Finite Group Databasebeta

← #11878503

Subgroups — #11878503

Order 1152.

951 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596304C211yesmaximal, characteristic, complemented
2C3×#5833C211yesmaximal, characteristic, complemented
3C3×#5234C211yesmaximal, characteristic, complemented
4#10591187C211yesmaximal, characteristic, complemented
5#10591184C211yesmaximal, characteristic, complemented
6#10591182C211yesmaximal, characteristic, complemented
7#10591178C211yesmaximal, characteristic, complemented
8#10591176C211yesmaximal, characteristic, complemented
9#10591173C211yesmaximal, characteristic, complemented
10#10591164C211yesmaximal, characteristic, complemented
11#10591163C211yesmaximal, characteristic, complemented
12#10591135C211yesmaximal, characteristic, complemented
13#10591133C211yesmaximal, characteristic, complemented
14#10591103C211yesmaximal, characteristic, complemented
15#10591094C211yesmaximal, characteristic, complemented
16#83426—31nomaximal
17#78676—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×#3828C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21#64155—21no—
22#64148—21no—
23#64148—21no—
24#64147—21no—
25#64139C2211yescharacteristic
26#64139C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28#64133C2211yescharacteristic
29#64133C2211yescharacteristic
30C3×#946—21no—
31C3×#939—21no—
32C3×#939—21no—
33C3×#938—21no—
34C3×#930C2211yescharacteristic
35C3×#930C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C3×#924C2211yescharacteristic
38C3×#924C2211yescharacteristic
39C2×C3×#208C2211yescharacteristic
40C22×C3×C3⋊C8C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45C3×#830C2211yescharacteristic
46C3×#830C2211yescharacteristic
47C3×#830C2211yescharacteristic
48C3×#830C2211yescharacteristic
49#63575C2211yescharacteristic
50#63575C2211yescharacteristic
51#63575C2211yescharacteristic
52#63575C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61C3×#537—31no—
62#5833—31no—
63#5833—31no—
64#5833—61no—
65#5833D311yescharacteristic, complemented
66C3×#408—31no—
67#5239—31no—
68#5238—31no—
69#5234D311yescharacteristic, complemented
70#5134—31no—
71#5134—31no—
72#5116—31no—
73#5115—31no—
74#5051—31no—
75#5049—31no—
76#5047—31no—
77#5044—31no—
78#5042—31no—
79#5038—31no—
80#5037—31no—
81#5033—31no—
82#4970—31no—
83#4967—31no—
84#4736—31no—
85#4736—31no—
86#4734—31no—
87#4734—31no—
88#4733—31no—
89#4733—31no—
90#4722—31no—
91#4722—31no—
92C32×#41—41no—
93C32×#41—41no—
94C2×C32×Q8D411yescharacteristic
95C2×C32×D4D411yescharacteristic
96C2×C32×D4D411yescharacteristic
97C2×C32×D4D411yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×#638—21no—
102C2×#638—21no—
103C2×#638—21no—
104C22×C3⋊Dic3—21no—
105#3828—41no—
106#3828—41no—
107C2×C4⋊(C3⋊D3)C2311yescharacteristic
108C2×C4×C3⋊D3—21no—
109C2×#634C2311yescharacteristic
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C2×C3×#67—21no—
113C22×C3×Dic3—21no—
114C3×#235—41no—
115C3×#235—41no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×Dic6C2311yescharacteristic
119#3757—21no—
120#3757—21no—
121#3752—21no—
122#3752—21no—
123C4⋊(C3⋊Dic3)—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127#3750—21no—
128C3×#217—21no—
