Subgroups — C₈×C₂₉×#135 #20312745

Order 7424.

750 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#41×C₂₉	C₂	1	2	yes	maximal, complemented
2	C₄×C₂₉×#135	C₂	1	1	yes	maximal, characteristic
3	C₈×Q₁₆×C₂₉	C₂	1	2	yes	maximal, complemented
4	C₈×SD₁₆×C₂₉	C₂	1	4	yes	maximal, complemented
5	C₈×D₈×C₂₉	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1476	C₂	1	2	yes	maximal, complemented
8	C₂×C₈²×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₉×#135	C₄	1	1	yes	characteristic
10	C₄×#41×C₂₉	C₂²	1	2	yes	—
11	C₈×Q₈×C₂₉	C₂²	1	4	yes	—
12	C₄×Q₁₆×C₂₉	C₄	1	1	yes	characteristic
13	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
14	C₄×SD₁₆×C₂₉	C₄	1	2	yes	—
15	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	—
16	C₄×D₈×C₂₉	C₄	1	1	yes	characteristic
17	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
18	C₈×D₄×C₂₉	—	2	4	no	—
19	C₈×D₄×C₂₉	C₂²	1	4	yes	—
20	C₂₉×#431	—	2	2	no	—
21	C₂₉×#431	C₂²	1	2	yes	—
22	C₂₉×#427	C₄	1	1	yes	characteristic
23	C₂₉×#416	C₄	1	2	yes	—
24	C₂×C₄×C₈×C₂₉	—	2	2	no	—
25	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
28	C₂₉×#335	C₂²	1	2	yes	—
29	C₂₉×#334	C₂²	1	2	yes	—
30	C₂₉×Q₈⋊C₈	C₂²	1	4	yes	—
31	C₂₉×D₄⋊C₈	C₂²	1	4	yes	—
32	C₈²×C₂₉	C₂²	1	2	yes	—
33	C₈²×C₂₉	C₂²	1	2	yes	—
34	C₂×#41×C₂₉	C₂×C₄	1	2	yes	—
35	C₂₉×#135	C₈	1	8	yes	direct product factor
36	C₂×Q₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
37	C₂×SD₁₆×C₂₉	C₂×C₄	1	2	yes	—
38	C₂×D₈×C₂₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₂₉	—	2	1	no	—
40	C₂²×C₈×C₂₉	—	2	4	no	—
41	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₂₉	D₄	1	2	yes	—
44	C₄×Q₈×C₂₉	C₂×C₄	1	2	yes	—
45	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
46	C₄×D₄×C₂₉	—	2	2	no	—
47	C₄×D₄×C₂₉	—	2	2	no	—
48	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₂₉	C₂³	1	2	yes	—
50	C₂₉×#117	—	2	2	no	—
51	C₂₉×#117	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₂₉	—	2	2	no	—
53	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
54	C₂₉×#107	C₂×C₄	1	1	yes	characteristic
55	C₂₉×#107	C₂×C₄	1	1	yes	characteristic
56	C₂₉×#106	C₂×C₄	1	2	yes	—
57	C₂₉×C₄⋊C₈	—	2	4	no	—
58	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
59	C₂₉×#103	C₂×C₄	1	2	yes	—
60	C₂₉×#103	C₂×C₄	1	2	yes	—
61	C₂₉×#102	C₂×C₄	1	2	yes	—
62	C₂₉×#102	C₂×C₄	1	2	yes	—
63	C₂₉×C₂²⋊C₈	—	2	2	no	—
64	C₂₉×C₂²⋊C₈	—	2	4	no	—
65	C₄×C₈×C₂₉	—	2	4	no	—
66	C₄×C₈×C₂₉	—	2	2	no	—
67	C₄×C₈×C₂₉	—	2	1	no	—
68	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
69	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
71	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
72	C₄×C₈×C₂₉	C₂³	1	2	yes	—
73	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₂₉	C₂³	1	2	yes	—
76	#41×C₂₉	—	2	4	no	—
77	#41×C₂₉	C₂×C₈	1	8	yes	complemented
78	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
79	C₂×D₄×C₂₉	—	2	2	no	—
80	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₂₉	—	2	2	no	—
82	C₂²×C₄×C₂₉	—	2	2	no	—
83	C₂²×C₄×C₂₉	—	2	2	no	—
84	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
87	Q₁₆×C₂₉	C₂×C₈	1	4	yes	complemented
88	SD₁₆×C₂₉	C₂×C₈	1	8	yes	complemented
89	D₈×C₂₉	C₂×C₈	1	4	yes	complemented
90	C₂×C₈×C₂₉	—	2	4	no	—
91	C₂×C₈×C₂₉	—	2	2	no	—
