Finite Group Databasebeta

← #11909745

Subgroups — #11909745

Order 1152.

3312 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#554C211yesmaximal, characteristic, complemented
2#10596196C211yesmaximal, characteristic, complemented
3#10596193C211yesmaximal, characteristic, complemented
4#10596162C212yesmaximal, complemented
5#10596161C212yesmaximal, complemented
6#10596114C212yesmaximal, complemented
7#10596111C214yesmaximal, complemented
8#10596104C212yesmaximal, complemented
9#10596102C214yesmaximal, complemented
10#10596056C211yesmaximal, characteristic, complemented
11C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
12#10596030C212yesmaximal, complemented
13#10596028C211yesmaximal, characteristic, complemented
14#10596024C211yesmaximal, characteristic, complemented
15#10596019C212yesmaximal, complemented
16#10595978C212yesmaximal, complemented
17#10595975C212yesmaximal, complemented
18#86936—34nomaximal
19C2×#3832C2212yes—
20C2×Q8×C3⋊D3C2211yescharacteristic
21C2×#3828C2212yes—
22C2×#3828C2214yes—
23C32×C4⋊Q8C2211yescharacteristic
24C32×#125C2212yes—
25C32×C22⋊Q8C2214yes—
26C32×C22⋊Q8C2212yes—
27C32×C4×Q8C2211yescharacteristic
28C32×C4×D4C2212yes—
29C32×C4×D4C2211yescharacteristic
30C2×C32×C4⋊C4C2212yes—
31#64156C2212yes—
32#64156C2212yes—
33Q8×C3⋊Dic3C2211yescharacteristic
34#64153C2214yes—
35#64149C2212yes—
36#64147C2211yescharacteristic
37#64145C2211yescharacteristic
38#64139C2212yes—
39#64138C2214yes—
40C4×#638C2214yes—
41C4×#638C2212yes—
42C4×#638C2214yes—
43#64135C2212yes—
44#64107C2214yes—
45#64106C2214yes—
46#64106C2211yescharacteristic
47#64105C2214yes—
48#64105C2214yes—
49#64104C2212yes—
50#64104C2212yes—
51#64103C2214yes—
52#64103C2214yes—
53#64102C2214yes—
54#64102C2212yes—
55#64102C2212yes—
56#64102C2212yes—
57#64102C2212yes—
58#64101C2214yes—
59C4⋊C4×C3⋊D3C2212yes—
60C4⋊C4×C3⋊D3C2214yes—
61C4⋊C4×C3⋊D3C2211yescharacteristic
62#64099C2211yescharacteristic
63#64097C2212yes—
64#64097C2212yes—
65#64096C2212yes—
66#64096C2212yes—
67#64096C2212yes—
68#64096C2211yescharacteristic
69#64094C2214yes—
70#64094C2214yes—
71#64093C2214yes—
72#64093C2214yes—
73#64092C2212yes—
74#64092C2214yes—
75#64088C2212yes—
76#64084C2212yes—
77#64083C2211yescharacteristic
78C4×C4⋊(C3⋊D3)C2212yes—
79C42×C3⋊D3C2212yes—
80C42×C3⋊D3C2211yescharacteristic
81C4×#634C2212yes—
82C4×#634C2211yescharacteristic
83C4×#634C2211yescharacteristic
