Subgroups — #16834507

Order 3712.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272084	C₂	1	1	yes	maximal, characteristic
2	#14272027	C₂	1	1	yes	maximal, characteristic
3	#14271541	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₂₉	C₄	1	1	yes	characteristic
5	#11745306	—	2	1	no	—
6	C₂×#90785	—	2	1	no	—
7	C₂×Dic₁₁₆	C₄	1	1	yes	characteristic
8	C₄⋊#6599	—	2	1	no	—
9	C₂×#90770	—	2	1	no	—
10	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₂₉	—	2	1	no	—
12	C₂×Dic₅₈	—	2	1	no	—
13	C₂×#6599	—	4	1	no	—
14	Q₁₆×C₂₉	—	4	1	no	—
15	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
16	#90785	—	4	1	no	—
17	#90785	—	4	1	no	—
18	#90779	—	4	1	no	—
19	#90779	—	4	1	no	—
20	C₄×Dic₂₉	D₄	1	1	yes	characteristic
21	C₂×#6597	D₄	1	1	yes	characteristic
22	Dic₁₁₆	—	4	1	no	—
23	#90770	—	4	1	no	—
24	Q₈×C₂₉	—	4	1	no	—
25	Q₈×C₂₉	—	4	1	no	—
26	C₂×C₄×C₂₉	—	4	1	no	—
27	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₂₉	—	4	1	no	—
29	C₂×Dic₂₉	D₈	1	1	yes	characteristic
30	C₂×Dic₂₉	SD₁₆	1	1	yes	characteristic
31	Dic₅₈	—	4	1	no	—
32	Dic₅₈	—	4	1	no	—
33	#6599	—	8	1	no	—
34	C₈×C₂₉	—	2	1	no	—
35	#6597	D₈	1	1	yes	characteristic
36	#6597	SD₁₆	1	1	yes	characteristic
37	#1362	—	29	1	no	maximal, Sylow
38	C₂²×C₂₉	#102	1	1	yes	characteristic
39	C₄×C₂₉	—	8	1	no	—
40	C₄×C₂₉	#100	1	1	yes	characteristic
41	C₄×C₂₉	#102	1	1	yes	characteristic
42	Dic₂₉	—	2	1	no	—
43	Dic₂₉	—	8	1	no	—
44	Dic₂₉	SD₃₂	1	1	yes	characteristic
45	Dic₂₉	Q₃₂	1	1	yes	characteristic
46	#494	—	29	1	no	—
47	C₄⋊C₁₆	—	29	1	no	—
48	#335	—	29	1	no	—
49	C₂×C₂₉	#331	1	1	yes	characteristic
50	C₂×C₂₉	#358	1	1	yes	characteristic
51	C₂×C₂₉	#362	1	1	yes	characteristic
52	C₂×Q₁₆	—	29	1	no	—
53	C₂×Q₁₆	—	58	1	no	—
54	C₂×Q₁₆	#1181	1	1	yes	characteristic
55	C₄⋊Q₈	—	58	1	no	—
56	C₂×C₁₆	—	58	1	no	—
57	C₄⋊C₈	—	58	1	no	—
58	C₄×C₈	—	29	1	no	—
59	C₂₉	#1362	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	—	2	1	no	—
61	C₂×Q₈	—	58	1	no	—
62	Q₁₆	—	4	1	no	—
63	Q₁₆	—	116	1	no	—
64	Q₁₆	—	116	1	no	—
65	Q₁₆	—	116	1	no	—
66	C₂×C₈	—	29	1	no	—
67	C₂×C₈	—	116	1	no	—
68	C₂×C₈	C₂×#1181	1	1	yes	characteristic
69	C₄⋊C₄	—	116	1	no	—
70	C₄⋊C₄	—	116	1	no	—
71	C₄²	—	29	1	no	—
72	C₁₆	—	116	1	no	—
73	Q₈	—	4	1	no	—
74	Q₈	—	4	1	no	—
75	Q₈	—	116	1	no	—
76	Q₈	—	116	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	29	1	no	—
79	C₂×C₄	—	29	1	no	—
80	C₂×C₄	—	116	1	no	—
81	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	29	1	no	—
84	C₈	—	29	1	no	—
85	C₈	—	232	1	no	—
86	C₂²	#11745223	1	1	yes	characteristic
87	C₄	—	8	1	no	—
88	C₄	—	29	1	no	—
89	C₄	—	29	1	no	—
90	C₄	—	58	1	no	—
91	C₄	—	232	1	no	—
92	C₄	#11745223	1	1	yes	characteristic
93	C₄	#11745229	1	1	yes	characteristic
94	C₂	#14272021	1	1	yes	characteristic
95	C₂	#14272076	1	1	yes	characteristic
96	C₂	#14272082	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11745223
commutator	C₂×C₈×C₂₉	C₂×C₄
Frattini	C₂×C₈	C₂×#1181
Fitting	C₂×Q₁₆×C₂₉	C₄
socle, prime radical	C₂²×C₂₉	#102
cosocle	C₈×Dic₂₉	C₂²
hypercenter	C₂×Q₁₆	#1181
hypocenter	C₂₉	#1362
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
59. C₂₉	#1362	semidirect

Maximal subgroups

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

subgroup	index
#14272084	2
#14272027	2
#14271541	2
#1362	29