Subgroups — C₂₉×#33303 #20328203

Order 7424.

1526 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#495	C₂	1	8	yes	maximal, complemented
2	C₂×C₂₉×#494	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×#493	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₉×#492	C₂	1	2	yes	maximal, complemented
5	C₂₉×#2858	C₂	1	2	yes	maximal, complemented
6	C₄²×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×Q₁₆×C₂₉	C₂²	1	4	yes	—
8	C₂²×SD₁₆×C₂₉	C₂²	1	8	yes	—
9	C₂²×D₈×C₂₉	C₂²	1	4	yes	—
10	C₂×C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
11	C₂×C₂₉×#127	C₂²	1	2	yes	—
12	C₂×C₂₉×#124	C₂²	1	8	yes	—
13	C₂₉×#495	—	2	32	no	—
14	C₂₉×#494	—	2	4	no	—
15	C₂₉×#493	—	2	4	no	—
16	C₂₉×#492	—	2	8	no	—
17	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₂₉	C₂²	1	4	yes	—
20	C₂₉×#390	—	2	8	no	—
21	C₄³×C₂₉	C₂²	1	1	yes	characteristic
22	C₂²×Q₈×C₂₉	C₂³	1	4	yes	—
23	C₂²×D₄×C₂₉	—	2	4	no	—
24	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
25	C₂×Q₁₆×C₂₉	—	2	8	no	—
26	C₂×Q₁₆×C₂₉	—	2	16	no	—
27	C₂×SD₁₆×C₂₉	—	2	16	no	—
28	C₂×SD₁₆×C₂₉	—	2	32	no	—
29	C₂×D₈×C₂₉	—	2	8	no	—
30	C₂×D₈×C₂₉	—	2	16	no	—
31	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
32	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
33	C₂₉×C₄⋊Q₈	—	2	4	no	—
34	C₂₉×C₄⋊Q₈	—	2	4	no	—
35	C₂₉×#127	—	2	4	no	—
36	C₂₉×#127	—	2	4	no	—
37	C₂₉×#124	—	2	32	no	—
38	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
39	C₂×C₂²⋊C₄×C₂₉	—	2	16	no	—
40	C₂×C₄²×C₂₉	D₄	1	4	yes	—
41	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
42	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
43	C₄×C₈×C₂₉	D₄	1	4	yes	—
44	C₄×C₈×C₂₉	D₄	1	4	yes	—
45	C₄×C₈×C₂₉	D₄	1	16	yes	complemented
46	C₂⁴×C₂₉	—	2	4	no	—
47	C₂×Q₈×C₂₉	—	2	16	no	—
48	C₂×Q₈×C₂₉	—	2	4	no	—
49	C₂×Q₈×C₂₉	—	2	4	no	—
50	C₂×D₄×C₂₉	—	2	16	no	—
51	C₂×D₄×C₂₉	—	2	4	no	—
52	C₂×D₄×C₂₉	—	2	4	no	—
53	C₂×D₄×C₂₉	—	4	8	no	—
54	C₂×D₄×C₂₉	—	4	16	no	—
55	C₂²×C₄×C₂₉	—	2	4	no	—
56	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
57	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
58	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
59	Q₁₆×C₂₉	—	4	16	no	—
60	SD₁₆×C₂₉	—	4	32	no	—
61	D₈×C₂₉	—	4	16	no	—
62	C₂×C₈×C₂₉	C₂×D₄	1	4	yes	—
63	C₂×C₈×C₂₉	C₂×D₄	1	8	yes	—
64	C₂×C₈×C₂₉	C₂×D₄	1	4	yes	—
65	C₂×C₈×C₂₉	C₂×D₄	1	8	yes	—
66	C₄⋊C₄×C₂₉	—	4	8	no	—
67	C₂²⋊C₄×C₂₉	—	4	32	no	—
68	C₄²×C₂₉	—	2	8	no	—
69	C₄²×C₂₉	C₂×D₄	1	8	yes	—
70	C₄²×C₂₉	C₂×D₄	1	2	yes	—
71	C₄²×C₂₉	C₂×D₄	1	2	yes	—
72	#33303	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂³×C₂₉	—	4	8	no	—
74	C₂³×C₂₉	—	4	4	no	—
