Subgroups — C₄×SD₁₆×D₂₉ #16828245

Order 3712.

552 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₂₉	C₂	1	1	yes	maximal, characteristic
4	#14271254	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#90773	C₂	1	1	yes	maximal, characteristic, complemented
6	SD₁₆×Dic₂₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×#90784	C₂	1	1	yes	maximal, characteristic, complemented
8	#14271250	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#90783	C₂	1	1	yes	maximal, characteristic, complemented
10	#14271248	C₂	1	1	yes	maximal, characteristic, complemented
11	#106×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#103×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#102×D₂₉	C₂	1	1	yes	maximal, characteristic
14	C₄×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₂₉	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₂₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₂₉	—	2	1	no	—
19	C₂×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
20	C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
21	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
22	Q₈×Dic₂₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×#90784	C₂²	1	1	yes	characteristic
24	D₄×Dic₂₉	C₂²	1	1	yes	characteristic
25	C₂×#90783	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊D₂₉	—	2	1	no	—
27	SD₁₆×D₂₉	C₄	1	8	yes	direct product factor
28	C₂×#90773	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
30	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
31	#11745255	C₂²	1	1	yes	characteristic
32	C₄⋊C₄×D₂₉	—	2	1	no	—
33	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic
34	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic
35	#11745249	—	2	1	no	—
36	#11745249	C₂²	1	1	yes	characteristic, complemented
37	#11745243	—	2	1	no	—
38	C₂²⋊C₄×D₂₉	—	2	1	no	—
39	C₄×D₁₁₆	C₂²	1	1	yes	characteristic
40	C₄²×D₂₉	—	2	1	no	—
41	C₄²×D₂₉	C₂²	1	1	yes	characteristic
42	C₄×Dic₅₈	—	2	1	no	—
43	C₄×Dic₅₈	C₂²	1	1	yes	characteristic, complemented
44	C₂₉×#106	C₂²	1	1	yes	characteristic, complemented
45	C₂₉×#103	C₂²	1	1	yes	characteristic, complemented
46	C₂₉×#102	C₂²	1	1	yes	characteristic
47	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
48	#11745183	C₂²	1	1	yes	characteristic, complemented
49	#11745180	C₂²	1	1	yes	characteristic
50	#11745169	C₂²	1	1	yes	characteristic
51	#11745165	C₂²	1	1	yes	characteristic, complemented
52	#11745164	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₂₉	C₂²	1	1	yes	characteristic, complemented
54	C₈×Dic₂₉	C₂²	1	1	yes	characteristic, complemented
55	#11745158	C₂²	1	1	yes	characteristic, complemented
56	#11745157	C₂²	1	1	yes	characteristic
57	#11745156	C₂²	1	1	yes	characteristic, complemented
58	#11745156	C₂²	1	1	yes	characteristic, complemented
