Subgroups — C₂₉×#2970 #16816684

Order 3712.

406 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#41×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#446	C₂	1	2	yes	maximal, complemented
3	C₂₉×#435	C₂	1	4	yes	maximal, complemented
4	C₈×D₄×C₂₉	C₂	1	2	yes	maximal, complemented
5	C₂₉×#432	C₂	1	2	yes	maximal, complemented
6	C₂₉×#432	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×M₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₉×#97	C₂	1	2	yes	maximal, complemented
9	C₂×#41×C₂₉	C₄	1	1	yes	characteristic
10	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
11	C₂²×C₈×C₂₉	C₂²	1	4	yes	—
12	C₄×Q₈×C₂₉	C₄	1	1	yes	characteristic
13	C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
14	C₄×D₄×C₂₉	C₄	1	2	yes	—
15	C₄×D₄×C₂₉	C₄	1	1	yes	characteristic
16	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
17	C₄×D₄×C₂₉	C₂²	1	2	yes	—
18	C₂₉×#117	C₄	1	1	yes	characteristic
19	C₂₉×#117	C₄	1	2	yes	—
20	C₂×C₄²×C₂₉	C₂²	1	2	yes	—
21	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
22	C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂₉×C₄⋊C₈	C₂²	1	4	yes	—
24	C₂₉×C₂²⋊C₈	C₂²	1	4	yes	—
25	C₂₉×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂₉×#97	C₂²	1	2	yes	—
27	C₂₉×#97	C₂²	1	1	yes	characteristic
28	C₂₉×#97	C₂²	1	4	yes	—
29	C₂₉×#97	C₂²	1	1	yes	characteristic
30	C₄×C₈×C₂₉	C₂²	1	2	yes	—
31	#41×C₂₉	—	2	4	no	—
32	C₂×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
33	C₂×D₄×C₂₉	C₂×C₄	1	2	yes	—
34	C₂×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
36	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
39	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
40	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
41	M₁₆×C₂₉	—	2	4	no	—
42	C₂×C₈×C₂₉	—	2	8	no	—
43	C₂×C₈×C₂₉	C₂³	1	4	yes	—
44	C₂×C₈×C₂₉	C₂³	1	2	yes	—
45	C₂×C₈×C₂₉	C₂³	1	2	yes	—
46	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
47	C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
48	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
49	C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
50	C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
51	C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
52	C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
53	C₄²×C₂₉	C₂×C₄	1	2	yes	—
54	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
55	C₄²×C₂₉	C₂×C₄	1	2	yes	—
56	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
57	C₄²×C₂₉	C₂³	1	1	yes	characteristic
58	C₄²×C₂₉	C₂³	1	1	yes	characteristic
59	C₄²×C₂₉	C₂³	1	2	yes	—
60	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
61	C₂³×C₂₉	C₂²×C₄	1	2	yes	—
62	Q₈×C₂₉	—	2	2	no	—
63	D₄×C₂₉	—	2	4	no	—
64	D₄×C₂₉	M₁₆	1	4	yes	complemented
65	C₂×C₄×C₂₉	—	2	4	no	—
66	C₂×C₄×C₂₉	—	2	2	no	—
67	C₂×C₄×C₂₉	—	2	4	no	—
68	C₂×C₄×C₂₉	—	2	2	no	—
69	C₂×C₄×C₂₉	—	4	2	no	—
70	C₂×C₄×C₂₉	—	4	1	no	—
71	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
