Finite Group Databasebeta

← #11904911

Subgroups — #11904911

Order 1152.

2829 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595964C211yesmaximal, characteristic, complemented
2C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
3C3×#5483C211yesmaximal, characteristic, complemented
4C2×#63977C212yesmaximal, complemented
5#10595510C212yesmaximal, complemented
6#10595038C214yesmaximal, complemented
7#10595005C214yesmaximal, complemented
8#10594214C218yesmaximal, complemented
9#10594187C218yesmaximal, complemented
10#86579—31nomaximal
11#85697—31nomaximal
12C24×C3×D3C2211yescharacteristic
13C22×#638C2212yes—
14C22×C3×C4×D3C2212yescomplemented
15C22×#626C2214yescomplemented
16C2×#3799C2214yescomplemented
17C2×C32×C22⋊C4C2211yescharacteristic
18#64139C2214yescomplemented
19#64095C2214yescomplemented
20#64091C2214yescomplemented
21C2×C3×#217C2211yescharacteristic
22C2×C3×#217C2212yes—
23C2×C3×(C2×D3)⋊C4C2212yescomplemented
24C3×#924C2214yescomplemented
25C3×D3×C22⋊C4C2218yescomplemented
26C3×#878C2218yescomplemented
27#63977C2218yes—
28#63977C2214yescomplemented
29#63977C2214yescomplemented
30#63974C2214yescomplemented
31C2×(C2×D3)⋊Dic3C2214yescomplemented
32#63957C2214yescomplemented
33#63952C2218yescomplemented
34#63952C2218yescomplemented
35#63910C2218yescomplemented
36#63909C2214yescomplemented
37#63907C2218yescomplemented
38#63904C2218yescomplemented
39#63861C2218yescomplemented
40#63856C2214yescomplemented
41#63854C2218yescomplemented
42#63850C2218yescomplemented
43#63841C2214yescomplemented
44C3×#543—31no—
45C22×C3×C22⋊C4—31no—
46C2×#953—32no—
47#5791—34no—
48#5644—34no—
49#5637—38no—
50#5630—38no—
51#5627—34no—
52#5495—38no—
53#5494—34no—
54#5493—31no—
55#5493—31no—
56#5493—61no—
57#5490—38no—
58C2×#882—32no—
59#5486—32no—
60#5486—32no—
61C2×D3×C22⋊C4D311yescharacteristic, complemented
62#5483D311yescharacteristic, complemented
63C24×C32C2311yescharacteristic
64C23×C3⋊D3C2312yes—
65C23×C3×D3—24no—
66C23×C3×D3—44no—
67C23×C3×D3C2311yescharacteristic
68C23×C3×D3C2314yes—
69C23×C3×D3C2311yescharacteristic
70C22×C32×C4C2312yes—
71C2×#638—28no—
72C2×#638C2314yes—
73C2×#638C2314yes—
74C22×C3⋊Dic3C2312yes—
75C2×C4⋊(C3⋊D3)C2314yescomplemented
76C22×C3×Dic3C2314yes—
77C22×C3×Dic3C2312yes—
78C2×C3×C4×D3—44no—
79C2×C3×C4×D3C2314yes—
80C2×C3×C4×D3C2314yes—
81C2×C3×Dic6C2314yescomplemented
82C2×#626—48no—
83C2×#626C2318yes—
84C2×#626C2318yes—
85C2×#624C2318yescomplemented
86#3799—48no—
87C32×C22⋊C4C2314yes—
88#3752C2318yescomplemented
89C4⋊(C3⋊Dic3)C2314yescomplemented
90C3×#217C2314yes—
91C3×#217C2314yes—
92C3×#217C2314yes—
93C3×(C2×D3)⋊C4C2318yes—
94C3×C4⋊Dic3C2314yescomplemented
95C3×Dic3⋊C4C2318yescomplemented
96#3724C2318yescomplemented
97#3722C2318yescomplemented
98(C2×D3)⋊Dic3C2318yes—
99(C2×D3)⋊Dic3C2318yes—
100Dic32C2318yescomplemented
