Finite Group Databasebeta

← #11889266

Subgroups — #11889266

Order 1152.

857 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595229C211yesmaximal, characteristic
2#10594557C211yesmaximal, characteristic, complemented
3#10592483C211yesmaximal, characteristic, complemented
4C3×#4776C211yesmaximal, characteristic, complemented
5C3×#4765C211yesmaximal, characteristic, complemented
6#10591465C211yesmaximal, characteristic, complemented
7#10591442C211yesmaximal, characteristic, complemented
8#10591421C211yesmaximal, characteristic, complemented
9#10590961C211yesmaximal, characteristic, complemented
10#10590766C211yesmaximal, characteristic, complemented
11#10590739C211yesmaximal, characteristic, complemented
12#10590710C211yesmaximal, characteristic, complemented
13#10590611C211yesmaximal, characteristic, complemented
14#10590520C211yesmaximal, characteristic, complemented
15#10590465C211yesmaximal, characteristic, complemented
16#81698—31nomaximal
17#80162—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20#64147C2211yescharacteristic
21#64101C2211yescharacteristic, complemented
22C3×#936C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×#888C2211yescharacteristic, complemented
27#63977—21no—
28#63971—21no—
29#63969—21no—
30D3×#217—21no—
31#63907—21no—
32C4×#626C2211yescharacteristic
33Dic3×D12C2211yescharacteristic
34#63871C2211yescharacteristic, complemented
35#63862—21no—
36#63856C2211yescharacteristic
37#63848—21no—
38#63843—21no—
39Dic3×Dic6C2211yescharacteristic, complemented
40#63841C2211yescharacteristic
41C2×#3718C2211yescharacteristic, complemented
42C2×#3711C2211yescharacteristic
43C2×#3710C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63647C2211yescharacteristic, complemented
47#63645C2211yescharacteristic, complemented
48#63635C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×#810C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61#5806—31no—
62#5732—31no—
63#5676—31no—
64#5641—31no—
65C3×#489—31no—
66C3×#450—31no—
67#5215—31no—
68#5173—31no—
69#5171—31no—
70#5166—31no—
71#5164—31no—
72#5084—31no—
73#5054—31no—
74#5052—31no—
75#4816—31no—
76#4814—31no—
77#4808—31no—
78#4804—31no—
79#4784—31no—
80#4784—31no—
81#4784—61no—
82#4778—31no—
83#4776D311yescharacteristic, complemented
84#4772—31no—
85#4770—31no—
86#4765D311yescharacteristic, complemented
87#4761—31no—
88#4728—31no—
89#4723—31no—
90#4710—31no—
91#4706—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×#67—21no—
97C3×D3×D4—22no—
98C3×D3×D4—41no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626D411yescharacteristic
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3796—22no—
109#3796—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3757—21no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#214—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×#204—22no—
129#3724—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133#3722—21no—
134#3722D411yescharacteristic
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139Dic32—21no—
140Dic32—21no—
141#3718—41no—
142#3711—41no—
143#3710—41no—
144#3311—91noSylow
145C22×C3×D4—31no—
146C2×#239—31no—
147C2×#237—31no—
148C2×D3×D4C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C3×C4⋊Q8—31no—
152C3×#124—31no—
153C3×C22⋊Q8—31no—
154#953—61no—
155C2×#217—61no—
156#947—61no—
157#946—31no—
158#946—31no—
159Q8×Dic3—31no—
160Q8×Dic3—61no—
161C2×#216—31no—
162C2×#216—31no—
163#939—61no—
164#938—31no—
165#938—31no—
166#938—61no—
167#936C2×D311yescharacteristic
168#935—61no—
169D4×Dic3—31no—
170C2×#214C2×D311yescharacteristic
171C4×#67—31no—
172#926—31no—
173#924—31no—
174C2×#208—31no—
175C2×#204C2×D311yescharacteristic
176C2×ΓL(1,𝔽25)—31no—
177C2×D3×C8—31no—
178C2×D3×C8—31no—
179#898—61no—
180#898—61no—
181#898—61no—
182#897—31no—
183#897C2×D311yescharacteristic
184#892—31no—
185#892—31no—
186#892—31no—
187#892—61no—
188#888C2×D311yescharacteristic, complemented
189#887—61no—
190#885—61no—
191#884—61no—
192#883—61no—
193#882—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196C4×D12—31no—
197C4×D12—31no—
198C4×Dic6—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#102—21no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102C2×D311yescharacteristic
205C3×#102C2×D311yescharacteristic
206C3×C22⋊C8—31no—
207C3×#97—31no—
208#835—31no—
209#835—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—61no—
215#832C2×D311yescharacteristic
216#821—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—61no—
