Subgroups — #16834501

Order 3712.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272086	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	C₄	1	1	yes	characteristic
6	#11745214	—	2	2	no	—
7	C₄×#6597	C₂²	1	1	yes	characteristic
8	C₂×Q₈×C₂₉	—	2	1	no	—
9	C₂×Dic₅₈	—	2	1	no	—
10	C₄⋊C₄×C₂₉	—	4	1	no	—
11	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
12	#90785	—	4	2	no	—
13	#90785	—	4	2	no	—
14	C₄⋊Dic₂₉	—	4	1	no	—
15	C₂×#6597	D₄	1	2	yes	—
16	#90770	—	4	2	no	—
17	Q₈×C₂₉	—	4	2	no	—
18	C₂×C₄×C₂₉	—	2	1	no	—
19	C₂×C₄×C₂₉	—	4	1	no	—
20	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×Dic₂₉	—	4	1	no	—
22	Dic₅₈	—	4	2	no	—
23	#6597	D₈	1	2	yes	—
24	#6597	SD₁₆	1	2	yes	—
25	#1358	—	29	1	no	maximal, Sylow
26	C₂²×C₂₉	#100	1	1	yes	characteristic
27	C₄×C₂₉	—	2	2	no	—
28	C₄×C₂₉	—	8	1	no	—
29	C₄×C₂₉	#102	1	2	yes	—
30	Dic₂₉	—	8	1	no	—
31	#494	—	29	1	no	—
32	#364	—	29	2	no	—
33	C₂×C₂₉	—	2	1	no	—
34	C₂×C₂₉	#331	1	1	yes	characteristic
35	C₂×Q₁₆	—	58	2	no	—
36	C₄⋊Q₈	—	29	1	no	—
37	C₄⋊Q₈	#1181	1	1	yes	characteristic
38	M₃₂	—	58	2	no	—
39	C₄×C₈	—	29	1	no	—
40	C₂₉	#1358	1	1	yes	characteristic, complemented, Sylow
41	C₂×Q₈	—	2	1	no	—
42	C₂×Q₈	—	58	1	no	—
43	Q₁₆	—	116	2	no	—
44	Q₁₆	—	116	2	no	—
45	C₂×C₈	—	29	2	no	—
46	C₄⋊C₄	—	4	1	no	—
47	C₄⋊C₄	—	116	1	no	—
48	C₄²	C₂×#1181	1	1	yes	characteristic
49	C₁₆	—	116	2	no	—
50	Q₈	—	4	2	no	—
51	Q₈	—	116	2	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	4	1	no	—
54	C₂×C₄	—	116	1	no	—
55	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
56	C₈	—	29	2	no	—
57	C₈	—	29	2	no	—
58	C₂²	#11745229	1	1	yes	characteristic
59	C₄	—	2	2	no	—
60	C₄	—	8	1	no	—
61	C₄	—	232	1	no	—
62	C₄	#11745223	1	2	yes	—
63	C₂	—	2	1	no	—
64	C₂	#14272021	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14272021
commutator	C₄²×C₂₉	C₂×C₄
Frattini	C₄²	C₂×#1181
Fitting	C₂₉×C₄⋊Q₈	C₄
socle	C₂×C₂₉	#331
prime radical	C₂²×C₂₉	#100
cosocle	C₄×#6597	C₂²
hypercenter	C₄⋊Q₈	#1181
hypocenter	C₂₉	#1358
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
40. C₂₉	#1358	semidirect

Maximal subgroups

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

subgroup	index
#14272086	2
#14271542	2
#1358	29