Subgroups — D₂₉×#405 #16827902

Order 3712.

592 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
3	#117×D₂₉	C₂	1	1	yes	maximal, characteristic
4	#14271121	C₂	1	1	yes	maximal, characteristic, complemented
5	#14271120	C₂	1	2	yes	maximal, complemented
6	#14271119	C₂	1	1	yes	maximal, characteristic, complemented
7	#14271118	C₂	1	1	yes	maximal, characteristic, complemented
8	#14271117	C₂	1	2	yes	maximal, complemented
9	#97×D₂₉	C₂	1	2	yes	maximal, complemented
10	C₄×C₈×D₂₉	C₂	1	2	yes	maximal, complemented
11	C₂₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₄×D₂₉	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
15	C₂₉×#117	C₂²	1	1	yes	characteristic
16	#11745288	C₂²	1	1	yes	characteristic
17	C₂×#90777	C₂²	1	1	yes	characteristic
18	C₂²×#6597	C₂²	1	1	yes	characteristic
19	M₁₆×D₂₉	C₄	1	8	yes	complemented
20	C₂×#90772	C₂²	1	2	yes	—
21	C₂×C₈×D₂₉	C₄	1	8	yes	complemented
22	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
23	C₂×C₈×D₂₉	C₂²	1	2	yes	—
24	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
25	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
26	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
27	#11745254	C₄	1	2	yes	—
28	C₄⋊C₄×D₂₉	C₄	1	2	yes	—
29	C₂²⋊C₄×D₂₉	C₄	1	2	yes	—
30	#11745239	C₄	1	2	yes	—
31	#11745234	C₂²	1	2	yes	—
32	C₄²×D₂₉	C₂²	1	2	yes	—
33	C₂₉×#97	C₂²	1	2	yes	complemented
34	C₄×C₈×C₂₉	C₂²	1	2	yes	complemented
35	#11745163	C₂²	1	2	yes	complemented
36	#11745163	C₂²	1	2	yes	complemented
37	C₈×Dic₂₉	C₂²	1	2	yes	complemented
38	C₈×Dic₂₉	C₂²	1	2	yes	complemented
39	#11745151	C₂²	1	2	yes	complemented
40	C₄×#6597	C₂²	1	2	yes	complemented
41	C₂³×D₂₉	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
43	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×D₂₉	C₂×C₄	1	4	yes	—
45	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×D₂₉	C₂×C₄	1	4	yes	—
48	C₂×C₄×D₂₉	C₂×C₄	1	4	yes	—
49	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
50	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
51	M₁₆×C₂₉	C₂×C₄	1	4	yes	complemented
52	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	complemented
53	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
54	C₂×C₈×C₂₉	C₂³	1	2	yes	—
55	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
56	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
57	C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
58	C₄²×C₂₉	C₂³	1	2	yes	—
59	C₂²⋊Dic₂₉	C₂×C₄	1	2	yes	—
60	#90781	C₂×C₄	1	4	yes	—
61	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
62	#90779	C₂×C₄	1	4	yes	—
63	C₄×Dic₂₉	C₂×C₄	1	4	yes	—
64	C₄×Dic₂₉	C₂³	1	2	yes	—
65	#90777	C₂×C₄	1	4	yes	complemented
66	C₂×#6597	C₂×C₄	1	4	yes	complemented
67	C₂×#6597	C₂³	1	1	yes	characteristic
68	C₂×#6597	C₂³	1	1	yes	characteristic
69	C₂×#6597	C₂³	1	2	yes	—
70	#90772	C₂×C₄	1	8	yes	complemented
71	C₈×D₂₉	C₂×C₄	1	4	yes	—
72	C₈×D₂₉	C₂×C₄	1	4	yes	—
73	C₈×D₂₉	C₂×C₄	1	8	yes	—
74	C₈×D₂₉	C₂×C₄	1	4	yes	complemented
75	C₈×D₂₉	C₂×C₄	1	4	yes	complemented
76	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
77	C₂²×D₂₉	—	2	4	no	—
78	C₂²×D₂₉	C₄²	1	4	yes	—
79	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
