Subgroups — #16834468

Order 3712.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272060	C₂	1	1	yes	maximal, characteristic
2	#14272032	C₂	1	1	yes	maximal, characteristic
3	#14271418	C₂	1	1	yes	maximal, characteristic
4	D₂₉⋊M₁₆	—	2	1	no	—
5	C₂×Q₁₆×C₂₉	C₄	1	1	yes	characteristic
6	#11745308	—	2	1	no	—
7	C₂×#90772	C₂²	1	1	yes	characteristic
8	#11745214	—	2	1	no	—
9	#11745183	—	2	1	no	—
10	#11745165	C₄	1	1	yes	characteristic
11	C₂×Q₈×C₂₉	—	2	1	no	—
12	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
13	#90800	—	4	1	no	—
14	#90796	—	4	1	no	—
15	D₂₉⋊C₈	—	2	2	no	—
16	Q₁₆×C₂₉	—	4	1	no	—
17	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
18	#90781	—	4	1	no	—
19	C₄⋊Dic₂₉	—	2	1	no	—
20	#90779	—	4	1	no	—
21	C₂×#6597	D₄	1	1	yes	characteristic
22	#90772	—	4	1	no	—
23	#90770	—	4	1	no	—
24	C₂²×D₂₉	SD₁₆	1	1	yes	characteristic
25	Q₈×C₂₉	—	4	1	no	—
26	Q₈×C₂₉	—	4	1	no	—
27	C₂×C₄×C₂₉	—	4	1	no	—
28	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×Dic₂₉	—	4	1	no	—
30	C₂×Dic₂₉	D₈	1	1	yes	characteristic
31	C₄×D₂₉	—	2	1	no	—
32	C₄×D₂₉	—	2	1	no	—
33	#6599	—	4	2	no	—
34	C₈×C₂₉	—	2	1	no	—
35	#6597	—	2	1	no	—
36	#1342	—	29	1	no	maximal, Sylow
37	C₂²×C₂₉	#102	1	1	yes	characteristic
38	C₂×D₂₉	—	2	1	no	—
39	C₂×D₂₉	—	4	1	no	—
40	C₄×C₂₉	—	8	1	no	—
41	C₄×C₂₉	#99	1	1	yes	characteristic
42	C₄×C₂₉	#104	1	1	yes	characteristic
43	Dic₂₉	—	2	1	no	—
44	Dic₂₉	—	8	1	no	—
45	#470	—	29	1	no	—
46	#349	—	29	1	no	—
47	#338	—	29	1	no	—
48	C₂×C₂₉	—	2	1	no	—
49	C₂×C₂₉	#327	1	1	yes	characteristic
50	D₂₉	—	4	1	no	—
51	C₂×Q₁₆	#1181	1	1	yes	characteristic
52	C₂×M₁₆	—	29	1	no	—
53	C₂×M₁₆	—	58	1	no	—
54	C₂²⋊Q₈	—	58	1	no	—
55	M₃₂	—	58	1	no	—
56	#106	—	29	1	no	—
57	#103	—	58	1	no	—
58	C₂₉	#1342	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₈	—	2	1	no	—
60	C₂²×C₄	—	29	1	no	—
61	Q₁₆	—	4	1	no	—
62	M₁₆	—	116	1	no	—
63	M₁₆	—	116	1	no	—
64	M₁₆	—	116	1	no	—
65	C₂×C₈	—	29	1	no	—
66	C₂×C₈	—	58	2	no	—
67	C₂×C₈	C₂×#1181	1	1	yes	characteristic
68	C₄⋊C₄	—	58	1	no	—
69	C₄⋊C₄	—	116	1	no	—
70	C₂²⋊C₄	—	116	1	no	—
71	C₁₆	—	116	1	no	—
72	C₂³	—	29	1	no	—
73	Q₈	—	4	1	no	—
74	Q₈	—	4	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	29	1	no	—
77	C₂×C₄	—	58	1	no	—
78	C₂×C₄	—	58	1	no	—
79	C₂×C₄	—	116	1	no	—
80	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	58	1	no	—
83	C₈	—	116	2	no	—
84	C₂²	—	58	1	no	—
85	C₂²	—	116	1	no	—
86	C₂²	#11745223	1	1	yes	characteristic
87	C₄	—	8	1	no	—
88	C₄	—	58	1	no	—
89	C₄	—	232	1	no	—
90	C₄	#11745224	1	1	yes	characteristic
91	C₄	#11745227	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	116	1	no	—
94	C₂	#14272014	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14272014
commutator	C₂×C₈×C₂₉	C₂×C₄
Frattini	C₂×C₈	C₂×#1181
Fitting	C₂×Q₁₆×C₂₉	C₄
socle	C₂×C₂₉	#327
prime radical	C₂²×D₂₉	SD₁₆
cosocle	C₂×#90772	C₂²
hypercenter	C₂×Q₁₆	#1181
hypocenter	C₂₉	#1342
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
58. C₂₉	#1342	semidirect

Maximal subgroups

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

subgroup	index
#14272060	2
#14272032	2
#14271418	2
#1342	29