Subgroups — D₂₉×#339 #16819196

Order 3712.

488 conjugacy classes of subgroups.

The subgroup lattice has 256 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	#117×D₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×D₂₉	C₂	1	1	yes	maximal, characteristic
4	#14270924	C₂	1	1	yes	maximal, characteristic, complemented
5	#14270923	C₂	1	1	yes	maximal, characteristic, complemented
6	#14270922	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₂₉	—	2	1	no	—
9	C₂²×C₄×D₂₉	C₂²	1	1	yes	characteristic
10	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
11	C₂₉×#117	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
13	#11745288	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₂₉	—	2	1	no	—
15	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
16	C₂×#90777	C₂²	1	1	yes	characteristic
17	M₁₆×D₂₉	—	2	2	no	—
18	M₁₆×D₂₉	C₄	1	4	yes	complemented
19	C₂×#90772	—	2	1	no	—
20	C₂×C₈×D₂₉	—	2	1	no	—
21	#11745254	C₄	1	2	yes	complemented
22	C₄⋊C₄×D₂₉	C₄	1	2	yes	complemented
23	C₂²⋊C₄×D₂₉	—	2	1	no	—
24	#11745239	—	2	1	no	—
25	#11745234	—	2	1	no	—
26	C₄²×D₂₉	—	2	2	no	—
27	C₄²×D₂₉	—	2	1	no	—
28	C₄²×D₂₉	C₄	1	4	yes	complemented
29	C₂³×D₂₉	D₄	1	1	yes	characteristic
30	C₂²×C₄×C₂₉	—	2	1	no	—
31	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
32	C₂²×Dic₂₉	—	2	1	no	—
33	C₂²×Dic₂₉	D₄	1	1	yes	characteristic
34	C₂×C₄×D₂₉	—	2	8	no	—
35	C₂×C₄×D₂₉	—	2	4	no	—
36	C₂×C₄×D₂₉	—	2	2	no	—
37	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
38	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
39	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
42	C₂×C₄×D₂₉	D₄	1	2	yes	—
43	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
44	C₂×C₄×D₂₉	Q₈	1	2	yes	—
45	M₁₆×C₂₉	—	2	1	no	—
46	M₁₆×C₂₉	C₂×C₄	1	2	yes	complemented
47	C₂×C₈×C₂₉	—	2	1	no	—
48	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	complemented
49	C₂²⋊C₄×C₂₉	—	2	1	no	—
50	C₄²×C₂₉	—	2	1	no	—
51	C₄²×C₂₉	—	2	1	no	—
52	C₄²×C₂₉	C₂×C₄	1	2	yes	complemented
53	C₂²⋊Dic₂₉	—	2	1	no	—
54	#90781	—	2	2	no	—
55	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	complemented
56	#90779	—	2	2	no	—
57	C₄×Dic₂₉	—	2	1	no	—
58	C₄×Dic₂₉	—	2	1	no	—
59	C₄×Dic₂₉	—	2	4	no	—
60	C₄×Dic₂₉	—	2	2	no	—
61	C₄×Dic₂₉	C₂×C₄	1	2	yes	complemented
62	#90777	—	2	1	no	—
63	#90777	C₂×C₄	1	2	yes	complemented
64	C₂×#6597	—	2	1	no	—
65	#90772	—	2	4	no	—
66	C₈×D₂₉	—	2	4	no	—
67	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×D₂₉	—	2	4	no	—
69	C₂²×D₂₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×D₂₉	C₂²⋊C₄	1	2	yes	—
71	C₂²×D₂₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×D₂₉	C₄⋊C₄	1	2	yes	—
73	C₂×C₄×C₂₉	—	2	4	no	—
74	C₂×C₄×C₂₉	—	2	2	no	—
75	C₂×C₄×C₂₉	—	2	2	no	—
76	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
