Finite Group Databasebeta

← #11884617

Subgroups — #11884617

Order 1152.

1018 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5677C211yesmaximal, characteristic, complemented
2C2×#63946C211yesmaximal, characteristic, complemented
3C2×#63933C211yesmaximal, characteristic, complemented
4#10593895C211yesmaximal, characteristic, complemented
5#10592759C211yesmaximal, characteristic, complemented
6C3×#5057C211yesmaximal, characteristic, complemented
7#10591655C211yesmaximal, characteristic, complemented
8#10591596C211yesmaximal, characteristic, complemented
9#10591595C211yesmaximal, characteristic, complemented
10#10591519C211yesmaximal, characteristic, complemented
11#10591463C211yesmaximal, characteristic, complemented
12#10591462C211yesmaximal, characteristic, complemented
13#10590385C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590330C211yesmaximal, characteristic, complemented
16#83543—31nomaximal
17#80554—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C32×#124C2211yescharacteristic
23C2×#3756C2211yescharacteristic
24C2×#3756C2211yescharacteristic
25C2×#3754C2211yescharacteristic
26C2×#3754C2211yescharacteristic
27#64078C2211yescharacteristic
28C3×#946C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic
30C3×#938C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#885—21no—
33C3×#884—21no—
34C3×#67⋊C4—21no—
35C3×#878—21no—
36C3×C4×D12C2211yescharacteristic
37C3×C4×D12C2211yescharacteristic
38C3×C4×Dic6C2211yescharacteristic
39#63946—24no—
40#63933—24no—
41#63908—21no—
42#63891—21no—
43#63891—21no—
44D3×C4⋊Dic3—21no—
45#63857C2211yescharacteristic
46#63857C2211yescharacteristic
47C2×#3719C2211yescharacteristic
48C2×#3719C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52#63630C2211yescharacteristic
53C3×#835C2211yescharacteristic
54C3×#832C2211yescharacteristic
55C3×C4⋊(C3⋊C8)C2211yescharacteristic
56#63576C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63565C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
63C3×#548—31no—
64C2×#950—31no—
65C2×#942—31no—
66C2×#915—31no—
67C2×#912—31no—
68#5677D311yescharacteristic, complemented
69#5555—31no—
70#5551—31no—
71C3×#463—31no—
72#5239—31no—
73#5228—31no—
74#5173—31no—
75#5158—31no—
76#5060—31no—
77#5060—31no—
78#5060—61no—
79#5057D311yescharacteristic, complemented
80#5051—31no—
81#5047—31no—
82#5042—31no—
83#5037—31no—
84#5031—31no—
85#5026—31no—
86#5018—31no—
87#5011—31no—
88#4849—31no—
89#4836—31no—
90#4813—31no—
91#4809—31no—
92#4783—31no—
93#4780—31no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×D3×Q8—22no—
102C3×D3×Q8—41no—
103C3×#237—22no—
104C3×#237—41no—
105C2×C3×D12D411yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6—21no—
112C2×C3×Dic6C2311yescharacteristic
113C2×#625—21no—
114C2×#625—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117#3795—22no—
118#3795—22no—
119#3795—41no—
120#3795—41no—
121C32×C22⋊C4—21no—
122C32×C22⋊C4—21no—
123C32×C42C2311yescharacteristic
124#3756—22no—
125#3756—41no—
126#3754—22no—
127#3754—41no—
128C4⋊(C3⋊Dic3)—21no—
129C4⋊(C3⋊Dic3)—21no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#217—21no—
133C3×#215—22no—
134C3×#213—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×(C2×D3)⋊C4D411yescharacteristic
