Subgroups — #20260937

Order 6208.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13095498	C₂	1	2	yes	maximal
2	C₄×D₃₈₈	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11715895	C₂	1	1	yes	maximal, characteristic, complemented
4	#15690734	C₂	1	2	yes	maximal, complemented
5	C₄⋊Q₈×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃₈₈	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₉₇	—	2	1	no	—
8	#13095498	—	2	4	no	—
9	C₂×#11715895	C₂²	1	2	yes	—
10	C₄⋊Dic₉₇	C₂²	1	1	yes	characteristic
11	#13095488	—	2	1	no	—
12	C₂×Q₈×C₉₇	C₂²	1	2	yes	—
13	C₄⋊C₄×C₉₇	—	2	1	no	—
14	C₄⋊C₄×C₉₇	—	2	1	no	—
15	C₄²×C₉₇	C₂²	1	1	yes	characteristic
16	C₂²×D₉₇	—	2	1	no	—
17	Q₈×C₉₇	—	2	2	no	—
18	Q₈×C₉₇	—	2	2	no	—
19	C₂×C₄×C₉₇	—	2	2	no	—
20	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
21	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
22	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
23	C₂×Dic₉₇	—	2	1	no	—
24	D₃₈₈	—	2	1	no	—
25	D₃₈₈	D₄	1	2	yes	—
26	C₄×D₉₇	—	4	2	no	—
27	#11715895	—	2	2	no	—
28	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
29	C₂×D₉₇	—	2	2	no	—
30	C₂×D₉₇	—	4	1	no	—
31	C₂×D₉₇	—	4	1	no	—
32	C₄×C₉₇	—	2	1	no	—
33	C₄×C₉₇	—	4	2	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	1	no	—
38	C₂×C₉₇	#121	1	1	yes	characteristic
39	C₂×C₉₇	C₂×SD₁₆	1	1	yes	characteristic
40	C₂×C₉₇	#137	1	1	yes	characteristic
41	D₉₇	—	4	2	no	—
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	D₉₇	1	1	yes	characteristic, complemented
46	C₄×D₄	—	97	1	no	—
47	C₄⋊C₈	—	97	1	no	—
48	#103	—	97	2	no	—
49	C₂×Q₈	C₂×D₉₇	1	2	yes	—
50	C₂×D₄	—	97	1	no	—
51	C₂²×C₄	—	194	1	no	—
52	SD₁₆	—	194	4	no	—
53	C₂×C₈	—	97	2	no	—
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	2	1	no	—
56	C₄⋊C₄	—	97	1	no	—
57	C₂²⋊C₄	—	194	1	no	—
58	C₄²	C₂×D₉₇	1	1	yes	characteristic
59	C₂³	—	194	1	no	—
60	Q₈	—	2	2	no	—
61	Q₈	—	2	2	no	—
62	D₄	—	97	2	no	—
63	D₄	—	194	1	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	388	2	no	—
66	C₂×C₄	—	194	1	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	—	388	1	no	—
72	C₂²	—	388	1	no	—
73	C₂²	—	194	2	no	—
74	C₂²	C₂×C₂²⋊D₉₇	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	2	no	—
77	C₄	—	388	1	no	—
78	C₄	#13095498	1	2	yes	complemented
79	C₄	D₄×D₉₇	1	1	yes	characteristic
80	C₄	#13095510	1	1	yes	characteristic
81	C₂	—	388	2	no	—
82	C₂	#15690781	1	1	yes	characteristic
83	C₂	C₂×#13095498	1	1	yes	characteristic
84	C₂	#15690841	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₉₇
commutator	C₂×C₄×C₉₇	C₂³
Frattini	C₂×C₄	C₂²×D₉₇
Fitting	C₄⋊Q₈×C₉₇	C₂
socle	C₂²×C₉₇	C₂×D₄
hypercenter	C₄⋊Q₈	D₉₇
hypocenter	C₉₇	#461
LCS	G ▷ C₂×C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
3. C₄⋊#11715895	C₂	semidirect
4. #15690734	C₂	semidirect
5. C₄⋊Q₈×C₉₇	C₂	semidirect
34. C₄×C₉₇	SD₁₆	semidirect
42. C₉₇	#461	semidirect
45. C₄⋊Q₈	D₉₇	semidirect
78. C₄	#13095498	semidirect