59	C₄×#6597	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₂₉	—	2	1	no	—
61	C₂×Q₈×C₂₉	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₂₉	—	2	1	no	—
64	C₂×C₂²⋊D₂₉	—	2	1	no	—
65	C₂²×Dic₂₉	—	2	1	no	—
66	Q₈×D₂₉	—	2	2	no	—
67	Q₈×D₂₉	C₂×C₄	1	4	yes	complemented
68	D₄×D₂₉	—	2	2	no	—
69	D₄×D₂₉	C₂×C₄	1	4	yes	—
70	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
71	C₂×C₄×D₂₉	—	2	1	no	—
72	C₂×C₄×D₂₉	—	2	1	no	—
73	C₂×C₄×D₂₉	—	2	1	no	—
74	C₂×C₄×D₂₉	—	2	1	no	—
75	C₂×C₄×D₂₉	—	2	1	no	—
76	C₂×C₄×D₂₉	—	4	4	no	—
77	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
78	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
79	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
80	C₂×Dic₅₈	—	2	1	no	—
81	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
82	SD₁₆×C₂₉	C₂×C₄	1	4	yes	complemented
83	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
84	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
85	C₄⋊C₄×C₂₉	—	2	1	no	—
86	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
87	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
88	C₂²⋊C₄×C₂₉	—	2	1	no	—
89	C₄²×C₂₉	—	2	1	no	—
90	C₄²×C₂₉	C₂³	1	1	yes	characteristic
91	C₂²⋊Dic₂₉	—	2	1	no	—
92	#90784	C₂×C₄	1	4	yes	complemented
93	#90783	C₂×C₄	1	4	yes	complemented
94	#90781	—	2	1	no	—
95	#90781	—	2	1	no	—
96	C₄⋊Dic₂₉	—	2	1	no	—
97	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
98	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
99	#90779	—	2	1	no	—
100	#90779	—	2	1	no	—
101	#90779	—	2	1	no	—
102	#90779	—	2	1	no	—
103	C₄×Dic₂₉	—	2	1	no	—
104	C₄×Dic₂₉	—	2	1	no	—
105	C₄×Dic₂₉	—	2	1	no	—
106	C₄×Dic₂₉	D₄	1	1	yes	characteristic
107	C₄×Dic₂₉	D₄	1	1	yes	characteristic
108	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
109	C₂×#6597	C₂³	1	1	yes	characteristic
110	C₂×#6597	C₂³	1	1	yes	characteristic
111	#90773	C₂×C₄	1	4	yes	complemented
112	C₈×D₂₉	—	2	2	no	—
113	C₈×D₂₉	C₂×C₄	1	4	yes	complemented
114	C₂³×C₂₉	—	2	1	no	—
115	C₂²×D₂₉	—	2	1	no	—
116	C₂²×D₂₉	—	2	4	no	—
117	C₂²×D₂₉	—	4	2	no	—
118	C₂²×D₂₉	—	4	2	no	—
119	C₂²×D₂₉	C₂×D₄	1	1	yes	characteristic
120	Q₈×C₂₉	—	2	1	no	—
121	Q₈×C₂₉	C₂²×C₄	1	2	yes	complemented
122	D₄×C₂₉	—	2	1	no	—
123	D₄×C₂₉	C₂²×C₄	1	2	yes	—
124	C₂×C₄×C₂₉	—	2	1	no	—
125	C₂×C₄×C₂₉	—	2	1	no	—
126	C₂×C₄×C₂₉	—	2	1	no	—
127	C₂×C₄×C₂₉	—	4	2	no	—
128	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
131	C₂²⋊D₂₉	—	2	4	no	—
132	C₂×Dic₂₉	—	2	1	no	—
133	C₂×Dic₂₉	—	2	1	no	—
134	C₂×Dic₂₉	—	2	1	no	—
135	C₂×Dic₂₉	—	4	2	no	—
136	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
137	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
138	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
139	D₁₁₆	—	2	1	no	—
140	D₁₁₆	C₂²×C₄	1	2	yes	—
141	C₄×D₂₉	—	2	4	no	—
142	C₄×D₂₉	—	2	2	no	—
143	C₄×D₂₉	—	4	2	no	—
144	C₄×D₂₉	—	4	2	no	—
