Finite Group Databasebeta

← #11884597

Subgroups — #11884597

Order 1152.

1016 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5555C211yesmaximal, characteristic, complemented
2C2×#63933C211yesmaximal, characteristic, complemented
3C2×#63929C211yesmaximal, characteristic, complemented
4#10593905C211yesmaximal, characteristic, complemented
5#10592717C211yesmaximal, characteristic, complemented
6C3×#5016C211yesmaximal, characteristic, complemented
7#10591461C211yesmaximal, characteristic, complemented
8#10591450C211yesmaximal, characteristic, complemented
9#10590614C211yesmaximal, characteristic, complemented
10#10590604C211yesmaximal, characteristic, complemented
11#10590518C211yesmaximal, characteristic, complemented
12#10590503C211yesmaximal, characteristic, complemented
13#10590388C211yesmaximal, characteristic, complemented
14#10590376C211yesmaximal, characteristic, complemented
15#10590330C211yesmaximal, characteristic, complemented
16#83528—31nomaximal
17#80554—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24C4×#634C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C3×#930—21no—
28C2×C3×C4⋊Dic3—21no—
29C3×#897C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#886—21no—
32C3×#886—21no—
33C3×#875C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35C3×#869C2211yescharacteristic
36#63933—24no—
37#63929—24no—
38#63915—21no—
39#63908C2211yescharacteristic
40#63902—21no—
41#63899—21no—
42#63885—21no—
43#63856C2211yescharacteristic
44C2×#3719C2211yescharacteristic
45C2×#3719C2211yescharacteristic
46C2×#3718C2211yescharacteristic
47C2×#3718C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52#63659C2211yescharacteristic
53#63637C2211yescharacteristic
54#63634C2211yescharacteristic
55#63630C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×C4⋊(C3⋊C8)C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
63C3×#547—31no—
64C2×#951—31no—
65C2×#950—31no—
66C2×#915—31no—
67C2×#912—31no—
68#5677—31no—
69#5555D311yescharacteristic, complemented
70#5552—31no—
71C3×#463—31no—
72#5239—31no—
73#5238—31no—
74#5173—31no—
75#5158—31no—
76#5090—31no—
77#5086—31no—
78#5060—31no—
79#5051—31no—
80#5050—31no—
81#5049—31no—
82#5047—31no—
83#5018—31no—
84#5018—31no—
85#5018—61no—
86#5016D311yescharacteristic, complemented
87#5011—31no—
88#4849—31no—
89#4836—31no—
90#4813—31no—
91#4809—31no—
92#4783—31no—
93#4780—31no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C3×#237—22no—
102C3×#237—22no—
103C3×#237—41no—
104C3×#237—41no—
105C2×C3×D12D411yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#627—21no—
113C2×#625—21no—
114C2×#625—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117#3795—22no—
118#3795—41no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121C32×C4⋊C4C2311yescharacteristic
122C32×C22⋊C4—21no—
123C32×C42C2311yescharacteristic
124#3754D414yescomplemented
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127C4×C3⋊Dic3—21no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#214—22no—
131C3×#213—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×C4⋊Dic3—21no—
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3—21no—
141C3×C4⋊Dic3—21no—
142C3×C4⋊Dic3D411yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145#3724—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148#3719—22no—
