Finite Group Databasebeta

← #33968162

Subgroups — #33968162

Order 18688.

1846 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#22623543C211yesmaximal, characteristic, complemented
2#22623482C211yesmaximal, characteristic, complemented
3#22622959C211yesmaximal, characteristic, complemented
4#22622831C211yesmaximal, characteristic, complemented
5#22622707C211yesmaximal, characteristic, complemented
6#22622644C211yesmaximal, characteristic, complemented
7#22622463C211yesmaximal, characteristic, complemented
8#22622456C211yesmaximal, characteristic, complemented
9#22622339C211yesmaximal, characteristic, complemented
10#22622027C211yesmaximal, characteristic, complemented
11#22622020C211yesmaximal, characteristic, complemented
12#22621967C211yesmaximal, characteristic, complemented
13#22621960C211yesmaximal, characteristic, complemented
14#22621852C211yesmaximal, characteristic, complemented
15#22621841C211yesmaximal, characteristic, complemented
16#22621647C211yesmaximal, characteristic, complemented
17#22621450C211yesmaximal, characteristic, complemented
18#22620671C211yesmaximal, characteristic, complemented
19#22620637C211yesmaximal, characteristic, complemented
20#22620633C211yesmaximal, characteristic, complemented
21#22620090C211yesmaximal, characteristic, complemented
22#22620086C211yesmaximal, characteristic, complemented
23#22620086C211yesmaximal, characteristic, complemented
24#22620037C211yesmaximal, characteristic, complemented
25#22620033C211yesmaximal, characteristic, complemented
26#22620025C211yesmaximal, characteristic, complemented
27#22618941C211yesmaximal, characteristic, complemented
28AGL(1,ℤ/8)×Dic73C211yesmaximal, characteristic, complemented
29#22618732C211yesmaximal, characteristic, complemented
30#22618728C211yesmaximal, characteristic, complemented
31C73×#3267C211yesmaximal, characteristic, complemented
32C2×#14556610C2211yescharacteristic
33#17989312C2211yescharacteristic, complemented
34#17989308C2211yescharacteristic
35#17989308C2211yescharacteristic, complemented
36#17989307C2211yescharacteristic
37#17989306C2211yescharacteristic
38#17989301C2211yescharacteristic
39#17989296C2211yescharacteristic
40#17989280—21no—
41#17989279C2211yescharacteristic
42#17989277C2211yescharacteristic
43#17989274—21no—
44#17989274—21no—
45#17989274—21no—
46#17989272—21no—
47#17989268—21no—
48#17989263—21no—
49D4×Dic146C2211yescharacteristic, complemented
50#17989243—21no—
51#17989236C2211yescharacteristic
52#17989236C2211yescharacteristic
53#17989236C2211yescharacteristic, complemented
54#17989231C2211yescharacteristic
55#17989142C2211yescharacteristic, complemented
56#17989139C2211yescharacteristic
57#17989139C2211yescharacteristic
58#17989139C2211yescharacteristic, complemented
59#17989118—21no—
60#17989118—21no—
61#17989118C2211yescharacteristic
62#17989116C2211yescharacteristic
63#17989114—21no—
64#17989114—21no—
65#17989114—21no—
66#17989093—21no—
67#41×Dic73C2211yescharacteristic
68#41×Dic73C2211yescharacteristic
69#41×Dic73C2211yescharacteristic, complemented
70C4×#11924027C2211yescharacteristic
71C4×#11924027C2211yescharacteristic
72C4×#11924027C2211yescharacteristic, complemented
73C2×#14556556—21no—
74C2×D4×Dic73C2211yescharacteristic
75C2×#14556547—21no—
76#17988996C2211yescharacteristic, complemented
77#17988994C2211yescharacteristic, complemented
78#17988984C2211yescharacteristic, complemented
79#17988978C2211yescharacteristic
80#17988965C2211yescharacteristic, complemented
81#17988955C2211yescharacteristic, complemented
82#17988954C2211yescharacteristic, complemented
83#17988946C2211yescharacteristic
84#17988945C2211yescharacteristic
85#17988936C2211yescharacteristic, complemented
86#17988936C2211yescharacteristic, complemented
87#17988929C2211yescharacteristic
88#17988929C2211yescharacteristic, complemented
89#17988929C2211yescharacteristic, complemented
90#17988927C2211yescharacteristic, complemented
91#17988927C2211yescharacteristic, complemented
92#17988926C2211yescharacteristic, complemented
93#17988925C2211yescharacteristic
94#17988925C2211yescharacteristic, complemented
95#17988923C2211yescharacteristic
96#17988920C2211yescharacteristic
97#17988909C2211yescharacteristic
