Finite Group Databasebeta

← #11889407

Subgroups — #11889407

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 777 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596113C211yesmaximal, characteristic
2#10594803C211yesmaximal, characteristic
3C3×#5051C211yesmaximal, characteristic, complemented
4C3×#5050C211yesmaximal, characteristic, complemented
5#10591654C211yesmaximal, characteristic, complemented
6#10591633C211yesmaximal, characteristic, complemented
7#10591600C211yesmaximal, characteristic, complemented
8#10591582C211yesmaximal, characteristic, complemented
9#10591157C211yesmaximal, characteristic
10#10591126C211yesmaximal, characteristic, complemented
11C2×#63566C211yesmaximal, characteristic, complemented
12#10590602C211yesmaximal, characteristic, complemented
13#10590568C211yesmaximal, characteristic, complemented
14#10590526C211yesmaximal, characteristic, complemented
15#10590494C211yesmaximal, characteristic, complemented
16#80782—31nomaximal
17#80195—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C2×#3797C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21#64155C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23C4×#638C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25#64107—21no—
26#64101C2211yescharacteristic
27#64099—21no—
28#64099C2211yescharacteristic
29#64095—21no—
30#64086—21no—
31C2×C3×#216C2211yescharacteristic
32C2×C3×#216C2211yescharacteristic
33C2×C3×#216C2211yescharacteristic
34C3×#924C2211yescharacteristic
35C22×C3×C3⋊C8C2211yescharacteristic
36#63964—21no—
37#63952—21no—
38#63888—21no—
39#63873C2211yescharacteristic
40#63871C2211yescharacteristic
41#63843C2211yescharacteristic
42#63839—21no—
43C2×#3712C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#830C2211yescharacteristic
46C3×#810C2211yescharacteristic
47C3×#810C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#807C2211yescharacteristic
50#63573C2211yescharacteristic
51#63573C2211yescharacteristic
52#63572C2211yescharacteristic
53#63566C2211yescharacteristic
54#63566C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63557C2211yescharacteristic
60#63555C2211yescharacteristic
61Q8×#67—31no—
62#5642—31no—
63#5642—31no—
64#5642—61no—
65#5632—31no—
66C3×#467—31no—
67C3×#451—31no—
68C2×#835—31no—
69#5189—31no—
70#5186—31no—
71#5186—31no—
72#5184—31no—
73#5182—31no—
74#5182—31no—
75#5111—31no—
76C2×#816—31no—
77#5051D311yescharacteristic, complemented
78#5050D311yescharacteristic, complemented
79#5043—31no—
80#4888—31no—
81#4877—31no—
82#4816—31no—
83#4815—31no—
84#4802—31no—
85#4802—31no—
86#4799—31no—
87#4797—31no—
88#4797—31no—
89#4789—31no—
90#4730—31no—
91#4721—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638D411yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C22×C3×Dic3—21no—
98C2×C3×Dic6—22no—
99C2×C3×Dic6—21no—
100C2×C3×Dic6—41no—
101C2×C3×Dic6C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#624—21no—
106#3797—22no—
107#3797—41no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111#3757D411yescharacteristic
112#3752—21no—
113#3752—21no—
114#3752D411yescharacteristic
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121#3750—21no—
122#3750D411yescharacteristic
123C4×C3⋊Dic3—21no—
124C4×C3⋊Dic3—21no—
125C4×C3⋊Dic3C2311yescharacteristic
126C3×#217—21no—
127C3×#216—22no—
128C3×#216—41no—
129C3×#216—41no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C2×C3×C3⋊C8—41no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138#3724—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141#3722—21no—
142Dic32—21no—
143#3712—41no—
144#3312—91noSylow
145C22×C3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8—31no—
148C22×Dic6C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C2×C3×Q16—31no—
152C22×C3×C8—31no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8C2×D311yescharacteristic
156C3×C22⋊Q8C2×D311yescharacteristic
157#946—31no—
158#946—31no—
159#946—31no—
160#946—61no—
161#946—61no—
162Q8×Dic3—31no—
163Q8×Dic3—31no—
164Q8×Dic3—31no—
165Q8×Dic3—61no—
166#944—31no—
167#944—31no—
168#944—61no—
169C2×#216C2×D311yescharacteristic
170C2×#216C2×D311yescharacteristic
171C2×#216C2×D311yescharacteristic
172C4×#67—31no—
173C4×#67—31no—
174C4×#67—61no—
175C4×#67—61no—
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—61no—
179#924—61no—
180#924C2×D311yescharacteristic
181C22×C3⋊C8C2×D311yescharacteristic
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—31no—
184#898—61no—
185#898—61no—
186#898—62no—
187#897—31no—
188#896—61no—
189#892—31no—
190#892—31no—
191#892—61no—
192#890—31no—
193#890—31no—
194#890—61no—
195#890—61no—
196#890—61no—
197#890—62no—
