Subgroups — C₄×#20238593 #37559372

Order 23872.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20238593	C₂	1	2	yes	maximal
2	C₄²×D₃₇₃	C₂	1	1	yes	maximal, characteristic
3	#26045702	C₂	1	2	yes	maximal, complemented
4	C₄×#15688412	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₈×C₃₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₃₇₃	C₄	1	2	yes	—
7	C₂×C₄×D₃₇₃	C₂²	1	1	yes	characteristic
8	#20238593	C₄	1	8	yes	direct product factor
9	C₂×#15688412	C₂²	1	2	yes	—
10	C₄×Dic₃₇₃	C₄	1	2	yes	—
11	C₄×Dic₃₇₃	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₃₇₃	C₂²	1	2	yes	—
13	C₄²×C₃₇₃	C₂²	1	1	yes	characteristic
14	C₂²×D₃₇₃	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₃₇₃	C₂×C₄	1	2	yes	—
16	C₂×Dic₃₇₃	C₂×C₄	1	1	yes	characteristic
17	C₄×D₃₇₃	—	2	4	no	—
18	C₄×D₃₇₃	C₂×C₄	1	4	yes	—
19	#15688412	C₂×C₄	1	4	yes	complemented
20	C₂×C₄×C₃₇₃	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₃₇₃	C₂³	1	1	yes	characteristic
22	C₈×C₃₇₃	C₂×C₄	1	4	yes	complemented
23	C₂²×C₃₇₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×D₃₇₃	—	2	2	no	—
25	C₂×D₃₇₃	C₄²	1	2	yes	—
26	C₄×C₃₇₃	M₁₆	1	4	yes	complemented
27	C₄×C₃₇₃	C₂²×C₄	1	2	yes	—
28	Dic₃₇₃	—	2	2	no	—
29	Dic₃₇₃	C₄²	1	2	yes	—
30	C₂×C₃₇₃	C₂×C₄²	1	1	yes	characteristic
31	C₂×C₃₇₃	C₂×M₁₆	1	2	yes	—
32	D₃₇₃	—	2	2	no	—
33	C₃₇₃	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₄×M₁₆	—	373	1	no	maximal, Sylow
35	C₂×M₁₆	—	373	2	no	—
36	C₂×C₄²	—	373	1	no	—
37	#97	—	373	2	no	—
38	C₄×C₈	—	373	1	no	—
39	C₄×C₈	D₃₇₃	1	1	yes	characteristic, complemented
40	C₂²×C₄	—	373	1	no	—
41	C₂²×C₄	—	373	2	no	—
42	M₁₆	—	373	8	no	—
43	C₂×C₈	—	373	2	no	—
44	C₂×C₈	C₂×D₃₇₃	1	2	yes	—
45	C₄²	—	373	2	no	—
46	C₄²	—	373	1	no	—
47	C₄²	C₂×D₃₇₃	1	1	yes	characteristic
48	C₂³	—	373	1	no	—
49	C₂×C₄	—	373	1	no	—
50	C₂×C₄	—	373	4	no	—
51	C₂×C₄	—	373	2	no	—
52	C₂×C₄	—	746	4	no	—
53	C₂×C₄	C₄×D₃₇₃	1	2	yes	—
54	C₂×C₄	C₂²×D₃₇₃	1	1	yes	characteristic
55	C₈	—	373	4	no	—
56	C₈	C₄×D₃₇₃	1	4	yes	complemented
57	C₂²	—	373	2	no	—
58	C₂²	—	746	2	no	—
59	C₂²	C₂×C₄×D₃₇₃	1	1	yes	characteristic
60	C₄	—	373	2	no	—
61	C₄	—	746	2	no	—
62	C₄	#20238593	1	4	yes	direct product factor
63	C₄	C₂×C₄×D₃₇₃	1	2	yes	—
64	C₂	—	746	2	no	—
65	C₂	C₄²×D₃₇₃	1	1	yes	characteristic
66	C₂	C₂×#20238593	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂×D₃₇₃
commutator	C₂×C₃₇₃	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₃₇₃
Fitting	C₄×C₈×C₃₇₃	C₂
socle	C₂²×C₃₇₃	C₂²×C₄
prime radical	C₂²×D₃₇₃	C₂×C₄
cosocle	C₂×C₄×C₃₇₃	C₂³
hypercenter	C₄×C₈	D₃₇₃
hypocenter	C₃₇₃	C₄×M₁₆
LCS	G ▷ C₂×C₃₇₃ ▷ C₃₇₃
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #26045702	C₂	semidirect
4. C₄×#15688412	C₂	semidirect
5. C₄×C₈×C₃₇₃	C₂	semidirect
8. #20238593	C₄	direct (N × H)
19. #15688412	C₂×C₄	semidirect
22. C₈×C₃₇₃	C₂×C₄	semidirect
26. C₄×C₃₇₃	M₁₆	semidirect
33. C₃₇₃	C₄×M₁₆	semidirect
39. C₄×C₈	D₃₇₃	semidirect
56. C₈	C₄×D₃₇₃	semidirect
62. C₄	#20238593	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×#20238593	2
C₄²×D₃₇₃	2
#26045702	2
C₄×#15688412	2
C₄×C₈×C₃₇₃	2
C₄×M₁₆	373

Subgroups — C4×#20238593 #37559372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#20238593 #37559372