Finite Group Databasebeta

← #11884328

Subgroups — #11884328

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595428C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic, complemented
3C2×#63798C211yesmaximal, characteristic, complemented
4#10594381C211yesmaximal, characteristic, complemented
5#10592515C211yesmaximal, characteristic, complemented
6C3×#4819C211yesmaximal, characteristic, complemented
7C3×#4808C211yesmaximal, characteristic, complemented
8#10591656C211yesmaximal, characteristic, complemented
9#10591627C211yesmaximal, characteristic, complemented
10#10590962C211yesmaximal, characteristic, complemented
11#10590907C211yesmaximal, characteristic, complemented
12#10590752C211yesmaximal, characteristic, complemented
13#10590597C211yesmaximal, characteristic, complemented
14#10590501C211yesmaximal, characteristic, complemented
15#10590455C211yesmaximal, characteristic, complemented
16#80567—31nomaximal
17#80264—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22#64155C2211yescharacteristic
23C2×#3756C2211yescharacteristic, complemented
24C2×#3743C2211yescharacteristic
25#64106C2211yescharacteristic
26C3×#947C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic, complemented
29C2×C3×D24C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic
31C3×#897C2211yescharacteristic, complemented
32C3×#893C2211yescharacteristic, complemented
33#63947—24no—
34#63922—21no—
35D3×(C2×D3)⋊C4—21no—
36#63908C2211yescharacteristic
37#63906—21no—
38#63905—21no—
39C4×#626C2211yescharacteristic
40Dic3×D12C2211yescharacteristic
41#63891—21no—
42#63890—21no—
43D3×C4⋊Dic3—21no—
44#63885—21no—
45#63866C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic
47C2×#3716C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic, complemented
51#63798—24no—
52C32×#103C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63635C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63557C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63#5829—31no—
64C2×#950—31no—
65C2×#916—31no—
66C2×#914—31no—
67C2×#911—31no—
68#5676—31no—
69#5631—31no—
70#5555—31no—
71C3×#463—31no—
72C3×#452—31no—
73#5190—31no—
74#5187—31no—
75#5173—31no—
76#5162—31no—
77#5158—31no—
78#5060—31no—
79#5048—31no—
80#5014—31no—
81#4841—31no—
82#4836—31no—
83#4819D311yescharacteristic, complemented
84#4816—31no—
85#4816—31no—
86#4816—61no—
87#4808D311yescharacteristic, complemented
88#4785—31no—
89#4778—31no—
90#4776—31no—
91#4776—31no—
92#4734—31no—
93#4730—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C3×#239—22no—
99C3×#239—41no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#626—21no—
109C2×#626D411yescharacteristic
110C2×#625—21no—
111C2×#625—21no—
112C2×#625—21no—
113C2×D3×Dic3—21no—
114C2×D3×Dic3—21no—
115C2×D3×Dic3—21no—
116#3802—22no—
117#3802—41no—
118#3796—22no—
119#3796—41no—
120#3795—22no—
121#3795—41no—
122C2×C32×C8C2311yescharacteristic
123C32×C4⋊C4C2311yescharacteristic
124#3756—22no—
125#3752—21no—
126#3752—21no—
127C4⋊(C3⋊Dic3)—21no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3750—21no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131#3743—22no—
132C3×#216—41no—
133C3×#215—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×C4⋊Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24—22no—
143C3×#204—22no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146Dic3⋊Dic3D411yescharacteristic
