Finite Group Databasebeta

← #11860600

Subgroups — #11860600

Order 1152.

1069 conjugacy classes of subgroups.

The subgroup lattice has 775 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64127C211yesmaximal, characteristic
2#10595353C211yesmaximal, characteristic
3#10595339C211yesmaximal, characteristic, complemented
4C3×#5184C211yesmaximal, characteristic, complemented
5C3×Dic3×Q16C211yesmaximal, characteristic, complemented
6#10591560C211yesmaximal, characteristic
7#10591552C211yesmaximal, characteristic, complemented
8#10591541C211yesmaximal, characteristic, complemented
9#10591540C211yesmaximal, characteristic, complemented
10#10591537C211yesmaximal, characteristic, complemented
11#10591536C211yesmaximal, characteristic, complemented
12#10590910C211yesmaximal, characteristic, complemented
13#10590773C211yesmaximal, characteristic, complemented
14#10590758C211yesmaximal, characteristic, complemented
15#10590688C211yesmaximal, characteristic, complemented
16#79830—31nomaximal
17#79719—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23#64127C418yescomplemented
24C2×#3744C2211yescharacteristic
25C2×#3743C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic
27C3×Q8×Dic3C2211yescharacteristic
28C3×Q8×Dic3C2211yescharacteristic
29C3×Q8×Dic3C2211yescharacteristic
30#63900—21no—
31#63900C2211yescharacteristic
32#63894—21no—
33#63894—21no—
34#63894C2211yescharacteristic
35#63894C2211yescharacteristic
36#63874—21no—
37#63874—21no—
38#63874C2211yescharacteristic
39#63849—21no—
40#63849C2211yescharacteristic
41#63844—21no—
42#63844—21no—
43#63844C2211yescharacteristic
44#63844C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#818C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54#63576C2211yescharacteristic
55#63574C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63554C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C2×#918—31no—
63C2×#918—31no—
64C2×#918—61no—
65#5574—31no—
66#5574—31no—
67#5572—31no—
68#5572—31no—
69C3×#441—31no—
70C3×C4×Q16—31no—
71#5184D311yescharacteristic, complemented
72Dic3×Q16D311yescharacteristic, complemented
73#5030—31no—
74C4×#216—31no—
75#5026—31no—
76C4×#215—31no—
77#4889—31no—
78#4881—31no—
79#4861—31no—
80#4852—31no—
81#4817—31no—
82#4804—31no—
83#4804—31no—
84D3×#103—31no—
85D3×#103—31no—
86#4790—31no—
87#4789—31no—
88#4788—31no—
89#4710—31no—
90#4708—31no—
91C4×#204—31no—
92#4689—31no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×Q8C2311yescharacteristic
95#3832—22no—
96#3832C2×C414yes—
97Q8×C3⋊D3—22no—
98Q8×C3⋊D3C2×C414yescomplemented
99C2×C4⋊(C3⋊D3)—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×#634—21no—
105C2×#634C2311yescharacteristic
106C2×#624—21no—
107C2×#624—21no—
108C2×#624—21no—
109C32×Q16C2×C414yescomplemented
110C2×C32×C8C2311yescharacteristic
111#3756C2×C414yescomplemented
112#3755C2×C414yescomplemented
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114#3744C2×C414yescomplemented
115#3743C2×C414yescomplemented
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132#3724—21no—
133#3724—21no—
134#3724—21no—
135#3724D411yescharacteristic
136#3724D411yescharacteristic
137#3722—21no—
138#3722—21no—
139#3722—21no—
140#3722D411yescharacteristic
141#3722D411yescharacteristic
142Dic32—21no—
143Dic32—21no—
144Dic32—21no—
145#3710—22no—
146#2947—91noSylow
147C2×#239—31no—
148C2×#239—31no—
149C2×#239—61no—
150C2×D3×Q8—31no—
151C2×D3×Q8—31no—
152C2×D3×Q8—61no—
153C2×C3×Q16—21no—
154C2×C3×Q16C2×D311yescharacteristic
155C2×C3×Q16C2×D311yescharacteristic
