Finite Group Databasebeta

← #11889228

Subgroups — #11889228

Order 1152.

858 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595244C211yesmaximal, characteristic
2#10594576C211yesmaximal, characteristic, complemented
3#10592460C211yesmaximal, characteristic, complemented
4C3×#4776C211yesmaximal, characteristic, complemented
5C3×#4772C211yesmaximal, characteristic, complemented
6#10591461C211yesmaximal, characteristic, complemented
7#10591446C211yesmaximal, characteristic, complemented
8#10591421C211yesmaximal, characteristic, complemented
9#10590829C211yesmaximal, characteristic, complemented
10#10590796C211yesmaximal, characteristic, complemented
11#10590723C211yesmaximal, characteristic, complemented
12#10590711C211yesmaximal, characteristic, complemented
13#10590541C211yesmaximal, characteristic, complemented
14#10590520C211yesmaximal, characteristic, complemented
15#10590505C211yesmaximal, characteristic, complemented
16#80162—31nomaximal
17#78855—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21#64097C2211yescharacteristic, complemented
22C2×C3×#214C2211yescharacteristic
23C2×C3×#204C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic, complemented
25C3×#897C2211yescharacteristic
26C3×#892C2211yescharacteristic, complemented
27#63980—21no—
28#63976—21no—
29#63961—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63913—21no—
32#63908C2211yescharacteristic
33C4×#625C2211yescharacteristic
34#63863C2211yescharacteristic
35#63859—21no—
36#63858—21no—
37#63856C2211yescharacteristic
38#63856C2211yescharacteristic, complemented
39#63844—21no—
40#63843C2211yescharacteristic, complemented
41#63841C2211yescharacteristic
42C2×#3718C2211yescharacteristic, complemented
43C2×#3711C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63644C2211yescharacteristic, complemented
47#63641C2211yescharacteristic, complemented
48#63635C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54#63575C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61#5829—31no—
62#5806—31no—
63#5641—31no—
64#5533—31no—
65C3×#450—31no—
66C3×#416—31no—
67#5239—31no—
68#5215—31no—
69#5173—31no—
70#5171—31no—
71#5166—31no—
72#5164—31no—
73#5114—31no—
74#5111—31no—
75#5052—31no—
76#5003—31no—
77#4816—31no—
78#4815—31no—
79#4798—31no—
80#4794—31no—
81#4784—31no—
82#4776D311yescharacteristic, complemented
83#4772D311yescharacteristic, complemented
84#4770—31no—
85#4765—31no—
86#4761—31no—
87#4761—31no—
88#4761—61no—
89#4757—31no—
90#4728—31no—
91#4723—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×#237—22no—
100C3×#237—41no—
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#625—21no—
109C2×#625D411yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3757—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#214—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4×Dic3—21no—
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C3×#204—41no—
127C3×D3×C8—41no—
128#3724—21no—
129#3724—21no—
130#3724D411yescharacteristic
131Dic3⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141Dic32—21no—
142#3718—41no—
143#3711—41no—
144#3311—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#237C2×D311yescharacteristic
148C2×D3×D4C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C22×C3×C8—31no—
152C3×C22⋊Q8—31no—
153C3×#117—31no—
154#953—61no—
155C2×#217—61no—
156#947—31no—
157#946—31no—
158#946—31no—
159Q8×Dic3—31no—
160C2×#216—31no—
161C2×#216—31no—
162#939—61no—
163#939—61no—
164#938—31no—
165#937—61no—
166#936—31no—
167#935—61no—
168D4×Dic3—31no—
169D4×Dic3—31no—
170D4×Dic3—61no—
171C2×#214C2×D311yescharacteristic
172#930—31no—
173#929—61no—
174C4×#67—31no—
175C4×#67—31no—
176C2×(C2×D3)⋊C4—61no—
177#926—31no—
178#924—31no—
179#924—31no—
180C2×#208—31no—
181C2×#204C2×D311yescharacteristic
182C2×ΓL(1,𝔽25)—31no—
183C2×D3×C8C2×D311yescharacteristic, complemented
184#898—61no—
185#897C2×D311yescharacteristic
186#892—31no—
187#892C2×D311yescharacteristic, complemented
188#888—31no—
189#888—31no—
190#888—61no—
191#887—31no—
192#887—61no—
193#885—61no—
194#885—61no—
195#879—61no—
196#879—61no—
197#876—61no—
198C4×Dic6—61no—
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—
207#835—31no—
208#835—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—61no—
214#832C2×D311yescharacteristic
