Subgroups — C₂₉×#9087 #20303987

Order 7424.

532 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2972	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#440	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#1479	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#1478	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1461	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1281	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1275	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₂₉	C₄	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
11	C₂₉×#440	—	2	2	no	—
12	C₂₉×#440	—	2	2	no	—
13	C₈×D₄×C₂₉	—	2	2	no	—
14	C₈×D₄×C₂₉	—	2	2	no	—
15	C₂₉×#431	C₂²	1	1	yes	characteristic
16	C₂₉×#431	C₂²	1	1	yes	characteristic
17	C₂₉×#431	C₂²	1	1	yes	characteristic
18	C₂₉×#431	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#107	C₄	1	1	yes	characteristic
20	C₂×C₂₉×#103	C₄	1	1	yes	characteristic
21	C₂×C₂₉×#102	C₄	1	1	yes	characteristic
22	C₂×C₂₉×C₂²⋊C₈	—	2	2	no	—
23	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
24	C₂₉×Q₈⋊C₈	—	2	2	no	—
25	C₂₉×D₄⋊C₈	—	2	2	no	—
26	C₂₉×#324	—	2	2	no	—
27	C₂²×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₂₉	—	2	1	no	—
30	C₂×SD₁₆×C₂₉	—	2	2	no	—
31	C₂×SD₁₆×C₂₉	—	2	2	no	—
32	C₂×SD₁₆×C₂₉	C₈	1	4	yes	complemented
33	C₂²×C₈×C₂₉	—	2	4	no	—
34	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
36	C₄×Q₈×C₂₉	—	2	1	no	—
37	C₄×Q₈×C₂₉	—	2	1	no	—
38	C₄×Q₈×C₂₉	—	2	1	no	—
39	C₄×Q₈×C₂₉	—	2	1	no	—
40	C₄×D₄×C₂₉	—	2	1	no	—
41	C₄×D₄×C₂₉	—	2	1	no	—
42	C₄×D₄×C₂₉	D₄	1	2	yes	—
43	C₄×D₄×C₂₉	D₄	1	2	yes	—
44	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
48	C₂×C₄²×C₂₉	—	2	1	no	—
49	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
50	C₂₉×#107	—	2	2	no	—
51	C₂₉×C₄⋊C₈	—	2	1	no	—
52	C₂₉×C₄⋊C₈	—	2	1	no	—
53	C₂₉×C₄⋊C₈	—	2	1	no	—
54	C₂₉×C₄⋊C₈	—	2	1	no	—
55	C₂₉×#103	—	2	2	no	—
56	C₂₉×#102	—	2	2	no	—
57	C₂₉×C₂²⋊C₈	—	2	4	no	—
58	C₂₉×C₂²⋊C₈	—	2	1	no	—
59	C₂₉×C₂²⋊C₈	—	2	1	no	—
60	C₂₉×C₂²⋊C₈	—	2	1	no	—
61	C₂₉×C₂²⋊C₈	D₄	1	2	yes	—
62	C₂₉×#97	—	2	1	no	—
63	C₂₉×#97	—	2	1	no	—
64	C₄×C₈×C₂₉	—	2	1	no	—
65	C₄×C₈×C₂₉	—	2	1	no	—
66	C₄×C₈×C₂₉	—	2	1	no	—
67	C₄×C₈×C₂₉	D₄	1	2	yes	—
68	C₂⁴×C₂₉	—	2	1	no	—
69	C₂×Q₈×C₂₉	—	2	1	no	—
70	C₂×Q₈×C₂₉	—	2	1	no	—
71	C₂×Q₈×C₂₉	—	2	1	no	—
72	C₂×Q₈×C₂₉	—	2	1	no	—
73	C₂×Q₈×C₂₉	—	2	1	no	—
74	C₂×Q₈×C₂₉	C₂×C₈	1	2	yes	complemented
75	C₂×D₄×C₂₉	—	2	1	no	—
76	C₂×D₄×C₂₉	—	2	1	no	—
77	C₂×D₄×C₂₉	—	2	1	no	—
78	C₂×D₄×C₂₉	C₂²⋊C₄	1	2	yes	—
79	C₂×D₄×C₂₉	C₂×C₈	1	2	yes	—
80	C₂×D₄×C₂₉	M₁₆	1	2	yes	—
81	C₂²×C₄×C₂₉	—	2	1	no	—
82	C₂²×C₄×C₂₉	—	2	1	no	—
83	C₂²×C₄×C₂₉	—	2	2	no	—
84	C₂²×C₄×C₂₉	—	2	2	no	—
85	C₂²×C₄×C₂₉	—	2	1	no	—
86	C₂²×C₄×C₂₉	—	8	2	no	—
87	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
90	SD₁₆×C₂₉	—	2	8	no	—
91	C₂×C₈×C₂₉	—	2	1	no	—
92	C₂×C₈×C₂₉	—	2	1	no	—