101#3490—91noSylow
102C25×C3—31no—
103C24×D3C2×D311yescharacteristic
104C23×C3×C4—32no—
105C22×#67—32no—
106C22×#67—32no—
107C22×#67—34no—
108C22×#67—62no—
109C2×#239—34no—
110C2×#235—34no—
111C22×D12—34no—
112C22×C4×D3C2×D312yescomplemented
113C3×C22⋊Q8—34no—
114C3×C22⋊Q8—38no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—31no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C22⋊C4—32no—
119C2×C3×C22⋊C4—38no—
120C2×C3×C22⋊C4C2×D311yescharacteristic
121C2×C3×C22⋊C4C2×D311yescharacteristic
122#953—38no—
123#953—34no—
124#953—34no—
125C2×#217—34no—
126C2×#217C2×D312yes—
127C2×#217C2×D311yescharacteristic
128#947—38no—
129#946—34no—
130#930—34no—
131#930—34no—
132#930—34no—
133#930—64no—
134#929—38no—
135C4×#67—38no—
136C4×#67—38no—
137C4×#67—38no—
138C2×(C2×D3)⋊C4—34no—
139C2×(C2×D3)⋊C4C2×D312yescomplemented
140#926—34no—
141#924—34no—
142#924C2×D314yescomplemented
143#898—38no—
144#895—34no—
145#895—38no—
146#894—38no—
147#894—38no—
148#893—38no—
149#892—34no—
150#886—34no—
151#886—34no—
152#886—64no—
153#885—38no—
154#884—38no—
155#883—38no—
156#882—38no—
157#882—34no—
158#882—34no—
159#882—34no—
160#882—34no—
161#882—64no—
162#67⋊C4—38no—
163#67⋊C4—38no—
164D3×C22⋊C4—34no—
165D3×C22⋊C4—34no—
166D3×C22⋊C4C2×D318yescomplemented
167#879—38no—
168#878C2×D318yescomplemented
169#877—34no—
170#877—34no—
171C23×C32—42no—
172C23×C32#4114yescomplemented
173C23×C32C2412yes—
174C23×C32C2411yescharacteristic
175C22×C3⋊D3—24no—
176C22×C3⋊D3—44no—
177C22×C3⋊D3C2414yes—
178C22×C3×D3—22no—
179C22×C3×D3—24no—
180C22×C3×D3—28no—
181C22×C3×D3—22no—
182C22×C3×D3—28no—
183C22×C3×D3—44no—
184C22×C3×D3—42no—
185C22×C3×D3—416no—
186C22×C3×D3C2412yes—
187C22×C3×D3C2412yes—
188C2×C32×C4—42no—
189C2×C32×C4C2414yes—
190#638—28no—
191#638—28no—
192C2×C3⋊Dic3—24no—
193C2×C3⋊Dic3C2414yes—
194C4⋊(C3⋊D3)—44no—
195C2×C3×Dic3—44no—
196C2×C3×Dic3—42no—
197C2×C3×Dic3C2414yes—
198C2×C3×Dic3C2418yes—
199C3×C4×D3—28no—
200C3×C4×D3—44no—
201C3×Dic6—44no—
202#626—216no—
203#626—48no—
204#624—48no—
205#551—98no—
206#546—98no—
207#543—31no—
208#538—94no—
209#534—91no—
210#525—94no—
211C2×#120—92no—
212#518—92no—
213C22×C22⋊C4—31no—
214C24×C3—21no—
215C24×C3—31no—
216C24×C3—34no—
217C24×C3—31no—
218C24×C3—64no—
219C24×C3—124no—
220C24×C3C22×D311yescharacteristic
221C24×C3C22×D311yescharacteristic
222C23×D3—24no—
223C23×D3—32no—
224C23×D3—32no—
225C23×D3—44no—
226C23×D3—62no—
227C23×D3C22×D311yescharacteristic
228C23×D3C22×D314yes—
229C23×D3C22×D311yescharacteristic
230C2×C3×Q8—34no—
231C22×C3×C4—22no—
232C22×C3×C4—34no—
233C22×C3×C4—32no—
234C22×C3×C4—34no—
235C22×C3×C4—34no—
236C22×C3×C4—124no—
237C22×C3×C4C22×D312yes—
238C22×C3×C4C22×D312yes—
239C2×#67—34no—
240C2×#67—34no—
241C2×#67—34no—
242C2×#67—34no—
243C2×#67—38no—
244C2×#67—38no—
245C2×#67—64no—
246C2×#67—64no—
247C2×#67—68no—
