Subgroups — D₂₉×#462 #16828926

Order 3712.

480 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×D₂₉	C₂	1	2	yes	maximal
2	C₄⋊Q₈×D₂₉	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₈×D₂₉	C₂	1	1	yes	maximal, characteristic
4	#14271374	C₂	1	1	yes	maximal, characteristic, complemented
5	#14271373	C₂	1	1	yes	maximal, characteristic, complemented
6	#14271372	C₂	1	2	yes	maximal, complemented
7	#14271371	C₂	1	2	yes	maximal, complemented
8	#14271370	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄⋊C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
10	#103×D₂₉	C₂	1	2	yes	maximal
11	C₂₉×#462	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₈×D₂₉	C₂²	1	2	yes	—
13	C₂×Q₈×D₂₉	C₂²	1	1	yes	characteristic
14	C₂×Q₁₆×C₂₉	C₂²	1	2	yes	—
15	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
17	Q₈×Dic₂₉	C₂²	1	1	yes	characteristic
18	#11745306	C₂²	1	2	yes	—
19	C₂×#90785	C₂²	1	2	yes	—
20	C₂×#90785	C₂²	1	2	yes	—
21	Q₁₆×D₂₉	—	2	8	no	—
22	C₂×Dic₁₁₆	C₂²	1	2	yes	—
23	C₂×C₈×D₂₉	C₂²	1	2	yes	—
24	C₄⋊C₄×D₂₉	—	2	1	no	—
25	C₄⋊C₄×D₂₉	—	2	1	no	—
26	C₄⋊C₄×D₂₉	—	2	1	no	—
27	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic
28	#11745250	—	2	1	no	—
29	#11745250	—	2	1	no	—
30	#11745249	—	2	1	no	—
31	#11745249	C₂²	1	1	yes	characteristic
32	C₄²×D₂₉	—	2	1	no	—
33	C₄²×D₂₉	C₂²	1	1	yes	characteristic
34	#11745231	C₂²	1	1	yes	characteristic
35	C₄×Dic₅₈	—	2	1	no	—
36	C₄×Dic₅₈	C₂²	1	1	yes	characteristic
37	C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂₉×#103	C₂²	1	2	yes	—
39	#11745183	C₂²	1	2	yes	—
40	#11745164	C₂²	1	2	yes	—
41	#11745162	C₂²	1	2	yes	—
42	#11745158	C₂²	1	2	yes	—
43	C₄⋊#6597	C₂²	1	1	yes	characteristic
44	C₂×Q₈×C₂₉	C₂³	1	2	yes	—
45	C₂×Q₈×C₂₉	C₂³	1	1	yes	characteristic
46	Q₈×D₂₉	—	2	2	no	—
47	Q₈×D₂₉	—	2	4	no	—
48	Q₈×D₂₉	—	2	4	no	—
49	Q₈×D₂₉	D₄	1	4	yes	—
50	C₂×C₄×D₂₉	—	2	1	no	—
51	C₂×C₄×D₂₉	—	2	2	no	—
52	C₂×C₄×D₂₉	—	2	1	no	—
53	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
54	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
55	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
56	C₂×Dic₅₈	—	2	1	no	—
57	C₂×Dic₅₈	—	2	2	no	—
58	C₂×Dic₅₈	C₂³	1	2	yes	—
59	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
60	Q₁₆×C₂₉	—	2	4	no	—
61	C₂×C₈×C₂₉	C₂³	1	2	yes	—
62	C₄⋊C₄×C₂₉	—	2	1	no	—
