Subgroups — #21445421

Order 7808.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840135	C₂	1	1	yes	maximal, characteristic
2	#16840112	C₂	1	2	yes	maximal, complemented
3	#16840110	C₂	1	2	yes	maximal
4	C₈×#92418	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#498	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11758190	—	2	2	no	—
7	#14519777	C₂²	1	1	yes	characteristic
8	#14519774	C₂²	1	1	yes	characteristic
9	#14519701	—	2	4	no	—
10	#14519697	—	2	4	no	—
11	C₄×#92418	C₂²	1	2	yes	—
12	C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
13	#106×C₆₁	—	2	2	no	—
14	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₆₁	—	2	2	no	—
16	C₂×D₂₄₄	—	2	2	no	—
17	C₂×D₂₄₄	—	2	1	no	—
18	C₂×Dic₁₂₂	—	2	1	no	—
19	C₂×C₈×C₆₁	D₄	1	2	yes	—
20	C₄⋊C₄×C₆₁	—	2	2	no	—
21	C₄⋊C₄×C₆₁	—	2	2	no	—
22	C₄²×C₆₁	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₆₁	—	2	2	no	—
24	C₂×#92418	D₄	1	4	yes	—
25	#11758190	—	4	4	no	—
26	C₂²×D₆₁	—	4	1	no	—
27	Q₈×C₆₁	—	4	4	no	—
28	C₂×C₄×C₆₁	—	4	2	no	—
29	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
31	C₂×Dic₆₁	—	4	1	no	—
32	D₂₄₄	—	4	2	no	—
33	D₂₄₄	—	4	4	no	—
34	Dic₁₂₂	—	4	2	no	—
35	C₈×C₆₁	SD₁₆	1	4	yes	—
36	#92418	—	2	4	no	—
37	C₂²×C₆₁	#127	1	1	yes	characteristic
38	C₂×D₆₁	—	8	1	no	—
39	C₂×D₆₁	—	8	2	no	—
40	C₄×C₆₁	—	8	2	no	—
41	C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
42	C₄×C₆₁	#135	1	4	yes	—
43	Dic₆₁	—	8	1	no	—
44	#1708	—	61	1	no	maximal, Sylow
45	C₂×C₆₁	#492	1	1	yes	characteristic
46	C₂×C₆₁	#495	1	2	yes	—
47	D₆₁	—	16	1	no	—
48	#498	D₆₁	1	1	yes	characteristic, complemented
49	#492	—	61	1	no	—
50	#487	—	61	2	no	—
51	#486	—	61	2	no	—
52	C₈²	—	61	1	no	—
53	C₆₁	#1708	1	1	yes	characteristic, complemented, Sylow
54	C₂×SD₁₆	—	122	2	no	—
55	C₄⋊Q₈	—	61	1	no	—
56	C₄⋊Q₈	C₂×D₆₁	1	2	yes	—
57	#127	—	61	1	no	—
58	#106	—	2	2	no	—
59	#103	—	122	4	no	—
60	#102	—	122	4	no	—
61	C₄×C₈	—	61	2	no	—
62	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
63	C₂×Q₈	—	2	2	no	—
64	C₂×Q₈	—	122	1	no	—
65	C₂×D₄	—	122	2	no	—
66	C₂×D₄	—	122	1	no	—
67	SD₁₆	—	244	4	no	—
68	C₂×C₈	—	61	4	no	—
69	C₂×C₈	C₂²⋊D₆₁	1	2	yes	—
70	C₄⋊C₄	—	2	2	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	122	2	no	—
73	C₄²	C₂²×D₆₁	1	1	yes	characteristic
74	C₂³	—	244	1	no	—
75	Q₈	—	4	4	no	—
76	Q₈	—	244	2	no	—
77	D₄	—	244	2	no	—
78	D₄	—	244	4	no	—
79	C₂×C₄	—	4	2	no	—
80	C₂×C₄	—	244	1	no	—
81	C₂×C₄	D₄×D₆₁	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
83	C₈	—	122	4	no	—
84	C₈	#11758201	1	4	yes	—
85	C₂²	—	488	1	no	—
86	C₂²	—	488	2	no	—
87	C₂²	#14519773	1	1	yes	characteristic
88	C₄	—	8	2	no	—
89	C₄	—	488	1	no	—
90	C₄	C₂×#11758201	1	2	yes	—
91	C₄	#14519798	1	4	yes	—
92	C₂	—	976	1	no	—
93	C₂	#16840136	1	1	yes	characteristic
94	C₂	#16840143	1	2	yes	—

	subgroup	G/H
center	C₂²	#14519773
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#498	C₂
socle	C₂²×C₆₁	#127
hypercenter	#498	D₆₁
hypocenter	C₆₁	#1708
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

Complements

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

N	H ≅ G/N	type
2. #16840112	C₂	semidirect
4. C₈×#92418	C₂	semidirect
5. C₆₁×#498	C₂	semidirect
48. #498	D₆₁	semidirect
53. C₆₁	#1708	semidirect