Subgroups — #37560341

Order 23872.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26045867	C₂	1	1	yes	maximal, characteristic
2	#26045862	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×D₃₇₃	C₂	1	1	yes	maximal, characteristic
4	#20238620	—	2	1	no	—
5	#20238613	—	2	1	no	—
6	Q₈×D₃₇₃	—	2	1	no	—
7	Dic₁₄₉₂	C₄	1	1	yes	characteristic
8	#20238600	—	2	1	no	—
9	C₈×D₃₇₃	C₂²	1	1	yes	characteristic
10	Q₁₆×C₃₇₃	C₄	1	1	yes	characteristic
11	#15688419	—	4	1	no	—
12	Dic₇₄₆	—	2	1	no	—
13	Dic₇₄₆	—	4	1	no	—
14	C₄×D₃₇₃	—	4	1	no	—
15	C₄×D₃₇₃	D₄	1	1	yes	characteristic
16	#15688412	D₄	1	1	yes	characteristic
17	Q₈×C₃₇₃	—	2	1	no	—
18	C₈×C₃₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂×D₃₇₃	SD₁₆	1	1	yes	characteristic
20	C₄×C₃₇₃	—	4	1	no	—
21	C₄×C₃₇₃	C₂²⋊C₄	1	1	yes	characteristic
22	Dic₃₇₃	—	4	1	no	—
23	Dic₃₇₃	D₈	1	1	yes	characteristic
24	C₂×C₃₇₃	#102	1	1	yes	characteristic
25	D₃₇₃	—	2	1	no	—
26	C₃₇₃	#362	1	1	yes	characteristic, complemented, Sylow
27	#362	—	373	1	no	maximal, Sylow
28	C₂×Q₁₆	—	373	1	no	—
29	M₃₂	—	373	1	no	—
30	#108	—	373	1	no	—
31	C₂×Q₈	—	746	1	no	—
32	Q₁₆	—	373	1	no	—
33	Q₁₆	—	746	1	no	—
34	Q₁₆	#13093637	1	1	yes	characteristic
35	M₁₆	—	746	1	no	—
36	C₂×C₈	—	373	1	no	—
37	C₁₆	—	746	1	no	—
38	Q₈	—	2	1	no	—
39	Q₈	—	1492	1	no	—
40	Q₈	—	746	1	no	—
41	C₂×C₄	—	373	1	no	—
42	C₂×C₄	—	1492	1	no	—
43	C₈	—	373	1	no	—
44	C₈	—	1492	1	no	—
45	C₈	C₂×#13093637	1	1	yes	characteristic
46	C₂²	—	373	1	no	—
47	C₄	—	4	1	no	—
48	C₄	—	373	1	no	—
49	C₄	—	1492	1	no	—
50	C₄	C₂²⋊#13093637	1	1	yes	characteristic
51	C₂	—	746	1	no	—
52	C₂	#26045854	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26045854
commutator	C₈×C₃₇₃	C₂×C₄
Frattini	C₈	C₂×#13093637
Fitting	Q₁₆×C₃₇₃	C₄
socle	C₂×C₃₇₃	#102
prime radical	C₂×D₃₇₃	SD₁₆
cosocle	C₈×D₃₇₃	C₂²
hypercenter	Q₁₆	#13093637
hypocenter	C₃₇₃	#362
LCS	G ▷ C₈×C₃₇₃ ▷ C₄×C₃₇₃ ▷ C₂×C₃₇₃ ▷ C₃₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
26. C₃₇₃	#362	semidirect

Maximal subgroups

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

subgroup	index
#26045867	2
#26045862	2
Q₁₆×D₃₇₃	2
#362	373