Subgroups — C₂×C₂²⋊C₈×C₃₇₃ #37558960

Order 23872.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₃₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×C₃₇₃	C₂	1	2	yes	maximal, complemented
3	C₂²⋊C₈×C₃₇₃	C₂	1	4	yes	maximal, direct product factor
4	C₂⁴×C₃₇₃	C₄	1	1	yes	characteristic
5	C₂²×C₄×C₃₇₃	—	2	4	no	—
6	C₂²×C₄×C₃₇₃	C₄	1	1	yes	characteristic
7	C₂²×C₄×C₃₇₃	C₄	1	2	yes	—
8	C₂²×C₄×C₃₇₃	C₂²	1	2	yes	—
9	C₂²×C₄×C₃₇₃	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₃₇₃	—	2	4	no	—
11	C₂×C₈×C₃₇₃	C₂²	1	4	yes	complemented
12	C₂³×C₃₇₃	—	2	2	no	—
13	C₂³×C₃₇₃	—	2	2	no	—
14	C₂³×C₃₇₃	C₈	1	4	yes	complemented
15	C₂³×C₃₇₃	C₂×C₄	1	2	yes	—
16	C₂³×C₃₇₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₃₇₃	—	2	2	no	—
18	C₂×C₄×C₃₇₃	—	2	4	no	—
19	C₂×C₄×C₃₇₃	—	2	4	no	—
20	C₂×C₄×C₃₇₃	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₃₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₃₇₃	D₄	1	4	yes	—
23	C₂×C₄×C₃₇₃	C₂³	1	1	yes	characteristic
24	C₈×C₃₇₃	—	2	4	no	—
25	C₂²×C₃₇₃	—	2	8	no	—
26	C₂²×C₃₇₃	—	2	2	no	—
27	C₂²×C₃₇₃	—	2	2	no	—
28	C₂²×C₃₇₃	C₂²⋊C₄	1	2	yes	—
29	C₂²×C₃₇₃	C₂×C₈	1	2	yes	—
30	C₂²×C₃₇₃	C₂×C₈	1	4	yes	complemented
31	C₂²×C₃₇₃	M₁₆	1	2	yes	—
32	C₂²×C₃₇₃	C₂²×C₄	1	1	yes	characteristic
33	C₄×C₃₇₃	—	2	2	no	—
34	C₄×C₃₇₃	C₂²⋊C₄	1	2	yes	—
35	C₄×C₃₇₃	C₂×D₄	1	2	yes	—
36	C₂×C₃₇₃	—	2	4	no	—
37	C₂×C₃₇₃	C₂²⋊C₈	1	4	yes	direct product factor
38	C₂×C₃₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₃₇₃	C₂²×C₈	1	1	yes	characteristic
40	C₂×C₃₇₃	C₂×M₁₆	1	1	yes	characteristic
41	C₃₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₂²⋊C₈	C₃₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂³×C₄	C₂×C₃₇₃	1	1	yes	characteristic
44	C₂²×C₈	C₂×C₃₇₃	1	2	yes	complemented
45	C₂²⋊C₈	C₂×C₃₇₃	1	4	yes	direct product factor
46	C₂⁴	C₄×C₃₇₃	1	1	yes	characteristic
47	C₂²×C₄	—	2	4	no	—
48	C₂²×C₄	C₄×C₃₇₃	1	1	yes	characteristic
49	C₂²×C₄	C₄×C₃₇₃	1	2	yes	—
50	C₂²×C₄	C₂²×C₃₇₃	1	2	yes	—
51	C₂²×C₄	C₂²×C₃₇₃	1	1	yes	characteristic
52	C₂×C₈	—	2	4	no	—
53	C₂×C₈	C₂²×C₃₇₃	1	4	yes	complemented
54	C₂³	—	2	2	no	—
55	C₂³	—	2	2	no	—
56	C₂³	C₈×C₃₇₃	1	4	yes	complemented
57	C₂³	C₂×C₄×C₃₇₃	1	2	yes	—
58	C₂³	C₂×C₄×C₃₇₃	1	1	yes	characteristic
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	2	4	no	—
61	C₂×C₄	—	2	4	no	—
62	C₂×C₄	C₂×C₄×C₃₇₃	1	2	yes	—
63	C₂×C₄	C₂×C₄×C₃₇₃	1	1	yes	characteristic
64	C₂×C₄	D₄×C₃₇₃	1	4	yes	—
65	C₂×C₄	C₂³×C₃₇₃	1	1	yes	characteristic
66	C₈	—	2	4	no	—
67	C₂²	—	2	8	no	—
68	C₂²	—	2	2	no	—
69	C₂²	—	2	2	no	—
70	C₂²	C₂²⋊C₄×C₃₇₃	1	2	yes	—
71	C₂²	C₂×C₈×C₃₇₃	1	2	yes	—
72	C₂²	C₂×C₈×C₃₇₃	1	4	yes	complemented
73	C₂²	M₁₆×C₃₇₃	1	2	yes	—
74	C₂²	C₂²×C₄×C₃₇₃	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	C₂²⋊C₄×C₃₇₃	1	2	yes	—
77	C₄	C₂×D₄×C₃₇₃	1	2	yes	—
78	C₂	—	2	4	no	—
79	C₂	C₂²⋊C₈×C₃₇₃	1	4	yes	direct product factor
80	C₂	C₂×C₂²⋊C₄×C₃₇₃	1	1	yes	characteristic
81	C₂	C₂²×C₈×C₃₇₃	1	1	yes	characteristic
82	C₂	C₂×M₁₆×C₃₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₇₃	C₂²
commutator	C₂	C₂²×C₈×C₃₇₃
Frattini, cosocle	C₂×C₄	C₂³×C₃₇₃
socle	C₂³×C₃₇₃	C₂×C₄
prime radical	C₂⁴×C₃₇₃	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₈×C₃₇₃	C₂	semidirect
3. C₂²⋊C₈×C₃₇₃	C₂	direct (N × H)
11. C₂×C₈×C₃₇₃	C₂²	semidirect
14. C₂³×C₃₇₃	C₈	semidirect
30. C₂²×C₃₇₃	C₂×C₈	semidirect
37. C₂×C₃₇₃	C₂²⋊C₈	direct (N × H)
41. C₃₇₃	C₂×C₂²⋊C₈	direct (N × H)
42. C₂×C₂²⋊C₈	C₃₇₃	direct (N × H)
44. C₂²×C₈	C₂×C₃₇₃	semidirect
45. C₂²⋊C₈	C₂×C₃₇₃	direct (N × H)
53. C₂×C₈	C₂²×C₃₇₃	semidirect
56. C₂³	C₈×C₃₇₃	semidirect
72. C₂²	C₂×C₈×C₃₇₃	semidirect
79. C₂	C₂²⋊C₈×C₃₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₃₇₃	2
C₂²×C₈×C₃₇₃	2
C₂²⋊C₈×C₃₇₃	2
C₂×C₂²⋊C₈	373

Subgroups — C2×C22⋊C8×C373 #37558960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂²⋊C₈×C₃₇₃ #37558960