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160Q8×Dic3C2×D311yescharacteristic
161Q8×Dic3C2×D311yescharacteristic
162Q8×Dic3C2×D311yescharacteristic
163Q8×Dic3C2×D311yescharacteristic
164C2×#216—31no—
165C2×#216—31no—
166C2×#216—61no—
167C2×#215—31no—
168C2×#215—31no—
169C2×#215—61no—
170#918—38no—
171#918—38no—
172#918—68no—
173C2×#204—31no—
174C2×#204—31no—
175C2×#204—61no—
176C2×ΓL(1,𝔽25)—31no—
177C2×ΓL(1,𝔽25)—31no—
178C2×ΓL(1,𝔽25)—61no—
179C2×D3×C8—31no—
180C2×D3×C8—31no—
181#893—31no—
182#893—31no—
183#893—61no—
184#893—61no—
185#892—31no—
186#892—31no—
187#892—61no—
188#892—61no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—31no—
191D3×C4⋊C4—61no—
192D3×C4⋊C4—61no—
193#887—31no—
194#887—31no—
195#887—61no—
196#887—61no—
197C4×D12—31no—
198C4×D12—31no—
199C4×D12—61no—
200C4×D12—61no—
201#872—31no—
202#872—31no—
203#872—61no—
204#872—61no—
205#872—61no—
206#872—61no—
207C4×Dic6—31no—
208C4×Dic6—31no—
209C4×Dic6—61no—
210C4×Dic6—61no—
211C3×#107—31no—
212C3×#106—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103—31no—
217C3×#97—31no—
218C3×C4×C8—31no—
219#835C2×D311yescharacteristic
220#835C2×D311yescharacteristic
221#835C2×D311yescharacteristic
222#835C2×D311yescharacteristic
223#821—31no—
224#821—31no—
225#818C2×D311yescharacteristic
226#817C2×D311yescharacteristic
227#816—31no—
228#816—31no—
229#815—31no—
230#815C2×D311yescharacteristic
231C8×Dic3—31no—
232C8×Dic3C2×D311yescharacteristic
233#810—31no—
234#810—31no—
235#809—31no—
236#809—31no—
237#808—31no—
238#808—31no—
239#807—31no—
240#807—31no—
241#803—31no—
242C4×C3⋊C8—31no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C32×Q8C22×C412yes—
248C32×Q8C22×C412yes—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4⋊(C3⋊D3)—24no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)C22×C412yes—
257C4×C3⋊D3—24no—
258C4×C3⋊D3—24no—
259C4×C3⋊D3C22×C412yes—
260C4×C3⋊D3#4112yes—
261#634—21no—
262#634—24no—
263#634C22×C412yes—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272#624—81no—
273#624—81no—
274#624—81no—
275C32×C8C22×C412yes—
276C3⋊(C3⋊C8)C22×C412yes—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279C2×#137—91no—
280#520—91no—
281#519—91no—
282#441—31no—
283#441—91no—
284#440—91no—
285#440—91no—
286C4×Q16—31no—
287C4×Q16—91no—
288C4×SD16—91no—
289C4×SD16—91no—
290#428—91no—
291#416—91no—
292C2×#103—91no—
293#405—91no—
294C2×C3×Q8—21no—
295C2×C3×Q8—21no—
296C2×C3×Q8C22×D311yescharacteristic
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300#239—34no—
301#239—34no—
302#239—64no—
303#239—62no—
304#239—62no—
305#239—122no—
306D3×Q8—34no—
307D3×Q8—34no—
308D3×Q8—64no—
309D3×Q8—62no—
310D3×Q8—62no—
311D3×Q8—122no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—61no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—121no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—121no—
332C2×C4×D3—121no—
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6—121no—
339C3×Q16—24no—
340C3×Q16C4×D314yescomplemented
341C3×Q16C4×D314yescomplemented
342C2×C3×C8—21no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C42—31no—
356C3×C42—31no—
357C3×C42—61no—
358C3×C42—61no—
359C3×C42—61no—
360C3×C42—61no—
361#216—34no—
362#216—34no—
363#216—64no—
364#215—34no—
365#215—34no—
366#215—64no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
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—
377C4⋊Dic3—21no—
378C4⋊Dic3—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3—21no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—31no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395C4×Dic3—21no—
