Subgroups — C₂₉×#9047 #20303947

Order 7424.

492 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3103	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2932	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#1985	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#1540	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1487	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1301	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1281	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₉×#131	—	2	1	no	—
9	C₂₉×#532	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
11	C₂₉×#481	C₄	1	2	yes	—
12	C₂₉×#475	—	2	1	no	—
13	C₂₉×#460	—	2	1	no	—
14	C₂₉×#448	C₄	1	2	yes	—
15	C₄×SD₁₆×C₂₉	—	2	2	no	—
16	C₂₉×#435	—	2	2	no	—
17	C₂₉×#435	—	2	2	no	—
18	C₂₉×#431	C₂²	1	1	yes	characteristic
19	C₂₉×#431	C₂²	1	1	yes	characteristic
20	C₂₉×#423	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂₉×#408	—	2	1	no	—
23	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
24	C₂₉×#336	—	2	1	no	—
25	C₂₉×#336	—	2	1	no	—
26	C₂₉×#332	—	2	1	no	—
27	C₂₉×#331	—	2	1	no	—
28	C₂₉×Q₈⋊C₈	—	2	2	no	—
29	C₂×#41×C₂₉	—	2	1	no	—
30	C₂²×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
31	C₂×SD₁₆×C₂₉	—	2	2	no	—
32	C₂₉×#131	—	4	2	no	—
33	C₂₉×#131	—	4	2	no	—
34	C₂×M₁₆×C₂₉	—	2	2	no	—
35	C₂×M₁₆×C₂₉	—	2	1	no	—
36	C₂²×C₈×C₂₉	—	2	2	no	—
37	C₂²×C₈×C₂₉	—	2	1	no	—
38	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
40	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
41	C₂₉×#127	D₄	1	1	yes	characteristic
42	C₂₉×#124	—	2	1	no	—
43	C₂₉×#121	—	2	1	no	—
44	C₂₉×#121	C₂×C₄	1	2	yes	—
45	C₄×Q₈×C₂₉	—	2	1	no	—
46	C₄×Q₈×C₂₉	—	2	1	no	—
47	C₄×Q₈×C₂₉	—	2	1	no	—
48	C₄×Q₈×C₂₉	—	2	1	no	—
49	C₄×D₄×C₂₉	—	2	1	no	—
50	C₄×D₄×C₂₉	D₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₂₉	—	2	1	no	—
54	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
55	C₂₉×#106	—	2	2	no	—
56	C₂₉×C₄⋊C₈	—	2	1	no	—
57	C₂₉×C₄⋊C₈	—	2	1	no	—
58	C₂₉×C₄⋊C₈	—	2	1	no	—
59	C₂₉×C₄⋊C₈	—	2	1	no	—
60	C₂₉×C₄⋊C₈	—	2	1	no	—
61	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
62	C₂₉×#103	—	2	2	no	—
63	C₂₉×#102	—	2	2	no	—
64	C₂₉×C₂²⋊C₈	—	2	4	no	—
65	C₂₉×C₂²⋊C₈	—	2	1	no	—
66	C₂₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
67	C₂₉×#97	—	2	1	no	—
68	C₂₉×#97	—	2	1	no	—
69	C₄×C₈×C₂₉	—	2	1	no	—
70	C₄×C₈×C₂₉	—	2	1	no	—
71	#41×C₂₉	—	4	1	no	—
72	#41×C₂₉	—	4	1	no	—
73	#41×C₂₉	—	4	1	no	—
74	#41×C₂₉	—	4	1	no	—
75	C₂×Q₈×C₂₉	—	2	1	no	—
76	C₂×Q₈×C₂₉	—	2	1	no	—
77	C₂×Q₈×C₂₉	—	2	1	no	—
78	C₂×Q₈×C₂₉	—	4	2	no	—
79	C₂×D₄×C₂₉	—	2	2	no	—
80	C₂×D₄×C₂₉	—	2	1	no	—
81	C₂×D₄×C₂₉	—	2	1	no	—
82	C₂×D₄×C₂₉	C₂²⋊C₄	1	2	yes	—
83	C₂²×C₄×C₂₉	—	2	1	no	—
84	C₂²×C₄×C₂₉	—	2	2	no	—
85	C₂²×C₄×C₂₉	—	2	1	no	—
86	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
89	SD₁₆×C₂₉	—	4	4	no	—
90	M₁₆×C₂₉	—	4	4	no	—
91	M₁₆×C₂₉	—	4	1	no	—
92	M₁₆×C₂₉	—	4	1	no	—
