—
525C22×Dic73—21no—
526C22×Dic73—21no—
527C22×Dic73—21no—
528C22×Dic73—21no—
529C22×Dic73—21no—
530C22×Dic73—21no—
531C22×Dic73—44no—
532C22×Dic73—44no—
533C22×Dic73C2×D411yescharacteristic
534C22×Dic73C2×D411yescharacteristic
535C22×Dic73C2×D411yescharacteristic
536C22×Dic73C2×D411yescharacteristic
537C2×C4×D73—21no—
538C2×C4×D73—21no—
539C2×C4×D73—21no—
540C2×C4×D73—21no—
541C2×C4×D73—21no—
542C2×C4×D73—44no—
543C2×C4×D73C2×D411yescharacteristic
544C2×C4×D73C2×D411yescharacteristic
545C2×C4×D73C2411yescharacteristic
546#11924017—22no—
547#11924016—22no—
548#11924016—41no—
549#11924016—41no—
550#11924015—22no—
551#11924015—41no—
552#11924013—41no—
553#11924012—41no—
554C2×#10596831—41no—
555C2×#10596831C2411yescharacteristic
556C2×#10596831C2411yescharacteristic
557C2×#10596831C2411yescharacteristic
558C2×#10596831C2411yescharacteristic
559C8×D73—22no—
560C8×D73—41no—
561C4⋊Dic73—21no—
562C4⋊Dic73—21no—
563C4⋊Dic73—21no—
564C4⋊Dic73—21no—
565C4⋊Dic73—21no—
566C4⋊Dic73—21no—
567C4⋊Dic73—21no—
568C4⋊Dic73—21no—
569C4⋊Dic73—21no—
570C4⋊Dic73—21no—
571C4⋊Dic73C2×D411yescharacteristic
572C4⋊Dic73C2411yescharacteristic
573C4⋊Dic73C2411yescharacteristic
574C4⋊Dic73C2411yescharacteristic
575C4⋊Dic73C2411yescharacteristic
576C4⋊Dic73C2411yescharacteristic
577C4⋊Dic73C2411yescharacteristic
578#11924007—21no—
579#11924007—21no—
580#11924007—21no—
581#11924007—21no—
582#11924007—21no—
583#11924007—21no—
584#11924007—21no—
585#11924007—21no—
586#11924007—21no—
587#11924007—21no—
588#11924007—21no—
589#11924007—21no—
590#11924007—21no—
591#11924007—21no—
592#11924007—21no—
593#11924007C2×D411yescharacteristic
594#11924007C2×D411yescharacteristic
595#11924007C2×D411yescharacteristic
596#11924007C2×D411yescharacteristic
597C22⋊Dic73—21no—
598C22⋊Dic73—21no—
599C22⋊Dic73—21no—
600C22⋊Dic73—21no—
601C22⋊Dic73—21no—
602C22⋊Dic73—21no—
603C22⋊Dic73—21no—
604C22⋊Dic73—21no—
605C22⋊Dic73—21no—
606C22⋊Dic73—21no—
607C22⋊Dic73—21no—
608C22⋊Dic73—21no—
609C22⋊Dic73—21no—
610C22⋊Dic73—21no—
611C22⋊Dic73—21no—
612C22⋊Dic73—21no—
613C22⋊Dic73—21no—
614C22⋊Dic73C2×D411yescharacteristic
615C22⋊Dic73C2×D411yescharacteristic
616#11924005—21no—
617#11924005—21no—
618#11924005—21no—
619#11924005—21no—
620#11924005—21no—
621#11924005C2×D411yescharacteristic
622#11924005C2×D411yescharacteristic
623C4×Dic73—21no—
624C4×Dic73—21no—
625C4×Dic73—21no—
626C4×Dic73—21no—
627C4×Dic73—21no—
628C4×Dic73—21no—
629C4×Dic73—21no—
630C4×Dic73—21no—
631C4×Dic73C2×D411yescharacteristic
632C4×Dic73C2×D411yescharacteristic
633C4×Dic73C2×D411yescharacteristic
634C4×Dic73C2×D411yescharacteristic
635C4×Dic73C2×D411yescharacteristic
636C4×Dic73C2×D411yescharacteristic
637C4×Dic73C2411yescharacteristic
638C4×Dic73C2411yescharacteristic
639C4×Dic73C2411yescharacteristic
640C24×C73—21no—
641C24×C73—21no—
642#41×C73—22no—
643#41×C73—41no—
644C2×Q8×C73—21no—
645C2×Q8×C73—22no—
646C2×Q8×C73—41no—
647C2×Q8×C73C2411yescharacteristic
648C2×Q8×C73C2411yescharacteristic
649C2×D4×C73—22no—
650C2×D4×C73—22no—
651C2×D4×C73—21no—
652C2×D4×C73—21no—
653C2×D4×C73—21no—
654C2×D4×C73—21no—
655C2×D4×C73—21no—
656C2×D4×C73—21no—
657C2×D4×C73—21no—
658C2×D4×C73—21no—
659C2×D4×C73—41no—
660C2×D4×C73—41no—
661C2×D4×C73—44no—
662C2×D4×C73C2×D411yescharacteristic
663C2×D4×C73C2411yescharacteristic
664C2×D4×C73C2411yescharacteristic
665C2×D4×C73C2411yescharacteristic
666C2×D4×C73C2411yescharacteristic
667C22×C4×C73—21no—
668C22×C4×C73—21no—
669C22×C4×C73—21no—
670C22×C4×C73C2411yescharacteristic
671C22×C4×C73C2411yescharacteristic
672SD16×C73—22no—
673SD16×C73—22no—
674SD16×C73—22no—
675SD16×C73—22no—
676SD16×C73—41no—
677SD16×C73#4114yescomplemented
678D8×C73—22no—
679D8×C73—22no—
680D8×C73—41no—
681M16×C73—22no—
