Subgroups — C₂₉×#3183 #16816897

Order 3712.

370 conjugacy classes of subgroups.

The subgroup lattice has 220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#529	C₂	1	2	yes	maximal, complemented
2	C₂₉×#499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#488	C₂	1	2	yes	maximal, complemented
5	C₂₉×#470	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#469	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#468	C₂	1	2	yes	maximal, complemented
8	C₂₉×#442	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#441	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#440	C₂	1	2	yes	maximal, complemented
11	C₄×M₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
13	C₂×SD₁₆×C₂₉	C₂²	1	2	yes	—
14	C₂×D₈×C₂₉	C₂²	1	1	yes	characteristic
15	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
16	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
17	C₂₉×#126	—	2	2	no	—
18	C₂₉×#125	C₂²	1	2	yes	—
19	C₂₉×#124	C₂²	1	2	yes	—
20	C₂₉×#123	—	2	2	no	—
21	C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂₉×#121	C₂²	1	2	yes	—
23	C₄×Q₈×C₂₉	C₂²	1	2	yes	—
24	C₄×D₄×C₂₉	—	2	2	no	—
25	C₄×D₄×C₂₉	C₂²	1	2	yes	—
26	C₂₉×#117	—	2	2	no	—
27	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
28	C₂₉×#107	C₂²	1	2	yes	—
29	C₂₉×#106	C₂²	1	1	yes	characteristic
30	C₂₉×#106	C₂²	1	1	yes	characteristic
31	C₂₉×#103	C₂²	1	2	yes	—
32	C₂₉×#103	C₂²	1	2	yes	—
33	C₂₉×#102	C₂²	1	2	yes	—
34	C₂₉×#102	C₂²	1	2	yes	—
35	C₂₉×#97	C₂²	1	1	yes	characteristic
36	C₂₉×#97	C₂²	1	1	yes	characteristic
37	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
38	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
39	C₂×Q₈×C₂₉	C₂³	1	2	yes	—
40	C₂×D₄×C₂₉	—	2	2	no	—
41	C₂×D₄×C₂₉	C₂³	1	2	yes	—
42	C₂²×C₄×C₂₉	—	2	2	no	—
43	C₂²×C₄×C₂₉	D₄	1	2	yes	—
44	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
45	Q₁₆×C₂₉	—	2	2	no	—
46	SD₁₆×C₂₉	—	2	4	no	—
47	D₈×C₂₉	—	2	2	no	—
48	M₁₆×C₂₉	—	2	2	no	—
49	M₁₆×C₂₉	—	2	2	no	—
50	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
51	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
52	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
53	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
54	C₄⋊C₄×C₂₉	—	2	2	no	—
55	C₄⋊C₄×C₂₉	—	2	2	no	—
56	C₄⋊C₄×C₂₉	—	2	2	no	—
57	C₄⋊C₄×C₂₉	—	2	2	no	—
58	C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
59	C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
60	C₂²⋊C₄×C₂₉	—	2	2	no	—
61	C₂²⋊C₄×C₂₉	—	2	2	no	—
62	C₂²⋊C₄×C₂₉	—	2	2	no	—
63	C₂²⋊C₄×C₂₉	—	2	2	no	—
64	C₂²⋊C₄×C₂₉	—	2	2	no	—
65	C₄²×C₂₉	—	2	2	no	—
66	C₄²×C₂₉	D₄	1	2	yes	—
67	C₄²×C₂₉	C₂³	1	1	yes	characteristic
68	C₄²×C₂₉	C₂³	1	1	yes	characteristic
69	C₂³×C₂₉	—	2	2	no	—
70	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
71	Q₈×C₂₉	—	2	2	no	—
72	Q₈×C₂₉	—	2	2	no	—
