Subgroups — #37560337

Order 23872.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₇₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#26045863	C₂	1	1	yes	maximal, characteristic, complemented
3	#26045815	C₂	1	1	yes	maximal, characteristic
4	#20238620	—	2	1	no	—
5	#20238613	—	2	1	no	—
6	#20238611	—	2	1	no	—
7	#20238597	—	2	1	no	—
8	D₂₉₈₄	C₄	1	1	yes	characteristic
9	C₈×D₃₇₃	C₂²	1	1	yes	characteristic
10	Q₁₆×C₃₇₃	C₄	1	1	yes	characteristic
11	#15688419	—	4	1	no	—
12	D₁₄₉₂	—	2	1	no	—
13	D₁₄₉₂	—	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	—	4	1	no	—
20	C₂×D₃₇₃	SD₁₆	1	1	yes	characteristic
21	C₄×C₃₇₃	—	4	1	no	—
22	C₄×C₃₇₃	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₃₇₃	D₈	1	1	yes	characteristic
24	C₂×C₃₇₃	#102	1	1	yes	characteristic
25	D₃₇₃	—	2	1	no	—
26	D₃₇₃	—	8	1	no	—
27	C₃₇₃	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	373	1	no	maximal, Sylow
29	#135	—	373	1	no	—
30	C₂×C₁₆	—	373	1	no	—
31	#108	—	373	1	no	—
32	#41	—	746	1	no	—
33	Q₁₆	#13093637	1	1	yes	characteristic
34	SD₁₆	—	746	1	no	—
35	D₈	—	373	1	no	—
36	M₁₆	—	746	1	no	—
37	C₂×C₈	—	373	1	no	—
38	C₁₆	—	746	1	no	—
39	Q₈	—	2	1	no	—
40	D₄	—	1492	1	no	—
41	D₄	—	746	1	no	—
42	C₂×C₄	—	373	1	no	—
43	C₂×C₄	—	1492	1	no	—
44	C₈	—	373	1	no	—
45	C₈	—	1492	1	no	—
46	C₈	C₂×#13093637	1	1	yes	characteristic
47	C₂²	—	373	1	no	—
48	C₂²	—	1492	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	373	1	no	—
51	C₄	C₂²⋊#13093637	1	1	yes	characteristic
52	C₂	—	2984	1	no	—
53	C₂	—	746	1	no	—
54	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	#26045815	C₂
cosocle	C₈×D₃₇₃	C₂²
hypercenter	Q₁₆	#13093637
hypocenter	C₃₇₃	#359
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
1. D₃₇₃⋊C₁₆	C₂	semidirect
2. #26045863	C₂	semidirect
27. C₃₇₃	#359	semidirect

Maximal subgroups

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

subgroup	index
D₃₇₃⋊C₁₆	2
#26045863	2
#26045815	2
#359	373