Finite Group Databasebeta

← #11884593

Subgroups — #11884593

Order 1152.

1032 conjugacy classes of subgroups.

The subgroup lattice has 869 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5824C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic, complemented
3C2×#63929C211yesmaximal, characteristic, complemented
4#10594899C211yesmaximal, characteristic, complemented
5#10592938C211yesmaximal, characteristic, complemented
6#10591653C211yesmaximal, characteristic, complemented
7#10591605C211yesmaximal, characteristic, complemented
8#10591587C211yesmaximal, characteristic, complemented
9#10591574C211yesmaximal, characteristic, complemented
10#10591468C211yesmaximal, characteristic, complemented
11#10591450C211yesmaximal, characteristic, complemented
12#10591440C211yesmaximal, characteristic, complemented
13#10591187C211yesmaximal, characteristic, complemented
14#10591170C211yesmaximal, characteristic, complemented
15#10591155C211yesmaximal, characteristic, complemented
16#83925—31nomaximal
17#83528—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24#64133C2211yescharacteristic
25C3×#950—24no—
26C3×#946C2211yescharacteristic
27C3×#944C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic
30C3×#939—21no—
31C3×#935—21no—
32C3×D4×Dic3C2211yescharacteristic
33C2×C3×#214C2211yescharacteristic
34C2×C3×#213C2211yescharacteristic
35C3×#929—21no—
36C3×C4×#67C2211yescharacteristic
37C3×#924C2211yescharacteristic
38C2×C3×Dic3⋊C4—21no—
39C22×C3×C3⋊C8C2211yescharacteristic
40#63970—21no—
41#63959—21no—
42#63929—24no—
43#63908C2211yescharacteristic
44#63879—21no—
45#63860C2211yescharacteristic
46#63851—21no—
47Dic3×Dic6C2211yescharacteristic
48C2×#3719C2211yescharacteristic
49C2×#3718C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52#63662C2211yescharacteristic
53#63659C2211yescharacteristic
54#63657C2211yescharacteristic
55#63575C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59#63565C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic
63C2×C3×#135—31no—
64C3×#547—31no—
65#5831—31no—
66#5824D311yescharacteristic, complemented
67C2×#951—31no—
68C2×#950D311yescharacteristic, complemented
69C2×#915—31no—
70#5552—31no—
71#5239—31no—
72#5239—31no—
73#5239—31no—
74#5239—61no—
75#5238—31no—
76#5186—31no—
77#5182—31no—
78#5174—31no—
79#5167—31no—
80#5164—31no—
81#5158—31no—
82#5153—31no—
83#5116—31no—
84#5111—31no—
85#5090—31no—
86#5086—31no—
87#5051—31no—
88#5050—31no—
89#5049—31no—
90#5047—31no—
91#5018—31no—
92#5016—31no—
93#5011—31no—
94C32×#41—22no—
95C32×#41—41no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4—21no—
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4—21no—
100C22×C32×C4C2311yescharacteristic
101C2×#634C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67D411yescharacteristic
105C22×C3×Dic3—21no—
106C22×C3×Dic3—21no—
107C3×#237—22no—
108C3×#237—41no—
109C3×#235—22no—
110C3×#235—41no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×#627—21no—
117C2×#625—21no—
118C2×D3×Dic3—21no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121#3757—21no—
122#3756—41no—
123#3754—22no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#217—21no—
130C3×#217D411yescharacteristic
131C3×#216—22no—
132C3×#215—22no—
133C3×#214D414yescomplemented
134C3×#213—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4D411yescharacteristic
