Subgroups — C₂₉×#552 #14270847

Order 1856.

214 conjugacy classes of subgroups.

The subgroup lattice has 146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#126	C₂	1	2	yes	maximal, complemented
2	C₂₉×#125	C₂	1	2	yes	maximal, complemented
3	C₂₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#123	C₂	1	2	yes	maximal
5	C₂₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×D₄×C₂₉	C₂	1	1	yes	maximal, characteristic
9	C₂₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#117	C₂	1	2	yes	maximal, complemented
11	C₂×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₈×C₂₉	C₂²	1	1	yes	characteristic
13	C₂×D₄×C₂₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₂₉	C₂²	1	2	yes	—
15	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
20	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
21	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
22	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
23	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
24	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
25	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
26	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
27	C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
28	C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
29	C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
30	C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
31	C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
32	C₄²×C₂₉	C₂²	1	2	yes	—
33	C₄²×C₂₉	C₂²	1	2	yes	—
34	C₄²×C₂₉	C₂²	1	1	yes	characteristic
35	C₂³×C₂₉	C₂³	1	1	yes	characteristic
36	C₂³×C₂₉	C₂³	1	1	yes	characteristic
37	Q₈×C₂₉	—	2	2	no	—
38	D₄×C₂₉	—	2	2	no	—
39	C₂×C₄×C₂₉	—	2	4	no	—
40	C₂×C₄×C₂₉	—	2	2	no	—
41	C₂×C₄×C₂₉	—	2	2	no	—
42	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
43	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
44	C₂×C₄×C₂₉	C₂³	1	2	yes	—
45	C₂×C₄×C₂₉	C₂³	1	2	yes	—
46	C₂×C₄×C₂₉	C₂³	1	2	yes	—
47	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
48	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
49	C₂×C₄×C₂₉	C₂³	1	2	yes	—
50	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
51	C₂²×C₂₉	—	2	1	no	—
52	C₂²×C₂₉	—	2	1	no	—
53	C₂²×C₂₉	—	2	1	no	—
54	C₂²×C₂₉	—	2	1	no	—
55	C₂²×C₂₉	—	2	1	no	—
56	C₂²×C₂₉	#41	1	2	yes	—
57	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
58	C₄×C₂₉	—	2	2	no	—
59	C₄×C₂₉	—	2	2	no	—
60	C₄×C₂₉	—	2	1	no	—
61	C₄×C₂₉	—	2	1	no	—
62	C₄×C₂₉	—	2	1	no	—
63	C₄×C₂₉	—	2	2	no	—
64	C₄×C₂₉	—	2	1	no	—
65	C₄×C₂₉	—	2	2	no	—
66	C₄×C₂₉	#41	1	2	yes	—
67	#552	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₂₉	—	2	2	no	—
69	C₂×C₂₉	—	4	1	no	—
70	C₂×C₂₉	C₂×#41	1	1	yes	characteristic
71	C₂×C₂₉	C₂×#41	1	1	yes	characteristic
72	C₂×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
73	#126	C₂×C₂₉	1	2	yes	complemented
74	#125	C₂×C₂₉	1	2	yes	complemented
75	#125	C₂×C₂₉	1	1	yes	characteristic, complemented
76	#123	C₂×C₂₉	1	2	yes	—
77	C₂²⋊Q₈	C₂×C₂₉	1	1	yes	characteristic, complemented
78	C₂²⋊Q₈	C₂×C₂₉	1	1	yes	characteristic, complemented
79	C₄×Q₈	C₂×C₂₉	1	1	yes	characteristic, complemented
80	C₄×D₄	C₂×C₂₉	1	1	yes	characteristic
81	#117	C₂×C₂₉	1	1	yes	characteristic, complemented