75	C₂³×C₂₉	—	4	16	no	—
76	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
77	Q₈×C₂₉	—	4	8	no	—
78	Q₈×C₂₉	—	4	8	no	—
79	D₄×C₂₉	—	4	8	no	—
80	D₄×C₂₉	—	4	8	no	—
81	D₄×C₂₉	—	8	16	no	—
82	C₂×C₄×C₂₉	—	2	8	no	—
83	C₂×C₄×C₂₉	—	4	8	no	—
84	C₂×C₄×C₂₉	—	4	4	no	—
85	C₂×C₄×C₂₉	#127	1	8	yes	—
86	C₂×C₄×C₂₉	#127	1	4	yes	—
87	C₂×C₄×C₂₉	#135	1	8	yes	—
88	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
89	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
90	C₂×C₄×C₂₉	C₂²×D₄	1	4	yes	—
91	C₈×C₂₉	#127	1	8	yes	—
92	C₈×C₂₉	#127	1	8	yes	—
93	C₂×#495	C₂×C₂₉	1	8	yes	complemented
94	C₂×#494	C₂×C₂₉	1	1	yes	characteristic, complemented
95	C₂×#493	C₂×C₂₉	1	1	yes	characteristic
96	C₂×#492	C₂×C₂₉	1	2	yes	complemented
97	#2858	C₂×C₂₉	1	2	yes	complemented
98	C₄²×C₈	C₂×C₂₉	1	1	yes	characteristic, complemented
99	C₂²×C₂₉	—	8	4	no	—
100	C₂²×C₂₉	—	8	8	no	—
101	C₂²×C₂₉	—	8	16	no	—
102	C₂²×C₂₉	C₂×#127	1	1	yes	characteristic
103	C₂²×C₂₉	C₂×#127	1	2	yes	—
104	C₂²×C₂₉	C₂×#135	1	4	yes	—
105	C₄×C₂₉	—	2	8	no	—
106	C₄×C₂₉	—	8	4	no	—
107	C₄×C₂₉	#495	1	8	yes	complemented
108	C₄×C₂₉	C₂×#127	1	2	yes	—
109	C₄×C₂₉	C₂×#127	1	2	yes	—
110	C₂²×Q₁₆	C₂²×C₂₉	1	4	yes	—
111	C₂²×SD₁₆	C₂²×C₂₉	1	8	yes	—
112	C₂²×D₈	C₂²×C₂₉	1	4	yes	—
113	C₂×C₄⋊Q₈	C₂²×C₂₉	1	2	yes	—
114	C₂×#127	C₂²×C₂₉	1	2	yes	—
115	C₂×#124	C₂²×C₂₉	1	8	yes	—
116	#495	—	2	32	no	—
117	#494	—	2	4	no	—
118	#493	—	2	4	no	—
119	#492	—	2	8	no	—
120	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
121	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
122	C₂×C₄×C₈	C₂²×C₂₉	1	4	yes	—
123	#390	—	2	8	no	—
124	C₄³	C₂²×C₂₉	1	1	yes	characteristic
125	C₂×C₂₉	—	16	4	no	—
126	C₂×C₂₉	#2867	1	1	yes	characteristic
127	C₂×C₂₉	C₂×#495	1	2	yes	—
128	C₂×C₂₉	#3147	1	4	yes	—
129	C₂²×Q₈	C₂³×C₂₉	1	4	yes	—
130	C₂²×D₄	—	2	4	no	—
131	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
132	C₂×Q₁₆	—	2	8	no	—
133	C₂×Q₁₆	—	2	16	no	—
134	C₂×SD₁₆	—	2	16	no	—
135	C₂×SD₁₆	—	2	32	no	—
136	C₂×D₈	—	2	8	no	—
137	C₂×D₈	—	2	16	no	—
138	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
139	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
140	C₄⋊Q₈	—	2	4	no	—
141	C₄⋊Q₈	—	2	4	no	—
142	#127	—	2	4	no	—
143	#127	—	2	4	no	—
144	#124	—	2	32	no	—
145	C₂×C₄⋊C₄	—	2	4	no	—
146	C₂×C₂²⋊C₄	—	2	16	no	—
147	C₂×C₄²	D₄×C₂₉	1	4	yes	—
148	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
149	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
150	C₄×C₈	D₄×C₂₉	1	4	yes	—
151	C₄×C₈	D₄×C₂₉	1	4	yes	—
152	C₄×C₈	D₄×C₂₉	1	16	yes	complemented
153	C₂₉	#33303	1	1	yes	characteristic, direct product factor, Sylow