248C2×#67—68no—
249C2×#67—128no—
250C2×#67—128no—
251C22×Dic3—32no—
252C22×Dic3—32no—
253C22×Dic3—62no—
254C22×Dic3C22×D314yes—
255C22×Dic3C22×D312yes—
256#239—128no—
257#235—128no—
258C2×D12—38no—
259C2×D12—38no—
260C2×D12—34no—
261C2×D12—34no—
262C2×D12—64no—
263C2×D12—128no—
264C2×C4×D3—38no—
265C2×C4×D3—38no—
266C2×C4×D3—44no—
267C2×C4×D3C22×D314yes—
268C2×C4×D3C22×D314yes—
269C2×Dic6C22×D314yescomplemented
270C3×C4⋊C4—34no—
271C3×C4⋊C4—38no—
272C3×C22⋊C4—24no—
273C3×C22⋊C4—34no—
274C3×C22⋊C4—34no—
275C3×C22⋊C4—34no—
276C3×C22⋊C4—38no—
277C3×C22⋊C4C22×D314yes—
278C3×C22⋊C4C22×D314yes—
279#217—38no—
280#217—38no—
281#217C22×D314yes—
282#217C22×D314yes—
283#217C22×D314yes—
284(C2×D3)⋊C4—38no—
285(C2×D3)⋊C4—38no—
286(C2×D3)⋊C4—38no—
287(C2×D3)⋊C4—38no—
288(C2×D3)⋊C4—38no—
289(C2×D3)⋊C4—38no—
290(C2×D3)⋊C4—68no—
291(C2×D3)⋊C4C22×D318yes—
292C4⋊Dic3—34no—
293C4⋊Dic3—34no—
294C4⋊Dic3—64no—
295C4⋊Dic3C22×D314yescomplemented
296Dic3⋊C4—38no—
297Dic3⋊C4—38no—
298Dic3⋊C4C22×D318yescomplemented
299C4×Dic3—38no—
300C4×Dic3—38no—
301C22×C32—22no—
302C22×C32—24no—
303C22×C32—44no—
304C22×C32C2×#4114yes—
305C22×C32C2×#4112yes—
306C22×C32C2511yescharacteristic
307C2×C3⋊D3—24no—
308C2×C3⋊D3—28no—
309C2×C3⋊D3—84no—
310C2×C3×D3—28no—
311C2×C3×D3—22no—
312C2×C3×D3—22no—
313C2×C3×D3—22no—
314C2×C3×D3—24no—
315C2×C3×D3—416no—
316C2×C3×D3—44no—
317C2×C3×D3H(5,𝔽2)14yes—
318C32×C4—24no—
319C3⋊Dic3—24no—
320C3×Dic3—24no—
321C3×Dic3—28no—
322C25—31no—
323C2×#41—94no—
324C22×D4—94no—
325C22×D4—92no—
326C23×C4—32no—
327#126—98no—
328#124—98no—
329#123—98no—
330#123—98no—
331#123—94no—
332C22⋊Q8—34no—
333C22⋊Q8—38no—
334C22⋊Q8—94no—
335#121—98no—
336#121—94no—
337#121—94no—
338#120—94no—
339#120—94no—
340#120—98no—
341#120—94no—
342C4×D4—98no—
343C4×D4—98no—
344C4×D4—98no—
345#117—94no—
346#117—94no—
347C2×C22⋊C4—31no—
348C2×C22⋊C4—32no—
349C2×C22⋊C4—32no—
350C2×C22⋊C4—38no—
351C2×C22⋊C4—94no—
352C2×C22⋊C4—94no—
353C2×C22⋊C4D3211yescharacteristic
354C23×C3—22no—
355C23×C3—21no—
356C23×C3—24no—
357C23×C3—32no—
358C23×C3—32no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—64no—
362C23×C3—68no—
363C23×C3—62no—
364C23×C3—68no—
365C23×C3—62no—
366C23×C3—82no—
367C23×C3—124no—
368C23×C3—122no—
369C23×C3—1216no—
370C23×C3#23514yescomplemented
371C23×C3#23914yescomplemented
372C23×C3C23×D312yes—
373C23×C3C23×D311yescharacteristic
374C23×C3C23×D311yescharacteristic
375C23×C3C23×D312yes—
376C22×D3—22no—
377C22×D3—24no—
378C22×D3—28no—
379C22×D3—22no—
380C22×D3—28no—
381C22×D3—34no—
382C22×D3—34no—
383C22×D3—44no—
384C22×D3—42no—
385C22×D3—416no—
386C22×D3—64no—
387C22×D3—64no—
388C22×D3—64no—
389C22×D3—124no—
390C22×D3—124no—
391C22×D3—124no—
392C22×D3—244no—
393C22×D3C23×D312yes—
394C22×D3C23×D312yes—
395C3×Q8—124no—
396C2×C3×C4—24no—
397C2×C3×C4—34no—
