Subgroups — #20261064

Order 6208.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690786	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₉₇	C₂	1	1	yes	maximal, characteristic
3	#15690742	C₂	1	1	yes	maximal, characteristic, complemented
4	#15690741	C₂	1	1	yes	maximal, characteristic, complemented
5	#15690734	C₂	1	1	yes	maximal, characteristic, complemented
6	#15690722	C₂	1	1	yes	maximal, characteristic
7	#103×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	C₂×#11715895	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₉₇	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₉₇	C₂²	1	1	yes	characteristic
13	#13095490	—	2	1	no	—
14	#13095490	—	2	1	no	—
15	#13095488	—	2	1	no	—
16	C₂×Q₈×C₉₇	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₉₇	C₂²	1	1	yes	characteristic
19	C₂²×D₉₇	D₄	1	1	yes	characteristic
20	Q₈×C₉₇	—	2	1	no	—
21	Q₈×C₉₇	—	2	1	no	—
22	C₂×C₄×C₉₇	—	2	1	no	—
23	C₂×C₄×C₉₇	—	2	1	no	—
24	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
25	C₂×Dic₉₇	—	2	1	no	—
26	C₂×Dic₉₇	—	2	1	no	—
27	C₂×Dic₉₇	D₄	1	1	yes	characteristic
28	C₄×D₉₇	—	2	1	no	—
29	C₄×D₉₇	—	2	1	no	—
30	C₄×D₉₇	—	4	2	no	—
31	C₈×C₉₇	—	2	1	no	—
32	#11715895	—	2	1	no	—
33	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
34	C₂×D₉₇	—	2	1	no	—
35	C₂×D₉₇	—	2	1	no	—
36	C₂×D₉₇	SD₁₆	1	2	yes	—
37	C₄×C₉₇	—	4	1	no	—
38	C₄×C₉₇	—	4	1	no	—
39	C₄×C₉₇	#41	1	1	yes	characteristic
40	C₄×C₉₇	#41	1	1	yes	characteristic
41	Dic₉₇	—	2	1	no	—
42	Dic₉₇	—	4	1	no	—
43	Dic₉₇	—	4	1	no	—
44	C₂×C₉₇	#123	1	1	yes	characteristic
45	C₂×C₉₇	C₂×SD₁₆	1	1	yes	characteristic
46	C₂×C₉₇	#137	1	1	yes	characteristic
47	D₉₇	—	2	2	no	—
48	C₉₇	#483	1	1	yes	characteristic, complemented, Sylow
49	#483	—	97	1	no	maximal, Sylow
50	C₂²⋊Q₈	—	97	1	no	—
51	C₂×C₄⋊C₄	—	97	1	no	—
52	#106	—	97	1	no	—
53	#106	—	97	1	no	—
54	#103	—	97	1	no	—
55	#103	D₉₇	1	1	yes	characteristic, complemented
56	C₂²⋊C₈	—	97	1	no	—
57	C₂×Q₈	C₂×D₉₇	1	1	yes	characteristic
58	C₂²×C₄	—	97	1	no	—
59	C₂²×C₄	—	194	1	no	—
60	C₂×C₈	—	97	1	no	—
61	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
62	C₄⋊C₄	—	97	1	no	—
63	C₄⋊C₄	—	97	1	no	—
64	C₄⋊C₄	—	194	1	no	—
65	C₄⋊C₄	—	194	1	no	—
66	C₄⋊C₄	C₂×D₉₇	1	1	yes	characteristic
67	C₂²⋊C₄	—	194	1	no	—
68	C₂³	—	97	1	no	—
69	Q₈	—	2	1	no	—
70	Q₈	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	97	1	no	—
74	C₂×C₄	—	388	2	no	—
75	C₂×C₄	—	194	1	no	—
76	C₂×C₄	—	194	1	no	—
77	C₂×C₄	—	194	1	no	—
78	C₂×C₄	—	194	1	no	—
79	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	194	1	no	—
82	C₂²	—	97	2	no	—
83	C₂²	—	194	1	no	—
84	C₂²	—	194	1	no	—
85	C₂²	D₄×D₉₇	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	388	1	no	—
89	C₄	—	388	1	no	—
90	C₄	—	194	1	no	—
91	C₄	#13095510	1	1	yes	characteristic
92	C₄	#13095511	1	1	yes	characteristic
93	C₂	—	194	2	no	—
94	C₂	#15690792	1	1	yes	characteristic
95	C₂	SD₁₆×D₉₇	1	1	yes	characteristic
96	C₂	#15690842	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	#483
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
3. #15690742	C₂	semidirect
4. #15690741	C₂	semidirect
5. #15690734	C₂	semidirect
7. #103×C₉₇	C₂	semidirect
48. C₉₇	#483	semidirect
55. #103	D₉₇	semidirect