149#3719—22no—
150#3718—22no—
151#3718—41no—
152#3715—22no—
153#3715—41no—
154#3711—22no—
155D3×C3⋊C8—22no—
156#3269—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×D3×Q8—31no—
160C2×#237—31no—
161C2×#237C2×D311yescharacteristic
162C2×#237C2×D311yescharacteristic
163C2×#235—31no—
164C22×Dic6—31no—
165C2×C3×SD16—31no—
166C2×C3×D8—31no—
167C3×C4⋊Q8—31no—
168C3×#124—31no—
169C3×#123—61no—
170C3×#123—61no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—31no—
173C3×#121—61no—
174C3×C4×D4—21no—
175C3×C4×D4—31no—
176C3×C4×D4C2×D311yescharacteristic
177C3×C4×D4C2×D311yescharacteristic
178C2×C3×C4⋊C4—61no—
179#951—64no—
180#950—64no—
181#946—31no—
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—31no—
188C2×#215—31no—
189C2×#215—31no—
190#939—61no—
191#938—31no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214—31no—
195C2×#214—31no—
196C2×#214—61no—
197C2×#214C2×D311yescharacteristic
198C2×#213C2×D311yescharacteristic
199#930—21no—
200#930—31no—
201C2×C4⋊Dic3—21no—
202#924—31no—
203C2×#208—31no—
204C22×C3⋊C8—31no—
205#915—64no—
206#912—64no—
207C2×Dic12—31no—
208C2×Dic12—31no—
209C2×ΓL(1,𝔽25)—31no—
210C2×D3×C8—31no—
211#897C2×D311yescharacteristic
212#897C2×D311yescharacteristic
213#896—61no—
214#886—21no—
215#886—21no—
216#885—61no—
217#885—61no—
218#884—61no—
219#67⋊C4—61no—
220#67⋊C4—61no—
221#878—61no—
222#875C2×D311yescharacteristic
223C4×D12C2×D311yescharacteristic
224#869C2×D311yescharacteristic
225C4×Dic6—31no—
226C4×Dic6—31no—
227C4×Dic6—61no—
228C3×C4⋊C8—31no—
229C3×#103—31no—
230C3×#102—31no—
231#835—31no—
232#835—31no—
233#832—31no—
234#832—31no—
235#832—61no—
236#830—31no—
237#830—31no—
238(C2×D3)⋊C8—31no—
239(C2×D3)⋊C8—31no—
240#816—31no—
241#816—31no—
242#810—31no—
243#810—31no—
244#810—61no—
245#810C2×D311yescharacteristic
246#809C2×D311yescharacteristic
247#807—31no—
248#807—31no—
249#807—61no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic
251#803—31no—
252#803—31no—
253#803—61no—
254C23×C32—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C22×C3×D3C2×D411yescharacteristic
258C32×D4—21no—
259C32×D4C2×D412yes—
260C2×C32×C4—21no—
261C2×C32×C4—42no—
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267#634—21no—
268#634C2×D412yes—
269C3×#67—42no—
270C3×#67—42no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—42no—
275C2×C3×Dic3—42no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—41no—
281C3×C4×D3—21no—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#627—42no—
292#625—42no—
293#625—42no—
294D3×Dic3—42no—
295D3×Dic3—42no—
296C3⋊(C3⋊C8)—21no—
297C3⋊(C3⋊C8)C2×D412yes—
298C3×C3⋊C8—21no—
299C3×C3⋊C8—21no—
300C2×#137—91no—
301C2×#135—91no—
302#548—91no—
303#547—31no—
304#497—91no—
305#468—91no—
306#467—91no—
307#463—31no—
308#462—91no—
309#452—91no—
310#452—91no—
311#451—91no—
312#449—91no—
313#440—91no—
314#435—91no—
315C3×#41—62no—
316C3×#41—62no—
317C3×#41—121no—
318C3×#41—121no—
319C2×C3×Q8—31no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×D4—21no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—61no—
326C2×C3×D4—61no—
327C2×C3×D4C22×D311yescharacteristic
328C2×C3×D4C22×D311yescharacteristic
