Finite Group Databasebeta

← #33970618

Subgroups — #33970618

Order 18688.

1820 conjugacy classes of subgroups.

The subgroup lattice has 1694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623967C211yesmaximal, characteristic, complemented
2#22623939C211yesmaximal, characteristic, complemented
3#22622916C211yesmaximal, characteristic, complemented
4SD16×Dic146C211yesmaximal, characteristic, complemented
5#22622666C211yesmaximal, characteristic, complemented
6#22622644C211yesmaximal, characteristic, complemented
7#22622547C211yesmaximal, characteristic, complemented
8#22622541C211yesmaximal, characteristic, complemented
9#22622521C211yesmaximal, characteristic, complemented
10#22622042C211yesmaximal, characteristic, complemented
11#22622035C211yesmaximal, characteristic, complemented
12#22621967C211yesmaximal, characteristic, complemented
13#22621960C211yesmaximal, characteristic, complemented
14#22621852C211yesmaximal, characteristic, complemented
15#22621789C211yesmaximal, characteristic, complemented
16#22621571C211yesmaximal, characteristic, complemented
17#22621562C211yesmaximal, characteristic, complemented
18#22620671C211yesmaximal, characteristic, complemented
19#22620545C211yesmaximal, characteristic, complemented
20#22620543C211yesmaximal, characteristic, complemented
21#22620209C211yesmaximal, characteristic, complemented
22#22620205C211yesmaximal, characteristic, complemented
23#22620159C211yesmaximal, characteristic, complemented
24#22620153C211yesmaximal, characteristic, complemented
25#22619995C211yesmaximal, characteristic, complemented
26#22619934C211yesmaximal, characteristic, complemented
27#22618930C211yesmaximal, characteristic, complemented
28#22618775C211yesmaximal, characteristic, complemented
29#22618767C211yesmaximal, characteristic, complemented
30AGL(1,ℤ/8)×Dic73C211yesmaximal, characteristic, complemented
31C73×#3275C211yesmaximal, characteristic, complemented
32C2×#14556620C2211yescharacteristic
33Q8×Dic146C2211yescharacteristic, complemented
34#17989308—21no—
35#17989308C2211yescharacteristic
36#17989307—21no—
37#17989307C2211yescharacteristic
38#17989306—21no—
39#17989306C2211yescharacteristic
40#17989306C2211yescharacteristic, complemented
41#17989301—21no—
42#17989301C2211yescharacteristic, complemented
43#17989295C2211yescharacteristic
44#17989294C2211yescharacteristic
45#17989274—21no—
46#17989268—21no—
47#17989263—21no—
48D4×Dic146C2211yescharacteristic
49Q8×C22⋊D73C2211yescharacteristic, complemented
50#17989244C2211yescharacteristic
51#17989243—21no—
52#17989237C2211yescharacteristic
53#17989236C2211yescharacteristic
54#17989231C2211yescharacteristic
55#17989206—21no—
56#17989206C2211yescharacteristic
57#17989206C2211yescharacteristic, complemented
58#17989204—21no—
59#17989204C2211yescharacteristic
60#17989204C2211yescharacteristic, complemented
61#17989182—21no—
62#17989181—21no—
63#17989139—21no—
64#17989139C2211yescharacteristic
65#17989139C2211yescharacteristic
66#17989117—21no—
67#17989117C2211yescharacteristic
68#17989093—21no—
69C2×#14556568—21no—
70#17989070C2211yescharacteristic
71#17989066C2211yescharacteristic
72#17989065C2211yescharacteristic, complemented
73#17989063C2211yescharacteristic, complemented
74#41×Dic73C2211yescharacteristic
75C2×D4×Dic73C2211yescharacteristic
76#17988985C2211yescharacteristic, complemented
77#17988984C2211yescharacteristic, complemented
78#17988984C2211yescharacteristic, complemented
79#17988970C2211yescharacteristic
80#17988965C2211yescharacteristic, complemented
81#17988946C2211yescharacteristic
82#17988946C2211yescharacteristic, complemented
83#17988945C2211yescharacteristic
84#17988945C2211yescharacteristic, complemented
85#17988936C2211yescharacteristic, complemented
86#17988936C2211yescharacteristic, complemented
87#17988929C2211yescharacteristic
88#17988929C2211yescharacteristic, complemented
89#17988927C2211yescharacteristic, complemented
90#17988925C2211yescharacteristic
91#17988918C2211yescharacteristic
92#17988918C2211yescharacteristic, complemented
93#17988916C2211yescharacteristic, complemented
94#17988915C2211yescharacteristic
95#17988909C2211yescharacteristic
96#17988908C2211yescharacteristic
97#17988904C2211yescharacteristic, complemented
98#17988903C2211yescharacteristic, complemented
99#17988883C2211yescharacteristic, complemented
100#17988880C2211yescharacteristic, complemented
101#17988877C2211yescharacteristic
102#17988875C2211yescharacteristic
103#17988875C2211yescharacteristic
104#17988875C2211yescharacteristic
105#17988873C2211yescharacteristic, complemented
106#17988872C2211yescharacteristic, complemented
107#17988870C2211yescharacteristic, complemented
108#17988870C2211yescharacteristic, complemented
109#17988870C2211yescharacteristic, complemented
110#17988865C2211yescharacteristic, complemented
111#17988845C2211yescharacteristic
112#17988845C2211yescharacteristic, complemented
113#17988843C2211yescharacteristic
114#17988843C2211yescharacteristic
115#17988842C2211yescharacteristic, complemented
116#17988837C2211yescharacteristic
117#17988814C2211yescharacteristic
118#17988814C2211yescharacteristic, complemented
119#17988813C2211yescharacteristic
120#17988813C2211yescharacteristic, complemented
121#17988807C2211yescharacteristic
122#17988807C2211yescharacteristic
123#17988807C2211yescharacteristic, complemented
124#17988806C2211yescharacteristic
125#17988806C2211yescharacteristic, complemented
