Subgroups — #20261125

Order 6208.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13095498	C₂	1	2	yes	maximal, complemented
2	C₂×#13095496	C₂	1	2	yes	maximal, complemented
3	#15690807	C₂	1	1	yes	maximal, characteristic, complemented
4	#15690721	C₂	1	1	yes	maximal, characteristic, complemented
5	#124×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃₈₈	—	2	2	no	—
7	C₂×D₃₈₈	C₂²	1	2	yes	—
8	#13095498	—	2	4	no	—
9	#13095496	—	2	4	no	—
10	C₂×#11715895	C₂²	1	2	yes	—
11	C₂×Q₈×C₉₇	C₂²	1	1	yes	characteristic
12	C₂×D₄×C₉₇	C₂²	1	1	yes	characteristic
13	C₂²⋊C₄×C₉₇	—	2	2	no	—
14	C₄²×C₉₇	C₂²	1	1	yes	characteristic
15	C₂³×C₉₇	—	2	1	no	—
16	C₂²×D₉₇	—	2	2	no	—
17	Q₈×C₉₇	—	2	2	no	—
18	D₄×C₉₇	—	2	2	no	—
19	C₂×C₄×C₉₇	—	2	1	no	—
20	C₂×C₄×C₉₇	D₄	1	2	yes	—
21	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
22	D₃₈₈	—	2	2	no	—
23	D₃₈₈	—	2	2	no	—
24	D₃₈₈	—	4	4	no	—
25	#11715895	D₄	1	4	yes	complemented
26	C₂²×C₉₇	—	4	1	no	—
27	C₂²×C₉₇	—	4	2	no	—
28	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
29	C₂×D₉₇	—	4	2	no	—
30	C₂×D₉₇	—	4	4	no	—
31	C₄×C₉₇	—	2	2	no	—
32	C₄×C₉₇	—	4	1	no	—
33	C₄×C₉₇	C₂×D₄	1	2	yes	—
34	C₂×C₉₇	—	8	1	no	—
35	C₂×C₉₇	#127	1	1	yes	characteristic
36	C₂×C₉₇	AGL(1,ℤ/8)	1	2	yes	—
37	D₉₇	—	8	2	no	—
38	C₉₇	#496	1	1	yes	characteristic, complemented, Sylow
39	#496	—	97	1	no	maximal, Sylow
40	C₂×SD₁₆	—	97	2	no	—
41	C₂×D₈	—	97	2	no	—
42	#127	—	97	1	no	—
43	#124	D₉₇	1	1	yes	characteristic, complemented
44	#97	—	97	1	no	—
45	C₂×Q₈	C₂×D₉₇	1	1	yes	characteristic
46	C₂×D₄	—	97	2	no	—
47	C₂×D₄	—	194	2	no	—
48	C₂×D₄	C₂×D₉₇	1	1	yes	characteristic
49	SD₁₆	—	194	4	no	—
50	D₈	—	194	4	no	—
51	C₂×C₈	—	97	2	no	—
52	C₂²⋊C₄	—	2	2	no	—
53	C₄²	C₂×D₉₇	1	1	yes	characteristic
54	C₂³	—	2	1	no	—
55	C₂³	—	194	2	no	—
56	Q₈	—	2	2	no	—
57	D₄	—	2	2	no	—
58	D₄	—	388	4	no	—
59	D₄	—	194	2	no	—
60	D₄	—	194	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	C₂²⋊D₉₇	1	2	yes	—
63	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
64	C₈	—	97	4	no	—
65	C₂²	—	4	1	no	—
66	C₂²	—	4	2	no	—
67	C₂²	—	388	2	no	—
68	C₂²	—	388	4	no	—
69	C₂²	C₂×C₂²⋊D₉₇	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	4	1	no	—
72	C₄	D₄×D₉₇	1	2	yes	—
73	C₂	—	8	1	no	—
74	C₂	—	776	2	no	—
75	C₂	#15690806	1	1	yes	characteristic
76	C₂	#15690835	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₉₇
commutator	C₂×C₄×C₉₇	C₂³
Frattini	C₂×C₄	C₂²×D₉₇
Fitting	#124×C₉₇	C₂
socle	C₂²×C₉₇	C₂×D₄
hypercenter	#124	D₉₇
hypocenter	C₉₇	#496
LCS	G ▷ C₂×C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #124

Complements

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

N	H ≅ G/N	type
1. C₂×#13095498	C₂	semidirect
2. C₂×#13095496	C₂	semidirect
3. #15690807	C₂	semidirect
4. #15690721	C₂	semidirect
5. #124×C₉₇	C₂	semidirect
25. #11715895	D₄	semidirect
38. C₉₇	#496	semidirect
43. #124	D₉₇	semidirect