Subgroups — #15688419⋊C₈ #37560264

Order 23872.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#15688419	C₂	1	1	yes	maximal, characteristic
2	C₄×#15688419	C₂	1	1	yes	maximal, characteristic
3	C₈×Dic₃₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688419	C₄	1	2	yes	—
5	C₂×#15688419	C₄	1	2	yes	—
6	C₂×#15688412	C₄	1	1	yes	characteristic
7	C₄×Dic₃₇₃	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₃₇₃	C₄	1	1	yes	characteristic
9	#15688419	—	2	2	no	—
10	#15688419	C₈	1	4	yes	complemented
11	C₂×Dic₃₇₃	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₃₇₃	C₂×C₄	1	1	yes	characteristic
13	#15688412	—	2	1	no	—
14	C₂×C₄×C₃₇₃	C₂×C₄	1	1	yes	characteristic
15	C₈×C₃₇₃	—	2	1	no	—
16	C₂²×C₃₇₃	C₄²	1	1	yes	characteristic
17	C₄×C₃₇₃	M₁₆	1	1	yes	characteristic
18	C₄×C₃₇₃	M₁₆	1	1	yes	characteristic
19	Dic₃₇₃	C₂×C₈	1	2	yes	—
20	Dic₃₇₃	M₁₆	1	2	yes	—
21	C₂×C₃₇₃	C₄×C₈	1	1	yes	characteristic
22	C₂×C₃₇₃	#97	1	1	yes	characteristic
23	C₂×C₃₇₃	#97	1	1	yes	characteristic
24	C₃₇₃	#322	1	1	yes	characteristic, complemented, Sylow
25	#322	—	373	1	no	maximal, Sylow
26	C₄×C₈	—	373	1	no	—
27	C₄×C₈	—	373	1	no	—
28	C₄×C₈	—	373	1	no	—
29	C₂×C₈	—	373	2	no	—
30	C₂×C₈	—	373	2	no	—
31	C₂×C₈	—	373	1	no	—
32	C₂×C₈	#13093637	1	1	yes	characteristic
33	C₄²	—	373	1	no	—
34	C₂×C₄	—	373	1	no	—
35	C₂×C₄	—	373	1	no	—
36	C₂×C₄	C₂×#13093637	1	1	yes	characteristic
37	C₈	—	2	1	no	—
38	C₈	—	373	4	no	—
39	C₈	—	746	2	no	—
40	C₈	—	746	1	no	—
41	C₂²	C₄×#13093637	1	1	yes	characteristic
42	C₄	—	373	2	no	—
43	C₄	—	373	2	no	—
44	C₄	#20238619	1	1	yes	characteristic
45	C₄	#20238620	1	1	yes	characteristic
46	C₂	C₈×#13093637	1	1	yes	characteristic
47	C₂	#26045846	1	1	yes	characteristic
48	C₂	#26045847	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#13093637
commutator	C₂×C₃₇₃	C₄×C₈
Fitting	C₂×C₈×C₃₇₃	C₄
socle, prime radical	C₂²×C₃₇₃	C₄²
cosocle	C₄×Dic₃₇₃	C₂²
hypercenter	C₂×C₈	#13093637
hypocenter	C₃₇₃	#322
LCS	G ▷ C₂×C₃₇₃ ▷ C₃₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
10. #15688419	C₈	semidirect
24. C₃₇₃	#322	semidirect

Maximal subgroups

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

subgroup	index
C₄×#15688419	2
C₈×Dic₃₇₃	2
#322	373

Subgroups — #15688419⋊C8 #37560264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #15688419⋊C₈ #37560264