126#17988800C2211yescharacteristic
127#17988795C2211yescharacteristic, complemented
128#17988790C2211yescharacteristic
129#17988790C2211yescharacteristic
130#17988790C2211yescharacteristic, complemented
131#17988749C2211yescharacteristic
132#17988749C2211yescharacteristic
133#17988746C2211yescharacteristic
134#17988743C2211yescharacteristic, complemented
135#17988741C2211yescharacteristic, complemented
136#17988738C2211yescharacteristic
137#17988729C2211yescharacteristic
138#17988724C2211yescharacteristic
139#17988716C2211yescharacteristic, complemented
140C8×Dic146C2211yescharacteristic, complemented
141#17988699C2211yescharacteristic
142#17988699C2211yescharacteristic
143#17988694C2211yescharacteristic, complemented
144#17988694C2211yescharacteristic, complemented
145#17988693C2211yescharacteristic, complemented
146#17988692C2211yescharacteristic, complemented
147#17988691C2211yescharacteristic, complemented
148#17988691C2211yescharacteristic, complemented
149#17988688C2211yescharacteristic
150#17988688C2211yescharacteristic
151#17988688C2211yescharacteristic
152#17988687C2211yescharacteristic
153C4×Dic292C2211yescharacteristic, complemented
154Q16×Dic73C2211yescharacteristic, complemented
155Q16×Dic73C2211yescharacteristic, complemented
156#17988679C2211yescharacteristic, complemented
157#17988678C2211yescharacteristic
158#17988678C2211yescharacteristic
159#17988678C2211yescharacteristic, complemented
160SD16×Dic73C2211yescharacteristic
161SD16×Dic73C2211yescharacteristic
162SD16×Dic73C2211yescharacteristic
163SD16×Dic73C2211yescharacteristic
164SD16×Dic73C2211yescharacteristic
165SD16×Dic73C2211yescharacteristic, complemented
166D8×Dic73C2211yescharacteristic
167D8×Dic73C2211yescharacteristic
168#17988663C2211yescharacteristic
169#17988663C2211yescharacteristic, complemented
170#17988661C2211yescharacteristic
171#17988659C2211yescharacteristic
172#17988650C2211yescharacteristic, complemented
173#17988647C2211yescharacteristic, complemented
174#17988645C2211yescharacteristic, complemented
175#17988637C2211yescharacteristic
176#17988629C2211yescharacteristic
177#17988629C2211yescharacteristic, complemented
178#17988626C2211yescharacteristic, complemented
179#17988592C2211yescharacteristic
180#17988588C2211yescharacteristic
181#17988583C2211yescharacteristic
182#17988580C2211yescharacteristic
183C2×#14556515C2211yescharacteristic, complemented
184#103×D73C2211yescharacteristic, complemented
185#17988545C2211yescharacteristic, complemented
186#17988541C2211yescharacteristic, complemented
187M16×Dic73C2211yescharacteristic
188C2×#137×C73C2211yescharacteristic
189C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
190#548×C73C2211yescharacteristic
191#546×C73C2211yescharacteristic
192#495×C73C2211yescharacteristic
193#470×C73C2211yescharacteristic
194#469×C73C2211yescharacteristic
195#464×C73C2211yescharacteristic
196#463×C73C2211yescharacteristic
197#452×C73C2211yescharacteristic
198#450×C73C2211yescharacteristic
199#449×C73C2211yescharacteristic
200#448×C73C2211yescharacteristic
201C4×SD16×C73C2211yescharacteristic
202#436×C73C2211yescharacteristic
203C2×#11924027—21no—
204C2×#11924027C2311yescharacteristic
205C22×Dic146—21no—
206C2×Q8×D73C2311yescharacteristic
207C23×Dic73—21no—
208#14556620—24no—
209C2×Dic292C2311yescharacteristic
210C2×#11924018C2311yescharacteristic
211C2×#11924018C2311yescharacteristic
212C2×#11924018C2311yescharacteristic
213C2×#11924016C2311yescharacteristic
214C2×#11924016C2311yescharacteristic
215C2×#11924016C2311yescharacteristic
216C2×#11924012C2311yescharacteristic
217C2×#11924011C2311yescharacteristic
218C22×#10596831C2311yescharacteristic
219C2×C8×D73C2311yescharacteristic
220#14556591—21no—
221#14556591C2311yescharacteristic
222#14556591C2311yescharacteristic
223#14556590—21no—
224#14556590—21no—
225#14556590C2311yescharacteristic
226#14556590C2311yescharacteristic
227#14556590C2311yescharacteristic
228#14556590C2311yescharacteristic
229#14556589—21no—
230#14556589C2311yescharacteristic
231#14556589C2311yescharacteristic
232#14556586—21no—
233#14556586D411yescharacteristic
234#14556584—21no—
235#14556584—21no—
236#14556584—21no—
237#14556584—21no—
238#14556584—21no—
239#14556584—21no—
240#14556584—21no—
241#14556584—21no—
242#14556584—21no—
243#14556584—21no—
244#14556584—21no—
245#14556584D411yescharacteristic
246#14556582—21no—
247#14556581—21no—
248#14556581—21no—
249#14556581—21no—
250#14556581D411yescharacteristic
251#14556578—21no—
252#14556578—21no—
253#14556578—21no—
254#14556578—21no—
255#14556578—21no—
256#14556578C2311yescharacteristic
257#14556578C2311yescharacteristic
258#14556577—21no—
259#14556577—21no—
260#14556577—21no—
261#14556577—21no—
262#14556577D411yescharacteristic
263#14556575—21no—
264#14556575—21no—
265#14556575D411yescharacteristic
266#14556574—21no—
267#14556573—21no—
268#14556572—21no—
269#14556572—21no—
270#14556572—21no—
271#14556572—21no—
272#14556572—21no—
273#14556572D411yescharacteristic
274#14556571—21no—
275#14556570—21no—
276#14556570—21no—
277#14556570—21no—
278#14556570C2311yescharacteristic
279#14556570C2311yescharacteristic
280#14556570C2311yescharacteristic
281#14556570C2311yescharacteristic
282#14556568—21no—
283#14556568—21no—
284#14556568—21no—
285#14556568—21no—
286#14556568—21no—
287#14556568—21no—
288#14556568—21no—
289#14556568—21no—
290#14556568—21no—
291#14556568—21no—
292#14556568—21no—
293#14556568—21no—
294#14556568—21no—
295#14556568—21no—