74	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
77	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
78	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
80	C₈×C₂₉	—	2	4	no	—
81	C₈×C₂₉	—	2	2	no	—
82	C₈×C₂₉	#41	1	4	yes	complemented
83	#2970	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂²×C₂₉	—	2	2	no	—
85	C₂²×C₂₉	—	2	2	no	—
86	C₂²×C₂₉	—	2	1	no	—
87	C₂²×C₂₉	—	2	1	no	—
88	C₂²×C₂₉	—	2	1	no	—
89	C₂²×C₂₉	C₂×M₁₆	1	4	yes	—
90	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
91	C₄×C₂₉	—	2	2	no	—
92	C₄×C₂₉	—	2	1	no	—
93	C₄×C₂₉	—	2	1	no	—
94	C₄×C₂₉	—	2	2	no	—
95	C₄×C₂₉	—	2	1	no	—
96	C₄×C₂₉	—	2	2	no	—
97	C₄×C₂₉	—	2	1	no	—
98	C₄×C₂₉	C₂×M₁₆	1	2	yes	—
99	C₄×C₂₉	C₂×#41	1	2	yes	—
100	C₄×#41	C₂×C₂₉	1	1	yes	characteristic
101	#446	C₂×C₂₉	1	2	yes	complemented
102	#435	C₂×C₂₉	1	4	yes	complemented
103	C₈×D₄	C₂×C₂₉	1	2	yes	complemented
104	#432	C₂×C₂₉	1	1	yes	characteristic, complemented
105	#432	C₂×C₂₉	1	2	yes	complemented
106	C₄×M₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
107	C₂×#97	C₂×C₂₉	1	2	yes	complemented
108	C₂×C₂₉	—	2	4	no	—
109	C₂×C₂₉	—	4	1	no	—
110	C₂×C₂₉	C₄×#41	1	1	yes	characteristic
111	C₂×C₂₉	C₂²×M₁₆	1	1	yes	characteristic
112	C₂×C₂₉	#568	1	1	yes	characteristic
113	C₂×#41	C₄×C₂₉	1	1	yes	characteristic
114	C₂×M₁₆	C₂²×C₂₉	1	2	yes	—
115	C₂²×C₈	C₂²×C₂₉	1	4	yes	—
116	C₄×Q₈	C₄×C₂₉	1	1	yes	characteristic
117	C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
118	C₄×D₄	C₄×C₂₉	1	2	yes	—
119	C₄×D₄	C₄×C₂₉	1	1	yes	characteristic
120	C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
121	C₄×D₄	C₂²×C₂₉	1	2	yes	—
122	#117	C₄×C₂₉	1	1	yes	characteristic
123	#117	C₄×C₂₉	1	2	yes	—
124	C₂×C₄²	C₂²×C₂₉	1	2	yes	—
125	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic
126	C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
127	C₄⋊C₈	C₂²×C₂₉	1	4	yes	—
128	C₂²⋊C₈	C₂²×C₂₉	1	4	yes	—
129	C₂²⋊C₈	C₂²×C₂₉	1	2	yes	—
130	#97	C₂²×C₂₉	1	1	yes	characteristic
131	#97	C₂²×C₂₉	1	2	yes	—
132	#97	C₂²×C₂₉	1	4	yes	—
133	#97	C₂²×C₂₉	1	1	yes	characteristic
134	C₄×C₈	C₂²×C₂₉	1	2	yes	—
135	C₂₉	#2970	1	1	yes	characteristic, direct product factor, Sylow
136	#41	—	2	4	no	—
137	C₂×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
138	C₂×D₄	C₂×C₄×C₂₉	1	2	yes	—
139	C₂×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
140	C₂²×C₄	C₂×C₄×C₂₉	1	2	yes	—
141	C₂²×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
142	C₂²×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
143	C₂²×C₄	C₂×C₄×C₂₉	1	2	yes	—
144	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
145	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
146	M₁₆	—	2	4	no	—
147	C₂×C₈	—	2	8	no	—
148	C₂×C₈	C₂³×C₂₉	1	2	yes	—
149	C₂×C₈	C₂³×C₂₉	1	4	yes	—
150	C₂×C₈	C₂³×C₂₉	1	2	yes	—
151	C₄⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
152	C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
