Subgroups — #20260908

Order 6208.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690835	C₂	1	2	yes	maximal, complemented
2	#15690799	C₂	1	1	yes	maximal, characteristic, complemented
3	#15690737	C₂	1	2	yes	maximal, complemented
4	#15690729	C₂	1	1	yes	maximal, characteristic, complemented
5	2₋¹⁺⁴×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃₈₈	C₂²	1	1	yes	characteristic
7	#13095498	—	2	2	no	—
8	#13095496	—	2	2	no	—
9	#13095495	C₂²	1	2	yes	—
10	#13095488	—	2	2	no	—
11	C₄×Dic₉₇	C₂²	1	1	yes	characteristic
12	#41×C₉₇	—	2	2	no	—
13	#41×C₉₇	—	2	2	no	—
14	#41×C₉₇	C₂²	1	2	yes	—
15	C₂×Q₈×C₉₇	—	2	2	no	—
16	C₂×Q₈×C₉₇	C₂²	1	1	yes	characteristic
17	C₂²×D₉₇	—	2	1	no	—
18	Q₈×C₉₇	—	2	2	no	—
19	Q₈×C₉₇	—	2	2	no	—
20	Q₈×C₉₇	D₄	1	2	yes	—
21	D₄×C₉₇	—	2	2	no	—
22	D₄×C₉₇	—	2	2	no	—
23	D₄×C₉₇	D₄	1	2	yes	—
24	C₂×C₄×C₉₇	—	2	4	no	—
25	C₂×C₄×C₉₇	—	2	2	no	—
26	C₂×C₄×C₉₇	D₄	1	2	yes	—
27	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
28	C₂×Dic₉₇	—	2	1	no	—
29	D₃₈₈	—	2	2	no	—
30	#11715895	—	2	2	no	—
31	C₂²×C₉₇	—	2	2	no	—
32	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
33	C₂×D₉₇	—	4	2	no	—
34	C₂×D₉₇	—	4	1	no	—
35	C₄×C₉₇	—	2	2	no	—
36	C₄×C₉₇	—	2	2	no	—
37	C₄×C₉₇	C₂×D₄	1	2	yes	—
38	Dic₉₇	—	4	1	no	—
39	C₂×C₉₇	—	2	1	no	—
40	C₂×C₉₇	—	4	2	no	—
41	C₂×C₉₇	#120	1	1	yes	characteristic
42	D₉₇	—	8	1	no	—
43	C₉₇	#454	1	1	yes	characteristic, complemented, Sylow
44	#454	—	97	1	no	maximal, Sylow
45	2₋¹⁺⁴	D₉₇	1	1	yes	characteristic, complemented
46	AGL(1,ℤ/8)	—	97	2	no	—
47	#124	—	97	1	no	—
48	#104	—	97	2	no	—
49	#101	—	97	1	no	—
50	#41	—	2	2	no	—
51	#41	—	2	2	no	—
52	#41	C₂×D₉₇	1	2	yes	—
53	C₂×Q₈	—	2	2	no	—
54	C₂×Q₈	C₂×D₉₇	1	1	yes	characteristic
55	C₂×D₄	—	97	1	no	—
56	SD₁₆	—	194	2	no	—
57	D₈	—	194	2	no	—
58	M₁₆	—	97	2	no	—
59	C₂²⋊C₄	—	194	2	no	—
60	C₄²	—	97	1	no	—
61	C₂³	—	194	1	no	—
62	Q₈	—	2	2	no	—
63	Q₈	—	2	2	no	—
64	Q₈	C₂²⋊D₉₇	1	2	yes	—
65	D₄	—	2	2	no	—
66	D₄	—	2	2	no	—
67	D₄	—	194	2	no	—
68	D₄	C₂²⋊D₉₇	1	2	yes	—
69	C₂×C₄	—	2	4	no	—
70	C₂×C₄	—	2	2	no	—
71	C₂×C₄	—	194	1	no	—
72	C₂×C₄	C₂²⋊D₉₇	1	2	yes	—
73	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
74	C₈	—	194	2	no	—
75	C₂²	—	2	2	no	—
76	C₂²	—	388	2	no	—
77	C₂²	—	388	1	no	—
78	C₂²	C₂×C₂²⋊D₉₇	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	—	2	2	no	—
81	C₄	—	388	1	no	—
82	C₄	C₂×C₂²⋊D₉₇	1	2	yes	—
83	C₂	—	2	1	no	—
84	C₂	—	4	2	no	—
85	C₂	—	776	1	no	—
86	C₂	#15690779	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15690779
commutator	C₂×C₄×C₉₇	C₂³
Frattini	C₂×C₄	C₂²×D₉₇
Fitting	2₋¹⁺⁴×C₉₇	C₂
socle	C₂×C₉₇	#120
hypercenter	2₋¹⁺⁴	D₉₇
hypocenter	C₉₇	#454
LCS	G ▷ C₂×C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ 2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. #15690835	C₂	semidirect
2. #15690799	C₂	semidirect
3. #15690737	C₂	semidirect
4. #15690729	C₂	semidirect
5. 2₋¹⁺⁴×C₉₇	C₂	semidirect
43. C₉₇	#454	semidirect
45. 2₋¹⁺⁴	D₉₇	semidirect