Subgroups — C₂₉×#9693 #20304593

Order 7424.

478 conjugacy classes of subgroups.

The subgroup lattice has 236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2862	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#1831	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₉×#333	C₂	1	2	yes	maximal
5	C₂×C₂₉×#332	C₂	1	2	yes	maximal
6	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₂₉	—	2	1	no	—
11	C₂₉×#391	—	2	2	no	—
12	C₂₉×#391	C₄	1	4	yes	—
13	C₂₉×#382	—	2	1	no	—
14	C₂₉×#382	—	2	1	no	—
15	C₄³×C₂₉	C₂²	1	1	yes	characteristic
16	C₂₉×#336	—	2	1	no	—
17	C₂₉×#336	—	2	2	no	—
18	C₂₉×#333	—	2	4	no	—
19	C₂₉×#332	—	2	4	no	—
20	C₂²×Q₈×C₂₉	—	2	1	no	—
21	C₂²×Q₈×C₂₉	C₂×C₄	1	2	yes	—
22	C₂²×C₈×C₂₉	—	2	2	no	—
23	C₂²×C₈×C₂₉	—	2	2	no	—
24	C₂₉×C₄⋊Q₈	—	2	2	no	—
25	C₂₉×C₄⋊Q₈	—	2	2	no	—
26	C₂₉×C₄⋊Q₈	—	2	2	no	—
27	C₂₉×C₄⋊Q₈	—	2	2	no	—
28	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
32	C₂×C₄²×C₂₉	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₂₉	D₄	1	2	yes	—
35	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
37	C₂₉×C₄⋊C₈	—	2	2	no	—
38	C₂₉×C₄⋊C₈	—	2	2	no	—
39	C₂₉×C₄⋊C₈	—	2	2	no	—
40	C₂₉×C₄⋊C₈	D₄	1	4	yes	—
41	C₄×C₈×C₂₉	—	4	2	no	—
42	C₂₉×#95	—	2	4	no	—
43	C₂₉×#95	—	2	4	no	—
44	C₂×Q₈×C₂₉	—	2	4	no	—
45	C₂×Q₈×C₂₉	—	4	4	no	—
46	C₂×Q₈×C₂₉	—	4	1	no	—
47	C₂×Q₈×C₂₉	—	4	1	no	—
48	C₂×Q₈×C₂₉	—	4	4	no	—
49	C₂²×C₄×C₂₉	—	2	2	no	—
50	C₂²×C₄×C₂₉	—	2	2	no	—
51	C₂²×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
52	C₂²×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
53	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
56	C₂×C₈×C₂₉	—	2	4	no	—
57	C₂×C₈×C₂₉	—	4	2	no	—
58	C₂×C₈×C₂₉	—	4	2	no	—
59	C₂×C₈×C₂₉	—	4	2	no	—
60	C₂×C₈×C₂₉	—	4	4	no	—
61	C₄⋊C₄×C₂₉	—	2	4	no	—
62	C₄⋊C₄×C₂₉	—	4	2	no	—
63	C₄⋊C₄×C₂₉	—	4	2	no	—
64	C₄⋊C₄×C₂₉	—	4	1	no	—
65	C₄⋊C₄×C₂₉	—	4	1	no	—
66	C₄²×C₂₉	—	2	4	no	—
67	C₄²×C₂₉	—	2	2	no	—
68	C₄²×C₂₉	—	4	2	no	—
69	C₄²×C₂₉	SD₁₆	1	2	yes	—
70	C₄²×C₂₉	Q₁₆	1	2	yes	—
71	C₄²×C₂₉	C₂×D₄	1	2	yes	—
72	C₄²×C₂₉	#41	1	2	yes	—
73	#9693	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂³×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	Q₈×C₂₉	—	8	4	no	—
76	Q₈×C₂₉	—	8	2	no	—
77	Q₈×C₂₉	—	8	2	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	—	2	2	no	—
82	C₂×C₄×C₂₉	—	2	2	no	—
83	C₂×C₄×C₂₉	—	2	2	no	—
84	C₂×C₄×C₂₉	—	4	2	no	—
85	C₂×C₄×C₂₉	—	4	2	no	—
86	C₂×C₄×C₂₉	—	4	4	no	—
87	C₂×C₄×C₂₉	—	4	4	no	—
