Finite Group Databasebeta

← #11909724

Subgroups — #11909724

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×#532C211yesmaximal, characteristic, complemented
2#10596295C214yesmaximal, complemented
3#10596201C211yesmaximal, characteristic, complemented
4#10596193C211yesmaximal, characteristic, complemented
5#10596189C211yesmaximal, characteristic, complemented
6#10596184C211yesmaximal, characteristic, complemented
7#10596140C214yesmaximal, complemented
8#10596082C212yesmaximal, complemented
9#10596071C212yesmaximal, complemented
10#10596069C212yesmaximal, complemented
11#10596067C212yesmaximal, complemented
12#10596032C212yesmaximal, complemented
13#10596030C212yesmaximal, complemented
14#10596017C212yesmaximal, complemented
15#10596010C212yesmaximal, complemented
16#10595950C211yesmaximal, characteristic, complemented
17C2×C4×#634C211yesmaximal, characteristic, complemented
18#86229—34nomaximal
19C2×C32×#41C2212yes—
20C2×#3830C2212yes—
21C2×#3830C2214yes—
22C22×#634C2211yescharacteristic
23C32×C4⋊Q8C2211yescharacteristic
24C32×#127C2211yescharacteristic
25C32×#124C2212yes—
26C32×#121C2212yes—
27C32×#121C2212yes—
28C32×C4×D4C2212yes—
29C32×C4×D4C2212yes—
30C2×C32×C42C2211yescharacteristic
31#64155C2214yes—
32#64153C2214yes—
33#64149C2212yes—
34#64148C2214yes—
35#64148C2214yes—
36#64147C2212yes—
37#64145C2212yes—
38#64145C2212yes—
39#64144C2214yes—
40#64144C2214yes—
41D4×C3⋊Dic3C2212yes—
42D4×C3⋊Dic3C2212yes—
43D4×C3⋊Dic3C2212yes—
44D4×C3⋊Dic3C2214yes—
45#64139C2211yescharacteristic
46#64138C2212yes—
47#64138C2214yes—
48C4×#638C2212yes—
49C4×#638C2214yes—
50C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
51#64133C2211yescharacteristic
52#64133C2214yes—
53C2×#3750C2212yes—
54C2×#3750C2214yes—
55C2×C4×C3⋊Dic3C2212yes—
56#64106C2212yes—
57#64102C2212yes—
58C4⋊C4×C3⋊D3C2212yes—
59#64099C2212yes—
60#64097C2212yes—
61#64097C2212yes—
62#64096C2212yes—
63#64096C2212yes—
64#64094C2214yes—
65#64094C2214yes—
66#64092C2214yes—
67#64090C2214yes—
68#64088C2214yes—
69#64087C2214yes—
70#64087C2214yes—
71#64086C2214yes—
72#64085C2212yes—
73#64084C2211yescharacteristic
74C4×C4⋊(C3⋊D3)C2211yescharacteristic
75#64081C2212yes—
76#64079C2211yescharacteristic
77C4×#634C2212yes—
78C4×#634C2211yescharacteristic
79C4×#634C2211yescharacteristic
80C4×#634C2211yescharacteristic
81C4×#634C2212yes—
82C4×#634C2211yescharacteristic
83C4×#634C2211yescharacteristic
84C3×#532D314yescomplemented
85#5824—316no—
86#5730—34no—
87#5722—34no—
88#5718—34no—
89#5713—34no—
90#5669—316no—
91#5611—38no—
92#5600—38no—
93#5598—38no—
94#5596—38no—
95#5561—38no—
96#5559—38no—
97#5546—38no—
98#5539—38no—
99#5479—34no—
100C2×C4×Dic6—34no—
101C32×#41—44no—
102C2×C32×Q8C2312yes—
103C2×C32×D4C2314yes—
104C2×C32×D4C2312yes—
105C2×C32×D4C2312yes—
106C2×C32×D4C2312yes—
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2314yes—