129C3×#217—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×#208—41no—
138C2×C3×C3⋊C8—41no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143#3719—41no—
144#3717—41no—
145#3716—41no—
146#3714—41no—
147#3203—91noSylow
148C2×C3×#41—21no—
149C2×C3×#41—31no—
150C2×C3×#41C2×D311yescharacteristic
151C2×C3×#41C2×D311yescharacteristic
152C2×#235—31no—
153C2×#235—31no—
154C2×#235—61no—
155C2×#235C2×D311yescharacteristic
156C2×C3×M16—31no—
157C22×C3×C8—31no—
158C3×C22⋊Q8—31no—
159C3×C22⋊Q8—31no—
160C3×C22⋊Q8—61no—
161C3×#121—31no—
162C3×#121—31no—
163C3×#121—61no—
164C3×#121—61no—
165C3×#121—61no—
166C2×C3×C4⋊C4—31no—
167#946—21no—
168#946—62no—
169#946—61no—
170#946—61no—
171C2×#216—31no—
172C2×#215—31no—
173#939—21no—
174#939—21no—
175#939—62no—
176#939—62no—
177#939—61no—
178#939—61no—
179#939—61no—
180#939—61no—
181#938—21no—
182#938—62no—
183#938—61no—
184#938—61no—
185C2×#214—31no—
186C2×#213—31no—
187#930—31no—
188#930—31no—
189#930—31no—
190#930—31no—
191#930—61no—
192#930—61no—
193#930C2×D311yescharacteristic
194#930C2×D311yescharacteristic
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—61no—
198C2×C4⋊Dic3C2×D311yescharacteristic
199#924—31no—
200#924—31no—
201#924—31no—
202#924—31no—
203#924—61no—
204#924—61no—
205#924C2×D311yescharacteristic
206#924C2×D311yescharacteristic
207C2×#208C2×D311yescharacteristic
208C22×C3⋊C8C2×D311yescharacteristic
209C2×Dic12—31no—
210C2×D24—31no—
211C2×#204—31no—
212C2×#204—31no—
213C3×C22⋊C8—31no—
214C3×C22⋊C8—31no—
215C3×C22⋊C8—31no—
216C3×C22⋊C8—31no—
217#835—31no—
218#835—31no—
219#832—31no—
220#832—31no—
221#830C2×D311yescharacteristic
222#830C2×D311yescharacteristic
223#830C2×D311yescharacteristic
224#830C2×D311yescharacteristic
225#821—31no—
226#821—31no—
227#821—31no—
228#821—31no—
229#818—31no—
230#818—31no—
231#818—31no—
232#818—31no—
233#816—31no—
234#816—31no—
235#816—31no—
236#816—31no—
237#810—31no—
238#810—31no—
239#809—31no—
240#809—31no—
241#807—31no—
242#807—31no—
243#807—31no—
244#807—31no—
245C23×C32C2×D411yescharacteristic
246C23×C32C2×D411yescharacteristic
247C23×C32C2×D411yescharacteristic
248C22×C3⋊D3—21no—
249C22×C3×D3—21no—
250C32×Q8—41no—
251C32×D4—41no—
252C32×D4—41no—
253C32×D4—41no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4C2×D411yescharacteristic
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2411yescharacteristic
264#638—42no—
265#638—81no—
266#638—81no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—81no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4×C3⋊D3—42no—
274#634—21no—
275#634—21no—
276C3×#67—42no—
277C3×#67—81no—
278C3×#67—81no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—81no—
283C3×D12—21no—
284C3×D12—21no—
285C3×C4×D3—42no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×C3⋊C8—21no—
289C3×C3⋊C8—21no—
290C3×C3⋊C8—21no—
291C3×C3⋊C8—21no—
292#537—31no—
293#537—91no—
294#484—91no—
295#484—91no—
296#480—91no—
297#480—91no—
298#468—91no—
299#468—91no—
300#467—91no—
301#466—91no—
302#452—91no—
303#452—91no—
304#449—91no—
305#449—91no—
306#408—31no—
307C3×#41—41no—
308C3×#41—41no—
309C3×#41—41no—
310C3×#41—41no—
311C3×#41—42no—
312C3×#41—42no—
313C3×#41—121no—
314C3×#41—121no—
315C2×C3×Q8—21no—
316C2×C3×Q8—31no—