682C2×C8×C73—22no—
683C2×C8×C73C2411yescharacteristic
684C2×C8×C73C2411yescharacteristic
685C2×C8×C73C2411yescharacteristic
686C2×C8×C73C2411yescharacteristic
687C4⋊C4×C73—21no—
688C4⋊C4×C73—21no—
689C4⋊C4×C73C2×D411yescharacteristic
690C4⋊C4×C73C2411yescharacteristic
691C4⋊C4×C73C2411yescharacteristic
692C22⋊C4×C73—21no—
693C22⋊C4×C73—21no—
694C22⋊C4×C73—21no—
695C22⋊C4×C73—21no—
696C22⋊C4×C73—21no—
697C22⋊C4×C73—21no—
698C22⋊C4×C73—21no—
699C22⋊C4×C73C2×D411yescharacteristic
700C22⋊C4×C73C2×D411yescharacteristic
701C42×C73—21no—
702C42×C73C2411yescharacteristic
703C23×C73—21no—
704C23×C73—21no—
705C23×C73—21no—
706C23×C73—21no—
707C23×C73—42no—
708C23×C73—42no—
709C23×C73—42no—
710C23×C73—42no—
711C23×C73—81no—
712C23×C73—81no—
713C23×C73C22×D411yescharacteristic
714C23×C73C22×D411yescharacteristic
715C22×D73—21no—
716C22×D73—42no—
717C22×D73—42no—
718C22×D73—81no—
719C22×D73C22×D411yescharacteristic
720Q8×C73—21no—
721Q8×C73—21no—
722Q8×C73—21no—
723Q8×C73—42no—
724Q8×C73C2×#4112yescomplemented
725D4×C73—22no—
726D4×C73—21no—
727D4×C73—21no—
728D4×C73—21no—
729D4×C73—21no—
730D4×C73—21no—
731D4×C73—21no—
732D4×C73—21no—
733D4×C73—42no—
734D4×C73—42no—
735D4×C73—42no—
736D4×C73—42no—
737D4×C73—42no—
738D4×C73—42no—
739D4×C73—42no—
740D4×C73—81no—
741D4×C73C2×#4112yes—
742C2×C4×C73—21no—
743C2×C4×C73—21no—
744C2×C4×C73—21no—
745C2×C4×C73—21no—
746C2×C4×C73—21no—
747C2×C4×C73—21no—
748C2×C4×C73—21no—
749C2×C4×C73—21no—
750C2×C4×C73—42no—
751C2×C4×C73—42no—
752C2×C4×C73—42no—
753C2×C4×C73C22×D411yescharacteristic
754C2×C4×C73C22×D411yescharacteristic
755C2×C4×C73C22×D411yescharacteristic
756C2×C4×C73C22×D411yescharacteristic
757C2×C4×C73C2511yescharacteristic
758C22⋊D73—22no—
759C22⋊D73—42no—
760C22⋊D73—42no—
761C22⋊D73—42no—
762C22⋊D73—42no—
763C22⋊D73—42no—
764C22⋊D73—42no—
765C22⋊D73—42no—
766C22⋊D73—42no—
767C22⋊D73—81no—
768C22⋊D73—81no—
769C22⋊D73AGL(1,ℤ/8)14yescomplemented
770C2×Dic73—22no—
771C2×Dic73—22no—
772C2×Dic73—21no—
773C2×Dic73—21no—
774C2×Dic73—21no—
775C2×Dic73—21no—
776C2×Dic73—21no—
777C2×Dic73—21no—
778C2×Dic73—21no—
779C2×Dic73—41no—
780C2×Dic73—41no—
781C2×Dic73—42no—
782C2×Dic73—42no—
783C2×Dic73—42no—
784C2×Dic73—42no—
785C2×Dic73—42no—
786C2×Dic73—42no—
787C2×Dic73—42no—
788C2×Dic73—42no—
789C2×Dic73—42no—
790C2×Dic73—42no—
791C2×Dic73—42no—
792C2×Dic73—42no—
793C2×Dic73C22×D411yescharacteristic
794C2×Dic73C22×D411yescharacteristic
795C2×Dic73C22×D411yescharacteristic
796C2×Dic73C22×D411yescharacteristic
797C2×Dic73C22×D411yescharacteristic
798C2×Dic73C22×D411yescharacteristic
799C2×Dic73C22×D411yescharacteristic
800D292—21no—
801D292—21no—
802C4×D73—22no—
803C4×D73—21no—
804C4×D73—21no—
805C4×D73—41no—
806C4×D73—42no—
807C4×D73—42no—
808C4×D73—42no—
809C4×D73—42no—
810C4×D73—42no—
811Dic146—22no—
812Dic146—21no—
813Dic146—21no—
814Dic146—42no—
815Dic146—42no—
816Dic146—42no—
817Dic146—42no—
818Dic146—42no—
819C8×C73—21no—
820C8×C73—21no—
821C8×C73—21no—
822C8×C73C2×#4112yescomplemented
823#10596831—21no—
824#10596831—21no—
825#10596831—21no—
826#10596831—21no—
827C22×C73—21no—
828C22×C73—21no—
829C22×C73—21no—
830C22×C73—22no—
831C22×C73—21no—
832C22×C73—21no—
833C22×C73—41no—
834C22×C73—41no—
835C22×C73—41no—
836C22×C73—41no—
837C22×C73—41no—
838C22×C73—41no—
839C22×C73—41no—
840C22×C73—41no—
841C22×C73—41no—
842C22×C73—41no—
843C22×C73—41no—
844C22×C73—84no—
845C22×C73—84no—
846C22×C73C2×AGL(1,ℤ/8)12yes—
847C22×C73C23×D411yescharacteristic
848C2×D73—21no—
849C2×D73—21no—
850C2×D73—41no—
851C2×D73—41no—
852C2×D73—41no—
853C2×D73—84no—
854C2×D73C2×AGL(1,ℤ/8)12yes—
855C4×C73—21no—
856C4×C73—22no—
857C4×C73—21no—
858C4×C73—21no—
859C4×C73—21no—
860C4×C73—41no—
861C4×C73—41no—
862C4×C73—41no—
