Subgroups — #11772210

Order 1152.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#3708	C₂	1	2	yes	maximal
2	C₈×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×#3708	—	2	2	no	—
4	C₃²×C₄×C₈	C₄	1	1	yes	characteristic
5	C₄×C₃⋊(C₃⋊C₈)	C₄	1	1	yes	characteristic
6	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
7	C₈×C₃⋊C₈	—	6	2	no	—
8	C₂×C₃²×C₈	—	2	1	no	—
9	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
10	C₂×C₃⋊(C₃⋊C₈)	C₈	1	1	yes	characteristic
11	C₂×C₃⋊(C₃⋊C₈)	C₈	1	1	yes	characteristic
12	C₂×C₃⋊(C₃⋊C₈)	D₄	1	1	yes	characteristic
13	C₂×C₃⋊(C₃⋊C₈)	Q₈	1	1	yes	characteristic
14	#3708	—	4	2	no	—
15	#1370	—	9	1	no	maximal, Sylow
16	C₃×C₄×C₈	—	2	2	no	—
17	C₄×C₃⋊C₈	—	6	2	no	—
18	C₄×C₃⋊C₈	—	6	2	no	—
19	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
20	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
21	C₂×C₃²×C₄	M₁₆	1	1	yes	characteristic
22	C₃²×C₈	—	2	2	no	—
23	C₃⋊(C₃⋊C₈)	—	2	1	no	—
24	C₃⋊(C₃⋊C₈)	—	2	1	no	—
25	C₃⋊(C₃⋊C₈)	C₁₆	1	2	yes	complemented
26	C₃⋊(C₃⋊C₈)	D₈	1	1	yes	characteristic
27	C₃⋊(C₃⋊C₈)	Q₁₆	1	1	yes	characteristic
28	C₄⋊C₁₆	—	9	2	no	—
29	C₈²	—	9	1	no	—
30	C₂×C₃×C₈	—	2	4	no	—
31	C₃×C₄²	—	2	2	no	—
32	C₂×C₃⋊C₈	—	6	2	no	—
33	C₂×C₃⋊C₈	—	6	2	no	—
34	C₂×C₃⋊C₈	—	6	2	no	—
35	C₂×C₃⋊C₈	—	6	2	no	—
36	C₂²×C₃²	C₄⋊C₈	1	1	yes	characteristic
37	C₃²×C₄	—	2	1	no	—
38	C₃²×C₄	#107	1	1	yes	characteristic
39	C₃²×C₄	#108	1	1	yes	characteristic
40	C₃²×C₄	C₂×C₁₆	1	1	yes	characteristic
41	C₃²×C₄	M₃₂	1	1	yes	characteristic
42	C₂×C₁₆	—	18	2	no	—
43	C₄×C₈	—	9	1	no	—
44	C₄×C₈	—	9	1	no	—
45	C₄×C₈	#157	1	1	yes	characteristic
46	C₂×C₃×C₄	—	2	2	no	—
47	C₂×C₃×C₄	—	2	2	no	—
48	C₂×C₃×C₄	—	2	2	no	—
49	C₃×C₈	—	2	8	no	—
50	C₃⋊C₈	—	6	4	no	—
51	C₃⋊C₈	—	6	2	no	—
52	C₃⋊C₈	—	6	2	no	—
53	C₃⋊C₈	—	6	4	no	—
54	C₃⋊C₈	—	6	4	no	—
55	C₂×C₃²	#335	1	1	yes	characteristic
56	C₂×C₃²	C₄⋊C₁₆	1	1	yes	characteristic
57	C₂×C₃²	#364	1	1	yes	characteristic
58	C₂×C₈	—	2	1	no	—
59	C₂×C₈	—	9	1	no	—
60	C₂×C₈	—	9	1	no	—
61	C₂×C₈	—	9	1	no	—
62	C₂×C₈	—	9	1	no	—
63	C₄²	C₂×#157	1	1	yes	characteristic
64	C₁₆	—	36	2	no	—
65	C₂²×C₃	—	2	2	no	—
66	C₃×C₄	—	2	4	no	—
67	C₃×C₄	—	2	2	no	—
68	C₃×C₄	—	2	2	no	—
69	C₃×C₄	—	2	2	no	—
70	C₃×C₄	—	2	2	no	—
71	C₃²	#1370	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₄	#3787	1	1	yes	characteristic
73	C₂×C₄	C₄⋊#157	1	1	yes	characteristic
74	C₂×C₄	#3792	1	1	yes	characteristic
75	C₈	—	2	2	no	—
76	C₈	—	9	2	no	—
77	C₈	—	9	1	no	—
78	C₈	—	9	1	no	—
79	C₈	—	18	1	no	—
80	C₈	—	18	1	no	—
81	C₂×C₃	—	2	2	no	—
82	C₂×C₃	—	2	2	no	—
83	C₂×C₃	—	2	2	no	—
84	C₂²	#63779	1	1	yes	characteristic
85	C₄	—	2	1	no	—
86	C₄	#63764	1	1	yes	characteristic
87	C₄	#63765	1	1	yes	characteristic
88	C₄	#63769	1	1	yes	characteristic
89	C₄	#63770	1	1	yes	characteristic
90	C₃	—	2	2	no	—
91	C₂	#10590150	1	1	yes	characteristic
92	C₂	#10590173	1	1	yes	characteristic
93	C₂	#10590177	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄⋊#157
commutator	C₃²×C₄	C₂×C₁₆
Frattini	C₄²	C₂×#157
Fitting	C₃²×C₄×C₈	C₄
socle, prime radical	C₂²×C₃²	C₄⋊C₈
cosocle	C₄×C₃⋊(C₃⋊C₈)	C₂²
hypercenter	C₄×C₈	#157
hypocenter	C₃²	#1370
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
25. C₃⋊(C₃⋊C₈)	C₁₆	semidirect
71. C₃²	#1370	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#3708	2
C₈×C₃⋊(C₃⋊C₈)	2
#1370	9