Finite Group Databasebeta

← #11878442

Subgroups — #11878442

Order 1152.

804 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594884C211yesmaximal, characteristic
2#10594855C211yesmaximal, characteristic
3#10592422C211yesmaximal, characteristic, complemented
4C3×#4739C211yesmaximal, characteristic, complemented
5C3×#4727C211yesmaximal, characteristic
6#10591186C211yesmaximal, characteristic, complemented
7#10591127C211yesmaximal, characteristic, complemented
8#10590949C211yesmaximal, characteristic, complemented
9#10590949C211yesmaximal, characteristic, complemented
10#10590854C211yesmaximal, characteristic, complemented
11#10590851C211yesmaximal, characteristic, complemented
12#10590849C211yesmaximal, characteristic, complemented
13#10590848C211yesmaximal, characteristic, complemented
14#10590711C211yesmaximal, characteristic, complemented
15#10590710C211yesmaximal, characteristic, complemented
16#80192—31nomaximal
17#78682—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21#64135C2211yescharacteristic
22#64133C2211yescharacteristic
23C3×#924C2211yescharacteristic
24C2×C3×Dic12C2211yescharacteristic
25C2×C3×Dic12C2211yescharacteristic
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28#63969—21no—
29#63961—21no—
30#63961—21no—
31#63959—21no—
32#63884—21no—
33#63873—21no—
34#63863—21no—
35#63857C2211yescharacteristic
36#63856C2211yescharacteristic
37#63856C2211yescharacteristic
38#63856C2211yescharacteristic
39#63856C2211yescharacteristic
40#63856C2211yescharacteristic
41#63841C2211yescharacteristic
42#63839—21no—
43C2×#3719C2211yescharacteristic
44C2×#3719C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46#63645C2211yescharacteristic
47#63644C2211yescharacteristic
48#63643C2211yescharacteristic
49#63643C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55#63575C2211yescharacteristic
56#63573C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61#5825—31no—
62#5825—31no—
63#5816—31no—
64#5628—31no—
65C3×#451—31no—
66C3×#408—31no—
67#5228—31no—
68#5189—31no—
69#5188—31no—
70#5186—31no—
71#5186—31no—
72#5137—31no—
73#5137—31no—
74#5116—31no—
75#5116—31no—
76#5045—31no—
77#4816—31no—
78#4815—31no—
79#4814—31no—
80#4813—31no—
81#4739—31no—
82#4739—31no—
83#4739—31no—
84#4739D311yescharacteristic, complemented
85#4727D311yescharacteristic
86#4723—31no—
87#4723—31no—
88#4723—31no—
89#4723—31no—
90#4723—31no—
91#4723—61no—
92C22×C32×C4C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×#67D411yescharacteristic
95C2×C3×#67D411yescharacteristic
96C22×C3×Dic3—21no—
97C3×#235—41no—
98C3×#235—41no—
99C2×C3×D12D411yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×C3×Dic6—41no—
104C2×C3×Dic6—41no—
105C2×C3×Dic6D411yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C2×D3×Dic3—21no—
111D3×Dic6—41no—
112D3×Dic6—41no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115#3757—21no—
116#3757—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121C4×C3⋊Dic3—21no—
122C3×#217—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C3×Dic12—41no—
128C3×Dic12—41no—
129C3×ΓL(1,𝔽25)—41no—
130C3×D3×C8—41no—
131#3724—21no—
132#3724—21no—
133#3724—21no—
134#3724—21no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144Dic32—21no—
145#3719—41no—
146#3719—41no—
147#3202—91noSylow
148C2×C3×#41—31no—
149C22×C3×Q8—31no—
150C2×D3×Q8—31no—
151C2×#235C2×D311yescharacteristic
152C22×Dic6—31no—
153C22×Dic6C2×D311yescharacteristic
154C2×C3×Q16—31no—
155C2×C3×Q16—31no—
156C2×C3×M16—31no—
157C22×C3×C8—31no—
158C3×C22⋊Q8—31no—
159#947—61no—
160#946—31no—
161#946—31no—
162#946—31no—
163#946—31no—
164#946—31no—
165#944—61no—
166#944—61no—
167#944—61no—
168C2×#216—31no—
169C2×#216—31no—
170#936—61no—
171#936—61no—
172#935—61no—
173#935—61no—
174#935—61no—
175#935—61no—
176#929—61no—
177#929—61no—
178#926—31no—
179#926—31no—
180#926—31no—
181#926—61no—
182#924—31no—
183#924—31no—
184#924—31no—
185#924—31no—
186#924—31no—
187#924—31no—
188#924—31no—
189#924—31no—
190#924—61no—
191#924C2×D311yescharacteristic
192C2×Dic12—31no—
193C2×Dic12—31no—
194C2×Dic12C2×D311yescharacteristic
195C2×Dic12C2×D311yescharacteristic
196C2×ΓL(1,𝔽25)C2×D311yescharacteristic
197C2×D3×C8C2×D311yescharacteristic
198#897—31no—
199#894—61no—
200#892—31no—
201#888—61no—
202#885—61no—
203#883—61no—
204C3×#103—31no—
205C3×#103—31no—
206C3×C22⋊C8—21no—
207C3×C22⋊C8—31no—
208C3×C22⋊C8—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8C2×D311yescharacteristic
