Finite Group Databasebeta

← #11884473

Subgroups — #11884473

Order 1152.

1080 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63806C211yesmaximal, characteristic, complemented
2C2×#63795C211yesmaximal, characteristic, complemented
3#10594007C211yesmaximal, characteristic, complemented
4#10593906C211yesmaximal, characteristic, complemented
5#10592409C211yesmaximal, characteristic, complemented
6C3×#4712C211yesmaximal, characteristic, complemented
7C3×#4706C211yesmaximal, characteristic, complemented
8#10590962C211yesmaximal, characteristic, complemented
9#10590960C211yesmaximal, characteristic, complemented
10#10590944C211yesmaximal, characteristic, complemented
11#10590833C211yesmaximal, characteristic, complemented
12#10590831C211yesmaximal, characteristic, complemented
13#10590823C211yesmaximal, characteristic, complemented
14#10590378C211yesmaximal, characteristic, complemented
15#10590355C211yesmaximal, characteristic, complemented
16#81858—31nomaximal
17#79497—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C2×#3744C2211yescharacteristic
23C4×C4⋊(C3⋊D3)C2211yescharacteristic
24C4×#634C2211yescharacteristic, complemented
25C2×C3×D24C2211yescharacteristic
26C2×C3×D24C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic, complemented
28C2×C3×#204C2211yescharacteristic, complemented
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic, complemented
31C3×#875C2211yescharacteristic
32C3×#874C2211yescharacteristic, complemented
33C3×C4×D12C2211yescharacteristic
34#63922—21no—
35#63921—21no—
36#63914—21no—
37#63912—21no—
38#63908C2211yescharacteristic
39#63908C2211yescharacteristic
40#63908C2211yescharacteristic, complemented
41#63898—21no—
42#63885—21no—
43#63885—21no—
44#63856C2211yescharacteristic
45#63854—21no—
46C2×#3719C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50#63806—24no—
51#63795—24no—
52C32×#97C2211yescharacteristic, complemented
53#63648C2211yescharacteristic
54#63645C2211yescharacteristic, complemented
55#63643C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61#63563C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C2×#916—31no—
64C2×#911—31no—
65C2×#908—31no—
66C2×#904—31no—
67#5718—31no—
68#5676—31no—
69#5553—31no—
70#5550—31no—
71C3×#496—31no—
72C3×#435—31no—
73#5174—31no—
74#5173—31no—
75#5172—31no—
76#5158—31no—
77#5157—31no—
78#5156—31no—
79#5134—31no—
80#5115—31no—
81#5072—31no—
82#5054—31no—
83#4845—31no—
84#4843—31no—
85#4734—31no—
86#4734—31no—
87#4733—31no—
88#4732—31no—
89#4712D311yescharacteristic, complemented
90#4710—31no—
91#4710—31no—
92#4710—61no—
93#4706D311yescharacteristic, complemented
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×#634C2311yescharacteristic
98C2×C3×D12—21no—
99C2×C3×D12—21no—
100C2×C3×D12D411yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#625—21no—
110C2×#625—21no—
111C2×#625—21no—
112C2×#625—21no—
113C2×#625—21no—
114C2×#624—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12—41no—
119#3799—22no—
120#3799—41no—
121#3795—22no—
122#3795—22no—
123#3795—41no—
124#3795—41no—
125C2×C32×C8C2311yescharacteristic
126C2×C32×C8C2311yescharacteristic
127C32×C42C2311yescharacteristic
128#3752—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131#3750—21no—
132C4×C3⋊Dic3—21no—
133#3744D414yescomplemented
