Subgroups — #14271223

Order 1856.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745234	C₂	1	1	yes	maximal, characteristic
2	C₂₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#11745168	C₂	1	1	yes	maximal, characteristic
4	#11745168	C₂	1	1	yes	maximal, characteristic
5	#11745163	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄⋊#6597	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	C₄²×C₂₉	C₂²	1	1	yes	characteristic
12	#90781	C₄	1	1	yes	characteristic
13	#90781	C₄	1	1	yes	characteristic
14	#90779	C₄	1	1	yes	characteristic
15	#90779	C₄	1	1	yes	characteristic
16	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
17	C₂×#6597	C₂²	1	1	yes	characteristic
18	C₂×#6597	C₂²	1	1	yes	characteristic
19	C₂²×D₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
23	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
25	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
26	C₄×D₂₉	—	2	1	no	—
27	C₄×D₂₉	—	2	1	no	—
28	C₈×C₂₉	—	2	1	no	—
29	C₈×C₂₉	—	2	1	no	—
30	#6597	—	2	1	no	—
31	#6597	—	2	1	no	—
32	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×D₂₉	—	2	1	no	—
34	C₂×D₂₉	—	2	1	no	—
35	C₂×D₂₉	—	2	1	no	—
36	C₄×C₂₉	—	2	1	no	—
37	C₄×C₂₉	—	2	1	no	—
38	C₄×C₂₉	#41	1	1	yes	characteristic
39	C₄×C₂₉	#41	1	1	yes	characteristic
40	Dic₂₉	—	2	1	no	—
41	Dic₂₉	—	2	1	no	—
42	Dic₂₉	—	2	1	no	—
43	#433	—	29	1	no	maximal, Sylow
44	C₂×C₂₉	#117	1	1	yes	characteristic
45	C₂×C₂₉	#131	1	1	yes	characteristic
46	C₂×C₂₉	#131	1	1	yes	characteristic
47	D₂₉	—	4	1	no	—
48	#117	—	29	1	no	—
49	C₄⋊C₈	—	29	1	no	—
50	C₄⋊C₈	D₂₉	1	1	yes	characteristic, complemented
51	C₂²⋊C₈	—	29	1	no	—
52	C₂²⋊C₈	—	29	1	no	—
53	#97	—	29	1	no	—
54	C₄×C₈	—	29	1	no	—
55	C₂₉	#433	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₄	—	29	1	no	—
57	C₂×C₈	—	29	1	no	—
58	C₂×C₈	—	29	1	no	—
59	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
60	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
61	C₄⋊C₄	—	29	1	no	—
62	C₄⋊C₄	—	29	1	no	—
63	C₂²⋊C₄	—	29	1	no	—
64	C₂²⋊C₄	—	29	1	no	—
65	C₄²	—	29	1	no	—
66	C₄²	C₂×D₂₉	1	1	yes	characteristic
67	C₂³	—	29	1	no	—
68	C₂×C₄	—	29	1	no	—
69	C₂×C₄	—	29	1	no	—
70	C₂×C₄	—	29	1	no	—
71	C₂×C₄	—	58	1	no	—
72	C₂×C₄	—	58	1	no	—
73	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
74	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
75	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
76	C₈	—	2	1	no	—
77	C₈	—	2	1	no	—
78	C₈	—	58	1	no	—
79	C₈	—	58	1	no	—
80	C₂²	—	58	1	no	—
81	C₂²	—	58	1	no	—
82	C₂²	—	58	1	no	—
83	C₂²	C₂×C₄×D₂₉	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	2	1	no	—
86	C₄	—	58	1	no	—
87	C₄	—	58	1	no	—
88	C₄	—	58	1	no	—
89	C₄	#90807	1	1	yes	characteristic
90	C₄	#90809	1	1	yes	characteristic
91	C₂	—	116	1	no	—
92	C₂	#11745254	1	1	yes	characteristic
93	C₂	#11745263	1	1	yes	characteristic
94	C₂	#11745269	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₉
commutator, socle	C₂²×C₂₉	C₂²×C₄
Fitting	C₂₉×C₄⋊C₈	C₂
prime radical	C₂²×D₂₉	C₂×C₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	C₄⋊C₈	D₂₉
hypocenter	C₂₉	#433
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂₉×C₄⋊C₈	C₂	semidirect
5. #11745163	C₂	semidirect
6. C₈×Dic₂₉	C₂	semidirect
7. C₄⋊#6597	C₂	semidirect
50. C₄⋊C₈	D₂₉	semidirect
55. C₂₉	#433	semidirect

Maximal subgroups

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

subgroup	index
#11745234	2
C₂₉×C₄⋊C₈	2
#11745168	2
#11745163	2
C₈×Dic₂₉	2
C₄⋊#6597	2
#433	29