Subgroups — #11783038

Order 1152.

984 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#376	C₂	1	1	yes	maximal, characteristic
2	C₂×#63630	C₂	1	3	yes	maximal
3	C₂×C₄×C₃⋊(C₃⋊C₈)	C₂	1	3	yes	maximal
4	#69434	—	3	4	no	maximal
5	C₂×C₃²×C₄²	C₂²	1	3	yes	—
6	C₂²×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
7	C₂²×C₃⋊(C₃⋊C₈)	C₂²	1	3	yes	—
8	C₃²×#95	C₄	1	4	yes	—
9	#63630	C₄	1	12	yes	complemented
10	C₄×C₃⋊(C₃⋊C₈)	C₄	1	12	yes	complemented
11	C₃×#376	D₃	1	4	yes	—
12	C₂×#803	—	3	12	no	—
13	C₂×C₄×C₃⋊C₈	—	3	12	no	—
14	C₂²×C₃²×C₄	C₂×C₄	1	6	yes	—
15	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
16	C₃²×C₄²	C₂×C₄	1	6	yes	—
17	C₃²×C₄²	C₂×C₄	1	6	yes	—
18	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	6	yes	—
19	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	6	yes	—
20	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	12	yes	—
21	#1726	—	9	1	no	Sylow
22	C₂×C₃×C₄²	C₂×D₃	1	12	yes	—
23	C₂²×C₃⋊C₈	—	3	4	no	—
24	C₂²×C₃⋊C₈	—	3	12	no	—
25	C₃×#95	Dic₃	1	16	yes	—
26	#803	—	3	48	no	—
27	C₄×C₃⋊C₈	—	3	48	no	—
28	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₃²×C₄	—	2	12	no	—
30	C₂×C₃²×C₄	C₄²	1	12	yes	—
31	C₂×C₃²×C₄	C₂²×C₄	1	3	yes	—
32	C₂×C₃²×C₄	C₂²×C₄	1	3	yes	—
33	C₃⋊(C₃⋊C₈)	C₄²	1	4	yes	—
34	C₃⋊(C₃⋊C₈)	C₄²	1	12	yes	—
35	C₂×#97	—	9	3	no	—
36	C₂×C₄×C₈	—	9	3	no	—
37	#376	C₃⋊D₃	1	1	yes	characteristic
38	C₂²×C₃×C₄	C₂×Dic₃	1	24	yes	—
39	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
40	C₃×C₄²	C₄×D₃	1	24	yes	—
41	C₃×C₄²	C₄×D₃	1	24	yes	—
42	C₂×C₃⋊C₈	—	3	24	no	—
43	C₂×C₃⋊C₈	—	3	24	no	—
44	C₂×C₃⋊C₈	—	3	48	no	—
45	C₂²×C₃²	C₂×C₄²	1	3	yes	—
46	C₂²×C₃²	#131	1	4	yes	—
47	C₃²×C₄	—	2	12	no	—
48	C₃²×C₄	C₂×C₄²	1	1	yes	characteristic
49	C₃²×C₄	C₂×C₄²	1	3	yes	—
50	C₂²×C₈	—	9	1	no	—
51	C₂²×C₈	—	9	3	no	—
52	C₂×C₄²	C₂×C₃⋊D₃	1	3	yes	—
53	#97	—	9	12	no	—
54	C₄×C₈	—	9	12	no	—
55	#95	C₃⋊Dic₃	1	4	yes	—
56	C₂³×C₃	C₂²×Dic₃	1	4	yes	—
57	C₂×C₃×C₄	—	2	48	no	—
58	C₂×C₃×C₄	C₄×Dic₃	1	48	yes	—
59	C₂×C₃×C₄	C₂×C₄×D₃	1	12	yes	—
60	C₂×C₃×C₄	C₂×C₄×D₃	1	12	yes	—
61	C₃⋊C₈	—	3	16	no	—
62	C₃⋊C₈	—	3	48	no	—
63	C₂×C₃²	C₄³	1	1	yes	characteristic
64	C₂×C₃²	#405	1	6	yes	—
65	C₂²×C₄	C₂×C₃⋊Dic₃	1	6	yes	—
66	C₂²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
67	C₂×C₈	—	9	6	no	—
68	C₂×C₈	—	9	6	no	—
69	C₂×C₈	—	9	12	no	—
70	C₄²	C₄×C₃⋊D₃	1	6	yes	—
71	C₄²	C₄×C₃⋊D₃	1	6	yes	—
72	C₂²×C₃	C₂×C₄×Dic₃	1	12	yes	—
73	C₂²×C₃	#948	1	16	yes	—
74	C₃×C₄	—	2	48	no	—
75	C₃×C₄	C₄²×D₃	1	4	yes	—
76	C₃×C₄	C₄²×D₃	1	12	yes	—
77	C₃²	#1726	1	1	yes	characteristic, complemented, Sylow
78	C₂³	C₂²×C₃⋊Dic₃	1	1	yes	characteristic
79	C₂×C₄	—	2	12	no	—
80	C₂×C₄	C₄×C₃⋊Dic₃	1	12	yes	—
81	C₂×C₄	C₂×C₄×C₃⋊D₃	1	3	yes	—
82	C₂×C₄	C₂×C₄×C₃⋊D₃	1	3	yes	—
83	C₈	—	9	4	no	—
84	C₈	—	9	12	no	—
85	C₂×C₃	C₄²×Dic₃	1	4	yes	—
86	C₂×C₃	#4997	1	24	yes	—
87	C₂²	C₂×C₄×C₃⋊Dic₃	1	3	yes	—
88	C₂²	#64157	1	4	yes	—
89	C₄	—	2	12	no	—
90	C₄	C₄²×C₃⋊D₃	1	1	yes	characteristic
91	C₄	C₄²×C₃⋊D₃	1	3	yes	—
92	C₃	#69434	1	4	yes	complemented
93	C₂	C₄²×C₃⋊Dic₃	1	1	yes	characteristic
94	C₂	#10592696	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×C₃⋊D₃
commutator	C₂×C₃²	C₄³
Fitting	C₃²×#376	C₂
socle, prime radical	C₂³×C₃²	C₂²×C₄
cosocle	C₂²×C₃²×C₄	C₂³
hypercenter	#376	C₃⋊D₃
hypocenter	C₃²	#1726
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
9. #63630	C₄	semidirect
10. C₄×C₃⋊(C₃⋊C₈)	C₄	semidirect
77. C₃²	#1726	semidirect
92. C₃	#69434	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#376	2
C₂×#63630	2
C₂×C₄×C₃⋊(C₃⋊C₈)	2
#69434	3