73	D₄×C₂₉	—	2	2	no	—
74	D₄×C₂₉	—	2	2	no	—
75	D₄×C₂₉	—	4	4	no	—
76	C₂×C₄×C₂₉	—	2	1	no	—
77	C₂×C₄×C₂₉	—	2	1	no	—
78	C₂×C₄×C₂₉	—	2	2	no	—
79	C₂×C₄×C₂₉	—	2	2	no	—
80	C₂×C₄×C₂₉	—	2	2	no	—
81	C₂×C₄×C₂₉	—	4	2	no	—
82	C₂×C₄×C₂₉	—	4	4	no	—
83	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
84	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
86	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
87	C₈×C₂₉	—	2	1	no	—
88	C₈×C₂₉	—	2	1	no	—
89	C₈×C₂₉	#41	1	2	yes	—
90	C₈×C₂₉	#41	1	2	yes	—
91	#3183	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂²×C₂₉	—	2	1	no	—
93	C₂²×C₂₉	—	2	2	no	—
94	C₂²×C₂₉	—	4	2	no	—
95	C₂²×C₂₉	—	4	2	no	—
96	C₂²×C₂₉	—	4	2	no	—
97	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
98	C₄×C₂₉	—	2	1	no	—
99	C₄×C₂₉	—	2	2	no	—
100	C₄×C₂₉	—	2	2	no	—
101	C₄×C₂₉	—	4	2	no	—
102	C₄×C₂₉	—	4	2	no	—
103	C₄×C₂₉	—	4	2	no	—
104	C₄×C₂₉	C₂×#41	1	1	yes	characteristic
105	C₄×C₂₉	C₂×#41	1	1	yes	characteristic
106	#529	C₂×C₂₉	1	2	yes	complemented
107	#499	C₂×C₂₉	1	1	yes	characteristic, complemented
108	#495	C₂×C₂₉	1	1	yes	characteristic, complemented
109	#488	C₂×C₂₉	1	2	yes	complemented
110	#470	C₂×C₂₉	1	1	yes	characteristic, complemented
111	#469	C₂×C₂₉	1	1	yes	characteristic
112	#468	C₂×C₂₉	1	2	yes	complemented
113	#442	C₂×C₂₉	1	1	yes	characteristic, complemented
114	#441	C₂×C₂₉	1	1	yes	characteristic, complemented
115	#440	C₂×C₂₉	1	2	yes	complemented
116	C₄×M₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
117	C₂×C₂₉	—	4	1	no	—
118	C₂×C₂₉	—	8	2	no	—
119	C₂×C₂₉	#532	1	1	yes	characteristic
120	C₂×C₂₉	#575	1	2	yes	—
121	C₂×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
122	C₂×SD₁₆	C₂²×C₂₉	1	2	yes	—
123	C₂×D₈	C₂²×C₂₉	1	1	yes	characteristic
124	C₂×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
125	C₂×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
126	#126	—	2	2	no	—
127	#125	C₂²×C₂₉	1	2	yes	—
128	#124	C₂²×C₂₉	1	2	yes	—
129	#123	—	2	2	no	—
130	C₂²⋊Q₈	C₂²×C₂₉	1	2	yes	—
131	#121	C₂²×C₂₉	1	2	yes	—
132	C₄×Q₈	C₂²×C₂₉	1	2	yes	—
133	C₄×D₄	—	2	2	no	—
134	C₄×D₄	C₂²×C₂₉	1	2	yes	—
135	#117	—	2	2	no	—
136	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic
137	#107	C₂²×C₂₉	1	2	yes	—
138	#106	C₂²×C₂₉	1	1	yes	characteristic
139	#106	C₂²×C₂₉	1	1	yes	characteristic
140	#103	C₂²×C₂₉	1	2	yes	—
141	#103	C₂²×C₂₉	1	2	yes	—
142	#102	C₂²×C₂₉	1	2	yes	—
143	#102	C₂²×C₂₉	1	2	yes	—
144	#97	C₂²×C₂₉	1	1	yes	characteristic
145	#97	C₂²×C₂₉	1	1	yes	characteristic
146	C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
147	C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
148	C₂₉	#3183	1	1	yes	characteristic, direct product factor, Sylow
149	C₂×Q₈	C₂³×C₂₉	1	2	yes	—
150	C₂×D₄	—	2	2	no	—
151	C₂×D₄	C₂³×C₂₉	1	2	yes	—
152	C₂²×C₄	—	2	2	no	—
153	C₂²×C₄	D₄×C₂₉	1	2	yes	—