93	C₂×C₈×C₂₉	—	2	1	no	—
94	C₂×C₈×C₂₉	—	2	2	no	—
95	C₂×C₈×C₂₉	—	2	2	no	—
96	C₂×C₈×C₂₉	—	2	1	no	—
97	C₂×C₈×C₂₉	—	2	1	no	—
98	C₂×C₈×C₂₉	—	4	1	no	—
99	C₂×C₈×C₂₉	—	4	1	no	—
100	C₂×C₈×C₂₉	—	8	4	no	—
101	C₂×C₈×C₂₉	C₂×C₈	1	2	yes	complemented
102	C₄⋊C₄×C₂₉	—	2	1	no	—
103	C₄⋊C₄×C₂₉	—	2	1	no	—
104	C₄⋊C₄×C₂₉	—	2	1	no	—
105	C₄⋊C₄×C₂₉	—	4	1	no	—
106	C₄⋊C₄×C₂₉	—	4	1	no	—
107	C₄⋊C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
108	C₂²⋊C₄×C₂₉	—	2	2	no	—
109	C₂²⋊C₄×C₂₉	—	2	2	no	—
110	C₄²×C₂₉	—	4	1	no	—
111	C₄²×C₂₉	—	4	1	no	—
112	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₂₉	#41	1	1	yes	characteristic
116	#9087	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₂₉	—	2	2	no	—
118	C₂³×C₂₉	—	2	2	no	—
119	C₂³×C₂₉	—	2	2	no	—
120	C₂³×C₂₉	—	8	1	no	—
121	C₂³×C₂₉	—	8	1	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	D₄×C₂₉	—	2	2	no	—
128	D₄×C₂₉	—	2	2	no	—
129	D₄×C₂₉	—	2	2	no	—
130	D₄×C₂₉	C₂²⋊C₈	1	4	yes	—
131	C₂×C₄×C₂₉	—	2	2	no	—
132	C₂×C₄×C₂₉	—	2	2	no	—
133	C₂×C₄×C₂₉	—	4	1	no	—
134	C₂×C₄×C₂₉	—	4	1	no	—
135	C₂×C₄×C₂₉	—	4	4	no	—
136	C₂×C₄×C₂₉	—	4	1	no	—
137	C₂×C₄×C₂₉	—	4	1	no	—
138	C₂×C₄×C₂₉	—	4	1	no	—
139	C₂×C₄×C₂₉	—	8	2	no	—
140	C₂×C₄×C₂₉	—	8	1	no	—
141	C₂×C₄×C₂₉	—	8	1	no	—
142	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
145	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
146	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
147	C₂×C₄×C₂₉	#123	1	1	yes	characteristic
148	C₂×C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
149	C₂×C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
150	C₂×C₄×C₂₉	#131	1	1	yes	characteristic
151	C₂×C₄×C₂₉	#131	1	1	yes	characteristic
152	C₈×C₂₉	—	2	2	no	—
153	C₈×C₂₉	—	4	2	no	—
154	C₈×C₂₉	—	4	2	no	—
155	C₈×C₂₉	—	4	1	no	—
156	C₈×C₂₉	—	8	1	no	—
157	C₈×C₂₉	—	8	1	no	—
158	#2972	C₂×C₂₉	1	1	yes	characteristic
159	C₂×#440	C₂×C₂₉	1	1	yes	characteristic
160	#1479	C₂×C₂₉	1	1	yes	characteristic, complemented
161	#1478	C₂×C₂₉	1	1	yes	characteristic
162	#1461	C₂×C₂₉	1	1	yes	characteristic, complemented
163	#1281	C₂×C₂₉	1	1	yes	characteristic, complemented
164	#1275	C₂×C₂₉	1	1	yes	characteristic, complemented
165	C₂²×C₂₉	—	2	1	no	—
166	C₂²×C₂₉	—	2	1	no	—
167	C₂²×C₂₉	—	2	4	no	—
168	C₂²×C₂₉	—	4	2	no	—
169	C₂²×C₂₉	—	4	2	no	—
170	C₂²×C₂₉	—	8	2	no	—
171	C₂²×C₂₉	—	8	2	no	—
172	C₂²×C₂₉	#386	1	1	yes	characteristic
173	C₂²×C₂₉	C₈×D₄	1	1	yes	characteristic
174	C₂²×C₂₉	#435	1	1	yes	characteristic
175	C₄×C₂₉	—	2	1	no	—
176	C₄×C₂₉	—	2	1	no	—
177	C₄×C₂₉	—	2	1	no	—
178	C₄×C₂₉	—	2	1	no	—
179	C₄×C₂₉	—	4	2	no	—
180	C₄×C₂₉	—	4	2	no	—
181	C₄×C₂₉	—	8	1	no	—
182	C₄×C₂₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
183	C₄×C₂₉	#408	1	1	yes	characteristic
184	C₄×C₂₉	C₈×D₄	1	1	yes	characteristic
185	C₄×C₂₉	#435	1	1	yes	characteristic
186	C₂²×SD₁₆	C₄×C₂₉	1	1	yes	characteristic
