Subgroups — D₄×C₂₉×M₃₂ #20328337

Order 7424.

734 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₉×M₃₂	C₂	1	2	yes	maximal, complemented
2	C₂×C₈×D₄×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2169	C₂	1	2	yes	maximal, complemented
4	C₂₉×#2168	C₂	1	4	yes	maximal, complemented
5	D₄×C₁₆×C₂₉	C₂	1	2	yes	maximal, complemented
6	C₂₉×#2150	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2112	C₂	1	2	yes	maximal, complemented
8	C₄×C₂₉×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₈×C₂₉	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₂₉	C₄	1	1	yes	characteristic
11	C₂×C₂₉×M₃₂	—	2	8	no	—
12	C₂×C₂₉×M₃₂	C₂²	1	1	yes	characteristic
13	C₂×C₂₉×M₃₂	C₂²	1	2	yes	—
14	C₂×C₂₉×M₃₂	C₂²	1	1	yes	characteristic
15	C₂×C₂₉×M₃₂	C₂²	1	4	yes	complemented
16	C₂²×C₁₆×C₂₉	C₂²	1	4	yes	complemented
17	C₈×D₄×C₂₉	C₄	1	2	yes	—
18	C₈×D₄×C₂₉	C₄	1	1	yes	characteristic
19	C₈×D₄×C₂₉	C₄	1	1	yes	characteristic
20	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
21	C₈×D₄×C₂₉	C₂²	1	2	yes	—
22	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×C₄⋊C₈	C₄	1	1	yes	characteristic
24	C₂×C₂₉×C₂²⋊C₈	C₄	1	2	yes	—
25	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
26	C₂₉×C₄⋊C₁₆	C₂²	1	2	yes	complemented
27	C₂₉×C₄⋊C₁₆	C₂²	1	2	yes	complemented
28	C₂₉×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
29	C₂₉×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
30	C₂₉×#346	C₂²	1	2	yes	complemented
31	C₄×C₁₆×C₂₉	C₂²	1	2	yes	complemented
32	C₂²×D₄×C₂₉	C₈	1	1	yes	characteristic
33	C₂³×C₄×C₂₉	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₂₉	—	2	4	no	—
35	C₂²×C₈×C₂₉	—	2	4	no	—
36	C₂²×C₈×C₂₉	C₂×C₄	1	2	yes	—
37	C₂²×C₈×C₂₉	C₂×C₄	1	2	yes	—
38	C₂²×C₈×C₂₉	C₂×C₄	1	2	yes	—
39	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
41	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
42	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
43	C₄×D₄×C₂₉	C₈	1	2	yes	—
44	C₄×D₄×C₂₉	C₈	1	1	yes	characteristic
45	C₄×D₄×C₂₉	C₈	1	1	yes	characteristic
46	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
47	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
48	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₂₉	C₈	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₂₉	C₈	1	2	yes	—
51	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
52	C₂₉×M₃₂	—	2	4	no	—
53	C₂₉×M₃₂	—	2	2	no	—
54	C₂₉×M₃₂	—	2	8	no	—
55	C₂₉×M₃₂	D₄	1	4	yes	direct product factor
56	C₂×C₁₆×C₂₉	—	2	8	no	—
57	C₂×C₁₆×C₂₉	C₂³	1	4	yes	—
58	C₂×C₁₆×C₂₉	C₂³	1	2	yes	—
59	C₂×C₁₆×C₂₉	C₂³	1	2	yes	—
60	C₂₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
61	C₂₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
62	C₂₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
63	C₂₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
64	C₂₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
65	C₂₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
