Subgroups — C₄×C₄⋊C₄×C₃₇₃ #37558932

Order 23872.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×C₃₇₃	C₂	1	2	yes	maximal
2	C₂×C₄²×C₃₇₃	C₂	1	2	yes	maximal
3	C₂×C₄²×C₃₇₃	C₂	1	1	yes	maximal, characteristic
4	#95×C₃₇₃	C₂	1	2	yes	maximal
5	C₂²×C₄×C₃₇₃	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₃₇₃	C₂²	1	4	yes	—
7	C₂²×C₄×C₃₇₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₃₇₃	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₃₇₃	C₄	1	8	yes	direct product factor
10	C₄²×C₃₇₃	—	2	4	no	—
11	C₄²×C₃₇₃	C₄	1	4	yes	complemented
12	C₂³×C₃₇₃	C₂³	1	1	yes	characteristic
13	C₂×C₄×C₃₇₃	—	2	4	no	—
14	C₂×C₄×C₃₇₃	—	2	2	no	—
15	C₂×C₄×C₃₇₃	—	2	4	no	—
16	C₂×C₄×C₃₇₃	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₃₇₃	C₂×C₄	1	8	yes	—
18	C₂×C₄×C₃₇₃	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₃₇₃	C₂×C₄	1	4	yes	—
20	C₂×C₄×C₃₇₃	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₃₇₃	D₄	1	2	yes	—
22	C₂×C₄×C₃₇₃	Q₈	1	2	yes	—
23	C₂²×C₃₇₃	C₂²×C₄	1	1	yes	characteristic
24	C₂²×C₃₇₃	C₂²×C₄	1	2	yes	—
25	C₂²×C₃₇₃	C₂×D₄	1	1	yes	characteristic
26	C₂²×C₃₇₃	C₂×Q₈	1	1	yes	characteristic
27	C₂²×C₃₇₃	#41	1	2	yes	—
28	C₄×C₃₇₃	—	2	2	no	—
29	C₄×C₃₇₃	—	2	8	no	—
30	C₄×C₃₇₃	C₄²	1	4	yes	complemented
31	C₄×C₃₇₃	C₄⋊C₄	1	4	yes	direct product factor
32	C₂×C₃₇₃	C₂×C₄²	1	1	yes	characteristic
33	C₂×C₃₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₃₇₃	#117	1	1	yes	characteristic
35	C₂×C₃₇₃	C₄×D₄	1	2	yes	—
36	C₂×C₃₇₃	C₄×Q₈	1	2	yes	—
37	C₃₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
38	C₄×C₄⋊C₄	C₃₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂×C₄⋊C₄	C₂×C₃₇₃	1	2	yes	—
40	C₂×C₄²	C₂×C₃₇₃	1	2	yes	—
41	C₂×C₄²	C₂×C₃₇₃	1	1	yes	characteristic
42	#95	C₂×C₃₇₃	1	2	yes	—
43	C₂²×C₄	C₂²×C₃₇₃	1	1	yes	characteristic
44	C₂²×C₄	C₂²×C₃₇₃	1	4	yes	—
45	C₂²×C₄	C₂²×C₃₇₃	1	1	yes	characteristic
46	C₂²×C₄	C₂²×C₃₇₃	1	1	yes	characteristic
47	C₄⋊C₄	C₄×C₃₇₃	1	8	yes	direct product factor
48	C₄²	—	2	4	no	—
49	C₄²	C₄×C₃₇₃	1	4	yes	complemented
50	C₂³	C₂³×C₃₇₃	1	1	yes	characteristic
51	C₂×C₄	—	2	4	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	—	2	4	no	—
54	C₂×C₄	C₂×C₄×C₃₇₃	1	2	yes	—
55	C₂×C₄	C₂×C₄×C₃₇₃	1	8	yes	—
56	C₂×C₄	C₂×C₄×C₃₇₃	1	2	yes	—
57	C₂×C₄	C₂×C₄×C₃₇₃	1	4	yes	—
58	C₂×C₄	C₂×C₄×C₃₇₃	1	2	yes	—
59	C₂×C₄	D₄×C₃₇₃	1	2	yes	—
60	C₂×C₄	Q₈×C₃₇₃	1	2	yes	—
61	C₂²	C₂²×C₄×C₃₇₃	1	1	yes	characteristic
62	C₂²	C₂²×C₄×C₃₇₃	1	2	yes	—
63	C₂²	C₂×D₄×C₃₇₃	1	1	yes	characteristic
64	C₂²	C₂×Q₈×C₃₇₃	1	1	yes	characteristic
65	C₂²	#41×C₃₇₃	1	2	yes	—
66	C₄	—	2	2	no	—
67	C₄	—	2	8	no	—
68	C₄	C₄²×C₃₇₃	1	4	yes	complemented
69	C₄	C₄⋊C₄×C₃₇₃	1	4	yes	direct product factor
70	C₂	C₂×C₄²×C₃₇₃	1	1	yes	characteristic
71	C₂	C₂×C₄⋊C₄×C₃₇₃	1	1	yes	characteristic
72	C₂	#117×C₃₇₃	1	1	yes	characteristic
73	C₂	C₄×D₄×C₃₇₃	1	2	yes	—
74	C₂	C₄×Q₈×C₃₇₃	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₃₇₃	C₂²
commutator	C₂	C₂×C₄²×C₃₇₃
Frattini, cosocle	C₂³	C₂³×C₃₇₃
socle, prime radical	C₂³×C₃₇₃	C₂³
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
9. C₄⋊C₄×C₃₇₃	C₄	direct (N × H)
11. C₄²×C₃₇₃	C₄	semidirect
30. C₄×C₃₇₃	C₄²	semidirect
31. C₄×C₃₇₃	C₄⋊C₄	direct (N × H)
37. C₃₇₃	C₄×C₄⋊C₄	direct (N × H)
38. C₄×C₄⋊C₄	C₃₇₃	direct (N × H)
47. C₄⋊C₄	C₄×C₃₇₃	direct (N × H)
49. C₄²	C₄×C₃₇₃	semidirect
68. C₄	C₄²×C₃₇₃	semidirect
69. C₄	C₄⋊C₄×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
C₂×C₄⋊C₄×C₃₇₃	2
C₂×C₄²×C₃₇₃	2
#95×C₃₇₃	2
C₄×C₄⋊C₄	373

Subgroups — C4×C4⋊C4×C373 #37558932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄⋊C₄×C₃₇₃ #37558932