Finite Group Databasebeta

← #11865383

Subgroups — #11865383

Order 1152.

1949 conjugacy classes of subgroups.

The subgroup lattice has 625 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596756C211yesmaximal, characteristic, complemented
2C3×#5830C211yesmaximal, characteristic, complemented
3#10595042C212yesmaximal, complemented
4C3×#5240C211yesmaximal, characteristic, complemented
5#10591532C218yesmaximal, complemented
6#10591232C212yesmaximal, complemented
7#83396—31nomaximal
8#78691—31nomaximal
9C2×C32×#41C2211yescharacteristic
10#64367—22no—
11#64366—22no—
12#41×C3⋊D3—24no—
13#64364—21no—
14#64361—21no—
15#64361C2214yes—
16C2×#3828—22no—
17C2×#3828C2212yes—
18C22×C3×D12C2211yescharacteristic, complemented
19C3×#947—21no—
20C3×#940—21no—
21C3×#937C2214yescomplemented
22C3×#930—22no—
23C3×#926C2211yescharacteristic, complemented
24C3×#926C2212yescomplemented
25#63977C2218yescomplemented
26#63916—24no—
27#63911—22no—
28#63860—22no—
29C3×#834C2214yescomplemented
30#63581C2218yescomplemented
31#5964—31no—
32#5964—31no—
33#5964—61no—
34C3×#535—31no—
35#5830D311yescharacteristic, complemented
36#5805—32no—
37#5525—32no—
38C3×#410—31no—
39#5240D311yescharacteristic, complemented
40#5032—38no—
41#5006—32no—
42#5006—32no—
43#4741—38no—
44C23×C3×D3C2312yes—
45C32×#41—22no—
46C32×#41—22no—
47C2×C32×Q8D411yescharacteristic, complemented
48C2×C32×D4D411yescharacteristic, complemented
49C2×C32×D4C2312yes—
50C22×C32×C4D412yescomplemented
51C22×C32×C4C2311yescharacteristic
52C2×#638—24no—
53C2×#638C2314yes—
54#3832—24no—
55Q8×C3⋊D3—24no—
56#3830—24no—
57#3830—28no—
58D4×C3⋊D3—24no—
59D4×C3⋊D3—28no—
60#3828—24no—
61#3828—24no—
62#3828—22no—
63#3828—24no—
64#3828—22no—
65#3828—22no—
66#3828—22no—
67C2×C4⋊(C3⋊D3)—22no—
68C2×C4⋊(C3⋊D3)D412yescomplemented
69C2×C4×C3⋊D3—24no—
70C2×C4×C3⋊D3D414yescomplemented
71C2×#634—22no—
72C2×#634D412yescomplemented
73C2×C3×#67—24no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12—22no—
77C2×C3×D12—22no—
78C2×#626—28no—
79C3×#217C2312yes—
80C3×#217C2314yes—
81C3×(C2×D3)⋊C4—24no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3—22no—
84C3×C4×Dic3—21no—
85C3×C4×Dic3—22no—
86(C2×D3)⋊Dic3—28no—
87#3027—91noSylow
88C2×C3×#41—21no—
89C2×C3×#41C2×D311yescharacteristic
90C2×C3×#41C2×D311yescharacteristic
91C22×C3×D4—31no—
92#1010—62no—
93#1010—62no—
94#1010—64no—
95#1009—62no—
96#1009—62no—
97#1009—64no—
98D3×#41—64no—
99D3×#41—64no—
100D3×#41—68no—
101#1007—62no—
102#1007—61no—
103#1007—61no—
104#1004—34no—
105#1004—34no—
106#1004—64no—
107#1004—62no—
108#1004—61no—
109#1004—61no—
110C2×#235—32no—
111C2×#235—32no—