66	C₂₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
67	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
68	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
69	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
70	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
71	C₂⁴×C₂₉	C₂×C₈	1	2	yes	—
72	C₂×D₄×C₂₉	—	2	4	no	—
73	C₂×D₄×C₂₉	C₂×C₈	1	2	yes	—
74	C₂×D₄×C₂₉	C₂×C₈	1	1	yes	characteristic
75	C₂×D₄×C₂₉	C₂×C₈	1	1	yes	characteristic
76	C₂²×C₄×C₂₉	—	2	4	no	—
77	C₂²×C₄×C₂₉	—	2	4	no	—
78	C₂²×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
79	C₂²×C₄×C₂₉	C₂×C₈	1	2	yes	—
80	C₂²×C₄×C₂₉	C₂×C₈	1	2	yes	—
81	C₂²×C₄×C₂₉	C₂×C₈	1	2	yes	—
82	C₂²×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
83	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₈×C₂₉	—	2	4	no	—
87	C₂×C₈×C₂₉	—	2	2	no	—
88	C₂×C₈×C₂₉	—	2	4	no	—
89	C₂×C₈×C₂₉	—	2	4	no	—
90	C₂×C₈×C₂₉	—	2	2	no	—
91	C₂×C₈×C₂₉	—	2	2	no	—
92	C₂×C₈×C₂₉	—	2	2	no	—
93	C₂×C₈×C₂₉	—	2	2	no	—
94	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
95	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
96	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
100	C₂×C₈×C₂₉	#41	1	2	yes	—
101	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
102	C₄⋊C₄×C₂₉	C₂×C₈	1	2	yes	—
103	C₄⋊C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
104	C₄⋊C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
105	C₂²⋊C₄×C₂₉	C₂×C₈	1	2	yes	—
106	C₂²⋊C₄×C₂₉	C₂×C₈	1	2	yes	—
107	C₂²⋊C₄×C₂₉	C₂×C₈	1	2	yes	—
108	C₂²⋊C₄×C₂₉	C₂×C₈	1	2	yes	—
109	C₄²×C₂₉	C₂×C₈	1	1	yes	characteristic
110	C₄²×C₂₉	C₂×C₈	1	1	yes	characteristic
111	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
113	C₁₆×C₂₉	—	2	4	no	—
114	C₁₆×C₂₉	—	2	2	no	—
115	C₁₆×C₂₉	C₂×D₄	1	4	yes	complemented
116	D₄×M₃₂	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₂₉	—	2	4	no	—
118	C₂³×C₂₉	—	2	4	no	—
119	C₂³×C₂₉	—	4	2	no	—
120	C₂³×C₂₉	C₂²×C₈	1	2	yes	—
121	C₂³×C₂₉	C₂²×C₈	1	1	yes	characteristic
122	C₂³×C₂₉	C₂²×C₈	1	2	yes	—
123	D₄×C₂₉	—	2	4	no	—
124	D₄×C₂₉	—	2	2	no	—
125	D₄×C₂₉	M₃₂	1	4	yes	direct product factor
126	C₂×C₄×C₂₉	—	2	4	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	2	no	—
131	C₂×C₄×C₂₉	—	2	4	no	—
132	C₂×C₄×C₂₉	—	2	4	no	—
133	C₂×C₄×C₂₉	—	2	2	no	—
134	C₂×C₄×C₂₉	—	4	1	no	—
135	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
136	C₂×C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
137	C₂×C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
138	C₂×C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
139	C₂×C₄×C₂₉	C₂²×C₈	1	2	yes	—
140	C₂×C₄×C₂₉	C₂²×C₈	1	2	yes	—
141	C₂×C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
143	C₂×C₄×C₂₉	#131	1	2	yes	—
144	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
145	C₈×C₂₉	—	2	2	no	—
146	C₈×C₂₉	—	2	2	no	—
147	C₈×C₂₉	—	2	1	no	—
148	C₈×C₂₉	—	2	1	no	—
149	C₈×C₂₉	C₄×D₄	1	2	yes	—
150	C₈×C₂₉	C₂²×D₄	1	1	yes	characteristic
151	C₈×C₂₉	C₂×#41	1	1	yes	characteristic
