Finite Group Databasebeta

← #11884616

Subgroups — #11884616

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×#63948C211yesmaximal, characteristic, complemented
3C2×#63935C211yesmaximal, characteristic, complemented
4#10593869C211yesmaximal, characteristic, complemented
5#10592756C211yesmaximal, characteristic, complemented
6C3×#5060C211yesmaximal, characteristic, complemented
7#10591657C211yesmaximal, characteristic, complemented
8#10591635C211yesmaximal, characteristic, complemented
9#10591594C211yesmaximal, characteristic, complemented
10#10591521C211yesmaximal, characteristic, complemented
11#10591502C211yesmaximal, characteristic, complemented
12#10591461C211yesmaximal, characteristic, complemented
13#10590384C211yesmaximal, characteristic, complemented
14#10590362C211yesmaximal, characteristic, complemented
15#10590326C211yesmaximal, characteristic, complemented
16#83543—31nomaximal
17#81883—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22C32×#124C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24C2×#3753C2211yescharacteristic
25C4×C4⋊(C3⋊D3)C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C3×#938C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C3×#885—21no—
33C3×#884—21no—
34C3×#67⋊C4—21no—
35C3×#878—21no—
36C3×C4×D12C2211yescharacteristic
37C3×#869C2211yescharacteristic
38C3×C4×Dic6C2211yescharacteristic
39#63948—24no—
40#63935—24no—
41#63916—21no—
42#63900—21no—
43#63856C2211yescharacteristic
44#63856C2211yescharacteristic
45#63854—21no—
46#63854—21no—
47C2×#3718C2211yescharacteristic
48C2×#3718C2211yescharacteristic
49C2×#3717C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52#63662C2211yescharacteristic
53#63659C2211yescharacteristic
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
55C3×#803C2211yescharacteristic
56#63575C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59#63565C2211yescharacteristic
60#63564C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
63C3×#548—31no—
64C2×#950—31no—
65C2×#942—31no—
66C2×#918—31no—
67C2×#916—31no—
68#5726—31no—
69#5677D311yescharacteristic, complemented
70#5551—31no—
71C3×#497—31no—
72#5239—31no—
73#5228—31no—
74#5188—31no—
75#5187—31no—
76#5186—31no—
77#5174—31no—
78#5173—31no—
79#5172—31no—
80#5090—31no—
81#5060D311yescharacteristic, complemented
82#5057—31no—
83#5057—31no—
84#5057—61no—
85#5051—31no—
86#5047—31no—
87#5042—31no—
88#5037—31no—
89#5031—31no—
90#5026—31no—
91#5011—31no—
92#4710—31no—
93#4706—31no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
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×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—21no—
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#626—21no—
115C2×#624—21no—
116C2×#624—21no—
117#3799—22no—
118#3799—22no—
119#3799—41no—
120#3799—41no—
121C32×C22⋊C4—21no—
122C32×C22⋊C4—21no—
123C32×C42C2311yescharacteristic
124#3755—22no—
125#3753—22no—
126#3752—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#217—21no—
131C3×#216—22no—
132C3×#216—41no—
133C3×#214—22no—
134C3×#214—41no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×C4⋊Dic3—21no—
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3D411yescharacteristic
141C3×C4⋊Dic3C2311yescharacteristic
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4—21no—
144C3×C4×Dic3—21no—
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147#3724—21no—
148#3724—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151#3718—22no—
152#3718—22no—
153#3717D414yescomplemented
154#3711—22no—
155D3×C3⋊C8—22no—
156#3269—91noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C2×#239—31no—
160C2×#239—31no—
161C2×D3×Q8C2×D311yescharacteristic
162C2×#237C2×D311yescharacteristic
163C2×#235—31no—
164C2×#235—31no—
165C2×C3×Q16—31no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C3×C4⋊Q8—31no—
170C3×#124—21no—
171C3×#124—61no—
172C3×#124C2×D311yescharacteristic
173C3×#124C2×D311yescharacteristic
