Finite Group Databasebeta

← #11889236

Subgroups — #11889236

Order 1152.

883 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595246C211yesmaximal, characteristic
2#10594565C211yesmaximal, characteristic, complemented
3#10592471C211yesmaximal, characteristic, complemented
4C3×#4770C211yesmaximal, characteristic, complemented
5C3×#4757C211yesmaximal, characteristic, complemented
6#10591466C211yesmaximal, characteristic, complemented
7#10591458C211yesmaximal, characteristic, complemented
8#10591408C211yesmaximal, characteristic, complemented
9#10590895C211yesmaximal, characteristic, complemented
10#10590849C211yesmaximal, characteristic, complemented
11#10590841C211yesmaximal, characteristic, complemented
12#10590736C211yesmaximal, characteristic, complemented
13#10590532C211yesmaximal, characteristic, complemented
14#10590512C211yesmaximal, characteristic, complemented
15#10590429C211yesmaximal, characteristic, complemented
16#79801—31nomaximal
17#78935—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic, complemented
21#64101C2211yescharacteristic, complemented
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
25C3×#892C2211yescharacteristic
26C3×#887C2211yescharacteristic, complemented
27#63978—21no—
28#63977—21no—
29#63962—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63918C2211yescharacteristic, complemented
32C4×#627—21no—
33#63916C2211yescharacteristic
34C4×#626C2211yescharacteristic
35#63871C2211yescharacteristic, complemented
36#63868—21no—
37#63862—21no—
38#63860C2211yescharacteristic
39#63857C2211yescharacteristic
40#63856C2211yescharacteristic
41#63852—21no—
42C2×#3719C2211yescharacteristic, complemented
43C2×#3715C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63643C2211yescharacteristic, complemented
47#63637C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#816C2211yescharacteristic, complemented
51C3×#815C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5806—31no—
62#5584—31no—
63#5554—31no—
64#5533—31no—
65C3×#440—31no—
66C3×#418—31no—
67#5218—31no—
68#5173—31no—
69#5169—31no—
70#5137—31no—
71#5127—31no—
72#5028—31no—
73#5008—31no—
74#4996—31no—
75#4888—31no—
76#4885—31no—
77#4816—31no—
78#4807—31no—
79#4783—31no—
80#4779—31no—
81#4778—31no—
82#4772—31no—
83#4772—31no—
84#4772—61no—
85#4770D311yescharacteristic, complemented
86#4767—31no—
87#4765—31no—
88#4761—31no—
89#4757D311yescharacteristic, complemented
90#4714—31no—
91#4706—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C22×C3⋊Dic3—21no—
96#3830—22no—
97#3830—41no—
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C3×D3×D4—22no—
103C3×D3×D4—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#627—21no—
108C2×#626—21no—
109C2×#626D411yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4×C3⋊Dic3—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C8×C3⋊D3—41no—
117C3×#217—21no—
118C3×#214—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×ΓL(1,𝔽25)—41no—
129#3724—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135#3722D411yescharacteristic
136(C2×D3)⋊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)⋊Dic3D411yescharacteristic
142#3719—41no—
143#3715—41no—
144#3311—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#237—31no—
148C2×#237—61no—
149C2×D3×D4C2×D311yescharacteristic
150C2×C3×SD16—31no—
151C2×C3×M16—31no—
152C3×C4×Q8—31no—
153C3×C4×D4—31no—
154C3×#117—31no—
155#953—61no—
156C2×#217—61no—
157#946—31no—
158#946—31no—
159C2×#216—31no—
160C2×#215—31no—
161#939—61no—
162#938—31no—
163#936—31no—
164#935—61no—
165D4×Dic3C2×D311yescharacteristic
166C2×#214—31no—
167C2×#214C2×D311yescharacteristic
168#930—61no—
169C4×#67—31no—
170C2×(C2×D3)⋊C4—61no—
171#924—31no—
172#924—31no—
173C2×Dic12—31no—
174C2×ΓL(1,𝔽25)C2×D311yescharacteristic
175C2×D3×C8—31no—
176C2×D3×C8—31no—
177C2×D3×C8—61no—
178#898—61no—
179#898—61no—
180#897—31no—
181#897—31no—
182#895—31no—
183#892—31no—
184#892—31no—
185#892—61no—
186#892C2×D311yescharacteristic
187#888—31no—
188#887C2×D311yescharacteristic, complemented
189#886—61no—
190#885—61no—
191#882—61no—
192#879—61no—
193#876—61no—
194#875—31no—
195#875—61no—
196C4×D12—31no—
197#869—31no—
198C4×Dic6—61no—
199C4×Dic6—61no—
200C3×#107—31no—
201C3×#103—31no—
202C3×#102—21no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic
207C3×#102C2×D311yescharacteristic
208C3×#97—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—61no—
213#832C2×D311yescharacteristic
214#830—31no—
215#821—31no—
216#821C2×D311yescharacteristic
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220#817—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—61no—
