Subgroups — C₂₉×#11674 #20306574

Order 7424.

330 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3168	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₉×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#1567	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#1332	C₂	1	2	yes	maximal, complemented
5	C₂₉×#1331	C₂	1	2	yes	maximal, complemented
6	C₂₉×#529	—	2	1	no	—
7	C₂×C₂₉×M₃₂	—	2	1	no	—
8	C₂₉×#499	C₄	1	1	yes	characteristic
9	C₂₉×#495	C₄	1	1	yes	characteristic
10	C₂₉×#488	—	2	1	no	—
11	C₂₉×#467	C₄	1	1	yes	characteristic
12	C₂₉×#466	C₄	1	1	yes	characteristic
13	C₂₉×#465	—	2	1	no	—
14	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
15	C₄×SD₁₆×C₂₉	—	2	1	no	—
16	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
17	C₂₉×#423	—	2	1	no	—
18	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
19	C₂₉×#346	—	2	1	no	—
20	C₄×C₁₆×C₂₉	C₂²	1	2	yes	—
21	C₂₉×#335	—	2	1	no	—
22	C₂₉×#335	C₂²	1	2	yes	—
23	C₂×Q₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
24	C₂×SD₁₆×C₂₉	—	2	1	no	—
25	C₂×D₈×C₂₉	C₂×C₄	1	1	yes	characteristic
26	C₂×M₁₆×C₂₉	—	4	1	no	—
27	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
29	C₂₉×#126	—	4	1	no	—
30	C₂₉×#125	—	2	1	no	—
31	C₂₉×#124	—	2	1	no	—
32	C₂₉×#123	—	4	1	no	—
33	C₂₉×C₂²⋊Q₈	—	2	1	no	—
34	C₂₉×#121	—	2	1	no	—
35	C₄×Q₈×C₂₉	—	2	1	no	—
36	C₄×D₄×C₂₉	—	2	1	no	—
37	C₄×D₄×C₂₉	—	4	1	no	—
38	C₂₉×#117	—	4	1	no	—
39	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
40	C₂₉×M₃₂	—	2	4	no	—
41	C₂×C₁₆×C₂₉	—	2	2	no	—
42	C₂₉×#107	C₂×C₄	1	1	yes	characteristic
43	C₂₉×#107	C₂×C₄	1	1	yes	characteristic
44	C₂₉×#106	—	2	1	no	—
45	C₂₉×C₄⋊C₈	—	2	2	no	—
46	C₂₉×C₄⋊C₈	—	4	1	no	—
47	C₂₉×#103	—	2	1	no	—
48	C₂₉×#103	—	2	1	no	—
49	C₂₉×#102	—	2	1	no	—
50	C₂₉×#102	—	2	1	no	—
51	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
52	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
53	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
54	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
55	C₂×Q₈×C₂₉	—	2	1	no	—
56	C₂×D₄×C₂₉	—	2	1	no	—
57	C₂×D₄×C₂₉	—	4	1	no	—
58	C₂²×C₄×C₂₉	—	4	1	no	—
59	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₂₉	D₈	1	1	yes	characteristic
61	C₂²×C₄×C₂₉	SD₁₆	1	1	yes	characteristic
62	Q₁₆×C₂₉	—	2	2	no	—
63	SD₁₆×C₂₉	—	4	2	no	—
64	D₈×C₂₉	—	2	2	no	—
65	M₁₆×C₂₉	—	8	2	no	—
66	C₂×C₈×C₂₉	—	2	2	no	—
67	C₂×C₈×C₂₉	—	2	2	no	—
68	C₂×C₈×C₂₉	—	4	2	no	—
69	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
73	C₄⋊C₄×C₂₉	—	2	1	no	—
74	C₄⋊C₄×C₂₉	—	2	1	no	—
75	C₄⋊C₄×C₂₉	—	4	1	no	—
76	C₄⋊C₄×C₂₉	—	4	1	no	—
77	C₄⋊C₄×C₂₉	—	4	1	no	—
78	C₄⋊C₄×C₂₉	—	4	1	no	—
79	C₂²⋊C₄×C₂₉	—	4	1	no	—
80	C₂²⋊C₄×C₂₉	—	4	1	no	—
81	C₂²⋊C₄×C₂₉	—	4	1	no	—
82	C₂²⋊C₄×C₂₉	—	4	1	no	—
83	C₂²⋊C₄×C₂₉	—	4	1	no	—
84	C₄²×C₂₉	—	4	1	no	—
85	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₄²×C₂₉	D₈	1	1	yes	characteristic
87	C₄²×C₂₉	SD₁₆	1	1	yes	characteristic
88	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
89	C₁₆×C₂₉	—	2	4	no	—
90	#11674	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂³×C₂₉	—	4	1	no	—
92	C₂³×C₂₉	#102	1	1	yes	characteristic
93	Q₈×C₂₉	—	4	1	no	—
94	Q₈×C₂₉	—	4	1	no	—
95	D₄×C₂₉	—	4	1	no	—
96	D₄×C₂₉	—	4	1	no	—
97	D₄×C₂₉	—	8	2	no	—
