Subgroups — C₂×#63733 #10593329

Order 576.

174 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3787	C₂	1	1	yes	maximal, characteristic
2	C₂×#3712	C₂	1	2	yes	maximal
3	#63733	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
5	C₂×#622	C₄	1	2	yes	—
6	#3787	C₄	1	2	yes	—
7	#3787	C₂²	1	2	yes	—
8	C₂×C₃×C₃⋊C₈	—	2	2	no	—
9	#3712	—	2	2	no	—
10	#3712	C₂²	1	4	yes	—
11	C₂×ΓL(1,𝔽₂₅)	—	6	2	no	—
12	C₂²×C₃⋊D₃	Q₈	1	1	yes	characteristic
13	C₂×C₃²×C₄	D₄	1	1	yes	characteristic
14	C₂×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
15	C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
16	C₄×C₃⋊D₃	D₄	1	1	yes	characteristic
17	C₄×C₃⋊D₃	Q₈	1	1	yes	characteristic
18	C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
19	#622	C₂×C₄	1	4	yes	—
20	C₃×C₃⋊C₈	—	2	4	no	—
21	C₂×#108	—	9	1	no	maximal, Sylow
22	C₂×C₄×D₃	—	6	2	no	—
23	C₂×C₃×C₈	—	6	2	no	—
24	C₂×C₃⋊C₈	—	2	2	no	—
25	ΓL(1,𝔽₂₅)	—	6	4	no	—
26	ΓL(1,𝔽₂₅)	—	6	4	no	—
27	C₂²×C₃²	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₃⋊D₃	—	2	2	no	—
29	C₂×C₃⋊D₃	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₃⋊D₃	C₂×Q₈	1	1	yes	characteristic
31	C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
32	C₃²×C₄	C₂×D₄	1	1	yes	characteristic
33	C₃⋊Dic₃	C₄⋊C₄	1	1	yes	characteristic
34	C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×M₁₆	—	9	2	no	—
36	C₂²×C₈	—	9	1	no	—
37	#108	—	9	4	no	—
38	C₂²×D₃	—	6	2	no	—
39	C₂×C₃×C₄	—	2	2	no	—
40	C₂×Dic₃	—	6	2	no	—
41	C₄×D₃	—	6	2	no	—
42	C₄×D₃	—	6	2	no	—
43	C₄×D₃	—	6	2	no	—
44	C₄×D₃	—	6	2	no	—
45	C₃×C₈	—	6	4	no	—
46	C₃⋊C₈	—	2	4	no	—
47	C₂×C₃²	#108	1	2	yes	complemented
48	C₂×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₃⋊D₃	—	2	1	no	—
50	C₃⋊D₃	—	2	1	no	—
51	C₂²×C₄	—	9	1	no	—
52	M₁₆	—	9	4	no	—
53	M₁₆	—	18	2	no	—
54	C₂×C₈	—	6	2	no	—
55	C₂×C₈	—	9	2	no	—
56	C₂×C₈	—	9	2	no	—
57	C₂×C₈	—	9	2	no	—
58	C₂²×C₃	—	2	2	no	—
59	C₂×D₃	—	6	2	no	—
60	C₂×D₃	—	6	2	no	—
61	C₂×D₃	—	12	4	no	—
62	C₃×C₄	—	2	2	no	—
63	C₃×C₄	—	2	2	no	—
64	Dic₃	—	6	2	no	—
65	Dic₃	—	6	2	no	—
66	C₃²	C₂×#108	1	1	yes	characteristic, complemented, Sylow
67	C₂³	—	9	1	no	—
68	C₂×C₄	—	9	1	no	—
69	C₂×C₄	—	9	1	no	—
70	C₂×C₄	—	9	1	no	—
71	C₂×C₄	—	9	1	no	—
72	C₂×C₄	—	9	1	no	—
73	C₂×C₄	GO⁺(4,𝔽₂)	1	1	yes	characteristic
74	C₈	—	6	4	no	—
75	C₈	—	9	4	no	—
76	C₂×C₃	—	2	2	no	—
77	C₂×C₃	—	2	4	no	—
78	D₃	—	12	2	no	—
79	D₃	—	12	2	no	—
80	C₂²	—	9	1	no	—
81	C₂²	—	9	1	no	—
82	C₂²	—	18	2	no	—
83	C₂²	#3773	1	1	yes	characteristic
84	C₄	—	9	1	no	—
85	C₄	—	9	1	no	—
86	C₄	#3773	1	1	yes	characteristic
87	C₄	C₂×GO⁺(4,𝔽₂)	1	1	yes	characteristic
88	C₃	—	2	2	no	—
89	C₂	—	18	1	no	—
90	C₂	—	18	1	no	—
91	C₂	#63733	1	2	yes	direct product factor
92	C₂	C₂×#3773	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	GO⁺(4,𝔽₂)
commutator	C₃⋊Dic₃	C₂²×C₄
Frattini	C₄	C₂×GO⁺(4,𝔽₂)
Fitting	C₂×C₃²×C₄	D₄
socle	C₂²×C₃²	C₄⋊C₄
prime radical	C₂²×C₃⋊D₃	Q₈
cosocle	C₄×C₃⋊D₃	C₂³
hypocenter	C₃²	C₂×#108
LCS	G ▷ C₃⋊Dic₃ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
3. #63733	C₂	direct (N × H)
47. C₂×C₃²	#108	semidirect
66. C₃²	C₂×#108	semidirect
91. C₂	#63733	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×#3787	2
C₂×#3712	2
#63733	2
C₂×#108	9

Subgroups — C2×#63733 #10593329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#63733 #10593329