63	C₄⋊C₄×C₂₉	—	2	1	no	—
64	C₄⋊C₄×C₂₉	—	2	1	no	—
65	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
66	C₄²×C₂₉	—	2	1	no	—
67	C₄²×C₂₉	C₂³	1	1	yes	characteristic
68	#90785	—	2	4	no	—
69	#90785	—	2	4	no	—
70	C₄⋊Dic₂₉	—	2	1	no	—
71	C₄⋊Dic₂₉	—	2	1	no	—
72	C₄⋊Dic₂₉	—	2	1	no	—
73	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
74	#90779	—	2	1	no	—
75	#90779	—	2	2	no	—
76	#90779	—	2	2	no	—
77	#90779	—	2	1	no	—
78	#90779	—	2	1	no	—
79	C₄×Dic₂₉	—	2	1	no	—
80	C₄×Dic₂₉	—	2	1	no	—
81	C₄×Dic₂₉	—	2	1	no	—
82	C₄×Dic₂₉	D₄	1	1	yes	characteristic
83	C₄×Dic₂₉	D₄	1	1	yes	characteristic
84	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
85	C₂×#6597	C₂³	1	2	yes	—
86	Dic₁₁₆	—	2	4	no	—
87	C₈×D₂₉	—	2	4	no	—
88	C₂²×D₂₉	C₂×D₄	1	1	yes	characteristic
89	Q₈×C₂₉	—	2	1	no	—
90	Q₈×C₂₉	—	2	2	no	—
91	Q₈×C₂₉	—	2	2	no	—
92	Q₈×C₂₉	C₂×D₄	1	2	yes	—
93	C₂×C₄×C₂₉	—	2	1	no	—
94	C₂×C₄×C₂₉	—	2	1	no	—
95	C₂×C₄×C₂₉	—	2	2	no	—
96	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
99	C₂×Dic₂₉	—	2	1	no	—
100	C₂×Dic₂₉	—	2	1	no	—
101	C₂×Dic₂₉	—	2	2	no	—
102	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
103	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
104	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
105	C₄×D₂₉	—	2	4	no	—
106	C₄×D₂₉	—	2	2	no	—
107	C₄×D₂₉	—	4	4	no	—
108	C₄×D₂₉	—	4	2	no	—
109	C₄×D₂₉	Q₁₆	1	4	yes	complemented
110	C₄×D₂₉	C₂×D₄	1	2	yes	—
111	C₄×D₂₉	#41	1	2	yes	—
112	Dic₅₈	—	2	1	no	—
113	Dic₅₈	—	2	4	no	—
114	Dic₅₈	—	2	2	no	—
115	Dic₅₈	—	2	2	no	—
116	Dic₅₈	—	4	4	no	—
117	Dic₅₈	C₂×D₄	1	2	yes	—
118	C₈×C₂₉	—	2	2	no	—
119	#6597	—	2	2	no	—
120	C₂×#462	—	29	1	no	maximal, Sylow
121	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
122	C₂×D₂₉	#121	1	2	yes	—
123	C₂×D₂₉	C₂×Q₁₆	1	2	yes	—
124	C₂×D₂₉	#137	1	2	yes	—
125	C₄×C₂₉	—	2	2	no	—
126	C₄×C₂₉	—	2	1	no	—
127	C₄×C₂₉	—	4	2	no	—
128	C₄×C₂₉	—	4	1	no	—
129	C₄×C₂₉	C₂×Q₁₆	1	2	yes	complemented
130	C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
131	C₄×C₂₉	C₂×#41	1	1	yes	characteristic
132	Dic₂₉	—	2	2	no	—
133	Dic₂₉	—	2	1	no	—
134	Dic₂₉	—	4	2	no	—
135	Dic₂₉	—	4	1	no	—
136	Dic₂₉	#121	1	2	yes	—
137	Dic₂₉	C₂×Q₁₆	1	2	yes	complemented
138	C₂²×Q₁₆	—	29	2	no	—
139	C₂×C₄⋊Q₈	—	29	1	no	—
140	C₂×C₄×Q₈	—	29	1	no	—
141	#462	—	29	2	no	—
