Subgroups — #14271203

Order 1856.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
2	#11745288	C₂	1	1	yes	maximal, characteristic
3	C₂×#90777	C₂	1	1	yes	maximal, characteristic
4	#11745156	C₂	1	2	yes	maximal, complemented
5	#11745155	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₂₉	—	2	1	no	—
7	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₂₉	—	2	1	no	—
9	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
10	C₂²⋊Dic₂₉	—	2	1	no	—
11	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
13	C₄×Dic₂₉	—	2	1	no	—
14	#90777	C₄	1	4	yes	complemented
15	C₂×#6597	C₂²	1	2	yes	—
16	C₂³×C₂₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₂₉	—	2	2	no	—
18	C₂×C₄×C₂₉	—	4	2	no	—
19	C₂×C₄×C₂₉	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
21	C₂×C₄×C₂₉	Q₈	1	2	yes	—
22	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
23	C₂×Dic₂₉	—	2	1	no	—
24	C₂×Dic₂₉	—	2	1	no	—
25	#6597	C₂×C₄	1	4	yes	complemented
26	C₂²×C₂₉	—	2	1	no	—
27	C₂²×C₂₉	—	2	1	no	—
28	C₂²×C₂₉	C₄⋊C₄	1	2	yes	—
29	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
30	C₄×C₂₉	—	4	2	no	—
31	C₄×C₂₉	C₄⋊C₄	1	2	yes	—
32	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
33	C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
34	Dic₂₉	—	4	1	no	—
35	Dic₂₉	—	4	1	no	—
36	#428	—	29	1	no	maximal, Sylow
37	C₂×C₂₉	—	2	2	no	—
38	C₂×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
40	C₂×C₂₉	#137	1	1	yes	characteristic
41	C₂×M₁₆	—	29	1	no	—
42	#117	—	29	1	no	—
43	C₂×C₄⋊C₄	D₂₉	1	1	yes	characteristic
44	#107	—	29	2	no	—
45	#106	—	29	2	no	—
46	C₂₉	#428	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₄	—	2	1	no	—
48	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
49	M₁₆	—	29	4	no	—
50	C₂×C₈	—	29	2	no	—
51	C₄⋊C₄	—	2	1	no	—
52	C₄⋊C₄	—	29	1	no	—
53	C₄⋊C₄	—	29	1	no	—
54	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
55	C₂²⋊C₄	—	58	1	no	—
56	C₄²	—	58	1	no	—
57	C₂³	C₂²⋊D₂₉	1	1	yes	characteristic
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	—	58	1	no	—
61	C₂×C₄	—	58	1	no	—
62	C₂×C₄	Dic₅₈	1	2	yes	—
63	C₂×C₄	C₄×D₂₉	1	2	yes	—
64	C₂×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
65	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
66	C₈	—	29	4	no	—
67	C₂²	—	2	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	#90779	1	2	yes	—
70	C₂²	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
71	C₄	—	4	2	no	—
72	C₄	—	116	1	no	—
73	C₄	—	116	1	no	—
74	C₄	#90779	1	2	yes	—
75	C₄	C₂×Dic₅₈	1	1	yes	characteristic
76	C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
77	C₂	—	2	2	no	—
78	C₂	C₂×#90779	1	1	yes	characteristic
79	C₂	#11745294	1	1	yes	characteristic
80	C₂	#11745304	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₂₉
commutator	C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂×C₄⋊C₄×C₂₉	C₂
socle	C₂²×C₂₉	C₂×D₄
prime radical	C₂³×C₂₉	D₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	C₂×C₄⋊C₄	D₂₉
hypocenter	C₂₉	#428
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. #11745156	C₂	semidirect
5. #11745155	C₂	semidirect
14. #90777	C₄	semidirect
25. #6597	C₂×C₄	semidirect
46. C₂₉	#428	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₄×C₂₉	2
#11745288	2
C₂×#90777	2
#11745156	2
#11745155	2
#428	29