Subgroups — #16834629

Order 3712.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272074	C₂	1	2	yes	maximal
2	#14271542	C₂	1	1	yes	maximal, characteristic
3	C₂₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
4	C₂×#90785	—	2	2	no	—
5	#11745231	C₂²	1	1	yes	characteristic
6	#11745221	—	2	2	no	—
7	C₄×#6597	C₄	1	1	yes	characteristic
8	C₂×Q₈×C₂₉	—	2	1	no	—
9	C₂×Dic₅₈	D₄	1	2	yes	—
10	#90800	—	4	2	no	—
11	C₄⋊C₄×C₂₉	—	4	1	no	—
12	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
13	#90785	—	4	4	no	—
14	C₄⋊Dic₂₉	—	4	1	no	—
15	C₂×#6597	—	2	1	no	—
16	Q₈×C₂₉	—	4	2	no	—
17	C₂×C₄×C₂₉	—	2	1	no	—
18	C₂×C₄×C₂₉	—	4	1	no	—
19	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×Dic₂₉	—	2	2	no	—
21	Dic₅₈	—	4	2	no	—
22	#6599	—	8	2	no	—
23	#6597	—	2	2	no	—
24	#1411	—	29	1	no	maximal, Sylow
25	C₂²×C₂₉	#99	1	1	yes	characteristic
26	C₄×C₂₉	—	2	2	no	—
27	C₄×C₂₉	—	2	1	no	—
28	C₄×C₂₉	—	8	1	no	—
29	Dic₂₉	—	4	2	no	—
30	#494	—	29	1	no	—
31	#356	—	29	2	no	—
32	C₂×C₂₉	—	2	1	no	—
33	C₂×C₂₉	#353	1	1	yes	characteristic
34	C₂×Q₁₆	—	58	2	no	—
35	C₄⋊Q₈	—	29	1	no	—
36	C₄⋊Q₈	#1181	1	1	yes	characteristic
37	#101	—	58	2	no	—
38	C₄×C₈	—	29	1	no	—
39	C₂₉	#1411	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	—	2	1	no	—
41	C₂×Q₈	—	29	2	no	—
42	Q₁₆	—	116	4	no	—
43	M₁₆	—	116	2	no	—
44	C₂×C₈	—	58	1	no	—
45	C₄⋊C₄	—	4	1	no	—
46	C₄⋊C₄	—	116	1	no	—
47	C₄²	C₂×#1181	1	1	yes	characteristic
48	Q₈	—	4	2	no	—
49	Q₈	—	116	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	4	1	no	—
52	C₂×C₄	—	58	2	no	—
53	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
54	C₈	—	58	2	no	—
55	C₈	—	232	2	no	—
56	C₂²	#11745227	1	1	yes	characteristic
57	C₄	—	2	2	no	—
58	C₄	—	2	1	no	—
59	C₄	—	8	1	no	—
60	C₄	—	116	2	no	—
61	C₂	—	2	1	no	—
62	C₂	#14272067	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14272067
commutator	C₄²×C₂₉	C₂×C₄
Frattini	C₄²	C₂×#1181
Fitting	C₂₉×C₄⋊Q₈	C₄
socle	C₂×C₂₉	#353
prime radical	C₂²×C₂₉	#99
cosocle	#11745231	C₂²
hypercenter	C₄⋊Q₈	#1181
hypocenter	C₂₉	#1411
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
39. C₂₉	#1411	semidirect

Maximal subgroups

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

subgroup	index
#14272074	2
#14271542	2
#1411	29