84C3×#554D314yescomplemented
85#5725—34no—
86#5722—34no—
87#5691—38no—
88#5690—38no—
89#5643—38no—
90#5640—316no—
91#5633—38no—
92#5631—316no—
93#5585—34no—
94C4×D3×Q8—34no—
95#5559—38no—
96#5557—34no—
97#5553—34no—
98#5548—38no—
99#5507—38no—
100#5504—38no—
101C2×C32×Q8C2311yescharacteristic
102C2×C32×Q8C2312yes—
103C2×C32×D4C2311yescharacteristic
104C22×C32×C4C2312yes—
105C22×C32×C4C2314yes—
106C2×#638C2312yes—
107C2×#638C2314yes—
108C2×#638C2314yes—
109#3832—44no—
110Q8×C3⋊D3—24no—
111#3828—28no—
112#3828—48no—
113C2×C4⋊(C3⋊D3)C2312yes—
114C2×C4⋊(C3⋊D3)C2312yes—
115C2×C4⋊(C3⋊D3)C2314yes—
116C2×C4⋊(C3⋊D3)C2312yes—
117C2×C4×C3⋊D3C2311yescharacteristic
118C2×C4×C3⋊D3C2311yescharacteristic
119C2×C4×C3⋊D3C2312yes—
120C2×C4×C3⋊D3C2312yes—
121C2×C4×C3⋊D3C2311yescharacteristic
122C2×C4×C3⋊D3C2314yes—
123C2×C4×C3⋊D3C2314yes—
124C2×C4×C3⋊D3C2314yes—
125C2×#634C2311yescharacteristic
126C2×#634C2312yes—
127C2×#634C2314yes—
128C2×#634C2311yescharacteristic
129C32×C4⋊C4C2312yes—
130C32×C4⋊C4C2312yes—
131C32×C4⋊C4C2311yescharacteristic
132C32×C4⋊C4C2312yes—
133C32×C4⋊C4C2311yescharacteristic
134C32×C4⋊C4C2314yes—
135C32×C4⋊C4C2314yes—
136C32×C22⋊C4C2312yes—
137C32×C22⋊C4C2314yes—
138C32×C42C2311yescharacteristic
139C32×C42C2312yes—
140#3757C2312yes—
141#3757C2312yes—
142#3757C2312yes—
143#3752C2314yes—
144#3752C2314yes—
145#3752C2314yes—
146#3752C2312yes—
147#3752C2314yes—
148#3752C2314yes—
149#3752C2314yes—
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151C4⋊(C3⋊Dic3)C2312yes—
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153C4⋊(C3⋊Dic3)C2312yes—
154C4⋊(C3⋊Dic3)C2312yes—
155#3750C2312yes—
156#3750C2312yes—
157#3750C2312yes—
158#3750C2312yes—
159#3750C2312yes—
160#3750C2314yes—
161#3750C2314yes—
162C4×C3⋊Dic3C2312yes—
163C4×C3⋊Dic3C2311yescharacteristic
164C4×C3⋊Dic3C2312yes—
165C4×C3⋊Dic3C2311yescharacteristic
166C4×C3⋊Dic3C2312yes—
167C4×C3⋊Dic3C2312yes—
168C4×C3⋊Dic3C2311yescharacteristic
169C4×C3⋊Dic3C2314yes—
170#3522—91noSylow
171C2×#239—38no—
172C2×D3×Q8—34no—
173C2×#235—38no—
174C2×#235—316no—
175C3×C4⋊Q8C2×D314yes—
176C3×#125C2×D318yes—
177C3×C22⋊Q8C2×D318yes—
178C3×C22⋊Q8C2×D3116yes—
179C3×C4×Q8C2×D314yes—
180C3×C4×D4C2×D318yes—
181C3×C4×D4C2×D314yes—
182C2×C3×C4⋊C4C2×D318yes—
183#947—38no—
184#947—38no—
185Q8×Dic3—34no—
186#944—316no—
187#940—38no—
188#938—34no—
189#936—34no—
190#930—38no—
191#929—316no—
192C4×#67—38no—
