Subgroups — #16821287

Order 3712.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745167	C₂	1	2	yes	maximal
2	#14270993	C₂	1	4	yes	maximal, complemented
3	C₂×C₂₉×M₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
5	C₂×#90777	—	2	2	no	—
6	C₂₉×M₃₂	C₄	1	4	yes	—
7	C₂×C₁₆×C₂₉	C₂²	1	2	yes	—
8	#11745167	—	2	2	no	—
9	#11745167	C₂²	1	4	yes	—
10	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
11	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
13	C₂×C₈×C₂₉	Q₈	1	2	yes	—
14	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
15	#90777	—	2	4	no	—
16	#90777	—	4	2	no	—
17	C₂×#6597	—	4	2	no	—
18	C₁₆×C₂₉	C₂×C₄	1	4	yes	—
19	C₂³×C₂₉	Q₁₆	1	1	yes	characteristic
20	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
21	C₂×C₄×C₂₉	D₈	1	2	yes	—
22	C₂×C₄×C₂₉	Q₁₆	1	1	yes	characteristic
23	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
24	C₈×C₂₉	C₄⋊C₄	1	2	yes	—
25	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
26	C₈×C₂₉	C₂×Q₈	1	1	yes	characteristic
27	#6597	—	4	4	no	—
28	#2161	—	29	1	no	maximal, Sylow
29	C₂²×C₂₉	—	4	1	no	—
30	C₂²×C₂₉	#107	1	2	yes	—
31	C₂²×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
32	C₄×C₂₉	#107	1	2	yes	—
33	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
35	C₂×M₃₂	D₂₉	1	1	yes	characteristic
36	C₂×#108	—	29	2	no	—
37	#368	—	29	4	no	—
38	C₂×C₂₉	—	2	2	no	—
39	C₂×C₂₉	—	2	1	no	—
40	C₂×C₂₉	C₂×#107	1	1	yes	characteristic
41	C₂×M₁₆	—	58	2	no	—
42	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
43	M₃₂	Dic₂₉	1	4	yes	—
44	C₂×C₁₆	C₂×D₂₉	1	2	yes	—
45	#108	—	29	4	no	—
46	#108	—	58	2	no	—
47	C₂₉	#2161	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₄	D₁₁₆	1	1	yes	characteristic
49	M₁₆	—	58	4	no	—
50	M₁₆	—	116	2	no	—
51	C₂×C₈	—	116	2	no	—
52	C₂×C₈	Dic₅₈	1	2	yes	—
53	C₂×C₈	D₁₁₆	1	1	yes	characteristic
54	C₂×C₈	C₂×Dic₂₉	1	2	yes	—
55	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
56	C₁₆	C₂×Dic₂₉	1	4	yes	—
57	C₂³	Dic₁₁₆	1	1	yes	characteristic
58	C₂×C₄	D₂₃₂	1	2	yes	—
59	C₂×C₄	Dic₁₁₆	1	1	yes	characteristic
60	C₂×C₄	C₄⋊Dic₂₉	1	2	yes	—
61	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
62	C₈	—	116	4	no	—
63	C₈	C₄⋊Dic₂₉	1	2	yes	—
64	C₈	C₂×Dic₅₈	1	1	yes	characteristic
65	C₈	C₂²×Dic₂₉	1	1	yes	characteristic
66	C₂²	—	4	1	no	—
67	C₂²	#11745166	1	2	yes	—
68	C₂²	C₂×Dic₁₁₆	1	1	yes	characteristic
69	C₄	#11745166	1	2	yes	—
70	C₄	C₂×D₂₃₂	1	1	yes	characteristic
71	C₄	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	C₂	C₂×#11745166	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₂₃₂
commutator	C₈×C₂₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₉
Fitting	C₂×C₂₉×M₃₂	C₂
socle	C₂×C₂₉	C₂×#107
prime radical	C₂³×C₂₉	Q₁₆
cosocle	C₂×C₈×C₂₉	C₂³
hypercenter	C₂×M₃₂	D₂₉
hypocenter	C₂₉	#2161
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
2. #14270993	C₂	semidirect
47. C₂₉	#2161	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745167	2
#14270993	2
C₂×C₂₉×M₃₂	2
#2161	29