Subgroups — #395⋊C₉ #10588317

Order 576.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊(Q₈⋊C₉)	C₂	1	1	yes	maximal, characteristic
2	C₃×#395	C₃	1	1	yes	maximal, characteristic
3	C₄×C₂²⋊C₉	—	4	1	no	maximal
4	C₂²×C₃×Q₈	C₂×C₃	1	1	yes	characteristic
5	C₂×C₃×C₄⋊C₄	—	3	1	no	—
6	C₃×#95	—	3	1	no	—
7	C₂×C₂²⋊C₉	—	4	1	no	—
8	Q₈⋊C₉	—	8	2	no	—
9	#395	C₉	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₃×Q₈	—	6	2	no	—
11	C₂²×C₃×C₄	—	3	1	no	—
12	C₂²×C₃×C₄	—	3	1	no	—
13	C₂²×C₃×C₄	A₄	1	1	yes	characteristic
14	C₃×C₄⋊C₄	—	6	2	no	—
15	C₂²⋊C₉	—	4	1	no	—
16	C₄×C₉	—	16	1	no	—
17	C₂²×Q₈	C₂×C₉	1	1	yes	characteristic
18	C₂×C₄⋊C₄	—	3	1	no	—
19	#95	—	3	1	no	—
20	C₂³×C₃	C₂×A₄	1	1	yes	characteristic
21	C₃×Q₈	—	2	2	no	—
22	C₃×Q₈	—	6	2	no	—
23	C₂×C₃×C₄	—	3	2	no	—
24	C₂×C₃×C₄	—	3	2	no	—
25	C₂×C₃×C₄	—	6	1	no	—
26	C₂×C₃×C₄	—	6	1	no	—
27	C₂×C₃×C₄	—	6	2	no	—
28	C₂×C₃×C₄	—	6	1	no	—
29	C₂×C₉	—	16	1	no	—
30	C₂×Q₈	—	6	2	no	—
31	C₂²×C₄	—	3	1	no	—
32	C₂²×C₄	—	3	1	no	—
33	C₂²×C₄	C₂²⋊C₉	1	1	yes	characteristic
34	C₄⋊C₄	—	6	2	no	—
35	C₂²×C₃	—	3	1	no	—
36	C₂²×C₃	—	3	1	no	—
37	C₂²×C₃	#41⋊C₃	1	1	yes	characteristic
38	C₃×C₄	—	4	1	no	—
39	C₃×C₄	—	6	2	no	—
40	C₃×C₄	—	6	2	no	—
41	C₉	—	16	1	no	Sylow
42	C₂³	C₂×C₂²⋊C₉	1	1	yes	characteristic
43	Q₈	—	2	2	no	—
44	Q₈	—	6	2	no	—
45	C₂×C₄	—	3	2	no	—
46	C₂×C₄	—	3	2	no	—
47	C₂×C₄	—	6	1	no	—
48	C₂×C₄	—	6	1	no	—
49	C₂×C₄	—	6	2	no	—
50	C₂×C₄	—	6	1	no	—
51	C₂×C₃	—	3	1	no	—
52	C₂×C₃	—	3	1	no	—
53	C₂×C₃	#120⋊C₃	1	1	yes	characteristic
54	C₂²	—	3	1	no	—
55	C₂²	—	3	1	no	—
56	C₂²	#41⋊C₉	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	6	2	no	—
59	C₄	—	6	2	no	—
60	C₃	#395⋊C₃	1	1	yes	characteristic
61	C₂	—	3	1	no	—
62	C₂	—	3	1	no	—
63	C₂	#120⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	#120⋊C₃
commutator, hypocenter	C₂²×Q₈	C₂×C₉
Frattini, socle, prime radical	C₂³×C₃	C₂×A₄
Fitting	C₃×#395	C₃
cosocle	C₂²×C₃×Q₈	C₂×C₃
LCS	G ▷ C₂²×Q₈
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
9. #395	C₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²⋊(Q₈⋊C₉)	2
C₃×#395	3
C₄×C₂²⋊C₉	4

Subgroups — #395⋊C9 #10588317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #395⋊C₉ #10588317