211C3×C22⋊C8C2×D311yescharacteristic
212#835—31no—
213#835—31no—
214#835—31no—
215#835—31no—
216#830C2×D311yescharacteristic
217(C2×D3)⋊C8C2×D311yescharacteristic
218(C2×D3)⋊C8C2×D311yescharacteristic
219#818—31no—
220#818—31no—
221#818—31no—
222#818—61no—
223#817—31no—
224#817—31no—
225#817—31no—
226#817—61no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232#816—31no—
233#816—31no—
234#816—31no—
235#816—61no—
236#816—61no—
237#816C2×D311yescharacteristic
238#816C2×D311yescharacteristic
239#808—31no—
240#807—31no—
241C23×C32C2×D411yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C22×C3×D3C2×D411yescharacteristic
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252#634—21no—
253#634—21no—
254C3×#67—41no—
255C3×#67—41no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—41no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—41no—
275C3×Dic6—42no—
276#627—42no—
277D3×Dic3—42no—
278C32×C8—21no—
279C32×C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#536—91no—
283#536—91no—
284#485—91no—
285#485—91no—
286#485—91no—
287#485—91no—
288#470—91no—
289#470—91no—
290#467—91no—
291#467—91no—
292#451—31no—
293#451—91no—
294#451—91no—
295#451—91no—
296#408—31no—
297C3×#41—121no—
298C3×#41—121no—
299C2×C3×Q8—31no—
300C2×C3×Q8—31no—
301C2×C3×Q8—31no—
302C2×C3×Q8—31no—
303C2×C3×Q8—61no—
304C2×C3×Q8—121no—
305C2×C3×Q8—121no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C22×C3×C4—21no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—61no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C2×#67D1211yescharacteristic
316C2×#67D1211yescharacteristic
317C22×Dic3—21no—
318C22×Dic3—61no—
319D3×Q8—121no—
320D3×Q8—121no—
321#235—41no—
322#235—41no—
323C2×D12D1211yescharacteristic
324C2×C4×D3—61no—
325C2×C4×D3C22×D311yescharacteristic
326C2×C4×D3C22×D311yescharacteristic
327C2×Dic6—21no—
328C2×Dic6—31no—
329C2×Dic6—31no—
330C2×Dic6—41no—
331C2×Dic6—41no—
332C2×Dic6—61no—
333C2×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6—121no—
336C2×Dic6—121no—
337C2×Dic6D1211yescharacteristic
338C2×Dic6C22×D311yescharacteristic
339C2×Dic6C22×D311yescharacteristic
340C2×Dic6C22×D311yescharacteristic
341C3×Q16—121no—
342C3×Q16—121no—
343C3×M16—121no—
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C2×C3×C8—121no—
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C22×D311yescharacteristic
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C3×C4⋊C4—31no—
354C3×C4⋊C4—61no—
355C3×C22⋊C4—61no—
356#217—21no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—121no—
369#217—121no—
370#216—121no—
371#216—121no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
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—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—121no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—121no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412Dic12—41no—
413Dic12—41no—
414Dic12—121no—
415Dic12—121no—
416ΓL(1,𝔽25)—41no—
417D3×C8—41no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32C22×D411yescharacteristic
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C32×C4—21no—
429C32×C4H(5,𝔽2)11yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—41no—
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3⋊Dic3—41no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C2×#41—31no—
442C22×Q8—31no—
443C22×Q8—91no—
444C2×Q16—31no—
445C2×Q16—31no—
446C2×Q16—91no—
447C2×Q16—91no—
448C2×M16—31no—
449C22×C8—31no—
450C4⋊Q8—181no—
451C4⋊Q8—181no—
452#124—181no—
453#124—181no—
454#123—181no—
455#123—181no—
456#123—181no—
457#123—181no—
458C22⋊Q8—31no—
459C22⋊Q8—91no—
460C22⋊Q8—91no—
461C22⋊Q8—91no—
462C22⋊Q8—91no—
463C22⋊Q8—91no—
464C22⋊Q8—91no—
465C22⋊Q8—91no—
466#117—91no—
467#117—91no—
468#107—91no—
469#107—91no—
470#106—91no—
471#106—91no—
472#103—31no—
473#103—31no—
474#103—91no—
475#103—91no—
476#103—91no—
477#103—91no—
478#103—91no—
479#103—91no—
480C22⋊C8—31no—
481C22⋊C8—31no—
482C22⋊C8—31no—
483C22⋊C8D3211yescharacteristic
484C23×C3—21no—
485C23×C3—31no—
486C23×C3—31no—
487C23×C3C2×D1211yescharacteristic
488C23×C3D3×D411yescharacteristic
489C22×D3C2×D1211yescharacteristic
490C22×D3C2×D1211yescharacteristic
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×Q8—121no—
498C3×Q8—122no—
499C3×D4—121no—
500C3×D4—121no—
501C3×D4—121no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—122no—
521C2×C3×C4C2×D1211yescharacteristic