153	C₄⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
154	C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
155	C₂²⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
156	C₂²⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
157	C₂²⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
158	C₄²	C₂×C₄×C₂₉	1	2	yes	—
159	C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
160	C₄²	C₂×C₄×C₂₉	1	2	yes	—
161	C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
162	C₄²	C₂³×C₂₉	1	1	yes	characteristic
163	C₄²	C₂³×C₂₉	1	1	yes	characteristic
164	C₄²	C₂³×C₂₉	1	2	yes	—
165	C₂³	C₂²×C₄×C₂₉	1	1	yes	characteristic
166	C₂³	C₂²×C₄×C₂₉	1	2	yes	—
167	Q₈	—	2	2	no	—
168	D₄	—	2	4	no	—
169	D₄	M₁₆×C₂₉	1	4	yes	complemented
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	4	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	4	2	no	—
175	C₂×C₄	—	4	1	no	—
176	C₂×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
177	C₂×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
178	C₂×C₄	C₂²×C₄×C₂₉	1	2	yes	—
179	C₂×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
180	C₂×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
181	C₂×C₄	C₂²×C₄×C₂₉	1	2	yes	—
182	C₂×C₄	C₂²×C₄×C₂₉	1	2	yes	—
183	C₂×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
184	C₂×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
185	C₈	—	2	4	no	—
186	C₈	—	2	2	no	—
187	C₈	#41×C₂₉	1	4	yes	complemented
188	C₂²	—	2	2	no	—
189	C₂²	—	2	2	no	—
190	C₂²	—	2	1	no	—
191	C₂²	—	2	1	no	—
192	C₂²	—	2	1	no	—
193	C₂²	C₂×M₁₆×C₂₉	1	4	yes	—
194	C₂²	C₂³×C₄×C₂₉	1	1	yes	characteristic
195	C₄	—	2	2	no	—
196	C₄	—	2	1	no	—
197	C₄	—	2	1	no	—
198	C₄	—	2	2	no	—
199	C₄	—	2	1	no	—
200	C₄	—	2	2	no	—
201	C₄	—	2	1	no	—
202	C₄	C₂×M₁₆×C₂₉	1	2	yes	—
203	C₄	C₂×#41×C₂₉	1	2	yes	—
204	C₂	—	2	4	no	—
205	C₂	—	4	1	no	—
206	C₂	C₄×#41×C₂₉	1	1	yes	characteristic
207	C₂	C₂²×M₁₆×C₂₉	1	1	yes	characteristic
208	C₂	C₂₉×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂³×C₄
prime radical	C₂×#41×C₂₉	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#446	C₂	semidirect
3. C₂₉×#435	C₂	semidirect
4. C₈×D₄×C₂₉	C₂	semidirect
5. C₂₉×#432	C₂	semidirect
6. C₂₉×#432	C₂	semidirect
7. C₄×M₁₆×C₂₉	C₂	semidirect
8. C₂×C₂₉×#97	C₂	semidirect
64. D₄×C₂₉	M₁₆	semidirect
82. C₈×C₂₉	#41	semidirect
83. #2970	C₂₉	direct (N × H)
101. #446	C₂×C₂₉	semidirect
102. #435	C₂×C₂₉	semidirect
103. C₈×D₄	C₂×C₂₉	semidirect
104. #432	C₂×C₂₉	semidirect
105. #432	C₂×C₂₉	semidirect
106. C₄×M₁₆	C₂×C₂₉	semidirect
107. C₂×#97	C₂×C₂₉	semidirect
135. C₂₉	#2970	direct (N × H)
169. D₄	M₁₆×C₂₉	semidirect
187. C₈	#41×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×#41×C₂₉	2
C₂₉×#446	2
C₂₉×#435	2
C₈×D₄×C₂₉	2
C₂₉×#432	2
C₄×M₁₆×C₂₉	2
C₂×C₂₉×#97	2
#2970	29

Subgroups — C29×#2970 #16816684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#2970 #16816684