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—41no—
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—61no—
345C22×Dic3—61no—
346D3×Q8—62no—
347D3×Q8—121no—
348#237—22no—
349#237—22no—
350#237—41no—
351#237—41no—
352#237—62no—
353#237—121no—
354#235—62no—
355#235—121no—
356C2×D12#6711yescharacteristic
357C2×D12C22×D311yescharacteristic
358C2×C4×D3—61no—
359C2×C4×D3—61no—
360C2×C4×D3C22×D311yescharacteristic
361C2×C4×D3C22×D311yescharacteristic
362C2×Dic6—31no—
363C2×Dic6—31no—
364C2×Dic6—61no—
365C2×Dic6—62no—
366C2×Dic6—61no—
367C2×Dic6—61no—
368C2×Dic6—121no—
369C2×Dic6C22×D311yescharacteristic
370C2×Dic6C22×D311yescharacteristic
371C2×Dic6C22×D311yescharacteristic
372C3×SD16—62no—
373C3×D8—62no—
374C2×C3×C8—31no—
375C2×C3×C8—31no—
376C3×C4⋊C4—21no—
377C3×C4⋊C4—31no—
378C3×C4⋊C4—61no—
379C3×C4⋊C4—61no—
380C3×C4⋊C4—61no—
381C3×C4⋊C4—61no—
382C3×C4⋊C4C22×D311yescharacteristic
383C3×C4⋊C4C22×D311yescharacteristic
384C3×C22⋊C4—21no—
385C3×C22⋊C4—21no—
386C3×C22⋊C4—31no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—41no—
389C3×C22⋊C4—61no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C42—21no—
394C3×C42C22×D311yescharacteristic
395C3×C42C22×D311yescharacteristic
396#217—61no—
397#217—61no—
398#216—62no—
399#216—62no—
400#216—62no—
401#216—62no—
402#216—121no—
403#216—121no—
404#215—62no—
405#215—121no—
406#214—22no—
407#214—34no—
408#214—34no—
409#214—64no—
410#214—62no—
411#214—121no—
412#213—22no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—21no—
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4#6711yescharacteristic
420(C2×D3)⋊C4#6711yescharacteristic
421C4⋊Dic3—21no—
422C4⋊Dic3—21no—
423C4⋊Dic3—21no—
424C4⋊Dic3—21no—
425C4⋊Dic3—31no—
426C4⋊Dic3—31no—
427C4⋊Dic3—61no—
428C4⋊Dic3#6711yescharacteristic
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—121no—
434C4×Dic3—61no—
435C4×Dic3—61no—
436C4×Dic3—121no—
437#208—62no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—61no—
443C2×C3⋊C8—61no—
444C2×C3⋊C8—62no—
445C2×C3⋊C8C22×D311yescharacteristic
446C2×C3⋊C8C22×D311yescharacteristic
447Dic12—62no—
448Dic12—62no—
449ΓL(1,𝔽25)—62no—
450D3×C8—62no—
451C22×C32—22no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32C22×D411yescharacteristic
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C32×C4—21no—
465C32×C4—21no—
466C32×C4—41no—
467C32×C4C22×D411yescharacteristic
468C32×C4H(5,𝔽2)11yescharacteristic
469C3⋊Dic3—22no—
470C3⋊Dic3—41no—
471C3×Dic3—21no—
472C3×Dic3—21no—
473C3×Dic3—41no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C2×#41—31no—
477C2×#41—31no—
478C2×#41—91no—
479C22×Q8—91no—
480#137—184no—
481#135—184no—
482C2×Q16—91no—
483C2×Q16—91no—
484C2×Q16—91no—
485C2×Q16—91no—
486C2×SD16—31no—
487C2×SD16—91no—
488C2×SD16—91no—
489C2×SD16—91no—
490C2×D8—31no—
491C2×M16—91no—
492C22×C8—91no—
493C4⋊Q8—31no—
494#124—31no—
495#124—181no—
496#123—61no—
497#123—61no—
498C22⋊Q8—31no—
499C22⋊Q8—31no—
500C22⋊Q8—91no—
501C22⋊Q8—181no—
502#121—61no—
503#121—91no—
504#121—181no—
505C4×Q8—91no—
506C4×D4—31no—
507C4×D4—181no—
508C4×D4D3211yescharacteristic
509C2×C4⋊C4—61no—
510#107—91no—
511C4⋊C8—31no—
512#103—31no—
513#103—91no—
514#103—91no—
515#103—91no—
516#102—31no—
517#102—91no—
518C22⋊C8—91no—
519C22⋊C8—91no—
