Subgroups — #37559809

Order 23872.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20238598	C₂	1	2	yes	maximal, complemented
2	C₂×#20238595	C₂	1	2	yes	maximal, complemented
3	#26045780	C₂	1	1	yes	maximal, characteristic, complemented
4	#26045703	C₂	1	1	yes	maximal, characteristic, complemented
5	#127×C₃₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₇₄₆	C₂²	1	1	yes	characteristic
7	C₂×D₁₄₉₂	C₂²	1	1	yes	characteristic
8	#20238598	—	2	4	no	—
9	#20238595	—	2	4	no	—
10	C₂×#15688412	C₂²	1	2	yes	—
11	#20238587	—	2	2	no	—
12	C₂×D₄×C₃₇₃	—	2	2	no	—
13	C₂×D₄×C₃₇₃	C₂²	1	2	yes	—
14	C₄²×C₃₇₃	C₂²	1	1	yes	characteristic
15	C₂²×D₃₇₃	—	2	1	no	—
16	Dic₇₄₆	—	2	2	no	—
17	D₁₄₉₂	—	2	2	no	—
18	C₂×Dic₃₇₃	—	2	1	no	—
19	#15688412	D₄	1	4	yes	complemented
20	C₂³×C₃₇₃	—	2	2	no	—
21	D₄×C₃₇₃	—	2	2	no	—
22	D₄×C₃₇₃	—	2	2	no	—
23	D₄×C₃₇₃	—	4	4	no	—
24	C₂×C₄×C₃₇₃	D₄	1	2	yes	—
25	C₂×C₄×C₃₇₃	C₂³	1	1	yes	characteristic
26	C₂²×C₃₇₃	—	4	2	no	—
27	C₂²×C₃₇₃	—	4	4	no	—
28	C₂²×C₃₇₃	C₂×D₄	1	1	yes	characteristic
29	C₂×D₃₇₃	—	4	1	no	—
30	C₂×D₃₇₃	—	4	2	no	—
31	C₄×C₃₇₃	—	2	2	no	—
32	C₄×C₃₇₃	C₂×D₄	1	2	yes	—
33	Dic₃₇₃	—	4	1	no	—
34	C₂×C₃₇₃	—	8	2	no	—
35	C₂×C₃₇₃	#127	1	1	yes	characteristic
36	C₂×C₃₇₃	AGL(1,ℤ/8)	1	2	yes	—
37	D₃₇₃	—	8	1	no	—
38	C₃₇₃	#496	1	1	yes	characteristic, complemented, Sylow
39	#496	—	373	1	no	maximal, Sylow
40	C₂×SD₁₆	—	373	2	no	—
41	C₂×D₈	—	373	2	no	—
42	#127	D₃₇₃	1	1	yes	characteristic, complemented
43	#124	—	373	1	no	—
44	#97	—	373	1	no	—
45	C₂×Q₈	—	373	1	no	—
46	C₂×D₄	—	2	2	no	—
47	C₂×D₄	—	373	1	no	—
48	C₂×D₄	C₂×D₃₇₃	1	2	yes	—
49	SD₁₆	—	746	4	no	—
50	D₈	—	746	4	no	—
51	C₂×C₈	—	373	2	no	—
52	C₂²⋊C₄	—	746	2	no	—
53	C₄²	C₂×D₃₇₃	1	1	yes	characteristic
54	C₂³	—	2	2	no	—
55	C₂³	—	746	1	no	—
56	Q₈	—	746	2	no	—
57	D₄	—	2	2	no	—
58	D₄	—	2	2	no	—
59	D₄	—	4	4	no	—
60	D₄	—	746	2	no	—
61	C₂×C₄	—	746	1	no	—
62	C₂×C₄	C₂²⋊D₃₇₃	1	2	yes	—
63	C₂×C₄	C₂²×D₃₇₃	1	1	yes	characteristic
64	C₈	—	373	4	no	—
65	C₂²	—	4	2	no	—
66	C₂²	—	4	4	no	—
67	C₂²	—	1492	1	no	—
68	C₂²	—	1492	2	no	—
69	C₂²	C₂×C₂²⋊D₃₇₃	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	1492	1	no	—
72	C₄	D₄×D₃₇₃	1	2	yes	—
73	C₂	—	8	2	no	—
74	C₂	—	2984	1	no	—
75	C₂	#26045788	1	1	yes	characteristic
76	C₂	#26045818	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₇₃
commutator, cosocle	C₂×C₄×C₃₇₃	C₂³
Frattini	C₂×C₄	C₂²×D₃₇₃
Fitting	#127×C₃₇₃	C₂
socle	C₂²×C₃₇₃	C₂×D₄
hypercenter	#127	D₃₇₃
hypocenter	C₃₇₃	#496
LCS	G ▷ C₂×C₄×C₃₇₃ ▷ C₂×C₃₇₃ ▷ C₃₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂×#20238598	C₂	semidirect
2. C₂×#20238595	C₂	semidirect
3. #26045780	C₂	semidirect
4. #26045703	C₂	semidirect
5. #127×C₃₇₃	C₂	semidirect
19. #15688412	D₄	semidirect
38. C₃₇₃	#496	semidirect
42. #127	D₃₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20238598	2
C₂×#20238595	2
#26045780	2
#26045703	2
#127×C₃₇₃	2
#496	373