98#17988908C2211yescharacteristic
99#17988895C2211yescharacteristic, complemented
100#17988892C2211yescharacteristic, complemented
101#17988887C2211yescharacteristic, complemented
102#17988885C2211yescharacteristic, complemented
103#17988883C2211yescharacteristic, complemented
104#17988880C2211yescharacteristic, complemented
105#17988880C2211yescharacteristic, complemented
106#17988877C2211yescharacteristic
107#17988875C2211yescharacteristic
108#17988875C2211yescharacteristic, complemented
109#17988865C2211yescharacteristic
110#17988865C2211yescharacteristic
111#17988845C2211yescharacteristic
112#17988843C2211yescharacteristic
113#17988843C2211yescharacteristic
114#17988828C2211yescharacteristic, complemented
115#17988826C2211yescharacteristic, complemented
116#17988825C2211yescharacteristic, complemented
117#17988825C2211yescharacteristic, complemented
118#17988814C2211yescharacteristic
119#17988813C2211yescharacteristic
120#17988813C2211yescharacteristic
121#17988807C2211yescharacteristic
122#17988806C2211yescharacteristic
123#17988800C2211yescharacteristic
124#17988795C2211yescharacteristic, complemented
125#17988795C2211yescharacteristic, complemented
126#17988794C2211yescharacteristic, complemented
127#17988790C2211yescharacteristic
128#17988790C2211yescharacteristic
129#17988790C2211yescharacteristic
130#17988790C2211yescharacteristic, complemented
131#17988749C2211yescharacteristic
132#17988749C2211yescharacteristic
133#17988749C2211yescharacteristic, complemented
134#17988746C2211yescharacteristic
135#17988746C2211yescharacteristic
136#17988746C2211yescharacteristic, complemented
137#17988738C2211yescharacteristic
138#17988729C2211yescharacteristic
139#17988716C2211yescharacteristic, complemented
140#17988715C2211yescharacteristic, complemented
141#17988699C2211yescharacteristic
142#17988699C2211yescharacteristic
143#17988699C2211yescharacteristic
144#17988695C2211yescharacteristic, complemented
145#17988694C2211yescharacteristic, complemented
146#17988694C2211yescharacteristic, complemented
147#17988694C2211yescharacteristic, complemented
148#17988693C2211yescharacteristic, complemented
149#17988691C2211yescharacteristic, complemented
150#17988691C2211yescharacteristic, complemented
151#17988691C2211yescharacteristic, complemented
152#17988688C2211yescharacteristic
153#17988688C2211yescharacteristic
154#17988688C2211yescharacteristic
155#17988688C2211yescharacteristic
156#17988688C2211yescharacteristic
157#17988688C2211yescharacteristic, complemented
158#17988688C2211yescharacteristic, complemented
159#17988687C2211yescharacteristic
160#17988687C2211yescharacteristic, complemented
161#17988684C2211yescharacteristic
162#17988684C2211yescharacteristic
163#17988684C2211yescharacteristic, complemented
164SD16×Dic73C2211yescharacteristic
165SD16×Dic73C2211yescharacteristic
166D8×Dic73C2211yescharacteristic
167D8×Dic73C2211yescharacteristic
168#17988661C2211yescharacteristic
169#17988659C2211yescharacteristic
170#17988656C2211yescharacteristic
171C8×C22⋊D73C2211yescharacteristic, complemented
172#17988650C2211yescharacteristic, complemented
173#17988643C2211yescharacteristic, complemented
174#17988641C2211yescharacteristic
175#17988641C2211yescharacteristic, complemented
176#17988629C2211yescharacteristic
177#17988625C2211yescharacteristic, complemented
178#17988622C2211yescharacteristic, complemented
179#17988592C2211yescharacteristic
180#17988588C2211yescharacteristic
181#17988583C2211yescharacteristic
182#17988583C2211yescharacteristic, complemented
183#17988580C2211yescharacteristic
184#17988580C2211yescharacteristic, complemented
185M16×Dic73C2211yescharacteristic
186C2×#14556501C2211yescharacteristic, complemented
187#97×D73C2211yescharacteristic, complemented
188C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
189C2×#135×C73C2211yescharacteristic
190#547×C73C2211yescharacteristic
191#546×C73C2211yescharacteristic
192#497×C73C2211yescharacteristic
193#470×C73C2211yescharacteristic
194#465×C73C2211yescharacteristic
195#463×C73C2211yescharacteristic
196#461×C73C2211yescharacteristic
197#452×C73C2211yescharacteristic
198#452×C73C2211yescharacteristic
199#450×C73C2211yescharacteristic
