Subgroups — C₄×C₂₉×#492 #20316586

Order 7424.

1254 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#492	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₂₉	C₂	1	4	yes	maximal, complemented
3	C₄×C₂₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₂₉×#127	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1968	C₂	1	4	yes	maximal, complemented
6	C₂₉×#1957	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#1956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1844	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄²×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₂₉	C₂²	1	4	yes	—
11	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₂₉	—	2	2	no	—
15	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
16	C₂₉×#492	C₄	1	8	yes	direct product factor
17	C₄×SD₁₆×C₂₉	—	2	16	no	—
18	C₂×C₂₉×#106	C₂²	1	4	yes	—
19	C₂×C₂₉×#103	C₂²	1	4	yes	—
20	C₂×C₂₉×#102	C₂²	1	4	yes	—
21	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₂₉	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₂₉	C₂²	1	2	yes	—
25	C₂₉×#391	C₂²	1	2	yes	—
26	C₂₉×#390	—	2	2	no	—
27	C₂₉×#390	C₂²	1	2	yes	—
28	C₂₉×#389	—	2	2	no	—
29	C₂₉×#384	C₂²	1	1	yes	characteristic
30	C₂₉×#384	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₂₉	—	2	2	no	—
32	C₄³×C₂₉	C₂²	1	1	yes	characteristic
33	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
34	C₂²×D₄×C₂₉	—	2	2	no	—
35	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
36	C₂³×C₄×C₂₉	—	2	2	no	—
37	C₂×SD₁₆×C₂₉	—	2	8	no	—
38	C₂×SD₁₆×C₂₉	—	2	8	no	—
39	C₂×SD₁₆×C₂₉	C₂×C₄	1	16	yes	complemented
40	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
41	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
42	C₂₉×C₄⋊Q₈	—	2	2	no	—
43	C₂₉×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
44	C₂₉×#127	—	2	2	no	—
45	C₂₉×#127	C₂×C₄	1	4	yes	—
46	C₄×Q₈×C₂₉	—	2	8	no	—
47	C₄×D₄×C₂₉	—	2	8	no	—
48	C₄×D₄×C₂₉	—	4	8	no	—
49	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₂₉	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
57	C₂×C₄²×C₂₉	—	2	2	no	—
58	C₂×C₄²×C₂₉	D₄	1	2	yes	—
59	C₂×C₄²×C₂₉	D₄	1	2	yes	—
60	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
63	C₂₉×#106	—	2	8	no	—
64	C₂₉×#103	—	2	8	no	—
65	C₂₉×#102	—	2	8	no	—
66	C₄×C₈×C₂₉	—	2	4	no	—
67	C₄×C₈×C₂₉	—	2	2	no	—
68	C₄×C₈×C₂₉	C₂×C₄	1	4	yes	complemented
69	C₄×C₈×C₂₉	D₄	1	8	yes	complemented
70	C₂₉×#95	—	2	4	no	—
71	C₂⁴×C₂₉	—	2	2	no	—
72	C₂×Q₈×C₂₉	—	2	2	no	—
73	C₂×Q₈×C₂₉	—	2	4	no	—
