Subgroups — #21422268

Order 7552.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837770	C₂	1	1	yes	maximal, characteristic
2	#16837201	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#356	C₂	1	1	yes	maximal, characteristic
4	#14273719	C₄	1	1	yes	characteristic
5	#14273651	—	2	1	no	—
6	#14273651	—	2	1	no	—
7	#14273646	—	2	1	no	—
8	#14273638	C₄	1	1	yes	characteristic
9	C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
10	#101×C₅₉	—	2	1	no	—
11	C₂×Q₈×C₅₉	D₄	1	1	yes	characteristic
12	C₂×Q₈×C₅₉	D₄	1	1	yes	characteristic
13	M₁₆×C₅₉	—	4	1	no	—
14	C₄⋊C₄×C₅₉	—	4	1	no	—
15	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
16	C₄⋊Dic₅₉	—	2	1	no	—
17	Dic₅₉⋊C₄	—	4	1	no	—
18	#11745664	—	4	1	no	—
19	C₂×C₅₉⋊C₈	—	2	1	no	—
20	Q₈×C₅₉	—	4	1	no	—
21	Q₈×C₅₉	—	4	1	no	—
22	C₂×C₄×C₅₉	—	2	1	no	—
23	C₂×C₄×C₅₉	—	2	1	no	—
24	C₂×C₄×C₅₉	—	2	1	no	—
25	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×Dic₅₉	—	4	1	no	—
27	C₈×C₅₉	—	8	1	no	—
28	C₅₉⋊C₈	—	4	1	no	—
29	C₅₉⋊C₈	—	8	1	no	—
30	C₂²×C₅₉	#99	1	1	yes	characteristic
31	C₄×C₅₉	—	2	1	no	—
32	C₄×C₅₉	—	4	1	no	—
33	C₄×C₅₉	—	4	1	no	—
34	C₄×C₅₉	—	4	1	no	—
35	Dic₅₉	—	8	1	no	—
36	#1413	—	59	1	no	maximal, Sylow
37	C₂×C₅₉	—	2	1	no	—
38	C₂×C₅₉	#354	1	1	yes	characteristic
39	#491	—	59	1	no	—
40	#356	—	59	1	no	—
41	#356	D₅₉	1	1	yes	characteristic
42	C₅₉	#1413	1	1	yes	characteristic, complemented, Sylow
43	C₄⋊Q₈	C₂×D₅₉	1	1	yes	characteristic
44	#125	—	59	1	no	—
45	#103	—	118	1	no	—
46	#103	—	118	1	no	—
47	#101	—	2	1	no	—
48	#101	—	118	1	no	—
49	#97	—	59	1	no	—
50	C₂×Q₈	D₂₃₆	1	1	yes	characteristic
51	C₂×Q₈	C₂²⋊D₅₉	1	1	yes	characteristic
52	M₁₆	—	4	1	no	—
53	M₁₆	—	236	1	no	—
54	C₂×C₈	—	118	1	no	—
55	C₄⋊C₄	—	4	1	no	—
56	C₄⋊C₄	—	118	1	no	—
57	C₄⋊C₄	—	236	1	no	—
58	C₄²	C₄×D₅₉	1	1	yes	characteristic
59	Q₈	—	4	1	no	—
60	Q₈	—	4	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	236	1	no	—
65	C₂×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
66	C₈	—	8	1	no	—
67	C₈	—	472	1	no	—
68	C₈	—	236	1	no	—
69	C₂²	#14273641	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	4	1	no	—
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	472	1	no	—
75	C₂	—	2	1	no	—
76	C₂	#16837196	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16837196
commutator	C₄²×C₅₉	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₅₉
Fitting	C₅₉×#356	C₂
socle	C₂×C₅₉	#354
hypercenter	#356	D₅₉
hypocenter	C₅₉	#1413
LCS	G ▷ C₄²×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #356

Complements

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

N	H ≅ G/N	type
42. C₅₉	#1413	semidirect