82	#117	C₂×C₂₉	1	2	yes	complemented
83	C₂×C₄⋊C₄	C₂×C₂₉	1	1	yes	characteristic, complemented
84	C₂₉	#552	1	1	yes	characteristic, direct product factor, Sylow
85	C₂×Q₈	C₂²×C₂₉	1	1	yes	characteristic
86	C₂×D₄	C₂²×C₂₉	1	1	yes	characteristic
87	C₂²×C₄	C₂²×C₂₉	1	2	yes	—
88	C₂²×C₄	C₂²×C₂₉	1	1	yes	characteristic
89	C₂²×C₄	C₂²×C₂₉	1	1	yes	characteristic
90	C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
91	C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
92	C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
93	C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
94	C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
95	C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
96	C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
97	C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
98	C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
99	C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
100	C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
101	C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
102	C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
103	C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
104	C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
105	C₄²	C₂²×C₂₉	1	2	yes	—
106	C₄²	C₂²×C₂₉	1	2	yes	—
107	C₄²	C₂²×C₂₉	1	1	yes	characteristic
108	C₂³	C₂³×C₂₉	1	1	yes	characteristic
109	C₂³	C₂³×C₂₉	1	1	yes	characteristic
110	Q₈	—	2	2	no	—
111	D₄	—	2	2	no	—
112	C₂×C₄	—	2	4	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	C₂³×C₂₉	1	1	yes	characteristic
116	C₂×C₄	C₂³×C₂₉	1	1	yes	characteristic
117	C₂×C₄	C₂³×C₂₉	1	2	yes	—
118	C₂×C₄	C₂³×C₂₉	1	2	yes	—
119	C₂×C₄	C₂³×C₂₉	1	2	yes	—
120	C₂×C₄	C₂³×C₂₉	1	1	yes	characteristic
121	C₂×C₄	C₂³×C₂₉	1	1	yes	characteristic
122	C₂×C₄	C₂³×C₂₉	1	2	yes	—
123	C₂×C₄	C₂³×C₂₉	1	1	yes	characteristic
124	C₂²	—	2	1	no	—
125	C₂²	—	2	1	no	—
126	C₂²	—	2	1	no	—
127	C₂²	—	2	1	no	—
128	C₂²	—	2	1	no	—
129	C₂²	#41×C₂₉	1	2	yes	—
130	C₂²	C₂⁴×C₂₉	1	1	yes	characteristic
131	C₄	—	2	2	no	—
132	C₄	—	2	2	no	—
133	C₄	—	2	1	no	—
134	C₄	—	2	1	no	—
135	C₄	—	2	1	no	—
136	C₄	—	2	2	no	—
137	C₄	—	2	1	no	—
138	C₄	—	2	2	no	—
139	C₄	#41×C₂₉	1	2	yes	—
140	C₂	—	2	2	no	—
141	C₂	—	4	1	no	—
142	C₂	C₂×#41×C₂₉	1	1	yes	characteristic
143	C₂	C₂×#41×C₂₉	1	1	yes	characteristic
144	C₂	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₂₉
prime radical	C₂×D₄×C₂₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#126	C₂	semidirect
2. C₂₉×#125	C₂	semidirect
3. C₂₉×#125	C₂	semidirect
5. C₂₉×C₂²⋊Q₈	C₂	semidirect
6. C₂₉×C₂²⋊Q₈	C₂	semidirect
7. C₄×Q₈×C₂₉	C₂	semidirect
9. C₂₉×#117	C₂	semidirect
10. C₂₉×#117	C₂	semidirect
11. C₂×C₄⋊C₄×C₂₉	C₂	semidirect
67. #552	C₂₉	direct (N × H)
73. #126	C₂×C₂₉	semidirect
74. #125	C₂×C₂₉	semidirect
75. #125	C₂×C₂₉	semidirect
77. C₂²⋊Q₈	C₂×C₂₉	semidirect
78. C₂²⋊Q₈	C₂×C₂₉	semidirect
79. C₄×Q₈	C₂×C₂₉	semidirect
81. #117	C₂×C₂₉	semidirect
82. #117	C₂×C₂₉	semidirect
83. C₂×C₄⋊C₄	C₂×C₂₉	semidirect
84. C₂₉	#552	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#126	2
C₂₉×#125	2
C₂₉×#123	2
C₂₉×C₂²⋊Q₈	2
C₄×Q₈×C₂₉	2
C₄×D₄×C₂₉	2
C₂₉×#117	2
C₂×C₄⋊C₄×C₂₉	2
#552	29

Subgroups — C29×#552 #14270847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#552 #14270847