863C4×C73C22×#4111yescharacteristic
864C4×C73#58511yescharacteristic
865Dic73—21no—
866Dic73—21no—
867Dic73—21no—
868Dic73—21no—
869Dic73—21no—
870Dic73—21no—
871Dic73—41no—
872Dic73—41no—
873Dic73—41no—
874Dic73—41no—
875Dic73—41no—
876Dic73—41no—
877Dic73—41no—
878Dic73C2×AGL(1,ℤ/8)12yes—
879#61452—731nomaximal, Sylow
880C2×C73—22no—
881C2×C73—42no—
882C2×C73—41no—
883C2×C73—81no—
884C2×C73—81no—
885C2×C73—81no—
886C2×C73D4×#4111yescharacteristic
887C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
888C2×C73#358611yescharacteristic
889D73—22no—
890D73—81no—
891#3482—731no—
892D4×#41—731no—
893#3397—731no—
894#3386—731no—
895#3368—731no—
896#3367—731no—
897#3343—731no—
898#3343—731no—
899#3334—731no—
900#3310—731no—
901#3310—731no—
902#3308—731no—
903#3308—731no—
904#3298—731no—
905#3294—731no—
906D4×SD16—731no—
907#3265—731no—
908#3265D7311yescharacteristic, complemented
909#3182—731no—
910#3180—731no—
911#3180—731no—
912#3115—731no—
913#3114—731no—
914#3114—731no—
915#3112—731no—
916#3112—731no—
917#3110—731no—
918#2970—731no—
919C4×AGL(1,ℤ/8)—731no—
920C2×#440—731no—
921C2×#440—731no—
922C73#6145211yescharacteristic, complemented, Sylow
923C22×#41—1461no—
924C2×AGL(1,ℤ/8)C2×D7311yescharacteristic
925C22×SD16—731no—
926C22×SD16C2×D7311yescharacteristic
927#557—731no—
928#556—731no—
929#556—1461no—
930#552—731no—
931#552—731no—
932#552—1461no—
933#552—1461no—
934#550—731no—
935D4×Q8—731no—
936D4×Q8—731no—
937#548—731no—
938#548—1461no—
939#548C2×D7311yescharacteristic, complemented
940#547—731no—
941#547—731no—
942#547—731no—
943#547—731no—
944#547—1461no—
945#546—1461no—
946#546—1461no—
947#546—1461no—
948D42—731no—
949D42—731no—
950D42C2×D7311yescharacteristic
951#533—731no—
952#533—1461no—
953#532—731no—
954#532—731no—
955#532—731no—
956#529—731no—
957#529—731no—
958#529—1461no—
959#529—1461no—
960#525—1461no—
961#525—1461no—
962#525—1461no—
963C4×#41—731no—
964C4×#41—731no—
965C4×#41—1461no—
966C2×C4×Q8—731no—
967C2×C4×Q8—731no—
968C2×C4×D4—731no—
969C2×C4×D4—731no—
970C2×C4×D4—731no—
971#501—731no—
972#501—731no—
973#500—731no—
974#496—731no—
975#496C2×D7311yescharacteristic, complemented
976#492—731no—
977#490—731no—
978#490—731no—
979#489—731no—
980#489—731no—
981#487—731no—
982#486—731no—
983#484—731no—
984#484—731no—
985#483—731no—
986#483—731no—
987#482—731no—
988#482—731no—
989#480—731no—
990#480—731no—
991#480—731no—
992#480—731no—
993#480—731no—
994#480—731no—
995#478—731no—
996#478—731no—
997#478—731no—
998#478—731no—
999#477—731no—
1000#477—731no—
1001#477—731no—
1002#477—731no—
1003#475—731no—
1004#474—731no—
1005#474—731no—
1006#474—731no—
1007#468—731no—
1008#468—731no—
1009#468—731no—
1010#468C2×D7311yescharacteristic, complemented
1011#466—731no—
1012#466—731no—
1013#466—731no—
1014#466C2×D7311yescharacteristic, complemented
1015#465—731no—
1016#465—731no—
1017#465—731no—
1018#465—731no—
1019#463—731no—
1020#463—731no—
1021#463—731no—
1022#463C2×D7311yescharacteristic
1023#461—731no—
1024#461—731no—
1025#460—731no—
1026#460—731no—
1027#460—731no—
1028#460—731no—
1029#460C2×D7311yescharacteristic, complemented
1030#459—731no—
1031#450—731no—
1032#450—731no—
1033#450—731no—
1034#450C2×D7311yescharacteristic
1035#449—731no—
1036#449C2×D7311yescharacteristic, complemented
1037#448—731no—
1038#448—731no—
1039#448—731no—
1040#448C2×D7311yescharacteristic, complemented
1041#447—731no—
1042#447C2×D7311yescharacteristic
1043#446—731no—
1044#446—731no—
1045#442—731no—
1046#442—731no—
1047#442—731no—
1048#442—731no—
1049#440—731no—
1050#440—731no—
1051#440—731no—
1052#440—731no—
1053#440—731no—
1054#440—731no—
1055#440—731no—
1056#440—731no—
1057#440—731no—
1058#440—731no—
1059#440—731no—
1060#440—731no—
1061#440—731no—
