Subgroups — #16817784

Order 3712.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271216	C₂	1	2	yes	maximal
2	#14270885	C₂	1	4	yes	maximal, complemented
3	C₂×C₄×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₉	C₄	1	2	yes	—
5	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₂₉	C₄	1	2	yes	—
7	C₄×C₈×C₂₉	C₂²	1	2	yes	—
8	C₂²⋊#6597	C₄	1	4	yes	—
9	C₄⋊#6597	C₄	1	4	yes	—
10	C₄×#6597	C₂²	1	4	yes	—
11	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
12	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₂₉	—	2	4	no	—
14	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	—
15	C₄²×C₂₉	C₂×C₄	1	2	yes	—
16	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₂₉	C₂³	1	1	yes	characteristic
18	C₂×#6597	C₂×C₄	1	8	yes	—
19	C₂³×C₂₉	C₄²	1	1	yes	characteristic
20	C₂×C₄×C₂₉	—	2	4	no	—
21	C₂×C₄×C₂₉	C₄²	1	2	yes	—
22	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₂₉	M₁₆	1	4	yes	—
24	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
25	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
26	C₈×C₂₉	—	2	4	no	—
27	#6597	—	2	8	no	—
28	#1452	—	29	1	no	maximal, Sylow
29	C₂²×C₂₉	—	2	2	no	—
30	C₂²×C₂₉	#97	1	2	yes	—
31	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
32	C₄×C₂₉	—	2	2	no	—
33	C₄×C₂₉	#97	1	2	yes	—
34	C₄×C₂₉	C₂×M₁₆	1	2	yes	—
35	C₄×C₂₉	#131	1	4	yes	—
36	#431	—	29	2	no	—
37	C₂×C₄×C₈	D₂₉	1	1	yes	characteristic
38	#322	—	29	4	no	—
39	C₂×C₂₉	—	2	2	no	—
40	C₂×C₂₉	C₂×#97	1	1	yes	characteristic
41	C₂×C₂₉	#405	1	2	yes	—
42	C₂²×C₈	Dic₂₉	1	2	yes	—
43	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
44	C₄⋊C₈	—	29	4	no	—
45	C₂²⋊C₈	—	29	4	no	—
46	C₄×C₈	—	29	4	no	—
47	C₄×C₈	Dic₂₉	1	2	yes	—
48	C₄×C₈	C₂×D₂₉	1	2	yes	—
49	C₂₉	#1452	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₄	C₄×D₂₉	1	2	yes	—
51	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
52	C₂×C₈	—	2	4	no	—
53	C₂×C₈	—	29	8	no	—
54	C₂×C₈	C₂×Dic₂₉	1	4	yes	—
55	C₄²	C₄×D₂₉	1	2	yes	—
56	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
57	C₄²	C₂²×D₂₉	1	1	yes	characteristic
58	C₂³	C₄×Dic₂₉	1	1	yes	characteristic
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	#90777	1	4	yes	—
61	C₂×C₄	C₄×Dic₂₉	1	2	yes	—
62	C₂×C₄	C₄×Dic₂₉	1	1	yes	characteristic
63	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
64	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
65	C₈	—	2	4	no	—
66	C₈	—	58	8	no	—
67	C₂²	—	2	2	no	—
68	C₂²	#11745151	1	2	yes	—
69	C₂²	C₂×C₄×Dic₂₉	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	#11745151	1	2	yes	—
72	C₄	#11745263	1	4	yes	—
73	C₄	C₂×#90777	1	2	yes	—
74	C₂	—	2	2	no	—
75	C₂	C₂×#11745151	1	1	yes	characteristic
76	C₂	#14271118	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₂₉
commutator, socle	C₂²×C₂₉	C₂×C₄²
Fitting	C₂×C₄×C₈×C₂₉	C₂
prime radical	C₂³×C₂₉	C₄²
cosocle	C₄²×C₂₉	C₂³
hypercenter	C₂×C₄×C₈	D₂₉
hypocenter	C₂₉	#1452
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #14270885	C₂	semidirect
49. C₂₉	#1452	semidirect

Maximal subgroups

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

subgroup	index
#14271216	2
#14270885	2
C₂×C₄×C₈×C₂₉	2
#1452	29