Finite Group Databasebeta

← #11889296

Subgroups — #11889296

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595431C211yesmaximal, characteristic
2#10595411C211yesmaximal, characteristic, complemented
3#10592886C211yesmaximal, characteristic, complemented
4C3×#5189C211yesmaximal, characteristic, complemented
5C3×#5185C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591624C211yesmaximal, characteristic, complemented
8#10591591C211yesmaximal, characteristic, complemented
9#10591560C211yesmaximal, characteristic, complemented
10#10591559C211yesmaximal, characteristic, complemented
11#10591540C211yesmaximal, characteristic, complemented
12#10590939C211yesmaximal, characteristic, complemented
13#10590759C211yesmaximal, characteristic, complemented
14#10590738C211yesmaximal, characteristic, complemented
15#10590652C211yesmaximal, characteristic, complemented
16#80914—31nomaximal
17#80617—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic, complemented
21#64155C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic
23C3×#947C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
29#63923—21no—
30#63921—21no—
31#63918C2211yescharacteristic, complemented
32#63916C2211yescharacteristic
33#63910—21no—
34C4×#626C2211yescharacteristic
35#63894C2211yescharacteristic
36#63858—21no—
37#63853—21no—
38#63852—21no—
39#63849C2211yescharacteristic, complemented
40#63848—21no—
41#63841C2211yescharacteristic
42#63837—21no—
43C2×#3710C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63647C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#835C2211yescharacteristic, complemented
49C3×#835C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×#817C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5676—31no—
62#5641—31no—
63#5630—31no—
64#5584—31no—
65C3×#470—31no—
66C3×#464—31no—
67#5189D311yescharacteristic, complemented
68#5187—31no—
69#5187—31no—
70#5187—61no—
71#5185D311yescharacteristic, complemented
72#5171—31no—
73#5169—31no—
74#5131—31no—
75#5127—31no—
76#5055—31no—
77#5046—31no—
78#5045—31no—
79#5026—31no—
80#4870—31no—
81#4866—31no—
82#4842—31no—
83#4836—31no—
84#4817—31no—
85#4815—31no—
86#4807—31no—
87#4804—31no—
88#4804—31no—
89#4794—31no—
90#4779—31no—
91#4770—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×Q8C2311yescharacteristic
95#3832—22no—
96#3832—41no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×#627—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#626D411yescharacteristic
107C2×#624—21no—
108D3×D12—22no—
109D3×D12—41no—
110C32×Q16—41no—
111C2×C32×C8C2311yescharacteristic
112#3755—22no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#215—41no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×ΓL(1,𝔽25)—41no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3D411yescharacteristic
135#3722—21no—
136#3722—21no—
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142Dic32—21no—
143#3710—41no—
144#3311—91noSylow
145C2×#239—31no—
146C2×#239—31no—
147C2×#239—61no—
148C2×D3×D4—31no—
149C22×D12—31no—
150C2×C3×Q16—21no—
151C2×C3×Q16C2×D311yescharacteristic, complemented
152C2×C3×Q16C2×D311yescharacteristic, complemented
153C2×C3×SD16—31no—
154C2×C3×M16—31no—
155C3×#124—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C4×Q8—31no—
159#947C2×D311yescharacteristic
160#946—31no—
161#946—31no—
162#946—61no—
163#946C2×D311yescharacteristic
164#946C2×D311yescharacteristic
165Q8×Dic3C2×D311yescharacteristic, complemented
166C2×#215—31no—
167C2×#215—31no—
168C2×#215—61no—
169C2×#215C2×D311yescharacteristic
170#938—31no—
171C4×#67—31no—
172#926—31no—
173C2×ΓL(1,𝔽25)C2×D311yescharacteristic
174C2×D3×C8—31no—
175C2×D3×C8—31no—
176#898—61no—
177#898—61no—
178#898—61no—
179#895—31no—
180#895—61no—
181#894—61no—
182#893—31no—
183#892—31no—
184#892—31no—
185#892—31no—
186#888—31no—
187#887—61no—
188#885—61no—
189#884—61no—
190#883—61no—
191#882—61no—
192#882—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196#875—61no—
197C4×D12—31no—
198C4×D12—31no—
199#869—31no—
200C4×Dic6—61no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#102—31no—
207#835—31no—
208#835—31no—
209#835—61no—
210#835C2×D311yescharacteristic, complemented
211#835C2×D311yescharacteristic, complemented
212#835C2×D311yescharacteristic, complemented
213#832—31no—
214#832—31no—
215#830—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—61no—
222#821C2×D311yescharacteristic
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—61no—
