Subgroups — #20260499

Order 6208.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13095495	C₂	1	1	yes	maximal, characteristic
2	C₂²×#11715895	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×C₉₇	C₂	1	1	yes	maximal, characteristic
4	#13095495	—	2	1	no	—
5	#13095495	C₄	1	2	yes	—
6	C₂×#11715895	—	2	1	no	—
7	C₂×#11715895	—	2	1	no	—
8	C₂×#11715895	—	2	1	no	—
9	C₂×#11715895	C₄	1	2	yes	—
10	C₂²×C₄×C₉₇	C₂²	1	1	yes	characteristic
11	M₁₆×C₉₇	—	2	1	no	—
12	M₁₆×C₉₇	C₄	1	2	yes	—
13	C₂×C₈×C₉₇	—	2	1	no	—
14	C₂³×C₉₇	Q₈	1	1	yes	characteristic
15	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
19	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
20	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
21	C₈×C₉₇	—	2	2	no	—
22	#11715895	—	2	2	no	—
23	#11715895	—	2	2	no	—
24	C₂²×C₉₇	—	2	2	no	—
25	C₂²×C₉₇	C₄⋊C₄	1	1	yes	characteristic
26	C₂²×C₉₇	C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₉₇	C₄⋊C₄	1	1	yes	characteristic
28	C₄×C₉₇	C₄²	1	1	yes	characteristic
29	C₄×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₄×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₉₇	—	2	1	no	—
33	C₂×C₉₇	—	2	1	no	—
34	C₂×C₉₇	#95	1	1	yes	characteristic
35	C₂×C₉₇	#108	1	2	yes	—
36	C₉₇	#341	1	1	yes	characteristic, complemented, Sylow
37	#341	—	97	1	no	maximal, Sylow
38	C₂×M₁₆	—	97	1	no	—
39	C₂×M₁₆	D₉₇	1	1	yes	characteristic
40	C₂²×C₈	—	97	1	no	—
41	C₂²×C₄	C₂×D₉₇	1	1	yes	characteristic
42	M₁₆	—	2	1	no	—
43	M₁₆	—	97	2	no	—
44	M₁₆	—	194	1	no	—
45	M₁₆	Dic₉₇	1	2	yes	—
46	C₂×C₈	—	2	1	no	—
47	C₂×C₈	—	97	2	no	—
48	C₂×C₈	—	194	1	no	—
49	C₂×C₈	—	194	1	no	—
50	C₂×C₈	—	194	1	no	—
51	C₂³	Dic₁₉₄	1	1	yes	characteristic
52	C₂×C₄	C₄×D₉₇	1	1	yes	characteristic
53	C₂×C₄	C₄×D₉₇	1	1	yes	characteristic
54	C₂×C₄	D₃₈₈	1	1	yes	characteristic
55	C₂×C₄	C₂×Dic₉₇	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
57	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₈	—	194	2	no	—
60	C₈	—	194	2	no	—
61	C₂²	—	2	2	no	—
62	C₂²	#13095490	1	1	yes	characteristic
63	C₂²	#13095490	1	1	yes	characteristic
64	C₂²	C₄⋊Dic₉₇	1	1	yes	characteristic
65	C₄	C₄×Dic₉₇	1	1	yes	characteristic
66	C₄	#13095488	1	1	yes	characteristic
67	C₄	#13095488	1	1	yes	characteristic
68	C₄	C₂²⋊Dic₉₇	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	—	2	1	no	—
71	C₂	#15690717	1	1	yes	characteristic
72	C₂	#15690745	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₉₇
commutator	C₄×C₉₇	C₄²
Frattini	C₂²×C₄	C₂×D₉₇
Fitting	C₂×M₁₆×C₉₇	C₂
socle	C₂²×C₉₇	C₄⋊C₄
hypercenter	C₂×M₁₆	D₉₇
hypocenter	C₉₇	#341
LCS	G ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
36. C₉₇	#341	semidirect