145	C₄×D₂₉	—	4	2	no	—
146	C₄×D₂₉	—	4	2	no	—
147	C₄×D₂₉	SD₁₆	1	4	yes	direct product factor
148	C₄×D₂₉	C₂²×C₄	1	2	yes	—
149	C₄×D₂₉	#41	1	2	yes	—
150	Dic₅₈	—	2	1	no	—
151	Dic₅₈	—	2	4	no	—
152	Dic₅₈	C₂²×C₄	1	2	yes	complemented
153	C₈×C₂₉	—	2	1	no	—
154	C₈×C₂₉	C₂²×C₄	1	2	yes	complemented
155	#6597	—	2	1	no	—
156	#6597	C₂²×C₄	1	2	yes	complemented
157	C₂×C₄×SD₁₆	—	29	1	no	maximal, Sylow
158	C₂²×C₂₉	—	2	2	no	—
159	C₂²×C₂₉	—	4	1	no	—
160	C₂²×C₂₉	—	4	1	no	—
161	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×D₂₉	—	2	2	no	—
163	C₂×D₂₉	—	4	1	no	—
164	C₂×D₂₉	—	4	1	no	—
165	C₂×D₂₉	—	4	8	no	—
166	C₂×D₂₉	C₄×D₄	1	2	yes	—
167	C₂×D₂₉	C₂×SD₁₆	1	2	yes	—
168	C₂×D₂₉	#135	1	2	yes	—
169	C₄×C₂₉	—	2	2	no	—
170	C₄×C₂₉	—	2	1	no	—
171	C₄×C₂₉	—	4	1	no	—
172	C₄×C₂₉	—	4	1	no	—
173	C₄×C₂₉	C₂×SD₁₆	1	2	yes	complemented
174	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
175	C₄×C₂₉	C₂×#41	1	1	yes	characteristic
176	Dic₂₉	—	2	2	no	—
177	Dic₂₉	—	2	1	no	—
178	Dic₂₉	—	4	1	no	—
179	Dic₂₉	—	4	1	no	—
180	Dic₂₉	C₄×D₄	1	2	yes	—
181	Dic₂₉	C₂×SD₁₆	1	2	yes	complemented
182	C₂²×SD₁₆	—	29	1	no	—
183	C₂×C₄×Q₈	—	29	1	no	—
184	C₂×C₄×D₄	—	29	1	no	—
185	C₄×SD₁₆	—	29	1	no	—
186	C₄×SD₁₆	—	29	1	no	—
187	C₄×SD₁₆	—	29	1	no	—
188	C₄×SD₁₆	—	29	1	no	—
189	C₄×SD₁₆	—	29	1	no	—
190	C₄×SD₁₆	—	29	1	no	—
191	C₄×SD₁₆	—	29	1	no	—
192	C₄×SD₁₆	D₂₉	1	1	yes	characteristic, direct product factor
193	C₂×#106	—	29	1	no	—
194	C₂×#103	—	29	1	no	—
195	C₂×#102	—	29	1	no	—
196	C₂×C₄×C₈	—	29	1	no	—
197	C₂×C₂₉	—	4	2	no	—
198	C₂×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂×C₂₉	C₂²×SD₁₆	1	1	yes	characteristic
200	C₂×C₂₉	C₂×#135	1	1	yes	characteristic
201	D₂₉	—	4	2	no	—
202	D₂₉	C₄×SD₁₆	1	4	yes	direct product factor
203	C₂²×Q₈	—	29	1	no	—
204	C₂²×D₄	—	29	1	no	—
205	C₂³×C₄	—	58	1	no	—
206	C₂×SD₁₆	—	29	1	no	—
207	C₂×SD₁₆	—	29	1	no	—
208	C₂×SD₁₆	—	29	8	no	—
209	C₂×SD₁₆	—	29	1	no	—
210	C₂×SD₁₆	C₂×D₂₉	1	1	yes	characteristic
211	C₂²×C₈	—	29	1	no	—
212	C₂²×C₈	—	29	1	no	—
213	C₄×Q₈	—	29	1	no	—
214	C₄×Q₈	—	29	1	no	—
215	C₄×Q₈	—	29	1	no	—
216	C₄×Q₈	—	58	1	no	—
217	C₄×Q₈	—	58	1	no	—
218	C₄×Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
219	C₄×D₄	—	29	1	no	—
220	C₄×D₄	—	29	1	no	—
221	C₄×D₄	—	29	1	no	—
222	C₄×D₄	—	58	1	no	—
223	C₄×D₄	—	58	1	no	—
224	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic
225	C₂×C₄⋊C₄	—	29	1	no	—
226	C₂×C₄⋊C₄	—	29	1	no	—
227	C₂×C₄⋊C₄	—	58	1	no	—
228	C₂×C₂²⋊C₄	—	58	1	no	—
229	C₂×C₄²	—	29	1	no	—
230	C₂×C₄²	—	58	1	no	—
231	#106	—	29	1	no	—
232	#106	—	29	1	no	—
233	#106	—	29	1	no	—
234	#106	C₂×D₂₉	1	1	yes	characteristic, complemented
235	#103	—	29	1	no	—
236	#103	—	29	1	no	—
237	#103	—	29	1	no	—
238	#103	C₂×D₂₉	1	1	yes	characteristic, complemented
239	#102	—	29	1	no	—
240	#102	—	29	1	no	—
241	#102	—	29	1	no	—