200#449×C73C2211yescharacteristic
201#442×C73C2211yescharacteristic
202#435×C73C2211yescharacteristic
203C2×#11924027D411yescharacteristic
204C2×#11924027C2311yescharacteristic
205C2×#11924027C2311yescharacteristic
206C22×Dic146—21no—
207C23×Dic73—21no—
208#14556610—24no—
209C2×Dic292C2311yescharacteristic
210C2×#11924018C2311yescharacteristic
211C2×#11924018C2311yescharacteristic
212C2×#11924018C2311yescharacteristic
213C2×#11924016C2311yescharacteristic
214C2×#11924016C2311yescharacteristic
215C2×#11924016C2311yescharacteristic
216C2×#11924012C2311yescharacteristic
217C22×#10596831C2311yescharacteristic
218C2×C8×D73C2311yescharacteristic
219C2×C8×D73C2311yescharacteristic
220#14556591C2311yescharacteristic
221#14556590C2311yescharacteristic
222#14556590C2311yescharacteristic
223#14556590C2311yescharacteristic
224#14556589C2311yescharacteristic
225#14556589C2311yescharacteristic
226#14556589C2311yescharacteristic
227#14556586—21no—
228#14556586—21no—
229#14556586—21no—
230#14556584—21no—
231#14556584—21no—
232#14556584—21no—
233#14556584—21no—
234#14556584—21no—
235#14556584—21no—
236#14556584—21no—
237#14556584—21no—
238#14556584—21no—
239#14556583C2311yescharacteristic
240#14556582—21no—
241#14556582—21no—
242#14556582—21no—
243#14556582C2311yescharacteristic
244#14556581—21no—
245#14556581—21no—
246#14556581—21no—
247#14556581—21no—
248#14556581—21no—
249#14556581—21no—
250#14556578—21no—
251#14556578—21no—
252#14556578C2311yescharacteristic
253#14556577—21no—
254#14556577—21no—
255#14556577—21no—
256#14556575—21no—
257#14556574—21no—
258#14556574—21no—
259#14556574—21no—
260#14556573—21no—
261#14556572—21no—
262#14556572—21no—
263#14556572—21no—
264#14556572—21no—
265#14556572—21no—
266#14556572—21no—
267#14556571—21no—
268#14556570—21no—
269#14556570—21no—
270#14556570C2311yescharacteristic
271#14556570C2311yescharacteristic
272#14556570C2311yescharacteristic
273#14556570C2311yescharacteristic
274#14556568—21no—
275#14556568—21no—
276#14556568—21no—
277#14556568—21no—
278#14556568—21no—
279#14556568—21no—
280#14556568—21no—
281#14556568—21no—
282#14556567C2311yescharacteristic
283#14556567C2311yescharacteristic
284#14556567C2311yescharacteristic
285#14556563—21no—
286#14556563—21no—
287#14556563—21no—
288#14556563—21no—
289#14556563—21no—
290#14556562C2311yescharacteristic
291#14556560—21no—
292Q8×Dic73C2311yescharacteristic
293Q8×Dic73C2311yescharacteristic
294Q8×Dic73C2311yescharacteristic
295Q8×Dic73C2311yescharacteristic
296Q8×Dic73C2311yescharacteristic
297Q8×Dic73C2311yescharacteristic
298C4×Dic146C2311yescharacteristic
299C4×Dic146C2311yescharacteristic
300C4×Dic146C2311yescharacteristic
301#14556556—21no—
302#14556556—21no—
303#14556556—21no—
304#14556556—21no—
305#14556556—21no—
306#14556556—21no—
307#14556556—21no—
308#14556556—21no—
309#14556556D411yescharacteristic
310#14556556C2311yescharacteristic
311#14556556C2311yescharacteristic
312D4×Dic73—21no—
313D4×Dic73—21no—
314D4×Dic73—21no—
315D4×Dic73—21no—
316D4×Dic73—21no—
317D4×Dic73—21no—
318D4×Dic73—21no—
319D4×Dic73—21no—
320D4×Dic73—21no—
321D4×Dic73D411yescharacteristic
322D4×Dic73C2311yescharacteristic
323D4×Dic73C2311yescharacteristic
324D4×Dic73C2311yescharacteristic
325D4×Dic73C2311yescharacteristic
326D4×Dic73C2311yescharacteristic
327D4×Dic73C2311yescharacteristic
328D4×Dic73C2311yescharacteristic
329D4×Dic73C2311yescharacteristic
330C4×C22⋊D73—21no—
331C4×C22⋊D73—21no—
332C4×C22⋊D73C2311yescharacteristic
333C4×C22⋊D73C2311yescharacteristic
334#14556551—21no—
335#14556551—21no—
336#14556551—21no—
337#14556551D411yescharacteristic
338#14556551D411yescharacteristic
339#14556550—21no—
340#14556550—21no—
341#14556550—21no—
342#14556550C2311yescharacteristic
343#14556550C2311yescharacteristic
344#14556550C2311yescharacteristic
345#14556549—21no—
346#14556549D411yescharacteristic
347#14556549C2311yescharacteristic
348#14556549C2311yescharacteristic
349#14556547—21no—
350#14556547—21no—
351#14556547—21no—
352#14556547—21no—
353#14556547—21no—
354#14556547—21no—
355#14556547—21no—
356#14556547—21no—
357#14556547—21no—
358#14556547—21no—
359#14556547—21no—
360#14556547D411yescharacteristic
361#14556547D411yescharacteristic
362C2×C4⋊Dic73C2311yescharacteristic