520#97—91no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—31no—
524C23×C3—31no—
525C23×C3—41no—
526C23×C3—61no—
527C22×D3—21no—
528C22×D3C2×#6711yescharacteristic
529C22×D3C2×#6711yescharacteristic
530C3×Q8—61no—
531C3×Q8—61no—
532C3×Q8—61no—
533C3×Q8—61no—
534C3×Q8—61no—
535C3×Q8—61no—
536C3×D4—21no—
537C3×D4—21no—
538C3×D4—22no—
539C3×D4—41no—
540C3×D4—61no—
541C3×D4—61no—
542C3×D4—121no—
543C3×D4—122no—
544C3×D4—122no—
545C3×D4D3×D412yes—
546C3×D4D3×D412yes—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—41no—
555C2×C3×C4—42no—
556C2×C3×C4—42no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—82no—
565C2×C3×C4—122no—
566C2×C3×C4—122no—
567C2×C3×C4D3×D411yescharacteristic
568C2×C3×C4D3×D411yescharacteristic
569C2×C3×C4C2×#6711yescharacteristic
570C2×C3×C4C2×#6711yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573#67—42no—
574#67—42no—
575#67—122no—
576#67—122no—
577#67—122no—
578#67—122no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—42no—
583C2×Dic3—42no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—121no—
589C2×Dic3—121no—
590C2×Dic3—122no—
591C2×Dic3—122no—
592C2×Dic3C2×#6711yescharacteristic
593C2×Dic3C2×#6711yescharacteristic
594D12—21no—
595D12—21no—
596D12—41no—
597C4×D3—21no—
598C4×D3—21no—
599C4×D3—21no—
600C4×D3—21no—
601C4×D3—122no—
602C4×D3—122no—
603Dic6—21no—
604Dic6—21no—
605Dic6—21no—
606Dic6—21no—
607Dic6—21no—
608Dic6—21no—
609Dic6—32no—
610Dic6—32no—
611Dic6—62no—
612Dic6—61no—
613Dic6—61no—
614Dic6—121no—
615Dic6—122no—
616Dic6—122no—
617C3×C8—61no—
618C3×C8—61no—
619C3⋊C8—21no—
620C3⋊C8—21no—
621C3⋊C8—32no—
622C3⋊C8—32no—
623C3⋊C8—62no—
624C3⋊C8—61no—
625C3⋊C8—61no—
626C3⋊C8—121no—
627C2×C32—42no—
628C2×C32D4211yescharacteristic
629C2×C32#57511yescharacteristic
630C2×C32#57811yescharacteristic
631C3×D3—41no—
632C3×D3—41no—
633C3×D3—81no—
634#41—62no—
635#41—62no—
636#41—121no—
637#41—121no—
638#41—182no—
639#41—361no—
640C2×Q8—31no—
641C2×Q8—31no—
642C2×Q8—31no—
643C2×Q8—91no—
644C2×Q8—181no—
645C2×Q8—182no—
646C2×Q8—361no—
647C2×D4—31no—
648C2×D4—31no—
649C2×D4—61no—
650C2×D4—61no—
651C2×D4—181no—
652C2×D4—181no—
653C2×D4C2×D3211yescharacteristic
654C22×C4—21no—
655C22×C4—31no—
656C22×C4—31no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—181no—
660C22×C4—181no—
661Q16—182no—
662Q16—182no—
663Q16—182no—
664Q16—361no—
665SD16—62no—
666SD16—94no—
667SD16—182no—
668SD16—361no—
669D8—62no—
670M16—182no—
671C2×C8—31no—
672C2×C8—31no—
673C2×C8—91no—
674C2×C8—91no—
675C2×C8—182no—
676C4⋊C4—31no—
677C4⋊C4—61no—
678C4⋊C4—61no—
679C4⋊C4—61no—
680C4⋊C4—61no—
681C4⋊C4—91no—
682C4⋊C4—181no—
683C4⋊C4—181no—
684C4⋊C4C2×D3211yescharacteristic
685C22⋊C4—21no—
686C22⋊C4—31no—
687C22⋊C4—31no—
688C22⋊C4—61no—
689C22⋊C4—61no—
690C22⋊C4—61no—
691C22⋊C4—61no—
692C22⋊C4—181no—
693C22⋊C4—181no—
694C42—181no—
695C42C2×D3211yescharacteristic
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—21no—
699C22×C3—42no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—61no—
705C22×C3—61no—
706C22×C3—61no—
707C22×C3—61no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—81no—
711C22×C3—81no—
712C22×C3—121no—
713C22×C3—121no—
714C22×C3—121no—
715C22×C3C2×D3×D411yescharacteristic
716C22×C3C22×#6711yescharacteristic