296#14556568D411yescharacteristic
297#14556567—21no—
298#14556567C2311yescharacteristic
299#14556567C2311yescharacteristic
300#14556563—21no—
301#14556563—21no—
302#14556563—21no—
303#14556563D411yescharacteristic
304#14556562—21no—
305#14556562C2311yescharacteristic
306#14556562C2311yescharacteristic
307#14556560—21no—
308Q8×Dic73—21no—
309Q8×Dic73—21no—
310Q8×Dic73C2311yescharacteristic
311Q8×Dic73C2311yescharacteristic
312Q8×Dic73C2311yescharacteristic
313Q8×Dic73C2311yescharacteristic
314Q8×Dic73C2311yescharacteristic
315Q8×Dic73C2311yescharacteristic
316Q8×Dic73C2311yescharacteristic
317C4×Dic146—21no—
318C4×Dic146—21no—
319C4×Dic146C2311yescharacteristic
320C4×Dic146C2311yescharacteristic
321C4×Dic146C2311yescharacteristic
322#14556556—21no—
323#14556556—21no—
324#14556556—21no—
325#14556556—21no—
326#14556556—21no—
327#14556556C2311yescharacteristic
328#14556556C2311yescharacteristic
329D4×Dic73—21no—
330D4×Dic73—21no—
331D4×Dic73—21no—
332D4×Dic73—21no—
333D4×Dic73—21no—
334D4×Dic73—21no—
335D4×Dic73—21no—
336D4×Dic73C2311yescharacteristic
337D4×Dic73C2311yescharacteristic
338D4×Dic73C2311yescharacteristic
339D4×Dic73C2311yescharacteristic
340D4×Dic73C2311yescharacteristic
341D4×Dic73C2311yescharacteristic
342D4×Dic73C2311yescharacteristic
343C4×C22⋊D73—21no—
344C4×C22⋊D73—21no—
345C4×C22⋊D73—21no—
346C4×C22⋊D73C2311yescharacteristic
347C4×C22⋊D73C2311yescharacteristic
348#14556551—21no—
349#14556551—21no—
350#14556550—21no—
351#14556550—21no—
352#14556550—21no—
353#14556550—21no—
354#14556550C2311yescharacteristic
355#14556550C2311yescharacteristic
356#14556550C2311yescharacteristic
357#14556549—21no—
358#14556549C2311yescharacteristic
359#14556548—21no—
360#14556548C2311yescharacteristic
361#14556547—21no—
362#14556547—21no—
363#14556547—21no—
364#14556547—21no—
365#14556547—21no—
366#14556547—21no—
367C2×C4⋊Dic73—21no—
368C2×C4⋊Dic73C2311yescharacteristic
369C2×C4⋊Dic73C2311yescharacteristic
370C2×#11924007—21no—
371C2×#11924007—21no—
372C4⋊C4×D73C2311yescharacteristic
373C2×C22⋊Dic73—21no—
374C2×C22⋊Dic73—21no—
375C2×C4×Dic73—21no—
376C2×C4×Dic73C2311yescharacteristic
377#14556525C2311yescharacteristic
378#14556525C2311yescharacteristic
379#14556525C2311yescharacteristic
380#14556524C2311yescharacteristic
381#14556523C2311yescharacteristic
382#14556523C2311yescharacteristic
383#14556523C2311yescharacteristic
384#14556523C2311yescharacteristic
385#14556523C2311yescharacteristic
386#14556523C2311yescharacteristic
387#14556522C2311yescharacteristic
388#14556522C2311yescharacteristic
389#14556522C2311yescharacteristic
390#14556522C2311yescharacteristic
391#14556522C2311yescharacteristic
392C4⋊#10596831C2311yescharacteristic
393#14556520C2311yescharacteristic
394#14556520C2311yescharacteristic
395#14556520C2311yescharacteristic
396#14556520C2311yescharacteristic
397#14556516C2311yescharacteristic
398#14556516C2311yescharacteristic
399#14556516C2311yescharacteristic
400#14556516C2311yescharacteristic
401#14556516C2311yescharacteristic
402#14556516C2311yescharacteristic
403#14556515C2311yescharacteristic
404#14556515C2311yescharacteristic
405#14556515C2311yescharacteristic
406#14556515C2311yescharacteristic
407#14556515C2311yescharacteristic
408#14556515C2311yescharacteristic
409#14556515C2311yescharacteristic
410#14556515C2311yescharacteristic
411#14556515C2311yescharacteristic
412#14556514C2311yescharacteristic
413#14556514C2311yescharacteristic
414#14556512C2311yescharacteristic
415#14556512C2311yescharacteristic
416#14556512C2311yescharacteristic
417#14556512C2311yescharacteristic
418#14556512C2311yescharacteristic
419#14556512C2311yescharacteristic
420#14556512C2311yescharacteristic
421#14556512C2311yescharacteristic
422#14556512C2311yescharacteristic
423C22⋊#10596831C2311yescharacteristic
424C22⋊#10596831C2311yescharacteristic
425#14556503C2311yescharacteristic
426#14556503C2311yescharacteristic
427#14556502C2311yescharacteristic
428#14556501C2311yescharacteristic
429#14556501C2311yescharacteristic
430#14556501C2311yescharacteristic
431C8×Dic73C2311yescharacteristic
432C8×Dic73C2311yescharacteristic
433C8×Dic73C2311yescharacteristic
434C8×Dic73C2311yescharacteristic
435C8×Dic73C2311yescharacteristic
436C2×#41×C73C2311yescharacteristic
437C2×#41×C73C2311yescharacteristic
438C22×Q8×C73C2311yescharacteristic
439C22×D4×C73C2311yescharacteristic
440#137×C73—24no—
441AGL(1,ℤ/8)×C73—24no—
442C2×Q16×C73C2311yescharacteristic
443C2×Q16×C73C2311yescharacteristic
444C2×SD16×C73C2311yescharacteristic
445C2×SD16×C73C2311yescharacteristic
446C2×SD16×C73C2311yescharacteristic
447C2×SD16×C73C2311yescharacteristic
448C2×SD16×C73C2311yescharacteristic
449C2×D8×C73C2311yescharacteristic
450C2×D8×C73C2311yescharacteristic
451C2×M16×C73C2311yescharacteristic
452C2×M16×C73C2311yescharacteristic
453#124×C73—21no—
454#124×C73C2311yescharacteristic
455#124×C73C2311yescharacteristic
456#123×C73—21no—
457C22⋊Q8×C73—21no—
458C22⋊Q8×C73C2311yescharacteristic
459C22⋊Q8×C73C2311yescharacteristic
460#121×C73—21no—
461#121×C73—21no—
462#121×C73C2311yescharacteristic
463#121×C73C2311yescharacteristic
464#120×C73—21no—
465C4×Q8×C73C2311yescharacteristic
466C4×D4×C73—21no—
467C4×D4×C73C2311yescharacteristic
468C4×D4×C73C2311yescharacteristic
469C2×C22⋊C4×C73—21no—
470#106×C73C2311yescharacteristic
471C4⋊C8×C73C2311yescharacteristic
472#103×C73C2311yescharacteristic
473#103×C73C2311yescharacteristic
474#103×C73C2311yescharacteristic
475#102×C73C2311yescharacteristic
