Subgroups — C₂₉×#3104 #16816818

Order 3712.

384 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#484	C₂	1	2	yes	maximal
4	C₂₉×#477	C₂	1	2	yes	maximal, complemented
5	C₂₉×#462	C₂	1	2	yes	maximal, complemented
6	C₂₉×#451	C₂	1	2	yes	maximal
7	C₄×Q₁₆×C₂₉	C₂	1	4	yes	maximal, complemented
8	C₂₉×#431	C₂	1	1	yes	maximal, characteristic
9	C₂²×Q₈×C₂₉	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₂₉	C₂²	1	4	yes	—
11	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂₉×#125	—	2	1	no	—
14	C₂₉×C₂²⋊Q₈	—	2	1	no	—
15	C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₄×Q₈×C₂₉	—	2	1	no	—
17	C₄×Q₈×C₂₉	—	2	1	no	—
18	C₄×Q₈×C₂₉	—	2	1	no	—
19	C₄×Q₈×C₂₉	C₂²	1	2	yes	—
20	C₄×Q₈×C₂₉	C₂²	1	2	yes	—
21	C₄×Q₈×C₂₉	C₂²	1	2	yes	—
22	C₂₉×#117	—	2	1	no	—
23	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
24	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
25	C₂×C₄²×C₂₉	—	2	1	no	—
26	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
27	C₂₉×#107	C₂²	1	4	yes	—
28	C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
29	C₂₉×#103	C₂²	1	4	yes	—
30	C₂₉×#103	C₂²	1	4	yes	—
31	C₂₉×C₂²⋊C₈	C₂²	1	2	yes	—
32	C₄×C₈×C₂₉	C₂²	1	2	yes	—
33	C₂×Q₈×C₂₉	—	2	4	no	—
34	C₂×Q₈×C₂₉	—	2	1	no	—
35	C₂×Q₈×C₂₉	—	2	1	no	—
36	C₂×Q₈×C₂₉	C₂³	1	2	yes	—
37	C₂×Q₈×C₂₉	C₂³	1	2	yes	—
38	C₂²×C₄×C₂₉	—	2	1	no	—
39	C₂²×C₄×C₂₉	—	2	1	no	—
40	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
41	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
42	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
43	Q₁₆×C₂₉	—	2	8	no	—
44	C₂×C₈×C₂₉	C₂³	1	4	yes	—
45	C₄⋊C₄×C₂₉	—	2	2	no	—
46	C₄⋊C₄×C₂₉	—	2	2	no	—
47	C₄⋊C₄×C₂₉	—	2	1	no	—
48	C₄⋊C₄×C₂₉	—	2	1	no	—
49	C₄⋊C₄×C₂₉	—	2	1	no	—
50	C₄⋊C₄×C₂₉	—	2	1	no	—
51	C₄⋊C₄×C₂₉	—	2	2	no	—
52	C₄⋊C₄×C₂₉	—	2	2	no	—
53	C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
54	C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
55	C₂²⋊C₄×C₂₉	—	2	2	no	—
56	C₄²×C₂₉	—	2	2	no	—
57	C₄²×C₂₉	—	2	2	no	—
58	C₄²×C₂₉	—	2	2	no	—
59	C₄²×C₂₉	D₄	1	1	yes	characteristic
60	C₄²×C₂₉	D₄	1	1	yes	characteristic
61	C₄²×C₂₉	C₂³	1	1	yes	characteristic
62	C₄²×C₂₉	C₂³	1	1	yes	characteristic
63	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
64	Q₈×C₂₉	—	2	4	no	—
65	Q₈×C₂₉	—	2	2	no	—
66	Q₈×C₂₉	—	2	4	no	—
67	Q₈×C₂₉	—	4	2	no	—
68	Q₈×C₂₉	#41	1	4	yes	—
69	C₂×C₄×C₂₉	—	2	4	no	—
70	C₂×C₄×C₂₉	—	2	2	no	—
71	C₂×C₄×C₂₉	—	2	2	no	—
