Subgroups — #37559607

Order 23872.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26045840	C₂	1	1	yes	maximal, characteristic
2	#26045825	C₂	1	2	yes	maximal, complemented
3	#26045790	C₂	1	1	yes	maximal, characteristic, complemented
4	#26045718	C₂	1	2	yes	maximal, complemented
5	#101×C₃₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#20238611	—	2	2	no	—
7	#20238610	—	2	2	no	—
8	#20238610	C₂²	1	2	yes	—
9	C₂×Dic₇₄₆	C₂²	1	1	yes	characteristic
10	Q₈×D₃₇₃	—	2	2	no	—
11	Dic₁₄₉₂	—	2	2	no	—
12	#20238599	—	2	2	no	—
13	#20238589	—	2	2	no	—
14	C₄×Dic₃₇₃	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₃₇₃	C₂²	1	1	yes	characteristic
16	M₁₆×C₃₇₃	C₂²	1	2	yes	—
17	Dic₇₄₆	—	2	2	no	—
18	Dic₇₄₆	—	2	2	no	—
19	Dic₇₄₆	D₄	1	2	yes	—
20	D₁₄₉₂	—	2	2	no	—
21	D₁₄₉₂	D₄	1	2	yes	—
22	C₂²⋊D₃₇₃	—	2	2	no	—
23	C₂×Dic₃₇₃	—	2	1	no	—
24	C₂×Dic₃₇₃	—	2	1	no	—
25	C₄×D₃₇₃	—	2	4	no	—
26	C₄×D₃₇₃	—	2	2	no	—
27	Q₈×C₃₇₃	—	2	2	no	—
28	C₂×C₄×C₃₇₃	D₄	1	2	yes	—
29	C₂×C₄×C₃₇₃	C₂³	1	1	yes	characteristic
30	C₈×C₃₇₃	—	2	2	no	—
31	C₂²×C₃₇₃	C₂×D₄	1	1	yes	characteristic
32	C₂×D₃₇₃	—	2	2	no	—
33	C₄×C₃₇₃	—	2	2	no	—
34	C₄×C₃₇₃	C₂×D₄	1	2	yes	—
35	Dic₃₇₃	—	2	2	no	—
36	Dic₃₇₃	—	2	2	no	—
37	Dic₃₇₃	—	4	1	no	—
38	C₂×C₃₇₃	—	2	1	no	—
39	C₂×C₃₇₃	#120	1	1	yes	characteristic
40	D₃₇₃	—	4	2	no	—
41	C₃₇₃	#456	1	1	yes	characteristic, complemented, Sylow
42	#456	—	373	1	no	maximal, Sylow
43	2₋¹⁺⁴	—	373	1	no	—
44	#137	—	373	2	no	—
45	C₄⋊Q₈	—	373	1	no	—
46	#104	—	373	2	no	—
47	#101	D₃₇₃	1	1	yes	characteristic, complemented
48	#41	—	373	2	no	—
49	#41	—	746	2	no	—
50	#41	—	746	2	no	—
51	C₂×Q₈	—	373	1	no	—
52	C₂×Q₈	—	746	2	no	—
53	C₂×Q₈	C₂×D₃₇₃	1	1	yes	characteristic
54	Q₁₆	—	746	2	no	—
55	SD₁₆	—	746	2	no	—
56	M₁₆	C₂×D₃₇₃	1	2	yes	—
57	C₄⋊C₄	—	746	2	no	—
58	C₄²	—	373	1	no	—
59	Q₈	—	2	2	no	—
60	Q₈	—	373	2	no	—
61	Q₈	—	746	2	no	—
62	Q₈	—	746	2	no	—
63	D₄	—	373	2	no	—
64	D₄	—	746	2	no	—
65	D₄	—	746	2	no	—
66	C₂×C₄	—	746	4	no	—
67	C₂×C₄	—	746	1	no	—
68	C₂×C₄	—	746	1	no	—
69	C₂×C₄	—	746	2	no	—
70	C₂×C₄	D₁₄₉₂	1	2	yes	—
71	C₂×C₄	C₂²×D₃₇₃	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₂²	—	746	2	no	—
74	C₂²	C₂×D₁₄₉₂	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	1492	1	no	—
77	C₄	—	746	2	no	—
78	C₄	—	746	2	no	—
79	C₄	D₄×D₃₇₃	1	2	yes	—
80	C₂	—	2	1	no	—
81	C₂	—	1492	2	no	—
82	C₂	#26045762	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26045762
commutator, cosocle	C₂×C₄×C₃₇₃	C₂³
Frattini	C₂×C₄	C₂²×D₃₇₃
Fitting	#101×C₃₇₃	C₂
socle	C₂×C₃₇₃	#120
prime radical	#26045840	C₂
hypercenter	#101	D₃₇₃
hypocenter	C₃₇₃	#456
LCS	G ▷ C₂×C₄×C₃₇₃ ▷ C₂×C₃₇₃ ▷ C₃₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #101

Complements

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

N	H ≅ G/N	type
2. #26045825	C₂	semidirect
3. #26045790	C₂	semidirect
4. #26045718	C₂	semidirect
5. #101×C₃₇₃	C₂	semidirect
41. C₃₇₃	#456	semidirect
47. #101	D₃₇₃	semidirect

Maximal subgroups

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

subgroup	index
#26045840	2
#26045825	2
#26045790	2
#26045718	2
#101×C₃₇₃	2
#456	373