476#102×C73C2311yescharacteristic
477#102×C73C2311yescharacteristic
478C22⋊C8×C73C2311yescharacteristic
479C22⋊C8×C73C2311yescharacteristic
480C4×C8×C73C2311yescharacteristic
481#11924027—22no—
482#11924027—41no—
483#11924027—82no—
484C2×Dic146—21no—
485C2×Dic146—21no—
486C2×Dic146—21no—
487C2×Dic146—21no—
488C2×Dic146—21no—
489C2×Dic146—21no—
490C2×Dic146—21no—
491C2×Dic146—82no—
492C2×Dic146C2×D411yescharacteristic
493C2×Dic146C2411yescharacteristic
494C2×Dic146C2411yescharacteristic
495Q8×D73—22no—
496Q8×D73—41no—
497C2×C22⋊D73—21no—
498C2×C22⋊D73—21no—
499C2×C22⋊D73—21no—
500C2×C22⋊D73C2×D411yescharacteristic
501C2×C22⋊D73C2×D411yescharacteristic
502C22×Dic73—21no—
503C22×Dic73—21no—
504C22×Dic73—21no—
505C22×Dic73—21no—
506C22×Dic73—21no—
507C22×Dic73—21no—
508C22×Dic73—21no—
509C22×Dic73—21no—
510C22×Dic73—21no—
511C22×Dic73—21no—
512C22×Dic73—82no—
513C22×Dic73C2×D411yescharacteristic
514C22×Dic73C2×D411yescharacteristic
515C2×C4×D73—21no—
516C2×C4×D73—21no—
517C2×C4×D73C2411yescharacteristic
518Dic292—22no—
519#11924018—22no—
520#11924018—41no—
521#11924018—41no—
522#11924016—22no—
523#11924016—41no—
524#11924016—41no—
525#11924012—41no—
526#11924011—22no—
527C2×#10596831—41no—
528C2×#10596831C2411yescharacteristic
529C2×#10596831C2411yescharacteristic
530C2×#10596831C2411yescharacteristic
531C2×#10596831C2411yescharacteristic
532C8×D73—41no—
533C4⋊Dic73—21no—
534C4⋊Dic73—21no—
535C4⋊Dic73—21no—
536C4⋊Dic73—21no—
537C4⋊Dic73—21no—
538C4⋊Dic73—21no—
539C4⋊Dic73—21no—
540C4⋊Dic73—21no—
541C4⋊Dic73—21no—
542C4⋊Dic73—21no—
543C4⋊Dic73—21no—
544C4⋊Dic73C2×D411yescharacteristic
545C4⋊Dic73C2×D411yescharacteristic
546C4⋊Dic73C2×D411yescharacteristic
547C4⋊Dic73C2411yescharacteristic
548C4⋊Dic73C2411yescharacteristic
549C4⋊Dic73C2411yescharacteristic
550C4⋊Dic73C2411yescharacteristic
551C4⋊Dic73C2411yescharacteristic
552C4⋊Dic73C2411yescharacteristic
553#11924007—21no—
554#11924007—21no—
555#11924007—21no—
556#11924007—21no—
557#11924007—21no—
558#11924007—21no—
559#11924007—21no—
560#11924007—21no—
561#11924007—21no—
562#11924007—21no—
563#11924007—21no—
564#11924007—21no—
565#11924007—21no—
566#11924007—21no—
567#11924007—21no—
568#11924007—21no—
569#11924007—21no—
570#11924007—21no—
571#11924007—21no—
572#11924007C2×D411yescharacteristic
573#11924007C2×D411yescharacteristic
574#11924007C2×D411yescharacteristic
575#11924007C2×D411yescharacteristic
576#11924007C2×D411yescharacteristic
577#11924007C2×D411yescharacteristic
578C22⋊Dic73—21no—
579C22⋊Dic73—21no—
580C22⋊Dic73—21no—
581C22⋊Dic73—21no—
582C22⋊Dic73—21no—
583C22⋊Dic73—21no—
584C22⋊Dic73—21no—
585C22⋊Dic73—21no—
586C22⋊Dic73—21no—
587C22⋊Dic73—21no—
588C22⋊Dic73—21no—
589C22⋊Dic73—21no—
590C22⋊Dic73—21no—
591C22⋊Dic73—21no—
592C22⋊Dic73—21no—
593C22⋊Dic73—21no—
594C22⋊Dic73—21no—
595C22⋊Dic73—21no—
596C22⋊Dic73—21no—
597C22⋊Dic73C2×D411yescharacteristic
598C22⋊Dic73C2×D411yescharacteristic
599C22⋊Dic73C2×D411yescharacteristic
600C22⋊Dic73C2×D411yescharacteristic
601#11924005—21no—
602#11924005—21no—
603#11924005—21no—
604#11924005C2×D411yescharacteristic
605#11924005C2×D411yescharacteristic
606#11924005C2×D411yescharacteristic
607#11924005C2×D411yescharacteristic
608C4×Dic73—21no—
609C4×Dic73—21no—
610C4×Dic73—21no—
611C4×Dic73—21no—
612C4×Dic73—21no—
613C4×Dic73—21no—
614C4×Dic73—21no—
615C4×Dic73—21no—
616C4×Dic73—21no—
617C4×Dic73—21no—
618C4×Dic73—21no—
619C4×Dic73—21no—
620C4×Dic73—21no—
621C4×Dic73—21no—
622C4×Dic73C2×D411yescharacteristic
623C4×Dic73C2×D411yescharacteristic
624C4×Dic73C2411yescharacteristic
625C4×Dic73C2411yescharacteristic
626C4×Dic73C2411yescharacteristic
627C24×C73—21no—
628#41×C73—22no—
629#41×C73—22no—
630#41×C73—41no—
631#41×C73—41no—
632C2×Q8×C73—21no—
633C2×Q8×C73—22no—
634C2×Q8×C73—41no—
635C2×Q8×C73C2411yescharacteristic
636C2×Q8×C73C2411yescharacteristic
637C2×Q8×C73C2411yescharacteristic
638C2×D4×C73—22no—
639C2×D4×C73—21no—
640C2×D4×C73—21no—
641C2×D4×C73—21no—
642C2×D4×C73—21no—
643C2×D4×C73—21no—
644C2×D4×C73—41no—
645C2×D4×C73C2×D411yescharacteristic
646C2×D4×C73C2411yescharacteristic
647C2×D4×C73C2411yescharacteristic
648C2×D4×C73C2411yescharacteristic
649C22×C4×C73—21no—
650C22×C4×C73—21no—
651C22×C4×C73—21no—
652C22×C4×C73—21no—
653C22×C4×C73C2411yescharacteristic
654C22×C4×C73C2411yescharacteristic
655Q16×C73—22no—
656Q16×C73—22no—
657SD16×C73—22no—
658SD16×C73—22no—
659SD16×C73—41no—
660SD16×C73—41no—
661SD16×C73#4114yescomplemented
662D8×C73—22no—
663D8×C73—22no—
664M16×C73—22no—
665M16×C73—22no—
666C2×C8×C73C2411yescharacteristic
667C2×C8×C73C2411yescharacteristic
668C2×C8×C73C2411yescharacteristic
669C2×C8×C73C2411yescharacteristic
670C4⋊C4×C73—21no—
671C4⋊C4×C73—21no—
672C4⋊C4×C73—21no—
673C4⋊C4×C73C2×D411yescharacteristic
674C4⋊C4×C73C2411yescharacteristic
675C4⋊C4×C73C2411yescharacteristic
676C22⋊C4×C73—21no—
677C22⋊C4×C73—21no—
678C22⋊C4×C73—21no—
679C22⋊C4×C73—21no—
680C22⋊C4×C73—21no—
681C22⋊C4×C73—21no—
682C22⋊C4×C73—21no—
683C22⋊C4×C73—21no—
684C22⋊C4×C73—21no—
685C22⋊C4×C73C2×D411yescharacteristic
686C22⋊C4×C73C2×D411yescharacteristic
687C42×C73—21no—
688C42×C73C2411yescharacteristic
689C23×C73—21no—
690C23×C73—21no—
691C23×C73—21no—
692C23×C73—42no—
693C23×C73—42no—
694C23×C73—81no—
695C23×C73C22×D411yescharacteristic
696C23×C73C22×D411yescharacteristic
697C22×D73C22×D411yescharacteristic
698Q8×C73—21no—
699Q8×C73—21no—
700Q8×C73—21no—
701Q8×C73—21no—
702Q8×C73—21no—
703Q8×C73—42no—
704Q8×C73C2×#4112yes—
