Subgroups — #20260497

Order 6208.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11715895	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₄×C₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₉₇	—	2	1	no	—
5	C₂×#11715895	—	2	1	no	—
6	C₂×#11715895	—	2	1	no	—
7	C₂×#11715895	C₄	1	2	yes	complemented
8	C₄⋊Dic₉₇	—	2	1	no	—
9	C₄⋊Dic₉₇	C₄	1	2	yes	complemented
10	C₂²×C₄×C₉₇	—	2	1	no	—
11	C₂²×C₄×C₉₇	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₉₇	—	2	1	no	—
13	C₄⋊C₄×C₉₇	C₄	1	2	yes	complemented
14	C₂³×C₉₇	D₄	1	1	yes	characteristic
15	C₂×C₄×C₉₇	—	2	2	no	—
16	C₂×C₄×C₉₇	—	4	1	no	—
17	C₂×C₄×C₉₇	—	4	1	no	—
18	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
22	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
23	C₂×C₄×C₉₇	Q₈	1	1	yes	characteristic
24	C₂×Dic₉₇	—	2	2	no	—
25	C₂×Dic₉₇	—	4	1	no	—
26	C₂×Dic₉₇	—	4	1	no	—
27	#11715895	—	2	2	no	—
28	C₂²×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₉₇	C₄⋊C₄	1	1	yes	characteristic
31	C₂²×C₉₇	D₈	1	1	yes	characteristic
32	C₂²×C₉₇	SD₁₆	1	1	yes	characteristic
33	C₂²×C₉₇	SD₁₆	1	1	yes	characteristic
34	C₂²×C₉₇	Q₁₆	1	1	yes	characteristic
35	C₄×C₉₇	—	4	2	no	—
36	C₄×C₉₇	C₄²	1	1	yes	characteristic
37	C₄×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
38	C₄×C₉₇	C₄⋊C₄	1	1	yes	characteristic
39	C₄×C₉₇	C₄⋊C₄	1	1	yes	characteristic
40	Dic₉₇	—	4	2	no	—
41	C₂×C₉₇	#95	1	1	yes	characteristic
42	C₂×C₉₇	#102	1	1	yes	characteristic
43	C₂×C₉₇	#102	1	1	yes	characteristic
44	C₂×C₉₇	#103	1	1	yes	characteristic
45	C₂×C₉₇	#103	1	1	yes	characteristic
46	C₂×C₉₇	#106	1	1	yes	characteristic
47	C₂×C₉₇	#107	1	1	yes	characteristic
48	C₉₇	#340	1	1	yes	characteristic, complemented, Sylow
49	#340	—	97	1	no	maximal, Sylow
50	C₂²×C₈	—	97	1	no	—
51	C₂×C₄⋊C₄	—	97	1	no	—
52	C₂×C₄⋊C₄	D₉₇	1	1	yes	characteristic
53	C₂²×C₄	—	2	1	no	—
54	C₂²×C₄	—	194	1	no	—
55	C₂²×C₄	C₂×D₉₇	1	1	yes	characteristic
56	C₂×C₈	—	97	2	no	—
57	C₂×C₈	—	194	1	no	—
58	C₂×C₈	—	194	1	no	—
59	C₄⋊C₄	—	2	1	no	—
60	C₄⋊C₄	—	97	2	no	—
61	C₄⋊C₄	—	194	1	no	—
62	C₄⋊C₄	Dic₉₇	1	2	yes	complemented
63	C₂³	C₂²⋊D₉₇	1	1	yes	characteristic
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	4	1	no	—
66	C₂×C₄	—	4	1	no	—
67	C₂×C₄	—	388	1	no	—
68	C₂×C₄	—	388	1	no	—
69	C₂×C₄	—	194	2	no	—
70	C₂×C₄	Dic₁₉₄	1	1	yes	characteristic
71	C₂×C₄	C₄×D₉₇	1	1	yes	characteristic
72	C₂×C₄	C₄×D₉₇	1	1	yes	characteristic
73	C₂×C₄	D₃₈₈	1	1	yes	characteristic
74	C₂×C₄	C₂×Dic₉₇	1	1	yes	characteristic
75	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
76	C₈	—	194	2	no	—
77	C₂²	#13095488	1	1	yes	characteristic
78	C₂²	C₂²⋊Dic₉₇	1	1	yes	characteristic
79	C₂²	#13095490	1	1	yes	characteristic
80	C₂²	#13095496	1	1	yes	characteristic
81	C₂²	#13095498	1	1	yes	characteristic
82	C₂²	#13095499	1	1	yes	characteristic
83	C₂²	#13095501	1	1	yes	characteristic
84	C₄	—	4	2	no	—
85	C₄	—	388	2	no	—
86	C₄	C₄×Dic₉₇	1	1	yes	characteristic
87	C₄	#13095488	1	1	yes	characteristic
88	C₄	#13095490	1	1	yes	characteristic
89	C₄	C₄⋊Dic₉₇	1	1	yes	characteristic
90	C₂	#15690717	1	1	yes	characteristic
91	C₂	#15690730	1	1	yes	characteristic
92	C₂	#15690731	1	1	yes	characteristic
93	C₂	#15690733	1	1	yes	characteristic
94	C₂	#15690734	1	1	yes	characteristic
95	C₂	#15690741	1	1	yes	characteristic
96	C₂	#15690743	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₉₇
commutator	C₄×C₉₇	C₄²
Frattini	C₂²×C₄	C₂×D₉₇
Fitting	C₂×C₄⋊C₄×C₉₇	C₂
socle	C₂³×C₉₇	D₄
hypercenter	C₂×C₄⋊C₄	D₉₇
hypocenter	C₉₇	#340
LCS	G ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
7. C₂×#11715895	C₄	semidirect
9. C₄⋊Dic₉₇	C₄	semidirect
13. C₄⋊C₄×C₉₇	C₄	semidirect
48. C₉₇	#340	semidirect
62. C₄⋊C₄	Dic₉₇	semidirect