143C3×C4×Dic3C2311yescharacteristic
144C2×C3×C3⋊C8—22no—
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147Dic3⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3719—22no—
153#3718—22no—
154#3715—41no—
155#3711—22no—
156#3269—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C2×C3×#41C2×D311yescharacteristic
161C2×C3×#41C2×D311yescharacteristic
162C2×D3×Q8—31no—
163C2×#237C2×D311yescharacteristic
164C2×#235C2×D311yescharacteristic
165C22×Dic6—31no—
166C3×#135—64no—
167C2×C3×Q16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×D8—31no—
171C22×C3×C8—31no—
172C3×C4⋊Q8—31no—
173C3×#123—61no—
174C3×#123—61no—
175C3×C22⋊Q8—31no—
176C3×C22⋊Q8—31no—
177C3×#121—61no—
178C3×C4×D4—31no—
179C3×C4×D4—31no—
180C2×C3×C4⋊C4—61no—
181#951—64no—
182#950—24no—
183#946C2×D311yescharacteristic
184Q8×Dic3—31no—
185#944C2×D311yescharacteristic
186C2×#216—31no—
187C2×#216—31no—
188C2×#216—31no—
189C2×#216—31no—
190C2×#216—31no—
191C2×#216—61no—
192C2×#216C2×D311yescharacteristic
193C2×#215—31no—
194C2×#215C2×D311yescharacteristic
195#939—21no—
196#939—61no—
197#938—31no—
198#938—61no—
199#936—31no—
200#936—61no—
201#935—21no—
202D4×Dic3C2×D311yescharacteristic
203C2×#214—31no—
204C2×#214—31no—
205C2×#214—31no—
206C2×#214—61no—
207C2×#214C2×D311yescharacteristic
208C2×#213C2×D311yescharacteristic
209#930—31no—
210#929—21no—
211C4×#67—61no—
212C4×#67C2×D311yescharacteristic
213#924—31no—
214#924—31no—
215#924—61no—
216#924—61no—
217#924C2×D311yescharacteristic
218C2×Dic3⋊C4—21no—
219C2×#208—31no—
220C22×C3⋊C8C2×D311yescharacteristic
221#915—64no—
222C2×Dic12—31no—
223C2×ΓL(1,𝔽25)—31no—
224#896—61no—
225#885—61no—
226#67⋊C4—61no—
227#875—31no—
228C4×Dic6—31no—
229#835—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#835—61no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#830—31no—
239#830—31no—
240#830—31no—
241#830—61no—
242(C2×D3)⋊C8—31no—
243#818—31no—
244#816—31no—
245#816—31no—
246#815—31no—
247Dic3⋊C8—31no—
248#810—31no—
249#810—31no—
250#809—31no—
251#807—31no—
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32—21no—
255C23×C32C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C32×Q8—21no—
259C32×Q8—21no—
260C32×D4—21no—
261C32×D4—42no—
262C32×D4C2×D412yes—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—42no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2411yescharacteristic
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271#634—21no—
272#634—21no—
273C3×#67—41no—
274C3×#67—42no—
275C3×#67—42no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3—42no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—42no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6C2×D412yes—
293#627—42no—
294#625—42no—
295D3×Dic3—42no—
296C3⋊(C3⋊C8)—21no—
297C3⋊(C3⋊C8)—21no—
298C3×C3⋊C8—21no—
299C3×C3⋊C8C2×D412yes—
300C2×#137—91no—
301C2×#135—31no—
302#548—91no—
303#547—31no—
304#497—91no—
305#468—91no—
306#467—91no—
307#463—91no—
308#462—91no—
309#452—91no—
310#452—91no—
311#451—91no—
312#449—91no—
313#440—91no—
314#435—91no—
315C3×#41—22no—
316C3×#41—22no—
317C3×#41—42no—
318C3×#41—41no—
319C3×#41—41no—
320C3×#41—42no—
321C3×#41—62no—
322C3×#41—62no—
323C3×#41—121no—
324C3×#41—121no—
325C2×C3×Q8—21no—
326C2×C3×Q8—31no—
327C2×C3×Q8—31no—