152	C₂²×M₃₂	C₂×C₂₉	1	2	yes	complemented
153	C₂×C₈×D₄	C₂×C₂₉	1	1	yes	characteristic
154	#2169	C₂×C₂₉	1	2	yes	complemented
155	#2168	C₂×C₂₉	1	4	yes	complemented
156	D₄×C₁₆	C₂×C₂₉	1	2	yes	complemented
157	#2150	C₂×C₂₉	1	1	yes	characteristic, complemented
158	#2112	C₂×C₂₉	1	2	yes	complemented
159	C₄×M₃₂	C₂×C₂₉	1	1	yes	characteristic, complemented
160	C₂²×C₂₉	—	2	1	no	—
161	C₂²×C₂₉	—	2	1	no	—
162	C₂²×C₂₉	—	2	2	no	—
163	C₂²×C₂₉	—	2	2	no	—
164	C₂²×C₂₉	—	2	2	no	—
165	C₂²×C₂₉	—	2	2	no	—
166	C₂²×C₂₉	—	2	2	no	—
167	C₂²×C₂₉	—	4	8	no	—
168	C₂²×C₂₉	C₈×D₄	1	2	yes	—
169	C₂²×C₂₉	C₂×M₃₂	1	4	yes	complemented
170	C₂²×C₂₉	C₂³×C₈	1	1	yes	characteristic
171	C₄×C₂₉	—	2	1	no	—
172	C₄×C₂₉	—	2	1	no	—
173	C₄×C₂₉	—	2	1	no	—
174	C₄×C₂₉	—	2	2	no	—
175	C₄×C₂₉	—	2	2	no	—
176	C₄×C₂₉	C₈×D₄	1	2	yes	—
177	C₄×C₂₉	C₂×M₃₂	1	2	yes	complemented
178	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
179	C₄×C₂₉	C₂×#131	1	1	yes	characteristic
180	C₂³×C₈	C₂²×C₂₉	1	2	yes	—
181	C₂×C₄×D₄	C₄×C₂₉	1	1	yes	characteristic
182	C₂×M₃₂	—	2	8	no	—
183	C₂×M₃₂	C₂²×C₂₉	1	1	yes	characteristic
184	C₂×M₃₂	C₂²×C₂₉	1	2	yes	—
185	C₂×M₃₂	C₂²×C₂₉	1	1	yes	characteristic
186	C₂×M₃₂	C₂²×C₂₉	1	4	yes	complemented
187	C₂²×C₁₆	C₂²×C₂₉	1	4	yes	complemented
188	C₈×D₄	C₄×C₂₉	1	2	yes	—
189	C₈×D₄	C₄×C₂₉	1	1	yes	characteristic
190	C₈×D₄	C₄×C₂₉	1	1	yes	characteristic
191	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
192	C₈×D₄	C₂²×C₂₉	1	2	yes	—
193	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
194	C₂×C₄⋊C₈	C₄×C₂₉	1	1	yes	characteristic
195	C₂×C₂²⋊C₈	C₄×C₂₉	1	2	yes	—
196	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
197	C₄⋊C₁₆	C₂²×C₂₉	1	2	yes	complemented
198	C₄⋊C₁₆	C₂²×C₂₉	1	2	yes	complemented
199	C₂²⋊C₁₆	C₂²×C₂₉	1	4	yes	complemented
200	C₂²⋊C₁₆	C₂²×C₂₉	1	4	yes	complemented
201	#346	C₂²×C₂₉	1	2	yes	complemented
202	C₄×C₁₆	C₂²×C₂₉	1	2	yes	complemented
203	C₂×C₂₉	—	2	2	no	—
204	C₂×C₂₉	—	2	4	no	—
205	C₂×C₂₉	—	4	2	no	—
206	C₂×C₂₉	C₂×C₈×D₄	1	1	yes	characteristic
207	C₂×C₂₉	C₂²×M₃₂	1	1	yes	characteristic
208	C₂×C₂₉	#3407	1	1	yes	characteristic
209	C₂²×D₄	C₈×C₂₉	1	1	yes	characteristic
210	C₂³×C₄	C₂×C₄×C₂₉	1	2	yes	—
211	C₂²×C₈	—	2	4	no	—
212	C₂²×C₈	—	2	4	no	—
213	C₂²×C₈	C₂×C₄×C₂₉	1	2	yes	—
214	C₂²×C₈	C₂×C₄×C₂₉	1	2	yes	—
215	C₂²×C₈	C₂×C₄×C₂₉	1	2	yes	—
216	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
217	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
218	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
219	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
220	C₄×D₄	C₈×C₂₉	1	2	yes	—
221	C₄×D₄	C₈×C₂₉	1	1	yes	characteristic
222	C₄×D₄	C₈×C₂₉	1	1	yes	characteristic
223	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
224	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
225	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₈×C₂₉	1	1	yes	characteristic
227	C₂×C₂²⋊C₄	C₈×C₂₉	1	2	yes	—