92	C₂×C₈×C₂₉	—	2	2	no	—
93	C₂×C₈×C₂₉	—	2	4	no	—
94	C₂×C₈×C₂₉	—	2	4	no	—
95	C₂×C₈×C₂₉	—	4	8	no	—
96	C₂×C₈×C₂₉	C₂×C₈	1	4	yes	complemented
97	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
103	C₄⋊C₄×C₂₉	—	2	2	no	—
104	C₄⋊C₄×C₂₉	—	2	2	no	—
105	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
106	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
107	C₂²⋊C₄×C₂₉	—	2	2	no	—
108	C₂²⋊C₄×C₂₉	—	2	2	no	—
109	C₂²⋊C₄×C₂₉	—	2	2	no	—
110	C₄²×C₂₉	—	2	2	no	—
111	C₄²×C₂₉	—	2	2	no	—
112	C₄²×C₂₉	—	2	2	no	—
113	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₂₉	#41	1	1	yes	characteristic
116	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
117	C₈×#135	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₂₉	—	2	2	no	—
119	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
120	Q₈×C₂₉	—	2	2	no	—
121	Q₈×C₂₉	C₂²×C₈	1	4	yes	—
122	D₄×C₂₉	—	2	8	no	—
123	D₄×C₂₉	—	2	2	no	—
124	D₄×C₂₉	C₂²×C₈	1	4	yes	—
125	C₂×C₄×C₂₉	—	2	2	no	—
126	C₂×C₄×C₂₉	—	2	2	no	—
127	C₂×C₄×C₂₉	—	2	8	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	—	4	4	no	—
132	C₂×C₄×C₂₉	—	4	4	no	—
133	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
135	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
136	C₂×C₄×C₂₉	C₂²×C₈	1	2	yes	—
137	C₂×C₄×C₂₉	#131	1	2	yes	—
138	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
139	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
140	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
141	C₈×C₂₉	—	2	4	no	—
142	C₈×C₂₉	—	2	1	no	—
143	C₈×C₂₉	—	2	1	no	—
144	C₈×C₂₉	—	2	2	no	—
145	C₈×C₂₉	—	4	4	no	—
146	C₈×C₂₉	C₂²×C₈	1	2	yes	—
147	C₈×C₂₉	C₂²×C₈	1	2	yes	—
148	C₈×C₂₉	#135	1	4	yes	direct product factor
149	C₈×#41	C₂×C₂₉	1	2	yes	complemented
150	C₄×#135	C₂×C₂₉	1	1	yes	characteristic
151	C₈×Q₁₆	C₂×C₂₉	1	2	yes	complemented
152	C₈×SD₁₆	C₂×C₂₉	1	4	yes	complemented
153	C₈×D₈	C₂×C₂₉	1	2	yes	complemented
154	#1564	C₂×C₂₉	1	1	yes	characteristic, complemented
155	#1476	C₂×C₂₉	1	2	yes	complemented
156	C₂×C₈²	C₂×C₂₉	1	1	yes	characteristic, complemented
157	C₂²×C₂₉	—	2	1	no	—
158	C₂²×C₂₉	—	2	1	no	—
159	C₂²×C₂₉	—	2	4	no	—
160	C₂²×C₂₉	—	4	2	no	—
161	C₂²×C₂₉	—	4	2	no	—
162	C₂²×C₂₉	C₈×D₄	1	2	yes	—
163	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
164	C₄×C₂₉	—	2	4	no	—
165	C₄×C₂₉	—	2	1	no	—
166	C₄×C₂₉	—	2	1	no	—
167	C₄×C₂₉	—	4	2	no	—
168	C₄×C₂₉	—	4	2	no	—
169	C₄×C₂₉	C₈×D₄	1	2	yes	—
170	C₄×C₂₉	#443	1	2	yes	—
171	C₄×C₂₉	C₂³×C₈	1	1	yes	characteristic
172	C₄×C₂₉	C₂×#131	1	1	yes	characteristic
173	C₄×C₂₉	C₂×#135	1	2	yes	—
174	C₂×#135	C₄×C₂₉	1	1	yes	characteristic
175	C₄×#41	C₂²×C₂₉	1	2	yes	—
176	C₈×Q₈	C₂²×C₂₉	1	4	yes	—
177	C₄×Q₁₆	C₄×C₂₉	1	1	yes	characteristic
178	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
179	C₄×SD₁₆	C₄×C₂₉	1	2	yes	—
180	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	—
181	C₄×D₈	C₄×C₂₉	1	1	yes	characteristic
182	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
183	C₈×D₄	—	2	4	no	—
184	C₈×D₄	C₂²×C₂₉	1	4	yes	—
185	#431	—	2	2	no	—
186	#431	C₂²×C₂₉	1	2	yes	—
187	#427	C₄×C₂₉	1	1	yes	characteristic
188	#416	C₄×C₂₉	1	2	yes	—
189	C₂×C₄×C₈	—	2	2	no	—
190	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
191	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