72	C₂×C₄×C₂₉	—	2	2	no	—
73	C₂×C₄×C₂₉	—	2	2	no	—
74	C₂×C₄×C₂₉	—	2	2	no	—
75	C₂×C₄×C₂₉	—	4	1	no	—
76	C₂×C₄×C₂₉	—	4	2	no	—
77	C₂×C₄×C₂₉	Q₁₆	1	4	yes	complemented
78	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
79	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
83	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
84	C₈×C₂₉	—	2	4	no	—
85	#3104	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂²×C₂₉	—	2	1	no	—
87	C₂²×C₂₉	—	2	1	no	—
88	C₂²×C₂₉	C₂×Q₁₆	1	2	yes	—
89	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
90	C₄×C₂₉	—	2	4	no	—
91	C₄×C₂₉	—	2	1	no	—
92	C₄×C₂₉	—	2	1	no	—
93	C₄×C₂₉	—	2	1	no	—
94	C₄×C₂₉	—	4	2	no	—
95	C₄×C₂₉	—	4	2	no	—
96	C₄×C₂₉	—	4	2	no	—
97	C₄×C₂₉	C₂×Q₁₆	1	2	yes	—
98	C₄×C₂₉	C₂×Q₁₆	1	2	yes	—
99	C₄×C₂₉	C₂×#41	1	2	yes	—
100	#533	C₂×C₂₉	1	1	yes	characteristic
101	C₂×C₄×Q₈	C₂×C₂₉	1	1	yes	characteristic
102	#484	C₂×C₂₉	1	2	yes	—
103	#477	C₂×C₂₉	1	2	yes	complemented
104	#462	C₂×C₂₉	1	2	yes	complemented
105	#451	C₂×C₂₉	1	2	yes	—
106	C₄×Q₁₆	C₂×C₂₉	1	4	yes	complemented
107	#431	C₂×C₂₉	1	1	yes	characteristic
108	C₂×C₂₉	—	2	2	no	—
109	C₂×C₂₉	#525	1	1	yes	characteristic
110	C₂×C₂₉	C₂²×Q₁₆	1	1	yes	characteristic
111	C₂×C₂₉	#575	1	1	yes	characteristic
112	C₂²×Q₈	C₂²×C₂₉	1	1	yes	characteristic
113	C₂×Q₁₆	C₂²×C₂₉	1	4	yes	—
114	C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
115	C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
116	#125	—	2	1	no	—
117	C₂²⋊Q₈	—	2	1	no	—
118	C₂²⋊Q₈	C₂²×C₂₉	1	2	yes	—
119	C₄×Q₈	—	2	1	no	—
120	C₄×Q₈	—	2	1	no	—
121	C₄×Q₈	—	2	1	no	—
122	C₄×Q₈	C₂²×C₂₉	1	2	yes	—
123	C₄×Q₈	C₂²×C₂₉	1	2	yes	—
124	C₄×Q₈	C₂²×C₂₉	1	2	yes	—
125	#117	—	2	1	no	—
126	C₂×C₄⋊C₄	—	2	1	no	—
127	C₂×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
128	C₂×C₄²	—	2	1	no	—
129	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic
130	#107	C₂²×C₂₉	1	4	yes	—
131	C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
132	#103	C₂²×C₂₉	1	4	yes	—
133	#103	C₂²×C₂₉	1	4	yes	—
134	C₂²⋊C₈	C₂²×C₂₉	1	2	yes	—
135	C₄×C₈	C₂²×C₂₉	1	2	yes	—
136	C₂₉	#3104	1	1	yes	characteristic, direct product factor, Sylow
137	C₂×Q₈	—	2	4	no	—
138	C₂×Q₈	—	2	1	no	—
139	C₂×Q₈	—	2	1	no	—
140	C₂×Q₈	C₂³×C₂₉	1	2	yes	—
141	C₂×Q₈	C₂³×C₂₉	1	2	yes	—
142	C₂²×C₄	—	2	1	no	—
143	C₂²×C₄	—	2	1	no	—
144	C₂²×C₄	D₄×C₂₉	1	1	yes	characteristic
145	C₂²×C₄	D₄×C₂₉	1	1	yes	characteristic