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×C4⋊Dic3D411yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×D24—22no—
142C3×D24—41no—
143C3×#204—22no—
144C3×#204—41no—
145C3×ΓL(1,𝔽25)—22no—
146C3×D3×C8—22no—
147#3724—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3719—22no—
153#3716—22no—
154#3714—22no—
155#3714—22no—
156#3268—91noSylow
157C2×#239—31no—
158C2×#237—31no—
159C2×#237—31no—
160C2×D3×D4—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×D8—31no—
168C2×C3×D8—31no—
169C2×C3×M16—31no—
170C22×C3×C8—31no—
171C3×#127—31no—
172C3×#124—31no—
173C3×C4×D4—31no—
174#946—31no—
175C2×#216—31no—
176#940—61no—
177#940—61no—
178#939—61no—
179#939—61no—
180#938—31no—
181#938—31no—
182#938—31no—
183#937—61no—
184D4×Dic3—61no—
185C2×#214—31no—
186C2×#213—31no—
187C2×#213—31no—
188#930—31no—
189#930—31no—
190#930—31no—
191#924—31no—
192#916—64no—
193#911—64no—
194#908—64no—
195C2×Dic12—31no—
196#904—64no—
197C2×D24—31no—
198C2×D24—31no—
199C2×D24C2×D311yescharacteristic
200C2×D24C2×D311yescharacteristic
201C2×#204—31no—
202C2×#204—31no—
203C2×#204—31no—
204C2×#204—61no—
205C2×#204C2×D311yescharacteristic, complemented
206C2×#204C2×D311yescharacteristic, complemented
207C2×ΓL(1,𝔽25)C2×D311yescharacteristic
208C2×D3×C8C2×D311yescharacteristic, complemented
209#894—61no—
210#893—61no—
211#884—61no—
212#884—61no—
213#884—61no—
214#884—61no—
215#883—61no—
216#882—61no—
217D3×C22⋊C4—61no—
218D3×C22⋊C4—61no—
219#875C2×D311yescharacteristic
220#874C2×D311yescharacteristic, complemented
221C4×D12—31no—
222C4×D12—31no—
223C4×D12—61no—
224C4×D12C2×D311yescharacteristic
225C4×Dic6—31no—
226C4×Dic6—31no—
227C4×Dic6—61no—
228C3×C4⋊C8—31no—
229C3×C22⋊C8—31no—
230C3×C22⋊C8—31no—
231C3×#97—21no—
232C3×#97C2×D311yescharacteristic, complemented
233C3×#97C2×D311yescharacteristic, complemented
234#835—31no—
235#832—31no—
236#832—31no—
237#832—31no—
238#821—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—31no—
243#821—61no—
244(C2×D3)⋊C8C2×D311yescharacteristic
245(C2×D3)⋊C8C2×D311yescharacteristic, complemented
246#818—31no—
247#818—31no—
248#818—61no—
249#816—31no—
250#816—31no—
251#816—31no—
252#816—61no—
253C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
254C22×C3⋊D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)C2×D412yes—
271C4×C3⋊D3—81no—
272#634—21no—
273#634C2×D412yes—
274C2×C3×Dic3—21no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—41no—
284C3×D12—42no—
285C3×D12—81no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292#626—42no—
293#626—42no—
294#625—42no—
295#625—42no—
296#625—81no—
297#625—81no—
298#625—81no—
299#624—42no—
300D3×Dic3—42no—
301D3×Dic3—42no—
302C32×C8—21no—
303C32×C8C2×D412yes—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—91no—
309#546—91no—
310#496—31no—
311#468—91no—
312#466—91no—
313#464—91no—
314#459—91no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—31no—
321C23×D3—61no—
322C23×D3—61no—
323C2×C3×Q8—31no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C22×Dic3—61no—
345C22×Dic3—61no—
346#239—62no—
347#239—121no—
348#237—62no—
349#237—62no—
350#237—121no—
351#237—121no—
352D3×D4—62no—
353D3×D4—121no—
354#235—62no—
355#235—62no—
356#235—62no—
357#235—121no—
358#235—121no—
359#235—121no—
360C2×D12—21no—
361C2×D12—21no—
362C2×D12—31no—
363C2×D12—31no—
364C2×D12—61no—