1062#440—731no—
1063#440—731no—
1064#440—731no—
1065#440—731no—
1066#440—731no—
1067#440—731no—
1068#440C2×D7311yescharacteristic
1069C4×SD16—731no—
1070C4×SD16—731no—
1071C4×D8—731no—
1072C4×D8—731no—
1073#435—731no—
1074#435—731no—
1075#435—731no—
1076#435C2×D7311yescharacteristic, complemented
1077C8×D4—731no—
1078C8×D4—731no—
1079#432—731no—
1080#432—731no—
1081#432—731no—
1082#428—731no—
1083C2×#107—731no—
1084C2×#107—731no—
1085#418—731no—
1086#417—731no—
1087C2×#103—731no—
1088C2×#103—731no—
1089C2×#102—731no—
1090C2×#102—731no—
1091C4×M16—731no—
1092C2×#97—731no—
1093C2×#97—731no—
1094C2×#41—2928no—
1095C2×#41—731no—
1096C2×#41—1461no—
1097C2×#41—1461no—
1098C2×#41—1461no—
1099C2×#41—1461no—
1100C2×#41—1461no—
1101C2×#41—1461no—
1102C2×#41—1461no—
1103C2×#41—1461no—
1104C2×#41C22×D7311yescharacteristic
1105C22×Q8—731no—
1106C22×Q8—1461no—
1107C22×Q8C22×D7311yescharacteristic
1108C22×D4—21no—
1109C22×D4—731no—
1110C22×D4—1461no—
1111C22×D4—1461no—
1112C22×D4C22×D7311yescharacteristic
1113C22×D4C22×D7311yescharacteristic
1114C23×C4—1461no—
1115C23×C4—1461no—
1116C23×C4—1461no—
1117AGL(1,ℤ/8)—24no—
1118C2×SD16—24no—
1119C2×SD16—731no—
1120C2×SD16—731no—
1121C2×SD16—731no—
1122C2×SD16—731no—
1123C2×SD16—731no—
1124C2×SD16—731no—
1125C2×SD16—1464no—
1126C2×SD16C22×D7311yescharacteristic
1127C2×SD16C22×D7311yescharacteristic
1128C2×SD16C22×D7311yescharacteristic
1129C2×SD16C22×D7311yescharacteristic
1130C2×SD16C22×D7311yescharacteristic
1131C2×SD16C22×D7311yescharacteristic
1132C2×D8—731no—
1133C2×D8C22×D7311yescharacteristic
1134C2×D8C22×D7311yescharacteristic
1135C2×D8C22×D7311yescharacteristic
1136C2×M16—731no—
1137C2×M16C22×D7311yescharacteristic
1138C22×C8—731no—
1139C22×C8—731no—
1140C22×C8—731no—
1141C22×C8C22×D7311yescharacteristic
1142C4⋊Q8—731no—
1143C4⋊Q8—731no—
1144C4⋊Q8—731no—
1145C4⋊Q8—731no—
1146C4⋊Q8—731no—
1147C4⋊Q8—1461no—
1148C4⋊Q8—1461no—
1149#127—731no—
1150#127—731no—
1151#127C22×D7311yescharacteristic
1152#126—1461no—
1153#126—1461no—
1154#126—1461no—
1155#126—1461no—
1156#126—1461no—
1157#126—1461no—
1158#125—731no—
1159#125—731no—
1160#125—1461no—
1161#125—1461no—
1162#125—1461no—
1163#125—1461no—
1164#125—1461no—
1165#124—21no—
1166#124—731no—
1167#124—1461no—
1168#124—1461no—
1169#124—1461no—
1170#124—1461no—
1171#124C22×D7311yescharacteristic
1172#123—1461no—
1173#123—1461no—
1174#123—1461no—
1175#123—1461no—
1176#123—1461no—
1177#123—1461no—
1178#123—1461no—
1179#123—1461no—
1180#123—1461no—
1181#123—1461no—
1182#123—1461no—
1183#123—1461no—
1184C22⋊Q8—21no—
1185C22⋊Q8—731no—
1186C22⋊Q8—731no—
1187C22⋊Q8—731no—
1188C22⋊Q8—1461no—
1189C22⋊Q8—1461no—
1190C22⋊Q8—1461no—
1191C22⋊Q8—1461no—
1192C22⋊Q8—1461no—
1193C22⋊Q8—1461no—
1194C22⋊Q8—1461no—
1195C22⋊Q8—1461no—
1196C22⋊Q8—1461no—
1197C22⋊Q8—1461no—
1198C22⋊Q8—1461no—
1199C22⋊Q8—1461no—
1200C22⋊Q8C22×D7311yescharacteristic
1201#121—21no—
1202#121—21no—
1203#121—731no—
1204#121—731no—
1205#121—731no—
1206#121—731no—
1207#121—731no—
1208#121—1461no—
1209#121—1461no—
1210#121—1461no—
1211#121—1461no—
1212#121—1461no—
1213#121—1461no—
1214#121—1461no—
1215#121—1461no—
1216#121—1461no—
1217#121C22×D7311yescharacteristic
1218#121C22×D7311yescharacteristic
1219#121C22×D7311yescharacteristic
1220#120—21no—
1221#120—21no—
1222#120—1461no—
1223#120—1461no—
1224#120—1461no—
1225#120—1461no—
1226C4×Q8—731no—
1227C4×Q8—731no—
1228C4×Q8—731no—
1229C4×Q8—731no—
1230C4×Q8—731no—
1231C4×Q8—731no—
1232C4×Q8—731no—
1233C4×Q8—731no—
1234C4×Q8—731no—
1235C4×Q8—1461no—
1236C4×Q8—1461no—
1237C4×Q8—1461no—
1238C4×Q8—1461no—
1239C4×Q8—1461no—
1240C4×Q8—1461no—
1241C4×Q8C22×D7311yescharacteristic
1242C4×D4—21no—
1243C4×D4—731no—
1244C4×D4—731no—
1245C4×D4—731no—
1246C4×D4—731no—