317C2×C3×Q8D1211yescharacteristic
318C2×C3×Q8#6711yescharacteristic
319C2×C3×D4—21no—
320C2×C3×D4—21no—
321C2×C3×D4—21no—
322C2×C3×D4—31no—
323C2×C3×D4—61no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C2×C3×D4D1211yescharacteristic
327C2×C3×D4D1211yescharacteristic
328C2×C3×D4D1211yescharacteristic
329C2×C3×D4#6711yescharacteristic
330C2×C3×D4#6711yescharacteristic
331C2×C3×D4#6711yescharacteristic
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C2×#67—21no—
344C2×#67—21no—
345C2×#67—21no—
346C2×#67—62no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—62no—
350C2×#67—62no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C22×Dic3—21no—
356C22×Dic3—62no—
357C22×Dic3—61no—
358C22×Dic3—61no—
359#235—41no—
360#235—41no—
361#235—121no—
362#235—121no—
363#235—121no—
364#235—121no—
365#235—122no—
366#235—122no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—61no—
370C2×D12C22×D311yescharacteristic
371C2×C4×D3—21no—
372C2×C4×D3—62no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×Dic6—31no—
376C2×Dic6—31no—
377C2×Dic6—61no—
378C2×Dic6C22×D311yescharacteristic
379C3×M16—121no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C2×C3×C8—31no—
383C2×C3×C8—31no—
384C2×C3×C8—121no—
385C3×C4⋊C4—31no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4—61no—
389C3×C4⋊C4—61no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394#217—21no—
395#217—21no—
396#217—62no—
397#217—62no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#216—121no—
403#215—121no—
404#214—121no—
405#213—121no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—62no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414C4⋊Dic3—21no—
415C4⋊Dic3—31no—
416C4⋊Dic3—31no—
417C4⋊Dic3—31no—
418C4⋊Dic3—31no—
419C4⋊Dic3—61no—
420C4⋊Dic3—61no—
421C4⋊Dic3—62no—
422C4⋊Dic3—61no—
423C4⋊Dic3—61no—
424C4⋊Dic3C22×D311yescharacteristic
425C4⋊Dic3C22×D311yescharacteristic
426Dic3⋊C4—21no—
427Dic3⋊C4—21no—
428Dic3⋊C4—62no—
429Dic3⋊C4—62no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434#208—41no—
435C2×C3⋊C8—41no—
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438C2×C3⋊C8C22×D311yescharacteristic
439C2×C3⋊C8C22×D311yescharacteristic
440Dic12—121no—
441D24—121no—
442#204—121no—
443#204—121no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32C22×D411yescharacteristic
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C32×C4—21no—
461C32×C4—21no—
462C32×C4—21no—
463C32×C4H(5,𝔽2)11yescharacteristic
464C32×C4H(5,𝔽2)11yescharacteristic
465C3⋊Dic3—41no—
466C3⋊Dic3—41no—
467C3⋊Dic3—41no—
468C3×Dic3—41no—
469C3×Dic3—41no—
470C3×Dic3—41no—
471C2×#41—31no—
472C2×#41—91no—
473C2×#41D3211yescharacteristic
474C2×Q16—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×D8—91no—
478C2×M16—31no—
479C22×C8—31no—
480C22⋊Q8—31no—
481C22⋊Q8—31no—
482C22⋊Q8—61no—
483C22⋊Q8—91no—
484C22⋊Q8—91no—
485C22⋊Q8—181no—
486#121—31no—
487#121—31no—
488#121—61no—
489#121—61no—
490#121—61no—
491#121—91no—
492#121—91no—
493#121—181no—
494#121—181no—
495#121—181no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—91no—
498#107—91no—
499#107—91no—
500#107—91no—
501#107—91no—
502#103—91no—
503#103—91no—
504#103—91no—
505#103—91no—
506#102—91no—
507#102—91no—