98	C₂×C₄×C₂₉	—	2	1	no	—
99	C₂×C₄×C₂₉	—	2	1	no	—
100	C₂×C₄×C₂₉	—	2	1	no	—
101	C₂×C₄×C₂₉	—	2	1	no	—
102	C₂×C₄×C₂₉	—	4	1	no	—
103	C₂×C₄×C₂₉	—	4	1	no	—
104	C₂×C₄×C₂₉	—	4	1	no	—
105	C₂×C₄×C₂₉	—	4	1	no	—
106	C₂×C₄×C₂₉	—	8	1	no	—
107	C₂×C₄×C₂₉	—	8	1	no	—
108	C₂×C₄×C₂₉	#102	1	1	yes	characteristic
109	C₂×C₄×C₂₉	#102	1	1	yes	characteristic
110	C₂×C₄×C₂₉	#102	1	1	yes	characteristic
111	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
113	C₂×C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
114	C₈×C₂₉	—	2	1	no	—
115	C₈×C₂₉	—	2	1	no	—
116	C₈×C₂₉	—	8	2	no	—
117	C₈×C₂₉	#104	1	2	yes	—
118	C₈×C₂₉	#131	1	2	yes	—
119	#3168	C₂×C₂₉	1	1	yes	characteristic
120	C₄×M₃₂	C₂×C₂₉	1	1	yes	characteristic, complemented
121	#1567	C₂×C₂₉	1	1	yes	characteristic, complemented
122	#1332	C₂×C₂₉	1	2	yes	complemented
123	#1331	C₂×C₂₉	1	2	yes	complemented
124	C₂²×C₂₉	—	2	1	no	—
125	C₂²×C₂₉	—	2	1	no	—
126	C₂²×C₂₉	—	2	1	no	—
127	C₂²×C₂₉	—	8	1	no	—
128	C₂²×C₂₉	—	8	1	no	—
129	C₂²×C₂₉	—	8	1	no	—
130	C₂²×C₂₉	C₂×#102	1	1	yes	characteristic
131	C₄×C₂₉	—	2	1	no	—
132	C₄×C₂₉	—	2	1	no	—
133	C₄×C₂₉	—	2	1	no	—
134	C₄×C₂₉	—	2	1	no	—
135	C₄×C₂₉	—	8	1	no	—
136	C₄×C₂₉	—	8	1	no	—
137	C₄×C₂₉	—	8	1	no	—
138	C₄×C₂₉	#408	1	1	yes	characteristic
139	C₄×C₂₉	C₂×#104	1	1	yes	characteristic
140	C₄×C₂₉	#509	1	1	yes	characteristic
141	C₄×C₂₉	#510	1	1	yes	characteristic
142	#529	—	2	1	no	—
143	C₂×M₃₂	—	2	1	no	—
144	#499	C₄×C₂₉	1	1	yes	characteristic
145	#495	C₄×C₂₉	1	1	yes	characteristic
146	#488	—	2	1	no	—
147	#467	C₄×C₂₉	1	1	yes	characteristic
148	#466	C₄×C₂₉	1	1	yes	characteristic
149	#465	—	2	1	no	—
150	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
151	C₄×SD₁₆	—	2	1	no	—
152	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
153	#423	—	2	1	no	—
154	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
155	#346	—	2	1	no	—
156	C₄×C₁₆	C₂²×C₂₉	1	2	yes	—
157	#335	—	2	1	no	—
158	#335	C₂²×C₂₉	1	2	yes	—
159	C₂×C₂₉	—	4	1	no	—
160	C₂×C₂₉	—	16	1	no	—
161	C₂×C₂₉	#1492	1	1	yes	characteristic
162	C₂×C₂₉	#2139	1	1	yes	characteristic
163	C₂×C₂₉	#2143	1	1	yes	characteristic
164	C₂×Q₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic
165	C₂×SD₁₆	—	2	1	no	—
166	C₂×D₈	C₂×C₄×C₂₉	1	1	yes	characteristic
167	C₂×M₁₆	—	4	1	no	—
168	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
169	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
170	#126	—	4	1	no	—
171	#125	—	2	1	no	—
172	#124	—	2	1	no	—
173	#123	—	4	1	no	—
174	C₂²⋊Q₈	—	2	1	no	—
175	#121	—	2	1	no	—
176	C₄×Q₈	—	2	1	no	—
177	C₄×D₄	—	2	1	no	—
178	C₄×D₄	—	4	1	no	—
179	#117	—	4	1	no	—
180	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
181	M₃₂	—	2	4	no	—
182	C₂×C₁₆	—	2	2	no	—
183	#107	C₂×C₄×C₂₉	1	1	yes	characteristic
184	#107	C₂×C₄×C₂₉	1	1	yes	characteristic
185	#106	—	2	1	no	—
186	C₄⋊C₈	—	2	2	no	—
187	C₄⋊C₈	—	4	1	no	—
188	#103	—	2	1	no	—
189	#103	—	2	1	no	—
190	#102	—	2	1	no	—
191	#102	—	2	1	no	—
192	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
193	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
194	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
195	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
196	C₂₉	#11674	1	1	yes	characteristic, direct product factor, Sylow