82	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
84	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
85	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
86	C₂×Dic₂₉	C₄²	1	4	yes	—
87	C₂×Dic₂₉	C₂²×C₄	1	4	yes	—
88	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
89	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
90	C₄×D₂₉	—	2	8	no	—
91	C₄×D₂₉	C₄²	1	4	yes	—
92	C₄×D₂₉	C₄²	1	4	yes	—
93	C₄×D₂₉	C₂²×C₄	1	2	yes	—
94	C₄×D₂₉	C₂²×C₄	1	2	yes	—
95	C₄×D₂₉	C₂²×C₄	1	2	yes	—
96	C₄×D₂₉	C₂²×C₄	1	2	yes	—
97	C₈×C₂₉	C₂²×C₄	1	2	yes	—
98	C₈×C₂₉	C₂²×C₄	1	2	yes	—
99	C₈×C₂₉	C₂²×C₄	1	4	yes	—
100	#6597	C₂²×C₄	1	2	yes	—
101	#6597	C₂²×C₄	1	2	yes	—
102	#6597	C₂²×C₄	1	4	yes	—
103	C₂×#405	—	29	1	no	maximal, Sylow
104	C₂²×C₂₉	—	2	2	no	—
105	C₂²×C₂₉	C₂×C₄²	1	2	yes	—
106	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
107	C₂×D₂₉	—	2	2	no	—
108	C₂×D₂₉	—	2	8	no	—
109	C₂×D₂₉	C₂×C₄²	1	2	yes	—
110	C₂×D₂₉	C₂×C₄²	1	2	yes	—
111	C₂×D₂₉	#131	1	4	yes	—
112	C₄×C₂₉	—	2	4	no	—
113	C₄×C₂₉	C₂×C₄²	1	2	yes	—
114	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
115	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
116	Dic₂₉	—	2	4	no	—
117	Dic₂₉	C₂×C₄²	1	2	yes	—
118	Dic₂₉	C₂×C₄²	1	2	yes	—
119	C₂²×M₁₆	—	29	1	no	—
120	C₂³×C₈	—	29	1	no	—
121	C₂×#117	—	29	1	no	—
122	#405	—	29	1	no	—
123	#405	—	29	1	no	—
124	#405	—	29	1	no	—
125	#405	—	29	2	no	—
126	#405	—	29	2	no	—
127	#405	D₂₉	1	1	yes	characteristic, direct product factor
128	C₂×#97	—	29	2	no	—
129	C₂×C₄×C₈	—	29	2	no	—
130	C₂×C₂₉	—	2	2	no	—
131	C₂×C₂₉	C₂²×C₄²	1	1	yes	characteristic
132	C₂×C₂₉	C₂×#131	1	2	yes	—
133	D₂₉	—	2	2	no	—
134	D₂₉	#405	1	4	yes	direct product factor
135	C₂³×C₄	—	29	1	no	—
136	C₂×M₁₆	—	29	1	no	—
137	C₂×M₁₆	—	29	8	no	—
138	C₂×M₁₆	—	29	2	no	—
139	C₂×M₁₆	C₂×D₂₉	1	1	yes	characteristic
140	C₂²×C₈	—	29	1	no	—
141	C₂²×C₈	—	29	8	no	—
142	C₂²×C₈	—	29	1	no	—
143	C₂²×C₈	—	29	1	no	—
144	C₂²×C₈	—	29	2	no	—
145	C₂²×C₈	—	29	1	no	—
146	C₂²×C₈	—	29	1	no	—
147	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
148	#117	—	29	1	no	—
149	#117	—	29	2	no	—
150	#117	—	29	2	no	—
151	#117	—	29	2	no	—
152	#117	C₂×D₂₉	1	1	yes	characteristic
153	C₂×C₄⋊C₄	—	29	2	no	—
154	C₂×C₂²⋊C₄	—	29	2	no	—
155	C₂×C₄²	—	29	2	no	—
156	#97	—	29	2	no	—
157	#97	—	29	2	no	—
158	#97	—	29	2	no	—
159	#97	C₂×D₂₉	1	2	yes	complemented
160	C₄×C₈	—	29	2	no	—
161	C₄×C₈	—	29	2	no	—
162	C₄×C₈	—	29	2	no	—
163	C₄×C₈	C₂×D₂₉	1	2	yes	complemented
164	C₂₉	C₂×#405	1	1	yes	characteristic, complemented, Sylow
165	C₂⁴	—	29	1	no	—
166	C₂²×C₄	—	29	1	no	—
167	C₂²×C₄	—	29	1	no	—
168	C₂²×C₄	—	29	1	no	—
169	C₂²×C₄	—	29	4	no	—
170	C₂²×C₄	—	29	4	no	—
171	C₂²×C₄	—	29	1	no	—
172	C₂²×C₄	—	29	1	no	—
173	C₂²×C₄	—	29	4	no	—
174	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
175	M₁₆	—	29	4	no	—
176	M₁₆	—	29	8	no	—
177	M₁₆	C₄×D₂₉	1	4	yes	complemented
178	C₂×C₈	—	29	4	no	—
179	C₂×C₈	—	29	1	no	—
180	C₂×C₈	—	29	2	no	—
181	C₂×C₈	—	29	1	no	—
182	C₂×C₈	—	29	4	no	—
183	C₂×C₈	—	29	4	no	—
184	C₂×C₈	—	29	4	no	—
185	C₂×C₈	—	29	4	no	—
186	C₂×C₈	—	29	8	no	—
187	C₂×C₈	C₄×D₂₉	1	4	yes	complemented
188	C₂×C₈	C₂²×D₂₉	1	2	yes	—