193C4×#67—316no—
194C4×#67—316no—
195#926—38no—
196#898—316no—
197#897—316no—
198#897—34no—
199#896—316no—
200#896—316no—
201#895—38no—
202#895—38no—
203#894—316no—
204#894—316no—
205#893—316no—
206#893—38no—
207#893—38no—
208#893—38no—
209#893—38no—
210#892—316no—
211D3×C4⋊C4—316no—
212D3×C4⋊C4—34no—
213D3×C4⋊C4—38no—
214#890—34no—
215#888—38no—
216#888—38no—
217#887—38no—
218#887—38no—
219#887—38no—
220#887—34no—
221#885—316no—
222#885—316no—
223#884—316no—
224#884—316no—
225#883—316no—
226#883—38no—
227#879—38no—
228#875—38no—
229#874—34no—
230C4×D12—38no—
231C42×D3—38no—
232C42×D3—34no—
233C4×Dic6—38no—
234C4×Dic6—34no—
235C4×Dic6—34no—
236C23×C32C2412yes—
237C22×C3⋊D3C2414yes—
238C22×C3⋊D3C2411yescharacteristic
239C32×Q8—22no—
240C32×Q8—42no—
241C32×D4—22no—
242C2×C32×C4—24no—
243C2×C32×C4—44no—
244C2×C32×C4C2411yescharacteristic
245C2×C32×C4C2412yes—
246C2×C32×C4C2414yes—
247C2×C32×C4C2412yes—
248C2×C32×C4C2412yes—
249C2×C32×C4C2411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251#638—24no—
252#638—28no—
253#638—44no—
254C2×C3⋊Dic3C2411yescharacteristic
255C2×C3⋊Dic3C2412yes—
256C2×C3⋊Dic3C2412yes—
257C2×C3⋊Dic3C2411yescharacteristic
258C2×C3⋊Dic3C2411yescharacteristic
259C2×C3⋊Dic3C2412yes—
260C2×C3⋊Dic3C2412yes—
261C4⋊(C3⋊D3)—28no—
262C4⋊(C3⋊D3)—24no—
263C4⋊(C3⋊D3)—24no—
264C4⋊(C3⋊D3)—42no—
265C4×C3⋊D3—24no—
266C4×C3⋊D3—22no—
267C4×C3⋊D3—22no—
268C4×C3⋊D3—22no—
269C4×C3⋊D3—28no—
270C4×C3⋊D3—24no—
271C4×C3⋊D3—44no—
272C4×C3⋊D3—44no—
273#634—22no—
274#634—24no—
275#634—44no—
276#634#4114yescomplemented
277#559—91no—
278#559—92no—
279Q82—91no—
280#554—92no—
281#554C3⋊D311yescharacteristic, complemented
282#550—91no—
283#548—92no—
284#547—94no—
285#547—92no—
286#542—94no—
287#542—92no—
288#532—91no—
289#532—92no—
290#529—92no—
291#529—91no—
292#520—92no—
293C2×C4×Q8—91no—
294C2×C3×Q8C22×D314yes—
295C2×C3×Q8C22×D318yes—
296C2×C3×D4C22×D314yes—
297C22×C3×C4C22×D318yes—
298C22×C3×C4C22×D3116yes—
299C2×#67—38no—
300C2×#67—316no—
301C2×#67—316no—
302#239—1216no—
303D3×Q8—616no—
304#235—632no—
305#235—1232no—
306C2×D12—38no—
307C2×D12—38no—
308C2×D12—316no—
309C2×D12—38no—
310C2×C4×D3—34no—
311C2×C4×D3—34no—
312C2×C4×D3—38no—
313C2×C4×D3—38no—
314C2×C4×D3—34no—
315C2×C4×D3—316no—
316C2×C4×D3—316no—
317C2×C4×D3—316no—
318C2×Dic6—34no—
319C2×Dic6—34no—
320C2×Dic6—38no—
321C2×Dic6—316no—
322C3×C4⋊C4C22×D318yes—