112C2×#235—62no—
113C2×#235—64no—
114C2×#235—62no—
115C2×#235—62no—
116C22×D12C2×D311yescharacteristic, complemented
117C3×#127—61no—
118C3×#124—61no—
119C3×#121—62no—
120C3×#120—34no—
121C3×#117—31no—
122C3×#117—32no—
123#953—38no—
124#947—21no—
125#940—21no—
126#940—62no—
127#938—64no—
128#937C2×D314yescomplemented
129#936—62no—
130#930—22no—
131#926C2×D312yescomplemented
132#926C2×D311yescharacteristic, complemented
133#895—64no—
134#882—38no—
135#875—62no—
136#874—62no—
137C3×#99—34no—
138#834C2×D314yescomplemented
139#806—38no—
140#806—38no—
141C23×C32C2×D412yes—
142C23×C32C2411yescharacteristic
143C22×C3⋊D3—24no—
144C22×C3⋊D3C2×D414yes—
145C22×C3×D3—24no—
146C22×C3×D3—22no—
147C22×C3×D3—82no—
148C32×Q8—22no—
149C32×D4—24no—
150C32×D4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4C2×D412yes—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2×D412yes—
158#638—28no—
159#638—24no—
160#638—24no—
161C2×C3⋊Dic3—24no—
162C2×C3⋊Dic3C2×D414yes—
163C4⋊(C3⋊D3)—24no—
164C4⋊(C3⋊D3)—22no—
165C4⋊(C3⋊D3)—22no—
166C4×C3⋊D3—28no—
167C4×C3⋊D3—24no—
168C4×C3⋊D3—24no—
169#634—24no—
170#634—22no—
171#634—22no—
172C3×#67—84no—
173C2×C3×Dic3—24no—
174C2×C3×Dic3—22no—
175C3×D12—41no—
176C3×D12—42no—
177C3×D12—41no—
178#626—88no—
179#585—91no—
180#535—31no—
181#535—92no—
182B(4,𝔽2)—98no—
183#410—31no—
184#410—92no—
185C24×C3—32no—
186C23×D3C22×D312yes—
187C3×#41—24no—
188C3×#41—24no—
189C3×#41—22no—
190C3×#41—22no—
191C3×#41—22no—
192C3×#41—22no—
193C2×C3×Q8—21no—
194C2×C3×Q8D1211yescharacteristic, complemented
195C2×C3×Q8#6711yescharacteristic, complemented
196C2×C3×D4—21no—
197C2×C3×D4—22no—
198C2×C3×D4—64no—
199C2×C3×D4—61no—
200C2×C3×D4—61no—
201C2×C3×D4—62no—
202C2×C3×D4—62no—
203C2×C3×D4D1211yescharacteristic, complemented
204C2×C3×D4#6711yescharacteristic, complemented
205C2×C3×D4C22×D312yes—
206C2×C3×D4C22×D312yes—
207C22×C3×C4—22no—
208C22×C3×C4—21no—
209C22×C3×C4D1212yescomplemented
210C22×C3×C4#6712yescomplemented
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C2×#67—24no—
214C2×#67—34no—
215C2×#67—34no—
216C2×#67—64no—
217C2×#67—68no—
218C2×#67—68no—
219C2×#67—64no—
220C2×#67—64no—
221#239—68no—
222#239—64no—
223#239—64no—
224D3×Q8—68no—
225D3×Q8—64no—
226D3×Q8—64no—
227#237—68no—
228#237—68no—
229#237—616no—
230#237—68no—
231#237—64no—
232#237—64no—
233D3×D4—68no—
234D3×D4—68no—
235D3×D4—616no—
236D3×D4—68no—
237D3×D4—64no—
238D3×D4—64no—
239#235—64no—
240#235—64no—
241#235—68no—
242#235—68no—
243#235—64no—
244#235—64no—
245#235—64no—
246#235—68no—
247#235—64no—
248#235—64no—
249#235—64no—
250#235—62no—
251#235—62no—
252#235—64no—