142	#462	—	29	1	no	—
143	#462	—	29	1	no	—
144	#462	—	29	1	no	—
145	#462	—	29	2	no	—
146	#462	D₂₉	1	1	yes	characteristic, direct product factor
147	C₂×C₄⋊C₈	—	29	1	no	—
148	C₂×#103	—	29	2	no	—
149	C₂×C₂₉	C₂×#121	1	1	yes	characteristic
150	C₂×C₂₉	C₂²×Q₁₆	1	1	yes	characteristic
151	C₂×C₂₉	C₂×#137	1	1	yes	characteristic
152	D₂₉	#462	1	4	yes	direct product factor
153	C₂²×Q₈	—	29	1	no	—
154	C₂²×Q₈	—	29	2	no	—
155	C₂×Q₁₆	—	29	2	no	—
156	C₂×Q₁₆	—	29	2	no	—
157	C₂×Q₁₆	—	29	2	no	—
158	C₂×Q₁₆	—	58	8	no	—
159	C₂×Q₁₆	C₂×D₂₉	1	2	yes	—
160	C₂²×C₈	—	29	2	no	—
161	C₄⋊Q₈	—	29	2	no	—
162	C₄⋊Q₈	—	29	1	no	—
163	C₄⋊Q₈	—	58	1	no	—
164	C₄⋊Q₈	—	58	1	no	—
165	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
166	C₄×Q₈	—	29	1	no	—
167	C₄×Q₈	—	29	1	no	—
168	C₄×Q₈	—	29	1	no	—
169	C₄×Q₈	—	58	1	no	—
170	C₄×Q₈	—	58	1	no	—
171	C₄×Q₈	C₂×D₂₉	1	1	yes	characteristic
172	C₂×C₄⋊C₄	—	29	1	no	—
173	C₂×C₄⋊C₄	—	58	1	no	—
174	C₂×C₄⋊C₄	—	58	1	no	—
175	C₂×C₄⋊C₄	—	58	1	no	—
176	C₂×C₄²	—	29	1	no	—
177	C₂×C₄²	—	58	1	no	—
178	C₄⋊C₈	—	29	2	no	—
179	C₄⋊C₈	—	29	1	no	—
180	C₄⋊C₈	C₂×D₂₉	1	1	yes	characteristic
181	#103	—	29	2	no	—
182	#103	—	29	2	no	—
183	#103	—	29	2	no	—
184	#103	C₂×D₂₉	1	2	yes	—
185	C₂₉	C₂×#462	1	1	yes	characteristic, complemented, Sylow
186	C₂×Q₈	—	29	4	no	—
187	C₂×Q₈	—	29	1	no	—
188	C₂×Q₈	—	29	2	no	—
189	C₂×Q₈	—	58	1	no	—
190	C₂×Q₈	—	58	2	no	—
191	C₂×Q₈	—	58	2	no	—
192	C₂×Q₈	—	58	4	no	—
193	C₂×Q₈	—	58	4	no	—
194	C₂×Q₈	C₂²×D₂₉	1	2	yes	—
195	C₂×Q₈	C₂²×D₂₉	1	1	yes	characteristic
196	C₂²×C₄	—	29	1	no	—
197	C₂²×C₄	—	29	1	no	—
198	C₂²×C₄	—	29	1	no	—
199	C₂²×C₄	—	58	1	no	—
200	C₂²×C₄	—	58	1	no	—
201	C₂²×C₄	—	58	2	no	—
202	Q₁₆	—	2	4	no	—
203	Q₁₆	—	58	4	no	—
204	Q₁₆	—	58	4	no	—
205	Q₁₆	—	58	4	no	—
206	C₂×C₈	—	29	2	no	—
207	C₂×C₈	—	58	4	no	—
208	C₂×C₈	C₂²×D₂₉	1	2	yes	—
209	C₄⋊C₄	—	2	1	no	—
210	C₄⋊C₄	—	2	1	no	—
211	C₄⋊C₄	—	2	1	no	—
212	C₄⋊C₄	—	29	1	no	—
213	C₄⋊C₄	—	58	1	no	—
214	C₄⋊C₄	—	58	1	no	—
215	C₄⋊C₄	—	58	1	no	—
216	C₄⋊C₄	—	58	2	no	—
217	C₄⋊C₄	—	58	2	no	—
218	C₄⋊C₄	—	58	1	no	—
219	C₄⋊C₄	—	58	1	no	—
220	C₄⋊C₄	—	58	1	no	—
221	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
222	C₄²	—	2	1	no	—
223	C₄²	—	29	1	no	—
224	C₄²	—	29	1	no	—
225	C₄²	—	29	1	no	—
226	C₄²	—	58	1	no	—
227	C₄²	—	58	1	no	—
228	C₄²	—	58	1	no	—
