Subgroups — #14271241

Order 1856.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#90777	C₂	1	2	yes	maximal, complemented
3	C₂²⋊#6597	C₂	1	2	yes	maximal, complemented
4	C₄⋊#6597	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#6597	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₂₉	C₄	1	1	yes	characteristic
7	C₂²×C₄×C₂₉	C₂²	1	2	yes	—
8	C₄⋊C₄×C₂₉	C₄	1	1	yes	characteristic
9	C₂²⋊C₄×C₂₉	C₄	1	2	yes	—
10	C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	#90777	—	2	4	no	—
12	C₂×#6597	C₂²	1	2	yes	—
13	C₂×#6597	C₂²	1	1	yes	characteristic
14	C₂×#6597	C₂²	1	1	yes	characteristic
15	C₂³×C₂₉	C₂×C₄	1	2	yes	—
16	D₄×C₂₉	—	2	2	no	—
17	C₂×C₄×C₂₉	—	2	2	no	—
18	C₂×C₄×C₂₉	—	2	2	no	—
19	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₂₉	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
23	#6597	—	2	2	no	—
24	#6597	—	2	1	no	—
25	#6597	D₄	1	2	yes	complemented
26	C₂²×C₂₉	—	2	2	no	—
27	C₂²×C₂₉	—	2	2	no	—
28	C₂²×C₂₉	—	2	2	no	—
29	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₂₉	—	2	2	no	—
31	C₄×C₂₉	—	2	1	no	—
32	C₄×C₂₉	M₁₆	1	2	yes	complemented
33	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
34	C₄×C₂₉	#41	1	1	yes	characteristic
35	#436	—	29	1	no	maximal, Sylow
36	C₂×C₂₉	—	4	2	no	—
37	C₂×C₂₉	C₄×D₄	1	1	yes	characteristic
38	C₂×C₂₉	C₂×M₁₆	1	1	yes	characteristic
39	C₂×C₂₉	#131	1	1	yes	characteristic
40	C₂×M₁₆	—	29	2	no	—
41	C₄×D₄	D₂₉	1	1	yes	characteristic
42	C₄⋊C₈	—	29	1	no	—
43	C₂²⋊C₈	—	29	2	no	—
44	C₄×C₈	—	29	1	no	—
45	C₂₉	#436	1	1	yes	characteristic, complemented, Sylow
46	C₂×D₄	Dic₂₉	1	1	yes	characteristic
47	C₂²×C₄	C₂×D₂₉	1	2	yes	—
48	M₁₆	—	58	4	no	—
49	C₂×C₈	—	29	1	no	—
50	C₂×C₈	—	29	1	no	—
51	C₂×C₈	—	29	2	no	—
52	C₄⋊C₄	Dic₂₉	1	1	yes	characteristic
53	C₂²⋊C₄	Dic₂₉	1	2	yes	—
54	C₄²	C₂×D₂₉	1	1	yes	characteristic
55	C₂³	C₂×Dic₂₉	1	2	yes	—
56	D₄	—	2	2	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	C₂×Dic₂₉	1	1	yes	characteristic
60	C₂×C₄	C₂×Dic₂₉	1	2	yes	—
61	C₂×C₄	C₂×Dic₂₉	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
63	C₈	—	29	2	no	—
64	C₈	—	58	2	no	—
65	C₈	—	58	1	no	—
66	C₂²	—	2	2	no	—
67	C₂²	—	2	2	no	—
68	C₂²	—	2	2	no	—
69	C₂²	C₂²×Dic₂₉	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	2	1	no	—
72	C₄	#90777	1	2	yes	complemented
73	C₄	D₄×D₂₉	1	1	yes	characteristic
74	C₄	#90807	1	1	yes	characteristic
75	C₂	—	4	2	no	—
76	C₂	C₂×#90777	1	1	yes	characteristic
77	C₂	D₄×Dic₂₉	1	1	yes	characteristic
78	C₂	#11745310	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₉
commutator, socle	C₂²×C₂₉	C₂²×C₄
Fitting	C₄×D₄×C₂₉	C₂
prime radical	C₂×D₄×C₂₉	C₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	C₄×D₄	D₂₉
hypocenter	C₂₉	#436
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×#90777	C₂	semidirect
3. C₂²⋊#6597	C₂	semidirect
4. C₄⋊#6597	C₂	semidirect
5. C₄×#6597	C₂	semidirect
25. #6597	D₄	semidirect
32. C₄×C₂₉	M₁₆	semidirect
45. C₂₉	#436	semidirect
72. C₄	#90777	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₄×C₂₉	2
C₂×#90777	2
C₂²⋊#6597	2
C₄⋊#6597	2
C₄×#6597	2
#436	29