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—41no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4C22×D311yescharacteristic
339C2×C3×D4C22×D311yescharacteristic
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—31no—
344C22×C3×C4—41no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4—61no—
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C2×#67—21no—
351C2×#67—21no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67#6711yescharacteristic
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—61no—
358D3×Q8—62no—
359D3×Q8—121no—
360#237—22no—
361#237—41no—
362#235—22no—
363#235—41no—
364C2×D12C22×D311yescharacteristic
365C2×C4×D3—21no—
366C2×C4×D3—61no—
367C2×C4×D3C22×D311yescharacteristic
368C2×Dic6—31no—
369C2×Dic6—31no—
370C2×Dic6—61no—
371C2×Dic6—62no—
372C2×Dic6—61no—
373C2×Dic6—61no—
374C2×Dic6—121no—
375C2×Dic6C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C3×Q16—62no—
378C3×SD16—34no—
379C3×SD16—62no—
380C3×D8—62no—
381C2×C3×C8—31no—
382C2×C3×C8—31no—
383C2×C3×C8—62no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4—31no—
386C3×C4⋊C4—61no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4—61no—
389C3×C4⋊C4—61no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—31no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C42—31no—
396#217—21no—
397#217—21no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—121no—
404#217#6711yescharacteristic
405#216—22no—
406#216—62no—
407#216—62no—
408#216—62no—
409#216—121no—
410#216—121no—
411#216—122no—
412#215—22no—
413#215—121no—
414#214—62no—
415#214—62no—
416#214—122no—
417#214—121no—
418#214#6714yescomplemented
419#213—22no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4#6711yescharacteristic
425C4⋊Dic3—31no—
426C4⋊Dic3—31no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3C22×D311yescharacteristic
430Dic3⋊C4—21no—
431Dic3⋊C4—21no—
432Dic3⋊C4—21no—
433Dic3⋊C4—21no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—121no—
438Dic3⋊C4#6711yescharacteristic
439C4×Dic3—61no—
440C4×Dic3—61no—
441C4×Dic3C22×D311yescharacteristic
442#208—62no—
443C2×C3⋊C8—22no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—61no—
449C2×C3⋊C8—61no—
450C2×C3⋊C8C22×D311yescharacteristic
451C2×C3⋊C8C22×D311yescharacteristic
452Dic12—62no—
453ΓL(1,𝔽25)—62no—
454C22×C32—22no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32C22×D411yescharacteristic
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C32×C4—21no—
468C32×C4—41no—
469C32×C4C22×D411yescharacteristic
470C32×C4H(5,𝔽2)11yescharacteristic
471C3⋊Dic3—41no—
472C3⋊Dic3—41no—
473C3×Dic3—22no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C2×#41—31no—
480C2×#41—31no—
481C2×#41D3211yescharacteristic
482C22×Q8—91no—
483#137—184no—
484#135—64no—
485C2×Q16—31no—
486C2×Q16—91no—
487C2×Q16—91no—
488C2×Q16—91no—
489C2×SD16—31no—
490C2×SD16—31no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×D8—31no—
494C2×M16—91no—
495C22×C8—31no—
496C4⋊Q8—31no—
497#124—91no—
498#124—181no—
499#123—61no—
500#123—61no—
501C22⋊Q8—31no—
502C22⋊Q8—31no—
503C22⋊Q8—91no—
504C22⋊Q8—181no—
505#121—61no—
506#121—91no—
507#121—181no—
508C4×Q8—91no—
509C4×D4—31no—
510C4×D4—31no—
511C4×D4—181no—
512C2×C4⋊C4—61no—
513#107—91no—
514C4⋊C8—91no—
515#103—91no—
516#103—91no—
517#103—91no—
518#103—91no—
519#102—91no—
520#102—91no—
521C22⋊C8—91no—
522C22⋊C8—91no—
