Subgroups — C₂₉×#8647 #20303547

Order 7424.

438 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#1834	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#1803	C₂	1	2	yes	maximal
4	C₂×C₂₉×#334	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1296	C₂	1	2	yes	maximal
6	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₈×Q₈×C₂₉	—	2	2	no	—
8	C₈×Q₈×C₂₉	C₄	1	4	yes	complemented
9	C₂×C₂₉×C₄⋊C₈	—	2	1	no	—
10	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
11	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₂₉×#103	—	2	2	no	—
13	C₂×C₄×C₈×C₂₉	—	2	1	no	—
14	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
15	C₂₉×#384	C₂²	1	2	yes	—
16	C₂₉×#340	—	2	1	no	—
17	C₂₉×#340	—	2	1	no	—
18	C₂₉×#340	—	2	2	no	—
19	C₂₉×#334	—	2	2	no	—
20	C₂²×Q₈×C₂₉	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₂₉	—	2	1	no	—
22	C₂²×C₈×C₂₉	—	2	2	no	—
23	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
24	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
25	C₄×Q₈×C₂₉	—	2	1	no	—
26	C₄×Q₈×C₂₉	—	2	1	no	—
27	C₄×Q₈×C₂₉	C₂×C₄	1	2	yes	—
28	C₄×Q₈×C₂₉	Q₈	1	2	yes	—
29	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₂₉	—	2	1	no	—
35	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
36	C₂₉×C₄⋊C₈	—	2	4	no	—
37	C₂₉×C₄⋊C₈	—	2	1	no	—
38	C₂₉×C₄⋊C₈	—	2	2	no	—
39	C₂₉×C₄⋊C₈	—	2	2	no	—
40	C₂₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
41	C₂₉×#103	—	4	4	no	—
42	C₄×C₈×C₂₉	—	2	4	no	—
43	C₄×C₈×C₂₉	C₂×C₄	1	2	yes	—
44	C₄×C₈×C₂₉	D₄	1	2	yes	—
45	C₂×Q₈×C₂₉	—	2	1	no	—
46	C₂×Q₈×C₂₉	—	2	2	no	—
47	C₂×Q₈×C₂₉	C₄⋊C₄	1	2	yes	—
48	C₂×Q₈×C₂₉	SD₁₆	1	4	yes	—
49	C₂²×C₄×C₂₉	—	2	1	no	—
50	C₂²×C₄×C₂₉	—	2	1	no	—
51	C₂²×C₄×C₂₉	—	4	2	no	—
52	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
55	C₂×C₈×C₂₉	—	2	2	no	—
56	C₂×C₈×C₂₉	—	2	2	no	—
57	C₂×C₈×C₂₉	—	2	2	no	—
58	C₂×C₈×C₂₉	—	4	2	no	—
59	C₂×C₈×C₂₉	—	4	2	no	—
60	C₂×C₈×C₂₉	—	4	2	no	—
61	C₂×C₈×C₂₉	—	4	2	no	—
62	C₂×C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
63	C₂×C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
64	C₄⋊C₄×C₂₉	—	2	2	no	—
65	C₄⋊C₄×C₂₉	—	2	1	no	—
66	C₄⋊C₄×C₂₉	—	2	2	no	—
67	C₄⋊C₄×C₂₉	—	4	2	no	—
68	C₄⋊C₄×C₂₉	—	4	2	no	—
69	C₄⋊C₄×C₂₉	—	4	2	no	—
70	C₄⋊C₄×C₂₉	—	4	2	no	—
71	C₄⋊C₄×C₂₉	—	8	2	no	—
72	C₄⋊C₄×C₂₉	C₄⋊C₄	1	2	yes	—
73	C₄²×C₂₉	—	2	2	no	—
74	C₄²×C₂₉	—	2	2	no	—
75	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₂₉	C₂×Q₈	1	1	yes	characteristic
78	C₄²×C₂₉	#41	1	1	yes	characteristic
79	#8647	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂³×C₂₉	#121	1	1	yes	characteristic
81	Q₈×C₂₉	—	2	2	no	—
82	Q₈×C₂₉	—	2	4	no	—
83	Q₈×C₂₉	#106	1	4	yes	—
84	C₂×C₄×C₂₉	—	2	2	no	—
85	C₂×C₄×C₂₉	—	2	4	no	—
86	C₂×C₄×C₂₉	—	2	1	no	—
87	C₂×C₄×C₂₉	—	2	1	no	—
88	C₂×C₄×C₂₉	—	2	2	no	—
89	C₂×C₄×C₂₉	—	4	1	no	—
90	C₂×C₄×C₂₉	—	4	1	no	—
91	C₂×C₄×C₂₉	—	8	2	no	—
92	C₂×C₄×C₂₉	—	8	2	no	—
93	C₂×C₄×C₂₉	—	8	2	no	—