228	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
229	M₃₂	—	2	4	no	—
230	M₃₂	—	2	2	no	—
231	M₃₂	—	2	8	no	—
232	M₃₂	D₄×C₂₉	1	4	yes	direct product factor
233	C₂×C₁₆	—	2	8	no	—
234	C₂×C₁₆	C₂³×C₂₉	1	2	yes	—
235	C₂×C₁₆	C₂³×C₂₉	1	4	yes	—
236	C₂×C₁₆	C₂³×C₂₉	1	2	yes	—
237	C₄⋊C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
238	C₄⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
239	C₄⋊C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
240	C₂²⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
241	C₂²⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
242	C₂²⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
243	C₂²⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
244	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
245	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
246	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
247	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
248	C₂₉	D₄×M₃₂	1	1	yes	characteristic, direct product factor, Sylow
249	C₂⁴	C₂×C₈×C₂₉	1	2	yes	—
250	C₂×D₄	—	2	4	no	—
251	C₂×D₄	C₂×C₈×C₂₉	1	2	yes	—
252	C₂×D₄	C₂×C₈×C₂₉	1	1	yes	characteristic
253	C₂×D₄	C₂×C₈×C₂₉	1	1	yes	characteristic
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	C₂×C₈×C₂₉	1	1	yes	characteristic
257	C₂²×C₄	C₂×C₈×C₂₉	1	2	yes	—
258	C₂²×C₄	C₂×C₈×C₂₉	1	2	yes	—
259	C₂²×C₄	C₂×C₈×C₂₉	1	2	yes	—
260	C₂²×C₄	C₂×C₈×C₂₉	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
262	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
263	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
264	C₂×C₈	—	2	4	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	4	no	—
267	C₂×C₈	—	2	4	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
273	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
274	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
275	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
276	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
277	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
278	C₂×C₈	#41×C₂₉	1	2	yes	—
279	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
280	C₄⋊C₄	C₂×C₈×C₂₉	1	2	yes	—
281	C₄⋊C₄	C₂×C₈×C₂₉	1	1	yes	characteristic
282	C₄⋊C₄	C₂×C₈×C₂₉	1	1	yes	characteristic
283	C₂²⋊C₄	C₂×C₈×C₂₉	1	2	yes	—
284	C₂²⋊C₄	C₂×C₈×C₂₉	1	2	yes	—
285	C₂²⋊C₄	C₂×C₈×C₂₉	1	2	yes	—
286	C₂²⋊C₄	C₂×C₈×C₂₉	1	2	yes	—
287	C₄²	C₂×C₈×C₂₉	1	1	yes	characteristic
288	C₄²	C₂×C₈×C₂₉	1	1	yes	characteristic
289	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
290	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
291	C₁₆	—	2	4	no	—
292	C₁₆	—	2	2	no	—
293	C₁₆	C₂×D₄×C₂₉	1	4	yes	complemented
294	C₂³	—	2	4	no	—
295	C₂³	—	2	4	no	—
296	C₂³	—	4	2	no	—
297	C₂³	C₂²×C₈×C₂₉	1	2	yes	—
298	C₂³	C₂²×C₈×C₂₉	1	1	yes	characteristic
299	C₂³	C₂²×C₈×C₂₉	1	2	yes	—
300	D₄	—	2	4	no	—
301	D₄	—	2	2	no	—
302	D₄	C₂₉×M₃₂	1	4	yes	direct product factor
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
