Subgroups — C₂²×#11924476 #18007692

Order 4736.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924476	C₂	1	12	yes	maximal, direct product factor
2	C₂²×#10596925	C₂	1	2	yes	maximal, complemented
3	C₂³×C₈×C₃₇	C₂	1	1	yes	maximal, characteristic
4	#11924476	C₂²	1	16	yes	direct product factor
5	C₂×#10596925	C₂²	1	12	yes	complemented
6	C₂³×C₄×C₃₇	C₄	1	1	yes	characteristic
7	C₂²×C₈×C₃₇	C₄	1	1	yes	characteristic
8	C₂²×C₈×C₃₇	C₄	1	6	yes	—
9	C₂²×C₈×C₃₇	C₂²	1	6	yes	—
10	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
11	C₂⁴×C₃₇	C₈	1	1	yes	characteristic
12	C₂²×C₄×C₃₇	C₈	1	6	yes	—
13	C₂²×C₄×C₃₇	C₈	1	1	yes	characteristic
14	C₂²×C₄×C₃₇	C₂×C₄	1	6	yes	—
15	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₃₇	C₂×C₄	1	12	yes	—
17	C₂×C₈×C₃₇	C₂×C₄	1	6	yes	—
18	C₂×C₈×C₃₇	C₂×C₄	1	3	yes	—
19	C₂×C₈×C₃₇	C₂³	1	3	yes	—
20	C₂×C₈×C₃₇	C₂³	1	4	yes	—
21	#10596925	C₂³	1	8	yes	complemented
22	C₂³×C₃₇	—	2	4	no	—
23	C₂³×C₃₇	C₂×C₈	1	6	yes	—
24	C₂³×C₃₇	C₂×C₈	1	1	yes	characteristic
25	C₂×C₄×C₃₇	C₂×C₈	1	12	yes	—
26	C₂×C₄×C₃₇	C₂×C₈	1	6	yes	—
27	C₂×C₄×C₃₇	C₂×C₈	1	3	yes	—
28	C₂×C₄×C₃₇	C₂²×C₄	1	4	yes	—
29	C₂×C₄×C₃₇	C₂²×C₄	1	3	yes	—
30	C₈×C₃₇	C₂²×C₄	1	3	yes	—
31	C₈×C₃₇	C₂²×C₄	1	4	yes	—
32	C₈×C₃₇	C₂⁴	1	1	yes	characteristic
33	C₂²×C₃₇	—	2	12	no	—
34	C₂²×C₃₇	M₃₂	1	4	yes	complemented
35	C₂²×C₃₇	C₂²×C₈	1	4	yes	—
36	C₂²×C₃₇	C₂²×C₈	1	3	yes	—
37	C₄×C₃₇	C₂²×C₈	1	3	yes	—
38	C₄×C₃₇	C₂²×C₈	1	4	yes	—
39	C₄×C₃₇	C₂³×C₄	1	1	yes	characteristic
40	C₂²×M₃₂	—	37	1	no	maximal, Sylow
41	C₂×C₃₇	—	2	4	no	—
42	C₂×C₃₇	C₂×M₃₂	1	6	yes	complemented
43	C₂×C₃₇	C₂³×C₈	1	1	yes	characteristic
44	C₂³×C₈	D₃₇	1	1	yes	characteristic
45	C₂×M₃₂	—	37	12	no	—
46	C₂²×C₁₆	—	37	2	no	—
47	C₃₇	C₂²×M₃₂	1	1	yes	characteristic, complemented, Sylow
48	C₂³×C₄	Dic₃₇	1	1	yes	characteristic
49	C₂²×C₈	Dic₃₇	1	1	yes	characteristic
50	C₂²×C₈	Dic₃₇	1	6	yes	—
51	C₂²×C₈	C₂×D₃₇	1	6	yes	—
52	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
53	M₃₂	—	37	16	no	—
54	C₂×C₁₆	—	37	12	no	—
55	C₂⁴	#64436	1	1	yes	characteristic
56	C₂²×C₄	#64436	1	6	yes	—
57	C₂²×C₄	#64436	1	1	yes	characteristic
58	C₂²×C₄	C₂×Dic₃₇	1	6	yes	—
59	C₂²×C₄	C₂×Dic₃₇	1	1	yes	characteristic
60	C₂×C₈	C₂×Dic₃₇	1	6	yes	—
61	C₂×C₈	C₂×Dic₃₇	1	12	yes	—
62	C₂×C₈	C₂×Dic₃₇	1	3	yes	—
63	C₂×C₈	C₂²×D₃₇	1	3	yes	—
64	C₂×C₈	C₂²×D₃₇	1	4	yes	—
65	C₁₆	—	37	8	no	—
66	C₂³	—	2	4	no	—
67	C₂³	C₂×#64436	1	6	yes	—
68	C₂³	C₂×#64436	1	1	yes	characteristic
69	C₂×C₄	C₂×#64436	1	12	yes	—
70	C₂×C₄	C₂×#64436	1	6	yes	—
71	C₂×C₄	C₂×#64436	1	3	yes	—
72	C₂×C₄	C₂²×Dic₃₇	1	4	yes	—
73	C₂×C₄	C₂²×Dic₃₇	1	3	yes	—
74	C₈	C₂²×Dic₃₇	1	4	yes	—
75	C₈	C₂²×Dic₃₇	1	3	yes	—
76	C₈	C₂³×D₃₇	1	1	yes	characteristic
77	C₂²	—	2	12	no	—
78	C₂²	#11924476	1	4	yes	direct product factor
79	C₂²	C₂²×#64436	1	4	yes	—
80	C₂²	C₂²×#64436	1	3	yes	—
81	C₄	C₂²×#64436	1	3	yes	—
82	C₄	C₂²×#64436	1	4	yes	—
83	C₄	C₂³×Dic₃₇	1	1	yes	characteristic
84	C₂	—	2	4	no	—
85	C₂	C₂×#11924476	1	6	yes	direct product factor
86	C₂	C₂³×#64436	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂×D₃₇
commutator	C₂×C₃₇	C₂³×C₈
Frattini	C₈	C₂³×D₃₇
Fitting	C₂³×C₈×C₃₇	C₂
socle	C₂³×C₃₇	C₂×C₈
prime radical	C₂⁴×C₃₇	C₈
cosocle	C₈×C₃₇	C₂⁴
hypercenter	C₂³×C₈	D₃₇
hypocenter	C₃₇	C₂²×M₃₂
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂²×C₈ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#11924476	C₂	direct (N × H)
2. C₂²×#10596925	C₂	semidirect
4. #11924476	C₂²	direct (N × H)
5. C₂×#10596925	C₂²	semidirect
21. #10596925	C₂³	semidirect
34. C₂²×C₃₇	M₃₂	semidirect
42. C₂×C₃₇	C₂×M₃₂	semidirect
47. C₃₇	C₂²×M₃₂	semidirect
78. C₂²	#11924476	direct (N × H)
85. C₂	C₂×#11924476	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×#11924476	2
C₂²×#10596925	2
C₂³×C₈×C₃₇	2
C₂²×M₃₂	37

Subgroups — C22×#11924476 #18007692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11924476 #18007692