363C2×#11924007—21no—
364C2×#11924007—21no—
365C2×#11924007—21no—
366C2×#11924007—21no—
367C2×C22⋊Dic73—21no—
368C2×C22⋊Dic73—21no—
369C2×C4×Dic73—21no—
370C2×C4×Dic73—21no—
371C2×C4×Dic73—21no—
372C2×C4×Dic73—21no—
373C2×C4×Dic73—21no—
374C2×C4×Dic73C2311yescharacteristic
375C2×C4×Dic73C2311yescharacteristic
376C42×D73C2311yescharacteristic
377#14556525C2311yescharacteristic
378#14556525C2311yescharacteristic
379#14556525C2311yescharacteristic
380#14556525C2311yescharacteristic
381#14556525C2311yescharacteristic
382#14556524C2311yescharacteristic
383#14556524C2311yescharacteristic
384#14556524C2311yescharacteristic
385#14556523C2311yescharacteristic
386#14556523C2311yescharacteristic
387#14556523C2311yescharacteristic
388#14556523C2311yescharacteristic
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
431#14556501C2311yescharacteristic
432#14556501C2311yescharacteristic
433#14556501C2311yescharacteristic
434C8×Dic73C2311yescharacteristic
435C8×Dic73C2311yescharacteristic
436C2×#41×C73C2311yescharacteristic
437C2×#41×C73C2311yescharacteristic
438C2×#41×C73C2311yescharacteristic
439C22×D4×C73C2311yescharacteristic
440AGL(1,ℤ/8)×C73—24no—
441#135×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
452C22×C8×C73C2311yescharacteristic
453C4⋊Q8×C73C2311yescharacteristic
454#124×C73C2311yescharacteristic
455#123×C73—21no—
456#123×C73—21no—
457#123×C73—21no—
458C22⋊Q8×C73C2311yescharacteristic
459C22⋊Q8×C73C2311yescharacteristic
460C22⋊Q8×C73C2311yescharacteristic
461#121×C73—21no—
462#121×C73—21no—
463#121×C73C2311yescharacteristic
464#120×C73—21no—
465C4×D4×C73C2311yescharacteristic
466C4×D4×C73C2311yescharacteristic
467C4×D4×C73C2311yescharacteristic
468C2×C4⋊C4×C73—21no—
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
480#97×C73C2311yescharacteristic
481#11924027—22no—
482#11924027—22no—
483#11924027—41no—
484#11924027—41no—
485#11924027—42no—
486C2×Dic146—21no—
487C2×Dic146—21no—
488C2×Dic146—21no—
489C2×Dic146—21no—
490C2×Dic146—44no—
491C2×Dic146C2×D411yescharacteristic
492C2×Dic146C2411yescharacteristic
493C2×Dic146C2411yescharacteristic
494C2×C22⋊D73—21no—
495C2×C22⋊D73—21no—
496C2×C22⋊D73—21no—
497C2×C22⋊D73C2×D411yescharacteristic
498C2×C22⋊D73C2×D411yescharacteristic
499C22×Dic73—21no—
500C22×Dic73—21no—
501C22×Dic73—21no—
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—44no—
511C22×Dic73C2×D411yescharacteristic
512C22×Dic73C2×D411yescharacteristic
513C22×Dic73C2×D411yescharacteristic
514C22×Dic73C2×D411yescharacteristic
515C2×C4×D73C2×D411yescharacteristic
516C2×C4×D73C2×D411yescharacteristic
517C2×C4×D73C2411yescharacteristic
518Dic292—22no—
519#11924018—41no—
520#11924018—41no—
521#11924018—41no—
522#11924016—22no—
523#11924016—22no—
524#11924016—41no—
525#11924012—41no—
526C2×#10596831—41no—
527C2×#10596831C2411yescharacteristic
528C2×#10596831C2411yescharacteristic
529C2×#10596831C2411yescharacteristic
530C2×#10596831C2411yescharacteristic
531C8×D73—22no—
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⋊Dic73C2×D411yescharacteristic
543C4⋊Dic73C2411yescharacteristic
544C4⋊Dic73C2411yescharacteristic
545C4⋊Dic73C2411yescharacteristic
546C4⋊Dic73C2411yescharacteristic
547C4⋊Dic73C2411yescharacteristic
548C4⋊Dic73C2411yescharacteristic
549#11924007—21no—
550#11924007—21no—
551#11924007—21no—
552#11924007—21no—
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
576C22⋊Dic73—21no—
577C22⋊Dic73—21no—
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⋊Dic73C2×D411yescharacteristic
595C22⋊Dic73C2×D411yescharacteristic
596#11924005—21no—
597#11924005—21no—
598#11924005—21no—
599#11924005—21no—
600#11924005—21no—
601#11924005C2×D411yescharacteristic
602#11924005C2×D411yescharacteristic
603C4×Dic73—21no—
604C4×Dic73—21no—
605C4×Dic73—21no—
606C4×Dic73—21no—
607C4×Dic73—21no—
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×Dic73C2×D411yescharacteristic
619C4×Dic73C2×D411yescharacteristic
620C4×Dic73C2×D411yescharacteristic
621C4×Dic73C2×D411yescharacteristic
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—22no—
631#41×C73—41no—
632#41×C73—41no—
633#41×C73—41no—
634C2×Q8×C73C2411yescharacteristic
635C2×Q8×C73C2411yescharacteristic
636C2×Q8×C73C2411yescharacteristic
