Subgroups — #20260944

Order 6208.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₈₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#13095501	C₂	1	1	yes	maximal, characteristic
3	#15690808	C₂	1	1	yes	maximal, characteristic
4	#15690775	C₂	1	1	yes	maximal, characteristic
5	#15690739	C₂	1	1	yes	maximal, characteristic
6	#15690733	C₂	1	1	yes	maximal, characteristic
7	#103×C₉₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₉₄	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₉₄	C₂²	1	1	yes	characteristic
10	Dic₃₈₈	—	2	2	no	—
11	#13095501	—	2	2	no	—
12	C₂×#11715895	C₂²	1	1	yes	characteristic
13	#13095490	—	2	1	no	—
14	#13095490	—	2	1	no	—
15	#13095490	—	2	1	no	—
16	C₄×Dic₉₇	—	2	1	no	—
17	C₄×Dic₉₇	C₂²	1	1	yes	characteristic
18	C₂×Q₈×C₉₇	C₂²	1	1	yes	characteristic
19	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
20	C₄⋊C₄×C₉₇	C₂²	1	1	yes	characteristic
21	Q₈×C₉₇	—	2	1	no	—
22	Q₈×C₉₇	—	2	1	no	—
23	C₂×C₄×C₉₇	—	2	1	no	—
24	C₂×C₄×C₉₇	—	2	1	no	—
25	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
26	C₂×Dic₉₇	—	2	1	no	—
27	C₂×Dic₉₇	—	2	1	no	—
28	C₂×Dic₉₇	D₄	1	1	yes	characteristic
29	C₂×Dic₉₇	D₄	1	1	yes	characteristic
30	Dic₁₉₄	—	2	1	no	—
31	Dic₁₉₄	—	2	1	no	—
32	Dic₁₉₄	—	2	1	no	—
33	Dic₁₉₄	D₄	1	2	yes	—
34	C₈×C₉₇	—	2	1	no	—
35	#11715895	—	2	1	no	—
36	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
37	C₄×C₉₇	—	4	1	no	—
38	C₄×C₉₇	—	4	1	no	—
39	C₄×C₉₇	C₂×D₄	1	1	yes	characteristic
40	C₄×C₉₇	#41	1	1	yes	characteristic
41	Dic₉₇	—	2	2	no	—
42	Dic₉₇	—	2	1	no	—
43	Dic₉₇	—	4	1	no	—
44	Dic₉₇	Q₁₆	1	2	yes	complemented
45	C₂×C₉₇	#121	1	1	yes	characteristic
46	C₂×C₉₇	C₂×Q₁₆	1	1	yes	characteristic
47	C₂×C₉₇	#137	1	1	yes	characteristic
48	C₉₇	#462	1	1	yes	characteristic, complemented, Sylow
49	#462	—	97	1	no	maximal, Sylow
50	C₂×Q₁₆	—	97	1	no	—
51	C₂×Q₁₆	—	97	1	no	—
52	C₄⋊Q₈	—	97	1	no	—
53	C₄×Q₈	—	97	1	no	—
54	C₄⋊C₈	—	97	1	no	—
55	#103	—	97	1	no	—
56	#103	D₉₇	1	1	yes	characteristic
57	C₂×Q₈	—	97	1	no	—
58	C₂×Q₈	—	97	1	no	—
59	C₂×Q₈	C₂×D₉₇	1	1	yes	characteristic
60	Q₁₆	—	194	2	no	—
61	Q₁₆	—	194	2	no	—
62	C₂×C₈	—	97	1	no	—
63	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
64	C₄⋊C₄	—	194	1	no	—
65	C₄⋊C₄	—	194	1	no	—
66	C₄⋊C₄	—	194	1	no	—
67	C₄⋊C₄	C₂×D₉₇	1	1	yes	characteristic
68	C₄²	—	97	1	no	—
69	C₄²	—	194	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	2	1	no	—
72	Q₈	—	97	2	no	—
73	Q₈	—	194	1	no	—
74	Q₈	—	194	1	no	—
75	Q₈	—	194	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	97	1	no	—
79	C₂×C₄	—	97	1	no	—
80	C₂×C₄	—	194	1	no	—
81	C₂×C₄	—	194	1	no	—
82	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	194	1	no	—
85	C₂²	D₄×D₉₇	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	97	2	no	—
89	C₄	—	388	1	no	—
90	C₄	—	194	2	no	—
91	C₄	—	194	1	no	—
92	C₄	D₄×D₉₇	1	1	yes	characteristic
93	C₄	#13095511	1	1	yes	characteristic
94	C₂	#15690783	1	1	yes	characteristic
95	C₂	Q₁₆×D₉₇	1	1	yes	characteristic
96	C₂	#15690839	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₉₇
commutator	C₂×C₄×C₉₇	C₂³
Frattini	C₂×C₄	C₂²×D₉₇
Fitting	#103×C₉₇	C₂
socle	C₂²×C₉₇	C₂×D₄
hypercenter	#103	D₉₇
hypocenter	C₉₇	#462
LCS	G ▷ C₂×C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
44. Dic₉₇	Q₁₆	semidirect
48. C₉₇	#462	semidirect