147#3722D411yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151#3716—22no—
152#3716—41no—
153#3715—22no—
154#3713D414yescomplemented
155D3×C3⋊C8—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×#239—31no—
159C2×#239C2×D311yescharacteristic
160C2×#237—31no—
161C2×#237—31no—
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×#235—31no—
165C2×C3×Q16—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×D8—31no—
169C3×#124—31no—
170C3×C22⋊Q8—31no—
171C3×C4×D4—31no—
172#950—64no—
173#947C2×D311yescharacteristic
174#946—31no—
175#946—31no—
176#946—61no—
177#944—31no—
178C2×#216—31no—
179C2×#216—31no—
180C2×#216—61no—
181C2×#216C2×D311yescharacteristic, complemented
182C2×#215—31no—
183C2×#215C2×D311yescharacteristic, complemented
184#939—61no—
185#938—31no—
186#937—61no—
187D4×Dic3—31no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#214—31no—
191C2×#213—31no—
192C2×#213—31no—
193#930—31no—
194#930—61no—
195#929—61no—
196C4×#67—31no—
197C2×(C2×D3)⋊C4—61no—
198C2×C4⋊Dic3—61no—
199C22×C3⋊C8—31no—
200#916—64no—
201#914—64no—
202#911—64no—
203C2×D24C2×D311yescharacteristic
204C2×#204—31no—
205C2×#204—31no—
206C2×#204C2×D311yescharacteristic
207C2×ΓL(1,𝔽25)—31no—
208C2×ΓL(1,𝔽25)—31no—
209C2×ΓL(1,𝔽25)—61no—
210C2×D3×C8—31no—
211#897—31no—
212#897—31no—
213#897—61no—
214#897C2×D311yescharacteristic, complemented
215#894—61no—
216#893C2×D311yescharacteristic, complemented
217D3×C4⋊C4—61no—
218#886—61no—
219#886—61no—
220#884—61no—
221#884—61no—
222#883—61no—
223#883—61no—
224#882—61no—
225D3×C22⋊C4—61no—
226C4×D12—31no—
227C4×D12—31no—
228#869—31no—
229C3×C4⋊C8—31no—
230C3×#103—21no—
231C3×#103C2×D311yescharacteristic, complemented
232C3×#103C2×D311yescharacteristic, complemented
233C3×#102—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236#835—31no—
237#832—31no—
238#821—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8C2×D311yescharacteristic, complemented
242#816—31no—
243#816—31no—
244#816—31no—
245#816—61no—
246#815—31no—
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#809C2×D311yescharacteristic
249#809C2×D311yescharacteristic
250#808—31no—
251#808—31no—
252#808—61no—
253#803—31no—
254C22×C3⋊D3C2×D411yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C32×Q8—21no—
263C32×Q8—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C2411yescharacteristic
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3C2×D411yescharacteristic
270C4×C3⋊D3—21no—
271C4×C3⋊D3—21no—
272#634—21no—
273#634—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—42no—
283C3×D12C2×D412yes—
284C3×D12C2×D412yes—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—42no—
288C3×C4×D3—42no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#626—41no—
292#626—42no—
293#625—42no—
294#625—42no—
295#625—81no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298D3×Dic3—81no—
299C32×C8—21no—
300C3⋊(C3⋊C8)C2×D412yes—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—91no—
306#546—91no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—31no—
311#461—91no—
312#452—31no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C3×#41—62no—
321C3×#41—121no—
322C2×C3×Q8—21no—
323C2×C3×Q8—31no—
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—61no—
330C22×C3×C4—31no—
331C22×C3×C4—61no—
332C22×C3×C4—61no—
333C2×#67—31no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C22×Dic3—61no—
342C22×Dic3—61no—
343C22×Dic3—61no—
344#239—22no—