187	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
188	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
189	#440	—	2	2	no	—
190	#440	—	2	2	no	—
191	C₈×D₄	—	2	2	no	—
192	C₈×D₄	—	2	2	no	—
193	#431	C₂²×C₂₉	1	1	yes	characteristic
194	#431	C₂²×C₂₉	1	1	yes	characteristic
195	#431	C₂²×C₂₉	1	1	yes	characteristic
196	#431	C₂²×C₂₉	1	1	yes	characteristic
197	C₂×#107	C₄×C₂₉	1	1	yes	characteristic
198	C₂×#103	C₄×C₂₉	1	1	yes	characteristic
199	C₂×#102	C₄×C₂₉	1	1	yes	characteristic
200	C₂×C₂²⋊C₈	—	2	2	no	—
201	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
202	Q₈⋊C₈	—	2	2	no	—
203	D₄⋊C₈	—	2	2	no	—
204	#324	—	2	2	no	—
205	C₂×C₂₉	—	2	1	no	—
206	C₂×C₂₉	—	2	1	no	—
207	C₂×C₂₉	—	4	4	no	—
208	C₂×C₂₉	#1869	1	1	yes	characteristic
209	C₂×C₂₉	#1902	1	1	yes	characteristic
210	C₂×C₂₉	#1904	1	1	yes	characteristic
211	C₂²×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
212	C₂²×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
213	C₂³×C₄	—	2	1	no	—
214	C₂×SD₁₆	—	2	2	no	—
215	C₂×SD₁₆	—	2	2	no	—
216	C₂×SD₁₆	C₈×C₂₉	1	4	yes	complemented
217	C₂²×C₈	—	2	4	no	—
218	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
219	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
220	C₄×Q₈	—	2	1	no	—
221	C₄×Q₈	—	2	1	no	—
222	C₄×Q₈	—	2	1	no	—
223	C₄×Q₈	—	2	1	no	—
224	C₄×D₄	—	2	1	no	—
225	C₄×D₄	—	2	1	no	—
226	C₄×D₄	D₄×C₂₉	1	2	yes	—
227	C₄×D₄	D₄×C₂₉	1	2	yes	—
228	C₂×C₄⋊C₄	—	2	1	no	—
229	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
231	C₂×C₂²⋊C₄	—	2	1	no	—
232	C₂×C₄²	—	2	1	no	—
233	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
234	#107	—	2	2	no	—
235	C₄⋊C₈	—	2	1	no	—
236	C₄⋊C₈	—	2	1	no	—
237	C₄⋊C₈	—	2	1	no	—
238	C₄⋊C₈	—	2	1	no	—
239	#103	—	2	2	no	—
240	#102	—	2	2	no	—
241	C₂²⋊C₈	—	2	4	no	—
242	C₂²⋊C₈	—	2	1	no	—
243	C₂²⋊C₈	—	2	1	no	—
244	C₂²⋊C₈	—	2	1	no	—
245	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
246	#97	—	2	1	no	—
247	#97	—	2	1	no	—
248	C₄×C₈	—	2	1	no	—
249	C₄×C₈	—	2	1	no	—
250	C₄×C₈	—	2	1	no	—
251	C₄×C₈	D₄×C₂₉	1	2	yes	—
252	C₂₉	#9087	1	1	yes	characteristic, direct product factor, Sylow
253	C₂⁴	—	2	1	no	—
254	C₂×Q₈	—	2	1	no	—
255	C₂×Q₈	—	2	1	no	—
256	C₂×Q₈	—	2	1	no	—
257	C₂×Q₈	—	2	1	no	—
258	C₂×Q₈	—	2	1	no	—
259	C₂×Q₈	C₂×C₈×C₂₉	1	2	yes	complemented
260	C₂×D₄	—	2	1	no	—
261	C₂×D₄	—	2	1	no	—
262	C₂×D₄	—	2	1	no	—
263	C₂×D₄	C₂²⋊C₄×C₂₉	1	2	yes	—
264	C₂×D₄	C₂×C₈×C₂₉	1	2	yes	—
265	C₂×D₄	M₁₆×C₂₉	1	2	yes	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	8	2	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	—	2	8	no	—
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	4	1	no	—
284	C₂×C₈	—	4	1	no	—
285	C₂×C₈	—	8	4	no	—
286	C₂×C₈	C₂×C₈×C₂₉	1	2	yes	complemented
287	C₄⋊C₄	—	2	1	no	—
288	C₄⋊C₄	—	2	1	no	—
289	C₄⋊C₄	—	2	1	no	—
290	C₄⋊C₄	—	4	1	no	—
291	C₄⋊C₄	—	4	1	no	—