94	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₂₉	#117	1	1	yes	characteristic
97	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
98	C₂×C₄×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
99	C₂×C₄×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
100	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
101	C₂×C₄×C₂₉	#135	1	2	yes	—
102	C₂×C₄×C₂₉	#135	1	2	yes	—
103	C₂×C₄×C₂₉	#137	1	2	yes	—
104	C₈×C₂₉	—	2	2	no	—
105	C₈×C₂₉	—	2	2	no	—
106	C₈×C₂₉	—	4	2	no	—
107	C₈×C₂₉	—	8	2	no	—
108	C₂×C₈×Q₈	C₂×C₂₉	1	1	yes	characteristic
109	#1834	C₂×C₂₉	1	1	yes	characteristic
110	#1803	C₂×C₂₉	1	2	yes	—
111	C₂×#334	C₂×C₂₉	1	1	yes	characteristic
112	#1296	C₂×C₂₉	1	2	yes	—
113	C₂²×C₂₉	#380	1	1	yes	characteristic
114	C₂²×C₂₉	#464	1	2	yes	—
115	C₂²×C₂₉	#465	1	2	yes	—
116	C₂²×C₂₉	#472	1	1	yes	characteristic
117	C₂²×C₂₉	#473	1	1	yes	characteristic
118	C₄×C₂₉	—	2	4	no	—
119	C₄×C₂₉	—	2	1	no	—
120	C₄×C₂₉	—	2	1	no	—
121	C₄×C₂₉	—	4	2	no	—
122	C₄×C₂₉	—	16	2	no	—
123	C₄×C₂₉	#416	1	1	yes	characteristic
124	C₄×C₂₉	#419	1	1	yes	characteristic
125	C₄×C₂₉	C₂×#106	1	1	yes	characteristic
126	C₄×C₂₉	#427	1	1	yes	characteristic
127	C₄×C₂₉	#465	1	2	yes	—
128	C₄×C₂₉	#479	1	2	yes	—
129	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
130	C₈×Q₈	—	2	2	no	—
131	C₈×Q₈	C₄×C₂₉	1	4	yes	complemented
132	C₂×C₄⋊C₈	—	2	1	no	—
133	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
134	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
135	C₂×#103	—	2	2	no	—
136	C₂×C₄×C₈	—	2	1	no	—
137	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
138	#384	C₂²×C₂₉	1	2	yes	—
139	#340	—	2	1	no	—
140	#340	—	2	1	no	—
141	#340	—	2	2	no	—
142	#334	—	2	2	no	—
143	C₂×C₂₉	#1678	1	2	yes	—
144	C₂×C₂₉	#1680	1	2	yes	—
145	C₂×C₂₉	#1805	1	1	yes	characteristic
146	C₂×C₂₉	#1807	1	1	yes	characteristic
147	C₂×C₂₉	#1816	1	1	yes	characteristic
148	C₂²×Q₈	D₄×C₂₉	1	1	yes	characteristic
149	C₂²×C₈	—	2	1	no	—
150	C₂²×C₈	—	2	2	no	—
151	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
152	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
153	C₄×Q₈	—	2	1	no	—
154	C₄×Q₈	—	2	1	no	—
155	C₄×Q₈	C₂×C₄×C₂₉	1	2	yes	—
156	C₄×Q₈	Q₈×C₂₉	1	2	yes	—
157	C₂×C₄⋊C₄	—	2	1	no	—
158	C₂×C₄⋊C₄	—	2	2	no	—
159	C₂×C₄⋊C₄	—	2	2	no	—
160	C₂×C₄⋊C₄	—	2	2	no	—
161	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
162	C₂×C₄²	—	2	1	no	—
163	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
164	C₄⋊C₈	—	2	4	no	—
165	C₄⋊C₈	—	2	1	no	—
166	C₄⋊C₈	—	2	2	no	—
167	C₄⋊C₈	—	2	2	no	—
168	C₄⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
169	#103	—	4	4	no	—
170	C₄×C₈	—	2	4	no	—
171	C₄×C₈	C₂×C₄×C₂₉	1	2	yes	—
172	C₄×C₈	D₄×C₂₉	1	2	yes	—
173	C₂₉	#8647	1	1	yes	characteristic, direct product factor, Sylow
174	C₂×Q₈	—	2	1	no	—
175	C₂×Q₈	—	2	2	no	—
176	C₂×Q₈	C₄⋊C₄×C₂₉	1	2	yes	—
177	C₂×Q₈	SD₁₆×C₂₉	1	4	yes	—
