Subgroups — #14271083

Order 1856.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₅₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#90779	C₂	1	2	yes	maximal
4	#11745179	C₂	1	2	yes	maximal
5	#11745179	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₂₉	C₂²	1	2	yes	—
10	C₂²×Dic₂₉	C₂²	1	2	yes	—
11	C₂×Dic₅₈	—	2	2	no	—
12	C₂×Dic₅₈	—	2	4	no	—
13	C₄⋊C₄×C₂₉	—	2	2	no	—
14	#90779	—	2	4	no	—
15	C₂³×C₂₉	C₂³	1	1	yes	characteristic
16	C₂×C₄×C₂₉	—	2	1	no	—
17	C₂×C₄×C₂₉	—	2	2	no	—
18	C₂×C₄×C₂₉	—	2	1	no	—
19	C₂×C₄×C₂₉	—	2	2	no	—
20	C₂×C₄×C₂₉	—	2	1	no	—
21	C₂×C₄×C₂₉	D₄	1	2	yes	—
22	C₂×C₄×C₂₉	Q₈	1	2	yes	complemented
23	C₂×Dic₂₉	—	2	2	no	—
24	C₂×Dic₂₉	—	2	2	no	—
25	C₂×Dic₂₉	—	2	2	no	—
26	C₂×Dic₂₉	—	2	2	no	—
27	C₂×Dic₂₉	D₄	1	4	yes	—
28	C₂×Dic₂₉	Q₈	1	4	yes	complemented
29	Dic₅₈	—	2	8	no	—
30	C₂²×C₂₉	C₂×D₄	1	2	yes	—
31	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
32	C₂²×C₂₉	C₂×Q₈	1	1	yes	characteristic
33	C₂²×C₂₉	C₂×Q₈	1	2	yes	—
34	C₂²×C₂₉	#41	1	1	yes	characteristic
35	C₄×C₂₉	—	2	2	no	—
36	C₄×C₂₉	—	2	2	no	—
37	C₄×C₂₉	—	4	1	no	—
38	Dic₂₉	—	2	4	no	—
39	Dic₂₉	—	2	4	no	—
40	#395	—	29	1	no	maximal, Sylow
41	C₂×C₂₉	#120	1	1	yes	characteristic
42	C₂×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
43	C₂×C₂₉	C₂²⋊Q₈	1	2	yes	—
44	C₂×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
45	C₂×C₂₉	C₄⋊Q₈	1	2	yes	—
46	C₂²×Q₈	—	29	1	no	—
47	C₂×C₄⋊C₄	—	29	2	no	—
48	C₂×C₄⋊C₄	D₂₉	1	1	yes	characteristic
49	#95	—	29	1	no	—
50	#95	—	29	2	no	—
51	C₂₉	#395	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₈	—	58	4	no	—
53	C₂×Q₈	—	58	2	no	—
54	C₂²×C₄	—	29	2	no	—
55	C₂²×C₄	—	29	2	no	—
56	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
57	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
58	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
59	C₄⋊C₄	—	2	2	no	—
60	C₄⋊C₄	—	58	4	no	—
61	C₂³	C₂²×D₂₉	1	1	yes	characteristic
62	Q₈	—	58	8	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	2	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	29	4	no	—
69	C₂×C₄	—	29	4	no	—
70	C₂×C₄	—	58	2	no	—
71	C₂×C₄	—	58	2	no	—
72	C₂×C₄	—	58	2	no	—
73	C₂×C₄	—	58	2	no	—
74	C₂×C₄	Dic₅₈	1	2	yes	complemented
75	C₂×C₄	C₂²⋊D₂₉	1	2	yes	—
76	C₂²	C₂×Dic₅₈	1	1	yes	characteristic
77	C₂²	#90805	1	1	yes	characteristic
78	C₂²	D₄×D₂₉	1	2	yes	—
79	C₂²	Q₈×D₂₉	1	2	yes	—
80	C₂²	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	2	2	no	—
83	C₄	—	4	1	no	—
84	C₄	—	58	4	no	—
85	C₄	—	58	4	no	—
86	C₂	#11745250	1	2	yes	—
87	C₂	#11745258	1	2	yes	—
88	C₂	#11745286	1	1	yes	characteristic
89	C₂	#11745299	1	1	yes	characteristic
90	C₂	#11745306	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₂₉
commutator, socle, prime radical, cosocle	C₂³×C₂₉	C₂³
Fitting	C₂×C₄⋊C₄×C₂₉	C₂
hypercenter	C₂×C₄⋊C₄	D₂₉
hypocenter	C₂₉	#395
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
22. C₂×C₄×C₂₉	Q₈	semidirect
28. C₂×Dic₂₉	Q₈	semidirect
51. C₂₉	#395	semidirect
74. C₂×C₄	Dic₅₈	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₅₈	2
C₂×C₄⋊C₄×C₂₉	2
C₂×#90779	2
#11745179	2
#395	29