345#239—41no—
346#239—62no—
347#239—121no—
348#237—62no—
349#237—62no—
350#237—121no—
351#237—121no—
352D3×D4—62no—
353D3×D4—62no—
354D3×D4—121no—
355D3×D4—121no—
356#235—62no—
357#235—121no—
358C2×D12—21no—
359C2×D12—31no—
360C2×D12—61no—
361C2×D12C22×D311yescharacteristic
362C2×D12C22×D311yescharacteristic
363C2×D12C22×D311yescharacteristic
364C2×C4×D3—21no—
365C2×C4×D3—21no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3C22×D311yescharacteristic
373C2×Dic6—31no—
374C2×Dic6—31no—
375C2×Dic6—61no—
376C2×Dic6C22×D311yescharacteristic
377C3×Q16—121no—
378C3×SD16—62no—
379C3×SD16—62no—
380C3×D8—62no—
381C2×C3×C8—21no—
382C2×C3×C8—31no—
383C2×C3×C8—31no—
384C2×C3×C8C22×D311yescharacteristic
385C2×C3×C8C22×D311yescharacteristic
386C3×C4⋊C4—21no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4C22×D311yescharacteristic
389C3×C4⋊C4C22×D311yescharacteristic
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C42—31no—
395#217—31no—
396#217—61no—
397#217—61no—
398#216—41no—
399#216—62no—
400#216—62no—
401#216—122no—
402#215—22no—
403#215—62no—
404#214—62no—
405#214—62no—
406#214—121no—
407#213—34no—
408#213—34no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—31no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—121no—
423(C2×D3)⋊C4—121no—
424C4⋊Dic3—21no—
425C4⋊Dic3—31no—
426C4⋊Dic3—31no—
427C4⋊Dic3—31no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3—61no—
431C4⋊Dic3—61no—
432C4⋊Dic3—61no—
433C4⋊Dic3—121no—
434Dic3⋊C4—31no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—121no—
440C4×Dic3C22×D311yescharacteristic
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—61no—
444C2×C3⋊C8—62no—
445C2×C3⋊C8C22×D311yescharacteristic
446C2×C3⋊C8C22×D311yescharacteristic
447D24—22no—
448#204—22no—
449#204—62no—
450#204—121no—
451ΓL(1,𝔽25)—62no—
452ΓL(1,𝔽25)—62no—
453ΓL(1,𝔽25)—122no—
454D3×C8—62no—
455C22×C32C22×D411yescharacteristic
456C2×C3⋊D3—21no—
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3×D3—22no—
460C2×C3×D3—21no—
461C2×C3×D3—22no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471D32—84no—
472C32×C4—41no—
473C32×C4—41no—
474C32×C4C22×D411yescharacteristic
475C32×C4H(5,𝔽2)11yescharacteristic
476C3⋊Dic3—21no—
477C3⋊Dic3—41no—
478C3⋊Dic3—41no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—41no—
483C2×#41—31no—
484C2×#41—91no—
485C2×#41—91no—
486C22×D4—91no—
487AGL(1,ℤ/8)—184no—
488#135—184no—
489C2×Q16—31no—
490C2×Q16—91no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×D8—31no—
497C2×D8—91no—
498C2×M16—91no—
499C22×C8—91no—
500C4⋊Q8—91no—
501#124—31no—
502#123—181no—
503#123—181no—
504#123—181no—
505C22⋊Q8—31no—
506C22⋊Q8—91no—
507C22⋊Q8—91no—
508#121—91no—
509#121—181no—
510#121—181no—
511#120—181no—
512C4×D4—31no—
513C4×D4—91no—
514C4×D4—91no—
515C2×C4⋊C4—181no—
516C2×C22⋊C4—181no—
517#106—91no—
518C4⋊C8—31no—
519#103—91no—
520#103—91no—
521#103D3211yescharacteristic, complemented
522#102—31no—
523#102—31no—
524#102—91no—
525C22⋊C8—31no—
526C22⋊C8—91no—
527#97—91no—
528C23×C3—31no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—61no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—31no—
536C22×D3—31no—
537C22×D3—61no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—241no—
543C22×D3—241no—
544C22×D3D3×D411yescharacteristic
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—41no—
550C3×Q8—41no—
551C3×Q8—61no—
552C3×Q8—61no—
553C3×D4—32no—