189	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
190	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
191	C₄⋊C₄	—	29	4	no	—
192	C₄⋊C₄	—	29	2	no	—
193	C₄⋊C₄	C₄×D₂₉	1	2	yes	—
194	C₂²⋊C₄	—	29	2	no	—
195	C₂²⋊C₄	—	29	4	no	—
196	C₂²⋊C₄	C₄×D₂₉	1	2	yes	—
197	C₄²	—	29	4	no	—
198	C₄²	—	29	2	no	—
199	C₄²	C₂²×D₂₉	1	2	yes	—
200	C₂³	—	29	1	no	—
201	C₂³	—	29	1	no	—
202	C₂³	—	29	4	no	—
203	C₂³	—	58	4	no	—
204	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
205	C₂×C₄	—	29	1	no	—
206	C₂×C₄	—	29	1	no	—
207	C₂×C₄	—	29	4	no	—
208	C₂×C₄	—	29	2	no	—
209	C₂×C₄	—	29	2	no	—
210	C₂×C₄	—	29	2	no	—
211	C₂×C₄	—	29	2	no	—
212	C₂×C₄	—	29	4	no	—
213	C₂×C₄	—	29	4	no	—
214	C₂×C₄	—	29	4	no	—
215	C₂×C₄	—	58	8	no	—
216	C₂×C₄	C₂×C₄×D₂₉	1	4	yes	—
217	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
218	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
219	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
220	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
221	C₈	—	29	2	no	—
222	C₈	—	29	2	no	—
223	C₈	—	29	4	no	—
224	C₈	C₂×C₄×D₂₉	1	2	yes	—
225	C₈	C₂×C₄×D₂₉	1	2	yes	—
226	C₈	C₂×C₄×D₂₉	1	4	yes	—
227	C₂²	—	2	2	no	—
228	C₂²	—	29	2	no	—
229	C₂²	—	29	4	no	—
230	C₂²	—	29	2	no	—
231	C₂²	—	58	8	no	—
232	C₂²	—	58	2	no	—
233	C₂²	C₄²×D₂₉	1	2	yes	—
234	C₂²	C₂²×C₄×D₂₉	1	1	yes	characteristic
235	C₄	—	2	4	no	—
236	C₄	—	29	2	no	—
237	C₄	—	29	2	no	—
238	C₄	—	58	4	no	—
239	C₄	C₄²×D₂₉	1	2	yes	—
240	C₄	C₂²×C₄×D₂₉	1	1	yes	characteristic
241	C₄	C₂²×C₄×D₂₉	1	1	yes	characteristic
242	C₂	—	2	2	no	—
243	C₂	—	29	4	no	—
244	C₂	—	58	2	no	—
245	C₂	C₂×C₄²×D₂₉	1	1	yes	characteristic
246	C₂	#131×D₂₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂²×D₂₉
commutator	C₂×C₂₉	C₂²×C₄²
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₂₉×#405	C₂
socle	C₂²×C₂₉	C₂³×C₄
prime radical	C₂³×D₂₉	C₂×C₄
cosocle	C₂×C₄×C₂₉	C₂⁴
hypercenter	#405	D₂₉
hypocenter	C₂₉	C₂×#405
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
4. #14271121	C₂	semidirect
5. #14271120	C₂	semidirect
6. #14271119	C₂	semidirect
7. #14271118	C₂	semidirect
8. #14271117	C₂	semidirect
9. #97×D₂₉	C₂	semidirect
10. C₄×C₈×D₂₉	C₂	semidirect
11. C₂₉×#405	C₂	semidirect
19. M₁₆×D₂₉	C₄	semidirect
21. C₂×C₈×D₂₉	C₄	semidirect
33. C₂₉×#97	C₂²	semidirect
34. C₄×C₈×C₂₉	C₂²	semidirect
35. #11745163	C₂²	semidirect
36. #11745163	C₂²	semidirect
37. C₈×Dic₂₉	C₂²	semidirect
38. C₈×Dic₂₉	C₂²	semidirect
39. #11745151	C₂²	semidirect
40. C₄×#6597	C₂²	semidirect
51. M₁₆×C₂₉	C₂×C₄	semidirect
52. C₂×C₈×C₂₉	C₂×C₄	semidirect
65. #90777	C₂×C₄	semidirect
66. C₂×#6597	C₂×C₄	semidirect
70. #90772	C₂×C₄	semidirect
74. C₈×D₂₉	C₂×C₄	semidirect
75. C₈×D₂₉	C₂×C₄	semidirect
127. #405	D₂₉	direct (N × H)
134. D₂₉	#405	direct (N × H)
159. #97	C₂×D₂₉	semidirect
163. C₄×C₈	C₂×D₂₉	semidirect
164. C₂₉	C₂×#405	semidirect
177. M₁₆	C₄×D₂₉	semidirect
187. C₂×C₈	C₄×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×D₂₉	2
C₂²×C₈×D₂₉	2
#117×D₂₉	2
#14271121	2
#14271120	2
#14271119	2
#14271118	2
#14271117	2
#97×D₂₉	2
C₄×C₈×D₂₉	2
C₂₉×#405	2
C₂×#405	29

Subgroups — D29×#405 #16827902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉×#405 #16827902