Subgroups — #16817659

Order 3712.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14270962	C₂	1	2	yes	maximal, complemented
2	C₂₉×#492	C₂	1	1	yes	maximal, characteristic
3	C₂×SD₁₆×C₂₉	—	2	2	no	—
4	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
5	C₂₉×#127	C₄	1	1	yes	characteristic
6	C₄×C₈×C₂₉	C₄	1	1	yes	characteristic
7	#11745184	—	2	2	no	—
8	C₂×Q₈×C₂₉	D₄	1	2	yes	—
9	C₂×D₄×C₂₉	—	2	1	no	—
10	C₂×D₄×C₂₉	—	4	1	no	—
11	SD₁₆×C₂₉	—	4	4	no	—
12	C₂×C₈×C₂₉	—	2	1	no	—
13	C₄⋊C₄×C₂₉	—	4	1	no	—
14	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
15	#90777	—	4	2	no	—
16	C₂³×C₂₉	—	4	1	no	—
17	Q₈×C₂₉	—	4	2	no	—
18	D₄×C₂₉	—	4	2	no	—
19	D₄×C₂₉	—	8	2	no	—
20	C₂×C₄×C₂₉	—	2	1	no	—
21	C₂×C₄×C₂₉	—	2	2	no	—
22	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₂₉	—	2	2	no	—
24	#6597	—	8	2	no	—
25	#1410	—	29	1	no	maximal, Sylow
26	C₂²×C₂₉	—	8	2	no	—
27	C₂²×C₂₉	—	8	1	no	—
28	C₂²×C₂₉	#99	1	1	yes	characteristic
29	C₄×C₂₉	—	2	2	no	—
30	C₄×C₂₉	—	2	1	no	—
31	C₄×C₂₉	—	4	2	no	—
32	#492	D₂₉	1	1	yes	characteristic
33	#356	—	29	2	no	—
34	C₂×C₂₉	—	2	1	no	—
35	C₂×C₂₉	—	16	1	no	—
36	C₂×C₂₉	#353	1	1	yes	characteristic
37	C₂×SD₁₆	—	2	2	no	—
38	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
39	#127	Dic₂₉	1	1	yes	characteristic
40	#101	—	58	2	no	—
41	C₄×C₈	Dic₂₉	1	1	yes	characteristic
42	C₂₉	#1410	1	1	yes	characteristic, complemented, Sylow
43	C₂×Q₈	C₂²⋊D₂₉	1	2	yes	—
44	C₂×D₄	—	2	1	no	—
45	C₂×D₄	—	4	1	no	—
46	SD₁₆	—	4	4	no	—
47	M₁₆	—	116	2	no	—
48	C₂×C₈	—	2	1	no	—
49	C₄⋊C₄	—	4	1	no	—
50	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
51	C₂³	—	4	1	no	—
52	Q₈	—	4	2	no	—
53	D₄	—	4	2	no	—
54	D₄	—	8	2	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₈	—	232	2	no	—
60	C₂²	—	8	2	no	—
61	C₂²	—	8	1	no	—
62	C₂²	#11745182	1	1	yes	characteristic
63	C₄	—	2	2	no	—
64	C₄	—	2	1	no	—
65	C₄	—	4	2	no	—
66	C₂	—	2	1	no	—
67	C₂	—	16	1	no	—
68	C₂	#14270956	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14270956
commutator	C₄²×C₂₉	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₂₉
Fitting	C₂₉×#492	C₂
socle	C₂×C₂₉	#353
prime radical	C₂₉×#127	C₄
cosocle	C₂₉×C₄⋊Q₈	C₂²
hypercenter	#492	D₂₉
hypocenter	C₂₉	#1410
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #492

Complements

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

N	H ≅ G/N	type
1. #14270962	C₂	semidirect
42. C₂₉	#1410	semidirect

Maximal subgroups

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

subgroup	index
#14270962	2
C₂₉×#492	2
#1410	29