242	#102	C₂×D₂₉	1	1	yes	characteristic
243	C₄×C₈	—	29	1	no	—
244	C₄×C₈	—	29	1	no	—
245	C₄×C₈	—	29	1	no	—
246	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic, complemented
247	C₂₉	C₂×C₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
248	C₂⁴	—	58	1	no	—
249	C₂×Q₈	—	29	4	no	—
250	C₂×Q₈	—	29	1	no	—
251	C₂×Q₈	—	58	1	no	—
252	C₂×Q₈	—	58	2	no	—
253	C₂×Q₈	C₂²×D₂₉	1	1	yes	characteristic
254	C₂×D₄	—	29	4	no	—
255	C₂×D₄	—	29	1	no	—
256	C₂×D₄	—	58	2	no	—
257	C₂×D₄	—	58	1	no	—
258	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	29	1	no	—
261	C₂²×C₄	—	29	1	no	—
262	C₂²×C₄	—	29	1	no	—
263	C₂²×C₄	—	58	1	no	—
264	C₂²×C₄	—	58	1	no	—
265	C₂²×C₄	—	58	1	no	—
266	C₂²×C₄	—	58	1	no	—
267	C₂²×C₄	—	58	1	no	—
268	C₂²×C₄	—	58	1	no	—
269	C₂²×C₄	—	116	4	no	—
270	SD₁₆	—	29	4	no	—
271	SD₁₆	—	29	4	no	—
272	SD₁₆	—	29	4	no	—
273	SD₁₆	C₄×D₂₉	1	4	yes	direct product factor
274	C₂×C₈	—	29	1	no	—
275	C₂×C₈	—	29	4	no	—
276	C₂×C₈	—	29	1	no	—
277	C₂×C₈	—	58	2	no	—
278	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
279	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	29	1	no	—
282	C₄⋊C₄	—	29	1	no	—
283	C₄⋊C₄	—	58	1	no	—
284	C₄⋊C₄	—	58	1	no	—
285	C₄⋊C₄	—	58	1	no	—
286	C₄⋊C₄	—	58	1	no	—
287	C₄⋊C₄	—	58	1	no	—
288	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
289	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	58	1	no	—
292	C₂²⋊C₄	—	58	1	no	—
293	C₂²⋊C₄	—	58	1	no	—
294	C₄²	—	2	1	no	—
295	C₄²	—	29	1	no	—
296	C₄²	—	29	1	no	—
297	C₄²	—	29	1	no	—
298	C₄²	—	58	1	no	—
299	C₄²	—	58	1	no	—
300	C₄²	—	58	1	no	—
301	C₄²	C₂²×D₂₉	1	1	yes	characteristic
302	C₂³	—	2	1	no	—
303	C₂³	—	29	1	no	—
304	C₂³	—	58	4	no	—
305	C₂³	—	58	1	no	—
306	C₂³	—	116	2	no	—
307	C₂³	—	116	2	no	—
308	Q₈	—	2	1	no	—
309	Q₈	—	29	2	no	—
310	Q₈	—	58	4	no	—
311	Q₈	—	58	1	no	—
312	Q₈	C₂×C₄×D₂₉	1	2	yes	complemented
313	D₄	—	2	1	no	—
314	D₄	—	29	2	no	—
315	D₄	—	58	4	no	—
316	D₄	—	58	1	no	—
317	D₄	C₂×C₄×D₂₉	1	2	yes	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	29	1	no	—
323	C₂×C₄	—	29	1	no	—
324	C₂×C₄	—	29	2	no	—
325	C₂×C₄	—	29	2	no	—
326	C₂×C₄	—	29	4	no	—
327	C₂×C₄	—	29	1	no	—
328	C₂×C₄	—	58	2	no	—
329	C₂×C₄	—	58	4	no	—
330	C₂×C₄	—	58	1	no	—
331	C₂×C₄	—	58	1	no	—
332	C₂×C₄	—	58	1	no	—
333	C₂×C₄	—	116	2	no	—
334	C₂×C₄	—	116	2	no	—
335	C₂×C₄	—	116	2	no	—
336	C₂×C₄	—	116	2	no	—
337	C₂×C₄	—	116	2	no	—
338	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
339	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
340	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
341	C₈	—	2	1	no	—
342	C₈	—	29	2	no	—
343	C₈	—	58	1	no	—
344	C₈	C₂×C₄×D₂₉	1	2	yes	complemented
345	C₂²	—	2	2	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	29	2	no	—
349	C₂²	—	29	2	no	—
350	C₂²	—	29	2	no	—
351	C₂²	—	58	2	no	—
352	C₂²	—	116	8	no	—