637C2×D4×C73—22no—
638C2×D4×C73—21no—
639C2×D4×C73—21no—
640C2×D4×C73—21no—
641C2×D4×C73—21no—
642C2×D4×C73—21no—
643C2×D4×C73—41no—
644C2×D4×C73C2×D411yescharacteristic
645C2×D4×C73C2411yescharacteristic
646C2×D4×C73C2411yescharacteristic
647C2×D4×C73C2411yescharacteristic
648C22×C4×C73—21no—
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—41no—
657SD16×C73—22no—
658SD16×C73—22no—
659SD16×C73—22no—
660SD16×C73—22no—
661SD16×C73—41no—
662D8×C73—22no—
663D8×C73#4114yescomplemented
664M16×C73—22no—
665C2×C8×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×C73—21no—
674C4⋊C4×C73—21no—
675C4⋊C4×C73C2×D411yescharacteristic
676C4⋊C4×C73C2411yescharacteristic
677C4⋊C4×C73C2411yescharacteristic
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×C73—21no—
686C22⋊C4×C73C2×D411yescharacteristic
687C22⋊C4×C73C2×D411yescharacteristic
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—21no—
704D4×C73—21no—
705D4×C73—21no—
706D4×C73—21no—
707D4×C73—21no—
708D4×C73—41no—
709D4×C73—42no—
710D4×C73—42no—
711D4×C73—42no—
712D4×C73—42no—
713D4×C73—81no—
714D4×C73C2×#4112yes—
715D4×C73C2×#4112yes—
716C2×C4×C73—21no—
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—42no—
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—42no—
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—41no—
751C2×Dic73—41no—
752C2×Dic73—42no—
753C2×Dic73—42no—
754C2×Dic73—42no—
755C2×Dic73—42no—
756C2×Dic73—42no—
757C2×Dic73—42no—
758C2×Dic73—42no—
759C2×Dic73—42no—
760C2×Dic73—42no—
761C2×Dic73—42no—
762C2×Dic73—81no—
763C2×Dic73C22×D411yescharacteristic
764C2×Dic73C22×D411yescharacteristic
765C2×Dic73C22×D411yescharacteristic
766C2×Dic73C22×D411yescharacteristic
767C2×Dic73C22×D411yescharacteristic
768C2×Dic73C22×D411yescharacteristic
769C2×Dic73C22×D411yescharacteristic
770C4×D73—21no—
771C4×D73—21no—
772C4×D73—41no—
773C4×D73—41no—
774Dic146—22no—
775Dic146—21no—
776Dic146—21no—
777Dic146—21no—
778Dic146—21no—
779Dic146—42no—
780Dic146—42no—
781Dic146—42no—
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—22no—
795C22×C73—21no—
796C22×C73—21no—
797C22×C73—21no—
798C22×C73—21no—
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—21no—
813C4×C73—21no—
814C4×C73—21no—
815C4×C73—41no—
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#57512yes—
837#61461—731nomaximal, Sylow
838C2×C73—41no—
839C2×C73—41no—
840C2×C73—42no—
841C2×C73—42no—
842C2×C73—81no—
843C2×C73D4×#4111yescharacteristic
844C2×C73C2×#57511yescharacteristic
845C2×C73#358611yescharacteristic
846D73—41no—
847#3482—731no—
848#3475—731no—
849#3398—731no—
850#3384—731no—
851#3372—731no—
852#3367—731no—
853#3349—731no—
854#3349—731no—
855#3340—731no—
856#3315—731no—
857#3315—731no—
858#3311—731no—
859#3311—731no—
860#3303—731no—
861#3302—731no—
862#3283—731no—
863#3267—731no—
864#3267D7311yescharacteristic, complemented
865#3185—731no—
866#3181—731no—
867#3181—731no—
868#3116—731no—
869#3116—731no—
870#3116—731no—
871#3111—731no—
872#3111—731no—
873#3110—731no—
874#2970—731no—
875C4×AGL(1,ℤ/8)—731no—
876#2943—731no—
877#2943—731no—
878C73#6146111yescharacteristic, complemented, Sylow
879C2×AGL(1,ℤ/8)C2×D7311yescharacteristic
880C2×#135—731no—
881C2×#135C2×D7311yescharacteristic
882#557—731no—
883#556—731no—
884#556—731no—
885#556—731no—
886#556—731no—
887#555—731no—
888#554—731no—
889#553—1461no—
890#552—731no—
891#552—731no—
892#552—1461no—
893#552—1461no—
894#552—1461no—
895#552—1461no—
896#551—1461no—
897#551—1461no—
898D4×Q8—731no—
899#548—1461no—
900#547—731no—
901#547—731no—
902#547—731no—
903#547C2×D7311yescharacteristic
904#546—731no—
905#546C2×D7311yescharacteristic
906#533—731no—
907#533—731no—
908#533—731no—
909#533—731no—
910#529—731no—
911#529—731no—
912#529—1461no—
913#529—1461no—
914#529—1461no—
915#529—1461no—
916#529—1461no—
917#525—1461no—
918C4×#41—731no—
919C4×#41—731no—
920C4×#41—731no—
921C4×#41—731no—
922C4×#41—731no—
923C4×#41—731no—
924C2×C4×Q8—1461no—
925C2×C4×D4—731no—
926C2×#117—1461no—
927#501—731no—
928#501—731no—
929#498—731no—
930#497—731no—
931#497C2×D7311yescharacteristic
932#494—731no—
933#491—731no—
934#491—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#485—731no—
944#485—731no—
945#485—731no—
946#485—731no—
