Subgroups — #20260490

Order 6208.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11715895	C₂	1	2	yes	maximal
2	C₂×C₄²×C₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#11715895	—	2	2	no	—
4	C₂×#11715895	—	2	2	no	—
5	C₂×#11715895	C₄	1	4	yes	complemented
6	C₂²×C₄×C₉₇	C₄	1	2	yes	—
7	C₂²×C₄×C₉₇	C₂²	1	1	yes	characteristic
8	C₄²×C₉₇	—	2	2	no	—
9	C₂³×C₉₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₉₇	—	2	2	no	—
11	C₂×C₄×C₉₇	—	2	2	no	—
12	C₂×C₄×C₉₇	C₈	1	4	yes	complemented
13	C₂×C₄×C₉₇	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
15	C₂×C₄×C₉₇	D₄	1	2	yes	—
16	C₂×C₄×C₉₇	Q₈	1	1	yes	characteristic
17	#11715895	—	2	4	no	—
18	C₂²×C₉₇	C₄²	1	1	yes	characteristic
19	C₂²×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₂²×C₉₇	C₄⋊C₄	1	1	yes	characteristic
21	C₂²×C₉₇	C₂×C₈	1	2	yes	—
22	C₂²×C₉₇	M₁₆	1	2	yes	—
23	C₄×C₉₇	—	2	4	no	—
24	C₄×C₉₇	C₂²⋊C₄	1	2	yes	—
25	C₄×C₉₇	C₄⋊C₄	1	2	yes	—
26	C₂×C₉₇	#95	1	1	yes	characteristic
27	C₂×C₉₇	C₄×C₈	1	1	yes	characteristic
28	C₂×C₉₇	#97	1	1	yes	characteristic
29	C₂×C₉₇	C₂²⋊C₈	1	2	yes	—
30	C₂×C₉₇	C₄⋊C₈	1	2	yes	—
31	C₉₇	#336	1	1	yes	characteristic, complemented, Sylow
32	#336	—	97	1	no	maximal, Sylow
33	C₂²×C₈	—	97	2	no	—
34	C₂×C₄²	D₉₇	1	1	yes	characteristic
35	C₂²×C₄	Dic₉₇	1	2	yes	—
36	C₂²×C₄	C₂×D₉₇	1	1	yes	characteristic
37	C₂×C₈	—	97	4	no	—
38	C₂×C₈	—	194	2	no	—
39	C₂×C₈	—	194	2	no	—
40	C₄²	—	2	2	no	—
41	C₂³	C₂×Dic₉₇	1	1	yes	characteristic
42	C₂×C₄	—	2	2	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	#11715895	1	4	yes	complemented
45	C₂×C₄	Dic₁₉₄	1	1	yes	characteristic
46	C₂×C₄	C₄×D₉₇	1	2	yes	—
47	C₂×C₄	D₃₈₈	1	1	yes	characteristic
48	C₂×C₄	C₂²⋊D₉₇	1	2	yes	—
49	C₈	—	194	4	no	—
50	C₂²	C₄×Dic₉₇	1	1	yes	characteristic
51	C₂²	C₂²⋊Dic₉₇	1	1	yes	characteristic
52	C₂²	C₄⋊Dic₉₇	1	1	yes	characteristic
53	C₂²	C₂×#11715895	1	2	yes	—
54	C₂²	#13095495	1	2	yes	—
55	C₄	—	2	4	no	—
56	C₄	#13095488	1	2	yes	—
57	C₄	#13095490	1	2	yes	—
58	C₂	#15690717	1	1	yes	characteristic
59	C₂	C₄×#11715895	1	1	yes	characteristic
60	C₂	#15690721	1	1	yes	characteristic
61	C₂	C₂²⋊#11715895	1	2	yes	—
62	C₂	C₄⋊#11715895	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×D₉₇
commutator	C₂×C₉₇	C₄×C₈
Fitting	C₂×C₄²×C₉₇	C₂
socle	C₂³×C₉₇	C₂×C₄
hypercenter	C₂×C₄²	D₉₇
hypocenter	C₉₇	#336
LCS	G ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
5. C₂×#11715895	C₄	semidirect
12. C₂×C₄×C₉₇	C₈	semidirect
31. C₉₇	#336	semidirect
44. C₂×C₄	#11715895	semidirect