Subgroups — #11772000

Order 1152.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10592781	C₂	1	1	yes	maximal, characteristic
2	#10590149	C₂	1	2	yes	maximal
3	C₃²×C₄⋊Q₈	C₄	1	1	yes	characteristic
4	#64079	C₄	1	1	yes	characteristic
5	#63773	—	2	2	no	—
6	#63662	—	2	2	no	—
7	#63630	C₂²	1	1	yes	characteristic
8	#5082	—	6	2	no	—
9	C₂×C₃²×Q₈	—	2	1	no	—
10	C₃²×C₄⋊C₄	—	4	1	no	—
11	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
12	C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
13	#3750	—	4	1	no	—
14	C₂×C₃⋊(C₃⋊C₈)	D₄	1	2	yes	—
15	#3708	—	2	4	no	—
16	#1356	—	9	1	no	maximal, Sylow
17	C₃×C₄⋊Q₈	—	2	2	no	—
18	#870	—	6	2	no	—
19	#835	—	6	8	no	—
20	#803	—	6	2	no	—
21	C₃²×Q₈	—	4	2	no	—
22	C₂×C₃²×C₄	—	2	1	no	—
23	C₂×C₃²×C₄	—	4	1	no	—
24	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₃⋊Dic₃	—	4	1	no	—
26	C₃⋊(C₃⋊C₈)	—	2	2	no	—
27	#491	—	9	1	no	—
28	#347	—	9	2	no	—
29	C₂×C₃×Q₈	—	2	4	no	—
30	C₃×C₄⋊C₄	—	4	4	no	—
31	C₃×C₄²	—	2	2	no	—
32	C₄⋊Dic₃	—	6	4	no	—
33	Dic₃⋊C₄	—	12	4	no	—
34	C₂×C₃⋊C₈	—	6	4	no	—
35	C₂²×C₃²	#100	1	1	yes	characteristic
36	C₃²×C₄	—	4	1	no	—
37	C₃²×C₄	—	8	1	no	—
38	C₃²×C₄	#104	1	2	yes	—
39	C₃⋊Dic₃	—	8	1	no	—
40	C₄⋊Q₈	#157	1	1	yes	characteristic
41	#125	—	9	1	no	—
42	M₃₂	—	18	2	no	—
43	#103	—	18	2	no	—
44	#97	—	9	1	no	—
45	C₃×Q₈	—	4	8	no	—
46	C₂×C₃×C₄	—	2	4	no	—
47	C₂×C₃×C₄	—	2	2	no	—
48	C₂×C₃×C₄	—	4	4	no	—
49	C₂×Dic₃	—	12	4	no	—
50	C₃⋊C₈	—	12	4	no	—
51	C₂×C₃²	—	2	1	no	—
52	C₂×C₃²	#329	1	1	yes	characteristic
53	C₂×Q₈	—	2	1	no	—
54	C₂×C₈	—	9	2	no	—
55	C₄⋊C₄	—	4	1	no	—
56	C₄⋊C₄	—	18	1	no	—
57	C₄⋊C₄	—	36	1	no	—
58	C₄²	C₂×#157	1	1	yes	characteristic
59	C₁₆	—	18	4	no	—
60	C₂²×C₃	—	2	2	no	—
61	C₃×C₄	—	2	4	no	—
62	C₃×C₄	—	4	4	no	—
63	C₃×C₄	—	8	4	no	—
64	Dic₃	—	24	4	no	—
65	C₃²	#1356	1	1	yes	characteristic, complemented, Sylow
66	Q₈	—	4	2	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	4	1	no	—
69	C₂×C₄	—	36	1	no	—
70	C₂×C₄	C₂²⋊#157	1	1	yes	characteristic
71	C₈	—	18	2	no	—
72	C₂×C₃	—	2	4	no	—
73	C₂×C₃	—	2	2	no	—
74	C₂²	#63788	1	1	yes	characteristic
75	C₄	—	4	1	no	—
76	C₄	—	8	1	no	—
77	C₄	—	72	1	no	—
78	C₄	#63783	1	2	yes	—
79	C₃	—	2	2	no	—
80	C₂	—	2	1	no	—
81	C₂	#10590210	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10590210
commutator	C₃²×C₄²	C₂×C₄
Frattini	C₄²	C₂×#157
Fitting	C₃²×C₄⋊Q₈	C₄
socle	C₂×C₃²	#329
prime radical	C₂²×C₃²	#100
cosocle	#63630	C₂²
hypercenter	C₄⋊Q₈	#157
hypocenter	C₃²	#1356
LCS	G ▷ C₃²×C₄² ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
65. C₃²	#1356	semidirect

Maximal subgroups

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

subgroup	index
#10592781	2
#10590149	2
#1356	9