Finite Group Databasebeta

← #11884630

Subgroups — #11884630

Order 1152.

1010 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5726C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic, complemented
3C2×#63943C211yesmaximal, characteristic, complemented
4#10593905C211yesmaximal, characteristic, complemented
5#10592789C211yesmaximal, characteristic, complemented
6C3×#5086C211yesmaximal, characteristic, complemented
7#10591655C211yesmaximal, characteristic, complemented
8#10591653C211yesmaximal, characteristic, complemented
9#10591635C211yesmaximal, characteristic, complemented
10#10591597C211yesmaximal, characteristic, complemented
11#10591587C211yesmaximal, characteristic, complemented
12#10591586C211yesmaximal, characteristic, complemented
13#10590360C211yesmaximal, characteristic, complemented
14#10590348C211yesmaximal, characteristic, complemented
15#10590326C211yesmaximal, characteristic, complemented
16#83528—31nomaximal
17#81883—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic
22C32×C4⋊Q8C2211yescharacteristic
23C2×#3756C2211yescharacteristic
24C2×#3756C2211yescharacteristic
25C4×#634C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C3×#946C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×#895—21no—
33C3×#894—21no—
34C3×#894—21no—
35C3×D3×C4⋊C4—21no—
36C3×#875C2211yescharacteristic
37C3×C4×D12C2211yescharacteristic
38C3×C4×D12C2211yescharacteristic
39#63947—24no—
40#63943—24no—
41#63915—21no—
42#63908C2211yescharacteristic
43#63902—21no—
44#63899—21no—
45#63885—21no—
46#63856C2211yescharacteristic
47C2×#3716C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52#63662C2211yescharacteristic
53#63662C2211yescharacteristic
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
55C3×#803C2211yescharacteristic
56#63575C2211yescharacteristic
57#63567C2211yescharacteristic
58#63565C2211yescharacteristic
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
63C3×#547—31no—
64C2×#951—31no—
65C2×#950—31no—
66C2×#918—31no—
67C2×#916—31no—
68#5726D311yescharacteristic, complemented
69#5677—31no—
70#5552—31no—
71C3×#497—31no—
72#5239—31no—
73#5238—31no—
74#5188—31no—
75#5187—31no—
76#5186—31no—
77#5174—31no—
78#5173—31no—
79#5172—31no—
80#5090—31no—
81#5090—31no—
82#5090—61no—
83#5086D311yescharacteristic, complemented
84#5057—31no—
85#5051—31no—
86#5050—31no—
87#5049—31no—
88#5047—31no—
89#5018—31no—
90#5016—31no—
91#5011—31no—
92#4710—31no—
93#4706—31no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×Q8C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C3×#239—22no—
98C3×#239—22no—
99C3×#239—41no—
100C3×#239—41no—
101C2×C3×D12—21no—
102C2×C3×D12—21no—
103C2×C3×D12D411yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
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⋊C4—21no—
122C32×C4⋊C4—21no—
123C32×C42C2311yescharacteristic
124#3756—22no—
125#3756—22no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127#3750—21no—
128C4×C3⋊Dic3—21no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#216—22no—
132C3×#216—41no—
133C3×#215—22no—
134C3×#215—41no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×C4⋊Dic3D411yescharacteristic
143C3×C4⋊Dic3C2311yescharacteristic
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148#3724—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151#3716D414yescomplemented
152#3715—22no—
153#3713—22no—
154#3711—22no—
155D3×C3⋊C8—22no—
156#3269—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239C2×D311yescharacteristic
160C2×#239C2×D311yescharacteristic
161C2×D3×Q8—31no—
162C2×#237—31no—
