Subgroups — #16819099

Order 3712.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271540	C₂	1	1	yes	maximal, characteristic
2	#14271511	C₂	1	4	yes	maximal, complemented
3	C₈×#6597	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₁₆×C₂₉	—	2	2	no	—
6	C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₂×D₂₃₂	—	2	2	no	—
8	#11745236	C₂²	1	2	yes	—
9	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	#11745157	—	2	8	no	—
11	C₄×#6597	C₂²	1	2	yes	—
12	C₂×Q₈×C₂₉	—	2	2	no	—
13	C₂×D₁₁₆	—	2	4	no	—
14	C₂×D₁₁₆	—	2	2	no	—
15	Q₁₆×C₂₉	—	4	4	no	—
16	C₂×C₈×C₂₉	D₄	1	2	yes	—
17	C₄⋊C₄×C₂₉	—	2	4	no	—
18	C₄²×C₂₉	C₂³	1	1	yes	characteristic
19	C₂×#6597	D₄	1	4	yes	—
20	D₂₃₂	—	4	4	no	—
21	C₂²×D₂₉	—	4	2	no	—
22	Q₈×C₂₉	—	4	4	no	—
23	C₂×C₄×C₂₉	—	4	2	no	—
24	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
25	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
26	D₁₁₆	—	4	4	no	—
27	D₁₁₆	—	4	8	no	—
28	C₈×C₂₉	D₈	1	4	yes	—
29	#6597	—	2	4	no	—
30	#1709	—	29	1	no	maximal, Sylow
31	C₂²×C₂₉	#127	1	1	yes	characteristic
32	C₂×D₂₉	—	8	2	no	—
33	C₂×D₂₉	—	8	4	no	—
34	C₄×C₂₉	—	8	2	no	—
35	C₄×C₂₉	C₂×D₈	1	2	yes	—
36	C₄×C₂₉	#135	1	4	yes	—
37	#494	D₂₉	1	1	yes	characteristic, complemented
38	#493	—	29	1	no	—
39	#486	—	29	4	no	—
40	C₈²	—	29	1	no	—
41	C₂×C₂₉	#493	1	1	yes	characteristic
42	C₂×C₂₉	#495	1	2	yes	—
43	D₂₉	—	16	2	no	—
44	C₂×Q₁₆	—	2	2	no	—
45	C₂×D₈	—	58	2	no	—
46	C₄⋊Q₈	C₂×D₂₉	1	2	yes	—
47	#127	—	29	2	no	—
48	#102	—	58	8	no	—
49	C₄×C₈	—	29	2	no	—
50	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
51	C₂₉	#1709	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₈	—	2	2	no	—
53	C₂×D₄	—	58	4	no	—
54	C₂×D₄	—	58	2	no	—
55	Q₁₆	—	4	4	no	—
56	D₈	—	116	4	no	—
57	C₂×C₈	—	29	4	no	—
58	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
59	C₄⋊C₄	—	2	4	no	—
60	C₄²	C₂²×D₂₉	1	1	yes	characteristic
61	C₂³	—	116	2	no	—
62	Q₈	—	4	4	no	—
63	D₄	—	116	8	no	—
64	D₄	—	116	4	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	D₄×D₂₉	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
68	C₈	—	58	4	no	—
69	C₈	#90782	1	4	yes	—
70	C₂²	—	232	2	no	—
71	C₂²	—	232	4	no	—
72	C₂²	#11745302	1	1	yes	characteristic
73	C₄	—	8	2	no	—
74	C₄	#11745281	1	4	yes	—
75	C₄	C₂×#90782	1	2	yes	—
76	C₂	—	464	2	no	—
77	C₂	#14271539	1	1	yes	characteristic
78	C₂	#14271548	1	2	yes	—

	subgroup	G/H
center	C₂²	#11745302
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#494	C₂
socle	C₂²×C₂₉	#127
prime radical	#14271540	C₂
hypercenter	#494	D₂₉
hypocenter	C₂₉	#1709
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

Complements

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

N	H ≅ G/N	type
2. #14271511	C₂	semidirect
3. C₈×#6597	C₂	semidirect
4. C₂₉×#494	C₂	semidirect
37. #494	D₂₉	semidirect
51. C₂₉	#1709	semidirect

Maximal subgroups

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

subgroup	index
#14271540	2
#14271511	2
C₈×#6597	2
C₂₉×#494	2
#1709	29