Subgroups — C₄⋊#63540 #11773011

Order 1152.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63540	C₂	1	2	yes	maximal
2	C₄×C₃⋊(C₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₃²×C₄×C₈	C₄	1	1	yes	characteristic
4	C₂×C₃⋊(C₃⋊C₁₆)	C₄	1	1	yes	characteristic
5	C₂×C₃⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic
6	#63540	—	2	2	no	—
7	C₄×C₃⋊C₁₆	—	6	2	no	—
8	C₂×C₃²×C₈	C₈	1	1	yes	characteristic
9	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
10	C₃²×C₄²	C₈	1	1	yes	characteristic
11	C₃⋊(C₃⋊C₁₆)	—	2	1	no	—
12	C₃⋊(C₃⋊C₁₆)	D₄	1	1	yes	characteristic
13	C₃⋊(C₃⋊C₁₆)	Q₈	1	1	yes	characteristic
14	C₄⋊C₃₂	—	9	1	no	maximal, Sylow
15	C₃×C₄×C₈	—	2	2	no	—
16	C₂×C₃⋊C₁₆	—	6	2	no	—
17	C₂×C₃⋊C₁₆	—	6	2	no	—
18	C₂×C₃²×C₄	C₁₆	1	1	yes	characteristic
19	C₂×C₃²×C₄	C₁₆	1	1	yes	characteristic
20	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
21	C₃²×C₈	—	2	1	no	—
22	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
23	C₃²×C₈	M₁₆	1	1	yes	characteristic
24	C₂×C₃₂	—	9	2	no	—
25	C₄×C₁₆	—	9	1	no	—
26	C₂×C₃×C₈	—	2	2	no	—
27	C₂×C₃×C₈	—	2	2	no	—
28	C₃×C₄²	—	2	2	no	—
29	C₃⋊C₁₆	—	6	2	no	—
30	C₃⋊C₁₆	—	6	2	no	—
31	C₃⋊C₁₆	—	6	4	no	—
32	C₂²×C₃²	C₂×C₁₆	1	1	yes	characteristic
33	C₃²×C₄	—	2	1	no	—
34	C₃²×C₄	C₃₂	1	2	yes	complemented
35	C₃²×C₄	C₄⋊C₈	1	1	yes	characteristic
36	C₃²×C₄	M₃₂	1	1	yes	characteristic
37	C₂×C₁₆	—	9	1	no	—
38	C₂×C₁₆	—	9	1	no	—
39	C₄×C₈	#157	1	1	yes	characteristic
40	C₃₂	—	18	2	no	—
41	C₂×C₃×C₄	—	2	2	no	—
42	C₂×C₃×C₄	—	2	2	no	—
43	C₂×C₃×C₄	—	2	2	no	—
44	C₃×C₈	—	2	4	no	—
45	C₃×C₈	—	2	2	no	—
46	C₃×C₈	—	2	2	no	—
47	C₂×C₃²	C₄⋊C₁₆	1	1	yes	characteristic
48	C₂×C₃²	C₂×C₃₂	1	1	yes	characteristic
49	C₂×C₃²	M₆₄	1	1	yes	characteristic
50	C₂×C₈	#622	1	1	yes	characteristic
51	C₂×C₈	C₂×#157	1	1	yes	characteristic
52	C₄²	#622	1	1	yes	characteristic
53	C₁₆	—	9	1	no	—
54	C₁₆	—	9	1	no	—
55	C₁₆	—	18	1	no	—
56	C₂²×C₃	—	2	2	no	—
57	C₃×C₄	—	2	4	no	—
58	C₃×C₄	—	2	2	no	—
59	C₃×C₄	—	2	2	no	—
60	C₃×C₄	—	2	4	no	—
61	C₃²	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₄	#3708	1	1	yes	characteristic
63	C₂×C₄	#3708	1	1	yes	characteristic
64	C₂×C₄	C₂×#622	1	1	yes	characteristic
65	C₈	—	2	1	no	—
66	C₈	#3788	1	1	yes	characteristic
67	C₈	C₄⋊#157	1	1	yes	characteristic
68	C₂×C₃	—	2	2	no	—
69	C₂×C₃	—	2	2	no	—
70	C₂×C₃	—	2	2	no	—
71	C₂²	C₂×#3708	1	1	yes	characteristic
72	C₄	—	2	1	no	—
73	C₄	#63540	1	2	yes	complemented
74	C₄	#63773	1	1	yes	characteristic
75	C₄	C₄⋊#622	1	1	yes	characteristic
76	C₃	—	2	2	no	—
77	C₂	C₄⋊#3708	1	1	yes	characteristic
78	C₂	C₂×#63540	1	1	yes	characteristic
79	C₂	#10590166	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#157
commutator	C₂×C₃²	C₂×C₃₂
Fitting	C₃²×C₄×C₈	C₄
socle, prime radical	C₂²×C₃²	C₂×C₁₆
cosocle	C₂×C₃⋊(C₃⋊C₁₆)	C₂²
hypercenter	C₄×C₈	#157
hypocenter	C₃²	C₄⋊C₃₂
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
34. C₃²×C₄	C₃₂	semidirect
61. C₃²	C₄⋊C₃₂	semidirect
73. C₄	#63540	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63540	2
C₄×C₃⋊(C₃⋊C₁₆)	2
C₄⋊C₃₂	9

Subgroups — C4⋊#63540 #11773011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊#63540 #11773011