146	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
147	Q₁₆	—	2	8	no	—
148	C₂×C₈	C₂³×C₂₉	1	4	yes	—
149	C₄⋊C₄	—	2	2	no	—
150	C₄⋊C₄	—	2	2	no	—
151	C₄⋊C₄	—	2	1	no	—
152	C₄⋊C₄	—	2	1	no	—
153	C₄⋊C₄	—	2	1	no	—
154	C₄⋊C₄	—	2	1	no	—
155	C₄⋊C₄	—	2	2	no	—
156	C₄⋊C₄	—	2	2	no	—
157	C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
158	C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
159	C₂²⋊C₄	—	2	2	no	—
160	C₄²	—	2	2	no	—
161	C₄²	—	2	2	no	—
162	C₄²	—	2	2	no	—
163	C₄²	D₄×C₂₉	1	1	yes	characteristic
164	C₄²	D₄×C₂₉	1	1	yes	characteristic
165	C₄²	C₂³×C₂₉	1	1	yes	characteristic
166	C₄²	C₂³×C₂₉	1	1	yes	characteristic
167	C₂³	C₂×D₄×C₂₉	1	1	yes	characteristic
168	Q₈	—	2	4	no	—
169	Q₈	—	2	2	no	—
170	Q₈	—	2	4	no	—
171	Q₈	—	4	2	no	—
172	Q₈	#41×C₂₉	1	4	yes	—
173	C₂×C₄	—	2	4	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	4	1	no	—
180	C₂×C₄	—	4	2	no	—
181	C₂×C₄	Q₁₆×C₂₉	1	4	yes	complemented
182	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
183	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
184	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
185	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
186	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
187	C₂×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
188	C₈	—	2	4	no	—
189	C₂²	—	2	1	no	—
190	C₂²	—	2	1	no	—
191	C₂²	C₂×Q₁₆×C₂₉	1	2	yes	—
192	C₂²	C₂²×D₄×C₂₉	1	1	yes	characteristic
193	C₄	—	2	4	no	—
194	C₄	—	2	1	no	—
195	C₄	—	2	1	no	—
196	C₄	—	2	1	no	—
197	C₄	—	4	2	no	—
198	C₄	—	4	2	no	—
199	C₄	—	4	2	no	—
200	C₄	C₂×Q₁₆×C₂₉	1	2	yes	—
201	C₄	C₂×Q₁₆×C₂₉	1	2	yes	—
202	C₄	C₂×#41×C₂₉	1	2	yes	—
203	C₂	—	2	2	no	—
204	C₂	C₂₉×#525	1	1	yes	characteristic
205	C₂	C₂²×Q₁₆×C₂₉	1	1	yes	characteristic
206	C₂	C₂₉×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂²×D₄
prime radical	C₂³×C₂₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₉×#477	C₂	semidirect
5. C₂₉×#462	C₂	semidirect
7. C₄×Q₁₆×C₂₉	C₂	semidirect
77. C₂×C₄×C₂₉	Q₁₆	semidirect
85. #3104	C₂₉	direct (N × H)
103. #477	C₂×C₂₉	semidirect
104. #462	C₂×C₂₉	semidirect
106. C₄×Q₁₆	C₂×C₂₉	semidirect
136. C₂₉	#3104	direct (N × H)
181. C₂×C₄	Q₁₆×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#533	2
C₂×C₄×Q₈×C₂₉	2
C₂₉×#484	2
C₂₉×#477	2
C₂₉×#462	2
C₂₉×#451	2
C₄×Q₁₆×C₂₉	2
C₂₉×#431	2
#3104	29

Subgroups — C29×#3104 #16816818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#3104 #16816818