111C2×#638C2314yes—
112C2×#638C2312yes—
113C2×#638C2314yes—
114C22×C3⋊Dic3C2314yes—
115C22×C3⋊Dic3C2312yes—
116C22×C3⋊Dic3C2312yes—
117C22×C3⋊Dic3C2314yes—
118#3830—28no—
119#3830—48no—
120C2×C4⋊(C3⋊D3)C2311yescharacteristic
121C2×C4×C3⋊D3C2312yes—
122C2×C4×C3⋊D3C2314yes—
123C2×#634—24no—
124C2×#634C2312yes—
125C2×#634C2311yescharacteristic
126C2×#634C2311yescharacteristic
127C2×#634C2314yes—
128C2×#634C2311yescharacteristic
129C32×C4⋊C4C2312yes—
130C32×C4⋊C4C2312yes—
131C32×C22⋊C4C2314yes—
132C32×C22⋊C4C2314yes—
133C32×C42C2311yescharacteristic
134C32×C42C2311yescharacteristic
135C32×C42C2311yescharacteristic
136C32×C42C2311yescharacteristic
137#3757C2314yes—
138#3757C2314yes—
139#3757C2314yes—
140#3757C2314yes—
141#3757C2312yes—
142#3752C2312yes—
143#3752C2312yes—
144#3752C2312yes—
145#3752C2312yes—
146#3752C2314yes—
147C4⋊(C3⋊Dic3)C2312yes—
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151C4⋊(C3⋊Dic3)C2311yescharacteristic
152C4⋊(C3⋊Dic3)C2314yes—
153#3750C2312yes—
154#3750C2312yes—
155#3750C2312yes—
156#3750C2312yes—
157#3750C2312yes—
158#3750C2312yes—
159#3750C2312yes—
160#3750C2312yes—
161#3750C2314yes—
162#3750C2314yes—
163#3750C2314yes—
164C4×C3⋊Dic3C2312yes—
165C4×C3⋊Dic3C2312yes—
166C4×C3⋊Dic3C2312yes—
167C4×C3⋊Dic3C2312yes—
168C4×C3⋊Dic3C2312yes—
169C4×C3⋊Dic3C2314yes—
170#3522—91noSylow
171C2×C3×#41C2×D318yes—
172C2×#237—38no—
173C2×#237—316no—
174C22×Dic6—34no—
175C3×C4⋊Q8C2×D314yes—
176C3×#127C2×D314yes—
177C3×#124C2×D318yes—
178C3×#121C2×D318yes—
179C3×#121C2×D318yes—
180C3×C4×D4C2×D318yes—
181C3×C4×D4C2×D318yes—
182C2×C3×C42C2×D314yes—
183#946—316no—
184#944—316no—
185#940—38no—
186#939—316no—
187#939—316no—
188#938—38no—
189#936—38no—
190#936—38no—
191#935—316no—
192#935—316no—
193D4×Dic3—38no—
194D4×Dic3—38no—
195D4×Dic3—38no—
196D4×Dic3—316no—
197#930—34no—
198#929—38no—
199#929—316no—
200C4×#67—38no—
201C4×#67—316no—
202C2×C4⋊Dic3—34no—
203#924—34no—
204#924—316no—
205C2×Dic3⋊C4—38no—
206C2×Dic3⋊C4—316no—
207C2×C4×Dic3—38no—
208#897—38no—
209#893—38no—
210D3×C4⋊C4—38no—
211#890—38no—
212#888—38no—
213#888—38no—
214#887—38no—
215#887—38no—
216#885—316no—
217#885—316no—
218#883—316no—
219#67⋊C4—316no—
220#879—316no—
221#878—316no—
222#878—316no—
223#877—316no—
224#876—38no—
225#875—34no—
226C4×D12—34no—
227#872—38no—
228#870—34no—
229C4×Dic6—38no—
230C4×Dic6—34no—
231C4×Dic6—34no—
232C4×Dic6—34no—
233C4×Dic6—38no—
234C4×Dic6—34no—
235C4×Dic6—34no—
236C23×C32C2414yes—
237C23×C32C2411yescharacteristic
238C22×C3⋊D3C2412yes—
239C32×Q8—42no—
240C32×D4—28no—
241C32×D4—24no—
242C32×D4—24no—
243C32×D4—42no—
244C2×C32×C4—22no—
245C2×C32×C4—22no—
246C2×C32×C4—22no—
247C2×C32×C4—44no—
248C2×C32×C4C2411yescharacteristic
249C2×C32×C4C2414yes—
250C2×C32×C4C2411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255#638—24no—
256#638—28no—