1247C4×D4—731no—
1248C4×D4—731no—
1249C4×D4—731no—
1250C4×D4—731no—
1251C4×D4—731no—
1252C4×D4—731no—
1253C4×D4—731no—
1254C4×D4—731no—
1255C4×D4—731no—
1256C4×D4—731no—
1257C4×D4—731no—
1258C4×D4—731no—
1259C4×D4—1461no—
1260C4×D4—1461no—
1261C4×D4—1461no—
1262C4×D4—1461no—
1263C4×D4—1461no—
1264C4×D4—1461no—
1265C4×D4—1461no—
1266C4×D4—1461no—
1267C4×D4—1461no—
1268C4×D4—1461no—
1269C4×D4—1461no—
1270C4×D4—1461no—
1271C4×D4—1461no—
1272C4×D4—1461no—
1273C4×D4—1461no—
1274C4×D4C22×D7311yescharacteristic
1275C4×D4C22×D7311yescharacteristic
1276#117—731no—
1277#117—731no—
1278#117—731no—
1279#117—731no—
1280#117—1461no—
1281#117—1461no—
1282#117—1461no—
1283#117—1461no—
1284#117—1461no—
1285#117—1461no—
1286#117—1461no—
1287C2×C4⋊C4—731no—
1288C2×C4⋊C4—731no—
1289C2×C4⋊C4—731no—
1290C2×C4⋊C4—731no—
1291C2×C4⋊C4—731no—
1292C2×C4⋊C4—1461no—
1293C2×C4⋊C4—1461no—
1294C2×C22⋊C4—1461no—
1295C2×C22⋊C4—1461no—
1296C2×C22⋊C4—1461no—
1297C2×C42—731no—
1298C2×C42—731no—
1299C2×C42—731no—
1300C2×C42—1461no—
1301C2×C42—1461no—
1302C2×C42—1461no—
1303#107—731no—
1304#107—731no—
1305#107—731no—
1306#107—731no—
1307#107—731no—
1308#107—731no—
1309#107—731no—
1310#107—731no—
1311#107—731no—
1312#107—731no—
1313#107—731no—
1314#107C22×D7311yescharacteristic
1315#106—731no—
1316#106—731no—
1317#106—731no—
1318#106—731no—
1319C4⋊C8—731no—
1320C4⋊C8—731no—
1321C4⋊C8—731no—
1322C4⋊C8—731no—
1323C4⋊C8—731no—
1324C4⋊C8C22×D7311yescharacteristic
1325#103—731no—
1326#103—731no—
1327#103—731no—
1328#103—731no—
1329#103—731no—
1330#103—731no—
1331#103—731no—
1332#103—731no—
1333#103—731no—
1334#103—731no—
1335#103C22×D7311yescharacteristic
1336#103C22×D7311yescharacteristic
1337#102—731no—
1338#102—731no—
1339#102—731no—
1340#102—731no—
1341#102—731no—
1342#102—731no—
1343#102—731no—
1344#102—731no—
1345#102—731no—
1346#102—731no—
1347#102—731no—
1348#102—731no—
1349#102—731no—
1350#102—731no—
1351#102—731no—
1352#102—731no—
1353#102C22×D7311yescharacteristic
1354#102C22×D7311yescharacteristic
1355#102C22×D7311yescharacteristic
1356#102C22×D7311yescharacteristic
1357C22⋊C8—731no—
1358C22⋊C8—731no—
1359C22⋊C8—731no—
1360C22⋊C8—731no—
1361C22⋊C8C22×D7311yescharacteristic
1362C22⋊C8C22×D7311yescharacteristic
1363#97—731no—
1364#97—731no—
1365#97—731no—
1366#97—731no—
1367#97—731no—
1368#97—731no—
1369#97—731no—
1370#97C22×D7311yescharacteristic
1371C4×C8—731no—
1372C4×C8—731no—
1373C24—21no—
1374C24—21no—
1375C24—1461no—
1376#41—22no—
1377#41—41no—
1378#41—2924no—
1379#41—2924no—
1380#41—2924no—
1381#41—2924no—
1382#41—2924no—
1383#41—2924no—
1384#41—2924no—
1385#41—2924no—
1386#41—1464no—
1387C2×Q8—21no—
1388C2×Q8—22no—
1389C2×Q8—41no—
1390C2×Q8—2924no—
1391C2×Q8—2921no—
1392C2×Q8—731no—
1393C2×Q8—731no—
1394C2×Q8—1461no—
1395C2×Q8—1461no—
1396C2×Q8—1461no—
1397C2×Q8—1461no—
1398C2×Q8—1462no—
1399C2×Q8—1461no—
1400C2×Q8C23×D7311yescharacteristic
1401C2×Q8C23×D7311yescharacteristic
1402C2×D4—22no—
1403C2×D4—22no—
1404C2×D4—21no—
1405C2×D4—21no—
1406C2×D4—21no—
1407C2×D4—21no—
1408C2×D4—21no—
1409C2×D4—21no—
1410C2×D4—21no—
1411C2×D4—21no—
1412C2×D4—41no—
1413C2×D4—41no—
1414C2×D4—44no—
1415C2×D4—2924no—
1416C2×D4—2924no—
1417C2×D4—2921no—
1418C2×D4—731no—
1419C2×D4—731no—
1420C2×D4—731no—
1421C2×D4—1461no—
1422C2×D4—1461no—
1423C2×D4—1461no—
1424C2×D4—1461no—
1425C2×D4—1461no—
1426C2×D4—1461no—
1427C2×D4—1461no—
1428C2×D4—1461no—
1429C2×D4—1461no—
1430C2×D4—1461no—
1431C2×D4—1462no—
1432C2×D4D4×D7311yescharacteristic
1433C2×D4C23×D7311yescharacteristic
1434C2×D4C23×D7311yescharacteristic
1435C2×D4C23×D7311yescharacteristic
1436C2×D4C23×D7311yescharacteristic
1437C22×C4—21no—
1438C22×C4—21no—
1439C22×C4—21no—
1440C22×C4—2924no—
1441C22×C4—2924no—