554C3×D4—32no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—122no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—31no—
566C2×C3×C4—31no—
567C2×C3×C4—31no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—122no—
574C2×C3×C4—122no—
575C2×C3×C4C23×D311yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577#67—121no—
578#67—122no—
579#67—122no—
580#67—122no—
581#67—122no—
582#67—122no—
583#67—241no—
584#67—241no—
585C2×Dic3—21no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—121no—
594C2×Dic3—121no—
595C2×Dic3—122no—
596C2×Dic3—122no—
597C2×Dic3—241no—
598C2×Dic3D3×D411yescharacteristic
599C2×Dic3D3×D411yescharacteristic
600C2×Dic3D3×D411yescharacteristic
601D12—21no—
602D12—21no—
603D12—21no—
604D12—21no—
605D12—42no—
606D12—121no—
607D12—122no—
608D12D3×D412yes—
609D12D3×D412yes—
610C4×D3—21no—
611C4×D3—21no—
612C4×D3—42no—
613C4×D3—42no—
614C4×D3—61no—
615C4×D3—61no—
616C4×D3—61no—
617C4×D3—61no—
618C4×D3—121no—
619C4×D3—121no—
620C4×D3—122no—
621C4×D3—122no—
622C4×D3—241no—
623Dic6—21no—
624Dic6—21no—
625Dic6—61no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—121no—
630Dic6—121no—
631C3×C8—21no—
632C3×C8—21no—
633C3×C8—41no—
634C3×C8—61no—
635C3×C8—61no—
636C3⋊C8—21no—
637C3⋊C8—21no—
638C3⋊C8—32no—
639C3⋊C8—32no—
640C3⋊C8—62no—
641C2×C32D4211yescharacteristic
642C2×C32#57511yescharacteristic
643C2×C32#57711yescharacteristic
644C3⋊D3—41no—
645C3×D3—42no—
646C3×D3—41no—
647C3×D3—42no—
648C3×D3—81no—
649C24—181no—
650#41—62no—
651#41—121no—
652#41—182no—
653#41—182no—
654#41—361no—
655#41—361no—
656C2×Q8—31no—
657C2×Q8—91no—
658C2×Q8C2×D3211yescharacteristic
659C2×D4—31no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—61no—
663C2×D4—91no—
664C2×D4—181no—
665C2×D4—181no—
666C2×D4—182no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—361no—
670C22×C4—31no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—91no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4—181no—
677Q16—121no—
678Q16—182no—
679SD16—62no—
680SD16—62no—
681SD16—182no—
682SD16—182no—
683SD16—361no—
684D8—62no—
685D8—94no—
686M16—182no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—91no—
690C2×C8—182no—
691C2×C8C2×D3211yescharacteristic
692C4⋊C4—61no—
693C4⋊C4—91no—
694C4⋊C4—91no—
695C4⋊C4—181no—
696C4⋊C4—181no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4C2×D3211yescharacteristic
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—91no—
705C22⋊C4—91no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C42—31no—
711C22×C3—21no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—62no—
715C22×C3—61no—
716C22×C3—62no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3C2×D3×D411yescharacteristic
725C22×C3C2×D3×D411yescharacteristic
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—22no—
730C2×D3—22no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—41no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—61no—
742C2×D3—61no—
743C2×D3—61no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—244no—
748C2×D3—244no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—41no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—41no—
755C3×C4—61no—
756C3×C4—61no—
757C3×C4—61no—
758C3×C4—81no—
759C3×C4—81no—
760C3×C4—121no—
761C3×C4C2×D3×D411yescharacteristic
762C3×C4C2×D3×D411yescharacteristic
763C3×C4#100411yescharacteristic
764C3×C4#100911yescharacteristic
765Dic3—21no—
766Dic3—21no—