192	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
193	#335	C₂²×C₂₉	1	2	yes	—
194	#334	C₂²×C₂₉	1	2	yes	—
195	Q₈⋊C₈	C₂²×C₂₉	1	4	yes	—
196	D₄⋊C₈	C₂²×C₂₉	1	4	yes	—
197	C₈²	C₂²×C₂₉	1	2	yes	—
198	C₈²	C₂²×C₂₉	1	2	yes	—
199	C₂×C₂₉	—	2	2	no	—
200	C₂×C₂₉	—	4	4	no	—
201	C₂×C₂₉	C₂×C₈×D₄	1	1	yes	characteristic
202	C₂×C₂₉	C₄×#135	1	1	yes	characteristic
203	C₂×C₂₉	C₂×#443	1	1	yes	characteristic
204	C₂×#41	C₂×C₄×C₂₉	1	2	yes	—
205	#135	C₈×C₂₉	1	8	yes	direct product factor
206	C₂×Q₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic
207	C₂×SD₁₆	C₂×C₄×C₂₉	1	2	yes	—
208	C₂×D₈	C₂×C₄×C₂₉	1	1	yes	characteristic
209	C₂²×C₈	—	2	1	no	—
210	C₂²×C₈	—	2	4	no	—
211	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
212	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
213	C₂²×C₈	D₄×C₂₉	1	2	yes	—
214	C₄×Q₈	C₂×C₄×C₂₉	1	2	yes	—
215	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
216	C₄×D₄	—	2	2	no	—
217	C₄×D₄	—	2	2	no	—
218	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
219	C₄×D₄	C₂³×C₂₉	1	2	yes	—
220	#117	—	2	2	no	—
221	#117	C₂×C₄×C₂₉	1	2	yes	—
222	C₂×C₄²	—	2	2	no	—
223	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
224	#107	C₂×C₄×C₂₉	1	1	yes	characteristic
225	#107	C₂×C₄×C₂₉	1	1	yes	characteristic
226	#106	C₂×C₄×C₂₉	1	2	yes	—
227	C₄⋊C₈	—	2	4	no	—
228	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
229	#103	C₂×C₄×C₂₉	1	2	yes	—
230	#103	C₂×C₄×C₂₉	1	2	yes	—
231	#102	C₂×C₄×C₂₉	1	2	yes	—
232	#102	C₂×C₄×C₂₉	1	2	yes	—
233	C₂²⋊C₈	—	2	2	no	—
234	C₂²⋊C₈	—	2	4	no	—
235	C₄×C₈	—	2	4	no	—
236	C₄×C₈	—	2	2	no	—
237	C₄×C₈	—	2	1	no	—
238	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
239	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
240	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
241	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
242	C₄×C₈	C₂³×C₂₉	1	2	yes	—
243	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
244	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
245	C₄×C₈	C₂³×C₂₉	1	2	yes	—
246	C₂₉	C₈×#135	1	1	yes	characteristic, direct product factor, Sylow
247	#41	—	2	4	no	—
248	#41	C₂×C₈×C₂₉	1	8	yes	complemented
249	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
250	C₂×D₄	—	2	2	no	—
251	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
256	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
257	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
258	Q₁₆	C₂×C₈×C₂₉	1	4	yes	complemented
259	SD₁₆	C₂×C₈×C₂₉	1	8	yes	complemented
260	D₈	C₂×C₈×C₂₉	1	4	yes	complemented
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	4	no	—
265	C₂×C₈	—	2	4	no	—
266	C₂×C₈	—	4	8	no	—
267	C₂×C₈	C₂×C₈×C₂₉	1	4	yes	complemented
268	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
269	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
270	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
271	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
272	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
273	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
277	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
278	C₂²⋊C₄	—	2	2	no	—
279	C₂²⋊C₄	—	2	2	no	—
280	C₂²⋊C₄	—	2	2	no	—
281	C₄²	—	2	2	no	—