154	C₂⁴	—	2	4	no	—
155	C₂×Q₈	—	2	16	no	—
156	C₂×Q₈	—	2	4	no	—
157	C₂×Q₈	—	2	4	no	—
158	C₂×D₄	—	2	16	no	—
159	C₂×D₄	—	2	4	no	—
160	C₂×D₄	—	2	4	no	—
161	C₂×D₄	—	4	8	no	—
162	C₂×D₄	—	4	16	no	—
163	C₂²×C₄	—	2	4	no	—
164	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
165	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
166	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
167	Q₁₆	—	4	16	no	—
168	SD₁₆	—	4	32	no	—
169	D₈	—	4	16	no	—
170	C₂×C₈	C₂×D₄×C₂₉	1	4	yes	—
171	C₂×C₈	C₂×D₄×C₂₉	1	4	yes	—
172	C₂×C₈	C₂×D₄×C₂₉	1	8	yes	—
173	C₂×C₈	C₂×D₄×C₂₉	1	8	yes	—
174	C₄⋊C₄	—	4	8	no	—
175	C₂²⋊C₄	—	4	32	no	—
176	C₄²	—	2	8	no	—
177	C₄²	C₂×D₄×C₂₉	1	2	yes	—
178	C₄²	C₂×D₄×C₂₉	1	2	yes	—
179	C₄²	C₂×D₄×C₂₉	1	8	yes	—
180	C₂³	—	4	8	no	—
181	C₂³	—	4	4	no	—
182	C₂³	—	4	16	no	—
183	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
184	Q₈	—	4	8	no	—
185	Q₈	—	4	8	no	—
186	D₄	—	4	8	no	—
187	D₄	—	4	8	no	—
188	D₄	—	8	16	no	—
189	C₂×C₄	—	2	8	no	—
190	C₂×C₄	—	4	8	no	—
191	C₂×C₄	—	4	4	no	—
192	C₂×C₄	C₂₉×#127	1	8	yes	—
193	C₂×C₄	C₂₉×#127	1	4	yes	—
194	C₂×C₄	C₂₉×#135	1	8	yes	—
195	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
196	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
197	C₂×C₄	C₂²×D₄×C₂₉	1	4	yes	—
198	C₈	C₂₉×#127	1	8	yes	—
199	C₈	C₂₉×#127	1	8	yes	—
200	C₂²	—	8	4	no	—
201	C₂²	—	8	8	no	—
202	C₂²	—	8	16	no	—
203	C₂²	C₂×C₂₉×#127	1	1	yes	characteristic
204	C₂²	C₂×C₂₉×#127	1	2	yes	—
205	C₂²	C₂×C₂₉×#135	1	4	yes	—
206	C₄	—	2	8	no	—
207	C₄	—	8	4	no	—
208	C₄	C₂₉×#495	1	8	yes	complemented
209	C₄	C₂×C₂₉×#127	1	2	yes	—
210	C₄	C₂×C₂₉×#127	1	2	yes	—
211	C₂	—	16	4	no	—
212	C₂	C₂₉×#2867	1	1	yes	characteristic
213	C₂	C₂×C₂₉×#495	1	2	yes	—
214	C₂	C₂₉×#3147	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#493	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₄³×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#495	C₂	semidirect
2. C₂×C₂₉×#494	C₂	semidirect
4. C₂×C₂₉×#492	C₂	semidirect
5. C₂₉×#2858	C₂	semidirect
6. C₄²×C₈×C₂₉	C₂	semidirect
45. C₄×C₈×C₂₉	D₄	semidirect
72. #33303	C₂₉	direct (N × H)
93. C₂×#495	C₂×C₂₉	semidirect
94. C₂×#494	C₂×C₂₉	semidirect
96. C₂×#492	C₂×C₂₉	semidirect
97. #2858	C₂×C₂₉	semidirect
98. C₄²×C₈	C₂×C₂₉	semidirect
107. C₄×C₂₉	#495	semidirect
152. C₄×C₈	D₄×C₂₉	semidirect
153. C₂₉	#33303	direct (N × H)
208. C₄	C₂₉×#495	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#495	2
C₂×C₂₉×#494	2
C₂×C₂₉×#493	2
C₂×C₂₉×#492	2
C₂₉×#2858	2
C₄²×C₈×C₂₉	2
#33303	29

Subgroups — C29×#33303 #20328203

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#33303 #20328203