705D4×C73—21no—
706D4×C73—21no—
707D4×C73—21no—
708D4×C73—21no—
709D4×C73—21no—
710D4×C73—41no—
711D4×C73—42no—
712D4×C73—42no—
713D4×C73—42no—
714D4×C73—81no—
715D4×C73—81no—
716D4×C73C2×#4112yes—
717C2×C4×C73—21no—
718C2×C4×C73—21no—
719C2×C4×C73—21no—
720C2×C4×C73—21no—
721C2×C4×C73—21no—
722C2×C4×C73—21no—
723C2×C4×C73—21no—
724C2×C4×C73—21no—
725C2×C4×C73—21no—
726C2×C4×C73—42no—
727C2×C4×C73—42no—
728C2×C4×C73—42no—
729C2×C4×C73—81no—
730C2×C4×C73C22×D411yescharacteristic
731C2×C4×C73C22×D411yescharacteristic
732C2×C4×C73C22×D411yescharacteristic
733C2×C4×C73C22×D411yescharacteristic
734C2×C4×C73C2511yescharacteristic
735C22⋊D73—22no—
736C22⋊D73—41no—
737C22⋊D73—42no—
738C22⋊D73—81no—
739C22⋊D73—81no—
740C2×Dic73—22no—
741C2×Dic73—21no—
742C2×Dic73—21no—
743C2×Dic73—21no—
744C2×Dic73—21no—
745C2×Dic73—21no—
746C2×Dic73—21no—
747C2×Dic73—21no—
748C2×Dic73—21no—
749C2×Dic73—41no—
750C2×Dic73—42no—
751C2×Dic73—42no—
752C2×Dic73—42no—
753C2×Dic73—42no—
754C2×Dic73—81no—
755C2×Dic73—81no—
756C2×Dic73—81no—
757C2×Dic73—81no—
758C2×Dic73—81no—
759C2×Dic73—81no—
760C2×Dic73C22×D411yescharacteristic
761C2×Dic73C22×D411yescharacteristic
762C2×Dic73C22×D411yescharacteristic
763C2×Dic73C22×D411yescharacteristic
764C2×Dic73C22×D411yescharacteristic
765C2×Dic73C22×D411yescharacteristic
766C2×Dic73C22×D411yescharacteristic
767C4×D73—21no—
768C4×D73—21no—
769C4×D73—42no—
770C4×D73—81no—
771Dic146—22no—
772Dic146—21no—
773Dic146—21no—
774Dic146—21no—
775Dic146—21no—
776Dic146—42no—
777Dic146—42no—
778Dic146—81no—
779Dic146—81no—
780Dic146—81no—
781Dic146—81no—
782Dic146—81no—
783C8×C73—21no—
784C8×C73—21no—
785C8×C73—21no—
786C8×C73C2×#4112yes—
787#10596831—21no—
788#10596831—21no—
789#10596831—21no—
790#10596831—21no—
791C22×C73—21no—
792C22×C73—21no—
793C22×C73—22no—
794C22×C73—21no—
795C22×C73—21no—
796C22×C73—21no—
797C22×C73—21no—
798C22×C73—41no—
799C22×C73—41no—
800C22×C73—41no—
801C22×C73—41no—
802C22×C73—41no—
803C22×C73—41no—
804C22×C73—41no—
805C22×C73—41no—
806C22×C73—84no—
807C22×C73C23×D411yescharacteristic
808C2×D73—21no—
809C2×D73—21no—
810C2×D73—21no—
811C4×C73—21no—
812C4×C73—22no—
813C4×C73—21no—
814C4×C73—21no—
815C4×C73—21no—
816C4×C73—41no—
817C4×C73—41no—
818C4×C73—41no—
819C4×C73—41no—
820C4×C73C22×#4111yescharacteristic
821C4×C73#58511yescharacteristic
822Dic73—21no—
823Dic73—21no—
824Dic73—21no—
825Dic73—21no—
826Dic73—21no—
827Dic73—21no—
828Dic73—41no—
829Dic73—41no—
830Dic73—41no—
831Dic73—41no—
832Dic73—41no—
833Dic73—41no—
834Dic73—41no—
835Dic73—41no—
836Dic73#57712yes—
837#61557—731nomaximal, Sylow
838C2×C73—41no—
839C2×C73—41no—
840C2×C73—42no—
841C2×C73—81no—
842C2×C73—81no—
843C2×C73D4×#4111yescharacteristic
844C2×C73C2×#57711yescharacteristic
845C2×C73#358611yescharacteristic
846D73—41no—
847#3520—731no—
848#3518—731no—
849#3393—731no—
850Q8×SD16—731no—
851#3369—731no—
852#3367—731no—
853#3356—731no—
854#3356—731no—
855#3354—731no—
856#3316—731no—
857#3316—731no—
858#3311—731no—
859#3311—731no—
860#3303—731no—
861#3298—731no—
862#3276—731no—
863#3275—731no—
864#3275D7311yescharacteristic, complemented
865#3185—731no—
866#3173—731no—
867#3173—731no—
868#3125—731no—
869#3125—731no—
870#3121—731no—
871#3121—731no—
872#3107—731no—
873#3101—731no—
874#2969—731no—
875#2947—731no—
876#2947—731no—
877C4×AGL(1,ℤ/8)—731no—
878C73#6155711yescharacteristic, complemented, Sylow
879C2×#137—731no—
880C2×#137C2×D7311yescharacteristic
881C2×AGL(1,ℤ/8)C2×D7311yescharacteristic
882Q82—731no—
883#556—731no—
884#556—731no—
885#556—731no—
886#556—731no—
887#556—1461no—
888#556—1461no—
889#556—1461no—
890#555—731no—
891#555—1461no—
892#554—731no—
893#554—731no—
894#552—1461no—
895#551—1461no—
896#551—1461no—
897D4×Q8—731no—
898D4×Q8—731no—
899#548—731no—
900#548—1461no—
901#548C2×D7311yescharacteristic
902#547—731no—
903#547—731no—
904#546—731no—
905#546C2×D7311yescharacteristic
906#542—731no—
907#542—731no—
908#542—731no—
909#542—731no—
910#542—1461no—
911#542—1461no—
912#539—1461no—
913#539—1461no—
914#533—731no—
915#533—731no—
916#533—1461no—
917#529—731no—
918#529—1461no—
919#525—1461no—
920C2×C22⋊Q8—1461no—
921#520—731no—
922#520—731no—
923#519—731no—
924#519—731no—
925C4×#41—731no—
926C2×C4×D4—731no—
927#498—731no—
928#498—731no—
929#498—731no—
930#495—731no—
931#495C2×D7311yescharacteristic
932#494—731no—
933#489—731no—
934#489—731no—
935#489—731no—
936#489—731no—
937#487—731no—
938#487—731no—
939#485—731no—
940#485—731no—
941#485—731no—
942#485—731no—
943#483—731no—
944#483—731no—
945#483—731no—
946#483—731no—
947#482—731no—
948#482—731no—
949#481—731no—
950#481—731no—
951#477—731no—
952#477—731no—
953#476—731no—
954#476—731no—
955#476—731no—
956#476—731no—
957#475—731no—
958#475—731no—
959#475—731no—
960#475—731no—
961#475—731no—
962#474—731no—
963#470—731no—
964#470—731no—
965#470—731no—
966#470—731no—
967#470—731no—
968#470C2×D7311yescharacteristic
969#469—731no—
970#469C2×D7311yescharacteristic
971#465—731no—
972#465—731no—
973#465—731no—
974#465—731no—
975#464—731no—
976#464—731no—
977#464—731no—
978#464—731no—
979#464—731no—
980#464C2×D7311yescharacteristic
981#463—731no—
982#463C2×D7311yescharacteristic
983#462—731no—
984#461—731no—
985#461—731no—
986#461—731no—
987#452—731no—
988#452—731no—
989#452—731no—
990#452C2×D7311yescharacteristic
991#451—731no—
992#451—731no—
993#450—731no—
994#450C2×D7311yescharacteristic
995#449—731no—
996#449C2×D7311yescharacteristic
997#448—731no—
998#448C2×D7311yescharacteristic