396C4×Dic3—21no—
397C4×Dic3—21no—
398C4×Dic3—21no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3C22×D311yescharacteristic
406C4×Dic3C22×D311yescharacteristic
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412#204—34no—
413#204—34no—
414#204—64no—
415ΓL(1,𝔽25)—34no—
416ΓL(1,𝔽25)—34no—
417ΓL(1,𝔽25)—64no—
418D3×C8—62no—
419D3×C8—62no—
420C22×C32C22×D411yescharacteristic
421C2×C3⋊D3—21no—
422C2×C3⋊D3—21no—
423C2×C3⋊D3—22no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3⋊D3C4×D412yes—
427C32×C4—22no—
428C32×C4—22no—
429C32×C4C23×C411yescharacteristic
430C32×C4C2×#4111yescharacteristic
431C3⋊Dic3—22no—
432C3⋊Dic3C4×D412yes—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C2×#41—91no—
442C22×Q8—91no—
443#137—98no—
444C2×Q16—91no—
445C2×Q16D3211yescharacteristic
446C2×SD16—91no—
447C2×SD16—91no—
448C2×M16—91no—
449C22×C8—91no—
450C4×Q8—31no—
451C4×Q8—31no—
452C4×Q8—31no—
453C4×Q8—31no—
454C4×Q8—91no—
455C4×Q8—91no—
456C4×Q8—181no—
457C4×Q8—181no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—181no—
461C4×D4—181no—
462#117—91no—
463#117—91no—
464#117—181no—
465#117—181no—
466#117—181no—
467C2×C4⋊C4—91no—
468C2×C4⋊C4—181no—
469#107—31no—
470#107—91no—
471#106—31no—
472#106—91no—
473#103—31no—
474#103—31no—
475#103—31no—
476#103—31no—
477#103—91no—
478#103—91no—
479#102—91no—
480#102—91no—
481#97—31no—
482#97—91no—
483C4×C8—31no—
484C4×C8—91no—
485C22×D3—31no—
486C22×D3—31no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—121no—
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—22no—
496C3×Q8—22no—
497C3×Q8—41no—
498C3×Q8—41no—
499C3×Q8C2×C4×D312yes—
500C3×Q8C2×C4×D312yes—
501C3×Q8C2×C4×D312yes—
502C3×Q8C2×C4×D312yes—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—121no—
530C2×Dic3D3×D411yescharacteristic
531C2×Dic3D3×D411yescharacteristic
532C2×Dic3D3×D411yescharacteristic
533C2×Dic3D3×D411yescharacteristic
534D12—32no—
535D12—32no—
536D12—62no—
537D12—64no—
538D12—64no—
539D12—61no—
540D12—61no—
541D12—121no—
542D12—124no—
543C4×D3—32no—
544C4×D3—32no—
545C4×D3—32no—
546C4×D3—32no—
547C4×D3—62no—
548C4×D3—62no—
549C4×D3—64no—
550C4×D3—64no—
551C4×D3—64no—
552C4×D3—64no—
553C4×D3—124no—
554C4×D3—124no—
555C4×D3—241no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—241no—
561Dic6—32no—
562Dic6—32no—
563Dic6—62no—
564Dic6—64no—
565Dic6—64no—
566Dic6—61no—
567Dic6—61no—
568Dic6—124no—
569Dic6—121no—
570C3×C8—22no—
571C3×C8—61no—
572C3×C8—61no—
573C3×C8C2×C4×D312yes—
574C3×C8C2×C4×D312yes—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—32no—
578C3⋊C8—32no—
579C3⋊C8—62no—
580C2×C32C2×C4×D411yescharacteristic
581C2×C32#57711yescharacteristic
582C2×C32#57811yescharacteristic
583C3⋊D3—22no—
584C3⋊D3—42no—
585#41—94no—
586#41—182no—
587C2×Q8—94no—
588C2×Q8—91no—
589C2×Q8—181no—
590C2×Q8—182no—
591C2×Q8C2×D3211yescharacteristic
592C2×Q8C2×D3211yescharacteristic
593C2×D4—91no—
594C2×D4—181no—
595C22×C4—91no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4—181no—
600C22×C4—181no—
601Q16—94no—
602Q16#62414yescomplemented
603SD16—94no—
604SD16—94no—
605M16—94no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—91no—
609C2×C8—182no—
610C2×C8C2×D3211yescharacteristic
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—91no—
620C4⋊C4—91no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C22⋊C4—91no—
625C22⋊C4—91no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C42—31no—
630C42—31no—
631C42—61no—
632C42—61no—
633C42—61no—