174C3×C22⋊Q8—31no—
175C3×C22⋊Q8—61no—
176C3×#121—31no—
177C3×#121—61no—
178C3×C4×Q8—31no—
179C3×C4×D4—31no—
180C3×C4×D4—61no—
181#950—64no—
182#946—31no—
183#946—31no—
184#946C2×D311yescharacteristic
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—31no—
188C2×#216—31no—
189C2×#216C2×D311yescharacteristic
190C2×#216C2×D311yescharacteristic
191#942—64no—
192C2×#215—31no—
193C2×#215—31no—
194C2×#215—31no—
195C2×#215—61no—
196#938—61no—
197#938C2×D311yescharacteristic
198C2×#214C2×D311yescharacteristic
199C2×#214C2×D311yescharacteristic
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—61no—
203#924—31no—
204#924—31no—
205C2×#208—31no—
206C22×C3⋊C8—31no—
207#918—64no—
208#916—64no—
209C2×#204—31no—
210C2×ΓL(1,𝔽25)—31no—
211C2×D3×C8—31no—
212#895—61no—
213#894—61no—
214#894—61no—
215D3×C4⋊C4—61no—
216D3×C4⋊C4—61no—
217#885—21no—
218#884—21no—
219#883—61no—
220#883—61no—
221#67⋊C4—21no—
222#878—21no—
223C4×D12—31no—
224C4×D12—31no—
225C4×D12—61no—
226C4×D12C2×D311yescharacteristic
227#869C2×D311yescharacteristic
228C4×Dic6C2×D311yescharacteristic
229C3×#97—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#835—31no—
234#835—31no—
235#835—61no—
236#832—31no—
237#832—31no—
238#832—61no—
239#830—31no—
240#830—31no—
241#821—31no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244#818—31no—
245#816—31no—
246#810—31no—
247#810—31no—
248#809—31no—
249#807—31no—
250C4⋊(C3⋊C8)—31no—
251C4⋊(C3⋊C8)—31no—
252C4⋊(C3⋊C8)—61no—
253#803C2×D311yescharacteristic
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—
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)C2×D412yes—
269C4×C3⋊D3—42no—
270C3×#67—42no—
271C3×#67—42no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—42no—
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C3×D12—41no—
280C3×C4×D3—21no—
281C3×C4×D3—21no—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—42no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—42no—
291C3×Dic6C2×D412yes—
292#626—42no—
293#626—42no—
294#624—42no—
295#624—42no—
296C3⋊(C3⋊C8)—21no—
297C3⋊(C3⋊C8)—21no—
298C3×C3⋊C8—21no—
299C3×C3⋊C8C2×D412yes—
300C2×#137—91no—
301C2×#135—91no—
302#548—31no—
303#547—91no—
304#497—31no—
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—62no—
316C3×#41—121no—
317C2×C3×Q8—21no—
318C2×C3×Q8—31no—
319C2×C3×Q8—31no—
320C2×C3×Q8—31no—
321C2×C3×Q8—61no—
322C2×C3×Q8—62no—
323C2×C3×Q8—121no—
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×D4—21no—
327C2×C3×D4—31no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4C22×D311yescharacteristic
331C2×C3×D4C22×D311yescharacteristic
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—61no—
339C2×#67—61no—
340C22×Dic3—21no—
341#239—62no—
342#239—62no—
343#239—121no—
344#239—121no—
345D3×Q8—22no—
346D3×Q8—41no—
347#237—22no—
348#237—41no—
349#235—62no—
350#235—62no—
351#235—121no—
352#235—121no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12#6711yescharacteristic
359C2×C4×D3—21no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—121no—
367C2×C4×D3C22×D311yescharacteristic
368C2×C4×D3C22×D311yescharacteristic
369C2×Dic6—21no—
370C2×Dic6C22×D311yescharacteristic
371C2×Dic6C22×D311yescharacteristic
372C2×Dic6C22×D311yescharacteristic
373C3×Q16—62no—
374C3×Q16—121no—
375C3×SD16—62no—
376C3×SD16—121no—
377C2×C3×C8—31no—
378C2×C3×C8—31no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—31no—
381C3×C4⋊C4—61no—
382C3×C4⋊C4—61no—
383C3×C4⋊C4—61no—
384C3×C4⋊C4—61no—
385C3×C22⋊C4—21no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—31no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—41no—
392C3×C22⋊C4—41no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C42—21no—
396C3×C42—61no—
397C3×C42C22×D311yescharacteristic
398C3×C42C22×D311yescharacteristic
399#217—21no—
400#217—61no—
401#217—61no—
402#216—22no—
403#216—41no—
404#216—62no—
405#216—62no—
406#216—62no—
407#216—62no—
408#215—34no—
409#215—62no—
