Subgroups — C₂×#63386 #10588828

Order 576.

135 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×D₈	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#63386	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#827	—	3	1	no	maximal
6	C₂×D₄×C₉	—	2	1	no	—
7	C₂×Dic₁₈	—	2	1	no	—
8	C₉×D₈	—	2	1	no	—
9	C₉×D₈	C₂²	1	2	yes	—
10	C₂×C₈×C₉	C₂²	1	1	yes	characteristic
11	Dic₃₆	—	2	1	no	—
12	Dic₃₆	C₂²	1	2	yes	complemented
13	C₉⋊C₁₆	C₂²	1	2	yes	complemented
14	C₂×C₃×D₈	D₃	1	1	yes	characteristic
15	C₂×Dic₁₂	—	3	1	no	—
16	#827	—	3	4	no	—
17	C₂×C₃⋊C₁₆	—	3	1	no	—
18	C₂³×C₉	—	4	1	no	—
19	D₄×C₉	—	2	2	no	—
20	D₄×C₉	—	4	1	no	—
21	C₂×C₄×C₉	D₄	1	1	yes	characteristic
22	C₂×Dic₉	—	4	1	no	—
23	Dic₁₈	—	2	2	no	—
24	Dic₁₈	—	4	1	no	—
25	C₈×C₉	D₄	1	1	yes	characteristic
26	C₈×C₉	C₂³	1	1	yes	characteristic
27	C₂×SD₃₂	—	9	1	no	Sylow
28	C₂×C₃×D₄	—	2	1	no	—
29	C₂×Dic₆	—	6	1	no	—
30	C₃×D₈	—	2	1	no	—
31	C₃×D₈	C₂×D₃	1	2	yes	—
32	C₂×C₃×C₈	C₂×D₃	1	1	yes	characteristic
33	Dic₁₂	—	3	2	no	—
34	Dic₁₂	—	6	1	no	—
35	C₃⋊C₁₆	—	3	2	no	—
36	C₂²×C₉	—	4	2	no	—
37	C₂²×C₉	—	8	2	no	—
38	C₂²×C₉	D₈	1	1	yes	characteristic
39	C₄×C₉	D₈	1	1	yes	characteristic
40	C₄×C₉	C₂×D₄	1	1	yes	characteristic
41	Dic₉	—	4	2	no	—
42	C₂×Q₁₆	—	9	1	no	—
43	C₂×D₈	D₉	1	1	yes	characteristic
44	SD₃₂	—	9	4	no	—
45	C₂×C₁₆	—	9	1	no	—
46	C₂³×C₃	—	4	1	no	—
47	C₃×D₄	—	2	2	no	—
48	C₃×D₄	—	4	1	no	—
49	C₂×C₃×C₄	#67	1	1	yes	characteristic
50	C₂×Dic₃	—	12	1	no	—
51	Dic₆	—	6	2	no	—
52	Dic₆	—	12	1	no	—
53	C₃×C₈	#67	1	1	yes	characteristic
54	C₃×C₈	C₂²×D₃	1	1	yes	characteristic
55	C₂×C₉	—	8	2	no	—
56	C₂×C₉	SD₃₂	1	2	yes	complemented
57	C₂×C₉	C₂×D₈	1	1	yes	characteristic
58	C₂×Q₈	—	18	1	no	—
59	C₂×D₄	—	2	1	no	—
60	Q₁₆	—	9	2	no	—
61	Q₁₆	—	18	1	no	—
62	D₈	—	2	1	no	—
63	D₈	C₂×D₉	1	2	yes	—
64	C₂×C₈	C₂×D₉	1	1	yes	characteristic
65	C₁₆	—	9	2	no	—
66	C₂²×C₃	—	4	2	no	—
67	C₂²×C₃	—	8	2	no	—
68	C₂²×C₃	#213	1	1	yes	characteristic
69	C₃×C₄	#213	1	1	yes	characteristic
70	C₃×C₄	C₂×#67	1	1	yes	characteristic
71	Dic₃	—	12	2	no	—
72	C₉	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
73	C₂³	—	4	1	no	—
74	Q₈	—	18	2	no	—
75	Q₈	—	36	1	no	—
76	D₄	—	2	2	no	—
77	D₄	—	4	1	no	—
78	C₂×C₄	—	36	1	no	—
79	C₂×C₄	#611	1	1	yes	characteristic
80	C₈	#611	1	1	yes	characteristic
81	C₈	C₂²×D₉	1	1	yes	characteristic
82	C₂×C₃	—	8	2	no	—
83	C₂×C₃	#827	1	2	yes	—
84	C₂×C₃	C₂×#213	1	1	yes	characteristic
85	C₂²	—	4	2	no	—
86	C₂²	—	8	2	no	—
87	C₂²	#3673	1	1	yes	characteristic
88	C₄	—	36	2	no	—
89	C₄	#3673	1	1	yes	characteristic
90	C₄	C₂×#611	1	1	yes	characteristic
91	C₃	C₂×#827	1	1	yes	characteristic
92	C₂	—	8	2	no	—
93	C₂	#63386	1	2	yes	direct product factor
94	C₂	C₂×#3673	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#3673
commutator, cosocle	C₈×C₉	C₂³
Frattini	C₃×C₈	C₂²×D₃
Fitting	C₂×C₉×D₈	C₂
socle	C₂²×C₃	#213
prime radical	C₂×C₃×D₈	D₃
hypercenter	C₂×D₈	D₉
hypocenter	C₉	C₂×SD₃₂
LCS	G ▷ C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₃₆	C₂	semidirect
3. #63386	C₂	direct (N × H)
4. C₂×C₉⋊C₁₆	C₂	semidirect
12. Dic₃₆	C₂²	semidirect
13. C₉⋊C₁₆	C₂²	semidirect
56. C₂×C₉	SD₃₂	semidirect
72. C₉	C₂×SD₃₂	semidirect
93. C₂	#63386	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×D₈	2
C₂×Dic₃₆	2
#63386	2
C₂×C₉⋊C₁₆	2
C₂×#827	3

Subgroups — C2×#63386 #10588828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#63386 #10588828