Subgroups — #20260776

Order 6208.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13095494	C₂	1	1	yes	maximal, characteristic
2	#15690768	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×D₉₇	C₂	1	1	yes	maximal, characteristic
4	#15690743	C₂	1	1	yes	maximal, characteristic, complemented
5	#15690742	C₂	1	1	yes	maximal, characteristic, complemented
6	#15690741	C₂	1	1	yes	maximal, characteristic, complemented
7	#107×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₉₇	—	2	1	no	—
9	C₂×C₄×D₉₇	C₂²	1	1	yes	characteristic
10	#13095494	C₄	1	4	yes	complemented
11	C₂×#11715895	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₉₇	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₉₇	C₂²	1	1	yes	characteristic
14	#13095490	—	2	1	no	—
15	#13095488	—	2	1	no	—
16	C₄×Dic₉₇	—	2	1	no	—
17	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₉₇	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×C₉₇	C₂²	1	1	yes	characteristic
20	C₂²×D₉₇	D₄	1	1	yes	characteristic
21	C₂×C₄×C₉₇	—	2	1	no	—
22	C₂×C₄×C₉₇	—	2	1	no	—
23	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
24	C₂×Dic₉₇	—	2	1	no	—
25	C₂×Dic₉₇	—	2	1	no	—
26	C₂×Dic₉₇	D₄	1	1	yes	characteristic
27	C₄×D₉₇	—	4	2	no	—
28	C₄×D₉₇	C₂×C₄	1	2	yes	—
29	C₄×D₉₇	Q₈	1	2	yes	—
30	C₈×C₉₇	C₂×C₄	1	2	yes	complemented
31	#11715895	C₂×C₄	1	2	yes	complemented
32	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
33	C₂×D₉₇	—	2	1	no	—
34	C₂×D₉₇	—	2	1	no	—
35	C₂×D₉₇	C₄⋊C₄	1	2	yes	—
36	C₄×C₉₇	—	4	1	no	—
37	C₄×C₉₇	—	4	1	no	—
38	C₄×C₉₇	C₂²×C₄	1	1	yes	characteristic
39	C₄×C₉₇	C₂×Q₈	1	1	yes	characteristic
40	Dic₉₇	—	4	1	no	—
41	Dic₉₇	—	4	1	no	—
42	Dic₉₇	C₄⋊C₄	1	2	yes	—
43	C₂×C₉₇	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₉₇	AGL(1,ℤ/8)	1	1	yes	characteristic
45	C₂×C₉₇	#137	1	1	yes	characteristic
46	D₉₇	—	2	2	no	—
47	C₉₇	#428	1	1	yes	characteristic, complemented, Sylow
48	#428	—	97	1	no	maximal, Sylow
49	C₂×M₁₆	—	97	1	no	—
50	#117	—	97	1	no	—
51	C₂×C₄⋊C₄	—	97	1	no	—
52	#107	—	97	1	no	—
53	#107	D₉₇	1	1	yes	characteristic, complemented
54	#106	—	97	1	no	—
55	#106	—	97	1	no	—
56	C₂²×C₄	—	97	1	no	—
57	C₂²×C₄	—	194	1	no	—
58	M₁₆	—	97	4	no	—
59	C₂×C₈	—	97	1	no	—
60	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
61	C₄⋊C₄	—	97	1	no	—
62	C₄⋊C₄	—	97	1	no	—
63	C₄⋊C₄	—	194	1	no	—
64	C₄⋊C₄	C₂×D₉₇	1	1	yes	characteristic
65	C₄⋊C₄	C₂×D₉₇	1	1	yes	characteristic
66	C₂²⋊C₄	—	194	1	no	—
67	C₄²	—	194	1	no	—
68	C₂³	—	97	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	97	1	no	—
72	C₂×C₄	—	97	2	no	—
73	C₂×C₄	—	97	2	no	—
74	C₂×C₄	—	388	2	no	—
75	C₂×C₄	—	194	1	no	—
76	C₂×C₄	—	194	1	no	—
77	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
78	C₈	—	97	2	no	—
79	C₈	C₄×D₉₇	1	2	yes	complemented
80	C₂²	—	97	2	no	—
81	C₂²	—	194	1	no	—
82	C₂²	—	194	1	no	—
83	C₂²	D₄×D₉₇	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	97	2	no	—
87	C₄	—	388	1	no	—
88	C₄	—	388	1	no	—
89	C₄	C₂×C₄×D₉₇	1	1	yes	characteristic
90	C₄	Q₈×D₉₇	1	1	yes	characteristic
91	C₂	—	194	2	no	—
92	C₂	C₄⋊C₄×D₉₇	1	1	yes	characteristic
93	C₂	#15690834	1	1	yes	characteristic
94	C₂	#15690842	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₉₇
commutator	C₄×C₉₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₉₇
Fitting	#107×C₉₇	C₂
socle	C₂²×C₉₇	C₂×D₄
hypercenter	#107	D₉₇
hypocenter	C₉₇	#428
LCS	G ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
4. #15690743	C₂	semidirect
5. #15690742	C₂	semidirect
6. #15690741	C₂	semidirect
7. #107×C₉₇	C₂	semidirect
10. #13095494	C₄	semidirect
30. C₈×C₉₇	C₂×C₄	semidirect
31. #11715895	C₂×C₄	semidirect
47. C₉₇	#428	semidirect
53. #107	D₉₇	semidirect
79. C₈	C₄×D₉₇	semidirect