353	C₂²	—	116	1	no	—
354	C₂²	—	116	1	no	—
355	C₂²	C₂×D₄×D₂₉	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	1	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	29	2	no	—
361	C₄	—	29	2	no	—
362	C₄	—	58	2	no	—
363	C₄	—	58	1	no	—
364	C₄	—	116	1	no	—
365	C₄	—	116	1	no	—
366	C₄	SD₁₆×D₂₉	1	2	yes	direct product factor
367	C₄	C₂²×C₄×D₂₉	1	1	yes	characteristic
368	C₄	#41×D₂₉	1	1	yes	characteristic
369	C₂	—	4	2	no	—
370	C₂	—	29	4	no	—
371	C₂	—	116	2	no	—
372	C₂	C₄×D₄×D₂₉	1	1	yes	characteristic
373	C₂	C₂×SD₁₆×D₂₉	1	1	yes	characteristic
374	C₂	#135×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₂₉
commutator	C₄×C₂₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₄×SD₁₆×C₂₉	C₂
socle	C₂²×C₂₉	C₂²×D₄
prime radical	C₂×D₄×D₂₉	C₂²
cosocle	C₂×C₄×C₂₉	C₂⁴
hypercenter	C₄×SD₁₆	D₂₉
hypocenter	C₂₉	C₂×C₄×SD₁₆
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×Q₈×D₂₉	C₂	semidirect
4. #14271254	C₂	semidirect
5. C₄×#90773	C₂	semidirect
6. SD₁₆×Dic₂₉	C₂	semidirect
7. C₄×#90784	C₂	semidirect
8. #14271250	C₂	semidirect
9. C₄×#90783	C₂	semidirect
10. #14271248	C₂	semidirect
11. #106×D₂₉	C₂	semidirect
12. #103×D₂₉	C₂	semidirect
14. C₄×C₈×D₂₉	C₂	semidirect
15. C₄×SD₁₆×C₂₉	C₂	semidirect
20. C₄×Q₈×C₂₉	C₂²	semidirect
22. Q₈×Dic₂₉	C₂²	semidirect
27. SD₁₆×D₂₉	C₄	direct (N × H)
36. #11745249	C₂²	semidirect
43. C₄×Dic₅₈	C₂²	semidirect
44. C₂₉×#106	C₂²	semidirect
45. C₂₉×#103	C₂²	semidirect
47. C₄×C₈×C₂₉	C₂²	semidirect
48. #11745183	C₂²	semidirect
51. #11745165	C₂²	semidirect
52. #11745164	C₂²	semidirect
53. C₈×Dic₂₉	C₂²	semidirect
54. C₈×Dic₂₉	C₂²	semidirect
55. #11745158	C₂²	semidirect
57. #11745156	C₂²	semidirect
58. #11745156	C₂²	semidirect
59. C₄×#6597	C₂²	semidirect
67. Q₈×D₂₉	C₂×C₄	semidirect
82. SD₁₆×C₂₉	C₂×C₄	semidirect
92. #90784	C₂×C₄	semidirect
93. #90783	C₂×C₄	semidirect
111. #90773	C₂×C₄	semidirect
113. C₈×D₂₉	C₂×C₄	semidirect
121. Q₈×C₂₉	C₂²×C₄	semidirect
147. C₄×D₂₉	SD₁₆	direct (N × H)
152. Dic₅₈	C₂²×C₄	semidirect
154. C₈×C₂₉	C₂²×C₄	semidirect
156. #6597	C₂²×C₄	semidirect
173. C₄×C₂₉	C₂×SD₁₆	semidirect
181. Dic₂₉	C₂×SD₁₆	semidirect
192. C₄×SD₁₆	D₂₉	direct (N × H)
202. D₂₉	C₄×SD₁₆	direct (N × H)
218. C₄×Q₈	C₂×D₂₉	semidirect
234. #106	C₂×D₂₉	semidirect
238. #103	C₂×D₂₉	semidirect
246. C₄×C₈	C₂×D₂₉	semidirect
247. C₂₉	C₂×C₄×SD₁₆	semidirect
273. SD₁₆	C₄×D₂₉	direct (N × H)
312. Q₈	C₂×C₄×D₂₉	semidirect
344. C₈	C₂×C₄×D₂₉	semidirect
366. C₄	SD₁₆×D₂₉	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×SD₁₆×D₂₉	2
C₄×Q₈×D₂₉	2
C₄×D₄×D₂₉	2
#14271254	2
C₄×#90773	2
SD₁₆×Dic₂₉	2
C₄×#90784	2
#14271250	2
C₄×#90783	2
#14271248	2
#106×D₂₉	2
#103×D₂₉	2
#102×D₂₉	2
C₄×C₈×D₂₉	2
C₄×SD₁₆×C₂₉	2
C₂×C₄×SD₁₆	29

Subgroups — C4×SD16×D29 #16828245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×SD₁₆×D₂₉ #16828245