93	C₂×C₈×C₂₉	—	2	1	no	—
94	C₂×C₈×C₂₉	—	2	1	no	—
95	C₂×C₈×C₂₉	—	2	2	no	—
96	C₂×C₈×C₂₉	—	2	2	no	—
97	C₂×C₈×C₂₉	—	2	1	no	—
98	C₂×C₈×C₂₉	—	2	1	no	—
99	C₂×C₈×C₂₉	—	2	1	no	—
100	C₂×C₈×C₂₉	—	4	4	no	—
101	C₂×C₈×C₂₉	—	4	1	no	—
102	C₂×C₈×C₂₉	—	4	1	no	—
103	C₂×C₈×C₂₉	—	4	1	no	—
104	C₂×C₈×C₂₉	—	4	1	no	—
105	C₂×C₈×C₂₉	SD₁₆	1	2	yes	complemented
106	C₄⋊C₄×C₂₉	—	2	1	no	—
107	C₄⋊C₄×C₂₉	—	2	1	no	—
108	C₄⋊C₄×C₂₉	—	2	1	no	—
109	C₄⋊C₄×C₂₉	—	4	1	no	—
110	C₄⋊C₄×C₂₉	—	4	1	no	—
111	C₄⋊C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
112	C₂²⋊C₄×C₂₉	—	2	2	no	—
113	C₂²⋊C₄×C₂₉	—	2	2	no	—
114	C₄²×C₂₉	—	4	1	no	—
115	C₄²×C₂₉	—	4	1	no	—
116	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₂₉	#41	1	1	yes	characteristic
120	#9047	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂³×C₂₉	—	2	2	no	—
122	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
123	Q₈×C₂₉	—	2	2	no	—
124	Q₈×C₂₉	—	2	2	no	—
125	Q₈×C₂₉	—	4	1	no	—
126	Q₈×C₂₉	—	4	1	no	—
127	Q₈×C₂₉	—	4	1	no	—
128	Q₈×C₂₉	—	4	1	no	—
129	D₄×C₂₉	—	4	2	no	—
130	D₄×C₂₉	—	4	2	no	—
131	D₄×C₂₉	—	4	2	no	—
132	D₄×C₂₉	—	4	1	no	—
133	D₄×C₂₉	—	4	1	no	—
134	D₄×C₂₉	—	8	1	no	—
135	C₂×C₄×C₂₉	—	2	2	no	—
136	C₂×C₄×C₂₉	—	2	2	no	—
137	C₂×C₄×C₂₉	—	4	1	no	—
138	C₂×C₄×C₂₉	—	4	1	no	—
139	C₂×C₄×C₂₉	—	4	1	no	—
140	C₂×C₄×C₂₉	—	4	1	no	—
141	C₂×C₄×C₂₉	—	4	2	no	—
142	C₂×C₄×C₂₉	—	4	2	no	—
143	C₂×C₄×C₂₉	—	4	2	no	—
144	C₂×C₄×C₂₉	—	4	1	no	—
145	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
148	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
149	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
150	C₂×C₄×C₂₉	#123	1	1	yes	characteristic
151	C₂×C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
152	C₂×C₄×C₂₉	#135	1	1	yes	characteristic
153	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₂₉	#137	1	1	yes	characteristic
155	C₈×C₂₉	—	2	2	no	—
156	C₈×C₂₉	—	4	2	no	—
157	C₈×C₂₉	—	4	2	no	—
158	C₈×C₂₉	—	4	1	no	—
159	C₈×C₂₉	—	8	1	no	—
160	C₈×C₂₉	—	8	1	no	—
161	#3103	C₂×C₂₉	1	1	yes	characteristic
162	#2932	C₂×C₂₉	1	1	yes	characteristic
163	#1985	C₂×C₂₉	1	1	yes	characteristic, complemented
164	#1540	C₂×C₂₉	1	1	yes	characteristic
165	#1487	C₂×C₂₉	1	1	yes	characteristic, complemented
166	#1301	C₂×C₂₉	1	1	yes	characteristic, complemented
167	#1281	C₂×C₂₉	1	1	yes	characteristic, complemented
168	C₂²×C₂₉	—	2	1	no	—
169	C₂²×C₂₉	—	2	1	no	—
170	C₂²×C₂₉	—	4	2	no	—
171	C₂²×C₂₉	—	4	2	no	—
172	C₂²×C₂₉	—	4	2	no	—
173	C₂²×C₂₉	#386	1	1	yes	characteristic
174	C₂²×C₂₉	C₄×SD₁₆	1	1	yes	characteristic
175	C₂²×C₂₉	#440	1	1	yes	characteristic
176	C₄×C₂₉	—	2	1	no	—
177	C₄×C₂₉	—	2	1	no	—
178	C₄×C₂₉	—	2	1	no	—
179	C₄×C₂₉	—	2	1	no	—
180	C₄×C₂₉	—	4	2	no	—
181	C₄×C₂₉	—	4	2	no	—
182	C₄×C₂₉	—	8	1	no	—
183	C₄×C₂₉	#450	1	1	yes	characteristic
184	C₄×C₂₉	#452	1	1	yes	characteristic
185	C₄×C₂₉	#461	1	1	yes	characteristic
186	C₄×C₂₉	#463	1	1	yes	characteristic
