Subgroups — #14271082

Order 1856.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#90779	C₂	1	3	yes	maximal
3	#11745179	C₂	1	3	yes	maximal
4	C₂×Q₈×C₂₉	—	2	6	no	—
5	C₂²×C₄×C₂₉	C₂²	1	3	yes	—
6	C₂²×Dic₂₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₉	C₂²	1	3	yes	—
8	#90779	—	2	6	no	—
9	C₂³×C₂₉	C₂³	1	1	yes	characteristic
10	Q₈×C₂₉	—	2	8	no	—
11	C₂×C₄×C₂₉	—	2	6	no	—
12	C₂×C₄×C₂₉	D₄	1	6	yes	—
13	C₂×Dic₂₉	—	2	3	no	—
14	C₂×Dic₂₉	—	2	3	no	—
15	C₂×Dic₂₉	—	2	3	no	—
16	C₂×Dic₂₉	Q₈	1	6	yes	complemented
17	C₂²×C₂₉	C₂×D₄	1	3	yes	—
18	C₂²×C₂₉	C₂×Q₈	1	3	yes	—
19	C₂²×C₂₉	#41	1	1	yes	characteristic
20	C₄×C₂₉	—	2	6	no	—
21	Dic₂₉	—	2	6	no	—
22	Dic₂₉	—	4	1	no	—
23	#395	—	29	1	no	maximal, Sylow
24	C₂×C₂₉	#120	1	1	yes	characteristic
25	C₂×C₂₉	C₂²⋊Q₈	1	3	yes	—
26	C₂×C₂₉	C₄⋊Q₈	1	3	yes	—
27	C₂²×Q₈	D₂₉	1	1	yes	characteristic
28	C₂×C₄⋊C₄	—	29	3	no	—
29	#95	—	29	3	no	—
30	C₂₉	#395	1	1	yes	characteristic, complemented, Sylow
31	C₂×Q₈	—	2	6	no	—
32	C₂²×C₄	—	29	3	no	—
33	C₂²×C₄	—	29	1	no	—
34	C₂²×C₄	C₂×D₂₉	1	3	yes	—
35	C₄⋊C₄	—	58	6	no	—
36	C₂³	C₂²×D₂₉	1	1	yes	characteristic
37	Q₈	—	2	8	no	—
38	C₂×C₄	—	2	6	no	—
39	C₂×C₄	—	29	6	no	—
40	C₂×C₄	—	58	3	no	—
41	C₂×C₄	—	58	3	no	—
42	C₂×C₄	—	58	3	no	—
43	C₂×C₄	C₂²⋊D₂₉	1	6	yes	—
44	C₂²	Q₈×D₂₉	1	3	yes	—
45	C₂²	#90809	1	1	yes	characteristic
46	C₂²	C₂×C₂²⋊D₂₉	1	3	yes	—
47	C₄	—	2	6	no	—
48	C₄	—	58	6	no	—
49	C₄	—	116	1	no	—
50	C₂	#11745306	1	3	yes	—
51	C₂	#11745308	1	3	yes	—
52	C₂	#11745315	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₂₉
commutator, socle, prime radical, cosocle	C₂³×C₂₉	C₂³
Fitting	C₂²×Q₈×C₂₉	C₂
hypercenter	C₂²×Q₈	D₂₉
hypocenter	C₂₉	#395
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
16. C₂×Dic₂₉	Q₈	semidirect
30. C₂₉	#395	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Q₈×C₂₉	2
C₂×#90779	2
#11745179	2
#395	29