198#888—61no—
199#887—31no—
200#886—61no—
201#886—61no—
202#886—62no—
203#67⋊C4—61no—
204#878—61no—
205#877—61no—
206#877—61no—
207#877—62no—
208C3×#107—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×C22⋊C8—31no—
214#835—31no—
215#835—31no—
216#835—31no—
217#835—31no—
218#835—31no—
219#835—31no—
220#835C2×D311yescharacteristic
221#830C2×D311yescharacteristic
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224#817—31no—
225#817—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232#815—31no—
233#815—31no—
234Dic3⋊C8—31no—
235Dic3⋊C8—31no—
236#810C2×D311yescharacteristic
237#810C2×D311yescharacteristic
238#810C2×D311yescharacteristic
239#808—31no—
240#808—31no—
241#807C2×D311yescharacteristic
242C23×C32C2×D411yescharacteristic
243C22×C3⋊D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252#638—22no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—42no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C4×C3⋊D3—21no—
260C4×C3⋊D3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—42no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—42no—
272C3×Dic6#4112yes—
273#627—42no—
274#624—42no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280D4×Q8—91no—
281#491—91no—
282#485—91no—
283#483—91no—
284#479—91no—
285#470—91no—
286#467—31no—
287#462—91no—
288#451—31no—
289#451—91no—
290#441—91no—
291#435—91no—
292#419—91no—
293C2×#103—91no—
294C2×C3×Q8—21no—
295C2×C3×Q8—31no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×Q8—62no—
299C2×C3×Q8—61no—
300C2×C3×Q8—121no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C22×C3×C4—21no—
304C22×C3×C4—61no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—31no—
308C2×#67—31no—
309C2×#67—61no—
310C22×Dic3—21no—
311C22×Dic3—62no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314D3×Q8—62no—
315D3×Q8—62no—
316D3×Q8—121no—
317D3×Q8—121no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×Dic6—22no—
324C2×Dic6—21no—
325C2×Dic6—41no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C3×Q16—62no—
332C3×Q16—121no—
333C3×Q16—121no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8—121no—
339C3×C4⋊C4—22no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C22⋊C4—22no—
348C3×C22⋊C4—21no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—61no—
351#217—21no—
352#217—31no—
353#217—31no—
354#217—61no—
355#216—22no—
356#216—41no—
357#216—41no—
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—31no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—62no—
368(C2×D3)⋊C4—62no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—62no—
382C4⋊Dic3—62no—
383C4⋊Dic3—62no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—31no—
389Dic3⋊C4—31no—
390Dic3⋊C4—61no—
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—62no—
402Dic3⋊C4—62no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—61no—
411C4×Dic3—61no—
412C4×Dic3—62no—
413C4×Dic3—62no—
414C2×C3⋊C8—41no—
415C2×C3⋊C8C22×D311yescharacteristic
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418C2×C3⋊C8C22×D311yescharacteristic
419ΓL(1,𝔽25)—121no—
420ΓL(1,𝔽25)—121no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32#13712yes—
424C22×C32C22×D411yescharacteristic
425C2×C3⋊D3—21no—
426C2×C3⋊D3—21no—
427C2×C3⋊D3—21no—
428C32×C4—21no—
429C32×C4—41no—
430C32×C4—41no—
431C32×C4C2×#4111yescharacteristic
432C32×C4H(5,𝔽2)11yescharacteristic
433C3⋊Dic3—21no—
434C3⋊Dic3—21no—
435C3⋊Dic3—21no—
436C3⋊Dic3—41no—
437C3⋊Dic3—41no—
438C3×Dic3—22no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C22×Q8—31no—
443C22×Q8—91no—
444C2×Q16—31no—
445C2×Q16—31no—
446C2×Q16—31no—
447C2×M16—91no—
448C22×C8—31no—
449C4⋊Q8—91no—
450C4⋊Q8—181no—
451#126—181no—
452#125—91no—
453#125—181no—
454#123—181no—
455C22⋊Q8—31no—
456C22⋊Q8—91no—
457C22⋊Q8—91no—
458C22⋊Q8—181no—
459C22⋊Q8—181no—
460C22⋊Q8D3211yescharacteristic
461C4×Q8—91no—
462C4×Q8—91no—
463C4×D4—91no—
464C4×D4—181no—
465#117—91no—
466#117—181no—
467C2×C4⋊C4—91no—
468#107—31no—
469#106—91no—
470#106—91no—
471C4⋊C8—91no—
472#103—31no—
473#103—31no—
474#103—31no—
475#103—31no—
476#103—91no—
477#103—91no—
478#103—91no—
479#103—91no—
480#103—91no—
481#103—91no—
482C22⋊C8—31no—
483C22⋊C8—91no—
484#97—91no—
485C23×C3—21no—
486C23×C3D3×D411yescharacteristic
487C23×C3D3×D411yescharacteristic
488C22×D3—31no—
489C22×D3—31no—
490C22×D3—61no—
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—32no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×Q8—61no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×Q8—61no—
502C3×Q8—61no—
503C3×Q8—122no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—122no—
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527#67—62no—