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—21no—
722C2×D3—21no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—41no—
726C3×C4—21no—
727C3×C4—21no—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—21no—
731C3×C4—21no—
732C3×C4—41no—
733C3×C4—41no—
734C3×C4—41no—
735C3×C4—41no—
736C3×C4—61no—
737C3×C4—61no—
738C3×C4—81no—
739C3×C4—121no—
740C3×C4—121no—
741C3×C4—121no—
742C3×C4C2×D3×D411yescharacteristic
743C3×C4C2×D3×D411yescharacteristic
744C3×C4#100411yescharacteristic
745C3×C4#100911yescharacteristic
746Dic3—21no—
747Dic3—21no—
748Dic3—41no—
749Dic3—41no—
750Dic3—41no—
751Dic3—62no—
752Dic3—62no—
753Dic3—122no—
754Dic3—121no—
755Dic3—121no—
756Dic3—241no—
757C32#326911yescharacteristic, complemented, Sylow
758C23—21no—
759C23—31no—
760C23—31no—
761C23—61no—
762Q8—61no—
763Q8—61no—
764Q8—61no—
765Q8—61no—
766Q8—61no—
767Q8—61no—
768Q8—92no—
769Q8—181no—
770Q8—362no—
771D4—21no—
772D4—61no—
773D4—61no—
774D4—121no—
775D4—122no—
776D4—122no—
777D4—362no—
778D4—362no—
779D4#380212yes—
780C2×C4—21no—
781C2×C4—31no—
782C2×C4—31no—
783C2×C4—42no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—122no—
792C2×C4—122no—
793C2×C4—181no—
794C2×C4—181no—
795C2×C4—362no—
796C2×C4—362no—
797C2×C4D3×#6711yescharacteristic
798C2×C4D3×#6711yescharacteristic
799C2×C4C22×D3211yescharacteristic
800C8—61no—
801C8—61no—
802C8—92no—
803C8—181no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—42no—
808C2×C3—42no—
809C2×C3—82no—
810C2×C3—121no—
811C2×C3—121no—
812C2×C3—241no—
813C2×C3#560911yescharacteristic
814C2×C3#577111yescharacteristic
815C2×C3#577311yescharacteristic
816C2×C3D4×#6711yescharacteristic
817C2×C3#582211yescharacteristic
818C2×C3#583811yescharacteristic
819D3—41no—
820D3—41no—
821D3—81no—
822C22—22no—
823C22—41no—
824C22—41no—
825C22—61no—
826C22—61no—
827C22—61no—
828C22—61no—
829C22—61no—
830C22—61no—
831C22—121no—
832C22—121no—
833C22—121no—
834C22C2×D3×#6711yescharacteristic
835C4—21no—
836C4—21no—
837C4—41no—
838C4—61no—
839C4—61no—
840C4—121no—
841C4—121no—
842C4—121no—
843C4—182no—
844C4—361no—
845C4C2×#380211yescharacteristic
846C4#6430711yescharacteristic
847C3—21no—
848C3#8055411yescharacteristic, complemented
849C3#8352811yescharacteristic, complemented
850C2—42no—
851C2—121no—
852C2—121no—
853C2—241no—
854C2#1059506911yescharacteristic
855C2#1059509511yescharacteristic
856C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3269
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5555C2semidirect
2. C2×#63933C2semidirect
3. C2×#63929C2semidirect
4. #10593905C2semidirect
5. #10592717C2semidirect
6. C3×#5016C2semidirect
7. #10591461C2semidirect
8. #10591450C2semidirect
9. #10590614C2semidirect
10. #10590604C2semidirect
11. #10590518C2semidirect
12. #10590503C2semidirect
13. #10590388C2semidirect
14. #10590376C2semidirect
15. #10590330C2semidirect
69. #5555D3semidirect
86. #5016D3semidirect
124. #3754D4semidirect
757. C32#3269semidirect
848. C3#80554semidirect
849. C3#83528semidirect

Maximal subgroups

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

subgroupindex
C3×#55552
C2×#639332
C2×#639292
#105939052
#105927172
C3×#50162
#105914612
#105914502
#105906142
#105906042
#105905182
#105905032
#105903882
#105903762
#105903302
#835283
#805543