225#816C2×D311yescharacteristic, complemented
226#815C2×D311yescharacteristic, complemented
227Dic3⋊C8—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—61no—
232#809C2×D311yescharacteristic
233#808—31no—
234#808—31no—
235#808—31no—
236#807C2×D311yescharacteristic, complemented
237C4⋊(C3⋊C8)—31no—
238C23×C32—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249#638—42no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—42no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4×C3⋊D3—21no—
255C4×C3⋊D3—21no—
256#634—21no—
257#634—21no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—81no—
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—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#627—42no—
273#626—41no—
274#626—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—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290#440—31no—
291#435—91no—
292#418—31no—
293#416—91no—
294C24×C3—61no—
295C23×D3—21no—
296C2×C3×Q8—31no—
297C2×C3×D4—21no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C2×C3×D4—62no—
301C2×C3×D4—121no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C2×#67—21no—
307C2×#67—31no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—121no—
312C22×Dic3—21no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—121no—
316#237—64no—
317#237—62no—
318#237—62no—
319#237—121no—
320#237—121no—
321#237—122no—
322D3×D4—22no—
323D3×D4—41no—
324C2×D12—31no—
325C2×D12—61no—
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—31no—
332C2×Dic6—31no—
333C2×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6C22×D311yescharacteristic
337C3×SD16—62no—
338C3×M16—121no—
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—31no—
353C3×C42—61no—
354C3×C42—61no—
355#217—21no—
356#217—31no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#216—121no—
363#215—121no—
364#214—22no—
365#214—121no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
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—
379(C2×D3)⋊C4—121no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—31no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396C4×Dic3—21no—
397C4×Dic3—21no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—121no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407Dic12—121no—
408ΓL(1,𝔽25)—41no—
409D3×C8—121no—
410D3×C8—121no—
411D3×C8—122no—
412C22×C32—22no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—84no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—91no—
439C22×D4—31no—
440C2×Q16—91no—
441C2×SD16—31no—
442C2×SD16—91no—
443C2×M16—31no—
444C22×C8—91no—
445C4⋊Q8—91no—
446#126—181no—
447#126—181no—
448#124—91no—
449#124—181no—
450#123—181no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453C22⋊Q8—91no—
454#121—91no—
455#121—181no—
456#120—181no—
457C4×Q8—31no—
458C4×Q8—181no—
459C4×D4—31no—
460C4×D4—91no—
461#117—31no—
462#117—91no—
463C2×C22⋊C4—181no—
464#107—31no—
465#106—91no—
466#106—91no—
467C4⋊C8—91no—
468#103—31no—
469#103—91no—
470#103—91no—
471#103—91no—
472#102—31no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102D3211yescharacteristic
478C22⋊C8—91no—
479C22⋊C8—91no—
480#97—31no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—41no—
485C23×C3—61no—
486C23×C3—122no—
487C23×C3—122no—
488C23×C3—241no—
489C22×D3—21no—
490C22×D3—31no—
491C22×D3—31no—
492C22×D3—42no—
493C22×D3—42no—
494C22×D3—61no—
495C22×D3—81no—
496C22×D3D3×D411yescharacteristic
497C3×Q8—61no—
498C3×Q8—61no—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—22no—
502C3×D4—41no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—122no—
506C3×D4#23512yes—
507C3×D4#23512yes—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—41no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—241no—
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—42no—
524#67—121no—
525#67—122no—
526#67—122no—
527#67—124no—
528#67—241no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—81no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—122no—
543C2×Dic3—122no—
544C2×Dic3—124no—
545C2×Dic3D3×D411yescharacteristic
546C2×Dic3D3×D411yescharacteristic
547C2×Dic3D3×D411yescharacteristic
548D12—21no—
549D12—21no—
550D12—121no—
551D12—241no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—62no—
555C4×D3—62no—
556C4×D3—61no—
557C4×D3—61no—
558C4×D3—61no—
559C4×D3—61no—
560Dic6—21no—
561Dic6—21no—
562Dic6—62no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—61no—
567Dic6—121no—
568Dic6—122no—