410#215—62no—
411#215—122no—
412#214—22no—
413#214—41no—
414#213—62no—
415#213—62no—
416#213—122no—
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—121no—
423(C2×D3)⋊C4#6711yescharacteristic
424(C2×D3)⋊C4#6711yescharacteristic
425C4⋊Dic3—21no—
426C4⋊Dic3—21no—
427C4⋊Dic3—31no—
428C4⋊Dic3—31no—
429C4⋊Dic3—61no—
430C4⋊Dic3#6711yescharacteristic
431C4⋊Dic3C22×D311yescharacteristic
432Dic3⋊C4—21no—
433Dic3⋊C4—21no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438C4×Dic3—21no—
439#208—62no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—61no—
445C2×C3⋊C8—61no—
446C2×C3⋊C8—62no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449#204—34no—
450ΓL(1,𝔽25)—62no—
451D3×C8—62no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32C22×D411yescharacteristic
456C2×C3⋊D3—22no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C32×C4—21no—
466C32×C4—21no—
467C32×C4—41no—
468C32×C4C22×D411yescharacteristic
469C32×C4H(5,𝔽2)11yescharacteristic
470C3⋊Dic3—41no—
471C3×Dic3—21no—
472C3×Dic3—21no—
473C3×Dic3—22no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C2×#41—31no—
478C2×#41—91no—
479C2×#41—91no—
480C22×Q8—31no—
481#137—184no—
482#135—184no—
483C2×Q16—31no—
484C2×Q16—31no—
485C2×Q16—91no—
486C2×Q16—91no—
487C2×SD16—31no—
488C2×SD16—31no—
489C2×SD16—91no—
490C2×SD16—91no—
491C2×D8—91no—
492C2×M16—91no—
493C22×C8—91no—
494C4⋊Q8—31no—
495#124—61no—
496#124D3211yescharacteristic
497#123—181no—
498#123—181no—
499C22⋊Q8—31no—
500C22⋊Q8—61no—
501C22⋊Q8—91no—
502C22⋊Q8—91no—
503#121—31no—
504#121—61no—
505#121—181no—
506C4×Q8—31no—
507C4×D4—31no—
508C4×D4—61no—
509C4×D4—91no—
510C2×C4⋊C4—181no—
511#107—91no—
512C4⋊C8—91no—
513#103—91no—
514#103—91no—
515#103—91no—
516#103—91no—
517#102—91no—
518#102—91no—
519C22⋊C8—91no—
520C22⋊C8—91no—
521#97—31no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—31no—
525C23×C3—31no—
526C23×C3—41no—
527C22×D3—61no—
528C22×D3—61no—
529C22×D3—121no—
530C22×D3C2×#6711yescharacteristic
531C22×D3C2×#6711yescharacteristic
532C3×Q8—21no—
533C3×Q8—21no—
534C3×Q8—21no—
535C3×Q8—21no—
536C3×Q8—32no—
537C3×Q8—41no—
538C3×Q8—41no—
539C3×Q8—61no—
540C3×Q8—61no—
541C3×Q8—61no—
542C3×Q8—61no—
543C3×Q8—61no—
544C3×Q8—122no—
545C3×D4—21no—
546C3×D4—21no—
547C3×D4—21no—
548C3×D4—21no—
549C3×D4—41no—
550C3×D4—41no—
551C3×D4—121no—
552C3×D4—122no—
553C3×D4—122no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—41no—
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—61no—
569C2×C3×C4—61no—
570C2×C3×C4—122no—
571C2×C3×C4—122no—
572C2×C3×C4D3×D411yescharacteristic
573C2×C3×C4D3×D411yescharacteristic
574C2×C3×C4C2×#6711yescharacteristic
575C2×C3×C4C2×#6711yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578#67—42no—
579#67—42no—
580#67—122no—
581#67—122no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—42no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—121no—
590C2×Dic3C2×#6711yescharacteristic
591C2×Dic3C2×#6711yescharacteristic
592D12—32no—
593D12—32no—
594D12—41no—
595D12—62no—
596D12—61no—
597D12—61no—
598D12—121no—
599D12—122no—
600D12—122no—
601C4×D3—21no—
602C4×D3—21no—
603C4×D3—21no—
604C4×D3—21no—
605C4×D3—42no—
606C4×D3—122no—
607C4×D3—122no—
608C4×D3—122no—
609C4×D3—122no—
610C4×D3—122no—
611C4×D3—122no—
612C4×D3—242no—
613Dic6—21no—
614Dic6—21no—
615Dic6—21no—
616Dic6—21no—
617Dic6—21no—
618Dic6—42no—
619Dic6D3×D412yes—
620C3×C8—32no—
621C3×C8—61no—
622C3⋊C8—21no—
623C3⋊C8—61no—
624C3⋊C8—61no—
625C3⋊C8—61no—
626C3⋊C8—61no—
627C3⋊C8—121no—
628C3⋊C8—121no—
629C3⋊C8D3×D412yes—
630C2×C32—81no—
631C2×C32D4211yescharacteristic
632C2×C32#57511yescharacteristic
633C2×C32#57811yescharacteristic
634C3⋊D3—42no—
635C3×D3—41no—
636C3×D3—41no—
637#41—62no—
638#41—121no—
639#41—182no—
640#41—182no—
641#41—361no—
642#41—361no—
643C2×Q8—31no—
644C2×Q8—31no—
645C2×Q8—31no—
646C2×Q8—61no—
647C2×Q8—62no—
648C2×Q8—121no—
649C2×Q8C2×D3211yescharacteristic
650C2×D4—31no—
