Subgroups — #20261109

Order 6208.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13095498	C₂	1	4	yes	maximal, complemented
2	#15690807	C₂	1	1	yes	maximal, characteristic
3	C₄×#11715895	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊Q₈×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₃₈₈	—	2	2	no	—
6	C₂×D₃₈₈	C₂²	1	2	yes	—
7	#13095498	—	2	8	no	—
8	C₂×#11715895	C₂²	1	2	yes	—
9	C₂×Q₈×C₉₇	C₂²	1	2	yes	—
10	C₄⋊C₄×C₉₇	—	2	2	no	—
11	C₄²×C₉₇	C₂²	1	1	yes	characteristic
12	C₂²×D₉₇	—	2	2	no	—
13	Q₈×C₉₇	—	2	4	no	—
14	C₂×C₄×C₉₇	—	2	2	no	—
15	C₂×C₄×C₉₇	D₄	1	2	yes	—
16	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
17	D₃₈₈	—	2	4	no	—
18	D₃₈₈	—	4	4	no	—
19	#11715895	D₄	1	4	yes	complemented
20	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
21	C₂×D₉₇	—	4	2	no	—
22	C₂×D₉₇	—	4	4	no	—
23	C₄×C₉₇	—	4	2	no	—
24	C₄×C₉₇	SD₁₆	1	4	yes	complemented
25	C₄×C₉₇	C₂×D₄	1	2	yes	—
26	C₂×C₉₇	#127	1	1	yes	characteristic
27	C₂×C₉₇	C₂×SD₁₆	1	2	yes	—
28	D₉₇	—	8	2	no	—
29	C₉₇	#492	1	1	yes	characteristic, complemented, Sylow
30	#492	—	97	1	no	maximal, Sylow
31	C₂×SD₁₆	—	97	4	no	—
32	C₄⋊Q₈	D₉₇	1	1	yes	characteristic, complemented
33	#127	—	97	1	no	—
34	C₄×C₈	—	97	1	no	—
35	C₂×Q₈	C₂×D₉₇	1	2	yes	—
36	C₂×D₄	—	97	2	no	—
37	C₂×D₄	—	194	2	no	—
38	SD₁₆	—	194	8	no	—
39	C₂×C₈	—	97	2	no	—
40	C₄⋊C₄	—	2	2	no	—
41	C₄²	C₂×D₉₇	1	1	yes	characteristic
42	C₂³	—	194	2	no	—
43	Q₈	—	2	4	no	—
44	D₄	—	388	4	no	—
45	D₄	—	194	4	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	C₂²⋊D₉₇	1	2	yes	—
48	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
49	C₈	—	97	4	no	—
50	C₂²	—	388	2	no	—
51	C₂²	—	388	4	no	—
52	C₂²	C₂×C₂²⋊D₉₇	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	#13095498	1	4	yes	complemented
55	C₄	D₄×D₉₇	1	2	yes	—
56	C₂	—	776	2	no	—
57	C₂	#15690806	1	1	yes	characteristic
58	C₂	C₂×#13095498	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₉₇
commutator	C₂×C₄×C₉₇	C₂³
Frattini	C₂×C₄	C₂²×D₉₇
Fitting	C₄⋊Q₈×C₉₇	C₂
socle	C₂²×C₉₇	C₂×D₄
hypercenter	C₄⋊Q₈	D₉₇
hypocenter	C₉₇	#492
LCS	G ▷ C₂×C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#13095498	C₂	semidirect
3. C₄×#11715895	C₂	semidirect
4. C₄⋊Q₈×C₉₇	C₂	semidirect
19. #11715895	D₄	semidirect
24. C₄×C₉₇	SD₁₆	semidirect
29. C₉₇	#492	semidirect
32. C₄⋊Q₈	D₉₇	semidirect
54. C₄	#13095498	semidirect