220(C2×D3)⋊C8C2×D311yescharacteristic
221#818—31no—
222#818—31no—
223#818—61no—
224#817—31no—
225#816—31no—
226#816—31no—
227#816C2×D311yescharacteristic, complemented
228#815C2×D311yescharacteristic, complemented
229Dic3⋊C8—31no—
230#810C2×D311yescharacteristic, complemented
231#809—31no—
232#809C2×D311yescharacteristic
233#808—31no—
234#808—31no—
235#808—31no—
236#808—61no—
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—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249#638—81no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255C3×#67—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—42no—
271#626—41no—
272#626—42no—
273D3×Dic3—42no—
274D3×Dic3—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—91no—
281#489—31no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—31no—
290#440—91no—
291#435—91no—
292#418—91no—
293#416—91no—
294C24×C3—61no—
295C23×D3—21no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×Q8—61no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C2×C3×D4—62no—
303C2×C3×D4—121no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C22×C3×C4—31no—
307C2×#67—21no—
308C2×#67—31no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—121no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315#239—62no—
316#239—121no—
317#237—62no—
318#237—121no—
319D3×D4—22no—
320D3×D4—41no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—31no—
325C2×C4×D3—31no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3C22×D311yescharacteristic
330C2×Dic6—21no—
331C2×Dic6C22×D311yescharacteristic
332C2×Dic6C22×D311yescharacteristic
333C3×SD16—62no—
334C3×SD16—121no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—31no—
350#217—21no—
351#217—21no—
352#217—31no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—121no—
359#216—121no—
360#216—121no—
361#214—41no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—31no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—121no—
374C4⋊Dic3—21no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—31no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—121no—
398C4×Dic3C22×D311yescharacteristic
399#208—121no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405#204—22no—
406ΓL(1,𝔽25)—121no—
407D3×C8—121no—
408D3×C8—121no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3×D3—22no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—84no—
423C32×C4—41no—
424C32×C4C2×#4111yescharacteristic
425C32×C4H(5,𝔽2)11yescharacteristic
426C3⋊Dic3—21no—
427C3⋊Dic3—41no—
428C3⋊Dic3—41no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—91no—
436C22×D4—31no—
437C2×Q16—91no—
438C2×SD16—31no—
439C2×SD16—31no—
440C2×M16—91no—
441C22×C8—91no—
442C4⋊Q8—31no—
443#126—181no—
444#126—181no—
445#124—31no—
446#124—181no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451#121—91no—
452#121—181no—
453#120—181no—
454C4×Q8—91no—
455C4×Q8—181no—
456C4×D4—91no—
457C4×D4—91no—
458#117—91no—
459#117—91no—
460C2×C22⋊C4—181no—
461#107—91no—
462#106—91no—
463#106—91no—
464C4⋊C8—91no—
465#103—31no—
466#103—31no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—31no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102D3211yescharacteristic
475C22⋊C8—31no—
476C22⋊C8—91no—
477#97—31no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—31no—
481C23×C3—41no—
482C23×C3—61no—
483C23×C3—122no—
484C23×C3—122no—
485C23×C3—241no—
486C22×D3—21no—
487C22×D3—31no—
488C22×D3—31no—
489C22×D3—42no—
490C22×D3—42no—
491C22×D3—61no—
492C22×D3—81no—
493C22×D3D3×D411yescharacteristic
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8—122no—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—32no—
504C3×D4—41no—
505C3×D4—41no—
506C3×D4—61no—
507C3×D4—122no—
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×C4C23×D311yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522#67—42no—
523#67—121no—
524#67—122no—
525#67—241no—
526#67—241no—
527#67—242no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—122no—
541C2×Dic3—241no—
542C2×Dic3D3×D411yescharacteristic
543C2×Dic3D3×D411yescharacteristic
544C2×Dic3D3×D411yescharacteristic
545D12—21no—
546D12—121no—
547D12—122no—
548D12#23712yes—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—61no—
555C4×D3—121no—
556C4×D3—121no—
557C4×D3—122no—
558C4×D3—241no—
559Dic6—21no—
560Dic6—21no—
561Dic6—21no—
562Dic6—21no—
563Dic6—42no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—41no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C3⋊C8—61no—
572C3⋊C8—61no—
573C3⋊C8—121no—
574C2×C32—81no—