523#97—91no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—31no—
528C23×C3—41no—
529C23×C3—61no—
530C23×C3D3×D411yescharacteristic
531C23×C3C2×#6711yescharacteristic
532C22×D3—21no—
533C22×D3C2×#6711yescharacteristic
534C3×Q8—22no—
535C3×Q8—21no—
536C3×Q8—21no—
537C3×Q8—21no—
538C3×Q8—21no—
539C3×Q8—32no—
540C3×Q8—41no—
541C3×Q8—61no—
542C3×Q8—61no—
543C3×Q8—61no—
544C3×D4—21no—
545C3×D4—21no—
546C3×D4—22no—
547C3×D4—41no—
548C3×D4—42no—
549C3×D4—42no—
550C3×D4—44no—
551C3×D4—61no—
552C3×D4—61no—
553C3×D4—121no—
554C3×D4—122no—
555C3×D4—122no—
556C3×D4D3×D412yes—
557C3×D4C2×#6712yes—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—31no—
567C2×C3×C4—31no—
568C2×C3×C4—31no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—42no—
573C2×C3×C4—42no—
574C2×C3×C4—44no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—122no—
581C2×C3×C4—122no—
582C2×C3×C4—122no—
583C2×C3×C4D3×D411yescharacteristic
584C2×C3×C4C2×#6711yescharacteristic
585C2×C3×C4C23×D311yescharacteristic
586C2×C3×C4C23×D311yescharacteristic
587#67—41no—
588#67—42no—
589#67—42no—
590#67—122no—
591#67—122no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—42no—
596C2×Dic3—42no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—121no—
602C2×Dic3—121no—
603C2×Dic3—122no—
604C2×Dic3C2×#6711yescharacteristic
605C2×Dic3C2×#6711yescharacteristic
606C2×Dic3C2×#6711yescharacteristic
607D12—21no—
608D12—21no—
609C4×D3—21no—
610C4×D3—21no—
611C4×D3—42no—
612C4×D3—122no—
613Dic6—21no—
614Dic6—21no—
615Dic6—21no—
616Dic6—61no—
617Dic6—61no—
618Dic6—61no—
619Dic6—61no—
620Dic6—121no—
621Dic6—121no—
622Dic6—122no—
623Dic6—122no—
624Dic6C2×#6712yes—
625C3×C8—32no—
626C3×C8—61no—
627C3⋊C8—21no—
628C3⋊C8—61no—
629C3⋊C8—61no—
630C3⋊C8—61no—
631C3⋊C8—61no—
632C3⋊C8—121no—
633C3⋊C8—121no—
634C3⋊C8C2×#6712yes—
635C2×C32—41no—
636C2×C32—42no—
637C2×C32D4211yescharacteristic
638C2×C32#57511yescharacteristic
639C2×C32#57811yescharacteristic
640C3×D3—41no—
641C3×D3—81no—
642#41—22no—
643#41—41no—
644#41—62no—
645#41—62no—
646#41—121no—
647#41—121no—
648C2×Q8—31no—
649C2×Q8—31no—
650C2×Q8—91no—
651C2×Q8—181no—
652C2×Q8—182no—
653C2×Q8—361no—
654C2×Q8C2×D3211yescharacteristic
655C2×D4—21no—
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—61no—
659C2×D4—61no—
660C2×D4—181no—
661C2×D4C2×D3211yescharacteristic
662C22×C4—21no—
663C22×C4—31no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—181no—
668C22×C4C2×D3211yescharacteristic
669Q16—62no—
670Q16—182no—
671Q16—182no—
672Q16—361no—
673SD16—34no—
674SD16—62no—
675SD16—182no—
676SD16—361no—
677D8—62no—
678M16—182no—
679C2×C8—31no—
680C2×C8—31no—
681C2×C8—62no—
682C2×C8—91no—
683C2×C8—91no—
684C4⋊C4—31no—
685C4⋊C4—31no—
686C4⋊C4—61no—
687C4⋊C4—61no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4—91no—
691C4⋊C4—181no—
692C4⋊C4—181no—
693C22⋊C4—31no—
694C22⋊C4—31no—
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—61no—
698C22⋊C4—181no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C42—31no—
703C42—181no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—22no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—22no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—42no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—81no—
725C22×C3—81no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3C2×D3×D411yescharacteristic
