Subgroups — #20261577

Order 6208.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11715897	C₂	1	1	yes	maximal, characteristic
2	C₄×#11715897	C₂	1	1	yes	maximal, characteristic
3	C₈×Dic₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#11715897	C₄	1	2	yes	—
5	C₂×#11715897	C₄	1	2	yes	—
6	C₂×#11715895	C₄	1	1	yes	characteristic
7	C₄×Dic₉₇	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₉₇	C₄	1	1	yes	characteristic
9	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₉₇	C₂×C₄	1	1	yes	characteristic
11	C₂×Dic₉₇	C₂×C₄	1	1	yes	characteristic
12	#11715897	—	2	2	no	—
13	#11715897	C₈	1	4	yes	complemented
14	C₈×C₉₇	—	2	1	no	—
15	#11715895	—	2	1	no	—
16	C₂²×C₉₇	C₄²	1	1	yes	characteristic
17	C₄×C₉₇	M₁₆	1	1	yes	characteristic
18	C₄×C₉₇	M₁₆	1	1	yes	characteristic
19	Dic₉₇	C₂×C₈	1	2	yes	—
20	Dic₉₇	M₁₆	1	2	yes	—
21	C₂×C₉₇	C₄×C₈	1	1	yes	characteristic
22	C₂×C₉₇	#97	1	1	yes	characteristic
23	C₂×C₉₇	#97	1	1	yes	characteristic
24	C₉₇	#322	1	1	yes	characteristic, complemented, Sylow
25	#322	—	97	1	no	maximal, Sylow
26	C₄×C₈	—	97	1	no	—
27	C₄×C₈	—	97	1	no	—
28	C₄×C₈	—	97	1	no	—
29	C₂×C₈	—	97	2	no	—
30	C₂×C₈	—	97	2	no	—
31	C₂×C₈	—	97	1	no	—
32	C₂×C₈	#87604	1	1	yes	characteristic
33	C₄²	—	97	1	no	—
34	C₂×C₄	—	97	1	no	—
35	C₂×C₄	—	97	1	no	—
36	C₂×C₄	C₂×#87604	1	1	yes	characteristic
37	C₈	—	2	1	no	—
38	C₈	—	97	4	no	—
39	C₈	—	194	2	no	—
40	C₈	—	194	1	no	—
41	C₂²	C₄×#87604	1	1	yes	characteristic
42	C₄	—	97	2	no	—
43	C₄	—	97	2	no	—
44	C₄	#13095520	1	1	yes	characteristic
45	C₄	#13095521	1	1	yes	characteristic
46	C₂	C₈×#87604	1	1	yes	characteristic
47	C₂	#15690864	1	1	yes	characteristic
48	C₂	#15690865	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#87604
commutator	C₂×C₉₇	C₄×C₈
Fitting	C₂×C₈×C₉₇	C₄
socle	C₂²×C₉₇	C₄²
hypercenter	C₂×C₈	#87604
hypocenter	C₉₇	#322
LCS	G ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
13. #11715897	C₈	semidirect
24. C₉₇	#322	semidirect