292	C₄⋊C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₄²	—	4	1	no	—
296	C₄²	—	4	1	no	—
297	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
298	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
299	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
300	C₄²	#41×C₂₉	1	1	yes	characteristic
301	C₂³	—	2	2	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	8	1	no	—
305	C₂³	—	8	1	no	—
306	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
307	Q₈	—	2	2	no	—
308	Q₈	—	2	2	no	—
309	Q₈	—	4	1	no	—
310	Q₈	—	4	1	no	—
311	D₄	—	2	2	no	—
312	D₄	—	2	2	no	—
313	D₄	—	2	2	no	—
314	D₄	C₂₉×C₂²⋊C₈	1	4	yes	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	8	2	no	—
324	C₂×C₄	—	8	1	no	—
325	C₂×C₄	—	8	1	no	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
327	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
328	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
329	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
330	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
331	C₂×C₄	C₂₉×#123	1	1	yes	characteristic
332	C₂×C₄	C₂²×C₈×C₂₉	1	1	yes	characteristic
333	C₂×C₄	C₂×M₁₆×C₂₉	1	1	yes	characteristic
334	C₂×C₄	C₂₉×#131	1	1	yes	characteristic
335	C₂×C₄	C₂₉×#131	1	1	yes	characteristic
336	C₈	—	2	2	no	—
337	C₈	—	4	2	no	—
338	C₈	—	4	2	no	—
339	C₈	—	4	1	no	—
340	C₈	—	8	1	no	—
341	C₈	—	8	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	8	2	no	—
348	C₂²	—	8	2	no	—
349	C₂²	C₂₉×#386	1	1	yes	characteristic
350	C₂²	C₈×D₄×C₂₉	1	1	yes	characteristic
351	C₂²	C₂₉×#435	1	1	yes	characteristic
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	4	2	no	—
357	C₄	—	4	2	no	—
358	C₄	—	8	1	no	—
359	C₄	C₂×C₂₉×C₂²⋊C₈	1	1	yes	characteristic
360	C₄	C₂₉×#408	1	1	yes	characteristic
361	C₄	C₈×D₄×C₂₉	1	1	yes	characteristic
362	C₄	C₂₉×#435	1	1	yes	characteristic
363	C₂	—	2	1	no	—
364	C₂	—	2	1	no	—
365	C₂	—	4	4	no	—
366	C₂	C₂₉×#1869	1	1	yes	characteristic
367	C₂	C₂₉×#1902	1	1	yes	characteristic
368	C₂	C₂₉×#1904	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	#386
commutator	C₂×C₄	C₂²×C₈×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₉×#1479	C₂	semidirect
5. C₂₉×#1461	C₂	semidirect
6. C₂₉×#1281	C₂	semidirect
7. C₂₉×#1275	C₂	semidirect
32. C₂×SD₁₆×C₂₉	C₈	semidirect
74. C₂×Q₈×C₂₉	C₂×C₈	semidirect
101. C₂×C₈×C₂₉	C₂×C₈	semidirect
116. #9087	C₂₉	direct (N × H)
160. #1479	C₂×C₂₉	semidirect
162. #1461	C₂×C₂₉	semidirect
163. #1281	C₂×C₂₉	semidirect
164. #1275	C₂×C₂₉	semidirect
216. C₂×SD₁₆	C₈×C₂₉	semidirect
252. C₂₉	#9087	direct (N × H)
259. C₂×Q₈	C₂×C₈×C₂₉	semidirect
286. C₂×C₈	C₂×C₈×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#2972	2
C₂×C₂₉×#440	2
C₂₉×#1479	2
C₂₉×#1478	2
C₂₉×#1461	2
C₂₉×#1281	2
C₂₉×#1275	2
#9087	29

Subgroups — C29×#9087 #20303987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#9087 #20303987