74	C₂×Q₈×C₂₉	—	2	4	no	—
75	C₂×Q₈×C₂₉	C₂²×C₄	1	4	yes	—
76	C₂×D₄×C₂₉	—	2	8	no	—
77	C₂×D₄×C₂₉	—	2	4	no	—
78	C₂×D₄×C₂₉	—	2	4	no	—
79	C₂×D₄×C₂₉	—	2	2	no	—
80	C₂×D₄×C₂₉	—	4	4	no	—
81	C₂×D₄×C₂₉	—	4	4	no	—
82	C₂×D₄×C₂₉	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₂₉	—	2	2	no	—
84	C₂²×C₄×C₂₉	—	2	2	no	—
85	C₂²×C₄×C₂₉	—	2	2	no	—
86	C₂²×C₄×C₂₉	—	4	4	no	—
87	C₂²×C₄×C₂₉	—	4	8	no	—
88	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
93	SD₁₆×C₂₉	—	2	32	no	—
94	C₂×C₈×C₂₉	—	2	2	no	—
95	C₂×C₈×C₂₉	—	2	2	no	—
96	C₂×C₈×C₂₉	C₂²×C₄	1	4	yes	—
97	C₂×C₈×C₂₉	C₂×D₄	1	4	yes	—
98	C₂×C₈×C₂₉	C₂×D₄	1	4	yes	—
99	C₂×C₈×C₂₉	#41	1	4	yes	—
100	C₄⋊C₄×C₂₉	—	2	8	no	—
101	C₄⋊C₄×C₂₉	—	2	4	no	—
102	C₄⋊C₄×C₂₉	—	2	4	no	—
103	C₄⋊C₄×C₂₉	—	4	4	no	—
104	C₄⋊C₄×C₂₉	—	4	4	no	—
105	C₄⋊C₄×C₂₉	—	4	4	no	—
106	C₂²⋊C₄×C₂₉	—	4	4	no	—
107	C₂²⋊C₄×C₂₉	—	4	8	no	—
108	C₄²×C₂₉	—	2	4	no	—
109	C₄²×C₂₉	—	2	2	no	—
110	C₄²×C₂₉	—	4	4	no	—
111	C₄²×C₂₉	SD₁₆	1	8	yes	complemented
112	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
113	C₄²×C₂₉	C₂×D₄	1	4	yes	—
114	C₄²×C₂₉	#41	1	2	yes	—
115	C₄×#492	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂³×C₂₉	—	2	4	no	—
117	C₂³×C₂₉	—	4	2	no	—
118	C₂³×C₂₉	—	4	2	no	—
119	C₂³×C₂₉	—	4	4	no	—
120	C₂³×C₂₉	—	4	4	no	—
121	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
122	Q₈×C₂₉	—	2	8	no	—
123	Q₈×C₂₉	—	4	4	no	—
124	D₄×C₂₉	—	2	8	no	—
125	D₄×C₂₉	—	4	4	no	—
126	D₄×C₂₉	—	4	16	no	—
127	C₂×C₄×C₂₉	—	2	2	no	—
128	C₂×C₄×C₂₉	—	2	2	no	—
129	C₂×C₄×C₂₉	—	2	2	no	—
130	C₂×C₄×C₂₉	—	2	4	no	—
131	C₂×C₄×C₂₉	—	4	2	no	—
132	C₂×C₄×C₂₉	—	4	2	no	—
133	C₂×C₄×C₂₉	—	4	2	no	—
134	C₂×C₄×C₂₉	—	4	2	no	—
135	C₂×C₄×C₂₉	—	4	4	no	—
136	C₂×C₄×C₂₉	—	4	4	no	—
137	C₂×C₄×C₂₉	—	8	8	no	—
138	C₂×C₄×C₂₉	C₄×D₄	1	4	yes	—
139	C₂×C₄×C₂₉	#127	1	2	yes	—
140	C₂×C₄×C₂₉	#127	1	2	yes	—
141	C₂×C₄×C₂₉	C₂×SD₁₆	1	4	yes	—
142	C₂×C₄×C₂₉	C₂×SD₁₆	1	4	yes	—
143	C₂×C₄×C₂₉	C₂×SD₁₆	1	4	yes	—
144	C₂×C₄×C₂₉	#135	1	4	yes	—
145	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
147	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
148	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
149	C₈×C₂₉	—	2	4	no	—
150	C₈×C₂₉	C₄×D₄	1	8	yes	complemented
151	C₂×#492	C₂×C₂₉	1	1	yes	characteristic
152	C₂×C₄×SD₁₆	C₂×C₂₉	1	4	yes	complemented
153	C₄×C₄⋊Q₈	C₂×C₂₉	1	1	yes	characteristic, complemented
154	C₄×#127	C₂×C₂₉	1	1	yes	characteristic
155	#1968	C₂×C₂₉	1	4	yes	complemented
156	#1957	C₂×C₂₉	1	1	yes	characteristic