398C2×C3×C4—38no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—68no—
402C2×C3×C4—82no—
403C2×C3×C4—124no—
404C2×C3×C4—124no—
405C2×C3×C4—122no—
406C2×C3×C4C23×D314yes—
407C2×C3×C4C23×D314yes—
408#67—616no—
409#67—68no—
410#67—68no—
411#67—68no—
412#67—68no—
413#67—128no—
414#67—128no—
415#67—128no—
416C2×Dic3—34no—
417C2×Dic3—34no—
418C2×Dic3—42no—
419C2×Dic3—44no—
420C2×Dic3—64no—
421C2×Dic3—64no—
422C2×Dic3—64no—
423C2×Dic3—124no—
424C2×Dic3C23×D314yes—
425C2×Dic3C23×D318yes—
426D12—616no—
427D12—124no—
428D12—124no—
429D12—128no—
430D12—244no—
431C4×D3—28no—
432C4×D3—44no—
433C4×D3—128no—
434C4×D3—128no—
435Dic6—44no—
436C2×C32—22no—
437C2×C32—24no—
438C2×C32C22×#4111yescharacteristic
439C2×C32C2×H(5,𝔽2)12yes—
440C3⋊D3—44no—
441C3×D3—24no—
442C3×D3—42no—
443C24—31no—
444C24—34no—
445C24—31no—
446C24—64no—
447C24—92no—
448C24—124no—
449C24C2×D3211yescharacteristic
450#41—368no—
451C2×Q8—34no—
452C2×D4—98no—
453C2×D4—98no—
454C2×D4—94no—
455C2×D4—94no—
456C2×D4—94no—
457C2×D4—188no—
458C2×D4—368no—
459C22×C4—32no—
460C22×C4—34no—
461C22×C4—34no—
462C22×C4—34no—
463C22×C4—98no—
464C22×C4—92no—
465C22×C4—124no—
466C22×C4C2×D3212yes—
467C4⋊C4—34no—
468C4⋊C4—38no—
469C4⋊C4—98no—
470C4⋊C4—94no—
471C22⋊C4—34no—
472C22⋊C4—34no—
473C22⋊C4—34no—
474C22⋊C4—38no—
475C22⋊C4—98no—
476C22⋊C4—98no—
477C22⋊C4—98no—
478C22⋊C4—98no—
479C22⋊C4C2×D3214yes—
480C42—98no—
481C22×C3—22no—
482C22×C3—24no—
483C22×C3—24no—
484C22×C3—22no—
485C22×C3—24no—
486C22×C3—22no—
487C22×C3—21no—
488C22×C3—34no—
489C22×C3—42no—
490C22×C3—44no—
491C22×C3—44no—
492C22×C3—44no—
493C22×C3—68no—
494C22×C3—62no—
495C22×C3—62no—
496C22×C3—62no—
497C22×C3—64no—
498C22×C3—84no—
499C22×C3—1216no—
500C22×C3—124no—
501C22×C3C2×#23514yes—
502C22×C3C2×#23512yes—
503C22×C3C2×#23914yes—
504C22×C3C2×#23912yes—
505C22×C3C24×D311yescharacteristic
506C22×C3C24×D311yescharacteristic
507C2×D3—28no—
508C2×D3—22no—
509C2×D3—22no—
510C2×D3—22no—
511C2×D3—24no—
512C2×D3—416no—
513C2×D3—44no—
514C2×D3—64no—
515C2×D3—68no—
516C2×D3—64no—
517C2×D3—68no—
518C2×D3—128no—
519C2×D3—124no—
520C2×D3—244no—
521C2×D3—244no—
522C2×D3—248no—
523C2×D3#100414yes—
524C3×C4—24no—
525C3×C4—24no—
526C3×C4—44no—
527C3×C4—68no—
528C3×C4—64no—
529Dic3—24no—
530Dic3—28no—
531Dic3—64no—
532Dic3—64no—
533Dic3—124no—
534C32#349011yescharacteristic, complemented, Sylow
535C23—32no—
536C23—32no—
537C23—42no—
538C23—64no—
539C23—68no—
540C23—62no—
541C23—68no—
542C23—62no—
543C23—94no—
544C23—122no—
545C23—124no—
546C23—1216no—
547C23—184no—
548C23—364no—
549C23#379914yescomplemented
550C23C22×D3212yes—
551C23C22×D3211yescharacteristic
552Q8—124no—
553D4—1816no—
554D4—188no—
555D4—188no—
556D4—364no—
557D4—368no—
558C2×C4—34no—
559C2×C4—38no—
560C2×C4—42no—
561C2×C4—68no—
562C2×C4—94no—
563C2×C4—124no—
564C2×C4—122no—
565C2×C4—124no—
566C2×C4—184no—
567C2×C4—368no—