253#235—62no—
254#235—62no—
255#235—62no—
256#235—62no—
257#235—62no—
258#235—62no—
259#235—64no—
260C2×D12—22no—
261C2×D12—22no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—32no—
265C2×D12—32no—
266C2×D12—62no—
267C2×D12—64no—
268C2×D12—62no—
269C2×D12—62no—
270C2×D12—68no—
271C2×C4×D3—34no—
272C2×C4×D3—34no—
273C2×C4×D3—64no—
274C2×C4×D3—68no—
275C2×C4×D3—64no—
276C2×C4×D3—64no—
277C2×Dic6—32no—
278C2×Dic6—32no—
279C2×Dic6—62no—
280C2×Dic6—64no—
281C2×Dic6—62no—
282C2×Dic6—62no—
283C3×C4⋊C4—61no—
284C3×C4⋊C4—62no—
285C3×C22⋊C4—32no—
286C3×C22⋊C4—34no—
287C3×C22⋊C4—64no—
288C3×C42—61no—
289C3×C42—62no—
290#217—68no—
291#217C22×D312yes—
292#217C22×D314yes—
293(C2×D3)⋊C4—24no—
294(C2×D3)⋊C4—68no—
295C4⋊Dic3—22no—
296C4⋊Dic3—21no—
297C4×Dic3—22no—
298C4×Dic3—21no—
299C22×C32—22no—
300C22×C32—41no—
301C22×C32—42no—
302C22×C32C22×D411yescharacteristic
303C22×C32C22×D412yes—
304C2×C3⋊D3—24no—
305C2×C3⋊D3—44no—
306C2×C3⋊D3—84no—
307C2×C3×D3—48no—
308C2×C3×D3—44no—
309C2×C3×D3—42no—
310C32×C4—22no—
311C32×C4#12011yescharacteristic
312C32×C4#12012yes—
313C32×C4#12011yescharacteristic
314C3⋊Dic3—24no—
315C3×Dic3—44no—
316C3×Dic3—42no—
3172−1+4—182no—
3182−1+4—181no—
319H(5,𝔽2)—94no—
320H(5,𝔽2)—182no—
321H(5,𝔽2)—181no—
322C2×#41—92no—
323C2×#41—184no—
324C2×#41—182no—
325C2×#41D3211yescharacteristic
326C22×D4—31no—
327#127—61no—
328#127—182no—
329#124—61no—
330#124—182no—
331#121—62no—
332#121—184no—
333#120—34no—
334#120—98no—
335#117—31no—
336#117—32no—
337#99—34no—
338#99—98no—
339C23×C3—21no—
340C23×C3—22no—
341C23×C3—62no—
342C23×C3—64no—
343C23×C3—242no—
344C23×C3C2×D1212yes—
345C23×C3C2×#6712yes—
346C23×C3C23×D311yescharacteristic
347C23×C3C23×D311yescharacteristic
348C22×D3—24no—
349C22×D3—22no—
350C22×D3—34no—
351C22×D3—34no—
352C22×D3—64no—
353C22×D3—68no—
354C22×D3—64no—
355C22×D3—64no—
356C22×D3—82no—
357C3×Q8—24no—
358C3×Q8—22no—
359C3×Q8—22no—
360C3×D4—28no—
361C3×D4—24no—
362C3×D4—24no—
363C3×D4—24no—
364C3×D4—22no—
365C3×D4—22no—
366C3×D4—121no—
367C3×D4—122no—
368C3×D4—121no—
369C3×D4—244no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—21no—
377C2×C3×C4—22no—
378C2×C3×C4—21no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—62no—
382C2×C3×C4—64no—
383C2×C3×C4C2×D1212yes—
384C2×C3×C4C2×D1211yescharacteristic
385C2×C3×C4C2×D1211yescharacteristic
386C2×C3×C4D3×D412yes—
387C2×C3×C4D3×D412yes—
388C2×C3×C4D3×D412yes—
389C2×C3×C4D3×D412yes—
390C2×C3×C4C2×#6712yes—
391C2×C3×C4C2×#6711yescharacteristic
392C2×C3×C4C2×#6711yescharacteristic
393#67—68no—
394#67—616no—
395#67—68no—
396#67—68no—
397#67—68no—
398#67—64no—
399#67—64no—