139C3×C4⋊Dic3D411yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×C4⋊Dic3C2311yescharacteristic
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4—21no—
144C3×C4×Dic3—21no—
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147Dic3⋊Dic3—21no—
148Dic3⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151#3719—22no—
152#3719—22no—
153#3715D414yescomplemented
154#3711—22no—
155D3×C3⋊C8—22no—
156#3269—91noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C2×D3×Q8C2×D311yescharacteristic
160C2×#237—31no—
161C2×#237—31no—
162C2×#237C2×D311yescharacteristic
163C2×#235—31no—
164C2×#235—31no—
165C2×C3×SD16—31no—
166C2×C3×D8—31no—
167C3×#124—21no—
168C3×#124—61no—
169C3×#124C2×D311yescharacteristic
170C3×#124C2×D311yescharacteristic
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—61no—
173C3×#121—31no—
174C3×#121—61no—
175C3×C4×Q8—31no—
176C3×C4×D4—31no—
177C3×C4×D4—31no—
178C3×C4×D4—61no—
179#950—64no—
180#946C2×D311yescharacteristic
181C2×#216—31no—
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—61no—
188C2×#216—61no—
189#942—64no—
190C2×#215—31no—
191C2×#215C2×D311yescharacteristic
192#938—61no—
193#938C2×D311yescharacteristic
194C2×#214—31no—
195C2×#214—31no—
196C2×#214—31no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#214—61no—
200C2×#214—61no—
201C2×#213C2×D311yescharacteristic
202#930—61no—
203C2×C4⋊Dic3—61no—
204#924—31no—
205#924—31no—
206C2×#208—31no—
207C22×C3⋊C8—31no—
208#915—64no—
209#912—64no—
210C2×Dic12—31no—
211C2×Dic12—31no—
212C2×ΓL(1,𝔽25)—31no—
213C2×D3×C8—31no—
214#897—31no—
215#897—31no—
216D3×C4⋊C4—61no—
217#886—61no—
218#886—61no—
219#885—21no—
220#884—21no—
221#883—61no—
222#883—61no—
223#67⋊C4—21no—
224#878—21no—
225C4×D12C2×D311yescharacteristic
226C4×D12C2×D311yescharacteristic
227#869—31no—
228#869—31no—
229#869—61no—
230C4×Dic6C2×D311yescharacteristic
231C3×C4⋊C8—31no—
232C3×#103—31no—
233C3×#102—31no—
234#835—31no—
235#835C2×D311yescharacteristic
236#832—31no—
237#832C2×D311yescharacteristic
238#830—31no—
239#830—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242#816—31no—
243#816—31no—
244#810—31no—
245#810—31no—
246#810—31no—
247#809—31no—
248#807—31no—
249#807—31no—
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×Q8—21no—
259C32×Q8—21no—
260C32×D4—21no—
261C32×D4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268#634—21no—
269#634—21no—
270#634—21no—
271#634—21no—
272C3×#67—42no—
273C3×#67—42no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—42no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—41no—
282C3×D12C2×D412yes—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—42no—
288C3×C4×D3—42no—
289C3×Dic6—21no—
290C3×Dic6—42no—
291C3×Dic6C2×D412yes—
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—31no—
303#547—91no—
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—121no—
317C2×C3×Q8—21no—
318C2×C3×Q8—31no—
319C2×C3×Q8—61no—
320C2×C3×Q8—62no—
321C2×C3×Q8—121no—
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×D4—21no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C2×C3×D4C22×D311yescharacteristic
330C2×C3×D4C22×D311yescharacteristic
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—61no—