575C2×C32#54611yescharacteristic
576C2×C32#57511yescharacteristic
577C2×C32#57711yescharacteristic
578C3⋊D3—41no—
579C3×D3—41no—
580C3×D3—42no—
581C24—61no—
582#41—182no—
583#41—361no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×Q8—61no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—62no—
590C2×D4—91no—
591C2×D4—121no—
592C2×D4—181no—
593C2×D4—181no—
594C2×D4C2×D3211yescharacteristic
595C22×C4—31no—
596C22×C4—91no—
597C22×C4—181no—
598C22×C4—181no—
599Q16—361no—
600SD16—62no—
601SD16—121no—
602M16—361no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—91no—
606C2×C8—361no—
607C2×C8C2×D3211yescharacteristic
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4C2×D3211yescharacteristic
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—91no—
622C22⋊C4—91no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C42—31no—
630C42—181no—
631C42—181no—
632C42—181no—
633C22×C3—21no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—62no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—244no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C2×D3×D411yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—22no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—84no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—81no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4C2×#23711yescharacteristic
680C3×C4#100411yescharacteristic
681C3×C4D3×#4111yescharacteristic
682C3×C4#100911yescharacteristic
683Dic3—21no—
684Dic3—21no—
685Dic3—21no—
686Dic3—41no—
687Dic3—41no—
688Dic3—41no—
689Dic3—61no—
690Dic3—61no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697Dic3—241no—
698C32#331111yescharacteristic, complemented, Sylow
699C23—21no—
700C23—31no—
701C23—61no—
702C23—91no—
703C23—122no—
704C23—122no—
705C23—241no—
706Q8—61no—
707Q8—61no—
708Q8—61no—
709Q8—61no—
710Q8—122no—
711D4—21no—
712D4—21no—
713D4—32no—
714D4—61no—
715D4—122no—
716D4—361no—
717D4—362no—
718D4—721no—
719C2×C4—21no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—91no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—362no—
734C2×C4—721no—
735C2×C4C22×D3211yescharacteristic
736C8—21no—
737C8—61no—
738C8—61no—
739C8—181no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—81no—
744C2×C3—81no—
745C2×C3—121no—
746C2×C3—122no—
747C2×C3—161no—
748C2×C3#559111yescharacteristic
749C2×C3#567611yescharacteristic
750C2×C3#576211yescharacteristic
751C2×C3#577311yescharacteristic
752C2×C3#577311yescharacteristic
753C2×C3#577811yescharacteristic
754D3—41no—
755D3—42no—
756D3—121no—
757D3—121no—
758D3—241no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—62no—
766C22—121no—
767C22—121no—
768C22—181no—
769C22—181no—
770C22—181no—
771C22—244no—
772C22D32×D411yescharacteristic
773C4—41no—
774C4—61no—
775C4—61no—
776C4—61no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4—181no—
781C4—361no—
782C4—361no—
783C4#6430711yescharacteristic
784C4D3×#23711yescharacteristic
785C3—21no—
786C3#8016211yescharacteristic, complemented
787C3#8169811yescharacteristic, complemented
788C2—81no—
789C2—121no—
790C2—122no—
791C2—361no—
792C2#1059428111yescharacteristic
793C2#1059472811yescharacteristic
794C2#1059475111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595229C2
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. #10594557C2semidirect
3. #10592483C2semidirect
4. C3×#4776C2semidirect
5. C3×#4765C2semidirect
6. #10591465C2semidirect
7. #10591442C2semidirect
8. #10591421C2semidirect
9. #10590961C2semidirect
10. #10590766C2semidirect
11. #10590739C2semidirect
12. #10590710C2semidirect
13. #10590611C2semidirect
14. #10590520C2semidirect
15. #10590465C2semidirect
21. #64101C22semidirect
26. C3×#888C22semidirect
34. #63871C22semidirect
39. Dic3×Dic6C22semidirect
41. C2×#3718C22semidirect
43. C2×#3710C22semidirect
46. #63647C22semidirect
47. #63645C22semidirect
48. #63635C22semidirect
51. C3×#816C22semidirect
52. C3×#815C22semidirect
53. C3×#810C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
58. #63566C22semidirect
83. #4776D3semidirect
86. #4765D3semidirect
188. #888C2×D3semidirect
227. #816C2×D3semidirect
228. #815C2×D3semidirect
230. #810C2×D3semidirect
698. C32#3311semidirect
786. C3#80162semidirect
787. C3#81698semidirect

Maximal subgroups

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

subgroupindex
#105952292
#105945572
#105924832
C3×#47762
C3×#47652
#105914652
#105914422
#105914212
#105909612
#105907662
#105907392
#105907102
#105906112
#105905202
#105904652
#816983
#801623