947#484—731no—
948#484—731no—
949#482—731no—
950#482—731no—
951#479—731no—
952#479—731no—
953#478—731no—
954#478—731no—
955#477—731no—
956#477—731no—
957#477—731no—
958#476—731no—
959#476—731no—
960#476—731no—
961#474—731no—
962#474—731no—
963#470—731no—
964#470—731no—
965#470—731no—
966#470C2×D7311yescharacteristic
967#467—731no—
968#467—731no—
969#467—731no—
970#467—731no—
971#465—731no—
972#465—731no—
973#465—731no—
974#465C2×D7311yescharacteristic
975#464—731no—
976#464—731no—
977#463—731no—
978#463C2×D7311yescharacteristic
979#462—731no—
980#462—731no—
981#462—731no—
982#461—731no—
983#461—731no—
984#461—731no—
985#461—731no—
986#461C2×D7311yescharacteristic
987#452—731no—
988#452—731no—
989#452—731no—
990#452—731no—
991#452—731no—
992#452—731no—
993#452C2×D7311yescharacteristic
994#452C2×D7311yescharacteristic
995#450—731no—
996#450C2×D7311yescharacteristic
997#449—731no—
998#449C2×D7311yescharacteristic
999#446—731no—
1000#446—731no—
1001#442—731no—
1002#442—731no—
1003#442—731no—
1004#442C2×D7311yescharacteristic
1005#441—731no—
1006#441—731no—
1007#441—731no—
1008#441—731no—
1009#441—731no—
1010#441—731no—
1011#441—731no—
1012#441—731no—
1013#440—731no—
1014#440—731no—
1015#440—731no—
1016#440—731no—
1017#440—731no—
1018#440—731no—
1019#440—731no—
1020#440—731no—
1021#440—731no—
1022#440—731no—
1023#440—731no—
1024#440—731no—
1025C4×SD16—731no—
1026C4×SD16—731no—
1027C4×D8—731no—
1028C4×D8—731no—
1029#435—731no—
1030#435—731no—
1031#435—731no—
1032#435C2×D7311yescharacteristic
1033C8×D4—731no—
1034C8×D4—731no—
1035#432—731no—
1036#432—731no—
1037#432—731no—
1038#428—731no—
1039#427—731no—
1040#427—731no—
1041#418—731no—
1042#417—731no—
1043#416—731no—
1044#416—731no—
1045#416—731no—
1046#416—731no—
1047C4×M16—731no—
1048C2×#97—731no—
1049C2×#97—731no—
1050C2×#41—731no—
1051C2×#41—731no—
1052C2×#41—731no—
1053C2×#41C22×D7311yescharacteristic
1054C2×#41C22×D7311yescharacteristic
1055C2×#41C22×D7311yescharacteristic
1056C22×Q8—1461no—
1057C22×D4C22×D7311yescharacteristic
1058C23×C4—1461no—
1059AGL(1,ℤ/8)—24no—
1060#135—24no—
1061#135—1464no—
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×M16C22×D7311yescharacteristic
1080C22×C8—731no—
1081C22×C8—731no—
1082C22×C8—731no—
1083C22×C8C22×D7311yescharacteristic
1084C4⋊Q8—731no—
1085C4⋊Q8—731no—
1086C4⋊Q8—731no—
1087C4⋊Q8—731no—
1088C4⋊Q8—731no—
1089C4⋊Q8—731no—
1090C4⋊Q8—731no—
1091C4⋊Q8C22×D7311yescharacteristic
1092#126—1461no—
1093#126—1461no—
1094#126—1461no—
1095#126—1461no—
1096#126—1461no—
1097#126—1461no—
1098#126—1461no—
1099#126—1461no—
1100#126—1461no—
1101#126—1461no—
1102#126—1461no—
1103#126—1461no—
1104#125—731no—
1105#125—731no—
1106#125—1461no—
1107#125—1461no—
1108#125—1461no—
1109#125—1461no—
1110#125—1461no—
1111#125—1461no—
1112#125—1461no—
1113#125—1461no—
1114#125—1461no—
1115#124—731no—
1116#124—1461no—
1117#124—1461no—
1118#124—1461no—
1119#124—1461no—
1120#124—1461no—
1121#124C22×D7311yescharacteristic
1122#123—21no—
1123#123—21no—
1124#123—21no—
1125#123—1461no—
1126#123—1461no—
1127#123—1461no—
1128#123—1461no—
1129#123—1461no—
1130#123—1461no—
1131#123—1461no—
1132#123—1461no—
1133#123—1461no—
1134#123—1461no—
1135#123—1461no—
1136C22⋊Q8—731no—
1137C22⋊Q8—731no—
1138C22⋊Q8—731no—
1139C22⋊Q8—731no—
1140C22⋊Q8—731no—
1141C22⋊Q8—731no—
1142C22⋊Q8—731no—
1143C22⋊Q8—1461no—
1144C22⋊Q8—1461no—
1145C22⋊Q8—1461no—
1146C22⋊Q8—1461no—
1147C22⋊Q8—1461no—
1148C22⋊Q8—1461no—
1149C22⋊Q8—1461no—
1150C22⋊Q8—1461no—
1151C22⋊Q8—1461no—
1152C22⋊Q8—1461no—
1153C22⋊Q8—1461no—
1154C22⋊Q8C22×D7311yescharacteristic
1155C22⋊Q8C22×D7311yescharacteristic
1156C22⋊Q8C22×D7311yescharacteristic
1157#121—21no—
1158#121—21no—
1159#121—731no—
1160#121—1461no—
1161#121—1461no—
1162#121—1461no—
1163#121—1461no—
1164#121—1461no—
1165#121C22×D7311yescharacteristic
1166#120—21no—
1167#120—1461no—
1168C4×Q8—731no—
1169C4×Q8—731no—
1170C4×Q8—731no—
1171C4×Q8—731no—
1172C4×Q8—731no—
1173C4×Q8—731no—
1174C4×Q8—731no—
1175C4×Q8—731no—
1176C4×Q8—731no—
1177C4×Q8—731no—
1178C4×Q8—731no—
1179C4×Q8—731no—
1180C4×Q8—1461no—
1181C4×Q8—1461no—
1182C4×Q8—1461no—
1183C4×Q8—1461no—
1184C4×Q8—1461no—
1185C4×Q8—1461no—
1186C4×Q8—1461no—
1187C4×Q8—1461no—
1188C4×D4—731no—