163C2×#235—31no—
164C22×Dic6—31no—
165C2×C3×Q16—31no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C3×C4⋊Q8—21no—
170C3×C4⋊Q8C2×D311yescharacteristic
171C3×C4⋊Q8C2×D311yescharacteristic
172C3×#124—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—64no—
183#946—31no—
184#946C2×D311yescharacteristic
185#946C2×D311yescharacteristic
186C2×#216—31no—
187C2×#216—31no—
188C2×#216—31no—
189C2×#216—31no—
190C2×#216—61no—
191C2×#216—61no—
192C2×#216C2×D311yescharacteristic
193C2×#216C2×D311yescharacteristic
194C2×#215—31no—
195C2×#215C2×D311yescharacteristic
196C2×#215C2×D311yescharacteristic
197#939—61no—
198#938—31no—
199C2×#214—31no—
200C2×#214—31no—
201C2×#213—31no—
202C2×#213—31no—
203#930—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#896—61no—
213#895—21no—
214#894—21no—
215#894—21no—
216D3×C4⋊C4—21no—
217#885—61no—
218#885—61no—
219#884—61no—
220#67⋊C4—61no—
221#67⋊C4—61no—
222#878—61no—
223#875C2×D311yescharacteristic
224C4×D12C2×D311yescharacteristic
225C4×D12C2×D311yescharacteristic
226C4×Dic6—31no—
227C4×Dic6—31no—
228C4×Dic6—61no—
229C3×#97—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#835—31no—
234#835—31no—
235#835—61no—
236#835—61no—
237#832—31no—
238#832—31no—
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
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C22×C3×D3C2×D411yescharacteristic
258C32×Q8—21no—
259C32×Q8—21no—
260C32×Q8—21no—
261C32×Q8—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269#634—21no—
270#634C2×D412yes—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—41no—
279C3×D12—42no—
280C3×D12—42no—
281C3×D12C2×D412yes—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—42no—
287C3×C4×D3—42no—
288C3×C4×D3—42no—
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)—21no—
298C3×C3⋊C8—21no—
299C3×C3⋊C8C2×D412yes—
300C2×#137—91no—
301C2×#135—91no—
302#548—91no—
303#547—31no—
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—62no—
317C3×#41—121no—
318C3×#41—121no—
319C2×C3×Q8—21no—
320C2×C3×Q8—21no—
321C2×C3×Q8—31no—
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—61no—
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C22×Dic3—61no—
341C22×Dic3—61no—
342#239—22no—
343#239—22no—
344#239—41no—
345#239—41no—
346D3×Q8—62no—
347D3×Q8—121no—
348#237—62no—
349#237—121no—
350#235—62no—
351#235—121no—
352C2×D12—21no—
353C2×D12—21no—
354C2×D12#6711yescharacteristic
355C2×D12C22×D311yescharacteristic
356C2×D12C22×D311yescharacteristic
357C2×C4×D3—21no—
358C2×C4×D3—21no—
359C2×C4×D3—21no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3C22×D311yescharacteristic
363C2×C4×D3C22×D311yescharacteristic
364C2×Dic6—31no—
365C2×Dic6—31no—
366C2×Dic6—61no—
367C2×Dic6—62no—
368C2×Dic6—61no—
369C2×Dic6—61no—
370C2×Dic6—121no—
371C2×Dic6C22×D311yescharacteristic
372C3×Q16—62no—
373C3×Q16—121no—
374C3×SD16—62no—
375C3×SD16—121no—
376C2×C3×C8—31no—
377C2×C3×C8—31no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—21no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—41no—
385C3×C4⋊C4—41no—
386C3×C4⋊C4—61no—
387C3×C4⋊C4—61no—
388C3×C22⋊C4—31no—
389C3×C22⋊C4—31no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C42—21no—
396C3×C42C22×D311yescharacteristic
397C3×C42C22×D311yescharacteristic
398#217—61no—
399#217—61no—
400#216—22no—
401#216—41no—
402#216—62no—
403#216—62no—
404#216—62no—
405#216—62no—
406#216—122no—
407#216—122no—
408#215—22no—
409#215—41no—
410#215—62no—
411#214—34no—
412#214—62no—
413#213—62no—
414#213—62no—
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—21no—