257#638—44no—
258C2×C3⋊Dic3—24no—
259C2×C3⋊Dic3—24no—
260C2×C3⋊Dic3—28no—
261C2×C3⋊Dic3—44no—
262C2×C3⋊Dic3C2412yes—
263C2×C3⋊Dic3C2412yes—
264C2×C3⋊Dic3C2412yes—
265C2×C3⋊Dic3C2412yes—
266C2×C3⋊Dic3C2412yes—
267C2×C3⋊Dic3C2412yes—
268C2×C3⋊Dic3C2412yes—
269C4⋊(C3⋊D3)—22no—
270C4×C3⋊D3—24no—
271C4×C3⋊D3—44no—
272#634—22no—
273#634—22no—
274#634—24no—
275#634—44no—
276#634#4114yescomplemented
277#559—91no—
278#559—92no—
279Q82—91no—
280#554—91no—
281#554—92no—
282#550—91no—
283#548—92no—
284#547—94no—
285#547—92no—
286#542—94no—
287#542—92no—
288#532—92no—
289#532C3⋊D311yescharacteristic, complemented
290#529—92no—
291#529—91no—
292#520—92no—
293C2×C4×Q8—91no—
294C3×#41—416no—
295C2×C3×Q8C22×D318yes—
296C2×C3×D4C22×D318yes—
297C2×C3×D4C22×D3116yes—
298C2×C3×D4C22×D318yes—
299C2×C3×D4C22×D318yes—
300C22×C3×C4C22×D314yes—
301C22×C3×C4C22×D314yes—
302C22×C3×C4C22×D314yes—
303C22×C3×C4C22×D3116yes—
304C2×#67—316no—
305C2×#67—38no—
306C2×#67—316no—
307C22×Dic3—316no—
308C22×Dic3—38no—
309C22×Dic3—38no—
310C22×Dic3—316no—
311#237—632no—
312#237—1232no—
313C2×D12—34no—
314C2×C4×D3—38no—
315C2×C4×D3—316no—
316C2×Dic6—34no—
317C2×Dic6—38no—
318C2×Dic6—34no—
319C2×Dic6—34no—
320C2×Dic6—316no—
321C2×Dic6—616no—
322C3×C4⋊C4C22×D318yes—
323C3×C4⋊C4C22×D318yes—
324C3×C22⋊C4C22×D3116yes—
325C3×C22⋊C4C22×D3116yes—
326C3×C42C22×D314yes—
327C3×C42C22×D314yes—
328C3×C42C22×D314yes—
329C3×C42C22×D314yes—
330#217—316no—
331#217—316no—
332#217—316no—
333#217—316no—
334#217—38no—
335(C2×D3)⋊C4—38no—
336(C2×D3)⋊C4—38no—
337(C2×D3)⋊C4—38no—
338(C2×D3)⋊C4—38no—
339(C2×D3)⋊C4—316no—
340C4⋊Dic3—38no—
341C4⋊Dic3—34no—
342C4⋊Dic3—34no—
343C4⋊Dic3—34no—
344C4⋊Dic3—34no—
345C4⋊Dic3—316no—
346Dic3⋊C4—38no—
347Dic3⋊C4—38no—
348Dic3⋊C4—38no—
349Dic3⋊C4—38no—
350Dic3⋊C4—38no—
351Dic3⋊C4—38no—
352Dic3⋊C4—38no—
353Dic3⋊C4—38no—
354Dic3⋊C4—316no—
355Dic3⋊C4—316no—
356Dic3⋊C4—316no—
357C4×Dic3—38no—
358C4×Dic3—38no—
359C4×Dic3—38no—
360C4×Dic3—38no—
361C4×Dic3—38no—
362C4×Dic3—316no—
363C22×C32—21no—
364C22×C32—21no—
365C22×C32—24no—
366C22×C32—24no—
367C22×C32—24no—
368C22×C32H(5,𝔽2)12yes—
369C22×C32C2511yescharacteristic
370C2×C3⋊D3—22no—
371C2×C3⋊D3—22no—
372C2×C3⋊D3—22no—
373C32×C4—21no—
374C32×C4—24no—
375C32×C4—21no—
376C32×C4—21no—
377C32×C4—21no—
378C32×C4C2×#4112yes—
379C32×C42−1+412yes—
380C3⋊Dic3—22no—
381C3⋊Dic3—22no—
382C3⋊Dic3—22no—
383C3⋊Dic3—22no—
384C3⋊Dic3—22no—
385C3⋊Dic3—22no—
386C3⋊Dic3C2×#4114yes—
387C2×#41—92no—
388C2×#41—94no—
389C2×#41C2×C3⋊D312yes—
390C22×Q8—91no—
391C4⋊Q8—94no—
392C4⋊Q8—92no—
393C4⋊Q8—92no—
394C4⋊Q8C2×C3⋊D311yescharacteristic
395#127—92no—
396#127C2×C3⋊D311yescharacteristic
397#126—94no—
398#126—92no—
399#125—92no—
400#125—91no—
401#124—92no—
402#124—92no—
403#124—94no—
404#124—94no—
405#124—91no—
406#124C2×C3⋊D312yes—
407#123—94no—
408#123—94no—
409#123—92no—