1442C22×C4—2924no—
1443C22×C4—731no—
1444C22×C4—731no—
1445C22×C4—731no—
1446C22×C4—731no—
1447C22×C4—731no—
1448C22×C4—731no—
1449C22×C4—731no—
1450C22×C4—1461no—
1451C22×C4—1461no—
1452C22×C4—1461no—
1453C22×C4—1461no—
1454C22×C4—1461no—
1455C22×C4—1461no—
1456C22×C4—1461no—
1457C22×C4—1461no—
1458C22×C4—1461no—
1459C22×C4—1461no—
1460C22×C4—1461no—
1461C22×C4—1461no—
1462C22×C4—1461no—
1463C22×C4—1461no—
1464C22×C4—1461no—
1465C22×C4—1461no—
1466C22×C4—1461no—
1467C22×C4C23×D7311yescharacteristic
1468C22×C4C23×D7311yescharacteristic
1469SD16—22no—
1470SD16—22no—
1471SD16—22no—
1472SD16—22no—
1473SD16—41no—
1474SD16—2921no—
1475SD16—2921no—
1476SD16—2921no—
1477SD16—1462no—
1478SD16—1462no—
1479SD16—1462no—
1480SD16#1192402714yescomplemented
1481D8—22no—
1482D8—22no—
1483D8—41no—
1484D8—2921no—
1485M16—22no—
1486M16—2921no—
1487C2×C8—22no—
1488C2×C8—2921no—
1489C2×C8—2921no—
1490C2×C8—731no—
1491C2×C8—731no—
1492C2×C8—731no—
1493C2×C8—731no—
1494C2×C8—1462no—
1495C2×C8C23×D7311yescharacteristic
1496C2×C8C23×D7311yescharacteristic
1497C2×C8C23×D7311yescharacteristic
1498C2×C8C23×D7311yescharacteristic
1499C4⋊C4—21no—
1500C4⋊C4—21no—
1501C4⋊C4—731no—
1502C4⋊C4—731no—
1503C4⋊C4—731no—
1504C4⋊C4—731no—
1505C4⋊C4—731no—
1506C4⋊C4—731no—
1507C4⋊C4—731no—
1508C4⋊C4—731no—
1509C4⋊C4—731no—
1510C4⋊C4—731no—
1511C4⋊C4—731no—
1512C4⋊C4—1461no—
1513C4⋊C4—1461no—
1514C4⋊C4—1461no—
1515C4⋊C4—1461no—
1516C4⋊C4—1461no—
1517C4⋊C4—1461no—
1518C4⋊C4—1461no—
1519C4⋊C4—1461no—
1520C4⋊C4—1461no—
1521C4⋊C4—1461no—
1522C4⋊C4—1461no—
1523C4⋊C4—1461no—
1524C4⋊C4—1461no—
1525C4⋊C4—1461no—
1526C4⋊C4—1461no—
1527C4⋊C4—1461no—
1528C4⋊C4—1461no—
1529C4⋊C4—1461no—
1530C4⋊C4—1461no—
1531C4⋊C4—1461no—
1532C4⋊C4—1461no—
1533C4⋊C4—1461no—
1534C4⋊C4—1461no—
1535C4⋊C4—1461no—
1536C4⋊C4—1461no—
1537C4⋊C4D4×D7311yescharacteristic
1538C4⋊C4C23×D7311yescharacteristic
1539C4⋊C4C23×D7311yescharacteristic
1540C22⋊C4—21no—
1541C22⋊C4—21no—
1542C22⋊C4—21no—
1543C22⋊C4—21no—
1544C22⋊C4—21no—
1545C22⋊C4—21no—
1546C22⋊C4—21no—
1547C22⋊C4—731no—
1548C22⋊C4—731no—
1549C22⋊C4—731no—
1550C22⋊C4—731no—
1551C22⋊C4—1461no—
1552C22⋊C4—1461no—
1553C22⋊C4—1461no—
1554C22⋊C4—1461no—
1555C22⋊C4—1461no—
1556C22⋊C4—1461no—
1557C22⋊C4—1461no—
1558C22⋊C4—1461no—
1559C22⋊C4—1461no—
1560C22⋊C4—1461no—
1561C22⋊C4—1461no—
1562C22⋊C4—1461no—
1563C22⋊C4—1461no—
1564C22⋊C4—1461no—
1565C22⋊C4—1461no—
1566C22⋊C4—1461no—
1567C22⋊C4—1461no—
1568C22⋊C4—1461no—
1569C22⋊C4—1461no—
1570C22⋊C4—1461no—
1571C22⋊C4—1461no—
1572C22⋊C4—1461no—
1573C22⋊C4D4×D7311yescharacteristic
1574C22⋊C4D4×D7311yescharacteristic
1575C42—21no—
1576C42—731no—
1577C42—731no—
1578C42—731no—
1579C42—731no—
1580C42—731no—
1581C42—731no—
1582C42—731no—
1583C42—731no—
1584C42—731no—
1585C42—1461no—
1586C42—1461no—
1587C42—1461no—
1588C42—1461no—
1589C42—1461no—
1590C42—1461no—
1591C42—1461no—
1592C42—1461no—
1593C42C23×D7311yescharacteristic
1594C23—21no—
1595C23—21no—
1596C23—21no—
1597C23—21no—
1598C23—42no—
1599C23—42no—
1600C23—42no—
1601C23—42no—
1602C23—81no—
1603C23—81no—
1604C23—2922no—
1605C23—2922no—
1606C23—5841no—
1607C23—731no—
1608C23—1461no—
1609C23C2×D4×D7311yescharacteristic
1610C23C2×D4×D7311yescharacteristic
1611Q8—21no—
1612Q8—21no—
1613Q8—21no—
1614Q8—42no—
1615Q8—2922no—
1616Q8—2922no—
1617Q8—2922no—
1618Q8—2922no—
1619Q8—2922no—
1620Q8—1462no—
1621Q8—1461no—
1622Q8—1461no—
1623Q8C2×#1192402712yescomplemented
1624D4—22no—
1625D4—21no—
1626D4—21no—
1627D4—21no—
1628D4—21no—
1629D4—21no—
1630D4—21no—
1631D4—21no—
1632D4—42no—
1633D4—42no—
1634D4—42no—
1635D4—42no—
1636D4—42no—
1637D4—42no—
1638D4—42no—
1639D4—81no—
1640D4—2922no—
1641D4—2922no—
1642D4—2922no—
1643D4—2922no—
1644D4—2922no—
1645D4—2922no—
1646D4—2922no—