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—31no—
425C4⋊Dic3—31no—
426C4⋊Dic3—61no—
427C4⋊Dic3#6711yescharacteristic
428C4⋊Dic3C22×D311yescharacteristic
429Dic3⋊C4—21no—
430Dic3⋊C4—21no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—121no—
436C4×Dic3—61no—
437C4×Dic3—61no—
438C4×Dic3—121no—
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×C32C22×D411yescharacteristic
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—22no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C32×C4—21no—
466C32×C4—21no—
467C32×C4—41no—
468C32×C4—41no—
469C32×C4C22×D411yescharacteristic
470C32×C4H(5,𝔽2)11yescharacteristic
471C3⋊Dic3—22no—
472C3⋊Dic3—41no—
473C3×Dic3—21no—
474C3×Dic3—21no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C2×#41—31no—
478C2×#41—31no—
479C2×#41—91no—
480C22×Q8—91no—
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⋊Q8D3211yescharacteristic
495#124—31no—
496#124—181no—
497#123—61no—
498#123—61no—
499C22⋊Q8—31no—
500C22⋊Q8—31no—
501C22⋊Q8—91no—
502C22⋊Q8—181no—
503#121—61no—
504#121—91no—
505#121—181no—
506C4×Q8—91no—
507C4×D4—31no—
508C4×D4—31no—
509C4×D4—181no—
510C2×C4⋊C4—61no—
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—31no—
523C23×C3—31no—
524C23×C3—61no—
525C23×C3—61no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3C2×#6711yescharacteristic
529C22×D3C2×#6711yescharacteristic
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—21no—
533C3×Q8—21no—
534C3×Q8—21no—
535C3×Q8—21no—
536C3×Q8—21no—
537C3×Q8—21no—
538C3×Q8—41no—
539C3×Q8—41no—
540C3×Q8—41no—
541C3×Q8—41no—
542C3×Q8—61no—
543C3×Q8—61no—
544C3×D4—32no—
545C3×D4—61no—
546C3×D4—61no—
547C3×D4—61no—
548C3×D4—121no—
549C3×D4—122no—
550C3×D4—122no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
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—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—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—122no—
578#67—122no—
579#67—122no—
580#67—122no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—122no—
590C2×Dic3—122no—
591C2×Dic3C2×#6711yescharacteristic
592C2×Dic3C2×#6711yescharacteristic
593D12—21no—
594D12—21no—
595D12—21no—
596D12—41no—
597D12—42no—
598D12—42no—
599D12D3×D412yes—
600C4×D3—21no—
601C4×D3—21no—
602C4×D3—21no—
603C4×D3—21no—
604C4×D3—42no—
605C4×D3—42no—
606C4×D3—42no—
607C4×D3—122no—
608C4×D3—122no—
609Dic6—21no—
610Dic6—21no—
611Dic6—32no—
612Dic6—32no—
613Dic6—62no—
614Dic6—61no—
615Dic6—61no—
616Dic6—121no—
617Dic6—122no—
618Dic6—122no—
619C3×C8—32no—
620C3×C8—61no—
621C3⋊C8—21no—
622C3⋊C8—61no—
623C3⋊C8—61no—
624C3⋊C8—61no—
625C3⋊C8—61no—
626C3⋊C8—121no—
627C3⋊C8—121no—
628C3⋊C8D3×D412yes—
629C2×C32D4211yescharacteristic
630C2×C32#57511yescharacteristic
631C2×C32#57811yescharacteristic
632C3×D3—41no—
633C3×D3—41no—
634C3×D3—42no—
635C3×D3—81no—
636#41—62no—
637#41—62no—
638#41—121no—
639#41—121no—
640#41—182no—
641#41—361no—
642C2×Q8—31no—
643C2×Q8—91no—
644C2×Q8—181no—
645C2×Q8—182no—
646C2×Q8—361no—
647C2×Q8C2×D3211yescharacteristic
648C2×Q8C2×D3211yescharacteristic
649C2×D4—31no—
650C2×D4—31no—
651C2×D4—31no—
652C2×D4—61no—
653C2×D4—61no—
654C2×D4—181no—
655C2×D4—181no—
656C22×C4—31no—
657C22×C4—31no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—181no—
662C22×C4—181no—
663Q16—62no—
664Q16—121no—
665Q16—182no—
666Q16—182no—
667SD16—62no—
668SD16—94no—
669SD16—121no—
670SD16—182no—
671D8—182no—
672M16—182no—
673C2×C8—31no—
674C2×C8—31no—
675C2×C8—91no—
676C2×C8—91no—
677C2×C8—182no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—31no—
681C4⋊C4—31no—
682C4⋊C4—61no—
683C4⋊C4—61no—