282	C₄²	—	2	2	no	—
283	C₄²	—	2	2	no	—
284	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
285	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
286	C₄²	#41×C₂₉	1	1	yes	characteristic
287	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
288	C₂³	—	2	2	no	—
289	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
290	Q₈	—	2	2	no	—
291	Q₈	C₂²×C₈×C₂₉	1	4	yes	—
292	D₄	—	2	8	no	—
293	D₄	—	2	2	no	—
294	D₄	C₂²×C₈×C₂₉	1	4	yes	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	4	4	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
304	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
305	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
306	C₂×C₄	C₂²×C₈×C₂₉	1	2	yes	—
307	C₂×C₄	C₂₉×#131	1	2	yes	—
308	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
309	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
310	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
311	C₈	—	2	4	no	—
312	C₈	—	2	1	no	—
313	C₈	—	2	1	no	—
314	C₈	—	2	2	no	—
315	C₈	—	4	4	no	—
316	C₈	C₂²×C₈×C₂₉	1	2	yes	—
317	C₈	C₂²×C₈×C₂₉	1	2	yes	—
318	C₈	C₂₉×#135	1	4	yes	direct product factor
319	C₂²	—	2	1	no	—
320	C₂²	—	2	1	no	—
321	C₂²	—	2	4	no	—
322	C₂²	—	4	2	no	—
323	C₂²	—	4	2	no	—
324	C₂²	C₈×D₄×C₂₉	1	2	yes	—
325	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
326	C₄	—	2	4	no	—
327	C₄	—	2	1	no	—
328	C₄	—	2	1	no	—
329	C₄	—	4	2	no	—
330	C₄	—	4	2	no	—
331	C₄	C₈×D₄×C₂₉	1	2	yes	—
332	C₄	C₂₉×#443	1	2	yes	—
333	C₄	C₂³×C₈×C₂₉	1	1	yes	characteristic
334	C₄	C₂×C₂₉×#131	1	1	yes	characteristic
335	C₄	C₂×C₂₉×#135	1	2	yes	—
336	C₂	—	2	2	no	—
337	C₂	—	4	4	no	—
338	C₂	C₂×C₈×D₄×C₂₉	1	1	yes	characteristic
339	C₂	C₄×C₂₉×#135	1	1	yes	characteristic
340	C₂	C₂×C₂₉×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈×C₂₉	D₄
commutator	C₄	C₂³×C₈×C₂₉
Frattini, cosocle	C₄²	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂×C₄×D₄
prime radical	C₂×C₂₉×#135	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₂₉ ◁ C₂×C₄×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈×#41×C₂₉	C₂	semidirect
3. C₈×Q₁₆×C₂₉	C₂	semidirect
4. C₈×SD₁₆×C₂₉	C₂	semidirect
5. C₈×D₈×C₂₉	C₂	semidirect
6. C₂₉×#1564	C₂	semidirect
7. C₂₉×#1476	C₂	semidirect
8. C₂×C₈²×C₂₉	C₂	semidirect
35. C₂₉×#135	C₈	direct (N × H)
77. #41×C₂₉	C₂×C₈	semidirect
87. Q₁₆×C₂₉	C₂×C₈	semidirect
88. SD₁₆×C₂₉	C₂×C₈	semidirect
89. D₈×C₂₉	C₂×C₈	semidirect
96. C₂×C₈×C₂₉	C₂×C₈	semidirect
117. C₈×#135	C₂₉	direct (N × H)
148. C₈×C₂₉	#135	direct (N × H)
149. C₈×#41	C₂×C₂₉	semidirect
151. C₈×Q₁₆	C₂×C₂₉	semidirect
152. C₈×SD₁₆	C₂×C₂₉	semidirect
153. C₈×D₈	C₂×C₂₉	semidirect
154. #1564	C₂×C₂₉	semidirect
155. #1476	C₂×C₂₉	semidirect
156. C₂×C₈²	C₂×C₂₉	semidirect
205. #135	C₈×C₂₉	direct (N × H)
246. C₂₉	C₈×#135	direct (N × H)
248. #41	C₂×C₈×C₂₉	semidirect
258. Q₁₆	C₂×C₈×C₂₉	semidirect
259. SD₁₆	C₂×C₈×C₂₉	semidirect
260. D₈	C₂×C₈×C₂₉	semidirect
267. C₂×C₈	C₂×C₈×C₂₉	semidirect
318. C₈	C₂₉×#135	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×#41×C₂₉	2
C₄×C₂₉×#135	2
C₈×Q₁₆×C₂₉	2
C₈×SD₁₆×C₂₉	2
C₈×D₈×C₂₉	2
C₂₉×#1564	2
C₂₉×#1476	2
C₂×C₈²×C₂₉	2
C₈×#135	29

Subgroups — C8×C29×#135 #20312745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₂₉×#135 #20312745