197	C₂×Q₈	—	2	1	no	—
198	C₂×D₄	—	2	1	no	—
199	C₂×D₄	—	4	1	no	—
200	C₂²×C₄	—	4	1	no	—
201	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
202	C₂²×C₄	D₈×C₂₉	1	1	yes	characteristic
203	C₂²×C₄	SD₁₆×C₂₉	1	1	yes	characteristic
204	Q₁₆	—	2	2	no	—
205	SD₁₆	—	4	2	no	—
206	D₈	—	2	2	no	—
207	M₁₆	—	8	2	no	—
208	C₂×C₈	—	2	2	no	—
209	C₂×C₈	—	2	2	no	—
210	C₂×C₈	—	4	2	no	—
211	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
212	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
213	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
214	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
215	C₄⋊C₄	—	2	1	no	—
216	C₄⋊C₄	—	2	1	no	—
217	C₄⋊C₄	—	4	1	no	—
218	C₄⋊C₄	—	4	1	no	—
219	C₄⋊C₄	—	4	1	no	—
220	C₄⋊C₄	—	4	1	no	—
221	C₂²⋊C₄	—	4	1	no	—
222	C₂²⋊C₄	—	4	1	no	—
223	C₂²⋊C₄	—	4	1	no	—
224	C₂²⋊C₄	—	4	1	no	—
225	C₂²⋊C₄	—	4	1	no	—
226	C₄²	—	4	1	no	—
227	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
228	C₄²	D₈×C₂₉	1	1	yes	characteristic
229	C₄²	SD₁₆×C₂₉	1	1	yes	characteristic
230	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
231	C₁₆	—	2	4	no	—
232	C₂³	—	4	1	no	—
233	C₂³	C₂₉×#102	1	1	yes	characteristic
234	Q₈	—	4	1	no	—
235	Q₈	—	4	1	no	—
236	D₄	—	4	1	no	—
237	D₄	—	4	1	no	—
238	D₄	—	8	2	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	4	1	no	—
244	C₂×C₄	—	4	1	no	—
245	C₂×C₄	—	4	1	no	—
246	C₂×C₄	—	4	1	no	—
247	C₂×C₄	—	8	1	no	—
248	C₂×C₄	—	8	1	no	—
249	C₂×C₄	C₂₉×#102	1	1	yes	characteristic
250	C₂×C₄	C₂₉×#102	1	1	yes	characteristic
251	C₂×C₄	C₂₉×#102	1	1	yes	characteristic
252	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
253	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
254	C₂×C₄	C₂×SD₁₆×C₂₉	1	1	yes	characteristic
255	C₈	—	2	1	no	—
256	C₈	—	2	1	no	—
257	C₈	—	8	2	no	—
258	C₈	C₂₉×#104	1	2	yes	—
259	C₈	C₂₉×#131	1	2	yes	—
260	C₂²	—	2	1	no	—
261	C₂²	—	2	1	no	—
262	C₂²	—	2	1	no	—
263	C₂²	—	8	1	no	—
264	C₂²	—	8	1	no	—
265	C₂²	—	8	1	no	—
266	C₂²	C₂×C₂₉×#102	1	1	yes	characteristic
267	C₄	—	2	1	no	—
268	C₄	—	2	1	no	—
269	C₄	—	2	1	no	—
270	C₄	—	2	1	no	—
271	C₄	—	8	1	no	—
272	C₄	—	8	1	no	—
273	C₄	—	8	1	no	—
274	C₄	C₂₉×#408	1	1	yes	characteristic
275	C₄	C₂×C₂₉×#104	1	1	yes	characteristic
276	C₄	C₂₉×#509	1	1	yes	characteristic
277	C₄	C₂₉×#510	1	1	yes	characteristic
278	C₂	—	4	1	no	—
279	C₂	—	16	1	no	—
280	C₂	C₂₉×#1492	1	1	yes	characteristic
281	C₂	C₂₉×#2139	1	1	yes	characteristic
282	C₂	C₂₉×#2143	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₂₉
Frattini, cosocle	C₄×C₈	C₂³×C₂₉
socle	C₂²×C₂₉	C₂×#102
prime radical	C₂₉×#466	C₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ C₂×C₄×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₂₉×M₃₂	C₂	semidirect
3. C₂₉×#1567	C₂	semidirect
4. C₂₉×#1332	C₂	semidirect
5. C₂₉×#1331	C₂	semidirect
90. #11674	C₂₉	direct (N × H)
120. C₄×M₃₂	C₂×C₂₉	semidirect
121. #1567	C₂×C₂₉	semidirect
122. #1332	C₂×C₂₉	semidirect
123. #1331	C₂×C₂₉	semidirect
196. C₂₉	#11674	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×#3168	2
C₄×C₂₉×M₃₂	2
C₂₉×#1567	2
C₂₉×#1332	2
C₂₉×#1331	2
#11674	29

Subgroups — C29×#11674 #20306574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#11674 #20306574