Subgroups — #11772704

Order 1152.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63639	C₂	1	1	yes	maximal, characteristic
2	#10590166	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃²×C₈	C₄	1	1	yes	characteristic
4	#63639	—	2	2	no	—
5	C₂×C₃⋊(C₃⋊C₁₆)	C₄	1	1	yes	characteristic
6	C₂×C₃⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic
7	#63540	—	2	2	no	—
8	C₂×#812	—	6	2	no	—
9	C₂²×C₃²×C₄	C₈	1	1	yes	characteristic
10	C₂×C₃²×C₈	—	2	1	no	—
11	C₂×C₃²×C₈	—	2	1	no	—
12	C₂×C₃²×C₈	C₈	1	1	yes	characteristic
13	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
14	C₃⋊(C₃⋊C₁₆)	—	2	1	no	—
15	C₃⋊(C₃⋊C₁₆)	D₄	1	2	yes	—
16	#1400	—	9	1	no	maximal, Sylow
17	C₂²×C₃×C₈	—	2	2	no	—
18	#812	—	6	8	no	—
19	C₂×C₃⋊C₁₆	—	6	2	no	—
20	C₂×C₃⋊C₁₆	—	6	2	no	—
21	C₂³×C₃²	C₁₆	1	1	yes	characteristic
22	C₂×C₃²×C₄	—	2	1	no	—
23	C₂×C₃²×C₄	—	2	1	no	—
24	C₂×C₃²×C₄	C₁₆	1	1	yes	characteristic
25	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
26	C₃²×C₈	—	2	1	no	—
27	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
28	C₃²×C₈	M₁₆	1	1	yes	characteristic
29	C₂×M₃₂	—	9	1	no	—
30	M₆₄	—	9	2	no	—
31	C₂²×C₃×C₄	—	2	2	no	—
32	C₂×C₃×C₈	—	2	4	no	—
33	C₂×C₃×C₈	—	2	4	no	—
34	C₂×C₃×C₈	—	2	2	no	—
35	C₂×C₃×C₈	—	2	2	no	—
36	C₃⋊C₁₆	—	6	4	no	—
37	C₃⋊C₁₆	—	6	4	no	—
38	C₂²×C₃²	—	2	1	no	—
39	C₂²×C₃²	—	4	1	no	—
40	C₂²×C₃²	C₂×C₁₆	1	1	yes	characteristic
41	C₃²×C₄	—	2	1	no	—
42	C₃²×C₄	C₂²⋊C₈	1	1	yes	characteristic
43	C₃²×C₄	M₃₂	1	1	yes	characteristic
44	C₂²×C₈	#157	1	1	yes	characteristic
45	M₃₂	—	18	2	no	—
46	C₂×C₁₆	—	9	1	no	—
47	C₂×C₁₆	—	9	1	no	—
48	C₃₂	—	18	2	no	—
49	C₂³×C₃	—	2	2	no	—
50	C₂×C₃×C₄	—	2	4	no	—
51	C₂×C₃×C₄	—	2	4	no	—
52	C₂×C₃×C₄	—	2	2	no	—
53	C₂×C₃×C₄	—	2	2	no	—
54	C₃×C₈	—	2	4	no	—
55	C₃×C₈	—	2	2	no	—
56	C₃×C₈	—	2	2	no	—
57	C₂×C₃²	—	2	1	no	—
58	C₂×C₃²	—	4	1	no	—
59	C₂×C₃²	C₂²⋊C₁₆	1	1	yes	characteristic
60	C₂²×C₄	#622	1	1	yes	characteristic
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	—	2	1	no	—
63	C₂×C₈	#622	1	1	yes	characteristic
64	C₂×C₈	C₂×#157	1	1	yes	characteristic
65	C₁₆	—	9	2	no	—
66	C₁₆	—	18	1	no	—
67	C₂²×C₃	—	2	4	no	—
68	C₂²×C₃	—	2	2	no	—
69	C₂²×C₃	—	4	4	no	—
70	C₃×C₄	—	2	4	no	—
71	C₃×C₄	—	2	2	no	—
72	C₃×C₄	—	2	2	no	—
73	C₃²	#1400	1	1	yes	characteristic, complemented, Sylow
74	C₂³	#3708	1	1	yes	characteristic
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	#3708	1	1	yes	characteristic
78	C₂×C₄	C₂×#622	1	1	yes	characteristic
79	C₈	—	2	1	no	—
80	C₈	#3792	1	1	yes	characteristic
81	C₈	C₂²⋊#157	1	1	yes	characteristic
82	C₂×C₃	—	2	4	no	—
83	C₂×C₃	—	2	2	no	—
84	C₂×C₃	—	4	4	no	—
85	C₂²	—	2	1	no	—
86	C₂²	—	4	1	no	—
87	C₂²	C₂×#3708	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	#63773	1	1	yes	characteristic
90	C₄	C₂²⋊#622	1	1	yes	characteristic
91	C₃	—	2	2	no	—
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	C₂²⋊#3708	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#157
commutator	C₂²×C₃²	C₂×C₁₆
Frattini	C₂×C₈	C₂×#157
Fitting	C₂²×C₃²×C₈	C₄
socle	C₂×C₃²	C₂²⋊C₁₆
prime radical	C₂³×C₃²	C₁₆
cosocle	C₂×C₃⋊(C₃⋊C₁₆)	C₂²
hypercenter	C₂²×C₈	#157
hypocenter	C₃²	#1400
LCS	G ▷ C₂²×C₃² ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #10590166	C₂	semidirect
73. C₃²	#1400	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63639	2
#10590166	2
#1400	9