Subgroups — #44542332

Order 31904.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30630128	C₂	1	1	yes	maximal, characteristic
2	#30630118	C₂	1	2	yes	maximal, complemented
3	#30630115	C₂	1	2	yes	maximal, complemented
4	#30630112	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₉₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₁₉₉₄	C₂²	1	1	yes	characteristic
7	D₃₉₈₈	C₂²	1	1	yes	characteristic
8	C₂²⋊D₉₉₇	—	2	1	no	—
9	C₄×D₉₉₇	—	2	1	no	—
10	#22547562	C₂²	1	2	yes	—
11	Q₈×C₉₉₇	—	2	1	no	—
12	Q₈×C₉₉₇	C₂²	1	2	yes	—
13	C₂×C₄×C₉₉₇	—	2	1	no	—
14	C₂×C₄×C₉₉₇	C₂²	1	1	yes	characteristic
15	C₂²×C₉₉₇	D₄	1	1	yes	characteristic
16	C₂×D₉₉₇	—	2	1	no	—
17	C₄×C₉₉₇	—	2	2	no	—
18	C₄×C₉₉₇	D₄	1	1	yes	characteristic
19	C₄×C₉₉₇	C₂³	1	1	yes	characteristic
20	Dic₉₉₇	—	2	1	no	—
21	C₂×C₉₉₇	—	2	1	no	—
22	C₂×C₉₉₇	C₂×D₄	1	1	yes	characteristic
23	D₉₉₇	—	4	1	no	—
24	C₉₉₇	#137	1	1	yes	characteristic, complemented, Sylow
25	#137	—	997	1	no	maximal, Sylow
26	#41	—	997	1	no	—
27	C₂×Q₈	D₉₉₇	1	1	yes	characteristic, complemented
28	Q₁₆	—	997	2	no	—
29	SD₁₆	—	997	2	no	—
30	M₁₆	—	997	1	no	—
31	Q₈	—	2	1	no	—
32	Q₈	—	997	1	no	—
33	Q₈	C₂×D₉₉₇	1	2	yes	—
34	D₄	—	1994	1	no	—
35	D₄	—	997	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	1994	1	no	—
38	C₂×C₄	C₂×D₉₉₇	1	1	yes	characteristic
39	C₈	—	997	2	no	—
40	C₂²	—	1994	1	no	—
41	C₂²	C₂²⋊D₉₉₇	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	—	1994	1	no	—
44	C₄	C₂²⋊D₉₉₇	1	1	yes	characteristic
45	C₄	C₂²×D₉₉₇	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	3988	1	no	—
48	C₂	C₂×C₂²⋊D₉₉₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊D₉₉₇
commutator, cosocle	C₄×C₉₉₇	C₂³
Frattini	C₄	C₂²×D₉₉₇
Fitting	C₂×Q₈×C₉₉₇	C₂
socle	C₂×C₉₉₇	C₂×D₄
prime radical	#30630128	C₂
hypercenter	C₂×Q₈	D₉₉₇
hypocenter	C₉₉₇	#137
LCS	G ▷ C₄×C₉₉₇ ▷ C₂×C₉₉₇ ▷ C₉₉₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #30630118	C₂	semidirect
3. #30630115	C₂	semidirect
4. #30630112	C₂	semidirect
5. C₂×Q₈×C₉₉₇	C₂	semidirect
24. C₉₉₇	#137	semidirect
27. C₂×Q₈	D₉₉₇	semidirect

Maximal subgroups

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

subgroup	index
#30630128	2
#30630118	2
#30630115	2
#30630112	2
C₂×Q₈×C₉₉₇	2
#137	997