Subgroups — #16834454

Order 3712.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272085	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈×#6599	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271280	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#135	C₄	1	1	yes	characteristic
5	#11745310	—	2	1	no	—
6	C₄×#6599	—	2	1	no	—
7	#11745214	—	2	1	no	—
8	#11745185	—	2	1	no	—
9	#11745167	C₄	1	1	yes	characteristic
10	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
11	#41×C₂₉	—	2	1	no	—
12	C₂×#6599	—	2	2	no	—
13	Q₁₆×C₂₉	C₈	1	1	yes	characteristic, complemented
14	SD₁₆×C₂₉	—	2	1	no	—
15	D₈×C₂₉	C₈	1	1	yes	characteristic, complemented
16	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₄×Dic₂₉	D₄	1	1	yes	characteristic
18	#90777	—	2	1	no	—
19	#90777	—	4	1	no	—
20	C₂×#6597	—	4	1	no	—
21	C₂×#6597	D₄	1	1	yes	characteristic
22	#90770	—	4	1	no	—
23	Q₈×C₂₉	—	2	1	no	—
24	D₄×C₂₉	—	2	1	no	—
25	D₄×C₂₉	—	4	1	no	—
26	C₂×C₄×C₂₉	—	4	1	no	—
27	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₂₉	—	2	1	no	—
29	#6599	—	2	4	no	—
30	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
31	C₈×C₂₉	M₁₆	1	1	yes	characteristic
32	#6597	—	4	1	no	—
33	#6597	D₈	1	1	yes	characteristic
34	#6597	SD₁₆	1	1	yes	characteristic
35	#1335	—	29	1	no	maximal, Sylow
36	C₂²×C₂₉	—	4	1	no	—
37	C₂²×C₂₉	#104	1	1	yes	characteristic
38	C₄×C₂₉	—	4	1	no	—
39	C₄×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
40	C₄×C₂₉	#102	1	1	yes	characteristic
41	Dic₂₉	—	2	2	no	—
42	#443	—	29	1	no	—
43	#364	—	29	1	no	—
44	C₈²	—	29	1	no	—
45	C₂×C₂₉	—	2	1	no	—
46	C₂×C₂₉	—	8	1	no	—
47	C₂×C₂₉	D₄⋊C₈	1	1	yes	characteristic
48	#135	#1181	1	1	yes	characteristic
49	#131	—	58	1	no	—
50	M₃₂	—	58	1	no	—
51	#108	—	29	1	no	—
52	#104	—	58	1	no	—
53	C₄×C₈	—	29	1	no	—
54	C₄×C₈	—	58	1	no	—
55	C₂₉	#1335	1	1	yes	characteristic, complemented, Sylow
56	#41	—	2	1	no	—
57	Q₁₆	#6599	1	1	yes	characteristic, complemented
58	SD₁₆	—	2	1	no	—
59	D₈	#6599	1	1	yes	characteristic, complemented
60	M₁₆	—	58	1	no	—
61	M₁₆	—	116	1	no	—
62	C₂×C₈	—	29	1	no	—
63	C₂×C₈	—	58	2	no	—
64	C₂×C₈	—	116	1	no	—
65	C₂×C₈	C₂×#1181	1	1	yes	characteristic
66	C₄²	—	29	1	no	—
67	C₁₆	—	116	1	no	—
68	Q₈	—	2	1	no	—
69	D₄	—	2	1	no	—
70	D₄	—	4	1	no	—
71	C₂×C₄	—	4	1	no	—
72	C₂×C₄	—	58	1	no	—
73	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
74	C₈	—	29	1	no	—
75	C₈	—	29	1	no	—
76	C₈	—	58	4	no	—
77	C₈	—	116	1	no	—
78	C₈	C₂×#6599	1	1	yes	characteristic
79	C₈	#90800	1	1	yes	characteristic
80	C₂²	—	4	1	no	—
81	C₂²	#11745224	1	1	yes	characteristic
82	C₄	—	4	1	no	—
83	C₄	—	58	2	no	—
84	C₄	#11745223	1	1	yes	characteristic
85	C₄	C₂²⋊#6599	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	8	1	no	—
88	C₂	D₄⋊#6599	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11745223
commutator	C₈×C₂₉	C₂×C₈
Frattini	C₂×C₈	C₂×#1181
Fitting, prime radical	C₂₉×#135	C₄
socle	C₂×C₂₉	D₄⋊C₈
cosocle	C₈×Dic₂₉	C₂²
hypercenter	#135	#1181
hypocenter	C₂₉	#1335
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #135

Complements

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

N	H ≅ G/N	type
1. #14272085	C₂	semidirect
2. C₈×#6599	C₂	semidirect
13. Q₁₆×C₂₉	C₈	semidirect
15. D₈×C₂₉	C₈	semidirect
55. C₂₉	#1335	semidirect
57. Q₁₆	#6599	semidirect
59. D₈	#6599	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#14272085	2
C₈×#6599	2
#14271280	2
#1335	29