Finite Group Databasebeta

← #11860970

Subgroups — #11860970

Order 1152.

1029 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595222C211yesmaximal, characteristic, complemented
2C2×#63933C211yesmaximal, characteristic
3#10594359C211yesmaximal, characteristic, complemented
4#10592457C211yesmaximal, characteristic, complemented
5C3×#4785C211yesmaximal, characteristic, complemented
6C3×#4771C211yesmaximal, characteristic, complemented
7#10591436C211yesmaximal, characteristic, complemented
8#10591401C211yesmaximal, characteristic, complemented
9#10590909C211yesmaximal, characteristic, complemented
10#10590794C211yesmaximal, characteristic, complemented
11#10590742C211yesmaximal, characteristic, complemented
12#10590670C211yesmaximal, characteristic, complemented
13D3×#808C211yesmaximal, characteristic, complemented
14#10590485C211yesmaximal, characteristic, complemented
15#10590475C211yesmaximal, characteristic, complemented
16#79868—31nomaximal
17#78869—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22#64096C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#213C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28#67⋊Dic3—21no—
29Dic3×#67—21no—
30C2×Dic3⋊Dic3—21no—
31#63955—21no—
32#63933C418yescomplemented
33C4×#625—21no—
34#63898C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic
36#63879—21no—
37#63878—21no—
38D3×Dic3⋊C4—21no—
39#63855C2211yescharacteristic
40#63844C2211yescharacteristic
41#63843C2211yescharacteristic
42Dic3×Dic6C2211yescharacteristic
43C2×#3719C2211yescharacteristic
44C2×#3715C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63643C2211yescharacteristic
48C8×C3⋊Dic3C2211yescharacteristic
49#63635C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#815C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#808C2211yescharacteristic
56#63574C2211yescharacteristic
57#63573C2211yescharacteristic
58#63567C2211yescharacteristic
59#63563C2211yescharacteristic
60#63555C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62#5827—31no—
63C2×#950—31no—
64C2×#912—31no—
65#5546—31no—
66#5546—31no—
67#5504—31no—
68C3×#442—31no—
69C3×#417—31no—
70#5152—31no—
71#5133—31no—
72#5122—31no—
73C4×#214—31no—
74C4×#214—31no—
75C2×#808—31no—
76D3×#106—31no—
77#4853—31no—
78#4789—31no—
79#4789—31no—
80#4788—31no—
81#4788—31no—
82#4785—31no—
83#4785D311yescharacteristic, complemented
84#4771—31no—
85#4771D311yescharacteristic, complemented
86#4758—31no—
87#4758—31no—
88#4758—31no—
89#4758—31no—
90#4758—61no—
91#4716—31no—
92#4708—31no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C3×#237—22no—
100C3×#237C2×C414yescomplemented
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#625—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795C2×C414yescomplemented
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3757—21no—
115#3754C2×C414yescomplemented
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×#213C2×C414yescomplemented
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×ΓL(1,𝔽25)—22no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136Dic3⋊Dic3D411yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143#3719C2×C414yescomplemented
144#3715C2×C414yescomplemented
145D3×C3⋊C8C2×C414yescomplemented
146#2952—91noSylow
147C2×C3×#41—31no—
148C2×#237—31no—
149C2×#237C2×D311yescharacteristic
150C2×#235—31no—
151C2×C3×D8—31no—
152C2×C3×M16—31no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155C2×C3×C4⋊C4—31no—
156#950—38no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159C2×#216—31no—
160C2×#215—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—61no—
165D4×Dic3—61no—
166D4×Dic3—61no—
167D4×Dic3C2×D311yescharacteristic
168C2×#214—31no—
169C2×#214—31no—
170C2×#214—31no—
171C2×#214—61no—
172C2×#213C2×D311yescharacteristic
173C4×#67—61no—
174C4×#67—61no—
175C4×#67—61no—
176C4×#67—61no—
177#926—31no—
178#926—61no—
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3—61no—
181C2×Dic3⋊C4—61no—
182C2×Dic3⋊C4—61no—
183C22×C3⋊C8—31no—
184#912—38no—
185C2×Dic12—31no—
186C2×ΓL(1,𝔽25)C2×D311yescharacteristic
187C2×D3×C8—31no—
188#893—31no—
189#893C2×D311yescharacteristic
190#892—61no—
191D3×C4⋊C4—31no—
192D3×C4⋊C4—61no—
193D3×C4⋊C4C2×D311yescharacteristic
194#887—31no—
195#887—31no—
196#887—31no—
197#887—31no—
198#887—61no—
199#67⋊C4—61no—
200#67⋊C4—61no—
201#877—61no—
202#877—61no—
203#872—31no—
204C4×Dic6—31no—
205C4×Dic6—31no—
206C3×#106—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#102—21no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102C2×D311yescharacteristic
213C3×#102C2×D311yescharacteristic
214C3×#97—31no—
215#832—31no—
216#832C2×D311yescharacteristic
217#821—31no—
218#821C2×D311yescharacteristic