365C2×D12—62no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—121no—
369C2×D12D1211yescharacteristic
370C2×D12C22×D311yescharacteristic
371C2×D12C22×D311yescharacteristic
372C2×D12C22×D311yescharacteristic
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3—121no—
380C2×C4×D3C22×D311yescharacteristic
381C2×C4×D3C22×D311yescharacteristic
382C2×Dic6—31no—
383C2×Dic6—31no—
384C2×Dic6—61no—
385C2×Dic6C22×D311yescharacteristic
386C3×SD16—62no—
387C3×SD16—121no—
388C3×D8—62no—
389C3×D8—121no—
390C3×M16—62no—
391C2×C3×C8—21no—
392C2×C3×C8—21no—
393C2×C3×C8—31no—
394C2×C3×C8—31no—
395C2×C3×C8—62no—
396C2×C3×C8C22×D311yescharacteristic
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C3×C4⋊C4—31no—
401C3×C22⋊C4—31no—
402C3×C22⋊C4—31no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C42—21no—
406C3×C42C22×D311yescharacteristic
407C3×C42C22×D311yescharacteristic
408#217—61no—
409#217—61no—
410#217—61no—
411#217—61no—
412#216—62no—
413#214—62no—
414#213—62no—
415#213—62no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—121no—
425(C2×D3)⋊C4D1211yescharacteristic
426(C2×D3)⋊C4D1211yescharacteristic
427C4⋊Dic3—31no—
428C4⋊Dic3—31no—
429C4⋊Dic3—31no—
430C4⋊Dic3—31no—
431C4⋊Dic3—61no—
432C4⋊Dic3—61no—
433C4⋊Dic3D1211yescharacteristic
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—121no—
439C4×Dic3—61no—
440C4×Dic3—61no—
441C4×Dic3—121no—
442C2×C3⋊C8C22×D311yescharacteristic
443C2×C3⋊C8C22×D311yescharacteristic
444Dic12—62no—
445D24—22no—
446D24—41no—
447D24—62no—
448D24—62no—
449#204—22no—
450#204—34no—
451#204—34no—
452#204—41no—
453#204—64no—
454#204—62no—
455ΓL(1,𝔽25)—22no—
456D3×C8—22no—
457C22×C32C22×D411yescharacteristic
458C2×C3⋊D3—22no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476D32—84no—
477C32×C4—21no—
478C32×C4—21no—
479C32×C4C22×D411yescharacteristic
480C32×C4H(5,𝔽2)11yescharacteristic
481C3⋊Dic3—22no—
482C3⋊Dic3—41no—
483C3⋊Dic3—41no—
484C3×Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—41no—
487C2×#41—91no—
488C2×#41—91no—
489C2×#41—91no—
490C22×D4—91no—
491AGL(1,ℤ/8)—184no—
492#135—184no—
493C2×Q16—91no—
494C2×SD16—31no—
495C2×SD16—31no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×D8—31no—
499C2×D8—31no—
500C2×D8—91no—
501C2×D8—91no—
502C2×M16—31no—
503C22×C8—31no—
504#127—31no—
505#127—181no—
506#124—31no—
507#123—181no—
508C22⋊Q8—91no—
509#121—91no—
510#121—91no—
511#121—91no—
512#121—181no—
513#121—181no—
514#121—181no—
515#120—181no—
516C4×Q8—91no—
517C4×D4—31no—
518C4×D4—91no—
519C4×D4—181no—
520C2×C22⋊C4—181no—
521#107—91no—
522C4⋊C8—31no—
523#103—91no—
524#103—91no—
525#102—91no—
526#102—91no—
527#102—91no—
528#102—91no—
529C22⋊C8—31no—
530C22⋊C8—31no—
531#97D3211yescharacteristic, complemented
532C23×C3—31no—
533C23×C3—31no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—61no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—121no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3—241no—
548C22×D3—241no—
549C22×D3C2×D1211yescharacteristic
550C22×D3C2×D1211yescharacteristic
551C3×Q8—61no—
552C3×Q8—61no—
553C3×D4—61no—
554C3×D4—61no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—121no—
560C3×D4—122no—
561C3×D4—241no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—31no—
566C2×C3×C4—31no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4C2×D1211yescharacteristic
