Subgroups — #11772998

Order 1152.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	#10590141	C₂	1	1	yes	maximal, characteristic
3	#10590133	C₂	1	1	yes	maximal, characteristic
4	Q₁₆×C₃⋊D₃	—	2	1	no	—
5	#63771	—	2	1	no	—
6	C₃²×Q₃₂	C₄	1	1	yes	characteristic
7	#63656	—	2	1	no	—
8	#63628	C₄	1	1	yes	characteristic
9	C₁₆×C₃⋊D₃	C₂²	1	1	yes	characteristic
10	#63540	—	2	1	no	—
11	D₃×Q₃₂	—	6	2	no	—
12	Q₈×C₃⋊D₃	—	4	1	no	—
13	#3788	—	4	1	no	—
14	C₃²×Q₁₆	—	2	1	no	—
15	#3756	—	4	1	no	—
16	#3746	—	2	1	no	—
17	C₈×C₃⋊D₃	D₄	1	1	yes	characteristic
18	C₃²×C₁₆	C₂×C₄	1	1	yes	characteristic
19	C₃⋊(C₃⋊C₁₆)	D₄	1	1	yes	characteristic
20	#1420	—	9	1	no	maximal, Sylow
21	D₃×Q₁₆	—	6	4	no	—
22	C₃×Q₃₂	—	2	2	no	—
23	#829	—	6	4	no	—
24	Dic₂₄	—	6	2	no	—
25	D₃×C₁₆	—	6	2	no	—
26	C₃²×Q₈	—	4	1	no	—
27	C₄×C₃⋊D₃	—	8	1	no	—
28	C₄×C₃⋊D₃	D₈	1	1	yes	characteristic
29	#634	—	4	1	no	—
30	#634	—	8	1	no	—
31	#622	—	8	1	no	—
32	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
33	C₃⋊(C₃⋊C₈)	SD₁₆	1	1	yes	characteristic
34	C₂×Q₃₂	—	9	1	no	—
35	M₆₄	—	9	1	no	—
36	#368	—	9	1	no	—
37	D₃×Q₈	—	12	4	no	—
38	C₃×Q₁₆	—	2	4	no	—
39	#216	—	12	4	no	—
40	Dic₁₂	—	6	4	no	—
41	D₃×C₈	—	6	2	no	—
42	C₃×C₁₆	—	2	2	no	—
43	C₃⋊C₁₆	—	6	2	no	—
44	C₂×C₃⋊D₃	SD₃₂	1	1	yes	characteristic
45	C₃²×C₄	—	8	1	no	—
46	C₃²×C₄	#102	1	1	yes	characteristic
47	C₃⋊Dic₃	—	8	1	no	—
48	C₃⋊Dic₃	D₁₆	1	1	yes	characteristic
49	C₂×Q₁₆	—	18	1	no	—
50	Q₃₂	—	9	1	no	—
51	Q₃₂	—	18	1	no	—
52	Q₃₂	#157	1	1	yes	characteristic
53	C₂×C₁₆	—	9	1	no	—
54	#108	—	18	1	no	—
55	C₃₂	—	18	1	no	—
56	C₃×Q₈	—	4	4	no	—
57	C₄×D₃	—	6	2	no	—
58	C₄×D₃	—	24	4	no	—
59	Dic₆	—	12	4	no	—
60	Dic₆	—	24	4	no	—
61	C₃×C₈	—	2	2	no	—
62	C₃⋊C₈	—	6	2	no	—
63	C₂×C₃²	#357	1	1	yes	characteristic
64	C₃⋊D₃	—	2	1	no	—
65	C₂×Q₈	—	36	1	no	—
66	Q₁₆	—	2	1	no	—
67	Q₁₆	—	18	1	no	—
68	Q₁₆	—	36	1	no	—
69	M₁₆	—	36	1	no	—
70	C₂×C₈	—	9	1	no	—
71	C₁₆	—	9	1	no	—
72	C₁₆	C₂×#157	1	1	yes	characteristic
73	C₂×D₃	—	6	2	no	—
74	C₃×C₄	—	2	2	no	—
75	C₃×C₄	—	8	4	no	—
76	Dic₃	—	6	2	no	—
77	Dic₃	—	24	4	no	—
78	C₃²	#1420	1	1	yes	characteristic, complemented, Sylow
79	Q₈	—	4	1	no	—
80	Q₈	—	36	1	no	—
81	Q₈	—	72	1	no	—
82	C₂×C₄	—	9	1	no	—
83	C₂×C₄	—	72	1	no	—
84	C₈	—	9	1	no	—
85	C₈	—	72	1	no	—
86	C₈	C₂²⋊#157	1	1	yes	characteristic
87	C₂×C₃	—	2	2	no	—
88	D₃	—	6	4	no	—
89	C₂²	—	9	1	no	—
90	C₄	—	8	1	no	—
91	C₄	—	9	1	no	—
92	C₄	—	72	1	no	—
93	C₄	#63782	1	1	yes	characteristic
94	C₃	—	2	2	no	—
95	C₂	—	18	1	no	—
96	C₂	#10590193	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10590193
commutator	C₃²×C₁₆	C₂×C₄
Frattini	C₁₆	C₂×#157
Fitting	C₃²×Q₃₂	C₄
socle	C₂×C₃²	#357
prime radical	C₂×C₃⋊D₃	SD₃₂
cosocle	C₁₆×C₃⋊D₃	C₂²
hypercenter	Q₃₂	#157
hypocenter	C₃²	#1420
LCS	G ▷ C₃²×C₁₆ ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
78. C₃²	#1420	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₃×Q₃₂	2
#10590141	2
#10590133	2
#1420	9