Subgroups — #20261781

Order 6208.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690898	C₂	1	2	yes	maximal, complemented
2	#15690880	C₂	1	1	yes	maximal, characteristic, complemented
3	#15690875	C₂	1	2	yes	maximal, complemented
4	#15690864	C₂	1	1	yes	maximal, characteristic, complemented
5	#15690833	C₂	1	1	yes	maximal, characteristic
6	#13095521	—	2	2	no	—
7	#13095521	C₂²	1	2	yes	—
8	#13095519	—	2	2	no	—
9	#13095519	C₂²	1	1	yes	characteristic
10	C₄×#87604	C₂²	1	1	yes	characteristic
11	#13095512	C₂²	1	2	yes	—
12	#13095498	C₄	1	2	yes	complemented
13	D₇₇₆	C₄	1	1	yes	characteristic, complemented
14	C₈×D₉₇	C₂²	1	1	yes	characteristic
15	Q₁₆×C₉₇	C₄	1	1	yes	characteristic, complemented
16	C₂×#87604	—	2	1	no	—
17	Q₈×C₉₇	C₂×C₄	1	2	yes	—
18	D₃₈₈	—	2	2	no	—
19	D₃₈₈	C₂×C₄	1	2	yes	—
20	C₄×D₉₇	—	2	2	no	—
21	C₄×D₉₇	C₂³	1	1	yes	characteristic
22	#11715897	—	2	2	no	—
23	#11715897	D₄	1	2	yes	—
24	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
25	#11715895	C₂×C₄	1	1	yes	characteristic
26	C₂×D₉₇	—	2	2	no	—
27	C₂×D₉₇	#41	1	1	yes	characteristic
28	#87604	—	4	1	no	—
29	C₄×C₉₇	—	2	2	no	—
30	C₄×C₉₇	C₂²×C₄	1	1	yes	characteristic
31	Dic₉₇	C₂×D₄	1	1	yes	characteristic
32	C₂×C₉₇	C₄×D₄	1	1	yes	characteristic
33	D₉₇	—	2	1	no	—
34	D₉₇	—	4	2	no	—
35	C₉₇	#444	1	1	yes	characteristic, complemented, Sylow
36	#444	—	97	1	no	maximal, Sylow
37	#135	—	97	1	no	—
38	#131	—	97	2	no	—
39	#108	—	97	1	no	—
40	#104	—	97	2	no	—
41	#97	—	97	1	no	—
42	#41	—	97	2	no	—
43	Q₁₆	#87604	1	1	yes	characteristic, complemented
44	SD₁₆	—	97	2	no	—
45	D₈	—	97	1	no	—
46	M₁₆	—	97	2	no	—
47	M₁₆	—	194	2	no	—
48	C₂×C₈	—	97	1	no	—
49	C₂×C₈	—	97	1	no	—
50	C₂×C₈	—	194	2	no	—
51	C₄²	—	97	1	no	—
52	Q₈	C₂×#87604	1	2	yes	—
53	D₄	—	97	2	no	—
54	D₄	—	194	2	no	—
55	C₂×C₄	—	97	1	no	—
56	C₂×C₄	—	194	2	no	—
57	C₂×C₄	—	194	1	no	—
58	C₈	—	97	2	no	—
59	C₈	—	97	1	no	—
60	C₈	—	194	2	no	—
61	C₈	C₂×#87604	1	1	yes	characteristic
62	C₂²	—	97	1	no	—
63	C₂²	—	194	2	no	—
64	C₄	—	2	2	no	—
65	C₄	—	97	1	no	—
66	C₄	—	388	1	no	—
67	C₄	C₂²×#87604	1	1	yes	characteristic
68	C₂	—	388	2	no	—
69	C₂	—	194	1	no	—
70	C₂	D₄×#87604	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#87604
commutator	C₄×C₉₇	C₂²×C₄
Frattini	C₄	C₂²×#87604
Fitting	Q₁₆×C₉₇	C₄
socle	C₂×C₉₇	C₄×D₄
hypercenter	Q₁₆	#87604
hypocenter	C₉₇	#444
LCS	G ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #15690898	C₂	semidirect
2. #15690880	C₂	semidirect
3. #15690875	C₂	semidirect
4. #15690864	C₂	semidirect
12. #13095498	C₄	semidirect
13. D₇₇₆	C₄	semidirect
15. Q₁₆×C₉₇	C₄	semidirect
35. C₉₇	#444	semidirect
43. Q₁₆	#87604	semidirect