215#830—31no—
216#821—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8C2×D311yescharacteristic
219#818—31no—
220#817—31no—
221#817—31no—
222#817—61no—
223#816—31no—
224#816—31no—
225#816C2×D311yescharacteristic, complemented
226#815—31no—
227#815—31no—
228Dic3⋊C8—31no—
229Dic3⋊C8—31no—
230Dic3⋊C8—61no—
231#810C2×D311yescharacteristic, complemented
232#809—31no—
233#809C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808—61no—
237#807—31no—
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3—42no—
241C22×C3×D3—42no—
242C22×C3×D3—81no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—81no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254#634—42no—
255C3×#67—42no—
256C3×#67—42no—
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—21no—
264C3×D12—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273#625—41no—
274#625—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—31no—
290#440—91no—
291#435—91no—
292#418—91no—
293#416—31no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4—62no—
304C2×C3×D4—61no—
305C2×C3×D4—121no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C2×#67—21no—
312C2×#67—21no—
313C2×#67—31no—
314C2×#67—31no—
315C2×#67—61no—
316C2×#67—61no—
317C22×Dic3—21no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—121no—
321#237—22no—
322#237—41no—
323D3×D4—22no—
324D3×D4—41no—
325C2×D12C22×D311yescharacteristic
326C2×C4×D3C22×D311yescharacteristic
327C2×C4×D3C22×D311yescharacteristic
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6—121no—
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×C8—121no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—61no—
349#217—31no—
350#217—31no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—121no—
360#216—121no—
361#216—121no—
362#214—22no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
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—
373C4⋊Dic3—21no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—31no—
383Dic3⋊C4—31no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—121no—
392C4×Dic3—21no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400#208—121no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406#204—41no—
407ΓL(1,𝔽25)—121no—
408D3×C8—41no—
409C22×C32—22no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
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—21no—
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—31no—
436C22×D4—31no—
437C2×Q16—91no—
438C2×SD16—31no—
439C2×SD16—31no—
440C2×M16—91no—
441C22×C8—31no—
442C4⋊Q8—91no—
443#126—181no—
444#126—181no—
445#124—91no—
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—31no—
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—91no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—31no—
481C23×C3—31no—
482C23×C3—41no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—241no—
487C22×D3—21no—
488C22×D3—42no—
489C22×D3—42no—
490C22×D3—81no—
491C22×D3D3×D411yescharacteristic
492C22×D3D3×D411yescharacteristic
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—22no—
500C3×D4—41no—
501C3×D4—61no—
502C3×D4—61no—
503C3×D4—122no—
504C3×D4—122no—
505C3×D4#23512yes—
506C3×D4#23712yes—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
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×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—42no—
524#67—42no—
525#67—121no—
526#67—121no—
527#67—241no—
528#67—241no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—42no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—121no—
544C2×Dic3—121no—
545C2×Dic3—241no—
546C2×Dic3—241no—
547C2×Dic3—242no—
548C2×Dic3D3×D411yescharacteristic
549C2×Dic3D3×D411yescharacteristic
550D12—21no—
551D12—21no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—21no—
556Dic6—21no—
557Dic6—21no—
558Dic6—21no—
559Dic6—21no—
560Dic6—122no—
561Dic6—122no—
562Dic6—242no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—41no—
566C3×C8—61no—
567C3×C8—61no—
568C3⋊C8—21no—
569C3⋊C8—21no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—121no—
573C2×C32—42no—
574C2×C32#54611yescharacteristic
575C2×C32#57511yescharacteristic
576C2×C32#57711yescharacteristic
577C3×D3—41no—
578C3×D3—41no—
579C3×D3—81no—
580C24—61no—
581#41—62no—
582#41—121no—
583C2×Q8—31no—
584C2×Q8—31no—