323C3×C4⋊C4C22×D318yes—
324C3×C4⋊C4C22×D314yes—
325C3×C4⋊C4C22×D318yes—
326C3×C4⋊C4C22×D314yes—
327C3×C4⋊C4C22×D3116yes—
328C3×C4⋊C4C22×D3116yes—
329C3×C22⋊C4C22×D318yes—
330C3×C22⋊C4C22×D3116yes—
331C3×C42C22×D314yes—
332C3×C42C22×D318yes—
333#217—38no—
334#217—38no—
335#217—38no—
336(C2×D3)⋊C4—316no—
337(C2×D3)⋊C4—316no—
338(C2×D3)⋊C4—316no—
339(C2×D3)⋊C4—38no—
340(C2×D3)⋊C4—316no—
341(C2×D3)⋊C4—316no—
342(C2×D3)⋊C4—316no—
343C4⋊Dic3—34no—
344C4⋊Dic3—38no—
345C4⋊Dic3—34no—
346C4⋊Dic3—38no—
347C4⋊Dic3—38no—
348Dic3⋊C4—38no—
349Dic3⋊C4—38no—
350Dic3⋊C4—38no—
351Dic3⋊C4—38no—
352Dic3⋊C4—38no—
353Dic3⋊C4—316no—
354Dic3⋊C4—316no—
355C4×Dic3—38no—
356C4×Dic3—34no—
357C4×Dic3—38no—
358C4×Dic3—34no—
359C4×Dic3—38no—
360C4×Dic3—38no—
361C4×Dic3—34no—
362C4×Dic3—316no—
363C22×C32—22no—
364C22×C32—22no—
365C22×C32—22no—
366C22×C32C2511yescharacteristic
367C2×C3⋊D3—21no—
368C2×C3⋊D3—21no—
369C2×C3⋊D3—24no—
370C2×C3⋊D3—24no—
371C2×C3⋊D3—24no—
372C2×C3⋊D3H(5,𝔽2)12yes—
373C32×C4—22no—
374C32×C4—22no—
375C32×C4—24no—
376C32×C4—22no—
377C32×C4—21no—
378C32×C4C2×#4112yes—
379C32×C42−1+412yes—
380C3⋊Dic3—21no—
381C3⋊Dic3—22no—
382C3⋊Dic3—22no—
383C3⋊Dic3—21no—
384C3⋊Dic3—22no—
385C3⋊Dic3—21no—
386C3⋊Dic3C2×#4114yes—
387C2×#41—92no—
388C2×#41—92no—
389C2×#41—94no—
390C22×Q8—91no—
391C4⋊Q8—94no—
392C4⋊Q8—92no—
393C4⋊Q8—92no—
394C4⋊Q8C2×C3⋊D311yescharacteristic
395#127—92no—
396#127—91no—
397#126—94no—
398#126—92no—
399#125—91no—
400#125C2×C3⋊D312yes—
401#124—92no—
402#124—92no—
403#124—91no—
404#124—94no—
405#124—94no—
406#124—92no—
407#123—94no—
408#123—94no—
409#123—94no—
410#123—92no—
411#123—94no—
412C22⋊Q8—91no—
413C22⋊Q8—94no—
414C22⋊Q8—94no—
415C22⋊Q8—94no—
416C22⋊Q8C2×C3⋊D314yes—
417C22⋊Q8C2×C3⋊D312yes—
418#121—91no—
419#121—92no—
420#121—92no—
421#121—92no—
422#121—94no—
423#121—94no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—92no—
427C4×Q8—92no—
428C4×Q8—92no—
429C4×Q8—91no—
430C4×Q8—92no—
431C4×Q8—91no—
432C4×Q8C2×C3⋊D311yescharacteristic
433C4×D4—94no—
434C4×D4—94no—
435C4×D4—92no—
436C4×D4—92no—
437C4×D4—92no—
438C4×D4—94no—
439C4×D4—92no—
440C4×D4—92no—
441C4×D4—92no—
442C4×D4C2×C3⋊D311yescharacteristic
443C4×D4C2×C3⋊D312yes—
444#117—92no—
445#117—94no—
446C2×C4⋊C4—92no—
447C2×C4⋊C4—91no—
448C2×C4⋊C4—94no—
449C2×C4⋊C4C2×C3⋊D312yes—
450C2×C42—91no—
451C2×C42—92no—
452C23×C3C23×D318yes—
453C22×D3—34no—
454C22×D3—316no—
455C3×Q8—28no—