88	C₂×C₄×C₂₉	#103	1	4	yes	—
89	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
90	C₂×C₄×C₂₉	#121	1	2	yes	—
91	C₂×C₄×C₂₉	#124	1	1	yes	characteristic
92	C₂×C₄×C₂₉	#127	1	1	yes	characteristic
93	C₂×C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
94	C₂×C₄×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
95	C₂×C₄×C₂₉	#135	1	4	yes	—
96	C₂×C₄×C₂₉	#137	1	2	yes	—
97	C₈×C₂₉	—	4	4	no	—
98	C₈×C₂₉	—	8	2	no	—
99	#2862	C₂×C₂₉	1	1	yes	characteristic
100	#1831	C₂×C₂₉	1	1	yes	characteristic
101	C₄×C₄⋊C₈	C₂×C₂₉	1	1	yes	characteristic
102	C₂×#333	C₂×C₂₉	1	2	yes	—
103	C₂×#332	C₂×C₂₉	1	2	yes	—
104	C₂²×C₂₉	#390	1	1	yes	characteristic
105	C₂²×C₂₉	#413	1	2	yes	—
106	C₂²×C₂₉	C₂×#103	1	1	yes	characteristic
107	C₂²×C₂₉	#416	1	2	yes	—
108	C₂²×C₂₉	#419	1	1	yes	characteristic
109	C₄×C₂₉	—	2	4	no	—
110	C₄×C₂₉	—	2	2	no	—
111	C₄×C₂₉	—	4	2	no	—
112	C₄×C₂₉	—	8	2	no	—
113	C₄×C₂₉	—	8	2	no	—
114	C₄×C₂₉	#461	1	2	yes	—
115	C₄×C₂₉	#462	1	2	yes	—
116	C₄×C₂₉	#488	1	2	yes	—
117	C₄×C₂₉	#495	1	2	yes	—
118	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
119	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
120	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
121	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
122	C₂×C₄×C₈	—	2	1	no	—
123	#391	—	2	2	no	—
124	#391	C₄×C₂₉	1	4	yes	—
125	#382	—	2	1	no	—
126	#382	—	2	1	no	—
127	C₄³	C₂²×C₂₉	1	1	yes	characteristic
128	#336	—	2	2	no	—
129	#336	—	2	1	no	—
130	#333	—	2	4	no	—
131	#332	—	2	4	no	—
132	C₂×C₂₉	#1542	1	2	yes	—
133	C₂×C₂₉	#1554	1	2	yes	—
134	C₂×C₂₉	#1958	1	1	yes	characteristic
135	C₂×C₂₉	#1967	1	1	yes	characteristic
136	C₂×C₂₉	#1981	1	1	yes	characteristic
137	C₂²×Q₈	—	2	1	no	—
138	C₂²×Q₈	C₂×C₄×C₂₉	1	2	yes	—
139	C₂²×C₈	—	2	2	no	—
140	C₂²×C₈	—	2	2	no	—
141	C₄⋊Q₈	—	2	2	no	—
142	C₄⋊Q₈	—	2	2	no	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₄⋊Q₈	—	2	2	no	—
145	C₂×C₄⋊C₄	—	2	1	no	—
146	C₂×C₄⋊C₄	—	2	1	no	—
147	C₂×C₄⋊C₄	—	2	1	no	—
148	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
149	C₂×C₄²	C₂×C₄×C₂₉	1	2	yes	—
150	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
151	C₂×C₄²	D₄×C₂₉	1	2	yes	—
152	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
153	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
154	C₄⋊C₈	—	2	2	no	—
155	C₄⋊C₈	—	2	2	no	—
156	C₄⋊C₈	—	2	2	no	—
157	C₄⋊C₈	D₄×C₂₉	1	4	yes	—
158	C₄×C₈	—	4	2	no	—
159	#95	—	2	4	no	—