573C2×C3×C4C2×D1211yescharacteristic
574C2×C3×C4D3×D411yescharacteristic
575C2×C3×C4D3×D411yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578#67—122no—
579#67—122no—
580#67—122no—
581#67—122no—
582#67—122no—
583#67—122no—
584#67—241no—
585#67—241no—
586#67—241no—
587#67—241no—
588#67—241no—
589#67—241no—
590C2×Dic3—21no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—121no—
598C2×Dic3—121no—
599C2×Dic3—121no—
600C2×Dic3—122no—
601C2×Dic3—122no—
602C2×Dic3C2×D1211yescharacteristic
603C2×Dic3C2×D1211yescharacteristic
604D12—21no—
605D12—21no—
606D12—21no—
607D12—21no—
608D12—21no—
609D12—21no—
610D12—32no—
611D12—32no—
612D12—41no—
613D12—42no—
614D12—62no—
615D12—61no—
616D12—61no—
617D12—81no—
618D12—121no—
619D12—122no—
620D12—122no—
621C4×D3—21no—
622C4×D3—21no—
623C4×D3—21no—
624C4×D3—21no—
625C4×D3—122no—
626C4×D3—122no—
627C4×D3—122no—
628C4×D3—122no—
629C4×D3—241no—
630C4×D3—241no—
631C4×D3—242no—
632Dic6—21no—
633Dic6—21no—
634Dic6—32no—
635Dic6—32no—
636Dic6—62no—
637Dic6—61no—
638Dic6—61no—
639Dic6—121no—
640C3×C8—21no—
641C3×C8—21no—
642C3×C8—22no—
643C3×C8—41no—
644C3×C8—61no—
645C3×C8—61no—
646C3×C8D3×D412yes—
647C3×C8D3×D412yes—
648C3⋊C8—21no—
649C3⋊C8—21no—
650C2×C32D4211yescharacteristic
651C2×C32#57511yescharacteristic
652C2×C32#57611yescharacteristic
653C3⋊D3—42no—
654C3×D3—41no—
655C3×D3—41no—
656C3×D3—81no—
657C3×D3—81no—
658C3×D3—81no—
659C24—181no—
660#41—182no—
661#41—182no—
662#41—182no—
663#41—361no—
664#41—361no—
665#41—361no—
666C2×Q8—31no—
667C2×Q8—91no—
668C2×D4—31no—
669C2×D4—31no—
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—91no—
675C2×D4—181no—
676C2×D4—182no—
677C2×D4—181no—
678C2×D4—181no—
679C2×D4—181no—
680C2×D4—181no—
681C2×D4—181no—
682C2×D4—181no—
683C2×D4—361no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—181no—
687C22×C4—181no—
688C22×C4—181no—
689C22×C4—181no—
690Q16—182no—
691SD16—62no—
692SD16—94no—
693SD16—121no—
694SD16—182no—
695D8—62no—
696D8—121no—
697D8—182no—
698D8—182no—
699M16—62no—
700C2×C8—31no—
701C2×C8—31no—
702C2×C8—62no—
703C2×C8C2×D3211yescharacteristic
704C2×C8C2×D3211yescharacteristic
705C4⋊C4—31no—
706C4⋊C4—91no—
707C4⋊C4—91no—
708C4⋊C4—181no—
709C4⋊C4—181no—
710C22⋊C4—31no—
711C22⋊C4—31no—
712C22⋊C4—61no—
713C22⋊C4—61no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C42—181no—
720C42C2×D3211yescharacteristic
721C22×C3—21no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3C22×D1211yescharacteristic
738C22×C3C2×D3×D411yescharacteristic
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—122no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—241no—
762C2×D3—241no—
763C2×D3—244no—
764C2×D3—244no—
765C3×C4—21no—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—21no—
771C3×C4—41no—
772C3×C4—41no—
773C3×C4—61no—
774C3×C4—61no—
775C3×C4—121no—
776C3×C4C2×D3×D411yescharacteristic
777C3×C4C2×D3×D411yescharacteristic
778C3×C4#100411yescharacteristic
779C3×C4#100911yescharacteristic
780Dic3—21no—
781Dic3—21no—
782Dic3—41no—
783Dic3—62no—
784Dic3—62no—
785Dic3—122no—
786Dic3—121no—
787Dic3—121no—
788Dic3—121no—
789Dic3—121no—
790Dic3—241no—
791Dic3—241no—
792C32#326811yescharacteristic, complemented, Sylow
793C23—31no—
794C23—31no—
795C23—61no—
796C23—61no—
797C23—61no—
798C23—181no—
799C23—362no—