456C3×Q8—48no—
457C3×D4—28no—
458C2×C3×C4—216no—
459C2×C3×C4—416no—
460C2×C3×C4C23×D314yes—
461C2×C3×C4C23×D318yes—
462C2×C3×C4C23×D3116yes—
463C2×C3×C4C23×D318yes—
464C2×C3×C4C23×D318yes—
465C2×C3×C4C23×D314yes—
466C2×C3×C4C23×D314yes—
467#67—632no—
468#67—616no—
469#67—1216no—
470C2×Dic3—38no—
471C2×Dic3—34no—
472C2×Dic3—38no—
473C2×Dic3—38no—
474C2×Dic3—34no—
475C2×Dic3—34no—
476C2×Dic3—38no—
477D12—632no—
478D12—616no—
479D12—616no—
480D12—128no—
481C4×D3—632no—
482C4×D3—616no—
483C4×D3—616no—
484C4×D3—68no—
485C4×D3—68no—
486C4×D3—68no—
487C4×D3—1216no—
488C4×D3—1216no—
489Dic6—316no—
490Dic6—616no—
491Dic6—68no—
492Dic6—1216no—
493C2×C32—42no—
494C2×C32C22×#4111yescharacteristic
495C2×C32C2×H(5,𝔽2)11yescharacteristic
496C2×C32C2×2−1+411yescharacteristic
497C3⋊D3—22no—
498C3⋊D3—44no—
499#41—188no—
500#41—368no—
501#41—364no—
502C2×Q8—91no—
503C2×Q8—91no—
504C2×Q8—92no—
505C2×Q8—94no—
506C2×Q8—184no—
507C2×Q8C22×C3⋊D311yescharacteristic
508C2×Q8C22×C3⋊D312yes—
509C2×D4—94no—
510C2×D4—92no—
511C2×D4—94no—
512C2×D4—92no—
513C2×D4—92no—
514C2×D4—94no—
515C2×D4—92no—
516C2×D4C22×C3⋊D311yescharacteristic
517C22×C4—91no—
518C22×C4—91no—
519C22×C4—92no—
520C22×C4—92no—
521C22×C4—91no—
522C22×C4—94no—
523C22×C4—94no—
524C22×C4—94no—
525C22×C4C22×C3⋊D312yes—
526C22×C4C22×C3⋊D314yes—
527C4⋊C4—92no—
528C4⋊C4—92no—
529C4⋊C4—94no—
530C4⋊C4—92no—
531C4⋊C4—91no—
532C4⋊C4—92no—
533C4⋊C4—92no—
534C4⋊C4—92no—
535C4⋊C4—91no—
536C4⋊C4—92no—
537C4⋊C4—94no—
538C4⋊C4—92no—
539C4⋊C4C22×C3⋊D311yescharacteristic
540C4⋊C4C22×C3⋊D314yes—
541C4⋊C4C22×C3⋊D312yes—
542C4⋊C4C22×C3⋊D312yes—
543C4⋊C4C22×C3⋊D311yescharacteristic
544C4⋊C4C22×C3⋊D312yes—
545C4⋊C4C22×C3⋊D314yes—
546C22⋊C4—92no—
547C22⋊C4—92no—
548C22⋊C4—92no—
549C22⋊C4—94no—
550C22⋊C4—94no—
551C22⋊C4—92no—
552C22⋊C4—94no—
553C22⋊C4—94no—
554C22⋊C4—94no—
555C22⋊C4—94no—
556C22⋊C4C22×C3⋊D312yes—
557C22⋊C4C22×C3⋊D314yes—
558C42—92no—
559C42—91no—
560C42—91no—
561C42—92no—
562C42—91no—
563C42—92no—
564C42—94no—
565C42—92no—
566C42C22×C3⋊D312yes—
567C42C22×C3⋊D311yescharacteristic
568C22×C3—28no—
569C22×C3—28no—
570C22×C3—28no—
571C22×C3C24×D314yes—
572C2×D3—38no—
573C2×D3—64no—
574C2×D3—64no—
575C2×D3—616no—
576C2×D3—616no—
577C2×D3—616no—
578C3×C4—28no—
579C3×C4—28no—
580C3×C4—216no—
581C3×C4—28no—
582C3×C4—24no—
583C3×C4#100718yes—
584C3×C4D3×#4118yes—
585Dic3—316no—
586Dic3—68no—
587Dic3—64no—
588Dic3—64no—