651C2×D4—61no—
652C2×D4—61no—
653C2×D4—91no—
654C2×D4—181no—
655C2×D4—181no—
656C2×D4C2×D3211yescharacteristic
657C22×C4—31no—
658C22×C4—31no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—181no—
662C22×C4—181no—
663C22×C4—181no—
664Q16—62no—
665Q16—121no—
666Q16—182no—
667Q16—182no—
668SD16—62no—
669SD16—94no—
670SD16—121no—
671SD16—182no—
672D8—182no—
673M16—182no—
674C2×C8—31no—
675C2×C8—31no—
676C2×C8—91no—
677C2×C8—91no—
678C2×C8—182no—
679C4⋊C4—31no—
680C4⋊C4—31no—
681C4⋊C4—61no—
682C4⋊C4—61no—
683C4⋊C4—61no—
684C4⋊C4—61no—
685C4⋊C4—91no—
686C4⋊C4—181no—
687C4⋊C4—181no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—31no—
691C22⋊C4—31no—
692C22⋊C4—61no—
693C22⋊C4—61no—
694C22⋊C4—181no—
695C22⋊C4—181no—
696C22⋊C4—181no—
697C42—61no—
698C42C2×D3211yescharacteristic
699C22×C3—21no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—61no—
707C22×C3—61no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3—81no—
713C22×C3—81no—
714C22×C3—81no—
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—62no—
724C2×D3—62no—
725C2×D3—122no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—241no—
731C2×D3—241no—
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×C4—121no—
749C3×C4C2×D3×D411yescharacteristic
750C3×C4C2×D3×D411yescharacteristic
751C3×C4#100411yescharacteristic
752C3×C4#100411yescharacteristic
753Dic3—22no—
754Dic3—21no—
755Dic3—21no—
756Dic3—41no—
757Dic3—41no—
758Dic3—41no—
759Dic3—121no—
760Dic3—121no—
761Dic3—241no—
762C32#326911yescharacteristic, complemented, Sylow
763C23—21no—
764C23—31no—
765C23—31no—
766C23—181no—
767Q8—21no—
768Q8—21no—
769Q8—32no—
770Q8—61no—
771Q8—61no—
772Q8—61no—
773Q8—61no—
774Q8—61no—
775Q8—122no—
776D4—21no—
777D4—21no—
778D4—92no—
779D4—121no—
780D4—122no—
781D4—122no—
782D4—181no—
783D4—362no—
784D4—362no—
785C2×C4—21no—
786C2×C4—31no—
787C2×C4—31no—
788C2×C4—61no—
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—181no—
799C2×C4—362no—
800C2×C4—362no—
801C2×C4—362no—
802C2×C4D3×#6711yescharacteristic
803C2×C4D3×#6711yescharacteristic
804C2×C4C22×D3211yescharacteristic
805C8—32no—
806C8—61no—
807C8—181no—
808C8—181no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—81no—
813C2×C3—81no—
814C2×C3—121no—
815C2×C3—121no—
816C2×C3—161no—
817C2×C3#571711yescharacteristic
818C2×C3#577711yescharacteristic
819C2×C3#577911yescharacteristic
820C2×C3D4×#6711yescharacteristic
821C2×C3#582211yescharacteristic
822C2×C3#583811yescharacteristic
823D3—41no—
824D3—41no—
825D3—122no—
826D3—122no—
827D3—242no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—61no—
832C22—61no—
833C22—61no—
834C22—61no—
835C22—61no—
836C22—61no—
837C22—182no—
838C22—361no—
839C22—361no—
840C22C2×D3×#6711yescharacteristic
841C4—21no—
842C4—21no—
843C4—41no—
844C4—61no—
845C4—61no—
846C4—62no—
847C4—121no—
848C4—121no—
849C4—121no—
850C4—361no—
851C4D32×D411yescharacteristic
852C4#6431311yescharacteristic
853C3—21no—
854C3#8188311yescharacteristic, complemented
855C3#8354311yescharacteristic, complemented
856C2—81no—
857C2—121no—
858C2—121no—
859C2—362no—
860C2#1059529311yescharacteristic
861C2#1059546511yescharacteristic
862C2#1059547011yescharacteristic
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×#63948C2semidirect
3. C2×#63935C2semidirect
4. #10593869C2semidirect
5. #10592756C2semidirect
6. C3×#5060C2semidirect
7. #10591657C2semidirect
8. #10591635C2semidirect
9. #10591594C2semidirect
10. #10591521C2semidirect
11. #10591502C2semidirect
12. #10591461C2semidirect
13. #10590384C2semidirect
14. #10590362C2semidirect
15. #10590326C2semidirect
69. #5677D3semidirect
81. #5060D3semidirect
153. #3717D4semidirect
762. C32#3269semidirect
854. C3#81883semidirect
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×#639482
C2×#639352
#105938692
#105927562
C3×#50602
#105916572
#105916352
#105915942
#105915212
#105915022
#105914612
#105903842
#105903622
#105903262
#835433
#818833