154	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
155	Q₁₆	—	2	2	no	—
156	SD₁₆	—	2	4	no	—
157	D₈	—	2	2	no	—
158	M₁₆	—	2	2	no	—
159	M₁₆	—	2	2	no	—
160	C₂×C₈	C₂³×C₂₉	1	1	yes	characteristic
161	C₂×C₈	C₂³×C₂₉	1	1	yes	characteristic
162	C₂×C₈	C₂³×C₂₉	1	1	yes	characteristic
163	C₂×C₈	C₂³×C₂₉	1	1	yes	characteristic
164	C₄⋊C₄	—	2	2	no	—
165	C₄⋊C₄	—	2	2	no	—
166	C₄⋊C₄	—	2	2	no	—
167	C₄⋊C₄	—	2	2	no	—
168	C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
169	C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
170	C₂²⋊C₄	—	2	2	no	—
171	C₂²⋊C₄	—	2	2	no	—
172	C₂²⋊C₄	—	2	2	no	—
173	C₂²⋊C₄	—	2	2	no	—
174	C₂²⋊C₄	—	2	2	no	—
175	C₄²	—	2	2	no	—
176	C₄²	D₄×C₂₉	1	2	yes	—
177	C₄²	C₂³×C₂₉	1	1	yes	characteristic
178	C₄²	C₂³×C₂₉	1	1	yes	characteristic
179	C₂³	—	2	2	no	—
180	C₂³	C₂×D₄×C₂₉	1	1	yes	characteristic
181	Q₈	—	2	2	no	—
182	Q₈	—	2	2	no	—
183	D₄	—	2	2	no	—
184	D₄	—	2	2	no	—
185	D₄	—	4	4	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	2	1	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	4	2	no	—
192	C₂×C₄	—	4	4	no	—
193	C₂×C₄	C₂×D₄×C₂₉	1	2	yes	—
194	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
195	C₂×C₄	C₂×D₄×C₂₉	1	2	yes	—
196	C₂×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
197	C₈	—	2	1	no	—
198	C₈	—	2	1	no	—
199	C₈	#41×C₂₉	1	2	yes	—
200	C₈	#41×C₂₉	1	2	yes	—
201	C₂²	—	2	1	no	—
202	C₂²	—	2	2	no	—
203	C₂²	—	4	2	no	—
204	C₂²	—	4	2	no	—
205	C₂²	—	4	2	no	—
206	C₂²	C₂²×D₄×C₂₉	1	1	yes	characteristic
207	C₄	—	2	1	no	—
208	C₄	—	2	2	no	—
209	C₄	—	2	2	no	—
210	C₄	—	4	2	no	—
211	C₄	—	4	2	no	—
212	C₄	—	4	2	no	—
213	C₄	C₂×#41×C₂₉	1	1	yes	characteristic
214	C₄	C₂×#41×C₂₉	1	1	yes	characteristic
215	C₂	—	4	1	no	—
216	C₂	—	8	2	no	—
217	C₂	C₂₉×#532	1	1	yes	characteristic
218	C₂	C₂₉×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
prime radical	C₂₉×#469	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#529	C₂	semidirect
2. C₂₉×#499	C₂	semidirect
3. C₂₉×#495	C₂	semidirect
4. C₂₉×#488	C₂	semidirect
5. C₂₉×#470	C₂	semidirect
7. C₂₉×#468	C₂	semidirect
8. C₂₉×#442	C₂	semidirect
9. C₂₉×#441	C₂	semidirect
10. C₂₉×#440	C₂	semidirect
11. C₄×M₁₆×C₂₉	C₂	semidirect
91. #3183	C₂₉	direct (N × H)
106. #529	C₂×C₂₉	semidirect
107. #499	C₂×C₂₉	semidirect
108. #495	C₂×C₂₉	semidirect
109. #488	C₂×C₂₉	semidirect
110. #470	C₂×C₂₉	semidirect
112. #468	C₂×C₂₉	semidirect
113. #442	C₂×C₂₉	semidirect
114. #441	C₂×C₂₉	semidirect
115. #440	C₂×C₂₉	semidirect
116. C₄×M₁₆	C₂×C₂₉	semidirect
148. C₂₉	#3183	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×#529	2
C₂₉×#499	2
C₂₉×#495	2
C₂₉×#488	2
C₂₉×#470	2
C₂₉×#469	2
C₂₉×#468	2
C₂₉×#442	2
C₂₉×#441	2
C₂₉×#440	2
C₄×M₁₆×C₂₉	2
#3183	29

Subgroups — C29×#3183 #16816897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#3183 #16816897