528#67—62no—
529#67—122no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—42no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—62no—
545C2×Dic3—62no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—124no—
551C2×Dic3—122no—
552C2×Dic3—122no—
553C4×D3—61no—
554C4×D3—61no—
555C4×D3—61no—
556C4×D3—61no—
557C4×D3—121no—
558C4×D3—121no—
559C4×D3—122no—
560C4×D3—122no—
561Dic6—21no—
562Dic6—21no—
563Dic6—21no—
564Dic6—21no—
565Dic6—21no—
566Dic6—42no—
567Dic6—122no—
568Dic6—122no—
569Dic6#23712yes—
570C3×C8—61no—
571C3×C8—61no—
572C3×C8—61no—
573C3×C8—61no—
574C3⋊C8—21no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C2×C32—22no—
579C2×C32#54611yescharacteristic
580C2×C32C2×#13711yescharacteristic
581C2×C32#57811yescharacteristic
582C3⋊D3—41no—
583C2×Q8—31no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×Q8—62no—
587C2×Q8—61no—
588C2×Q8—121no—
589C2×Q8—181no—
590C2×Q8—182no—
591C2×Q8—361no—
592C2×Q8C2×D3211yescharacteristic
593C2×D4—91no—
594C22×C4—61no—
595C22×C4—91no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4C2×D3211yescharacteristic
599Q16—62no—
600Q16—121no—
601Q16—121no—
602M16—361no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8—31no—
607C2×C8—121no—
608C4⋊C4—21no—
609C4⋊C4—31no—
610C4⋊C4—61no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4C2×D3211yescharacteristic
624C22⋊C4—21no—
625C22⋊C4—61no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C42—91no—
632C42—181no—
633C42—181no—
634C42—181no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—22no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3#91812yes—
644C22×C3#91812yes—
645C22×C3C2×D3×D411yescharacteristic
646C22×C3C2×D3×D411yescharacteristic
647C2×D3—61no—
648C2×D3—61no—
649C2×D3—61no—
650C2×D3—61no—
651C2×D3—61no—
652C2×D3—61no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—41no—
661C3×C4—42no—
662C3×C4—42no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—62no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4C2×#23711yescharacteristic
672C3×C4#100411yescharacteristic
673C3×C4#100411yescharacteristic
674C3×C4D3×#4111yescharacteristic
675Dic3—22no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—61no—
680Dic3—61no—
681Dic3—61no—
682Dic3—61no—
683Dic3—61no—
684Dic3—61no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—122no—
689Dic3—122no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694C32#331211yescharacteristic, complemented, Sylow
695C23—91no—
696C23#381111yescharacteristic
697Q8—21no—
698Q8—21no—
699Q8—32no—
700Q8—61no—
701Q8—61no—
702Q8—61no—
703Q8—61no—
704Q8—61no—
705Q8—122no—
706Q8—362no—
707D4—182no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—91no—
717C2×C4—91no—
718C2×C4—91no—
719C2×C4—122no—
720C2×C4—181no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4—181no—
724C2×C4—362no—
725C2×C4—362no—
726C2×C4#381111yescharacteristic
727C2×C4C22×D3211yescharacteristic
728C8—61no—
729C8—61no—
730C8—61no—
731C8—61no—
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3#559111yescharacteristic
739C2×C3#561011yescharacteristic
740C2×C3C2×#91811yescharacteristic
741C2×C3C2×#91811yescharacteristic
742C2×C3#577111yescharacteristic
743C2×C3#577911yescharacteristic
744D3—121no—
745D3—121no—
746D3—241no—
747C22—21no—
748C22—21no—
749C22—181no—
750C22—181no—
751C22—181no—
752C22#6394512yes—
753C22C2×#381111yescharacteristic
754C4—21no—
755C4—41no—
756C4—41no—
757C4—62no—
758C4—121no—
759C4—121no—
760C4—121no—
761C4—181no—
762C4—181no—
763C4—181no—
764C4—361no—
765C4—361no—
766C4D3×#23711yescharacteristic
767C4#6431311yescharacteristic
768C3—21no—
769C3#8019511yescharacteristic, complemented
770C3#8078211yescharacteristic, complemented
771C2—22no—
772C2—361no—
773C2#1059530711yescharacteristic
774C2C2×#6394511yescharacteristic
775C2#1059547211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#638D4
hypercenterC22⋊Q8D32
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5051C2semidirect
4. C3×#5050C2semidirect
5. #10591654C2semidirect
6. #10591633C2semidirect
7. #10591600C2semidirect
8. #10591582C2semidirect
10. #10591126C2semidirect
11. C2×#63566C2semidirect
12. #10590602C2semidirect
13. #10590568C2semidirect
14. #10590526C2semidirect
15. #10590494C2semidirect
77. #5051D3semidirect
78. #5050D3semidirect
694. C32#3312semidirect
769. C3#80195semidirect
770. C3#80782semidirect

Maximal subgroups

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

subgroupindex
#105961132
#105948032
C3×#50512
C3×#50502
#105916542
#105916332
#105916002
#105915822
#105911572
#105911262
C2×#635662
#105906022
#105905682
#105905262
#105904942
#807823
#801953