157	#1956	C₂×C₂₉	1	1	yes	characteristic, complemented
158	#1844	C₂×C₂₉	1	1	yes	characteristic, complemented
159	C₄²×C₈	C₂×C₂₉	1	1	yes	characteristic, complemented
160	C₂²×C₂₉	—	4	4	no	—
161	C₂²×C₂₉	—	4	8	no	—
162	C₂²×C₂₉	—	8	2	no	—
163	C₂²×C₂₉	—	8	2	no	—
164	C₂²×C₂₉	—	8	4	no	—
165	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
166	C₂²×C₂₉	C₂×#127	1	1	yes	characteristic
167	C₂²×C₂₉	#532	1	1	yes	characteristic
168	C₂²×C₂₉	C₂²×SD₁₆	1	2	yes	—
169	C₂²×C₂₉	C₂×#135	1	2	yes	—
170	C₄×C₂₉	—	2	2	no	—
171	C₄×C₂₉	—	2	4	no	—
172	C₄×C₂₉	—	4	4	no	—
173	C₄×C₂₉	—	8	2	no	—
174	C₄×C₂₉	—	8	2	no	—
175	C₄×C₂₉	C₄×SD₁₆	1	8	yes	complemented
176	C₄×C₂₉	#492	1	4	yes	direct product factor
177	C₄×C₂₉	C₂×C₄×D₄	1	2	yes	—
178	C₄×C₂₉	#532	1	2	yes	—
179	C₂²×SD₁₆	C₂²×C₂₉	1	4	yes	—
180	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
181	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
182	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
183	C₂×C₄×D₄	—	2	2	no	—
184	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
185	#492	C₄×C₂₉	1	8	yes	direct product factor
186	C₄×SD₁₆	—	2	16	no	—
187	C₂×#106	C₂²×C₂₉	1	4	yes	—
188	C₂×#103	C₂²×C₂₉	1	4	yes	—
189	C₂×#102	C₂²×C₂₉	1	4	yes	—
190	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
191	C₂×C₄×C₈	C₂²×C₂₉	1	2	yes	—
192	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
193	C₂×C₄×C₈	C₂²×C₂₉	1	2	yes	—
194	#391	C₂²×C₂₉	1	2	yes	—
195	#390	—	2	2	no	—
196	#390	C₂²×C₂₉	1	2	yes	—
197	#389	—	2	2	no	—
198	#384	C₂²×C₂₉	1	1	yes	characteristic
199	#384	C₂²×C₂₉	1	1	yes	characteristic
200	C₄×C₄⋊C₄	—	2	2	no	—
201	C₄³	C₂²×C₂₉	1	1	yes	characteristic
202	C₂×C₂₉	—	8	4	no	—
203	C₂×C₂₉	C₄×#127	1	1	yes	characteristic
204	C₂×C₂₉	C₂×C₄×SD₁₆	1	2	yes	—
205	C₂×C₂₉	C₂×#492	1	1	yes	characteristic
206	C₂×C₂₉	#3147	1	1	yes	characteristic
207	C₂×C₂₉	#3167	1	2	yes	—
208	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
209	C₂²×D₄	—	2	2	no	—
210	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
211	C₂³×C₄	—	2	2	no	—
212	C₂×SD₁₆	—	2	8	no	—
213	C₂×SD₁₆	—	2	8	no	—
214	C₂×SD₁₆	C₂×C₄×C₂₉	1	16	yes	complemented
215	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
216	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
217	C₄⋊Q₈	—	2	2	no	—
218	C₄⋊Q₈	C₂×C₄×C₂₉	1	4	yes	complemented
219	#127	—	2	2	no	—
220	#127	C₂×C₄×C₂₉	1	4	yes	—
221	C₄×Q₈	—	2	8	no	—
222	C₄×D₄	—	2	8	no	—
223	C₄×D₄	—	4	8	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	2	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