400#67—64no—
401#67—64no—
402#67—84no—
403#67—248no—
404C2×Dic3—24no—
405C2×Dic3—22no—
406C2×Dic3—34no—
407C2×Dic3—34no—
408C2×Dic3—64no—
409C2×Dic3—68no—
410C2×Dic3—64no—
411C2×Dic3—64no—
412D12—41no—
413D12—42no—
414D12—41no—
415D12—64no—
416D12—68no—
417D12—64no—
418D12—64no—
419D12—64no—
420D12—62no—
421D12—62no—
422D12—62no—
423D12—62no—
424D12—248no—
425C4×D3—68no—
426C4×D3—616no—
427C4×D3—68no—
428C4×D3—68no—
429C4×D3—68no—
430C4×D3—64no—
431C4×D3—64no—
432C4×D3—64no—
433C4×D3—64no—
434Dic6—64no—
435Dic6—68no—
436Dic6—64no—
437Dic6—64no—
438Dic6—64no—
439Dic6—62no—
440Dic6—62no—
441Dic6—62no—
442Dic6—62no—
443C2×C32—22no—
444C2×C32—21no—
445C2×C32—42no—
446C2×C32C2×#12011yescharacteristic
447C3⋊D3—44no—
448C3×D3—82no—
449C24—32no—
450#41—22no—
451#41—22no—
452#41—184no—
453#41—184no—
454#41—188no—
455#41—184no—
456#41—184no—
457#41—182no—
458#41—182no—
459#41—184no—
460#41—182no—
461#41—182no—
462C2×Q8—92no—
463C2×Q8—182no—
464C2×Q8—184no—
465C2×Q8#62611yescharacteristic, complemented
466C2×D4—64no—
467C2×D4—61no—
468C2×D4—61no—
469C2×D4—62no—
470C2×D4—62no—
471C2×D4—94no—
472C2×D4—92no—
473C2×D4—182no—
474C2×D4—188no—
475C2×D4—188no—
476C2×D4—184no—
477C2×D4—184no—
478C2×D4#62611yescharacteristic, complemented
479C2×D4C2×D3212yes—
480C22×C4—94no—
481C22×C4—184no—
482C22×C4#62612yescomplemented
483C22×C4C2×D3211yescharacteristic
484C4⋊C4—61no—
485C4⋊C4—62no—
486C22⋊C4—34no—
487C22⋊C4—32no—
488C22⋊C4—64no—
489C22⋊C4—188no—
490C42—61no—
491C42—62no—
492C22×C3—24no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—21no—
496C22×C3—22no—
497C22×C3—41no—
498C22×C3—41no—
499C22×C3—42no—
500C22×C3—42no—
501C22×C3—81no—
502C22×C3—82no—
503C22×C3—128no—
504C22×C3—124no—
505C22×C3—122no—
506C22×C3C22×D1211yescharacteristic
507C22×C3C2×D3×D412yes—
508C22×C3C2×D3×D412yes—
509C22×C3C22×#6711yescharacteristic
510C2×D3—48no—
511C2×D3—44no—
512C2×D3—42no—
513C2×D3—68no—
514C2×D3—64no—
515C2×D3—64no—
516C2×D3—124no—
517C2×D3—124no—
518C2×D3—244no—
519C2×D3—248no—
520C2×D3—244no—
521C2×D3—244no—
522C3×C4—24no—
523C3×C4—22no—
524C3×C4—22no—
525C3×C4—21no—
526C3×C4—22no—
527C3×C4—21no—
528C3×C4—124no—
529C3×C4—122no—
530C3×C4#88211yescharacteristic
531C3×C4#88212yes—
532C3×C4#88211yescharacteristic
533C3×C4#93711yescharacteristic
534C3×C4#93712yes—
535C3×C4#93711yescharacteristic
536Dic3—42no—
537Dic3—44no—
538Dic3—68no—
539Dic3—64no—
540Dic3—64no—
541C32#302711yescharacteristic, complemented, Sylow
542C23—62no—
543C23—64no—
544C23—94no—
545C23—184no—
546C23—242no—
547C23C2×#62612yes—
548C23C22×D3211yescharacteristic
549Q8—22no—
550Q8—184no—
551Q8—182no—
