Subgroups — #11857046

Order 1152.

1254 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄³	C₂	1	1	yes	maximal, characteristic, complemented
2	#10592639	C₂	1	7	yes	maximal
3	#10592632	C₂	1	7	yes	maximal, complemented
4	#73317	—	3	4	no	maximal
5	C₂×C₃²×C₄²	C₂²	1	7	yes	—
6	C₂×#3752	C₂²	1	7	yes	—
7	C₂×#3750	C₂²	1	7	yes	—
8	#63658	C₂²	1	14	yes	—
9	C₃×C₄³	D₃	1	4	yes	complemented
10	#4940	—	3	28	no	—
11	#4933	—	3	28	no	—
12	C₂³×C₃⋊D₃	C₂³	1	1	yes	characteristic
13	C₂²×C₃²×C₄	C₂³	1	7	yes	—
14	C₂²×C₃⋊Dic₃	C₂³	1	7	yes	—
15	C₃²×C₄²	—	2	14	no	—
16	#3752	—	2	14	no	—
17	#3750	—	2	14	no	—
18	#2866	—	9	1	no	Sylow
19	C₂×C₃×C₄²	C₂×D₃	1	28	yes	—
20	C₂×(C₂×D₃)⋊C₄	—	3	28	no	—
21	C₂×Dic₃⋊C₄	—	3	28	no	—
22	C₃⋊#95	—	3	56	no	—
23	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
24	C₂²×C₃⋊D₃	—	2	7	no	—
25	C₂×C₃²×C₄	—	2	14	no	—
26	C₂×C₃²×C₄	#41	1	14	yes	—
27	C₂×C₃⋊Dic₃	—	2	14	no	—
28	C₂×C₃⋊Dic₃	—	2	7	no	—
29	#388	—	9	7	no	—
30	#387	—	9	7	no	—
31	C₄³	C₃⋊D₃	1	1	yes	characteristic, complemented
32	C₂³×D₃	—	3	4	no	—
33	C₂²×C₃×C₄	C₂²×D₃	1	28	yes	—
34	C₂²×Dic₃	—	3	28	no	—
35	C₃×C₄²	—	2	56	no	—
36	(C₂×D₃)⋊C₄	—	6	56	no	—
37	Dic₃⋊C₄	—	6	56	no	—
38	C₂²×C₃²	C₂×#41	1	7	yes	—
39	C₂×C₃⋊D₃	—	4	7	no	—
40	C₃²×C₄	—	2	14	no	—
41	C₃⋊Dic₃	—	4	7	no	—
42	C₂×C₄⋊C₄	—	9	7	no	—
43	C₂×C₂²⋊C₄	—	9	7	no	—
44	C₂×C₄²	C₂×C₃⋊D₃	1	7	yes	—
45	#95	—	9	14	no	—
46	C₂³×C₃	C₂³×D₃	1	4	yes	—
47	C₂²×D₃	—	6	28	no	—
48	C₂×C₃×C₄	—	2	56	no	—
49	C₂×C₃×C₄	#235	1	56	yes	—
50	C₂×Dic₃	—	6	56	no	—
51	C₂×Dic₃	—	6	28	no	—
52	C₂×C₃²	#529	1	7	yes	—
53	C₃⋊D₃	—	8	1	no	—
54	C₂⁴	—	9	1	no	—
55	C₂²×C₄	—	9	7	no	—
56	C₂²×C₄	C₂²×C₃⋊D₃	1	7	yes	—
57	C₄⋊C₄	—	18	14	no	—
58	C₂²⋊C₄	—	18	14	no	—
59	C₄²	—	2	14	no	—
60	C₂²×C₃	C₂×#235	1	28	yes	—
61	C₂×D₃	—	12	28	no	—
62	C₃×C₄	—	2	56	no	—
63	Dic₃	—	12	28	no	—
64	C₃²	#2866	1	1	yes	characteristic, complemented, Sylow
65	C₂³	—	18	7	no	—
66	C₂³	C₂³×C₃⋊D₃	1	1	yes	characteristic
67	C₂×C₄	—	2	14	no	—
68	C₂×C₄	—	18	7	no	—
69	C₂×C₄	—	18	14	no	—
70	C₂×C₄	#3828	1	14	yes	—
71	C₂×C₃	#5479	1	28	yes	—
72	D₃	—	24	4	no	—
73	C₂²	—	36	7	no	—
74	C₂²	C₂×#3828	1	7	yes	—
75	C₄	—	2	14	no	—
76	C₄	—	36	7	no	—
77	C₃	#73317	1	4	yes	complemented
78	C₂	—	72	1	no	—
79	C₂	#10595950	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×C₃⋊D₃
commutator, socle, cosocle	C₂³×C₃²	C₂⁴
Fitting	C₃²×C₄³	C₂
prime radical	C₂³×C₃⋊D₃	C₂³
hypercenter	C₄³	C₃⋊D₃
hypocenter	C₃²	#2866
LCS	G ▷ C₂³×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
1. C₃²×C₄³	C₂	semidirect
3. #10592632	C₂	semidirect
9. C₃×C₄³	D₃	semidirect
31. C₄³	C₃⋊D₃	semidirect
64. C₃²	#2866	semidirect
77. C₃	#73317	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₄³	2
#10592639	2
#10592632	2
#73317	3