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525#67—41no—
526#67—41no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—42no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—121no—
543C2×Dic3—121no—
544C2×Dic3—122no—
545C2×Dic3C2×D1211yescharacteristic
546C2×Dic3C2×D1211yescharacteristic
547D12—41no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—122no—
553Dic6—21no—
554Dic6—21no—
555Dic6—21no—
556Dic6—21no—
557Dic6—21no—
558Dic6—21no—
559Dic6—41no—
560Dic6—42no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—121no—
566Dic6—121no—
567Dic6—122no—
568Dic6—122no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—41no—
574C3×C8—41no—
575C3×C8—61no—
576C3×C8—61no—
577C3⋊C8—21no—
578C3⋊C8—21no—
579C2×C32—41no—
580C2×C32#53411yescharacteristic
581C2×C32#57811yescharacteristic
582C2×C32#57811yescharacteristic
583C3×D3—41no—
584C3×D3—41no—
585#41—121no—
586#41—121no—
587C2×Q8—31no—
588C2×Q8—31no—
589C2×Q8—31no—
590C2×Q8—31no—
591C2×Q8—61no—
592C2×Q8—91no—
593C2×Q8—121no—
594C2×Q8—121no—
595C2×Q8—181no—
596C2×Q8—361no—
597C2×Q8—361no—
598C2×D4—31no—
599C2×D4—31no—
600C2×D4—31no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—61no—
604C22×C4—181no—
605C22×C4C2×D3211yescharacteristic
606Q16—121no—
607Q16—121no—
608Q16—361no—
609Q16—361no—
610M16—121no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—121no—
614C2×C8C2×D3211yescharacteristic
615C2×C8C2×D3211yescharacteristic
616C4⋊C4—31no—
617C4⋊C4—61no—
618C4⋊C4—91no—
619C4⋊C4—91no—
620C4⋊C4—91no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C22⋊C4—61no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—181no—
639C42—181no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3C22×D1211yescharacteristic
657C22×C3C2×D3×D411yescharacteristic
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—41no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4#100411yescharacteristic
676C3×C4#100411yescharacteristic
677C3×C4#100411yescharacteristic
678C3×C4#100411yescharacteristic
679Dic3—21no—
680Dic3—21no—
681Dic3—41no—
682Dic3—41no—
683Dic3—41no—
684Dic3—41no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—241no—
694Dic3—241no—
695Dic3—241no—
696Dic3—241no—
697C32#320211yescharacteristic, complemented, Sylow
698C23—31no—
699C23—31no—
700C23D3×D1211yescharacteristic
701Q8—61no—
702Q8—61no—
703Q8—61no—
704Q8—61no—
705Q8—61no—
706Q8—61no—
707Q8—121no—
708Q8—122no—
709Q8—181no—
710Q8—181no—
711Q8—362no—
712D4—121no—
713D4—121no—
714D4—121no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—31no—
718C2×C4—31no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—122no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—362no—
733C2×C4D3×D1211yescharacteristic
734C2×C4C22×D3211yescharacteristic
735C8—21no—
736C8—21no—
737C8—61no—
738C8—61no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—41no—
743C2×C3—41no—
744C2×C3—81no—
745C2×C3—121no—
746C2×C3—121no—
747C2×C3#549311yescharacteristic
748C2×C3#558911yescharacteristic
749C2×C3#575311yescharacteristic
750C2×C3#575311yescharacteristic
751C2×C3#576611yescharacteristic
752C2×C3#577911yescharacteristic
753D3—41no—
754D3—41no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22C2×D3×D1211yescharacteristic
765C4—21no—
766C4—61no—
767C4—61no—
768C4—121no—
769C4—121no—
770C4—121no—
771C4—121no—
772C4—361no—
773C4—361no—
774C4—361no—
775C4—361no—
776C4#6431311yescharacteristic
777C4#6431311yescharacteristic
778C3—21no—
779C3#7868211yescharacteristic, complemented
780C3#8019211yescharacteristic, complemented
781C2—41no—
782C2—121no—
783C2—121no—
784C2#1059429011yescharacteristic
785C2#1059469111yescharacteristic
786C2#1059472111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
hypercenterC22⋊C8D32
hypocenterC32#3202
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #10592422C2semidirect
4. C3×#4739C2semidirect
6. #10591186C2semidirect
7. #10591127C2semidirect
8. #10590949C2semidirect
9. #10590949C2semidirect
10. #10590854C2semidirect
11. #10590851C2semidirect
12. #10590849C2semidirect
13. #10590848C2semidirect
14. #10590711C2semidirect
15. #10590710C2semidirect
84. #4739D3semidirect
697. C32#3202semidirect
779. C3#78682semidirect
780. C3#80192semidirect

Maximal subgroups

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

subgroupindex
#105948842
#105948552
#105924222
C3×#47392
C3×#47272
#105911862
#105911272
#105909492
#105908542
#105908512
#105908492
#105908482
#105907112
#105907102
#801923
#786823