589Dic3—68no—
590Dic3—68no—
591Dic3—64no—
592C32#352211yescharacteristic, complemented, Sylow
593C23—91no—
594C23—94no—
595C23C23×C3⋊D312yes—
596Q8—22no—
597Q8—42no—
598Q8—94no—
599Q8—184no—
600Q8—182no—
601Q8—364no—
602D4—22no—
603D4—188no—
604D4—188no—
605D4—184no—
606D4—184no—
607D4—184no—
608D4—362no—
609D4—364no—
610C2×C4—24no—
611C2×C4—44no—
612C2×C4—92no—
613C2×C4—91no—
614C2×C4—92no—
615C2×C4—91no—
616C2×C4—91no—
617C2×C4—92no—
618C2×C4—92no—
619C2×C4—184no—
620C2×C4—188no—
621C2×C4—184no—
622C2×C4—182no—
623C2×C4—182no—
624C2×C4—182no—
625C2×C4—364no—
626C2×C4—364no—
627C2×C4C23×C3⋊D312yes—
628C2×C4C23×C3⋊D312yes—
629C2×C4C23×C3⋊D311yescharacteristic
630C2×C4C23×C3⋊D314yes—
631C2×C4C23×C3⋊D312yes—
632C2×C4C23×C3⋊D311yescharacteristic
633C2×C4C23×C3⋊D311yescharacteristic
634C2×C3—48no—
635C2×C3C2×#100714yes—
636C2×C3C2×D3×#4114yes—
637C2×C3D3×H(5,𝔽2)14yes—
638D3—68no—
639D3—1216no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—92no—
644C22—181no—
645C22—181no—
646C22—184no—
647C22—184no—
648C22—184no—
649C22C24×C3⋊D311yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—24no—
654C4—21no—
655C4—94no—
656C4—181no—
657C4—182no—
658C4—181no—
659C4—181no—
660C4—182no—
661C4—182no—
662C4#6436412yes—
663C4#41×C3⋊D312yes—
664C3#8693614yescomplemented
665C2—42no—
666C2—182no—
667C2—364no—
668C2C2×#6436411yescharacteristic
669C2C2×#41×C3⋊D311yescharacteristic
670C2C3⋊D3×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#554C2
hypercenter#554C3⋊D3
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C32×#554C2semidirect
2. #10596196C2semidirect
3. #10596193C2semidirect
4. #10596162C2semidirect
5. #10596161C2semidirect
6. #10596114C2semidirect
7. #10596111C2semidirect
8. #10596104C2semidirect
9. #10596102C2semidirect
10. #10596056C2semidirect
11. C4×Q8×C3⋊D3C2semidirect
12. #10596030C2semidirect
13. #10596028C2semidirect
14. #10596024C2semidirect
15. #10596019C2semidirect
16. #10595978C2semidirect
17. #10595975C2semidirect
84. C3×#554D3semidirect
276. #634#41semidirect
281. #554C3⋊D3semidirect
592. C32#3522semidirect
664. C3#86936semidirect

Maximal subgroups

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

subgroupindex
C32×#5542
#105961962
#105961932
#105961622
#105961612
#105961142
#105961112
#105961042
#105961022
#105960562
C4×Q8×C3⋊D32
#105960302
#105960282
#105960242
#105960192
#105959782
#105959752
#869363