569Dic6—122no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—41no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—121no—
580C2×C32—42no—
581C2×C32#54611yescharacteristic
582C2×C32#57511yescharacteristic
583C2×C32#57711yescharacteristic
584C3⋊D3—41no—
585C3×D3—41no—
586C3×D3—81no—
587C24—61no—
588#41—182no—
589#41—361no—
590C2×Q8—31no—
591C2×Q8—91no—
592C2×Q8—181no—
593C2×D4—31no—
594C2×D4—61no—
595C2×D4—62no—
596C2×D4—91no—
597C2×D4—121no—
598C2×D4—181no—
599C2×D4—181no—
600C2×D4C2×D3211yescharacteristic
601C22×C4—31no—
602C22×C4—61no—
603C22×C4—91no—
604C22×C4—181no—
605Q16—361no—
606SD16—62no—
607SD16—361no—
608M16—121no—
609C2×C8—31no—
610C2×C8—31no—
611C2×C8—91no—
612C2×C8—361no—
613C2×C8C2×D3211yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—91no—
618C4⋊C4—91no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4C2×D3211yescharacteristic
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C42—31no—
636C42—61no—
637C42—61no—
638C42—181no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—21no—
642C22×C3—42no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3—244no—
656C22×C3C2×D3×D411yescharacteristic
657C22×C3C2×D3×D411yescharacteristic
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—62no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—84no—
672C2×D3—121no—
673C2×D3—121no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—81no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4C2×#23511yescharacteristic
686C3×C4C2×#23511yescharacteristic
687C3×C4#100411yescharacteristic
688C3×C4#100911yescharacteristic
689Dic3—21no—
690Dic3—21no—
691Dic3—21no—
692Dic3—41no—
693Dic3—41no—
694Dic3—41no—
695Dic3—62no—
696Dic3—61no—
697Dic3—61no—
698Dic3—122no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—241no—
704C32#331111yescharacteristic, complemented, Sylow
705C23—21no—
706C23—31no—
707C23—61no—
708C23—91no—
709C23—122no—
710C23—122no—
711C23—241no—
712Q8—61no—
713Q8—61no—
714Q8—181no—
715Q8—181no—
716Q8—362no—
717D4—21no—
718D4—61no—
719D4—61no—
720D4—122no—
721D4—361no—
722D4—362no—
723D4—721no—
724D4#379812yes—
725C2×C4—21no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—91no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—241no—
740C2×C4—362no—
741C2×C4C22×D3211yescharacteristic
742C8—21no—
743C8—61no—
744C8—61no—
745C8—181no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—42no—
750C2×C3—42no—
751C2×C3—82no—
752C2×C3—121no—
753C2×C3—241no—
754C2×C3#549011yescharacteristic
755C2×C3#555011yescharacteristic
756C2×C3#577311yescharacteristic
757C2×C3#577511yescharacteristic
758C2×C3#577511yescharacteristic
759C2×C3#577711yescharacteristic
760D3—41no—
761D3—81no—
762D3—122no—
763D3—121no—
764D3—121no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—181no—
775C22—181no—
776C22—181no—
777C22—244no—
778C22D32×D411yescharacteristic
779C4—41no—
780C4—61no—
781C4—61no—
782C4—61no—
783C4—121no—
784C4—121no—
785C4—121no—
786C4—181no—
787C4—361no—
788C4—361no—
789C4C2×#379811yescharacteristic
790C4#6431411yescharacteristic
791C3—21no—
792C3#7893511yescharacteristic, complemented
793C3#7980111yescharacteristic, complemented
794C2—42no—
795C2—121no—
796C2—241no—
797C2—361no—
798C2#1059418611yescharacteristic
799C2#1059473311yescharacteristic
800C2#1059474411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595246C2
hypercenter#102D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594565C2semidirect
3. #10592471C2semidirect
4. C3×#4770C2semidirect
5. C3×#4757C2semidirect
6. #10591466C2semidirect
7. #10591458C2semidirect
8. #10591408C2semidirect
9. #10590895C2semidirect
10. #10590849C2semidirect
11. #10590841C2semidirect
12. #10590736C2semidirect
13. #10590532C2semidirect
14. #10590512C2semidirect
15. #10590429C2semidirect
20. C2×C8×C3⋊D3C22semidirect
21. #64101C22semidirect
26. C3×#887C22semidirect
31. #63918C22semidirect
35. #63871C22semidirect
42. C2×#3719C22semidirect
46. #63643C22semidirect
47. #63637C22semidirect
50. C3×#816C22semidirect
51. C3×#815C22semidirect
53. C3×#807C22semidirect
54. #63574C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
59. #63557C22semidirect
85. #4770D3semidirect
89. #4757D3semidirect
188. #887C2×D3semidirect
225. #816C2×D3semidirect
226. #815C2×D3semidirect
236. #807C2×D3semidirect
704. C32#3311semidirect
792. C3#78935semidirect
793. C3#79801semidirect

Maximal subgroups

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

subgroupindex
#105952462
#105945652
#105924712
C3×#47702
C3×#47572
#105914662
#105914582
#105914082
#105908952
#105908492
#105908412
#105907362
#105905322
#105905122
#105904292
#798013
#789353