229	C₄²	C₂²×D₂₉	1	1	yes	characteristic
230	C₂³	—	29	1	no	—
231	Q₈	—	2	1	no	—
232	Q₈	—	2	2	no	—
233	Q₈	—	2	2	no	—
234	Q₈	—	29	2	no	—
235	Q₈	—	58	4	no	—
236	Q₈	—	58	1	no	—
237	Q₈	—	58	2	no	—
238	Q₈	—	58	2	no	—
239	Q₈	—	116	4	no	—
240	Q₈	D₄×D₂₉	1	2	yes	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	29	1	no	—
245	C₂×C₄	—	29	1	no	—
246	C₂×C₄	—	29	2	no	—
247	C₂×C₄	—	29	2	no	—
248	C₂×C₄	—	29	4	no	—
249	C₂×C₄	—	29	1	no	—
250	C₂×C₄	—	58	2	no	—
251	C₂×C₄	—	58	4	no	—
252	C₂×C₄	—	58	1	no	—
253	C₂×C₄	—	58	1	no	—
254	C₂×C₄	—	58	2	no	—
255	C₂×C₄	—	116	4	no	—
256	C₂×C₄	—	116	2	no	—
257	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
258	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
259	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
260	C₈	—	2	2	no	—
261	C₈	—	58	2	no	—
262	C₂²	—	29	2	no	—
263	C₂²	—	29	2	no	—
264	C₂²	—	29	2	no	—
265	C₂²	C₂×D₄×D₂₉	1	1	yes	characteristic
266	C₄	—	2	2	no	—
267	C₄	—	2	1	no	—
268	C₄	—	4	2	no	—
269	C₄	—	4	1	no	—
270	C₄	—	29	2	no	—
271	C₄	—	29	2	no	—
272	C₄	—	58	2	no	—
273	C₄	—	58	1	no	—
274	C₄	—	116	2	no	—
275	C₄	—	116	1	no	—
276	C₄	Q₁₆×D₂₉	1	2	yes	complemented
277	C₄	C₂×D₄×D₂₉	1	1	yes	characteristic
278	C₄	#41×D₂₉	1	1	yes	characteristic
279	C₂	—	29	4	no	—
280	C₂	#121×D₂₉	1	1	yes	characteristic
281	C₂	C₂×Q₁₆×D₂₉	1	1	yes	characteristic
282	C₂	#137×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₂₉×#462	C₂
socle	C₂²×C₂₉	C₂²×D₄
prime radical	C₂²×D₂₉	C₂×D₄
hypercenter	#462	D₂₉
hypocenter	C₂₉	C₂×#462
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #462

Complements

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

N	H ≅ G/N	type
4. #14271374	C₂	semidirect
5. #14271373	C₂	semidirect
6. #14271372	C₂	semidirect
7. #14271371	C₂	semidirect
8. #14271370	C₂	semidirect
11. C₂₉×#462	C₂	semidirect
109. C₄×D₂₉	Q₁₆	semidirect
129. C₄×C₂₉	C₂×Q₁₆	semidirect
137. Dic₂₉	C₂×Q₁₆	semidirect
146. #462	D₂₉	direct (N × H)
152. D₂₉	#462	direct (N × H)
185. C₂₉	C₂×#462	semidirect
276. C₄	Q₁₆×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×D₂₉	2
C₄⋊Q₈×D₂₉	2
C₄×Q₈×D₂₉	2
#14271374	2
#14271373	2
#14271372	2
#14271371	2
#14271370	2
C₄⋊C₈×D₂₉	2
#103×D₂₉	2
C₂₉×#462	2
C₂×#462	29

Subgroups — D29×#462 #16828926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉×#462 #16828926