Subgroups — #21444123

Order 7808.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11758189	C₂	1	1	yes	maximal, characteristic
2	C₄×#11758189	C₂	1	2	yes	maximal
3	#16839484	C₂	1	2	yes	maximal, complemented
4	C₈×#92418	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11758189	C₄	1	2	yes	—
7	C₂×#11758189	C₄	1	4	yes	—
8	C₄²×D₆₁	C₂²	1	1	yes	characteristic
9	#14519687	C₄	1	2	yes	—
10	#14519687	C₄	1	4	yes	—
11	C₄×#92418	C₂²	1	2	yes	—
12	C₄×#92418	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₆₁	C₂²	1	2	yes	—
15	C₂×C₄×D₆₁	C₂×C₄	1	2	yes	—
16	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₆₁	C₂×C₄	1	4	yes	—
18	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
19	C₄²×C₆₁	C₂³	1	1	yes	characteristic
20	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
21	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂×#92418	C₂×C₄	1	2	yes	—
23	C₂×#92418	C₂×C₄	1	4	yes	—
24	#11758189	—	2	4	no	—
25	#11758189	—	2	8	no	—
26	C₂²×D₆₁	C₄²	1	1	yes	characteristic
27	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
28	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
29	C₂×Dic₆₁	C₄²	1	1	yes	characteristic
30	C₂×Dic₆₁	C₄²	1	2	yes	—
31	C₄×D₆₁	—	2	4	no	—
32	C₄×D₆₁	—	2	2	no	—
33	C₈×C₆₁	—	2	4	no	—
34	C₈×C₆₁	M₁₆	1	4	yes	complemented
35	#92418	—	2	2	no	—
36	#92418	M₁₆	1	8	yes	complemented
37	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
38	C₂×D₆₁	—	2	1	no	—
39	C₂×D₆₁	—	2	2	no	—
40	C₄×C₆₁	C₂×M₁₆	1	4	yes	—
41	C₄×C₆₁	C₂×M₁₆	1	2	yes	—
42	Dic₆₁	—	2	1	no	—
43	Dic₆₁	—	2	2	no	—
44	#1455	—	61	1	no	maximal, Sylow
45	C₂×C₆₁	C₄×M₁₆	1	1	yes	characteristic
46	C₂×C₆₁	C₄×M₁₆	1	2	yes	—
47	D₆₁	—	4	1	no	—
48	C₄×M₁₆	—	61	2	no	—
49	C₄×M₁₆	—	61	1	no	—
50	#322	—	61	2	no	—
51	#322	D₆₁	1	1	yes	characteristic, complemented
52	C₈²	—	61	1	no	—
53	C₆₁	#1455	1	1	yes	characteristic, complemented, Sylow
54	C₂×M₁₆	—	61	4	no	—
55	C₂×M₁₆	—	61	2	no	—
56	C₂×C₄²	—	61	1	no	—
57	#97	—	61	4	no	—
58	#97	—	61	2	no	—
59	C₄×C₈	—	61	2	no	—
60	C₄×C₈	—	61	1	no	—
61	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
62	C₄×C₈	C₂×D₆₁	1	2	yes	—
63	C₂²×C₄	—	61	2	no	—
64	C₂²×C₄	—	61	1	no	—
65	M₁₆	—	122	8	no	—
66	M₁₆	—	122	4	no	—
67	C₂×C₈	—	61	4	no	—
68	C₂×C₈	—	61	2	no	—
69	C₂×C₈	C₄×D₆₁	1	4	yes	—
70	C₂×C₈	C₄×D₆₁	1	2	yes	—
71	C₄²	—	61	2	no	—
72	C₄²	—	61	1	no	—
73	C₄²	C₂²×D₆₁	1	1	yes	characteristic
74	C₂³	—	61	1	no	—
75	C₂×C₄	—	61	1	no	—
76	C₂×C₄	—	61	2	no	—
77	C₂×C₄	—	122	4	no	—
78	C₂×C₄	—	122	2	no	—
79	C₂×C₄	C₂×C₄×D₆₁	1	2	yes	—
80	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
81	C₈	—	2	4	no	—
82	C₈	—	61	8	no	—
83	C₈	—	122	2	no	—
84	C₈	#11758189	1	4	yes	complemented
85	C₂²	—	122	1	no	—
86	C₂²	—	122	2	no	—
87	C₂²	C₄²×D₆₁	1	1	yes	characteristic
88	C₄	—	122	1	no	—
89	C₄	—	122	2	no	—
90	C₄	M₁₆×D₆₁	1	4	yes	—
91	C₄	C₂×#11758189	1	2	yes	—
92	C₂	—	244	1	no	—
93	C₂	C₄×#11758189	1	1	yes	characteristic
94	C₂	#16839714	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₆₁
commutator, socle	C₂²×C₆₁	C₂×C₄²
Fitting	C₆₁×#322	C₂
hypercenter	#322	D₆₁
hypocenter	C₆₁	#1455
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄² ◁ #322

Complements

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

N	H ≅ G/N	type
3. #16839484	C₂	semidirect
4. C₈×#92418	C₂	semidirect
5. C₆₁×#322	C₂	semidirect
34. C₈×C₆₁	M₁₆	semidirect
36. #92418	M₁₆	semidirect
51. #322	D₆₁	semidirect
53. C₆₁	#1455	semidirect
84. C₈	#11758189	semidirect