684C4⋊C4—91no—
685C4⋊C4—181no—
686C4⋊C4—181no—
687C22⋊C4—31no—
688C22⋊C4—31no—
689C22⋊C4—61no—
690C22⋊C4—61no—
691C22⋊C4—61no—
692C22⋊C4—61no—
693C22⋊C4—61no—
694C22⋊C4—181no—
695C22⋊C4—181no—
696C42—181no—
697C42C2×D3211yescharacteristic
698C22×C3—21no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—62no—
702C22×C3—61no—
703C22×C3—61no—
704C22×C3—61no—
705C22×C3—61no—
706C22×C3—121no—
707C22×C3—121no—
708C22×C3—121no—
709C22×C3—121no—
710C22×C3—121no—
711C22×C3C2×D3×D411yescharacteristic
712C22×C3C22×#6711yescharacteristic
713C2×D3—21no—
714C2×D3—21no—
715C2×D3—22no—
716C2×D3—21no—
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—21no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—41no—
725C3×C4—22no—
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—41no—
737C3×C4—61no—
738C3×C4—61no—
739C3×C4—81no—
740C3×C4—81no—
741C3×C4—121no—
742C3×C4—121no—
743C3×C4C2×D3×D411yescharacteristic
744C3×C4C2×D3×D411yescharacteristic
745C3×C4#100411yescharacteristic
746C3×C4#100411yescharacteristic
747Dic3—21no—
748Dic3—21no—
749Dic3—41no—
750Dic3—41no—
751Dic3—62no—
752Dic3—62no—
753Dic3—122no—
754Dic3—121no—
755Dic3—121no—
756Dic3—241no—
757C32#326911yescharacteristic, complemented, Sylow
758C23—31no—
759C23—31no—
760C23—61no—
761C23—61no—
762Q8—21no—
763Q8—21no—
764Q8—21no—
765Q8—21no—
766Q8—61no—
767Q8—61no—
768Q8—92no—
769Q8—181no—
770Q8—362no—
771D4—32no—
772D4—61no—
773D4—61no—
774D4—61no—
775D4—121no—
776D4—122no—
777D4—122no—
778D4—362no—
779D4—362no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—122no—
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—32no—
801C8—61no—
802C8—181no—
803C8—181no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—121no—
808C2×C3—121no—
809C2×C3—122no—
810C2×C3—241no—
811C2×C3#571711yescharacteristic
812C2×C3#577711yescharacteristic
813C2×C3#577911yescharacteristic
814C2×C3D4×#6711yescharacteristic
815C2×C3#582211yescharacteristic
816C2×C3#583811yescharacteristic
817D3—41no—
818D3—41no—
819D3—42no—
820D3—81no—
821C22—61no—
822C22—61no—
823C22—61no—
824C22—61no—
825C22—62no—
826C22—61no—
827C22—61no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22C2×D3×#6711yescharacteristic
834C4—21no—
835C4—21no—
836C4—41no—
837C4—41no—
838C4—61no—
839C4—61no—
840C4—121no—
841C4—121no—
842C4—182no—
843C4—361no—
844C4D32×D411yescharacteristic
845C4#6431311yescharacteristic
846C3—21no—
847C3#8188311yescharacteristic, complemented
848C3#8352811yescharacteristic, complemented
849C2—121no—
850C2—121no—
851C2—122no—
852C2—241no—
853C2#1059529311yescharacteristic
854C2#1059531711yescharacteristic
855C2#1059532811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
hypercenterC4⋊Q8D32
hypocenterC32#3269
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5726C2semidirect
2. C2×#63947C2semidirect
3. C2×#63943C2semidirect
4. #10593905C2semidirect
5. #10592789C2semidirect
6. C3×#5086C2semidirect
7. #10591655C2semidirect
8. #10591653C2semidirect
9. #10591635C2semidirect
10. #10591597C2semidirect
11. #10591587C2semidirect
12. #10591586C2semidirect
13. #10590360C2semidirect
14. #10590348C2semidirect
15. #10590326C2semidirect
68. #5726D3semidirect
83. #5086D3semidirect
151. #3716D4semidirect
757. C32#3269semidirect
847. C3#81883semidirect
848. C3#83528semidirect

Maximal subgroups

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

subgroupindex
C3×#57262
C2×#639472
C2×#639432
#105939052
#105927892
C3×#50862
#105916552
#105916532
#105916352
#105915972
#105915872
#105915862
#105903602
#105903482
#105903262
#835283
#818833