229	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
230	C₂×C₂²⋊C₄	—	2	4	no	—
231	C₂×C₂²⋊C₄	—	2	2	no	—
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	D₄×C₂₉	1	2	yes	—
234	C₂×C₄²	D₄×C₂₉	1	2	yes	—
235	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
236	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
238	#106	—	2	8	no	—
239	#103	—	2	8	no	—
240	#102	—	2	8	no	—
241	C₄×C₈	—	2	4	no	—
242	C₄×C₈	—	2	2	no	—
243	C₄×C₈	C₂×C₄×C₂₉	1	4	yes	complemented
244	C₄×C₈	D₄×C₂₉	1	8	yes	complemented
245	#95	—	2	4	no	—
246	C₂₉	C₄×#492	1	1	yes	characteristic, direct product factor, Sylow
247	C₂⁴	—	2	2	no	—
248	C₂×Q₈	—	2	2	no	—
249	C₂×Q₈	—	2	4	no	—
250	C₂×Q₈	—	2	4	no	—
251	C₂×Q₈	C₂²×C₄×C₂₉	1	4	yes	—
252	C₂×D₄	—	2	8	no	—
253	C₂×D₄	—	2	4	no	—
254	C₂×D₄	—	2	4	no	—
255	C₂×D₄	—	2	2	no	—
256	C₂×D₄	—	4	4	no	—
257	C₂×D₄	—	4	4	no	—
258	C₂×D₄	C₂²×C₄×C₂₉	1	4	yes	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	4	4	no	—
263	C₂²×C₄	—	4	8	no	—
264	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
266	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
267	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
268	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
269	SD₁₆	—	2	32	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	C₂²×C₄×C₂₉	1	4	yes	—
273	C₂×C₈	C₂×D₄×C₂₉	1	4	yes	—
274	C₂×C₈	C₂×D₄×C₂₉	1	4	yes	—
275	C₂×C₈	#41×C₂₉	1	4	yes	—
276	C₄⋊C₄	—	2	8	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	—	4	4	no	—
280	C₄⋊C₄	—	4	4	no	—
281	C₄⋊C₄	—	4	4	no	—
282	C₂²⋊C₄	—	4	4	no	—
283	C₂²⋊C₄	—	4	8	no	—
284	C₄²	—	2	4	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	4	4	no	—
287	C₄²	SD₁₆×C₂₉	1	8	yes	complemented
288	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
289	C₄²	C₂×D₄×C₂₉	1	4	yes	—
290	C₄²	#41×C₂₉	1	2	yes	—
291	C₂³	—	2	4	no	—
292	C₂³	—	4	2	no	—
293	C₂³	—	4	2	no	—
294	C₂³	—	4	4	no	—
295	C₂³	—	4	4	no	—
296	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
297	Q₈	—	2	8	no	—
298	Q₈	—	4	4	no	—
299	D₄	—	2	8	no	—
300	D₄	—	4	16	no	—
301	D₄	—	4	4	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	4	4	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	8	8	no	—
313	C₂×C₄	C₄×D₄×C₂₉	1	4	yes	—
314	C₂×C₄	C₂₉×#127	1	2	yes	—
315	C₂×C₄	C₂₉×#127	1	2	yes	—
316	C₂×C₄	C₂×SD₁₆×C₂₉	1	4	yes	—
317	C₂×C₄	C₂×SD₁₆×C₂₉	1	4	yes	—
318	C₂×C₄	C₂×SD₁₆×C₂₉	1	4	yes	—
319	C₂×C₄	C₂₉×#135	1	4	yes	—
320	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