999#446—731no—
1000C8×Q8—731no—
1001#442—731no—
1002#442—731no—
1003#441—731no—
1004#441—731no—
1005#441—731no—
1006#441—731no—
1007#441—731no—
1008#441—731no—
1009#440—731no—
1010#440—731no—
1011#440—731no—
1012#440—731no—
1013C4×Q16—731no—
1014C4×Q16—731no—
1015C4×Q16—731no—
1016C4×Q16—731no—
1017C4×SD16—731no—
1018C4×SD16—731no—
1019C4×SD16—731no—
1020C4×SD16—731no—
1021C4×SD16—731no—
1022C4×SD16—731no—
1023C4×SD16—731no—
1024C4×SD16—731no—
1025C4×SD16—731no—
1026C4×SD16C2×D7311yescharacteristic
1027C4×D8—731no—
1028C4×D8—731no—
1029#436—731no—
1030#436—731no—
1031#436C2×D7311yescharacteristic
1032#435—731no—
1033#435—731no—
1034C8×D4—731no—
1035#433—731no—
1036#433—731no—
1037#431—731no—
1038#428—731no—
1039#428—731no—
1040#428—731no—
1041#418—731no—
1042#417—731no—
1043#416—731no—
1044#416—731no—
1045C2×#103—731no—
1046C2×#103—731no—
1047#405—731no—
1048#405—731no—
1049C4×M16—731no—
1050C2×#41—731no—
1051C2×#41—1461no—
1052C2×#41C22×D7311yescharacteristic
1053C2×#41C22×D7311yescharacteristic
1054C22×Q8—731no—
1055C22×Q8—1461no—
1056C22×Q8C22×D7311yescharacteristic
1057C22×D4C22×D7311yescharacteristic
1058C23×C4—1461no—
1059#137—24no—
1060#137—1464no—
1061AGL(1,ℤ/8)—24no—
1062C2×Q16—731no—
1063C2×Q16—731no—
1064C2×Q16—731no—
1065C2×Q16—731no—
1066C2×Q16C22×D7311yescharacteristic
1067C2×Q16C22×D7311yescharacteristic
1068C2×SD16—731no—
1069C2×SD16—731no—
1070C2×SD16—731no—
1071C2×SD16C22×D7311yescharacteristic
1072C2×SD16C22×D7311yescharacteristic
1073C2×SD16C22×D7311yescharacteristic
1074C2×SD16C22×D7311yescharacteristic
1075C2×SD16C22×D7311yescharacteristic
1076C2×D8C22×D7311yescharacteristic
1077C2×D8C22×D7311yescharacteristic
1078C2×M16—731no—
1079C2×M16—731no—
1080C2×M16C22×D7311yescharacteristic
1081C2×M16C22×D7311yescharacteristic
1082C22×C8—731no—
1083C22×C8—731no—
1084C4⋊Q8—731no—
1085C4⋊Q8—731no—
1086C4⋊Q8—731no—
1087C4⋊Q8—731no—
1088C4⋊Q8—731no—
1089C4⋊Q8—731no—
1090C4⋊Q8—731no—
1091C4⋊Q8—731no—
1092C4⋊Q8—1461no—
1093C4⋊Q8—1461no—
1094C4⋊Q8—1461no—
1095C4⋊Q8—1461no—
1096#126—731no—
1097#126—731no—
1098#126—1461no—
1099#126—1461no—
1100#126—1461no—
1101#126—1461no—
1102#126—1461no—
1103#126—1461no—
1104#126—1461no—
1105#126—1461no—
1106#126—1461no—
1107#126—1461no—
1108#126—1461no—
1109#126—1461no—
1110#125—731no—
1111#125—1461no—
1112#125—1461no—
1113#125—1461no—
1114#125—1461no—
1115#124—21no—
1116#124—731no—
1117#124—731no—
1118#124—731no—
1119#124—1461no—
1120#124—1461no—
1121#124—1461no—
1122#124—1461no—
1123#124—1461no—
1124#124—1461no—
1125#124—1461no—
1126#124—1461no—
1127#124—1461no—
1128#124C22×D7311yescharacteristic
1129#124C22×D7311yescharacteristic
1130#123—21no—
1131#123—731no—
1132#123—731no—
1133#123—1461no—
1134#123—1461no—
1135#123—1461no—
1136#123—1461no—
1137#123—1461no—
1138#123—1461no—
1139#123—1461no—
1140#123—1461no—
1141#123—1461no—
1142C22⋊Q8—21no—
1143C22⋊Q8—731no—
1144C22⋊Q8—731no—
1145C22⋊Q8—731no—
1146C22⋊Q8—731no—
1147C22⋊Q8—731no—
1148C22⋊Q8—731no—
1149C22⋊Q8—731no—
1150C22⋊Q8—1461no—
1151C22⋊Q8—1461no—
1152C22⋊Q8—1461no—
1153C22⋊Q8—1461no—
1154C22⋊Q8—1461no—
1155C22⋊Q8—1461no—
1156C22⋊Q8—1461no—
1157C22⋊Q8—1461no—
1158C22⋊Q8—1461no—
1159C22⋊Q8—1461no—
1160C22⋊Q8—1461no—
1161C22⋊Q8—1461no—
1162C22⋊Q8—1461no—
1163C22⋊Q8—1461no—
1164C22⋊Q8—1461no—
1165C22⋊Q8—1461no—
1166C22⋊Q8—1461no—
1167C22⋊Q8—1461no—
1168C22⋊Q8—1461no—
1169C22⋊Q8C22×D7311yescharacteristic
1170C22⋊Q8C22×D7311yescharacteristic
1171#121—21no—
1172#121—21no—
1173#121—731no—
1174#121—731no—
1175#121—731no—
1176#121—1461no—
1177#121—1461no—
1178#121—1461no—
1179#121—1461no—
1180#121C22×D7311yescharacteristic
1181#121C22×D7311yescharacteristic
1182#120—21no—
1183#120—1461no—
1184C4×Q8—731no—
1185C4×Q8—731no—
1186C4×Q8—731no—
1187C4×Q8—731no—
1188C4×Q8—731no—
1189C4×Q8—731no—
1190C4×Q8—731no—
1191C4×Q8—731no—
1192C4×Q8—731no—
1193C4×Q8—731no—
1194C4×Q8—731no—
1195C4×Q8—731no—
1196C4×Q8—1461no—
1197C4×Q8—1461no—
1198C4×Q8—1461no—
1199C4×Q8—1461no—
1200C4×Q8—1461no—
1201C4×Q8—1461no—
1202C4×Q8—1461no—
1203C4×Q8—1461no—
1204C4×Q8—1461no—
1205C4×Q8C22×D7311yescharacteristic
1206C4×D4—21no—
1207C4×D4—731no—
1208C4×D4—731no—
1209C4×D4—731no—
1210C4×D4—731no—
1211C4×D4—731no—
1212C4×D4—731no—
1213C4×D4—731no—
1214C4×D4—731no—
1215C4×D4—731no—
1216C4×D4—1461no—
1217C4×D4—1461no—
1218C4×D4—1461no—
1219C4×D4—1461no—
1220C4×D4—1461no—
1221C4×D4—1461no—
1222C4×D4—1461no—
1223C4×D4—1461no—
1224C4×D4—1461no—
1225C4×D4—1461no—
1226C4×D4—1461no—
1227C4×D4—1461no—
1228C4×D4C22×D7311yescharacteristic
1229C4×D4C22×D7311yescharacteristic
1230#117—731no—
1231#117—731no—
1232#117—731no—
1233#117—731no—
1234#117—731no—
1235#117—1461no—
1236#117—1461no—
1237#117—1461no—
1238#117—1461no—
1239#117—1461no—
1240#117—1461no—
1241#117—1461no—
1242#117—1461no—
1243#117—1461no—
1244#117—1461no—
1245#117—1461no—
1246#117—1461no—
1247C2×C4⋊C4—731no—
1248C2×C4⋊C4—731no—
1249C2×C4⋊C4—731no—
1250C2×C4⋊C4—1461no—
1251C2×C4⋊C4—1461no—
1252C2×C4⋊C4—1461no—
1253C2×C22⋊C4—21no—
1254C2×C22⋊C4—1461no—
1255C2×C22⋊C4—1461no—
1256C2×C42—731no—
1257C2×C42—1461no—
1258#107—731no—
1259#107—731no—
1260#107—731no—
1261#107—731no—
1262#106—731no—
1263#106—731no—
1264#106—731no—
1265#106—731no—
1266#106—731no—
1267#106—731no—
1268#106—731no—
1269#106—731no—
1270#106—731no—
1271#106—731no—
1272#106—731no—
1273#106C22×D7311yescharacteristic
1274C4⋊C8—731no—
1275C4⋊C8—731no—
1276C4⋊C8—731no—
1277C4⋊C8—731no—
1278C4⋊C8—731no—
1279C4⋊C8C22×D7311yescharacteristic
