Subgroups — #37560285

Order 23872.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#15688419	C₂	1	2	yes	maximal
2	C₈×Dic₃₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688419	—	2	2	no	—
4	C₂×#15688412	C₄	1	1	yes	characteristic
5	C₄×Dic₃₇₃	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₃₇₃	C₄	1	1	yes	characteristic
7	#15688419	—	4	2	no	—
8	C₂×Dic₃₇₃	D₄	1	1	yes	characteristic
9	C₂×Dic₃₇₃	Q₈	1	1	yes	characteristic
10	#15688412	—	2	1	no	—
11	C₂×C₄×C₃₇₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₇₃	C₈	1	2	yes	complemented
13	C₂²×C₃₇₃	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₃₇₃	C₂×C₈	1	1	yes	characteristic
15	C₄×C₃₇₃	M₁₆	1	1	yes	characteristic
16	Dic₃₇₃	—	2	1	no	—
17	Dic₃₇₃	D₈	1	1	yes	characteristic
18	Dic₃₇₃	Q₁₆	1	1	yes	characteristic
19	C₂×C₃₇₃	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₃₇₃	#107	1	1	yes	characteristic
21	C₂×C₃₇₃	#108	1	1	yes	characteristic
22	C₃₇₃	#335	1	1	yes	characteristic, complemented, Sylow
23	#335	—	373	1	no	maximal, Sylow
24	C₄⋊C₈	—	373	2	no	—
25	C₄×C₈	—	373	1	no	—
26	C₂×C₈	—	373	1	no	—
27	C₂×C₈	—	746	2	no	—
28	C₂×C₈	#13093637	1	1	yes	characteristic
29	C₄²	—	373	1	no	—
30	C₂×C₄	—	373	1	no	—
31	C₂×C₄	—	373	1	no	—
32	C₂×C₄	C₂×#13093637	1	1	yes	characteristic
33	C₈	—	1492	2	no	—
34	C₈	—	746	1	no	—
35	C₈	#15688419	1	2	yes	complemented
36	C₂²	C₄⋊#13093637	1	1	yes	characteristic
37	C₄	—	373	1	no	—
38	C₄	—	373	1	no	—
39	C₄	—	746	1	no	—
40	C₄	C₂×#15688419	1	1	yes	characteristic
41	C₄	#20238620	1	1	yes	characteristic
42	C₂	C₄⋊#15688419	1	1	yes	characteristic
43	C₂	#26045861	1	1	yes	characteristic
44	C₂	#26045863	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#13093637
commutator	C₄×C₃₇₃	C₂×C₈
Frattini	C₂×C₄	C₂×#13093637
Fitting	C₂×C₈×C₃₇₃	C₄
socle, prime radical	C₂²×C₃₇₃	C₄⋊C₄
cosocle	C₄×Dic₃₇₃	C₂²
hypercenter	C₂×C₈	#13093637
hypocenter	C₃₇₃	#335
LCS	G ▷ C₄×C₃₇₃ ▷ C₂×C₃₇₃ ▷ C₃₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
12. C₈×C₃₇₃	C₈	semidirect
22. C₃₇₃	#335	semidirect
35. C₈	#15688419	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
#335	373