Subgroups — #16834705

Order 3712.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272179	C₂	1	2	yes	maximal
2	#6599⋊C₈	C₂	1	4	yes	maximal, complemented
3	C₂×C₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₉	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
6	C₂²×#6597	C₄	1	1	yes	characteristic
7	C₂²⋊#6599	C₄	1	4	yes	—
8	C₄⋊#6599	C₄	1	4	yes	—
9	C₄×#6599	C₂²	1	4	yes	—
10	C₈×Dic₂₉	C₄	1	2	yes	—
11	C₈×Dic₂₉	C₂²	1	2	yes	—
12	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
14	C₂×#6599	C₂×C₄	1	8	yes	—
15	C₂×C₈×C₂₉	—	2	2	no	—
16	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
17	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
19	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
20	C₂×#6597	—	2	2	no	—
21	C₂×#6597	C₂×C₄	1	2	yes	—
22	C₂³×C₂₉	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₂₉	M₁₆	1	2	yes	—
25	C₂×C₄×C₂₉	M₁₆	1	2	yes	—
26	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
27	C₂×Dic₂₉	—	2	4	no	—
28	C₂×Dic₂₉	C₄²	1	2	yes	—
29	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
30	#6599	—	2	8	no	—
31	C₈×C₂₉	—	2	2	no	—
32	#6597	—	2	2	no	—
33	#1452	—	29	1	no	maximal, Sylow
34	C₂²×C₂₉	—	2	2	no	—
35	C₂²×C₂₉	#97	1	2	yes	—
36	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
37	C₄×C₂₉	#97	1	2	yes	—
38	C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
39	C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
40	Dic₂₉	—	2	2	no	—
41	Dic₂₉	#131	1	4	yes	—
42	#431	—	29	2	no	—
43	C₂×C₄×C₈	—	29	1	no	—
44	#322	—	29	4	no	—
45	C₂×C₂₉	—	2	2	no	—
46	C₂×C₂₉	C₂×#97	1	1	yes	characteristic
47	C₂×C₂₉	#405	1	2	yes	—
48	C₂²×C₈	—	29	1	no	—
49	C₂²×C₈	#1181	1	1	yes	characteristic
50	C₂×C₄²	—	29	1	no	—
51	C₄⋊C₈	—	29	4	no	—
52	C₂²⋊C₈	—	29	4	no	—
53	C₄×C₈	—	29	4	no	—
54	C₄×C₈	—	29	2	no	—
55	C₄×C₈	—	29	2	no	—
56	C₂₉	#1452	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₄	—	29	2	no	—
58	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
59	C₂×C₈	—	2	2	no	—
60	C₂×C₈	—	29	8	no	—
61	C₂×C₈	—	29	2	no	—
62	C₂×C₈	—	58	2	no	—
63	C₂×C₈	C₂×#1181	1	2	yes	—
64	C₄²	—	29	2	no	—
65	C₄²	—	29	1	no	—
66	C₄²	—	29	1	no	—
67	C₂³	C₄×#1181	1	1	yes	characteristic
68	C₂×C₄	—	29	2	no	—
69	C₂×C₄	—	29	2	no	—
70	C₂×C₄	—	58	4	no	—
71	C₂×C₄	#90796	1	2	yes	—
72	C₂×C₄	C₄×#1181	1	1	yes	characteristic
73	C₂×C₄	#90800	1	2	yes	—
74	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
75	C₈	—	2	2	no	—
76	C₈	—	58	8	no	—
77	C₈	—	58	2	no	—
78	C₂²	—	2	2	no	—
79	C₂²	#11745218	1	2	yes	—
80	C₂²	C₂×C₄×#1181	1	1	yes	characteristic
81	C₄	—	29	4	no	—
82	C₄	—	58	2	no	—
83	C₄	#11745218	1	2	yes	—
84	C₄	C₂×#90796	1	1	yes	characteristic
85	C₄	C₂×#90800	1	1	yes	characteristic
86	C₂	—	2	2	no	—
87	C₂	C₂×#11745218	1	1	yes	characteristic
88	C₂	#14272126	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#1181
commutator, socle	C₂²×C₂₉	C₂×C₄²
Fitting	C₂²×C₈×C₂₉	C₄
prime radical	C₂³×C₂₉	C₄²
cosocle	C₄×Dic₂₉	C₂³
hypercenter	C₂²×C₈	#1181
hypocenter	C₂₉	#1452
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #6599⋊C₈	C₂	semidirect
56. C₂₉	#1452	semidirect

Maximal subgroups

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

subgroup	index
#14272179	2
#6599⋊C₈	2
C₂×C₈×Dic₂₉	2
#1452	29