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—61no—
344C22×Dic3—61no—
345D3×Q8—22no—
346D3×Q8—41no—
347#237—22no—
348#237—41no—
349#237—62no—
350#237—62no—
351#237—121no—
352#237—121no—
353#235—62no—
354#235—62no—
355#235—121no—
356#235—121no—
357C2×D12#6711yescharacteristic
358C2×D12C22×D311yescharacteristic
359C2×C4×D3—21no—
360C2×C4×D3—21no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3C22×D311yescharacteristic
364C2×C4×D3C22×D311yescharacteristic
365C2×Dic6—21no—
366C2×Dic6—31no—
367C2×Dic6—31no—
368C2×Dic6—31no—
369C2×Dic6—31no—
370C2×Dic6—61no—
371C2×Dic6—61no—
372C2×Dic6C22×D311yescharacteristic
373C3×SD16—62no—
374C3×D8—62no—
375C2×C3×C8—31no—
376C2×C3×C8—31no—
377C3×C4⋊C4—31no—
378C3×C4⋊C4—31no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—61no—
381C3×C4⋊C4—61no—
382C3×C22⋊C4—21no—
383C3×C22⋊C4—21no—
384C3×C22⋊C4—21no—
385C3×C22⋊C4—21no—
386C3×C22⋊C4—31no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—41no—
389C3×C22⋊C4—41no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C42—21no—
394C3×C42—61no—
395C3×C42C22×D311yescharacteristic
396C3×C42C22×D311yescharacteristic
397#217—21no—
398#217—61no—
399#217—61no—
400#216—62no—
401#216—62no—
402#216—62no—
403#216—62no—
404#216—122no—
405#216—121no—
406#216—121no—
407#216—122no—
408#215—22no—
409#215—34no—
410#214—34no—
411#214—62no—
412#214—62no—
413#214—122no—
414#214—121no—
415#214—121no—
416#214—122no—
417#213—22no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4#6711yescharacteristic
423(C2×D3)⋊C4#6711yescharacteristic
424C4⋊Dic3—61no—
425C4⋊Dic3—61no—
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3—121no—
431C4⋊Dic3—121no—
432C4⋊Dic3#6711yescharacteristic
433C4⋊Dic3C22×D311yescharacteristic
434C4⋊Dic3C22×D311yescharacteristic
435Dic3⋊C4—21no—
436Dic3⋊C4—21no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439C4×Dic3—21no—
440#208—62no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—61no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8—62no—
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450Dic12—62no—
451Dic12—62no—
452ΓL(1,𝔽25)—62no—
453D3×C8—62no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32—41no—
457C22×C32C22×D411yescharacteristic
458C2×C3×D3—22no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C32×C4—21no—
468C32×C4—21no—
469C32×C4—41no—
470C32×C4C22×D411yescharacteristic
471C32×C4H(5,𝔽2)11yescharacteristic
472C3⋊Dic3—41no—
473C3⋊Dic3—41no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—22no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C2×#41—31no—
480C2×#41—91no—
481C2×#41—91no—
482C22×Q8—31no—
483#137—184no—
484#135—184no—
485C2×Q16—91no—
486C2×Q16—91no—
487C2×Q16—91no—
488C2×Q16—91no—
489C2×SD16—31no—
490C2×SD16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×D8—31no—
494C2×M16—91no—
495C22×C8—91no—
496C4⋊Q8—91no—
497#124—61no—
498#124D3211yescharacteristic
499#123—181no—
500#123—181no—
501C22⋊Q8—31no—
502C22⋊Q8—61no—
503C22⋊Q8—91no—
504C22⋊Q8—91no—
505#121—31no—
506#121—61no—
507#121—181no—
508C4×Q8—31no—
509C4×D4—31no—
510C4×D4—31no—
511C4×D4—61no—
512C2×C4⋊C4—181no—
513#107—91no—
514C4⋊C8—31no—
515#103—31no—
516#103—91no—
517#103—91no—
518#103—91no—
519#102—31no—
520#102—91no—
521C22⋊C8—91no—
522C22⋊C8—91no—