634C42—61no—
635C42—181no—
636C42—181no—
637C42—181no—
638C22×C3—21no—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C2×D3×D411yescharacteristic
641C2×D3—32no—
642C2×D3—32no—
643C2×D3—62no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—61no—
648C2×D3—62no—
649C2×D3—62no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—122no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—241no—
658C2×D3—241no—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—22no—
662C3×C4—22no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—42no—
666C3×C4—42no—
667C3×C4—61no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4C22×C4×D311yescharacteristic
676C3×C4C22×C4×D311yescharacteristic
677C3×C4D3×#4111yescharacteristic
678C3×C4D3×#4111yescharacteristic
679Dic3—21no—
680Dic3—21no—
681Dic3—21no—
682Dic3—21no—
683Dic3—32no—
684Dic3—32no—
685Dic3—41no—
686Dic3—41no—
687Dic3—41no—
688Dic3—41no—
689Dic3—62no—
690Dic3—62no—
691Dic3—62no—
692Dic3—122no—
693C32#294711yescharacteristic, complemented, Sylow
694C23—91no—
695C23—181no—
696Q8—21no—
697Q8—21no—
698Q8—92no—
699Q8—184no—
700Q8—181no—
701Q8C2×#62412yes—
702Q8C2×#62412yes—
703D4—92no—
704D4—184no—
705D4—181no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—31no—
711C2×C4—31no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—91no—
717C2×C4—92no—
718C2×C4—92no—
719C2×C4—184no—
720C2×C4—184no—
721C2×C4—181no—
722C2×C4—721no—
723C2×C4—721no—
724C2×C4—721no—
725C2×C4C22×D3211yescharacteristic
726C8—61no—
727C8—61no—
728C8—92no—
729C8C2×#62412yes—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3C4×D3×D411yescharacteristic
734C2×C3C4×D3×D411yescharacteristic
735C2×C3#576611yescharacteristic
736C2×C3#577011yescharacteristic
737C2×C3#577811yescharacteristic
738C2×C3#577911yescharacteristic
739D3—62no—
740D3—62no—
741D3—122no—
742D3—122no—
743D3—122no—
744D3—242no—
745C22—92no—
746C22—181no—
747C22—181no—
748C22—182no—
749C22—361no—
750C22—361no—
751C22D32×D411yescharacteristic
752C4—22no—
753C4—22no—
754C4—61no—
755C4—61no—
756C4—61no—
757C4—61no—
758C4—92no—
759C4—121no—
760C4—121no—
761C4—121no—
762C4—121no—
763C4—182no—
764C4#6431211yescharacteristic
765C4C22×#62411yescharacteristic
766C3—21no—
767C3#7971911yescharacteristic, complemented
768C3#7983011yescharacteristic, complemented
769C2—182no—
770C2—362no—
771C2#1059476611yescharacteristic
772C2#1059477011yescharacteristic
773C2D4×#62411yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×#3832C22
cosocleC2×C32×C4C24
hypercenterC2×Q16D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. #10595339C2semidirect
4. C3×#5184C2semidirect
5. C3×Dic3×Q16C2semidirect
7. #10591552C2semidirect
8. #10591541C2semidirect
9. #10591540C2semidirect
10. #10591537C2semidirect
11. #10591536C2semidirect
12. #10590910C2semidirect
13. #10590773C2semidirect
14. #10590758C2semidirect
15. #10590688C2semidirect
23. #64127C4semidirect
71. #5184D3semidirect
72. Dic3×Q16D3semidirect
98. Q8×C3⋊D3C2×C4semidirect
109. C32×Q16C2×C4semidirect
111. #3756C2×C4semidirect
112. #3755C2×C4semidirect
114. #3744C2×C4semidirect
115. #3743C2×C4semidirect
340. C3×Q16C4×D3semidirect
341. C3×Q16C4×D3semidirect
602. Q16#624semidirect
693. C32#2947semidirect
767. C3#79719semidirect
768. C3#79830semidirect

Maximal subgroups

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

subgroupindex
C2×#641272
#105953532
#105953392
C3×#51842
C3×Dic3×Q162
#105915602
#105915522
#105915412
#105915402
#105915372
#105915362
#105909102
#105907732
#105907582
#105906882
#798303
#797193