1647D4—2922no—
1648D4—5841no—
1649D4—5841no—
1650D4—734no—
1651D4—1462no—
1652D4—1461no—
1653D4—1461no—
1654D4C2×#1192402712yes—
1655C2×C4—21no—
1656C2×C4—21no—
1657C2×C4—21no—
1658C2×C4—21no—
1659C2×C4—21no—
1660C2×C4—21no—
1661C2×C4—21no—
1662C2×C4—21no—
1663C2×C4—42no—
1664C2×C4—42no—
1665C2×C4—42no—
1666C2×C4—2922no—
1667C2×C4—2922no—
1668C2×C4—2921no—
1669C2×C4—2922no—
1670C2×C4—2922no—
1671C2×C4—2922no—
1672C2×C4—2922no—
1673C2×C4—2922no—
1674C2×C4—2922no—
1675C2×C4—2922no—
1676C2×C4—2922no—
1677C2×C4—2922no—
1678C2×C4—2922no—
1679C2×C4—2922no—
1680C2×C4—2922no—
1681C2×C4—2922no—
1682C2×C4—2922no—
1683C2×C4—2922no—
1684C2×C4—2921no—
1685C2×C4—2921no—
1686C2×C4—731no—
1687C2×C4—731no—
1688C2×C4—731no—
1689C2×C4—731no—
1690C2×C4—731no—
1691C2×C4—731no—
1692C2×C4—731no—
1693C2×C4—1462no—
1694C2×C4—1461no—
1695C2×C4—1461no—
1696C2×C4—1461no—
1697C2×C4—1461no—
1698C2×C4—1461no—
1699C2×C4—1461no—
1700C2×C4—1461no—
1701C2×C4—1462no—
1702C2×C4—1462no—
1703C2×C4—1461no—
1704C2×C4—1461no—
1705C2×C4C2×D4×D7311yescharacteristic
1706C2×C4C2×D4×D7311yescharacteristic
1707C2×C4C2×D4×D7311yescharacteristic
1708C2×C4C2×D4×D7311yescharacteristic
1709C2×C4C24×D7311yescharacteristic
1710C8—21no—
1711C8—21no—
1712C8—21no—
1713C8—1461no—
1714C8—1461no—
1715C8—1461no—
1716C8—1461no—
1717C8C2×#1192402712yescomplemented
1718C22—21no—
1719C22—21no—
1720C22—21no—
1721C22—21no—
1722C22—22no—
1723C22—21no—
1724C22—41no—
1725C22—41no—
1726C22—41no—
1727C22—41no—
1728C22—41no—
1729C22—41no—
1730C22—41no—
1731C22—41no—
1732C22—41no—
1733C22—41no—
1734C22—41no—
1735C22—84no—
1736C22—84no—
1737C22—2921no—
1738C22—2921no—
1739C22—2921no—
1740C22—5844no—
1741C22—732no—
1742C22—1461no—
1743C22—1461no—
1744C22AGL(1,ℤ/8)×D7312yes—
1745C22C22×D4×D7311yescharacteristic
1746C4—21no—
1747C4—21no—
1748C4—21no—
1749C4—22no—
1750C4—21no—
1751C4—41no—
1752C4—41no—
1753C4—41no—
1754C4—2921no—
1755C4—2921no—
1756C4—2921no—
1757C4—2921no—
1758C4—2921no—
1759C4—2921no—
1760C4—2921no—
1761C4—732no—
1762C4—1461no—
1763C4—1461no—
1764C4—1461no—
1765C4—1461no—
1766C4—1461no—
1767C4—1461no—
1768C4C22×#1192402711yescharacteristic
1769C4#1798942211yescharacteristic
1770C2—22no—
1771C2—41no—
1772C2—42no—
1773C2—81no—
1774C2—81no—
1775C2—81no—
1776C2—5841no—
1777C2—1462no—
1778C2D4×#1192402711yescharacteristic
1779C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
1780C2#2262471311yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3265C2
socleC22×C73C23×D4
hypercenter#3265D73
hypocenterC73#61452
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3265

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22623547C2semidirect
2. D4×#11924027C2semidirect
3. #22622948C2semidirect
4. #22622853C2semidirect
5. #22622655C2semidirect
6. #22622644C2semidirect
7. #22622373C2semidirect
8. #22622366C2semidirect
9. #22622275C2semidirect
10. #22621952C2semidirect
11. #22621945C2semidirect
12. #22621922C2semidirect
13. #22621915C2semidirect
14. #22621789C2semidirect
15. #22621737C2semidirect
16. SD16×C22⋊D73C2semidirect
17. #22621420C2semidirect
18. #22620644C2semidirect
19. #22620626C2semidirect
20. #22620624C2semidirect
21. #22620075C2semidirect
22. #22620068C2semidirect
23. #22620064C2semidirect
24. #22620052C2semidirect
25. #22620048C2semidirect
26. #22620025C2semidirect
27. #22618941C2semidirect
28. AGL(1,ℤ/8)×Dic73C2semidirect
29. C2×#17988688C2semidirect
30. #440×D73C2semidirect
31. C73×#3265C2semidirect
34. #17989313C22semidirect
36. #17989306C22semidirect
38. #17989277C22semidirect
40. #17989271C22semidirect
43. Q8×C22⋊D73C22semidirect
44. #17989244C22semidirect
50. #17989237C22semidirect
57. #17989139C22semidirect
62. #17989118C22semidirect
64. #17989116C22semidirect