321	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
322	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
323	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
324	C₈	—	2	4	no	—
325	C₈	C₄×D₄×C₂₉	1	8	yes	complemented
326	C₂²	—	4	8	no	—
327	C₂²	—	4	4	no	—
328	C₂²	—	8	2	no	—
329	C₂²	—	8	2	no	—
330	C₂²	—	8	4	no	—
331	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
332	C₂²	C₂×C₂₉×#127	1	1	yes	characteristic
333	C₂²	C₂₉×#532	1	1	yes	characteristic
334	C₂²	C₂²×SD₁₆×C₂₉	1	2	yes	—
335	C₂²	C₂×C₂₉×#135	1	2	yes	—
336	C₄	—	2	2	no	—
337	C₄	—	2	4	no	—
338	C₄	—	4	4	no	—
339	C₄	—	8	2	no	—
340	C₄	—	8	2	no	—
341	C₄	C₄×SD₁₆×C₂₉	1	8	yes	complemented
342	C₄	C₂₉×#492	1	4	yes	direct product factor
343	C₄	C₂×C₄×D₄×C₂₉	1	2	yes	—
344	C₄	C₂₉×#532	1	2	yes	—
345	C₂	—	8	4	no	—
346	C₂	C₄×C₂₉×#127	1	1	yes	characteristic
347	C₂	C₂×C₄×SD₁₆×C₂₉	1	2	yes	—
348	C₂	C₂×C₂₉×#492	1	1	yes	characteristic
349	C₂	C₂₉×#3147	1	1	yes	characteristic
350	C₂	C₂₉×#3167	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
socle	C₂³×C₂₉	C₂²×D₄
prime radical	C₂×C₂₉×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ C₄³×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×SD₁₆×C₂₉	C₂	semidirect
3. C₄×C₂₉×C₄⋊Q₈	C₂	semidirect
5. C₂₉×#1968	C₂	semidirect
7. C₂₉×#1956	C₂	semidirect
8. C₂₉×#1844	C₂	semidirect
9. C₄²×C₈×C₂₉	C₂	semidirect
16. C₂₉×#492	C₄	direct (N × H)
39. C₂×SD₁₆×C₂₉	C₂×C₄	semidirect
43. C₂₉×C₄⋊Q₈	C₂×C₄	semidirect
68. C₄×C₈×C₂₉	C₂×C₄	semidirect
69. C₄×C₈×C₂₉	D₄	semidirect
111. C₄²×C₂₉	SD₁₆	semidirect
115. C₄×#492	C₂₉	direct (N × H)
150. C₈×C₂₉	C₄×D₄	semidirect
152. C₂×C₄×SD₁₆	C₂×C₂₉	semidirect
153. C₄×C₄⋊Q₈	C₂×C₂₉	semidirect
155. #1968	C₂×C₂₉	semidirect
157. #1956	C₂×C₂₉	semidirect
158. #1844	C₂×C₂₉	semidirect
159. C₄²×C₈	C₂×C₂₉	semidirect
175. C₄×C₂₉	C₄×SD₁₆	semidirect
176. C₄×C₂₉	#492	direct (N × H)
185. #492	C₄×C₂₉	direct (N × H)
214. C₂×SD₁₆	C₂×C₄×C₂₉	semidirect
218. C₄⋊Q₈	C₂×C₄×C₂₉	semidirect
243. C₄×C₈	C₂×C₄×C₂₉	semidirect
244. C₄×C₈	D₄×C₂₉	semidirect
246. C₂₉	C₄×#492	direct (N × H)
287. C₄²	SD₁₆×C₂₉	semidirect
325. C₈	C₄×D₄×C₂₉	semidirect
341. C₄	C₄×SD₁₆×C₂₉	semidirect
342. C₄	C₂₉×#492	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×C₂₉×#492	2
C₂×C₄×SD₁₆×C₂₉	2
C₄×C₂₉×C₄⋊Q₈	2
C₄×C₂₉×#127	2
C₂₉×#1968	2
C₂₉×#1957	2
C₂₉×#1956	2
C₂₉×#1844	2
C₄²×C₈×C₂₉	2
C₄×#492	29

Subgroups — C4×C29×#492 #20316586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₉×#492 #20316586