219#817—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—61no—
224#816C2×D311yescharacteristic
225#815—31no—
226#815—31no—
227#815C2×D311yescharacteristic
228C8×Dic3—31no—
229C8×Dic3—31no—
230C8×Dic3—31no—
231C8×Dic3—61no—
232#810—31no—
233#810C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808—31no—
237#808—31no—
238#808—31no—
239#808—61no—
240#808C2×D311yescharacteristic
241C4×C3⋊C8—31no—
242C23×C32—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4C22×C412yes—
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—21no—
255#634C22×C412yes—
256C3×#67—24no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—24no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12C22×C412yes—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269C3×C4×D3C22×C412yes—
270C3×C4×D3#4112yes—
271C3×Dic6—21no—
272C3×Dic6C22×C412yes—
273#625—24no—
274D3×Dic3—24no—
275D3×Dic3—81no—
276D3×Dic3—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)C22×C412yes—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C2×#135—91no—
282#520—91no—
283#520—91no—
284#442—31no—
285#442—91no—
286#441—91no—
287#441—91no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291C4×SD16—91no—
292C2×#106—91no—
293#417—31no—
294#417—91no—
295#405—91no—
296C3×#41—34no—
297C3×#41—62no—
298C2×C3×Q8—31no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—21no—
310C2×#67—61no—
311C2×#67—61no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—121no—
320#237—22no—
321#237—34no—
322#237—62no—
323#237C4×D314yescomplemented
324#235—34no—
325#235—62no—
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×Dic6C22×D311yescharacteristic
337C3×D8—34no—
338C3×M16—62no—
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—
353#217—21no—
354#217—31no—
355#217—31no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—121no—
360#216—34no—
361#215—34no—
362#214—34no—
363#214—34no—
364#214—34no—
365#214—64no—
366#213C4×D314yescomplemented
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—61no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—21no—
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—31no—
393C4×Dic3—31no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—121no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—34no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411Dic12—34no—
412ΓL(1,𝔽25)—22no—
413D3×C8—34no—
414C22×C32—22no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3C4×D412yes—
424C32×C4—41no—
425C32×C4C23×C411yescharacteristic
426C32×C4C2×#4111yescharacteristic
427C3⋊Dic3—21no—
428C3⋊Dic3—22no—
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3×Dic3—22no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3C4×D412yes—
437C2×#41—31no—
438C2×#41—91no—
439#135—98no—
440C2×Q16—91no—
441C2×SD16—91no—
442C2×SD16—91no—
443C2×D8—31no—
444C2×M16—31no—
445C22×C8—91no—
446C4×Q8—91no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×Q8—91no—
450C4×D4—31no—
451C4×D4—31no—
452C4×D4—91no—
453C4×D4—91no—
454C4×D4—181no—
455C4×D4—181no—
456C4×D4—181no—
457C4×D4—181no—
458#117—91no—
459#117—181no—
460#117—181no—
461C2×C4⋊C4—31no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—181no—
464C2×C4⋊C4—181no—
465#106—31no—
466#106—91no—
467#106—91no—
468#106—91no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102D3211yescharacteristic
477#97—31no—
478#97—91no—
479C4×C8—91no—
480C4×C8—91no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—41no—
485C23×C3—61no—
486C22×D3—21no—
487C22×D3D3×D411yescharacteristic
488C3×Q8—32no—
489C3×Q8—61no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—22no—
493C3×D4—32no—
494C3×D4—41no—
495C3×D4—64no—
496C3×D4—61no—
497C3×D4C2×C4×D312yes—
498C3×D4C2×C4×D312yes—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—32no—
504C2×C3×C4—32no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—41no—
508C2×C3×C4—64no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—241no—
513C2×C3×C4—241no—
514C2×C3×C4—241no—
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—24no—
518#67—64no—
519#67—64no—
520C2×Dic3—21no—
521C2×Dic3—24no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—64no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—81no—
536C2×Dic3—121no—
537C2×Dic3—121no—
538C2×Dic3—241no—
539C2×Dic3—241no—
540C2×Dic3—241no—
541C2×Dic3—241no—
542C2×Dic3—242no—
543C2×Dic3D3×D411yescharacteristic
544C2×Dic3D3×D411yescharacteristic
545C2×Dic3D3×D411yescharacteristic
546D12—21no—
547D12C2×C4×D312yes—
548C4×D3—64no—
549C4×D3—81no—
550C4×D3—81no—
551C4×D3—241no—
552C4×D3—241no—
553C4×D3C2×C4×D312yes—
554C4×D3#23712yes—
555Dic6—21no—
556Dic6—32no—
557Dic6—32no—
558Dic6—62no—
559Dic6—61no—
560Dic6—61no—
561Dic6—121no—
