Subgroups — #14271294

Order 1856.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#6597	C₂	1	2	yes	maximal
3	C₄⋊#6597	C₂	1	1	yes	maximal, characteristic
4	#11745151	C₂	1	2	yes	maximal
5	C₄×#6597	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₂₉	C₄	1	1	yes	characteristic
7	C₄⋊C₄×C₂₉	C₄	1	2	yes	—
8	C₄⋊C₄×C₂₉	C₄	1	1	yes	characteristic
9	C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	C₄²×C₂₉	C₂²	1	2	yes	—
11	C₂×#6597	C₂²	1	1	yes	characteristic
12	C₂×#6597	C₂²	1	2	yes	—
13	C₂×#6597	C₂²	1	1	yes	characteristic
14	Q₈×C₂₉	—	2	2	no	—
15	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₂₉	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₂₉	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
20	#6597	—	2	1	no	—
21	#6597	—	2	2	no	—
22	#6597	Q₈	1	2	yes	complemented
23	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₂₉	—	2	2	no	—
25	C₄×C₂₉	—	2	1	no	—
26	C₄×C₂₉	—	2	2	no	—
27	C₄×C₂₉	M₁₆	1	2	yes	—
28	C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
29	C₄×C₂₉	#41	1	1	yes	characteristic
30	#446	—	29	1	no	maximal, Sylow
31	C₂×C₂₉	C₄×Q₈	1	1	yes	characteristic
32	C₂×C₂₉	C₂×M₁₆	1	1	yes	characteristic
33	C₂×C₂₉	#131	1	1	yes	characteristic
34	C₄×Q₈	D₂₉	1	1	yes	characteristic
35	C₄⋊C₈	—	29	1	no	—
36	C₄⋊C₈	—	29	2	no	—
37	#97	—	29	2	no	—
38	C₄×C₈	—	29	1	no	—
39	C₂₉	#446	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	Dic₂₉	1	1	yes	characteristic
41	C₂×C₈	—	29	1	no	—
42	C₂×C₈	—	29	1	no	—
43	C₂×C₈	—	29	2	no	—
44	C₄⋊C₄	Dic₂₉	1	2	yes	—
45	C₄⋊C₄	Dic₂₉	1	1	yes	characteristic
46	C₄²	C₂×D₂₉	1	1	yes	characteristic
47	C₄²	C₂×D₂₉	1	2	yes	—
48	Q₈	—	2	2	no	—
49	C₂×C₄	C₂×Dic₂₉	1	1	yes	characteristic
50	C₂×C₄	C₂×Dic₂₉	1	2	yes	—
51	C₂×C₄	C₂×Dic₂₉	1	2	yes	—
52	C₂×C₄	C₂×Dic₂₉	1	1	yes	characteristic
53	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
54	C₈	—	29	2	no	—
55	C₈	—	58	1	no	—
56	C₈	—	58	2	no	—
57	C₂²	C₂²×Dic₂₉	1	1	yes	characteristic
58	C₄	—	2	2	no	—
59	C₄	—	2	1	no	—
60	C₄	—	2	2	no	—
61	C₄	#90777	1	2	yes	—
62	C₄	Q₈×D₂₉	1	1	yes	characteristic
63	C₄	#90809	1	1	yes	characteristic
64	C₂	C₂×#90777	1	1	yes	characteristic
65	C₂	Q₈×Dic₂₉	1	1	yes	characteristic
66	C₂	#11745310	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₉
commutator, socle, prime radical	C₂²×C₂₉	C₂²×C₄
Fitting	C₄×Q₈×C₂₉	C₂
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	C₄×Q₈	D₂₉
hypocenter	C₂₉	#446
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
22. #6597	Q₈	semidirect
39. C₂₉	#446	semidirect

Maximal subgroups

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

subgroup	index
C₄×Q₈×C₂₉	2
C₄⋊#6597	2
#11745151	2
C₄×#6597	2
#446	29