1280#103—731no—
1281#103—731no—
1282#103—731no—
1283#103—731no—
1284#103—731no—
1285#103—731no—
1286#103—731no—
1287#103—731no—
1288#103—731no—
1289#103—731no—
1290#103—731no—
1291#103—731no—
1292#103—731no—
1293#103—731no—
1294#103—731no—
1295#103—731no—
1296#103—731no—
1297#103C22×D7311yescharacteristic
1298#103C22×D7311yescharacteristic
1299#103C22×D7311yescharacteristic
1300#102—731no—
1301#102—731no—
1302#102—731no—
1303#102—731no—
1304#102—731no—
1305#102—731no—
1306#102—731no—
1307#102—731no—
1308#102—731no—
1309#102C22×D7311yescharacteristic
1310#102C22×D7311yescharacteristic
1311#102C22×D7311yescharacteristic
1312C22⋊C8—731no—
1313C22⋊C8—731no—
1314C22⋊C8—731no—
1315C22⋊C8—731no—
1316C22⋊C8C22×D7311yescharacteristic
1317C22⋊C8C22×D7311yescharacteristic
1318#97—731no—
1319#97—731no—
1320#97—731no—
1321#97—731no—
1322C4×C8—731no—
1323C4×C8—731no—
1324C4×C8—731no—
1325C4×C8—731no—
1326C4×C8—731no—
1327C4×C8C22×D7311yescharacteristic
1328C24—21no—
1329#41—22no—
1330#41—22no—
1331#41—41no—
1332#41—41no—
1333#41—2921no—
1334#41—5842no—
1335#41—1462no—
1336C2×Q8—21no—
1337C2×Q8—22no—
1338C2×Q8—41no—
1339C2×Q8—2921no—
1340C2×Q8—5842no—
1341C2×Q8—731no—
1342C2×Q8—731no—
1343C2×Q8—731no—
1344C2×Q8—1461no—
1345C2×Q8—1461no—
1346C2×Q8—1461no—
1347C2×Q8—1461no—
1348C2×Q8—1461no—
1349C2×Q8—1462no—
1350C2×Q8—1461no—
1351C2×Q8—1461no—
1352C2×Q8C23×D7311yescharacteristic
1353C2×Q8C23×D7311yescharacteristic
1354C2×Q8C23×D7311yescharacteristic
1355C2×D4—22no—
1356C2×D4—21no—
1357C2×D4—21no—
1358C2×D4—21no—
1359C2×D4—21no—
1360C2×D4—21no—
1361C2×D4—41no—
1362C2×D4—731no—
1363C2×D4—731no—
1364C2×D4—1461no—
1365C2×D4—1461no—
1366C2×D4—1461no—
1367C2×D4D4×D7311yescharacteristic
1368C2×D4C23×D7311yescharacteristic
1369C2×D4C23×D7311yescharacteristic
1370C2×D4C23×D7311yescharacteristic
1371C22×C4—21no—
1372C22×C4—21no—
1373C22×C4—21no—
1374C22×C4—21no—
1375C22×C4—5842no—
1376C22×C4—731no—
1377C22×C4—731no—
1378C22×C4—731no—
1379C22×C4—1461no—
1380C22×C4—1461no—
1381C22×C4—1461no—
1382C22×C4—1461no—
1383C22×C4—1461no—
1384C22×C4—1461no—
1385C22×C4—1461no—
1386C22×C4—1461no—
1387C22×C4—1461no—
1388C22×C4—1461no—
1389C22×C4—1461no—
1390C22×C4—1461no—
1391C22×C4C23×D7311yescharacteristic
1392C22×C4C23×D7311yescharacteristic
1393Q16—22no—
1394Q16—22no—
1395Q16—2921no—
1396Q16—2921no—
1397Q16—1462no—
1398Q16—1462no—
1399SD16—22no—
1400SD16—22no—
1401SD16—41no—
1402SD16—41no—
1403SD16—2921no—
1404SD16—2921no—
1405SD16—1462no—
1406SD16#1192402714yescomplemented
1407D8—22no—
1408D8—22no—
1409M16—22no—
1410M16—22no—
1411M16—2921no—
1412M16—1462no—
1413C2×C8—2921no—
1414C2×C8—2921no—
1415C2×C8—731no—
1416C2×C8—731no—
1417C2×C8—731no—
1418C2×C8—731no—
1419C2×C8C23×D7311yescharacteristic
1420C2×C8C23×D7311yescharacteristic
1421C2×C8C23×D7311yescharacteristic
1422C2×C8C23×D7311yescharacteristic
1423C4⋊C4—21no—
1424C4⋊C4—21no—
1425C4⋊C4—21no—
1426C4⋊C4—731no—
1427C4⋊C4—731no—
1428C4⋊C4—731no—
1429C4⋊C4—731no—
1430C4⋊C4—731no—
1431C4⋊C4—731no—
1432C4⋊C4—731no—
1433C4⋊C4—731no—
1434C4⋊C4—731no—
1435C4⋊C4—731no—
1436C4⋊C4—731no—
1437C4⋊C4—731no—
1438C4⋊C4—731no—
1439C4⋊C4—731no—
1440C4⋊C4—731no—
1441C4⋊C4—1461no—
1442C4⋊C4—1461no—
1443C4⋊C4—1461no—
1444C4⋊C4—1461no—
1445C4⋊C4—1461no—
1446C4⋊C4—1461no—
1447C4⋊C4—1461no—
1448C4⋊C4—1461no—
1449C4⋊C4—1461no—
1450C4⋊C4—1461no—
1451C4⋊C4—1461no—
1452C4⋊C4—1461no—
1453C4⋊C4—1461no—
1454C4⋊C4—1461no—
1455C4⋊C4—1461no—
1456C4⋊C4—1461no—
1457C4⋊C4—1461no—
1458C4⋊C4—1461no—
1459C4⋊C4—1461no—
1460C4⋊C4—1461no—
1461C4⋊C4—1461no—
1462C4⋊C4—1461no—
1463C4⋊C4—1461no—
1464C4⋊C4—1461no—
1465C4⋊C4—1461no—
1466C4⋊C4—1461no—
1467C4⋊C4—1461no—
1468C4⋊C4—1461no—
1469C4⋊C4—1461no—
1470C4⋊C4—1461no—
1471C4⋊C4D4×D7311yescharacteristic
1472C4⋊C4C23×D7311yescharacteristic
1473C4⋊C4C23×D7311yescharacteristic
1474C22⋊C4—21no—
1475C22⋊C4—21no—
1476C22⋊C4—21no—
1477C22⋊C4—21no—
1478C22⋊C4—21no—
1479C22⋊C4—21no—
1480C22⋊C4—21no—
1481C22⋊C4—21no—
1482C22⋊C4—21no—
1483C22⋊C4—731no—
1484C22⋊C4—731no—
1485C22⋊C4—731no—
1486C22⋊C4—731no—
1487C22⋊C4—731no—
1488C22⋊C4—731no—
1489C22⋊C4—731no—
1490C22⋊C4—731no—
1491C22⋊C4—1461no—
1492C22⋊C4—1461no—
1493C22⋊C4—1461no—
1494C22⋊C4—1461no—
1495C22⋊C4—1461no—
1496C22⋊C4—1461no—
1497C22⋊C4—1461no—
1498C22⋊C4—1461no—
1499C22⋊C4—1461no—
1500C22⋊C4—1461no—
1501C22⋊C4—1461no—
1502C22⋊C4—1461no—
1503C22⋊C4—1461no—
1504C22⋊C4—1461no—
1505C22⋊C4—1461no—
1506C22⋊C4—1461no—
1507C22⋊C4—1461no—
1508C22⋊C4—1461no—
1509C22⋊C4—1461no—
1510C22⋊C4—1461no—
1511C22⋊C4—1461no—
1512C22⋊C4—1461no—
1513C22⋊C4D4×D7311yescharacteristic
1514C22⋊C4D4×D7311yescharacteristic
1515C42—21no—
1516C42—731no—
1517C42—731no—
1518C42—731no—
1519C42—731no—
1520C42—731no—
1521C42—1461no—
1522C42—1461no—
1523C42—1461no—
1524C42—1461no—
1525C42—1461no—
1526C42—1461no—
1527C42—1461no—
1528C42—1461no—
1529C42—1461no—
1530C42—1461no—
1531C42—1461no—
1532C42—1461no—
1533C42—1461no—
1534C42—1461no—
1535C42C23×D7311yescharacteristic
1536C23—21no—
1537C23—21no—
1538C23—21no—
1539C23—42no—
1540C23—42no—
1541C23—81no—
1542C23—731no—
1543C23C2×D4×D7311yescharacteristic
1544C23C2×D4×D7311yescharacteristic
1545Q8—21no—
1546Q8—21no—
1547Q8—21no—
1548Q8—21no—
1549Q8—21no—
1550Q8—42no—
1551Q8—2922no—
1552Q8—2922no—
1553Q8—5841no—
1554Q8—5841no—
1555Q8—5841no—
1556Q8—5841no—
1557Q8—5841no—
1558Q8—1462no—
1559Q8—1461no—
1560Q8—1461no—
1561Q8—1461no—
1562Q8—1461no—
1563Q8C2×#1192402712yes—
1564D4—21no—
1565D4—21no—
1566D4—21no—
1567D4—21no—
1568D4—21no—
1569D4—41no—