1189C4×D4—731no—
1190C4×D4—731no—
1191C4×D4—731no—
1192C4×D4—731no—
1193C4×D4—731no—
1194C4×D4—731no—
1195C4×D4—731no—
1196C4×D4—731no—
1197C4×D4—731no—
1198C4×D4—731no—
1199C4×D4—731no—
1200C4×D4—731no—
1201C4×D4—1461no—
1202C4×D4—1461no—
1203C4×D4—1461no—
1204C4×D4—1461no—
1205C4×D4—1461no—
1206C4×D4—1461no—
1207C4×D4—1461no—
1208C4×D4—1461no—
1209C4×D4—1461no—
1210C4×D4—1461no—
1211C4×D4—1461no—
1212C4×D4—1461no—
1213C4×D4—1461no—
1214C4×D4—1461no—
1215C4×D4C22×D7311yescharacteristic
1216C4×D4C22×D7311yescharacteristic
1217C4×D4C22×D7311yescharacteristic
1218#117—731no—
1219#117—731no—
1220#117—731no—
1221#117—731no—
1222#117—731no—
1223#117—731no—
1224#117—731no—
1225#117—731no—
1226#117—1461no—
1227#117—1461no—
1228#117—1461no—
1229#117—1461no—
1230#117—1461no—
1231#117—1461no—
1232#117—1461no—
1233#117—1461no—
1234#117—1461no—
1235#117—1461no—
1236#117—1461no—
1237#117—1461no—
1238#117—1461no—
1239#117—1461no—
1240#117—1461no—
1241C2×C4⋊C4—21no—
1242C2×C4⋊C4—731no—
1243C2×C4⋊C4—1461no—
1244C2×C4⋊C4—1461no—
1245C2×C4⋊C4—1461no—
1246C2×C4⋊C4—1461no—
1247C2×C22⋊C4—21no—
1248C2×C22⋊C4—1461no—
1249C2×C22⋊C4—1461no—
1250C2×C42—731no—
1251C2×C42—731no—
1252C2×C42—731no—
1253C2×C42—1461no—
1254C2×C42—1461no—
1255C2×C42—1461no—
1256C2×C42—1461no—
1257C2×C42—1461no—
1258#107—731no—
1259#107—731no—
1260#107—731no—
1261#107—731no—
1262#107—731no—
1263#107—731no—
1264#107—731no—
1265#107—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—
1322#97—731no—
1323#97—731no—
1324#97—731no—
1325#97C22×D7311yescharacteristic
1326C4×C8—731no—
1327C4×C8—731no—
1328C24—21no—
1329#41—22no—
1330#41—22no—
1331#41—22no—
1332#41—41no—
1333#41—41no—
1334#41—41no—
1335#41—2921no—
1336#41—2921no—
1337#41—2922no—
1338#41—1462no—
1339#41—1462no—
1340C2×Q8—2924no—
1341C2×Q8—731no—
1342C2×Q8—731no—
1343C2×Q8—731no—
1344C2×Q8—1461no—
1345C2×Q8—1461no—
1346C2×Q8—1461no—
1347C2×Q8—1461no—
1348C2×Q8C23×D7311yescharacteristic
1349C2×Q8C23×D7311yescharacteristic
1350C2×Q8C23×D7311yescharacteristic
1351C2×D4—22no—
1352C2×D4—21no—
1353C2×D4—21no—
1354C2×D4—21no—
1355C2×D4—21no—
1356C2×D4—21no—
1357C2×D4—41no—
1358C2×D4—731no—
1359C2×D4—731no—
1360C2×D4—1461no—
1361C2×D4—1461no—
1362C2×D4—1461no—
1363C2×D4D4×D7311yescharacteristic
1364C2×D4C23×D7311yescharacteristic
1365C2×D4C23×D7311yescharacteristic
1366C2×D4C23×D7311yescharacteristic
1367C22×C4—21no—
1368C22×C4—21no—
1369C22×C4—21no—
1370C22×C4—21no—
1371C22×C4—21no—
1372C22×C4—2924no—
1373C22×C4—731no—
1374C22×C4—731no—
1375C22×C4—731no—
1376C22×C4—731no—
1377C22×C4—731no—
1378C22×C4—731no—
1379C22×C4—731no—
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—41no—
1395Q16—2921no—
1396Q16—2921no—
1397Q16—2921no—
1398Q16—1462no—
1399SD16—22no—
1400SD16—22no—
1401SD16—22no—
1402SD16—22no—
1403SD16—41no—
1404SD16—2921no—
1405SD16—1462no—
1406SD16—1462no—
1407D8—22no—
1408D8#1192402714yescomplemented
1409M16—22no—
1410M16—2921no—
1411C2×C8—22no—
1412C2×C8—2921no—
1413C2×C8—2921no—
1414C2×C8—731no—
1415C2×C8—731no—
1416C2×C8—731no—
1417C2×C8—731no—
1418C2×C8—1462no—
1419C2×C8C23×D7311yescharacteristic
1420C2×C8C23×D7311yescharacteristic
1421C2×C8C23×D7311yescharacteristic
1422C2×C8C23×D7311yescharacteristic
1423C4⋊C4—21no—
1424C4⋊C4—21no—
1425C4⋊C4—21no—
1426C4⋊C4—21no—
1427C4⋊C4—21no—
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—1461no—
1440C4⋊C4—1461no—
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—731no—
1483C22⋊C4—731no—
1484C22⋊C4—731no—
1485C22⋊C4—731no—
1486C22⋊C4—1461no—
1487C22⋊C4—1461no—
1488C22⋊C4—1461no—
1489C22⋊C4—1461no—
1490C22⋊C4—1461no—
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⋊C4D4×D7311yescharacteristic
1510C22⋊C4D4×D7311yescharacteristic
1511C42—731no—
1512C42—731no—
1513C42—731no—
1514C42—731no—
1515C42—731no—
1516C42—731no—
1517C42—731no—
1518C42—731no—
1519C42—731no—
1520C42—1461no—
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—21no—
1551Q8—2922no—
1552Q8—2922no—
1553Q8—2922no—
1554Q8—5841no—
1555Q8—1462no—
1556Q8—1461no—
1557Q8—1461no—
1558Q8—1461no—
1559Q8—1461no—
1560D4—21no—
1561D4—21no—
1562D4—21no—
1563D4—21no—
1564D4—41no—
1565D4—42no—
1566D4—42no—
1567D4—42no—
1568D4—42no—
1569D4—81no—
1570D4—2922no—
1571D4—2922no—
1572D4—2921no—
