Subgroups — #11919639

Order 1152.

263 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×Q₈	C₃	1	1	yes	maximal, characteristic
2	C₂²⋊(Q₈⋊C₉)	—	4	1	no	maximal
3	C₂×C₄²⋊C₉	—	4	1	no	maximal
4	#95⋊C₉	—	4	3	no	maximal
5	C₂×C₃×C₄×Q₈	—	3	1	no	—
6	C₃×C₄×C₄⋊C₄	—	3	3	no	—
7	C₃×C₄³	—	3	1	no	—
8	C₄²⋊C₉	—	4	1	no	—
9	C₄²×Q₈	C₉	1	1	yes	characteristic, complemented, Sylow
10	C₂²×C₃×Q₈	A₄	1	1	yes	characteristic
11	C₃×C₄×Q₈	—	3	8	no	—
12	C₂×C₃×C₄⋊C₄	—	3	3	no	—
13	C₂×C₃×C₄²	—	3	3	no	—
14	C₂×C₃×C₄²	—	3	3	no	—
15	C₂×C₃×C₄²	A₄	1	1	yes	characteristic
16	C₃×#95	—	3	1	no	—
17	C₃×#95	A₄	1	3	yes	—
18	C₂×C₂²⋊C₉	—	16	1	no	—
19	Q₈⋊C₉	—	16	4	no	—
20	C₂×C₄×Q₈	—	3	1	no	—
21	C₄×C₄⋊C₄	—	3	3	no	—
22	C₄³	—	3	1	no	—
23	C₂×C₃×Q₈	—	3	4	no	—
24	C₂²×C₃×C₄	—	3	1	no	—
25	C₂²×C₃×C₄	—	3	1	no	—
26	C₂²×C₃×C₄	—	3	3	no	—
27	C₃×C₄⋊C₄	—	3	12	no	—
28	C₃×C₄²	—	3	1	no	—
29	C₃×C₄²	—	3	12	no	—
30	C₃×C₄²	—	6	6	no	—
31	C₃×C₄²	SL(2,𝔽₃)	1	1	yes	characteristic
32	C₂²⋊C₉	—	16	1	no	—
33	C₂²×Q₈	C₂²⋊C₉	1	1	yes	characteristic
34	C₄×Q₈	—	3	8	no	—
35	C₂×C₄⋊C₄	—	3	3	no	—
36	C₂×C₄²	—	3	3	no	—
37	C₂×C₄²	—	3	3	no	—
38	C₂×C₄²	C₂²⋊C₉	1	1	yes	characteristic
39	#95	—	3	1	no	—
40	#95	C₂²⋊C₉	1	3	yes	—
41	C₂³×C₃	C₂²⋊A₄	1	1	yes	characteristic
42	C₃×Q₈	—	3	4	no	—
43	C₃×Q₈	C₄²⋊C₃	1	4	yes	—
44	C₂×C₃×C₄	—	3	2	no	—
45	C₂×C₃×C₄	—	3	6	no	—
46	C₂×C₃×C₄	—	3	2	no	—
47	C₂×C₃×C₄	—	3	1	no	—
48	C₂×C₃×C₄	—	3	1	no	—
49	C₂×C₃×C₄	—	3	6	no	—
50	C₂×C₃×C₄	—	6	6	no	—
51	C₂×C₉	—	64	1	no	—
52	C₂×Q₈	—	3	4	no	—
53	C₂²×C₄	—	3	1	no	—
54	C₂²×C₄	—	3	1	no	—
55	C₂²×C₄	—	3	3	no	—
56	C₄⋊C₄	—	3	12	no	—
57	C₄²	—	3	1	no	—
58	C₄²	—	3	12	no	—
59	C₄²	—	6	6	no	—
60	C₄²	Q₈⋊C₉	1	1	yes	characteristic, complemented
61	C₂²×C₃	—	3	1	no	—
62	C₂²×C₃	—	3	1	no	—
63	C₂²×C₃	C₂²⋊SL(2,𝔽₃)	1	1	yes	characteristic
64	C₃×C₄	—	3	2	no	—
65	C₃×C₄	—	3	2	no	—
66	C₃×C₄	—	3	4	no	—
67	C₃×C₄	—	6	6	no	—
68	C₉	—	64	1	no	Sylow
69	C₂³	C₂²⋊(C₂²⋊C₉)	1	1	yes	characteristic
70	Q₈	—	3	4	no	—
71	Q₈	C₄²⋊C₉	1	4	yes	complemented
72	C₂×C₄	—	3	2	no	—
73	C₂×C₄	—	3	6	no	—
74	C₂×C₄	—	3	2	no	—
75	C₂×C₄	—	3	1	no	—
76	C₂×C₄	—	3	1	no	—
77	C₂×C₄	—	3	6	no	—
78	C₂×C₄	—	6	6	no	—
79	C₂×C₃	—	3	1	no	—
80	C₂×C₃	—	3	1	no	—
81	C₂×C₃	C₂²⋊(C₄²⋊C₃)	1	1	yes	characteristic
82	C₂²	—	3	1	no	—
83	C₂²	—	3	1	no	—
84	C₂²	C₂²⋊(Q₈⋊C₉)	1	1	yes	characteristic
85	C₄	—	3	2	no	—
86	C₄	—	3	2	no	—
87	C₄	—	3	4	no	—
88	C₄	—	6	6	no	—
89	C₃	#73284	1	1	yes	characteristic
90	C₂	—	3	1	no	—
91	C₂	—	3	1	no	—
92	C₂	C₂²⋊(C₄²⋊C₉)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	C₂²⋊(C₄²⋊C₃)
commutator, hypocenter	C₄²×Q₈	C₉
Frattini, socle, prime radical	C₂³×C₃	C₂²⋊A₄
Fitting, cosocle	C₃×C₄²×Q₈	C₃
LCS	G ▷ C₄²×Q₈
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
9. C₄²×Q₈	C₉	semidirect
60. C₄²	Q₈⋊C₉	semidirect
71. Q₈	C₄²⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄²×Q₈	3
C₂²⋊(Q₈⋊C₉)	4
C₂×C₄²⋊C₉	4
#95⋊C₉	4