227#817—31no—
228#817C2×D311yescharacteristic, complemented
229#815—31no—
230Dic3⋊C8C2×D311yescharacteristic, complemented
231#809—31no—
232#809—31no—
233#809—31no—
234#808—31no—
235#807—31no—
236#807—31no—
237#803—31no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C32×Q8—21no—
246C32×Q8—21no—
247C32×Q8—21no—
248C32×Q8—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—42no—
256C4⋊(C3⋊D3)#4112yes—
257C4×C3⋊D3—21no—
258C4×C3⋊D3—21no—
259C4×C3⋊D3—42no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270#627—42no—
271#626—41no—
272#626—42no—
273#626—81no—
274#624—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—91no—
281#489—91no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—31no—
286#465—91no—
287#464—31no—
288#452—91no—
289#450—91no—
290#440—91no—
291#435—91no—
292#418—91no—
293#416—91no—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×Q8—21no—
297C2×C3×Q8—21no—
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—31no—
303C22×C3×C4—31no—
304C2×#67—31no—
305C2×#67—61no—
306C2×#67—61no—
307#239—62no—
308#239—62no—
309#239—122no—
310#239—121no—
311#239—121no—
312#239—122no—
313D3×D4—62no—
314D3×D4—121no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—62no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—121no—
325C2×D12—121no—
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—121no—
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6—61no—
337C2×Dic6—61no—
338C3×Q16—41no—
339C3×Q16—41no—
340C3×Q16—42no—
341C3×SD16—121no—
342C3×M16—121no—
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C42—31no—
359C3×C42—61no—
360#217—31no—
361#217—61no—
362#217—61no—
363#215—41no—
364#215—62no—
365#215—62no—
366#215—122no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—121no—
383C4⋊Dic3—21no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—31no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—121no—
399C4×Dic3—21no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410ΓL(1,𝔽25)—41no—
411D3×C8—121no—
412D3×C8—121no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—22no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426D32—84no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—21no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—91no—
441C2×Q16D3211yescharacteristic, complemented
442C2×SD16—31no—
443C2×SD16—91no—
444C2×M16—31no—
445C22×C8—91no—
446C4⋊Q8—91no—
447#126—181no—
448#126—181no—
449#124—31no—
450#124—181no—
451#123—181no—
452C22⋊Q8—31no—
453C22⋊Q8—31no—
454C22⋊Q8—91no—
455#121—91no—
456#121—181no—
457#120—181no—
458C4×Q8—31no—
459C4×Q8—181no—
460C4×D4—91no—
461C4×D4—91no—
462#117—91no—
463#117—91no—
464C2×C22⋊C4—181no—
465#107—91no—
466#106—31no—
467#106—91no—
468C4⋊C8—31no—
469#103—31no—
470#103—31no—
471#103—31no—
472#103—91no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—91no—
480C22⋊C8—91no—
481#97—91no—
482C23×C3—31no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—31no—
486C22×D3—31no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—121no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—241no—
496C22×D3—241no—
497C22×D3D3×D411yescharacteristic
498C3×Q8—22no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—41no—
508C3×Q8—41no—
509C3×Q8—41no—
510C3×D4—61no—
511C3×D4—61no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—121no—
530#67—122no—
531#67—241no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—121no—
541C2×Dic3D3×D411yescharacteristic
542C2×Dic3D3×D411yescharacteristic
543C2×Dic3D3×D411yescharacteristic
544D12—21no—
545D12—21no—
546D12—32no—
547D12—32no—
548D12—62no—
549D12—61no—
550D12—61no—
551D12—121no—
552D12—122no—
553D12—122no—
554D12—124no—
555D12—121no—
556D12—122no—
557D12—241no—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—61no—
561C4×D3—61no—
562C4×D3—61no—
563C4×D3—61no—
564C4×D3—121no—
565C4×D3—121no—
566C4×D3—122no—
567C4×D3—122no—
568C4×D3—124no—
569C4×D3—241no—
570C4×D3—241no—
571Dic6—122no—
572Dic6—122no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—41no—
576C3×C8—61no—
577C3×C8—61no—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—121no—
583C2×C32#54611yescharacteristic
584C2×C32#57511yescharacteristic
585C2×C32#57711yescharacteristic
586C3⋊D3—42no—
587C3⋊D3—41no—
588C3×D3—41no—
589C3×D3—81no—
590C24—181no—
591#41—182no—
592#41—361no—
593C2×Q8—181no—
594C2×Q8C2×D3211yescharacteristic
595C2×Q8C2×D3211yescharacteristic
596C2×D4—31no—