313	C₂×C₄	C₂²×C₈×C₂₉	1	1	yes	characteristic
314	C₂×C₄	C₂²×C₈×C₂₉	1	1	yes	characteristic
315	C₂×C₄	C₂²×C₈×C₂₉	1	1	yes	characteristic
316	C₂×C₄	C₂²×C₈×C₂₉	1	2	yes	—
317	C₂×C₄	C₂²×C₈×C₂₉	1	2	yes	—
318	C₂×C₄	C₂²×C₈×C₂₉	1	1	yes	characteristic
319	C₂×C₄	C₂²×C₈×C₂₉	1	1	yes	characteristic
320	C₂×C₄	C₂₉×#131	1	2	yes	—
321	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
322	C₈	—	2	2	no	—
323	C₈	—	2	2	no	—
324	C₈	—	2	1	no	—
325	C₈	—	2	1	no	—
326	C₈	C₄×D₄×C₂₉	1	2	yes	—
327	C₈	C₂²×D₄×C₂₉	1	1	yes	characteristic
328	C₈	C₂×#41×C₂₉	1	1	yes	characteristic
329	C₂²	—	2	2	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	4	8	no	—
337	C₂²	C₈×D₄×C₂₉	1	2	yes	—
338	C₂²	C₂×C₂₉×M₃₂	1	4	yes	complemented
339	C₂²	C₂³×C₈×C₂₉	1	1	yes	characteristic
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	2	1	no	—
345	C₄	C₈×D₄×C₂₉	1	2	yes	—
346	C₄	C₂×C₂₉×M₃₂	1	2	yes	complemented
347	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
348	C₄	C₂×C₂₉×#131	1	1	yes	characteristic
349	C₂	—	2	2	no	—
350	C₂	—	2	4	no	—
351	C₂	—	4	2	no	—
352	C₂	C₂×C₈×D₄×C₂₉	1	1	yes	characteristic
353	C₂	C₂²×C₂₉×M₃₂	1	1	yes	characteristic
354	C₂	C₂₉×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₈×C₂₉
Frattini, cosocle	C₂×C₈	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂³×C₈
prime radical	C₂²×D₄×C₂₉	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₉×M₃₂	C₂	semidirect
3. C₂₉×#2169	C₂	semidirect
4. C₂₉×#2168	C₂	semidirect
5. D₄×C₁₆×C₂₉	C₂	semidirect
6. C₂₉×#2150	C₂	semidirect
7. C₂₉×#2112	C₂	semidirect
8. C₄×C₂₉×M₃₂	C₂	semidirect
15. C₂×C₂₉×M₃₂	C₂²	semidirect
16. C₂²×C₁₆×C₂₉	C₂²	semidirect
26. C₂₉×C₄⋊C₁₆	C₂²	semidirect
27. C₂₉×C₄⋊C₁₆	C₂²	semidirect
28. C₂₉×C₂²⋊C₁₆	C₂²	semidirect
29. C₂₉×C₂²⋊C₁₆	C₂²	semidirect
30. C₂₉×#346	C₂²	semidirect
31. C₄×C₁₆×C₂₉	C₂²	semidirect
55. C₂₉×M₃₂	D₄	direct (N × H)
115. C₁₆×C₂₉	C₂×D₄	semidirect
116. D₄×M₃₂	C₂₉	direct (N × H)
125. D₄×C₂₉	M₃₂	direct (N × H)
152. C₂²×M₃₂	C₂×C₂₉	semidirect
154. #2169	C₂×C₂₉	semidirect
155. #2168	C₂×C₂₉	semidirect
156. D₄×C₁₆	C₂×C₂₉	semidirect
157. #2150	C₂×C₂₉	semidirect
158. #2112	C₂×C₂₉	semidirect
159. C₄×M₃₂	C₂×C₂₉	semidirect
169. C₂²×C₂₉	C₂×M₃₂	semidirect
177. C₄×C₂₉	C₂×M₃₂	semidirect
186. C₂×M₃₂	C₂²×C₂₉	semidirect
187. C₂²×C₁₆	C₂²×C₂₉	semidirect
197. C₄⋊C₁₆	C₂²×C₂₉	semidirect
198. C₄⋊C₁₆	C₂²×C₂₉	semidirect
199. C₂²⋊C₁₆	C₂²×C₂₉	semidirect
200. C₂²⋊C₁₆	C₂²×C₂₉	semidirect
201. #346	C₂²×C₂₉	semidirect
202. C₄×C₁₆	C₂²×C₂₉	semidirect
232. M₃₂	D₄×C₂₉	direct (N × H)
248. C₂₉	D₄×M₃₂	direct (N × H)
293. C₁₆	C₂×D₄×C₂₉	semidirect
302. D₄	C₂₉×M₃₂	direct (N × H)
338. C₂²	C₂×C₂₉×M₃₂	semidirect
346. C₄	C₂×C₂₉×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂₉×M₃₂	2
C₂×C₈×D₄×C₂₉	2
C₂₉×#2169	2
C₂₉×#2168	2
D₄×C₁₆×C₂₉	2
C₂₉×#2150	2
C₂₉×#2112	2
C₄×C₂₉×M₃₂	2
D₄×M₃₂	29

Subgroups — D4×C29×M32 #20328337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₂₉×M₃₂ #20328337