523#97—91no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—31no—
527C23×C3—31no—
528C23×C3—41no—
529C23×C3—61no—
530C22×D3—21no—
531C22×D3C2×#6711yescharacteristic
532C22×D3C2×#6711yescharacteristic
533C3×Q8—21no—
534C3×Q8—21no—
535C3×Q8—21no—
536C3×Q8—21no—
537C3×Q8—32no—
538C3×Q8—41no—
539C3×Q8—41no—
540C3×Q8—61no—
541C3×Q8—122no—
542C3×D4—21no—
543C3×D4—21no—
544C3×D4—21no—
545C3×D4—21no—
546C3×D4—32no—
547C3×D4—41no—
548C3×D4—41no—
549C3×D4—61no—
550C3×D4—121no—
551C3×D4—122no—
552C3×D4—122no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—41no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—122no—
569C2×C3×C4—122no—
570C2×C3×C4—122no—
571C2×C3×C4D3×D411yescharacteristic
572C2×C3×C4D3×D411yescharacteristic
573C2×C3×C4C2×#6711yescharacteristic
574C2×C3×C4C2×#6711yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577#67—42no—
578#67—42no—
579#67—122no—
580#67—122no—
581#67—122no—
582#67—122no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—42no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—121no—
592C2×Dic3—121no—
593C2×Dic3—122no—
594C2×Dic3—122no—
595C2×Dic3C2×#6711yescharacteristic
596C2×Dic3C2×#6711yescharacteristic
597D12—21no—
598D12—41no—
599D12D3×D412yes—
600C4×D3—21no—
601C4×D3—21no—
602C4×D3—21no—
603C4×D3—21no—
604C4×D3—42no—
605C4×D3—42no—
606C4×D3—122no—
607C4×D3—122no—
608Dic6—21no—
609Dic6—42no—
610Dic6—61no—
611Dic6—61no—
612Dic6—61no—
613Dic6—61no—
614Dic6—61no—
615Dic6—61no—
616Dic6—61no—
617Dic6—61no—
618Dic6—121no—
619Dic6—121no—
620Dic6—121no—
621Dic6—121no—
622Dic6D3×D412yes—
623C3×C8—61no—
624C3×C8—61no—
625C3⋊C8—21no—
626C3⋊C8—21no—
627C3⋊C8—32no—
628C3⋊C8—32no—
629C3⋊C8—62no—
630C3⋊C8—62no—
631C3⋊C8—61no—
632C3⋊C8—61no—
633C2×C32—81no—
634C2×C32D4211yescharacteristic
635C2×C32#57511yescharacteristic
636C2×C32#57811yescharacteristic
637C3×D3—41no—
638C3×D3—41no—
639C3×D3—42no—
640#41—62no—
641#41—121no—
642#41—182no—
643#41—182no—
644#41—361no—
645#41—361no—
646C2×Q8—31no—
647C2×Q8—61no—
648C2×Q8—62no—
649C2×Q8—91no—
650C2×Q8—91no—
651C2×Q8—121no—
652C2×Q8C2×D3211yescharacteristic
653C2×D4—31no—
654C2×D4—31no—
655C2×D4—61no—
656C2×D4—61no—
657C2×D4—181no—
658C2×D4—181no—
659C2×D4C2×D3211yescharacteristic
660C22×C4—31no—
661C22×C4—31no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—61no—
665C22×C4—181no—
666C22×C4—181no—
667Q16—182no—
668Q16—182no—
669Q16—182no—
670Q16—361no—
671SD16—62no—
672SD16—94no—
673SD16—182no—
674SD16—361no—
675D8—62no—
676M16—182no—
677C2×C8—31no—
678C2×C8—31no—
679C2×C8—91no—
680C2×C8—91no—
681C2×C8—182no—
682C4⋊C4—31no—
683C4⋊C4—31no—
684C4⋊C4—31no—
685C4⋊C4—61no—
686C4⋊C4—61no—
687C4⋊C4—181no—
688C4⋊C4—181no—
689C4⋊C4—181no—
690C4⋊C4—181no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—31no—
694C22⋊C4—31no—
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—61no—
698C22⋊C4—181no—
699C22⋊C4—181no—
700C42—61no—
701C42C2×D3211yescharacteristic
702C22×C3—21no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3—61no—
713C22×C3—62no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—81no—
717C22×C3—81no—
718C22×C3—81no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3C2×D3×D411yescharacteristic
722C22×C3C22×#6711yescharacteristic