410#123—94no—
411#123—94no—
412C22⋊Q8—94no—
413C22⋊Q8—91no—
414C22⋊Q8—94no—
415C22⋊Q8—92no—
416C22⋊Q8—94no—
417C22⋊Q8—94no—
418#121—94no—
419#121—92no—
420#121—94no—
421#121—91no—
422#121C2×C3⋊D312yes—
423#121C2×C3⋊D312yes—
424C4×Q8—92no—
425C4×Q8—92no—
426C4×Q8—91no—
427C4×Q8—92no—
428C4×Q8—91no—
429C4×Q8—91no—
430C4×Q8—91no—
431C4×Q8—92no—
432C4×Q8—91no—
433C4×D4—92no—
434C4×D4—94no—
435C4×D4—92no—
436C4×D4—92no—
437C4×D4—94no—
438C4×D4—92no—
439C4×D4—92no—
440C4×D4—94no—
441C4×D4—91no—
442C4×D4C2×C3⋊D312yes—
443C4×D4C2×C3⋊D312yes—
444#117—94no—
445#117—92no—
446C2×C4⋊C4—92no—
447C2×C4⋊C4—91no—
448C2×C4⋊C4—94no—
449C2×C4⋊C4—92no—
450C2×C42—92no—
451C2×C42C2×C3⋊D311yescharacteristic
452C23×C3C23×D3116yes—
453C23×C3C23×D314yes—
454C22×D3—38no—
455C3×Q8—48no—
456C3×D4—232no—
457C3×D4—216no—
458C3×D4—216no—
459C3×D4—48no—
460C2×C3×C4—28no—
461C2×C3×C4—28no—
462C2×C3×C4—28no—
463C2×C3×C4—416no—
464C2×C3×C4C23×D314yes—
465C2×C3×C4C23×D3116yes—
466C2×C3×C4C23×D314yes—
467C2×C3×C4C23×D314yes—
468C2×C3×C4C23×D314yes—
469C2×C3×C4C23×D314yes—
470C2×C3×C4C23×D314yes—
471#67—632no—
472#67—616no—
473#67—1216no—
474C2×Dic3—38no—
475C2×Dic3—38no—
476C2×Dic3—38no—
477C2×Dic3—38no—
478C2×Dic3—38no—
479C2×Dic3—38no—
480C2×Dic3—38no—
481C2×Dic3—616no—
482C2×Dic3—632no—
483C2×Dic3—616no—
484C2×Dic3—1216no—
485D12—68no—
486C4×D3—616no—
487C4×D3—1216no—
488Dic6—316no—
489Dic6—616no—
490Dic6—68no—
491Dic6—68no—
492Dic6—1216no—
493C2×C32—22no—
494C2×C32—44no—
495C2×C32C22×#4111yescharacteristic
496C2×C32C2×H(5,𝔽2)11yescharacteristic
497C2×C32C2×2−1+411yescharacteristic
498C3⋊D3—42no—
499#41—44no—
500#41—188no—
501#41—368no—
502C2×Q8—91no—
503C2×Q8—91no—
504C2×Q8—92no—
505C2×Q8—91no—
506C2×Q8—94no—
507C2×Q8—184no—
508C2×Q8C22×C3⋊D312yes—
509C2×D4—94no—
510C2×D4—92no—
511C2×D4—94no—
512C2×D4—91no—
513C2×D4C22×C3⋊D312yes—
514C2×D4C22×C3⋊D312yes—
515C2×D4C22×C3⋊D314yes—
516C2×D4C22×C3⋊D312yes—
517C22×C4—92no—
518C22×C4—92no—
519C22×C4—94no—
520C22×C4—94no—
521C22×C4—92no—
522C22×C4—94no—
523C22×C4C22×C3⋊D311yescharacteristic
524C22×C4C22×C3⋊D311yescharacteristic
525C22×C4C22×C3⋊D311yescharacteristic
526C22×C4C22×C3⋊D314yes—
527C4⋊C4—92no—
528C4⋊C4—91no—
529C4⋊C4—94no—
530C4⋊C4—92no—
531C4⋊C4—94no—
532C4⋊C4—92no—
533C4⋊C4—91no—
534C4⋊C4—92no—
535C4⋊C4—92no—
536C4⋊C4—92no—
537C4⋊C4—92no—
538C4⋊C4—91no—
539C4⋊C4—91no—
540C4⋊C4—92no—
541C4⋊C4—94no—
542C4⋊C4—94no—
543C4⋊C4—92no—
544C4⋊C4C22×C3⋊D312yes—
545C4⋊C4C22×C3⋊D312yes—
546C22⋊C4—94no—
547C22⋊C4—92no—
548C22⋊C4—94no—
549C22⋊C4—94no—
550C22⋊C4—94no—
551C22⋊C4—92no—
552C22⋊C4—92no—
553C22⋊C4—92no—
554C22⋊C4—94no—
555C22⋊C4—92no—
556C22⋊C4C22×C3⋊D314yes—
557C22⋊C4C22×C3⋊D314yes—
558C42—92no—
559C42—92no—
560C42—92no—
561C42—92no—
562C42—94no—
563C42—92no—
564C42C22×C3⋊D311yescharacteristic
565C42C22×C3⋊D311yescharacteristic
566C42C22×C3⋊D311yescharacteristic