68. #41×Dic73C22semidirect
71. C2×Q8×Dic73C22semidirect
72. C4×Q8×D73C22semidirect
76. #17988996C22semidirect
77. #17988995C22semidirect
78. #17988991C22semidirect
79. #17988975C22semidirect
80. #17988958C22semidirect
81. #17988951C22semidirect
82. #17988950C22semidirect
83. #17988946C22semidirect
84. #17988945C22semidirect
85. #17988936C22semidirect
86. #17988932C22semidirect
87. #17988923C22semidirect
88. #17988920C22semidirect
89. #17988918C22semidirect
90. #17988916C22semidirect
91. #17988912C22semidirect
92. #17988908C22semidirect
93. #17988901C22semidirect
94. #17988899C22semidirect
95. #17988899C22semidirect
96. #17988899C22semidirect
97. #17988898C22semidirect
98. #17988898C22semidirect
100. #17988889C22semidirect
101. #17988888C22semidirect
103. #17988883C22semidirect
104. #17988882C22semidirect
105. #17988880C22semidirect
106. #17988880C22semidirect
107. #17988870C22semidirect
109. #17988865C22semidirect
110. #17988865C22semidirect
111. #17988835C22semidirect
112. #17988833C22semidirect
113. #17988831C22semidirect
114. #17988821C22semidirect
115. #17988820C22semidirect
116. #17988820C22semidirect
117. #17988816C22semidirect
118. #17988814C22semidirect
119. #17988813C22semidirect
120. #17988813C22semidirect
122. #17988800C22semidirect
123. #17988799C22semidirect
125. #17988790C22semidirect
126. #17988785C22semidirect
127. #17988785C22semidirect
128. #17988785C22semidirect
129. #17988784C22semidirect
130. #17988780C22semidirect
134. #17988732C22semidirect
135. #17988726C22semidirect
136. #17988724C22semidirect
137. #17988724C22semidirect
139. #17988716C22semidirect
140. #17988715C22semidirect
142. #17988699C22semidirect
143. #17988699C22semidirect
144. #17988696C22semidirect
145. #17988690C22semidirect
146. #17988690C22semidirect
147. #17988689C22semidirect
152. #17988688C22semidirect
153. #17988688C22semidirect
154. #17988688C22semidirect
155. #17988688C22semidirect
156. #17988688C22semidirect
157. #17988688C22semidirect
159. #17988686C22semidirect
160. #17988685C22semidirect
162. #17988684C22semidirect
163. #17988684C22semidirect
165. SD16×Dic73C22semidirect
167. D8×Dic73C22semidirect
168. #17988661C22semidirect
169. #17988659C22semidirect
170. #17988656C22semidirect
171. C8×C22⋊D73C22semidirect
172. #17988650C22semidirect
173. #17988643C22semidirect
174. #17988641C22semidirect
175. #17988641C22semidirect
176. #17988629C22semidirect
177. C2×#14556525C22semidirect
178. #107×D73C22semidirect
180. #17988588C22semidirect
181. C2×#14556515C22semidirect
182. #103×D73C22semidirect
185. M16×Dic73C22semidirect
186. C2×#14556501C22semidirect
187. #97×D73C22semidirect
190. #548×C73C22semidirect
192. #496×C73C22semidirect
193. #468×C73C22semidirect
194. #466×C73C22semidirect
196. #460×C73C22semidirect
198. #449×C73C22semidirect
199. #448×C73C22semidirect
202. #435×C73C22semidirect
677. SD16×C73#41semidirect
724. Q8×C73C2×#41semidirect
769. C22⋊D73AGL(1,ℤ/8)semidirect
822. C8×C73C2×#41semidirect
908. #3265D73semidirect
922. C73#61452semidirect
939. #548C2×D73semidirect
975. #496C2×D73semidirect
1010. #468C2×D73semidirect
1014. #466C2×D73semidirect
1029. #460C2×D73semidirect
1036. #449C2×D73semidirect
1040. #448C2×D73semidirect
1076. #435C2×D73semidirect
1480. SD16#11924027semidirect
1623. Q8C2×#11924027semidirect
1717. C8C2×#11924027semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226235472
D4×#119240272
#226229482
#226228532
#226226552
#226226442
#226223732
#226223662
#226222752
#226219522
#226219452
#226219222
#226219152
#226217892
#226217372
SD16×C22⋊D732
#226214202
#226206442
#226206262
#226206242
#226200752
#226200682
#226200642
#226200522
#226200482
#226200252
#226189412
AGL(1,ℤ/8)×Dic732
C2×#179886882
#440×D732
C73×#32652
#6145273