1573D4—5841no—
1574D4—1462no—
1575D4C2×#1192402712yes—
1576D4C2×#1192402712yes—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—42no—
1587C2×C4—42no—
1588C2×C4—42no—
1589C2×C4—42no—
1590C2×C4—81no—
1591C2×C4—2921no—
1592C2×C4—2921no—
1593C2×C4—2922no—
1594C2×C4—2922no—
1595C2×C4—2922no—
1596C2×C4—2922no—
1597C2×C4—2922no—
1598C2×C4—2922no—
1599C2×C4—2922no—
1600C2×C4—2922no—
1601C2×C4—2922no—
1602C2×C4—2922no—
1603C2×C4—2921no—
1604C2×C4—2921no—
1605C2×C4—2921no—
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—22no—
1644C22—21no—
1645C22—21no—
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—21no—
1662C4—41no—
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—42no—
1688C2—81no—
1689C2—2921no—
1690C2D4×#1192402711yescharacteristic
1691C2#575×D7311yescharacteristic
1692C2#2262471311yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3267C2
socleC22×C73C23×D4
hypercenter#3267D73
hypocenterC73#61461
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3267

Complements

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

NH ≅ G/Ntype
1. #22623543C2semidirect
2. #22623482C2semidirect
3. #22622959C2semidirect
4. #22622831C2semidirect
5. #22622707C2semidirect
6. #22622644C2semidirect
7. #22622463C2semidirect
8. #22622456C2semidirect
9. #22622339C2semidirect
10. #22622027C2semidirect
11. #22622020C2semidirect
12. #22621967C2semidirect
13. #22621960C2semidirect
14. #22621852C2semidirect
15. #22621841C2semidirect
16. #22621647C2semidirect
17. #22621450C2semidirect
18. #22620671C2semidirect
19. #22620637C2semidirect
20. #22620633C2semidirect
21. #22620090C2semidirect
22. #22620086C2semidirect
23. #22620086C2semidirect
24. #22620037C2semidirect
25. #22620033C2semidirect
26. #22620025C2semidirect
27. #22618941C2semidirect
28. AGL(1,ℤ/8)×Dic73C2semidirect
29. #22618732C2semidirect
30. #22618728C2semidirect
31. C73×#3267C2semidirect
33. #17989312C22semidirect
35. #17989308C22semidirect
49. D4×Dic146C22semidirect
53. #17989236C22semidirect
55. #17989142C22semidirect
58. #17989139C22semidirect
69. #41×Dic73C22semidirect
72. C4×#11924027C22semidirect
76. #17988996C22semidirect
77. #17988994C22semidirect
78. #17988984C22semidirect
80. #17988965C22semidirect
81. #17988955C22semidirect
82. #17988954C22semidirect
85. #17988936C22semidirect
86. #17988936C22semidirect
88. #17988929C22semidirect
89. #17988929C22semidirect
90. #17988927C22semidirect
91. #17988927C22semidirect
92. #17988926C22semidirect
94. #17988925C22semidirect
99. #17988895C22semidirect
100. #17988892C22semidirect
101. #17988887C22semidirect
102. #17988885C22semidirect
103. #17988883C22semidirect
104. #17988880C22semidirect
105. #17988880C22semidirect
108. #17988875C22semidirect
114. #17988828C22semidirect
115. #17988826C22semidirect
116. #17988825C22semidirect
117. #17988825C22semidirect
124. #17988795C22semidirect
125. #17988795C22semidirect
126. #17988794C22semidirect
130. #17988790C22semidirect
133. #17988749C22semidirect
136. #17988746C22semidirect
139. #17988716C22semidirect
140. #17988715C22semidirect
144. #17988695C22semidirect
145. #17988694C22semidirect
146. #17988694C22semidirect
147. #17988694C22semidirect
148. #17988693C22semidirect
149. #17988691C22semidirect
150. #17988691C22semidirect
151. #17988691C22semidirect
157. #17988688C22semidirect
158. #17988688C22semidirect
160. #17988687C22semidirect
163. #17988684C22semidirect
171. C8×C22⋊D73C22semidirect
172. #17988650C22semidirect
173. #17988643C22semidirect
175. #17988641C22semidirect
177. #17988625C22semidirect
178. #17988622C22semidirect
182. #17988583C22semidirect
184. #17988580C22semidirect
186. C2×#14556501C22semidirect
187. #97×D73C22semidirect
663. D8×C73#41semidirect
864. #3267D73semidirect
878. C73#61461semidirect
1408. D8#11924027semidirect

Maximal subgroups

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

subgroupindex
#226235432
#226234822
#226229592
#226228312
#226227072
#226226442
#226224632
#226224562
#226223392
#226220272
#226220202
#226219672
#226219602
#226218522
#226218412
#226216472
#226214502
#226206712
#226206372
#226206332
#226200902
#226200862
#226200372
#226200332
#226200252
#226189412
AGL(1,ℤ/8)×Dic732
#226187322
#226187282
C73×#32672
#6146173