1570D4—42no—
1571D4—42no—
1572D4—42no—
1573D4—81no—
1574D4—81no—
1575D4—2922no—
1576D4—2921no—
1577D4—5841no—
1578D4—5841no—
1579D4—1462no—
1580D4C2×#1192402712yes—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—42no—
1591C2×C4—42no—
1592C2×C4—42no—
1593C2×C4—81no—
1594C2×C4—2922no—
1595C2×C4—2922no—
1596C2×C4—2922no—
1597C2×C4—2922no—
1598C2×C4—2922no—
1599C2×C4—2921no—
1600C2×C4—5841no—
1601C2×C4—5841no—
1602C2×C4—5841no—
1603C2×C4—5841no—
1604C2×C4—5841no—
1605C2×C4—5841no—
1606C2×C4—5841no—
1607C2×C4—731no—
1608C2×C4—731no—
1609C2×C4—731no—
1610C2×C4—731no—
1611C2×C4—731no—
1612C2×C4—731no—
1613C2×C4—731no—
1614C2×C4—1461no—
1615C2×C4—1461no—
1616C2×C4—1461no—
1617C2×C4—1461no—
1618C2×C4—1461no—
1619C2×C4—1461no—
1620C2×C4—1461no—
1621C2×C4—1461no—
1622C2×C4—1462no—
1623C2×C4—1461no—
1624C2×C4—1461no—
1625C2×C4C2×D4×D7311yescharacteristic
1626C2×C4C2×D4×D7311yescharacteristic
1627C2×C4C2×D4×D7311yescharacteristic
1628C2×C4C2×D4×D7311yescharacteristic
1629C2×C4C24×D7311yescharacteristic
1630C8—21no—
1631C8—21no—
1632C8—21no—
1633C8—1461no—
1634C8—1461no—
1635C8—1461no—
1636C8—1461no—
1637C8C2×#1192402712yes—
1638C22—21no—
1639C22—21no—
1640C22—21no—
1641C22—21no—
1642C22—22no—
1643C22—21no—
1644C22—21no—
1645C22—41no—
1646C22—41no—
1647C22—41no—
1648C22—41no—
1649C22—41no—
1650C22—41no—
1651C22—41no—
1652C22—41no—
1653C22—84no—
1654C22—1461no—
1655C22—1461no—
1656C22—1461no—
1657C22C22×D4×D7311yescharacteristic
1658C4—21no—
1659C4—21no—
1660C4—21no—
1661C4—22no—
1662C4—21no—
1663C4—41no—
1664C4—41no—
1665C4—41no—
1666C4—41no—
1667C4—2921no—
1668C4—2921no—
1669C4—2921no—
1670C4—2921no—
1671C4—2921no—
1672C4—2921no—
1673C4—2921no—
1674C4—2921no—
1675C4—732no—
1676C4—1461no—
1677C4—1461no—
1678C4—1461no—
1679C4—1461no—
1680C4—1461no—
1681C4—1461no—
1682C4C22×#1192402711yescharacteristic
1683C4#1798942211yescharacteristic
1684C2—41no—
1685C2—41no—
1686C2—42no—
1687C2—81no—
1688C2—81no—
1689C2—2921no—
1690C2D4×#1192402711yescharacteristic
1691C2#577×D7311yescharacteristic
1692C2#2262471511yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3275C2
socleC22×C73C23×D4
hypercenter#3275D73
hypocenterC73#61557
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3275

Complements

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

NH ≅ G/Ntype
1. #22623967C2semidirect
2. #22623939C2semidirect
3. #22622916C2semidirect
4. SD16×Dic146C2semidirect
5. #22622666C2semidirect
6. #22622644C2semidirect
7. #22622547C2semidirect
8. #22622541C2semidirect
9. #22622521C2semidirect
10. #22622042C2semidirect
11. #22622035C2semidirect
12. #22621967C2semidirect
13. #22621960C2semidirect
14. #22621852C2semidirect
15. #22621789C2semidirect
16. #22621571C2semidirect
17. #22621562C2semidirect
18. #22620671C2semidirect
19. #22620545C2semidirect
20. #22620543C2semidirect
21. #22620209C2semidirect
22. #22620205C2semidirect
23. #22620159C2semidirect
24. #22620153C2semidirect
25. #22619995C2semidirect
26. #22619934C2semidirect
27. #22618930C2semidirect
28. #22618775C2semidirect
29. #22618767C2semidirect
30. AGL(1,ℤ/8)×Dic73C2semidirect
31. C73×#3275C2semidirect
33. Q8×Dic146C22semidirect
40. #17989306C22semidirect
42. #17989301C22semidirect
49. Q8×C22⋊D73C22semidirect
57. #17989206C22semidirect
60. #17989204C22semidirect
72. #17989065C22semidirect
73. #17989063C22semidirect
76. #17988985C22semidirect
77. #17988984C22semidirect
78. #17988984C22semidirect
80. #17988965C22semidirect
82. #17988946C22semidirect
84. #17988945C22semidirect
85. #17988936C22semidirect
86. #17988936C22semidirect
88. #17988929C22semidirect
89. #17988927C22semidirect
92. #17988918C22semidirect
93. #17988916C22semidirect
97. #17988904C22semidirect
98. #17988903C22semidirect
99. #17988883C22semidirect
100. #17988880C22semidirect
105. #17988873C22semidirect
106. #17988872C22semidirect
107. #17988870C22semidirect
108. #17988870C22semidirect
109. #17988870C22semidirect
110. #17988865C22semidirect
112. #17988845C22semidirect
115. #17988842C22semidirect
118. #17988814C22semidirect
120. #17988813C22semidirect
123. #17988807C22semidirect
125. #17988806C22semidirect
127. #17988795C22semidirect
130. #17988790C22semidirect
134. #17988743C22semidirect
135. #17988741C22semidirect
139. #17988716C22semidirect
140. C8×Dic146C22semidirect
143. #17988694C22semidirect
144. #17988694C22semidirect
145. #17988693C22semidirect
146. #17988692C22semidirect
147. #17988691C22semidirect
148. #17988691C22semidirect
153. C4×Dic292C22semidirect
154. Q16×Dic73C22semidirect
155. Q16×Dic73C22semidirect
156. #17988679C22semidirect
159. #17988678C22semidirect
165. SD16×Dic73C22semidirect
169. #17988663C22semidirect
172. #17988650C22semidirect
173. #17988647C22semidirect
174. #17988645C22semidirect
177. #17988629C22semidirect
178. #17988626C22semidirect
183. C2×#14556515C22semidirect
184. #103×D73C22semidirect
185. #17988545C22semidirect
186. #17988541C22semidirect
661. SD16×C73#41semidirect
864. #3275D73semidirect
878. C73#61557semidirect
1406. SD16#11924027semidirect

Maximal subgroups

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

subgroupindex
#226239672
#226239392
#226229162
SD16×Dic1462
#226226662
#226226442
#226225472
#226225412
#226225212
#226220422
#226220352
#226219672
#226219602
#226218522
#226217892
#226215712
#226215622
#226206712
#226205452
#226205432
#226202092
#226202052
#226201592
#226201532
#226199952
#226199342
#226189302
#226187752
#226187672
AGL(1,ℤ/8)×Dic732
C73×#32752
#6155773