Subgroups — #16821009

Order 3712.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271212	C₂	1	3	yes	maximal, complemented
2	#14271126	C₂	1	3	yes	maximal
3	C₂₉×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₂₉	C₂²	1	1	yes	characteristic
5	C₂×M₁₆×C₂₉	C₂²	1	3	yes	—
6	C₂×#90777	C₂²	1	3	yes	—
7	#11745168	—	2	6	no	—
8	#11745167	—	2	6	no	—
9	C₂³×D₂₉	Q₈	1	1	yes	characteristic
10	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
11	C₂²×Dic₂₉	Q₈	1	1	yes	characteristic
12	C₂×C₄×D₂₉	—	2	3	no	—
13	C₂×C₄×D₂₉	—	2	3	no	—
14	M₁₆×C₂₉	—	2	6	no	—
15	C₂×C₈×C₂₉	D₄	1	6	yes	—
16	#90777	—	2	6	no	—
17	C₂×#6597	—	2	3	no	—
18	C₂³×C₂₉	C₂×Q₈	1	1	yes	characteristic
19	C₂²×D₂₉	—	2	3	no	—
20	C₂²×D₂₉	—	4	2	no	—
21	C₂×C₄×C₂₉	C₂×D₄	1	3	yes	—
22	C₂×C₄×C₂₉	#41	1	3	yes	—
23	C₂×Dic₂₉	—	2	3	no	—
24	C₄×D₂₉	—	4	3	no	—
25	C₄×D₂₉	—	4	1	no	—
26	C₈×C₂₉	—	2	6	no	—
27	#6597	—	4	3	no	—
28	#2091	—	29	1	no	maximal, Sylow
29	C₂²×C₂₉	—	4	1	no	—
30	C₂²×C₂₉	C₂²⋊Q₈	1	3	yes	—
31	C₂×D₂₉	—	2	6	no	—
32	C₂×D₂₉	—	4	3	no	—
33	C₂×D₂₉	—	4	1	no	—
34	C₄×C₂₉	#123	1	3	yes	—
35	C₄×C₂₉	#127	1	1	yes	characteristic
36	Dic₂₉	—	4	1	no	—
37	#430	—	29	3	no	—
38	#407	—	29	3	no	—
39	#338	D₂₉	1	1	yes	characteristic, complemented
40	C₂×C₂₉	—	2	3	no	—
41	C₂×C₂₉	#399	1	1	yes	characteristic
42	D₂₉	—	4	2	no	—
43	C₂³×C₄	—	29	1	no	—
44	C₂×M₁₆	—	29	3	no	—
45	C₂×M₁₆	C₂×D₂₉	1	3	yes	—
46	#108	—	58	6	no	—
47	C₂²⋊C₈	—	58	6	no	—
48	C₂₉	#2091	1	1	yes	characteristic, complemented, Sylow
49	C₂⁴	—	29	1	no	—
50	C₂²×C₄	—	29	1	no	—
51	C₂²×C₄	—	58	3	no	—
52	C₂²×C₄	—	58	3	no	—
53	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
54	M₁₆	—	2	6	no	—
55	M₁₆	—	58	6	no	—
56	C₂×C₈	—	58	3	no	—
57	C₂×C₈	D₁₁₆	1	6	yes	—
58	C₂³	—	58	3	no	—
59	C₂³	—	116	2	no	—
60	C₂³	Q₈×D₂₉	1	1	yes	characteristic
61	C₂×C₄	—	58	3	no	—
62	C₂×C₄	—	116	1	no	—
63	C₂×C₄	—	116	3	no	—
64	C₂×C₄	C₂×D₁₁₆	1	3	yes	—
65	C₂×C₄	#90807	1	3	yes	—
66	C₈	—	2	6	no	—
67	C₈	—	116	3	no	—
68	C₂²	—	4	1	no	—
69	C₂²	—	58	6	no	—
70	C₂²	—	116	3	no	—
71	C₂²	—	116	1	no	—
72	C₂²	#11745259	1	3	yes	—
73	C₄	—	116	1	no	—
74	C₄	#11745236	1	1	yes	characteristic
75	C₄	#11745248	1	3	yes	—
76	C₂	—	2	3	no	—
77	C₂	—	116	2	no	—
78	C₂	#14271100	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11745236
commutator, cosocle	C₂²×C₄×C₂₉	C₂³
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#338	C₂
socle	C₂×C₂₉	#399
prime radical	C₂³×D₂₉	Q₈
hypercenter	#338	D₂₉
hypocenter	C₂₉	#2091
LCS	G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
1. #14271212	C₂	semidirect
3. C₂₉×#338	C₂	semidirect
39. #338	D₂₉	semidirect
48. C₂₉	#2091	semidirect

Maximal subgroups

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

subgroup	index
#14271212	2
#14271126	2
C₂₉×#338	2
#2091	29