Subgroups — C₂×#10590024 #11800508

Order 1152.

218 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63545	C₂	1	2	yes	maximal, complemented
2	C₂×#63540	C₂	1	1	yes	maximal, characteristic, complemented
3	#10590024	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃×D₂₄	—	2	2	no	—
5	C₂×C₃⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic
6	#63545	—	2	2	no	—
7	#63545	C₂²	1	4	yes	complemented
8	#63540	C₂²	1	2	yes	complemented
9	C₂×#826	—	6	2	no	—
10	C₂×C₃×D₁₂	—	4	2	no	—
11	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
12	C₃×D₂₄	—	2	4	no	—
13	C₃×D₂₄	—	4	2	no	—
14	C₃⋊(C₃⋊C₁₆)	D₄	1	1	yes	characteristic
15	C₃⋊(C₃⋊C₁₆)	C₂³	1	1	yes	characteristic
16	C₂×D₃₂	—	9	1	no	maximal, Sylow
17	C₂×C₃×D₈	—	6	2	no	—
18	C₂×D₂₄	—	2	2	no	—
19	#826	—	6	4	no	—
20	#826	—	6	4	no	—
21	C₂×C₃⋊C₁₆	—	6	2	no	—
22	C₂²×C₃×D₃	—	8	2	no	—
23	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
24	C₃×D₁₂	—	4	4	no	—
25	C₃×D₁₂	—	8	2	no	—
26	C₃²×C₈	D₈	1	1	yes	characteristic
27	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
28	C₂×D₁₆	—	9	2	no	—
29	D₃₂	—	9	4	no	—
30	C₂×C₃₂	—	9	1	no	—
31	C₂×C₃×D₄	—	12	2	no	—
32	C₂×D₁₂	—	4	2	no	—
33	C₃×D₈	—	6	4	no	—
34	C₃×D₈	—	12	2	no	—
35	C₂×C₃×C₈	—	2	2	no	—
36	D₂₄	—	2	4	no	—
37	D₂₄	—	4	2	no	—
38	C₃⋊C₁₆	—	6	2	no	—
39	C₃⋊C₁₆	—	6	2	no	—
40	C₂²×C₃²	D₁₆	1	1	yes	characteristic
41	C₂×C₃×D₃	—	8	4	no	—
42	C₂×C₃×D₃	—	16	4	no	—
43	C₃²×C₄	D₁₆	1	1	yes	characteristic
44	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
45	C₂×D₈	—	6	2	no	—
46	D₁₆	—	9	4	no	—
47	D₁₆	—	18	2	no	—
48	C₂×C₁₆	—	9	1	no	—
49	C₃₂	—	9	2	no	—
50	C₂³×C₃	—	24	2	no	—
51	C₂²×D₃	—	8	2	no	—
52	C₃×D₄	—	12	4	no	—
53	C₃×D₄	—	24	2	no	—
54	C₂×C₃×C₄	—	2	2	no	—
55	D₁₂	—	4	4	no	—
56	D₁₂	—	8	2	no	—
57	C₃×C₈	—	2	2	no	—
58	C₃×C₈	—	2	2	no	—
59	C₂×C₃²	D₃₂	1	2	yes	complemented
60	C₂×C₃²	C₂×D₁₆	1	1	yes	characteristic
61	C₃×D₃	—	16	4	no	—
62	C₂×D₄	—	12	2	no	—
63	D₈	—	6	4	no	—
64	D₈	—	12	2	no	—
65	C₂×C₈	GO⁺(4,𝔽₂)	1	1	yes	characteristic
66	C₁₆	—	9	1	no	—
67	C₁₆	—	9	1	no	—
68	C₂²×C₃	—	2	2	no	—
69	C₂²×C₃	—	24	4	no	—
70	C₂²×C₃	—	48	4	no	—
71	C₂×D₃	—	8	4	no	—
72	C₂×D₃	—	16	4	no	—
73	C₃×C₄	—	2	2	no	—
74	C₃×C₄	—	2	2	no	—
75	C₃²	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
76	C₂³	—	24	2	no	—
77	D₄	—	12	4	no	—
78	D₄	—	24	2	no	—
79	C₂×C₄	#3774	1	1	yes	characteristic
80	C₈	#3774	1	1	yes	characteristic
81	C₈	C₂×GO⁺(4,𝔽₂)	1	1	yes	characteristic
82	C₂×C₃	—	2	2	no	—
83	C₂×C₃	—	2	4	no	—
84	C₂×C₃	—	48	4	no	—
85	D₃	—	16	4	no	—
86	C₂²	—	24	4	no	—
87	C₂²	—	48	4	no	—
88	C₂²	#63734	1	1	yes	characteristic
89	C₄	#63734	1	1	yes	characteristic
90	C₄	C₂×#3774	1	1	yes	characteristic
91	C₃	—	2	2	no	—
92	C₂	—	48	4	no	—
93	C₂	#10590024	1	2	yes	direct product factor
94	C₂	C₂×#63734	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#63734
commutator, cosocle	C₃⋊(C₃⋊C₁₆)	C₂³
Frattini	C₈	C₂×GO⁺(4,𝔽₂)
Fitting	C₂×C₃²×C₈	D₄
socle	C₂²×C₃²	D₁₆
hypercenter	C₂×C₈	GO⁺(4,𝔽₂)
hypocenter	C₃²	C₂×D₃₂
LCS	G ▷ C₃⋊(C₃⋊C₁₆) ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#63545	C₂	semidirect
2. C₂×#63540	C₂	semidirect
3. #10590024	C₂	direct (N × H)
7. #63545	C₂²	semidirect
8. #63540	C₂²	semidirect
59. C₂×C₃²	D₃₂	semidirect
75. C₃²	C₂×D₃₂	semidirect
93. C₂	#10590024	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×#63545	2
C₂×#63540	2
#10590024	2
C₂×D₃₂	9

Subgroups — C2×#10590024 #11800508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10590024 #11800508