562Dic6C2×C4×D312yes—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—32no—
566C3×C8—41no—
567C3×C8—61no—
568C3⋊C8—21no—
569C3⋊C8—32no—
570C3⋊C8—32no—
571C3⋊C8—62no—
572C3⋊C8C2×C4×D312yes—
573C2×C32—42no—
574C2×C32C2×C4×D411yescharacteristic
575C2×C32#57711yescharacteristic
576C2×C32#57711yescharacteristic
577C3×D3—22no—
578C3×D3—42no—
579#41—34no—
580#41—62no—
581#41—94no—
582#41—182no—
583C2×Q8—31no—
584C2×Q8—91no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—181no—
588C2×D4C2×D3211yescharacteristic
589C22×C4—31no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598Q16—94no—
599SD16—94no—
600SD16—94no—
601D8—34no—
602M16—62no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—94no—
606C2×C8—91no—
607C2×C8C2×D3211yescharacteristic
608C4⋊C4—31no—
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⋊C4C2×D3211yescharacteristic
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—91no—
623C22⋊C4—91no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C42—31no—
627C42—91no—
628C42—181no—
629C42—181no—
630C42—181no—
631C42—181no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—32no—
636C22×C3—42no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—62no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3C2×D3×D411yescharacteristic
649C22×C3C2×D3×D411yescharacteristic
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—22no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3#67⋊C412yes—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—32no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—62no—
664C3×C4—81no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4C22×C4×D311yescharacteristic
668C3×C4C22×C4×D311yescharacteristic
669C3×C4C2×#23711yescharacteristic
670C3×C4D3×#4111yescharacteristic
671Dic3—22no—
672Dic3—21no—
673Dic3—21no—
674Dic3—41no—
675Dic3—41no—
676Dic3—62no—
677Dic3—62no—
678Dic3—61no—
679Dic3—61no—
680Dic3—61no—
681Dic3—61no—
682Dic3—62no—
683Dic3—122no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—241no—
688Dic3#67⋊C412yes—
689C32#295211yescharacteristic, complemented, Sylow
690C23—21no—
691C23—31no—
692C23—61no—
693Q8—32no—
694Q8—61no—
695Q8—92no—
696Q8—181no—
697D4—21no—
698D4—32no—
699D4—64no—
700D4—61no—
701D4—184no—
702D4C4×D3212yes—
703C2×C4—21no—
704C2×C4—31no—
705C2×C4—32no—
706C2×C4—32no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—64no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—91no—
714C2×C4—91no—
715C2×C4—184no—
716C2×C4—181no—
717C2×C4—181no—
718C2×C4—241no—
719C2×C4—241no—
720C2×C4—241no—
721C2×C4—721no—
722C2×C4—721no—
723C2×C4—721no—
724C2×C4C22×D3211yescharacteristic
725C8—21no—
726C8—32no—
727C8—61no—
728C8—92no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—42no—
733C2×C3—42no—
734C2×C3—62no—
735C2×C3—82no—
736C2×C3—122no—
737C2×C3C2×#67⋊C411yescharacteristic
738C2×C3C4×D3×D411yescharacteristic
739C2×C3#577511yescharacteristic
740C2×C3#577511yescharacteristic
741C2×C3#577511yescharacteristic
742C2×C3#577811yescharacteristic
743D3—22no—
744D3—42no—
745C22—22no—
746C22—32no—
747C22—41no—
748C22—41no—
749C22—61no—
750C22—61no—
751C22—62no—
752C22—121no—
753C22—121no—
754C22D32×D411yescharacteristic
755C4—32no—
756C4—41no—
757C4—61no—
758C4—61no—
759C4—62no—
760C4—121no—
761C4—121no—
762C4—181no—
763C4—181no—
764C4—182no—
765C4—361no—
766C4C2×C4×D3211yescharacteristic
767C4D3×#23711yescharacteristic
768C3—21no—
769C3#7886911yescharacteristic, complemented
770C3#7986811yescharacteristic, complemented
771C2—42no—
772C2—62no—
773C2—122no—
774C2D3×#67⋊C411yescharacteristic
775C2#1059473311yescharacteristic
776C2#1059475411yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#63933C2
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595222C2semidirect
3. #10594359C2semidirect
4. #10592457C2semidirect
5. C3×#4785C2semidirect
6. C3×#4771C2semidirect
7. #10591436C2semidirect
8. #10591401C2semidirect
9. #10590909C2semidirect
10. #10590794C2semidirect
11. #10590742C2semidirect
12. #10590670C2semidirect
13. D3×#808C2semidirect
14. #10590485C2semidirect
15. #10590475C2semidirect
32. #63933C4semidirect
83. #4785D3semidirect
85. #4771D3semidirect
100. C3×#237C2×C4semidirect
111. #3795C2×C4semidirect
115. #3754C2×C4semidirect
122. C3×#213C2×C4semidirect
143. #3719C2×C4semidirect
144. #3715C2×C4semidirect
145. D3×C3⋊C8C2×C4semidirect
323. #237C4×D3semidirect
366. #213C4×D3semidirect
689. C32#2952semidirect
769. C3#78869semidirect
770. C3#79868semidirect

Maximal subgroups

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

subgroupindex
#105952222
C2×#639332
#105943592
#105924572
C3×#47852
C3×#47712
#105914362
#105914012
#105909092
#105907942
#105907422
#105906702
D3×#8082
#105904852
#105904752
#798683
#788693