Subgroups — #16834460

Order 3712.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#90770	C₂	1	1	yes	maximal, characteristic
2	#14272051	C₂	1	1	yes	maximal, characteristic
3	#14271294	C₂	1	1	yes	maximal, characteristic
4	C₄×Q₈×C₂₉	C₄	1	1	yes	characteristic
5	C₂×#90770	—	2	1	no	—
6	C₂×#90770	—	2	1	no	—
7	C₄⋊#6597	—	2	1	no	—
8	C₄⋊#6597	C₄	1	1	yes	characteristic
9	#11745151	—	2	1	no	—
10	C₄×#6597	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₂₉	C₈	1	1	yes	characteristic
12	C₄⋊C₄×C₂₉	—	2	1	no	—
13	C₄⋊C₄×C₂₉	C₈	1	1	yes	characteristic
14	C₄²×C₂₉	—	2	1	no	—
15	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂×#6597	—	2	1	no	—
17	C₂×#6597	D₄	1	1	yes	characteristic
18	C₂×#6597	D₄	1	1	yes	characteristic
19	#90770	—	2	2	no	—
20	#90770	—	4	1	no	—
21	Q₈×C₂₉	—	4	1	no	—
22	C₂×C₄×C₂₉	—	2	1	no	—
23	C₂×C₄×C₂₉	—	2	1	no	—
24	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₂₉	M₁₆	1	1	yes	characteristic
27	#6597	—	2	1	no	—
28	#6597	—	4	1	no	—
29	#6597	SD₁₆	1	1	yes	characteristic
30	#6597	Q₁₆	1	1	yes	characteristic
31	#1338	—	29	1	no	maximal, Sylow
32	C₂²×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
33	C₄×C₂₉	—	2	1	no	—
34	C₄×C₂₉	—	2	1	no	—
35	C₄×C₂₉	—	4	1	no	—
36	C₄×C₂₉	—	4	1	no	—
37	C₄×C₂₉	#103	1	1	yes	characteristic
38	C₄×C₂₉	#104	1	1	yes	characteristic
39	#446	—	29	1	no	—
40	C₄⋊C₁₆	—	29	1	no	—
41	#346	—	29	1	no	—
42	C₂×C₂₉	Q₈⋊C₈	1	1	yes	characteristic
43	C₂×C₂₉	#349	1	1	yes	characteristic
44	C₂×C₂₉	#350	1	1	yes	characteristic
45	C₄×Q₈	#1181	1	1	yes	characteristic
46	C₂×C₁₆	—	58	1	no	—
47	C₂×C₁₆	—	58	1	no	—
48	C₄⋊C₈	—	29	1	no	—
49	C₄⋊C₈	—	58	1	no	—
50	#97	—	58	1	no	—
51	C₄×C₈	—	29	1	no	—
52	C₂₉	#1338	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₈	#6599	1	1	yes	characteristic
54	C₂×C₈	—	29	1	no	—
55	C₂×C₈	—	29	1	no	—
56	C₂×C₈	—	58	1	no	—
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	#6599	1	1	yes	characteristic
59	C₄²	—	2	1	no	—
60	C₄²	C₂×#1181	1	1	yes	characteristic
61	C₁₆	—	58	2	no	—
62	C₁₆	—	116	1	no	—
63	Q₈	—	4	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	C₂×#6599	1	1	yes	characteristic
67	C₂×C₄	#90800	1	1	yes	characteristic
68	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
69	C₈	—	29	1	no	—
70	C₈	—	29	1	no	—
71	C₈	—	58	1	no	—
72	C₈	—	116	1	no	—
73	C₂²	C₂²⋊#6599	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	#11745225	1	1	yes	characteristic
79	C₄	#11745226	1	1	yes	characteristic
80	C₂	Q₈⋊#6599	1	1	yes	characteristic
81	C₂	#14272059	1	1	yes	characteristic
82	C₂	#14272061	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#1181
commutator	C₂×C₄×C₂₉	C₂×C₈
Frattini	C₄²	C₂×#1181
Fitting	C₄×Q₈×C₂₉	C₄
socle, prime radical	C₂²×C₂₉	C₂²⋊C₈
cosocle	C₄×#6597	C₂²
hypercenter	C₄×Q₈	#1181
hypocenter	C₂₉	#1338
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
52. C₂₉	#1338	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#90770	2
#14272051	2
#14271294	2
#1338	29