597C2×D4—91no—
598C2×D4—91no—
599C2×D4—181no—
600C2×D4—181no—
601C2×D4—182no—
602C2×D4—181no—
603C2×D4—361no—
604C22×C4—31no—
605C22×C4—91no—
606C22×C4—181no—
607C22×C4—181no—
608Q16—41no—
609SD16—121no—
610SD16—182no—
611M16—121no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—91no—
615C2×C8—361no—
616C2×C8C2×D3211yescharacteristic
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—91no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—91no—
632C22⋊C4—91no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—31no—
639C42—61no—
640C42—181no—
641C42—181no—
642C22×C3—21no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3C2×D3×D411yescharacteristic
650C22×C3C2×D3×D411yescharacteristic
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—62no—
663C2×D3—61no—
664C2×D3—62no—
665C2×D3—122no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—241no—
674C2×D3—241no—
675C2×D3—244no—
676C2×D3—244no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—42no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—81no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4#100411yescharacteristic
692C3×C4#100411yescharacteristic
693C3×C4D3×#4111yescharacteristic
694C3×C4D3×#4111yescharacteristic
695Dic3—21no—
696Dic3—21no—
697Dic3—21no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—61no—
702Dic3—61no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—241no—
707C32#331111yescharacteristic, complemented, Sylow
708C23—31no—
709C23—61no—
710C23—91no—
711C23—181no—
712C23—362no—
713C23—362no—
714C23—721no—
715Q8—21no—
716Q8—21no—
717Q8—21no—
718Q8—21no—
719Q8—362no—
720D4—61no—
721D4—61no—
722D4—92no—
723D4—181no—
724D4—362no—
725D4—361no—
726D4—362no—
727D4—721no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—91no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—362no—
743C2×C4—721no—
744C2×C4C22×D3211yescharacteristic
745C8—21no—
746C8—61no—
747C8—61no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—121no—
753C2×C3—241no—
754C2×C3#561011yescharacteristic
755C2×C3#561211yescharacteristic
756C2×C3#577011yescharacteristic
757C2×C3#577711yescharacteristic
758C2×C3#577711yescharacteristic
759C2×C3#577811yescharacteristic
760D3—41no—
761D3—81no—
762D3—121no—
763D3—122no—
764D3—121no—
765D3—122no—
766D3—241no—
767D3—242no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—181no—
775C22—181no—
776C22—181no—
777C22—182no—
778C22—361no—
779C22—361no—
780C22—724no—
781C22D32×D411yescharacteristic
782C4—41no—
783C4—41no—
784C4—61no—
785C4—61no—
786C4—61no—
787C4—121no—
788C4—121no—
789C4—121no—
790C4—181no—
791C4—361no—
792C4#6431211yescharacteristic
793C4#6433011yescharacteristic
794C3—21no—
795C3#8061711yescharacteristic, complemented
796C3#8091411yescharacteristic, complemented
797C2—121no—
798C2—241no—
799C2—361no—
800C2—362no—
801C2#1059476211yescharacteristic
802C2#1059477011yescharacteristic
803C2#1059529611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radical#10595431C2
hypercenterC2×Q16D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. #10595411C2semidirect
3. #10592886C2semidirect
4. C3×#5189C2semidirect
5. C3×#5185C2semidirect
6. #10591651C2semidirect
7. #10591624C2semidirect
8. #10591591C2semidirect
9. #10591560C2semidirect
10. #10591559C2semidirect
11. #10591540C2semidirect
12. #10590939C2semidirect
13. #10590759C2semidirect
14. #10590738C2semidirect
15. #10590652C2semidirect
20. C2×C32×Q16C22semidirect
21. #64155C22semidirect
26. C3×Q8×Dic3C22semidirect
31. #63918C22semidirect
39. #63849C22semidirect
43. C2×#3710C22semidirect
44. #63662C22semidirect
46. #63647C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
49. C3×#835C22semidirect
51. C3×#817C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. #63576C22semidirect
54. #63573C22semidirect
60. #63554C22semidirect
67. #5189D3semidirect
71. #5185D3semidirect
151. C2×C3×Q16C2×D3semidirect
152. C2×C3×Q16C2×D3semidirect
165. Q8×Dic3C2×D3semidirect
210. #835C2×D3semidirect
211. #835C2×D3semidirect
212. #835C2×D3semidirect
228. #817C2×D3semidirect
230. Dic3⋊C8C2×D3semidirect
441. C2×Q16D32semidirect
707. C32#3311semidirect
795. C3#80617semidirect
796. C3#80914semidirect

Maximal subgroups

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

subgroupindex
#105954312
#105954112
#105928862
C3×#51892
C3×#51852
#105916512
#105916242
#105915912
#105915602
#105915592
#105915402
#105909392
#105907592
#105907382
#105906522
#809143
#806173