187	C₂×#131	—	2	1	no	—
188	#532	C₂²×C₂₉	1	1	yes	characteristic
189	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
190	#481	C₄×C₂₉	1	2	yes	—
191	#475	—	2	1	no	—
192	#460	—	2	1	no	—
193	#448	C₄×C₂₉	1	2	yes	—
194	C₄×SD₁₆	—	2	2	no	—
195	#435	—	2	2	no	—
196	#435	—	2	2	no	—
197	#431	C₂²×C₂₉	1	1	yes	characteristic
198	#431	C₂²×C₂₉	1	1	yes	characteristic
199	#423	C₂²×C₂₉	1	1	yes	characteristic
200	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
201	#408	—	2	1	no	—
202	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
203	#336	—	2	1	no	—
204	#336	—	2	1	no	—
205	#332	—	2	1	no	—
206	#331	—	2	1	no	—
207	Q₈⋊C₈	—	2	2	no	—
208	C₂×C₂₉	—	2	1	no	—
209	C₂×C₂₉	—	2	1	no	—
210	C₂×C₂₉	—	8	2	no	—
211	C₂×C₂₉	#1877	1	1	yes	characteristic
212	C₂×C₂₉	#1881	1	1	yes	characteristic
213	C₂×C₂₉	#1891	1	1	yes	characteristic
214	C₂×#41	—	2	1	no	—
215	C₂²×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
216	C₂×SD₁₆	—	2	2	no	—
217	#131	—	4	2	no	—
218	#131	—	4	2	no	—
219	C₂×M₁₆	—	2	2	no	—
220	C₂×M₁₆	—	2	1	no	—
221	C₂²×C₈	—	2	2	no	—
222	C₂²×C₈	—	2	1	no	—
223	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
224	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
225	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
226	#127	D₄×C₂₉	1	1	yes	characteristic
227	#124	—	2	1	no	—
228	#121	—	2	1	no	—
229	#121	C₂×C₄×C₂₉	1	2	yes	—
230	C₄×Q₈	—	2	1	no	—
231	C₄×Q₈	—	2	1	no	—
232	C₄×Q₈	—	2	1	no	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	D₄×C₂₉	1	2	yes	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
238	C₂×C₄²	—	2	1	no	—
239	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
240	#106	—	2	2	no	—
241	C₄⋊C₈	—	2	1	no	—
242	C₄⋊C₈	—	2	1	no	—
243	C₄⋊C₈	—	2	1	no	—
244	C₄⋊C₈	—	2	1	no	—
245	C₄⋊C₈	—	2	1	no	—
246	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
247	#103	—	2	2	no	—
248	#102	—	2	2	no	—
249	C₂²⋊C₈	—	2	4	no	—
250	C₂²⋊C₈	—	2	1	no	—
251	C₂²⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
252	#97	—	2	1	no	—
253	#97	—	2	1	no	—
254	C₄×C₈	—	2	1	no	—
255	C₄×C₈	—	2	1	no	—
256	C₂₉	#9047	1	1	yes	characteristic, direct product factor, Sylow
257	#41	—	4	1	no	—
258	#41	—	4	1	no	—
259	#41	—	4	1	no	—
260	#41	—	4	1	no	—
261	C₂×Q₈	—	2	1	no	—
262	C₂×Q₈	—	2	1	no	—
263	C₂×Q₈	—	2	1	no	—
264	C₂×Q₈	—	4	2	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	2	1	no	—
267	C₂×D₄	—	2	1	no	—
268	C₂×D₄	C₂²⋊C₄×C₂₉	1	2	yes	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
274	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
275	SD₁₆	—	4	4	no	—
276	M₁₆	—	4	4	no	—
277	M₁₆	—	4	1	no	—
278	M₁₆	—	4	1	no	—
279	C₂×C₈	—	2	1	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	4	4	no	—
287	C₂×C₈	—	4	1	no	—
288	C₂×C₈	—	4	1	no	—
289	C₂×C₈	—	4	1	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	SD₁₆×C₂₉	1	2	yes	complemented
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	2	1	no	—