508#102—91no—
509#102—91no—
510C22⋊C8—31no—
511C22⋊C8—31no—
512C22⋊C8—31no—
513C22⋊C8—31no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—61no—
518C23×C3C2×D1211yescharacteristic
519C23×C3C2×D1211yescharacteristic
520C23×C3C2×D1211yescharacteristic
521C23×C3C2×#6711yescharacteristic
522C23×C3C2×#6711yescharacteristic
523C23×C3C2×#6711yescharacteristic
524C22×D3—21no—
525C22×D3—62no—
526C22×D3—61no—
527C22×D3—61no—
528C3×Q8—41no—
529C3×Q8—41no—
530C3×Q8—42no—
531C3×Q8—61no—
532C3×Q8—61no—
533C3×D4—41no—
534C3×D4—41no—
535C3×D4—41no—
536C3×D4—41no—
537C3×D4—41no—
538C3×D4—41no—
539C3×D4—42no—
540C3×D4—42no—
541C3×D4—42no—
542C3×D4—61no—
543C3×D4—61no—
544C3×D4—122no—
545C3×D4—241no—
546C3×D4—241no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—122no—
573C2×C3×C4—241no—
574C2×C3×C4C2×D1211yescharacteristic
575C2×C3×C4C2×D1211yescharacteristic
576C2×C3×C4C2×D1211yescharacteristic
577C2×C3×C4C2×#6711yescharacteristic
578C2×C3×C4C2×#6711yescharacteristic
579C2×C3×C4C2×#6711yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581C2×C3×C4C23×D311yescharacteristic
582#67—42no—
583#67—81no—
584#67—81no—
585#67—124no—
586#67—122no—
587#67—122no—
588#67—241no—
589#67—241no—
590#67—241no—
591#67—241no—
592#67—242no—
593#67—242no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—62no—
598C2×Dic3—62no—
599C2×Dic3—62no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—81no—
607C2×Dic3—241no—
608C2×Dic3—241no—
609C2×Dic3—242no—
610D12—21no—
611D12—21no—
612D12—61no—
613D12—61no—
614D12—61no—
615D12—61no—
616D12—121no—
617D12—121no—
618C4×D3—42no—
619C4×D3—124no—
620C4×D3—122no—
621C4×D3—122no—
622Dic6—21no—
623Dic6—21no—
624Dic6—61no—
625Dic6—61no—
626Dic6—61no—
627Dic6—61no—
628Dic6—121no—
629Dic6—121no—
630C3×C8—61no—
631C3×C8—61no—
632C3×C8—61no—
633C3×C8—61no—
634C3⋊C8—21no—
635C3⋊C8—21no—
636C3⋊C8—21no—
637C3⋊C8—21no—
638C2×C32—41no—
639C2×C32—41no—
640C2×C32—41no—
641C2×C32#53411yescharacteristic
642C2×C32#57611yescharacteristic
643C2×C32#57811yescharacteristic
644C3⋊D3—81no—
645C3×D3—81no—
646#41—41no—
647#41—41no—
648#41—121no—
649#41—121no—
650#41—361no—
651#41—361no—
652C2×Q8—31no—
653C2×Q8—91no—
654C2×Q8#62611yescharacteristic
655C2×D4—31no—
656C2×D4—61no—
657C2×D4—61no—
658C2×D4—61no—
659C2×D4—91no—
660C2×D4—181no—
661C2×D4—181no—
662C2×D4—181no—
663C2×D4#62611yescharacteristic
664C2×D4#62611yescharacteristic
665C2×D4#62611yescharacteristic
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—181no—
669C22×C4—181no—
670C22×C4C2×D3211yescharacteristic
671C22×C4C2×D3211yescharacteristic
672C22×C4C2×D3211yescharacteristic
673Q16—361no—
674SD16—361no—
675SD16—361no—
676D8—361no—
677M16—121no—
678C2×C8—31no—
679C2×C8—31no—
680C2×C8—31no—
681C2×C8—31no—
682C2×C8—121no—
683C4⋊C4—31no—
684C4⋊C4—31no—
685C4⋊C4—61no—
686C4⋊C4—61no—
687C4⋊C4—61no—
688C4⋊C4—91no—
689C4⋊C4—91no—
690C4⋊C4—181no—
691C4⋊C4—181no—
692C4⋊C4—181no—
693C22⋊C4—61no—
694C22⋊C4—61no—
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—181no—
698C22⋊C4—181no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22×C3—22no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—121no—
732C22×C3C22×D1211yescharacteristic
733C22×C3C22×#6711yescharacteristic