178	C₂²×C₄	—	2	1	no	—
179	C₂²×C₄	—	2	1	no	—
180	C₂²×C₄	—	4	2	no	—
181	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
182	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
183	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	2	2	no	—
186	C₂×C₈	—	2	2	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	4	2	no	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	C₂²⋊C₄×C₂₉	1	2	yes	—
192	C₂×C₈	C₂²⋊C₄×C₂₉	1	2	yes	—
193	C₄⋊C₄	—	2	2	no	—
194	C₄⋊C₄	—	2	1	no	—
195	C₄⋊C₄	—	2	2	no	—
196	C₄⋊C₄	—	4	2	no	—
197	C₄⋊C₄	—	4	2	no	—
198	C₄⋊C₄	—	4	2	no	—
199	C₄⋊C₄	—	4	2	no	—
200	C₄⋊C₄	—	8	2	no	—
201	C₄⋊C₄	C₄⋊C₄×C₂₉	1	2	yes	—
202	C₄²	—	2	2	no	—
203	C₄²	—	2	2	no	—
204	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
205	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
206	C₄²	C₂×Q₈×C₂₉	1	1	yes	characteristic
207	C₄²	#41×C₂₉	1	1	yes	characteristic
208	C₂³	C₂₉×#121	1	1	yes	characteristic
209	Q₈	—	2	2	no	—
210	Q₈	—	2	4	no	—
211	Q₈	C₂₉×#106	1	4	yes	—
212	C₂×C₄	—	2	4	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	4	1	no	—
218	C₂×C₄	—	4	1	no	—
219	C₂×C₄	—	8	2	no	—
220	C₂×C₄	—	8	2	no	—
221	C₂×C₄	—	8	2	no	—
222	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
223	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
224	C₂×C₄	C₂₉×#117	1	1	yes	characteristic
225	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
226	C₂×C₄	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
227	C₂×C₄	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
228	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
229	C₂×C₄	C₂₉×#135	1	2	yes	—
230	C₂×C₄	C₂₉×#135	1	2	yes	—
231	C₂×C₄	C₂₉×#137	1	2	yes	—
232	C₈	—	2	2	no	—
233	C₈	—	2	2	no	—
234	C₈	—	4	2	no	—
235	C₈	—	8	2	no	—
236	C₂²	C₂₉×#380	1	1	yes	characteristic
237	C₂²	C₂₉×#464	1	2	yes	—
238	C₂²	C₂₉×#465	1	2	yes	—
239	C₂²	C₂₉×#472	1	1	yes	characteristic
240	C₂²	C₂₉×#473	1	1	yes	characteristic
241	C₄	—	2	4	no	—
242	C₄	—	2	1	no	—
243	C₄	—	2	1	no	—
244	C₄	—	4	2	no	—
245	C₄	—	16	2	no	—
246	C₄	C₂₉×#416	1	1	yes	characteristic
247	C₄	C₂₉×#419	1	1	yes	characteristic
248	C₄	C₂×C₂₉×#106	1	1	yes	characteristic
249	C₄	C₂₉×#427	1	1	yes	characteristic
250	C₄	C₂₉×#465	1	2	yes	—
251	C₄	C₂₉×#479	1	2	yes	—
252	C₂	C₂₉×#1678	1	2	yes	—
253	C₂	C₂₉×#1680	1	2	yes	—
254	C₂	C₂₉×#1805	1	1	yes	characteristic
255	C₂	C₂₉×#1807	1	1	yes	characteristic
256	C₂	C₂₉×#1816	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₉	#121
commutator	C₄²	C₂²×C₄×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₈×Q₈×C₂₉	C₄	semidirect
79. #8647	C₂₉	direct (N × H)
131. C₈×Q₈	C₄×C₂₉	semidirect
173. C₂₉	#8647	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₈×Q₈×C₂₉	2
C₂₉×#1834	2
C₂₉×#1803	2
C₂×C₂₉×#334	2
C₂₉×#1296	2
#8647	29

Subgroups — C29×#8647 #20303547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#8647 #20303547