800C23—362no—
801C23—721no—
802Q8—61no—
803Q8—61no—
804Q8—92no—
805Q8—181no—
806D4—61no—
807D4—61no—
808D4—61no—
809D4—61no—
810D4—61no—
811D4—61no—
812D4—92no—
813D4—121no—
814D4—122no—
815D4—181no—
816D4—241no—
817D4—362no—
818D4—362no—
819D4—362no—
820D4—362no—
821D4—721no—
822D4—721no—
823D4—721no—
824C2×C4—31no—
825C2×C4—31no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—181no—
832C2×C4—181no—
833C2×C4—181no—
834C2×C4—362no—
835C2×C4—362no—
836C2×C4—362no—
837C2×C4—721no—
838C2×C4D3×D1211yescharacteristic
839C2×C4D3×D1211yescharacteristic
840C2×C4C22×D3211yescharacteristic
841C8—21no—
842C8—61no—
843C8—61no—
844C8#380212yes—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—121no—
849C2×C3—121no—
850C2×C3—241no—
851C2×C3—241no—
852C2×C3—241no—
853C2×C3D4×D1211yescharacteristic
854C2×C3#571711yescharacteristic
855C2×C3#574811yescharacteristic
856C2×C3#575211yescharacteristic
857C2×C3#577311yescharacteristic
858C2×C3#577411yescharacteristic
859D3—41no—
860D3—41no—
861D3—81no—
862D3—81no—
863D3—81no—
864D3—122no—
865D3—122no—
866D3—242no—
867C22—61no—
868C22—61no—
869C22—61no—
870C22—61no—
871C22—61no—
872C22—61no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22—121no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—182no—
883C22—361no—
884C22—361no—
885C22—724no—
886C22C2×D3×D1211yescharacteristic
887C4—21no—
888C4—21no—
889C4—61no—
890C4—61no—
891C4—121no—
892C4—182no—
893C4—361no—
894C4—361no—
895C4C2×#380211yescharacteristic
896C4#6430711yescharacteristic
897C3—21no—
898C3#7949711yescharacteristic, complemented
899C3#8185811yescharacteristic, complemented
900C2—121no—
901C2—121no—
902C2—241no—
903C2—241no—
904C2—241no—
905C2—362no—
906C2#1059400411yescharacteristic
907C2#1059471211yescharacteristic
908C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
hypercenter#97D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. C2×#63806C2semidirect
2. C2×#63795C2semidirect
3. #10594007C2semidirect
4. #10593906C2semidirect
5. #10592409C2semidirect
6. C3×#4712C2semidirect
7. C3×#4706C2semidirect
8. #10590962C2semidirect
9. #10590960C2semidirect
10. #10590944C2semidirect
11. #10590833C2semidirect
12. #10590831C2semidirect
13. #10590823C2semidirect
14. #10590378C2semidirect
15. #10590355C2semidirect
21. C2×#3795C22semidirect
24. C4×#634C22semidirect
27. C2×C3×#204C22semidirect
28. C2×C3×#204C22semidirect
30. C2×C3×D3×C8C22semidirect
32. C3×#874C22semidirect
40. #63908C22semidirect
46. C2×#3719C22semidirect
52. C32×#97C22semidirect
54. #63645C22semidirect
55. #63643C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
61. #63563C22semidirect
62. #63563C22semidirect
89. #4712D3semidirect
93. #4706D3semidirect
133. #3744D4semidirect
205. C2×#204C2×D3semidirect
206. C2×#204C2×D3semidirect
208. C2×D3×C8C2×D3semidirect
220. #874C2×D3semidirect
232. C3×#97C2×D3semidirect
233. C3×#97C2×D3semidirect
245. (C2×D3)⋊C8C2×D3semidirect
253. C4⋊(C3⋊C8)C2×D3semidirect
531. #97D32semidirect
792. C32#3268semidirect
898. C3#79497semidirect
899. C3#81858semidirect

Maximal subgroups

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

subgroupindex
C2×#638062
C2×#637952
#105940072
#105939062
#105924092
C3×#47122
C3×#47062
#105909622
#105909602
#105909442
#105908332
#105908312
#105908232
#105903782
#105903552
#818583
#794973