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	—	4	1	no	—
296	C₄⋊C₄	—	4	1	no	—
297	C₄⋊C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	2	2	no	—
300	C₄²	—	4	1	no	—
301	C₄²	—	4	1	no	—
302	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
303	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
304	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
305	C₄²	#41×C₂₉	1	1	yes	characteristic
306	C₂³	—	2	2	no	—
307	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
308	Q₈	—	2	2	no	—
309	Q₈	—	2	2	no	—
310	Q₈	—	4	1	no	—
311	Q₈	—	4	1	no	—
312	Q₈	—	4	1	no	—
313	Q₈	—	4	1	no	—
314	D₄	—	4	2	no	—
315	D₄	—	4	2	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	1	no	—
318	D₄	—	4	1	no	—
319	D₄	—	8	1	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
331	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
332	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
333	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
334	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
335	C₂×C₄	C₂₉×#123	1	1	yes	characteristic
336	C₂×C₄	C₂×SD₁₆×C₂₉	1	1	yes	characteristic
337	C₂×C₄	C₂₉×#135	1	1	yes	characteristic
338	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
339	C₂×C₄	C₂₉×#137	1	1	yes	characteristic
340	C₈	—	2	2	no	—
341	C₈	—	4	2	no	—
342	C₈	—	4	2	no	—
343	C₈	—	4	1	no	—
344	C₈	—	8	1	no	—
345	C₈	—	8	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	4	2	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	4	2	no	—
351	C₂²	C₂₉×#386	1	1	yes	characteristic
352	C₂²	C₄×SD₁₆×C₂₉	1	1	yes	characteristic
353	C₂²	C₂₉×#440	1	1	yes	characteristic
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	4	2	no	—
359	C₄	—	4	2	no	—
360	C₄	—	8	1	no	—
361	C₄	C₂₉×#450	1	1	yes	characteristic
362	C₄	C₂₉×#452	1	1	yes	characteristic
363	C₄	C₂₉×#461	1	1	yes	characteristic
364	C₄	C₂₉×#463	1	1	yes	characteristic
365	C₂	—	2	1	no	—
366	C₂	—	2	1	no	—
367	C₂	—	8	2	no	—
368	C₂	C₂₉×#1877	1	1	yes	characteristic
369	C₂	C₂₉×#1881	1	1	yes	characteristic
370	C₂	C₂₉×#1891	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	#120
commutator	C₂²×C₄	C₂²×C₄×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
socle	C₂²×C₂₉	#386
prime radical	C₂₉×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₉×#1985	C₂	semidirect
5. C₂₉×#1487	C₂	semidirect
6. C₂₉×#1301	C₂	semidirect
7. C₂₉×#1281	C₂	semidirect
105. C₂×C₈×C₂₉	SD₁₆	semidirect
120. #9047	C₂₉	direct (N × H)
163. #1985	C₂×C₂₉	semidirect
165. #1487	C₂×C₂₉	semidirect
166. #1301	C₂×C₂₉	semidirect
167. #1281	C₂×C₂₉	semidirect
256. C₂₉	#9047	direct (N × H)
291. C₂×C₈	SD₁₆×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#3103	2
C₂₉×#2932	2
C₂₉×#1985	2
C₂₉×#1540	2
C₂₉×#1487	2
C₂₉×#1301	2
C₂₉×#1281	2
#9047	29

Subgroups — C29×#9047 #20303947

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#9047 #20303947