552Q8—182no—
553D4—24no—
554D4—22no—
555D4—121no—
556D4—121no—
557D4—122no—
558D4—184no—
559D4—188no—
560D4—184no—
561D4—184no—
562D4—182no—
563D4—182no—
564D4—244no—
565D4—728no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—62no—
569C2×C4—64no—
570C2×C4—94no—
571C2×C4—188no—
572C2×C4—184no—
573C2×C4—184no—
574C2×C4—184no—
575C2×C4C2×#62612yes—
576C2×C4C2×#62611yescharacteristic
577C2×C4C2×#62611yescharacteristic
578C2×C4#381112yes—
579C2×C4#381112yes—
580C2×C3—22no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—22no—
584C2×C3—21no—
585C2×C3—42no—
586C2×C3—41no—
587C2×C3—44no—
588C2×C3—42no—
589C2×C3—42no—
590C2×C3—242no—
591C2×C3C2×#88211yescharacteristic
592C2×C3C2×#93711yescharacteristic
593D3—82no—
594D3—128no—
595D3—124no—
596D3—124no—
597C22—22no—
598C22—41no—
599C22—42no—
600C22—124no—
601C22—128no—
602C22—122no—
603C22—184no—
604C22—364no—
605C22—724no—
606C22C22×#62611yescharacteristic
607C22C2×#381112yes—
608C4—22no—
609C4—122no—
610C4—124no—
611C4—184no—
612C4#6398111yescharacteristic
613C4#6398111yescharacteristic
614C4#6398112yes—
615C3—21no—
616C3#7869111yescharacteristic, complemented
617C3#8339611yescharacteristic, complemented
618C2—21no—
619C2—22no—
620C2—42no—
621C2—242no—
622C2—364no—
623C2C2×#6398111yescharacteristic
subgroupG/H
centerC2C2×#63981
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#120
hypercenterC2×#41D32
hypocenterC32#3027
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596756C2semidirect
2. C3×#5830C2semidirect
3. #10595042C2semidirect
4. C3×#5240C2semidirect
5. #10591532C2semidirect
6. #10591232C2semidirect
18. C22×C3×D12C22semidirect
21. C3×#937C22semidirect
23. C3×#926C22semidirect
24. C3×#926C22semidirect
25. #63977C22semidirect
29. C3×#834C22semidirect
30. #63581C22semidirect
35. #5830D3semidirect
39. #5240D3semidirect
47. C2×C32×Q8D4semidirect
48. C2×C32×D4D4semidirect
50. C22×C32×C4D4semidirect
68. C2×C4⋊(C3⋊D3)D4semidirect
70. C2×C4×C3⋊D3D4semidirect
72. C2×#634D4semidirect
116. C22×D12C2×D3semidirect
128. #937C2×D3semidirect
131. #926C2×D3semidirect
132. #926C2×D3semidirect
138. #834C2×D3semidirect
194. C2×C3×Q8D12semidirect
195. C2×C3×Q8#67semidirect
203. C2×C3×D4D12semidirect
204. C2×C3×D4#67semidirect
209. C22×C3×C4D12semidirect
210. C22×C3×C4#67semidirect
465. C2×Q8#626semidirect
478. C2×D4#626semidirect
482. C22×C4#626semidirect
541. C32#3027semidirect
616. C3#78691semidirect
617. C3#83396semidirect

Maximal subgroups

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

subgroupindex
#105967562
C3×#58302
#105950422
C3×#52402
#105915322
#105912322
#833963
#786913