723C2×D3—21no—
724C2×D3—21no—
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—22no—
730C2×D3—41no—
731C2×D3—41no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—41no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—61no—
743C3×C4—61no—
744C3×C4—62no—
745C3×C4—81no—
746C3×C4—121no—
747C3×C4—121no—
748C3×C4C2×D3×D411yescharacteristic
749C3×C4C2×D3×D411yescharacteristic
750C3×C4#100411yescharacteristic
751C3×C4#100911yescharacteristic
752Dic3—22no—
753Dic3—21no—
754Dic3—21no—
755Dic3—41no—
756Dic3—41no—
757Dic3—121no—
758Dic3—121no—
759Dic3—121no—
760Dic3—121no—
761Dic3—241no—
762Dic3—241no—
763C32#326911yescharacteristic, complemented, Sylow
764C23—21no—
765C23—31no—
766C23—31no—
767C23—61no—
768Q8—21no—
769Q8—21no—
770Q8—32no—
771Q8—61no—
772Q8—122no—
773Q8—181no—
774Q8—181no—
775Q8—181no—
776Q8—181no—
777D4—21no—
778D4—21no—
779D4—32no—
780D4—61no—
781D4—121no—
782D4—122no—
783D4—122no—
784D4—362no—
785D4—362no—
786C2×C4—21no—
787C2×C4—31no—
788C2×C4—31no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—122no—
797C2×C4—122no—
798C2×C4—122no—
799C2×C4—181no—
800C2×C4—181no—
801C2×C4—362no—
802C2×C4—362no—
803C2×C4D3×#6711yescharacteristic
804C2×C4D3×#6711yescharacteristic
805C2×C4C22×D3211yescharacteristic
806C8—61no—
807C8—61no—
808C8—92no—
809C8—181no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—81no—
814C2×C3—81no—
815C2×C3—122no—
816C2×C3—121no—
817C2×C3—121no—
818C2×C3—161no—
819C2×C3#560911yescharacteristic
820C2×C3#577111yescharacteristic
821C2×C3#577311yescharacteristic
822C2×C3D4×#6711yescharacteristic
823C2×C3#582211yescharacteristic
824C2×C3#583811yescharacteristic
825D3—41no—
826D3—41no—
827D3—42no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—61no—
832C22—61no—
833C22—61no—
834C22—61no—
835C22—61no—
836C22—61no—
837C22—62no—
838C22—121no—
839C22—121no—
840C22C2×D3×#6711yescharacteristic
841C4—21no—
842C4—21no—
843C4—41no—
844C4—61no—
845C4—61no—
846C4—62no—
847C4—121no—
848C4—121no—
849C4—361no—
850C4—361no—
851C4D32×D411yescharacteristic
852C4#6431411yescharacteristic
853C3—21no—
854C3#8055411yescharacteristic, complemented
855C3#8354311yescharacteristic, complemented
856C2—81no—
857C2—121no—
858C2—121no—
859C2—122no—
860C2#1059528811yescharacteristic
861C2#1059546711yescharacteristic
862C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
hypercenter#124D32
hypocenterC32#3269
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#5677C2semidirect
2. C2×#63946C2semidirect
3. C2×#63933C2semidirect
4. #10593895C2semidirect
5. #10592759C2semidirect
6. C3×#5057C2semidirect
7. #10591655C2semidirect
8. #10591596C2semidirect
9. #10591595C2semidirect
10. #10591519C2semidirect
11. #10591463C2semidirect
12. #10591462C2semidirect
13. #10590385C2semidirect
14. #10590358C2semidirect
15. #10590330C2semidirect
68. #5677D3semidirect
79. #5057D3semidirect
153. #3715D4semidirect
763. C32#3269semidirect
854. C3#80554semidirect
855. C3#83543semidirect

Maximal subgroups

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

subgroupindex
C3×#56772
C2×#639462
C2×#639332
#105938952
#105927592
C3×#50572
#105916552
#105915962
#105915952
#105915192
#105914632
#105914622
#105903852
#105903582
#105903302
#835433
#805543