585C2×Q8—181no—
586C2×D4—31no—
587C2×D4—61no—
588C2×D4—62no—
589C2×D4—61no—
590C2×D4—91no—
591C2×D4—121no—
592C2×D4—181no—
593C2×D4C2×D3211yescharacteristic
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—61no—
597C22×C4—181no—
598Q16—361no—
599SD16—62no—
600SD16—121no—
601M16—361no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—91no—
605C2×C8—121no—
606C2×C8C2×D3211yescharacteristic
607C4⋊C4—31no—
608C4⋊C4—61no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4C2×D3211yescharacteristic
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—91no—
620C22⋊C4—91no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C42—61no—
629C42—91no—
630C42—181no—
631C42—181no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—42no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—81no—
647C22×C3—81no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—244no—
652C22×C3C2×D3×D411yescharacteristic
653C22×C3C2×D3×D411yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—84no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—81no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4C2×#23511yescharacteristic
675C3×C4C2×#23711yescharacteristic
676C3×C4#100411yescharacteristic
677C3×C4#100411yescharacteristic
678Dic3—21no—
679Dic3—21no—
680Dic3—41no—
681Dic3—41no—
682Dic3—41no—
683Dic3—62no—
684Dic3—61no—
685Dic3—61no—
686Dic3—61no—
687Dic3—61no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—241no—
694Dic3—241no—
695C32#331111yescharacteristic, complemented, Sylow
696C23—21no—
697C23—31no—
698C23—31no—
699C23—61no—
700C23—122no—
701C23—122no—
702C23—241no—
703Q8—61no—
704Q8—61no—
705Q8—61no—
706Q8—61no—
707Q8—362no—
708D4—21no—
709D4—61no—
710D4—61no—
711D4—122no—
712D4—122no—
713D4—361no—
714D4—721no—
715D4#379512yes—
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—91no—
727C2×C4—91no—
728C2×C4—122no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—721no—
732C2×C4C22×D3211yescharacteristic
733C8—21no—
734C8—61no—
735C8—61no—
736C8—181no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—42no—
741C2×C3—42no—
742C2×C3—82no—
743C2×C3—121no—
744C2×C3—121no—
745C2×C3—241no—
746C2×C3#549011yescharacteristic
747C2×C3#559111yescharacteristic
748C2×C3#576211yescharacteristic
749C2×C3#576811yescharacteristic
750C2×C3#577011yescharacteristic
751C2×C3#577311yescharacteristic
752D3—41no—
753D3—41no—
754D3—81no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—244no—
768C22D32×D411yescharacteristic
769C4—41no—
770C4—61no—
771C4—61no—
772C4—121no—
773C4—121no—
774C4—121no—
775C4—181no—
776C4—181no—
777C4—361no—
778C4—361no—
779C4C2×#379511yescharacteristic
780C4#6431311yescharacteristic
781C3—21no—
782C3#7885511yescharacteristic, complemented
783C3#8016211yescharacteristic, complemented
784C2—42no—
785C2—121no—
786C2—121no—
787C2—241no—
788C2#1059418411yescharacteristic
789C2#1059472911yescharacteristic
790C2#1059475311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595244C2
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. #10594576C2semidirect
3. #10592460C2semidirect
4. C3×#4776C2semidirect
5. C3×#4772C2semidirect
6. #10591461C2semidirect
7. #10591446C2semidirect
8. #10591421C2semidirect
9. #10590829C2semidirect
10. #10590796C2semidirect
11. #10590723C2semidirect
12. #10590711C2semidirect
13. #10590541C2semidirect
14. #10590520C2semidirect
15. #10590505C2semidirect
21. #64097C22semidirect
24. C2×C3×D3×C8C22semidirect
26. C3×#892C22semidirect
38. #63856C22semidirect
40. #63843C22semidirect
42. C2×#3718C22semidirect
46. #63644C22semidirect
47. #63641C22semidirect
48. #63635C22semidirect
51. C3×#816C22semidirect
52. C3×#810C22semidirect
54. #63575C22semidirect
55. #63566C22semidirect
56. #63566C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63555C22semidirect
82. #4776D3semidirect
83. #4772D3semidirect
183. C2×D3×C8C2×D3semidirect
187. #892C2×D3semidirect
225. #816C2×D3semidirect
231. #810C2×D3semidirect
695. C32#3311semidirect
782. C3#78855semidirect
783. C3#80162semidirect

Maximal subgroups

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

subgroupindex
#105952442
#105945762
#105924602
C3×#47762
C3×#47722
#105914612
#105914462
#105914212
#105908292
#105907962
#105907232
#105907112
#105905412
#105905202
#105905052
#801623
#788553