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—122no—
738C2×D3—122no—
739C2×D3—122no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C3×C4—22no—
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—121no—
758C3×C4—121no—
759C3×C4—121no—
760C3×C4#100411yescharacteristic
761C3×C4#100411yescharacteristic
762C3×C4#100411yescharacteristic
763C3×C4#100411yescharacteristic
764Dic3—41no—
765Dic3—41no—
766Dic3—41no—
767Dic3—122no—
768Dic3—122no—
769Dic3—122no—
770Dic3—121no—
771Dic3—121no—
772Dic3—121no—
773Dic3—121no—
774Dic3—121no—
775Dic3—121no—
776C32#320311yescharacteristic, complemented, Sylow
777C23—61no—
778C23—181no—
779C23C2×#62611yescharacteristic
780C23C2×#62611yescharacteristic
781C23C2×#62611yescharacteristic
782Q8—41no—
783Q8—61no—
784Q8—61no—
785Q8—181no—
786Q8—181no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—61no—
791D4—61no—
792D4—122no—
793D4—181no—
794D4—181no—
795D4—241no—
796D4—241no—
797D4—362no—
798D4—721no—
799D4—721no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—122no—
810C2×C4—181no—
811C2×C4—181no—
812C2×C4—181no—
813C2×C4—241no—
814C2×C4—362no—
815C2×C4—721no—
816C2×C4C2×#62611yescharacteristic
817C2×C4C2×#62611yescharacteristic
818C2×C4C2×#62611yescharacteristic
819C2×C4C22×D3211yescharacteristic
820C8—61no—
821C8—61no—
822C8—61no—
823C8—61no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—42no—
828C2×C3—41no—
829C2×C3—41no—
830C2×C3—41no—
831C2×C3—41no—
832C2×C3—41no—
833C2×C3—41no—
834C2×C3—81no—
835C2×C3—81no—
836C2×C3—241no—
837C2×C3#549311yescharacteristic
838C2×C3#575211yescharacteristic
839C2×C3#575311yescharacteristic
840C2×C3#580411yescharacteristic
841C2×C3#583511yescharacteristic
842C2×C3#583811yescharacteristic
843D3—81no—
844D3—242no—
845D3—241no—
846D3—241no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—361no—
860C22—361no—
861C22—361no—
862C22C22×#62611yescharacteristic
863C4—21no—
864C4—21no—
865C4—21no—
866C4—121no—
867C4—121no—
868C4—121no—
869C4—361no—
870C4—361no—
871C4—361no—
872C4#6433011yescharacteristic
873C4#6433011yescharacteristic
874C3—21no—
875C3#7867611yescharacteristic, complemented
876C3#8342611yescharacteristic, complemented
877C2—41no—
878C2—41no—
879C2—41no—
880C2—241no—
881C2—721no—
882C2#1059544911yescharacteristic
883C2#1059545011yescharacteristic
884C2#1059551911yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3203
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596304C2semidirect
2. C3×#5833C2semidirect
3. C3×#5234C2semidirect
4. #10591187C2semidirect
5. #10591184C2semidirect
6. #10591182C2semidirect
7. #10591178C2semidirect
8. #10591176C2semidirect
9. #10591173C2semidirect
10. #10591164C2semidirect
11. #10591163C2semidirect
12. #10591135C2semidirect
13. #10591133C2semidirect
14. #10591103C2semidirect
15. #10591094C2semidirect
65. #5833D3semidirect
69. #5234D3semidirect
776. C32#3203semidirect
875. C3#78676semidirect
876. C3#83426semidirect

Maximal subgroups

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

subgroupindex
#105963042
C3×#58332
C3×#52342
#105911872
#105911842
#105911822
#105911782
#105911762
#105911732
#105911642
#105911632
#105911352
#105911332
#105911032
#105910942
#834263
#786763