Subgroups — #14271744

Order 1856.

294 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#90805	C₂	1	2	yes	maximal, complemented
2	C₂×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#11745292	C₂	1	4	yes	maximal, complemented
4	#11745259	C₂	1	4	yes	maximal, complemented
5	#11745257	C₂	1	4	yes	maximal, complemented
6	C₂²×C₄×C₂₉	C₂²	1	2	yes	—
7	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×C₂²⋊D₂₉	C₂²	1	4	yes	—
9	#90805	—	2	8	no	—
10	C₂×D₁₁₆	C₂²	1	2	yes	—
11	C₂×D₁₁₆	C₂²	1	4	yes	—
12	C₂×C₄×D₂₉	C₂²	1	4	yes	—
13	C₂×Dic₅₈	C₂²	1	2	yes	—
14	C₄⋊C₄×C₂₉	C₂²	1	4	yes	—
15	#90781	C₂²	1	8	yes	—
16	C₄⋊Dic₂₉	C₂²	1	4	yes	—
17	C₂³×C₂₉	C₂³	1	1	yes	characteristic
18	C₂²×D₂₉	C₂³	1	4	yes	—
19	C₂×C₄×C₂₉	—	4	2	no	—
20	C₂×C₄×C₂₉	D₄	1	4	yes	complemented
21	C₂×C₄×C₂₉	C₂³	1	4	yes	—
22	C₂×C₄×C₂₉	C₂³	1	2	yes	—
23	C₂²⋊D₂₉	—	2	8	no	—
24	C₂×Dic₂₉	C₂³	1	4	yes	—
25	D₁₁₆	—	2	4	no	—
26	D₁₁₆	—	4	4	no	—
27	C₄×D₂₉	—	2	8	no	—
28	Dic₅₈	—	2	4	no	—
29	C₂²×C₂₉	—	2	1	no	—
30	C₂²×C₂₉	—	2	1	no	—
31	C₂²×C₂₉	C₂×D₄	1	2	yes	—
32	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
33	C₂×D₂₉	—	2	4	no	—
34	C₂×D₂₉	—	2	4	no	—
35	C₂×D₂₉	—	2	4	no	—
36	C₄×C₂₉	—	2	4	no	—
37	C₄×C₂₉	C₂×D₄	1	4	yes	—
38	Dic₂₉	—	2	4	no	—
39	#537	—	29	1	no	maximal, Sylow
40	C₂×C₂₉	—	2	2	no	—
41	C₂×C₂₉	C₂²×D₄	1	1	yes	characteristic
42	C₂×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
43	C₂×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
44	D₂₉	—	4	4	no	—
45	C₂×#41	—	29	2	no	—
46	C₂²⋊Q₈	—	29	4	no	—
47	#121	—	29	4	no	—
48	#121	—	29	4	no	—
49	C₂×C₄⋊C₄	D₂₉	1	1	yes	characteristic, complemented
50	C₂₉	#537	1	1	yes	characteristic, complemented, Sylow
51	#41	—	58	8	no	—
52	C₂×Q₈	—	29	2	no	—
53	C₂×D₄	—	29	4	no	—
54	C₂×D₄	—	29	2	no	—
55	C₂×D₄	—	29	4	no	—
56	C₂²×C₄	—	29	4	no	—
57	C₂²×C₄	C₂×D₂₉	1	2	yes	—
58	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
59	C₄⋊C₄	—	29	4	no	—
60	C₄⋊C₄	C₂×D₂₉	1	4	yes	—
61	C₂²⋊C₄	—	29	8	no	—
62	C₂³	—	29	4	no	—
63	C₂³	C₂²×D₂₉	1	1	yes	characteristic
64	Q₈	—	58	4	no	—
65	D₄	—	58	8	no	—
66	D₄	—	58	4	no	—
67	D₄	—	116	4	no	—
68	C₂×C₄	—	4	2	no	—
69	C₂×C₄	—	29	4	no	—
70	C₂×C₄	—	58	8	no	—
71	C₂×C₄	D₁₁₆	1	4	yes	complemented
72	C₂×C₄	C₂²×D₂₉	1	4	yes	—
73	C₂×C₄	C₂²×D₂₉	1	2	yes	—
74	C₂²	—	2	1	no	—
75	C₂²	—	2	1	no	—
76	C₂²	—	58	4	no	—
77	C₂²	—	58	4	no	—
78	C₂²	—	58	4	no	—
79	C₂²	C₂×D₁₁₆	1	2	yes	—
80	C₂²	C₂³×D₂₉	1	1	yes	characteristic
81	C₄	—	2	4	no	—
82	C₄	—	58	4	no	—
83	C₄	C₂×D₁₁₆	1	4	yes	—
84	C₂	—	2	2	no	—
85	C₂	—	116	4	no	—
86	C₂	C₂²×D₁₁₆	1	1	yes	characteristic
87	C₂	#11745359	1	1	yes	characteristic
88	C₂	#11745362	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁴
Fitting	C₂×C₄⋊C₄×C₂₉	C₂
hypercenter	C₂×C₄⋊C₄	D₂₉
hypocenter	C₂₉	#537
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#90805	C₂	semidirect
2. C₂×C₄⋊C₄×C₂₉	C₂	semidirect
3. #11745292	C₂	semidirect
4. #11745259	C₂	semidirect
5. #11745257	C₂	semidirect
20. C₂×C₄×C₂₉	D₄	semidirect
49. C₂×C₄⋊C₄	D₂₉	semidirect
50. C₂₉	#537	semidirect
71. C₂×C₄	D₁₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#90805	2
C₂×C₄⋊C₄×C₂₉	2
#11745292	2
#11745259	2
#11745257	2
#537	29