160	#95	—	2	4	no	—
161	C₂₉	#9693	1	1	yes	characteristic, direct product factor, Sylow
162	C₂×Q₈	—	2	4	no	—
163	C₂×Q₈	—	4	4	no	—
164	C₂×Q₈	—	4	1	no	—
165	C₂×Q₈	—	4	1	no	—
166	C₂×Q₈	—	4	4	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
170	C₂²×C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
171	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
172	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
173	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
174	C₂×C₈	—	2	4	no	—
175	C₂×C₈	—	4	2	no	—
176	C₂×C₈	—	4	2	no	—
177	C₂×C₈	—	4	2	no	—
178	C₂×C₈	—	4	4	no	—
179	C₄⋊C₄	—	2	4	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	1	no	—
183	C₄⋊C₄	—	4	1	no	—
184	C₄²	—	2	4	no	—
185	C₄²	—	2	2	no	—
186	C₄²	—	4	2	no	—
187	C₄²	SD₁₆×C₂₉	1	2	yes	—
188	C₄²	Q₁₆×C₂₉	1	2	yes	—
189	C₄²	C₂×D₄×C₂₉	1	2	yes	—
190	C₄²	#41×C₂₉	1	2	yes	—
191	C₂³	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
192	Q₈	—	8	4	no	—
193	Q₈	—	8	2	no	—
194	Q₈	—	8	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	4	no	—
204	C₂×C₄	—	4	4	no	—
205	C₂×C₄	C₂₉×#103	1	4	yes	—
206	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
207	C₂×C₄	C₂₉×#121	1	2	yes	—
208	C₂×C₄	C₂₉×#124	1	1	yes	characteristic
209	C₂×C₄	C₂₉×#127	1	1	yes	characteristic
210	C₂×C₄	C₂×SD₁₆×C₂₉	1	1	yes	characteristic
211	C₂×C₄	C₂×Q₁₆×C₂₉	1	1	yes	characteristic
212	C₂×C₄	C₂₉×#135	1	4	yes	—
213	C₂×C₄	C₂₉×#137	1	2	yes	—
214	C₈	—	4	4	no	—
215	C₈	—	8	2	no	—
216	C₂²	C₂₉×#390	1	1	yes	characteristic
217	C₂²	C₂₉×#413	1	2	yes	—
218	C₂²	C₂×C₂₉×#103	1	1	yes	characteristic
219	C₂²	C₂₉×#416	1	2	yes	—
220	C₂²	C₂₉×#419	1	1	yes	characteristic
221	C₄	—	2	2	no	—
222	C₄	—	2	4	no	—
223	C₄	—	4	2	no	—
224	C₄	—	8	2	no	—
225	C₄	—	8	2	no	—
226	C₄	C₂₉×#461	1	2	yes	—
227	C₄	C₂₉×#462	1	2	yes	—
228	C₄	C₂₉×#488	1	2	yes	—
229	C₄	C₂₉×#495	1	2	yes	—
230	C₂	C₂₉×#1542	1	2	yes	—
231	C₂	C₂₉×#1554	1	2	yes	—
232	C₂	C₂₉×#1958	1	1	yes	characteristic
233	C₂	C₂₉×#1967	1	1	yes	characteristic
234	C₂	C₂₉×#1981	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₄³×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
73. #9693	C₂₉	direct (N × H)
161. C₂₉	#9693	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×#2862	2
C₂₉×#1831	2
C₄×C₂₉×C₄⋊C₈	2
C₂×C₂₉×#333	2
C₂×C₂₉×#332	2
#9693	29

Subgroups — C29×#9693 #20304593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#9693 #20304593