Subgroups — #21422252

Order 7552.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837792	C₂	1	1	yes	maximal, characteristic
2	#16837199	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#354	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11745671	—	2	1	no	—
5	C₂×#11745669	—	2	1	no	—
6	#14273724	C₄	1	1	yes	characteristic, complemented
7	#14273646	—	2	1	no	—
8	#14273638	C₄	1	1	yes	characteristic, complemented
9	#124×C₅₉	C₂²	1	1	yes	characteristic
10	#99×C₅₉	—	2	1	no	—
11	C₂×Q₈×C₅₉	D₄	1	1	yes	characteristic
12	C₂×D₄×C₅₉	D₄	1	1	yes	characteristic
13	C₂×D₂₃₆	—	2	1	no	—
14	C₂×D₂₃₆	—	4	1	no	—
15	C₂²⋊C₄×C₅₉	—	4	1	no	—
16	C₂²⋊C₄×C₅₉	—	4	1	no	—
17	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
18	#11745671	—	4	2	no	—
19	#11745669	—	4	2	no	—
20	#11745664	—	4	1	no	—
21	C₂×C₅₉⋊C₈	—	2	1	no	—
22	C₂³×C₅₉	—	2	1	no	—
23	C₂²×D₅₉	—	4	1	no	—
24	Q₈×C₅₉	—	4	1	no	—
25	D₄×C₅₉	—	4	1	no	—
26	C₂×C₄×C₅₉	—	2	1	no	—
27	C₂×C₄×C₅₉	—	2	1	no	—
28	C₂×C₄×C₅₉	—	8	1	no	—
29	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
30	D₂₃₆	—	4	1	no	—
31	D₂₃₆	—	4	1	no	—
32	D₂₃₆	—	8	2	no	—
33	C₅₉⋊C₈	—	2	2	no	—
34	C₅₉⋊C₈	—	8	1	no	—
35	C₂²×C₅₉	—	4	1	no	—
36	C₂²×C₅₉	—	8	1	no	—
37	C₂²×C₅₉	#99	1	1	yes	characteristic
38	C₂×D₅₉	—	8	2	no	—
39	C₂×D₅₉	—	8	1	no	—
40	C₄×C₅₉	—	2	1	no	—
41	C₄×C₅₉	—	4	1	no	—
42	C₄×C₅₉	—	4	1	no	—
43	C₄×C₅₉	—	16	1	no	—
44	#1406	—	59	1	no	maximal, Sylow
45	C₂×C₅₉	—	2	1	no	—
46	C₂×C₅₉	—	8	1	no	—
47	C₂×C₅₉	#353	1	1	yes	characteristic
48	D₅₉	—	16	1	no	—
49	#496	—	59	1	no	—
50	#355	—	59	1	no	—
51	#354	D₅₉	1	1	yes	characteristic, complemented
52	C₅₉	#1406	1	1	yes	characteristic, complemented, Sylow
53	C₂×SD₁₆	—	118	1	no	—
54	C₂×D₈	—	118	1	no	—
55	#127	—	59	1	no	—
56	#124	C₂×D₅₉	1	1	yes	characteristic
57	#101	—	118	1	no	—
58	#99	—	2	1	no	—
59	#97	—	59	1	no	—
60	C₂×Q₈	D₂₃₆	1	1	yes	characteristic
61	C₂×D₄	—	118	1	no	—
62	C₂×D₄	—	236	1	no	—
63	C₂×D₄	C₂²⋊D₅₉	1	1	yes	characteristic
64	SD₁₆	—	236	2	no	—
65	D₈	—	236	2	no	—
66	M₁₆	—	236	1	no	—
67	C₂×C₈	—	118	1	no	—
68	C₂²⋊C₄	—	4	1	no	—
69	C₂²⋊C₄	—	4	1	no	—
70	C₄²	C₄×D₅₉	1	1	yes	characteristic
71	C₂³	—	2	1	no	—
72	C₂³	—	236	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	472	2	no	—
76	D₄	—	236	1	no	—
77	D₄	—	236	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	8	1	no	—
81	C₂×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
82	C₈	—	118	2	no	—
83	C₈	—	472	1	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	472	2	no	—
87	C₂²	—	472	1	no	—
88	C₂²	#14273641	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	4	1	no	—
92	C₄	—	16	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	8	1	no	—
95	C₂	—	944	1	no	—
96	C₂	#16837194	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16837194
commutator	C₄²×C₅₉	C₂×C₄
Frattini	#124	C₂×D₅₉
Fitting	C₅₉×#354	C₂
socle	C₂×C₅₉	#353
hypercenter	#354	D₅₉
hypocenter	C₅₉	#1406
LCS	G ▷ C₄²×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #354

Complements

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

N	H ≅ G/N	type
2. #16837199	C₂	semidirect
3. C₅₉×#354	C₂	semidirect
6. #14273724	C₄	semidirect
8. #14273638	C₄	semidirect
51. #354	D₅₉	semidirect
52. C₅₉	#1406	semidirect