730C22×C3C22×#6711yescharacteristic
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—41no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—21no—
741C3×C4—41no—
742C3×C4—42no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—61no—
746C3×C4—61no—
747C3×C4—61no—
748C3×C4—62no—
749C3×C4—121no—
750C3×C4—121no—
751C3×C4C2×D3×D411yescharacteristic
752C3×C4#100411yescharacteristic
753C3×C4#100411yescharacteristic
754C3×C4C22×#6711yescharacteristic
755Dic3—22no—
756Dic3—21no—
757Dic3—21no—
758Dic3—21no—
759Dic3—41no—
760Dic3—41no—
761Dic3—121no—
762Dic3—121no—
763Dic3—121no—
764Dic3—121no—
765Dic3—241no—
766Dic3—241no—
767C32#326911yescharacteristic, complemented, Sylow
768C23—21no—
769C23—31no—
770C23—61no—
771C23D3×#6711yescharacteristic
772Q8—21no—
773Q8—21no—
774Q8—32no—
775Q8—61no—
776Q8—61no—
777Q8—61no—
778Q8—181no—
779Q8—181no—
780Q8—362no—
781D4—21no—
782D4—42no—
783D4—61no—
784D4—61no—
785D4—121no—
786D4—122no—
787D4—122no—
788D4—362no—
789D4D3×#6712yes—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—31no—
794C2×C4—31no—
795C2×C4—31no—
796C2×C4—42no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—122no—
803C2×C4—122no—
804C2×C4—122no—
805C2×C4—181no—
806C2×C4—181no—
807C2×C4—362no—
808C2×C4D3×#6711yescharacteristic
809C2×C4C22×D3211yescharacteristic
810C8—32no—
811C8—61no—
812C8—181no—
813C8—181no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—41no—
818C2×C3—42no—
819C2×C3—41no—
820C2×C3—42no—
821C2×C3—81no—
822C2×C3—82no—
823C2×C3—121no—
824C2×C3—241no—
825C2×C3#576811yescharacteristic
826C2×C3#577111yescharacteristic
827C2×C3D4×#6711yescharacteristic
828C2×C3D4×#6711yescharacteristic
829C2×C3#582211yescharacteristic
830C2×C3#583811yescharacteristic
831D3—41no—
832D3—81no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—22no—
837C22—41no—
838C22—41no—
839C22—61no—
840C22—61no—
841C22—61no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22C2×D3×#6711yescharacteristic
846C4—21no—
847C4—41no—
848C4—61no—
849C4—61no—
850C4—61no—
851C4—62no—
852C4—121no—
853C4—121no—
854C4—361no—
855C4—361no—
856C4C2×D3×#6711yescharacteristic
857C4#6433011yescharacteristic
858C3—21no—
859C3#8352811yescharacteristic, complemented
860C3#8392511yescharacteristic, complemented
861C2—41no—
862C2—42no—
863C2—121no—
864C2—241no—
865C2#1059545311yescharacteristic
866C2#1059546711yescharacteristic
867C2#67211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3269
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5824C2semidirect
2. C2×C3×#950C2semidirect
3. C2×#63929C2semidirect
4. #10594899C2semidirect
5. #10592938C2semidirect
6. #10591653C2semidirect
7. #10591605C2semidirect
8. #10591587C2semidirect
9. #10591574C2semidirect
10. #10591468C2semidirect
11. #10591450C2semidirect
12. #10591440C2semidirect
13. #10591187C2semidirect
14. #10591170C2semidirect
15. #10591155C2semidirect
66. #5824D3semidirect
68. C2×#950D3semidirect
133. C3×#214D4semidirect
418. #214#67semidirect
767. C32#3269semidirect
859. C3#83528semidirect
860. C3#83925semidirect

Maximal subgroups

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

subgroupindex
C3×#58242
C2×C3×#9502
C2×#639292
#105948992
#105929382
#105916532
#105916052
#105915872
#105915742
#105914682
#105914502
#105914402
#105911872
#105911702
#105911552
#839253
#835283