Subgroups — #14272231

Order 1856.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₂₉	C₂	1	1	yes	maximal, characteristic
2	Q₈×#1181	C₂	1	8	yes	maximal, complemented
3	#11745345	C₂	1	6	yes	maximal
4	C₂×Q₈×C₂₉	C₄	1	1	yes	characteristic, complemented
5	Q₈×D₂₉	C₄	1	4	yes	complemented
6	Q₈×D₂₉	C₂²	1	4	yes	—
7	C₂×C₄×D₂₉	C₂²	1	3	yes	—
8	C₂×Dic₅₈	C₄	1	3	yes	complemented
9	C₂²⋊#1181	C₂²	1	4	yes	—
10	C₄⋊#1181	C₂²	1	12	yes	—
11	C₄×#1181	C₂²	1	12	yes	—
12	C₂²×D₂₉	C₂³	1	1	yes	characteristic
13	C₂×#1181	C₂³	1	8	yes	—
14	Q₈×C₂₉	C₂×C₄	1	4	yes	—
15	C₂×C₄×C₂₉	C₂×C₄	1	3	yes	—
16	C₂×Dic₂₉	C₂×C₄	1	3	yes	—
17	C₄×D₂₉	C₂×C₄	1	6	yes	—
18	C₄×D₂₉	C₂³	1	6	yes	—
19	Dic₅₈	C₂×C₄	1	12	yes	—
20	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
21	C₂×D₂₉	—	2	2	no	—
22	C₂×D₂₉	C₂²×C₄	1	1	yes	characteristic
23	C₂×D₂₉	C₂⁴	1	1	yes	characteristic
24	#1181	—	2	8	no	—
25	C₄×C₂₉	C₂²×C₄	1	6	yes	—
26	Dic₂₉	C₂²×C₄	1	6	yes	—
27	#519	—	29	1	no	maximal, Sylow
28	C₂×C₂₉	—	2	1	no	—
29	C₂×C₂₉	C₂³×C₄	1	1	yes	characteristic
30	D₂₉	—	2	1	no	—
31	D₂₉	2₋¹⁺⁴	1	2	yes	—
32	C₂²×Q₈	—	29	1	no	—
33	C₄×Q₈	—	29	8	no	—
34	#117	—	29	6	no	—
35	C₂₉	#519	1	1	yes	characteristic, complemented, Sylow
36	C₂×Q₈	—	29	4	no	—
37	C₂×Q₈	—	29	4	no	—
38	C₂×Q₈	—	29	3	no	—
39	C₂×Q₈	#1181	1	1	yes	characteristic, complemented
40	C₂²×C₄	—	29	3	no	—
41	C₄⋊C₄	—	29	12	no	—
42	C₂²⋊C₄	—	29	4	no	—
43	C₄²	—	29	12	no	—
44	C₂³	—	29	1	no	—
45	Q₈	—	29	12	no	—
46	Q₈	C₂×#1181	1	4	yes	—
47	C₂×C₄	—	29	3	no	—
48	C₂×C₄	—	29	6	no	—
49	C₂×C₄	—	29	6	no	—
50	C₂×C₄	—	29	8	no	—
51	C₂×C₄	C₂×#1181	1	3	yes	—
52	C₂²	—	29	1	no	—
53	C₂²	—	29	1	no	—
54	C₂²	—	58	2	no	—
55	C₂²	C₂²×#1181	1	1	yes	characteristic
56	C₄	—	29	6	no	—
57	C₄	—	58	8	no	—
58	C₄	C₂²×#1181	1	6	yes	—
59	C₂	—	2	1	no	—
60	C₂	—	29	2	no	—
61	C₂	—	58	1	no	—
62	C₂	C₂³×#1181	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×#1181
commutator, socle	C₂×C₂₉	C₂³×C₄
Fitting	C₂×Q₈×C₂₉	C₄
prime radical	C₂²×D₂₉	C₂³
cosocle	C₂×D₂₉	C₂⁴
hypercenter	C₂×Q₈	#1181
hypocenter	C₂₉	#519
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. Q₈×#1181	C₂	semidirect
4. C₂×Q₈×C₂₉	C₄	semidirect
5. Q₈×D₂₉	C₄	semidirect
8. C₂×Dic₅₈	C₄	semidirect
35. C₂₉	#519	semidirect
39. C₂×Q₈	#1181	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×D₂₉	2
Q₈×#1181	2
#11745345	2
#519	29