Subgroups — #20260940

Order 6208.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13095499	C₂	1	2	yes	maximal
2	#15690810	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊#11715895	C₂	1	1	yes	maximal, characteristic, complemented
4	#15690733	C₂	1	2	yes	maximal, complemented
5	C₄×D₄×C₉₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₉₄	C₂²	1	2	yes	—
7	#13095499	—	2	4	no	—
8	C₂×#11715895	C₂²	1	2	yes	—
9	C₄⋊Dic₉₇	—	2	1	no	—
10	C₄⋊Dic₉₇	—	2	1	no	—
11	C₂×D₄×C₉₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₉₇	—	2	1	no	—
13	C₄⋊C₄×C₉₇	C₂²	1	1	yes	characteristic
14	C₂²⋊C₄×C₉₇	—	2	1	no	—
15	C₄²×C₉₇	C₂²	1	1	yes	characteristic
16	C₂³×C₉₇	—	2	1	no	—
17	D₄×C₉₇	—	2	1	no	—
18	D₄×C₉₇	D₄	1	2	yes	—
19	C₂×C₄×C₉₇	—	2	1	no	—
20	C₂×C₄×C₉₇	—	4	2	no	—
21	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
22	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
23	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
24	C₂×Dic₉₇	—	2	2	no	—
25	Dic₁₉₄	—	2	2	no	—
26	Dic₁₉₄	—	2	2	no	—
27	#11715895	—	2	2	no	—
28	C₂²×C₉₇	—	2	2	no	—
29	C₂²×C₉₇	—	4	1	no	—
30	C₂²×C₉₇	—	4	1	no	—
31	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
32	C₄×C₉₇	—	2	1	no	—
33	C₄×C₉₇	—	4	1	no	—
34	C₄×C₉₇	SD₁₆	1	2	yes	complemented
35	C₄×C₉₇	C₂×D₄	1	1	yes	characteristic
36	C₄×C₉₇	#41	1	1	yes	characteristic
37	Dic₉₇	—	4	2	no	—
38	C₂×C₉₇	—	4	2	no	—
39	C₂×C₉₇	#121	1	1	yes	characteristic
40	C₂×C₉₇	C₂×SD₁₆	1	1	yes	characteristic
41	C₂×C₉₇	#137	1	1	yes	characteristic
42	C₉₇	#461	1	1	yes	characteristic, complemented, Sylow
43	#461	—	97	1	no	maximal, Sylow
44	C₂×SD₁₆	—	97	2	no	—
45	C₄⋊Q₈	—	97	1	no	—
46	C₄×D₄	D₉₇	1	1	yes	characteristic
47	C₄⋊C₈	—	97	1	no	—
48	#103	—	97	2	no	—
49	C₂×Q₈	—	97	2	no	—
50	C₂×D₄	C₂×D₉₇	1	1	yes	characteristic
51	C₂²×C₄	—	2	1	no	—
52	SD₁₆	—	194	4	no	—
53	C₂×C₈	—	97	2	no	—
54	C₄⋊C₄	—	194	1	no	—
55	C₄⋊C₄	—	194	1	no	—
56	C₄⋊C₄	C₂×D₉₇	1	1	yes	characteristic
57	C₂²⋊C₄	—	2	1	no	—
58	C₄²	C₂×D₉₇	1	1	yes	characteristic
59	C₂³	—	2	1	no	—
60	Q₈	—	194	2	no	—
61	Q₈	—	194	2	no	—
62	D₄	—	2	1	no	—
63	D₄	D₃₈₈	1	2	yes	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	—	194	2	no	—
67	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
68	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
69	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
70	C₈	—	194	2	no	—
71	C₂²	—	2	2	no	—
72	C₂²	—	4	1	no	—
73	C₂²	—	4	1	no	—
74	C₂²	C₂×C₂²⋊D₉₇	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	388	2	no	—
78	C₄	#13095499	1	2	yes	complemented
79	C₄	C₂×D₃₈₈	1	1	yes	characteristic
80	C₄	#13095511	1	1	yes	characteristic
81	C₂	—	4	2	no	—
82	C₂	#15690784	1	1	yes	characteristic
83	C₂	C₂×#13095499	1	1	yes	characteristic
84	C₂	#15690840	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₉₇
commutator	C₂×C₄×C₉₇	C₂³
Frattini	C₂×C₄	C₂²×D₉₇
Fitting	C₄×D₄×C₉₇	C₂
socle	C₂²×C₉₇	C₂×D₄
hypercenter	C₄×D₄	D₉₇
hypocenter	C₉₇	#461
LCS	G ▷ C₂×C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. #15690810	C₂	semidirect
3. C₄⋊#11715895	C₂	semidirect
4. #15690733	C₂	semidirect
34. C₄×C₉₇	SD₁₆	semidirect
42. C₉₇	#461	semidirect
78. C₄	#13095499	semidirect