767Dic3—21no—
768Dic3—41no—
769Dic3—61no—
770Dic3—61no—
771Dic3—121no—
772Dic3—121no—
773Dic3—121no—
774Dic3—121no—
775Dic3—121no—
776Dic3—241no—
777Dic3—241no—
778C32#326711yescharacteristic, complemented, Sylow
779C23—31no—
780C23—61no—
781C23—61no—
782C23—61no—
783C23—91no—
784C23—362no—
785C23—362no—
786C23—721no—
787Q8—21no—
788Q8—21no—
789Q8—61no—
790Q8—61no—
791Q8—181no—
792Q8—181no—
793D4—32no—
794D4—32no—
795D4—61no—
796D4—61no—
797D4—61no—
798D4—61no—
799D4—122no—
800D4—361no—
801D4—362no—
802D4—362no—
803D4—362no—
804D4—721no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—91no—
814C2×C4—122no—
815C2×C4—122no—
816C2×C4—181no—
817C2×C4—181no—
818C2×C4—181no—
819C2×C4—181no—
820C2×C4—362no—
821C2×C4—362no—
822C2×C4—721no—
823C2×C4C22×D3211yescharacteristic
824C8—21no—
825C8—61no—
826C8—61no—
827C8—92no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—122no—
832C2×C3—122no—
833C2×C3—121no—
834C2×C3—241no—
835C2×C3#559011yescharacteristic
836C2×C3#560911yescharacteristic
837C2×C3#576811yescharacteristic
838C2×C3#577011yescharacteristic
839C2×C3#577311yescharacteristic
840C2×C3#577811yescharacteristic
841D3—41no—
842D3—42no—
843D3—42no—
844D3—81no—
845D3—121no—
846D3—121no—
847D3—241no—
848C22—61no—
849C22—61no—
850C22—61no—
851C22—62no—
852C22—62no—
853C22—121no—
854C22—121no—
855C22—121no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—181no—
861C22—181no—
862C22—181no—
863C22—724no—
864C22D32×D411yescharacteristic
865C4—41no—
866C4—41no—
867C4—61no—
868C4—61no—
869C4—61no—
870C4—121no—
871C4—181no—
872C4—361no—
873C4—361no—
874C4#6430711yescharacteristic
875C4D32×D411yescharacteristic
876C3—21no—
877C3#8026411yescharacteristic, complemented
878C3#8056711yescharacteristic, complemented
879C2—121no—
880C2—122no—
881C2—122no—
882C2—241no—
883C2—361no—
884C2#1059427511yescharacteristic
885C2#1059474511yescharacteristic
886C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595428C2semidirect
2. C2×#63947C2semidirect
3. C2×#63798C2semidirect
4. #10594381C2semidirect
5. #10592515C2semidirect
6. C3×#4819C2semidirect
7. C3×#4808C2semidirect
8. #10591656C2semidirect
9. #10591627C2semidirect
10. #10590962C2semidirect
11. #10590907C2semidirect
12. #10590752C2semidirect
13. #10590597C2semidirect
14. #10590501C2semidirect
15. #10590455C2semidirect
21. C2×#3795C22semidirect
23. C2×#3756C22semidirect
27. C2×C3×#216C22semidirect
28. C2×C3×#215C22semidirect
31. C3×#897C22semidirect
32. C3×#893C22semidirect
45. #63866C22semidirect
50. C2×D3×C3⋊C8C22semidirect
52. C32×#103C22semidirect
53. #63643C22semidirect
54. #63635C22semidirect
55. C3×(C2×D3)⋊C8C22semidirect
56. C3×Dic3⋊C8C22semidirect
59. #63566C22semidirect
60. #63563C22semidirect
62. #63554C22semidirect
83. #4819D3semidirect
87. #4808D3semidirect
154. #3713D4semidirect
181. C2×#216C2×D3semidirect
183. C2×#215C2×D3semidirect
214. #897C2×D3semidirect
216. #893C2×D3semidirect
231. C3×#103C2×D3semidirect
232. C3×#103C2×D3semidirect
241. (C2×D3)⋊C8C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
521. #103D32semidirect
778. C32#3267semidirect
877. C3#80264semidirect
878. C3#80567semidirect

Maximal subgroups

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

subgroupindex
#105954282
C2×#639472
C2×#637982
#105943812
#105925152
C3×#48192
C3×#48082
#105916562
#105916272
#105909622
#105909072
#105907522
#105905972
#105905012
#105904552
#805673
#802643