568C2×C4C22×D3214yes—
569C2×C3—24no—
570C2×C3—22no—
571C2×C3—22no—
572C2×C3—24no—
573C2×C3—21no—
574C2×C3—22no—
575C2×C3—44no—
576C2×C3—42no—
577C2×C3—64no—
578C2×C3—122no—
579C2×C3C22×#23511yescharacteristic
580C2×C3C2×#100412yes—
581C2×C3C22×#23911yescharacteristic
582C2×C3D3×H(5,𝔽2)12yes—
583D3—24no—
584D3—42no—
585D3—124no—
586D3—124no—
587D3—244no—
588C22—22no—
589C22—24no—
590C22—34no—
591C22—44no—
592C22—68no—
593C22—62no—
594C22—62no—
595C22—62no—
596C22—64no—
597C22—1216no—
598C22—124no—
599C22—184no—
600C22—188no—
601C22—724no—
602C22C2×#379914yes—
603C22C2×#379912yes—
604C22C23×D3211yescharacteristic
605C4—24no—
606C4—64no—
607C4—68no—
608C4—184no—
609C3—21no—
610C3#8569711yescharacteristic, complemented
611C3#8657911yescharacteristic, complemented
612C2—22no—
613C2—24no—
614C2—64no—
615C2—122no—
616C2—364no—
617C2C22×#379911yescharacteristic
618C2D3×#100412yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3490
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595964C2semidirect
2. C2×C3×D3×C22⋊C4C2semidirect
3. C3×#5483C2semidirect
4. C2×#63977C2semidirect
5. #10595510C2semidirect
6. #10595038C2semidirect
7. #10595005C2semidirect
8. #10594214C2semidirect
9. #10594187C2semidirect
14. C22×C3×C4×D3C22semidirect
15. C22×#626C22semidirect
16. C2×#3799C22semidirect
18. #64139C22semidirect
19. #64095C22semidirect
20. #64091C22semidirect
23. C2×C3×(C2×D3)⋊C4C22semidirect
24. C3×#924C22semidirect
25. C3×D3×C22⋊C4C22semidirect
26. C3×#878C22semidirect
28. #63977C22semidirect
29. #63977C22semidirect
30. #63974C22semidirect
31. C2×(C2×D3)⋊Dic3C22semidirect
32. #63957C22semidirect
33. #63952C22semidirect
34. #63952C22semidirect
35. #63910C22semidirect
36. #63909C22semidirect
37. #63907C22semidirect
38. #63904C22semidirect
39. #63861C22semidirect
40. #63856C22semidirect
41. #63854C22semidirect
42. #63850C22semidirect
43. #63841C22semidirect
61. C2×D3×C22⋊C4D3semidirect
62. #5483D3semidirect
75. C2×C4⋊(C3⋊D3)C23semidirect
81. C2×C3×Dic6C23semidirect
85. C2×#624C23semidirect
88. #3752C23semidirect
89. C4⋊(C3⋊Dic3)C23semidirect
94. C3×C4⋊Dic3C23semidirect
95. C3×Dic3⋊C4C23semidirect
96. #3724C23semidirect
97. #3722C23semidirect
100. Dic32C23semidirect
112. C22×C4×D3C2×D3semidirect
139. C2×(C2×D3)⋊C4C2×D3semidirect
142. #924C2×D3semidirect
166. D3×C22⋊C4C2×D3semidirect
168. #878C2×D3semidirect
172. C23×C32#41semidirect
269. C2×Dic6C22×D3semidirect
295. C4⋊Dic3C22×D3semidirect
298. Dic3⋊C4C22×D3semidirect
370. C23×C3#235semidirect
371. C23×C3#239semidirect
534. C32#3490semidirect
549. C23#3799semidirect
610. C3#85697semidirect
611. C3#86579semidirect

Maximal subgroups

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

subgroupindex
#105959642
C2×C3×D3×C22⋊C42
C3×#54832
C2×#639772
#105955102
#105950382
#105950052
#105942142
#105941872
#865793
#856973