567C42C22×C3⋊D311yescharacteristic
568C22×C3—24no—
569C22×C3—24no—
570C22×C3—216no—
571C22×C3—216no—
572C22×C3—216no—
573C22×C3#100418yes—
574C22×C3C24×D314yes—
575C2×D3—68no—
576C2×D3—68no—
577C2×D3—68no—
578C3×C4—216no—
579C3×C4—24no—
580C3×C4—24no—
581C3×C4—24no—
582C3×C4—24no—
583C3×C4D3×#4118yes—
584C3×C4#101018yes—
585Dic3—316no—
586Dic3—68no—
587Dic3—68no—
588Dic3—68no—
589Dic3—68no—
590Dic3—68no—
591Dic3—68no—
592C32#352211yescharacteristic, complemented, Sylow
593C23—92no—
594C23C23×C3⋊D314yes—
595C23C23×C3⋊D311yescharacteristic
596Q8—42no—
597Q8—94no—
598Q8—184no—
599Q8—182no—
600Q8—182no—
601Q8—364no—
602D4—28no—
603D4—24no—
604D4—24no—
605D4—42no—
606D4—188no—
607D4—184no—
608D4—182no—
609D4—364no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—44no—
614C2×C4—92no—
615C2×C4—92no—
616C2×C4—92no—
617C2×C4—92no—
618C2×C4—92no—
619C2×C4—92no—
620C2×C4—92no—
621C2×C4—184no—
622C2×C4—188no—
623C2×C4—184no—
624C2×C4—184no—
625C2×C4—364no—
626C2×C4—364no—
627C2×C4C23×C3⋊D311yescharacteristic
628C2×C4C23×C3⋊D314yes—
629C2×C4C23×C3⋊D311yescharacteristic
630C2×C4C23×C3⋊D311yescharacteristic
631C2×C4C23×C3⋊D311yescharacteristic
632C2×C4C23×C3⋊D311yescharacteristic
633C2×C4C23×C3⋊D311yescharacteristic
634C2×C3—28no—
635C2×C3—416no—
636C2×C3C2×#100414yes—
637C2×C3C2×D3×#4114yes—
638C2×C3C2×#101014yes—
639D3—128no—
640C22—21no—
641C22—21no—
642C22—24no—
643C22—24no—
644C22—24no—
645C22—182no—
646C22—182no—
647C22—182no—
648C22#6436112yes—
649C22C24×C3⋊D311yescharacteristic
650C4—21no—
651C4—21no—
652C4—24no—
653C4—21no—
654C4—21no—
655C4—94no—
656C4—182no—
657C4—182no—
658C4—182no—
659C4—182no—
660C4—182no—
661C4—182no—
662C4#41×C3⋊D312yes—
663C4#6436712yes—
664C3#8622914yescomplemented
665C2—22no—
666C2—44no—
667C2—362no—
668C2C2×#6436111yescharacteristic
669C2C2×#41×C3⋊D311yescharacteristic
670C2C2×#6436711yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#532C2
hypercenter#532C3⋊D3
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C32×#532C2semidirect
2. #10596295C2semidirect
3. #10596201C2semidirect
4. #10596193C2semidirect
5. #10596189C2semidirect
6. #10596184C2semidirect
7. #10596140C2semidirect
8. #10596082C2semidirect
9. #10596071C2semidirect
10. #10596069C2semidirect
11. #10596067C2semidirect
12. #10596032C2semidirect
13. #10596030C2semidirect
14. #10596017C2semidirect
15. #10596010C2semidirect
16. #10595950C2semidirect
17. C2×C4×#634C2semidirect
84. C3×#532D3semidirect
276. #634#41semidirect
289. #532C3⋊D3semidirect
592. C32#3522semidirect
664. C3#86229semidirect

Maximal subgroups

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

subgroupindex
C32×#5322
#105962952
#105962012
#105961932
#105961892
#105961842
#105961402
#105960822
#105960712
#105960692
#105960672
#105960322
#105960302
#105960172
#105960102
#105959502
C2×C4×#6342
#862293