82	C₂×Dic₂₉	—	2	4	no	—
83	C₂×Dic₂₉	—	2	2	no	—
84	C₂×Dic₂₉	—	2	2	no	—
85	C₂×Dic₂₉	C₂²⋊C₄	1	2	yes	—
86	C₂×Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
89	C₄×D₂₉	—	2	16	no	—
90	C₄×D₂₉	—	4	4	no	—
91	C₄×D₂₉	C₄²	1	2	yes	—
92	C₄×D₂₉	C₄²	1	2	yes	—
93	C₄×D₂₉	C₂²⋊C₄	1	2	yes	—
94	C₄×D₂₉	C₂²⋊C₄	1	2	yes	—
95	C₄×D₂₉	C₄⋊C₄	1	2	yes	—
96	C₄×D₂₉	C₄⋊C₄	1	2	yes	—
97	C₄×D₂₉	C₄⋊C₄	1	2	yes	—
98	C₄×D₂₉	C₄⋊C₄	1	2	yes	—
99	C₈×C₂₉	—	2	2	no	—
100	#6597	—	2	2	no	—
101	C₂×#339	—	29	1	no	maximal, Sylow
102	C₂²×C₂₉	—	2	2	no	—
103	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂×D₂₉	—	2	2	no	—
107	C₂×D₂₉	—	2	4	no	—
108	C₂×D₂₉	—	2	4	no	—
109	C₂×D₂₉	#95	1	2	yes	—
110	C₂×D₂₉	#95	1	2	yes	—
111	C₂×D₂₉	#104	1	4	yes	—
112	C₄×C₂₉	—	2	4	no	—
113	C₄×C₂₉	—	4	2	no	—
114	C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
115	C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
116	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
117	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
118	Dic₂₉	—	2	4	no	—
119	Dic₂₉	—	4	2	no	—
120	Dic₂₉	#95	1	2	yes	—
121	Dic₂₉	#95	1	2	yes	—
122	C₂²×M₁₆	—	29	1	no	—
123	C₂×#117	—	29	1	no	—
124	C₂²×C₄²	—	29	1	no	—
125	#339	—	29	1	no	—
126	#339	—	29	1	no	—
127	#339	—	29	1	no	—
128	#339	D₂₉	1	1	yes	characteristic, direct product factor
129	C₂×C₂₉	—	2	1	no	—
130	C₂×C₂₉	—	2	1	no	—
131	C₂×C₂₉	C₂×#95	1	1	yes	characteristic
132	C₂×C₂₉	C₂×#104	1	2	yes	—
133	D₂₉	—	2	2	no	—
134	D₂₉	#339	1	4	yes	direct product factor
135	C₂³×C₄	—	29	1	no	—
136	C₂³×C₄	—	58	1	no	—
137	C₂×M₁₆	—	29	1	no	—
138	C₂×M₁₆	—	29	4	no	—
139	C₂×M₁₆	—	58	1	no	—
140	C₂×M₁₆	—	58	2	no	—
141	C₂×M₁₆	C₂×D₂₉	1	1	yes	characteristic
142	C₂²×C₈	—	58	1	no	—
143	#117	—	29	1	no	—
144	#117	—	29	2	no	—
145	#117	—	58	1	no	—
146	#117	—	58	1	no	—
147	#117	C₂×D₂₉	1	1	yes	characteristic
148	C₂×C₄⋊C₄	—	29	2	no	—
149	C₂×C₂²⋊C₄	—	58	1	no	—
150	C₂×C₄²	—	29	1	no	—
151	C₂×C₄²	—	29	4	no	—
152	C₂×C₄²	—	58	1	no	—
153	C₂×C₄²	—	58	2	no	—
154	C₂×C₄²	—	58	1	no	—
155	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
156	C₂₉	C₂×#339	1	1	yes	characteristic, complemented, Sylow
157	C₂⁴	—	29	1	no	—
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	29	1	no	—
160	C₂²×C₄	—	29	2	no	—
161	C₂²×C₄	—	29	1	no	—
162	C₂²×C₄	—	29	1	no	—
163	C₂²×C₄	—	29	2	no	—
164	C₂²×C₄	—	29	2	no	—
165	C₂²×C₄	—	29	1	no	—
166	C₂²×C₄	—	29	1	no	—
167	C₂²×C₄	—	29	2	no	—
168	C₂²×C₄	—	58	4	no	—
169	C₂²×C₄	—	58	8	no	—
170	C₂²×C₄	—	58	2	no	—
171	C₂²×C₄	—	58	1	no	—
172	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
173	M₁₆	—	2	1	no	—
174	M₁₆	—	29	2	no	—
175	M₁₆	—	58	4	no	—
176	M₁₆	—	58	1	no	—
177	M₁₆	C₄×D₂₉	1	2	yes	complemented
178	C₂×C₈	—	2	1	no	—
179	C₂×C₈	—	58	4	no	—
180	C₂×C₈	—	58	1	no	—
181	C₄⋊C₄	—	29	2	no	—
182	C₄⋊C₄	—	58	2	no	—
183	C₄⋊C₄	C₄×D₂₉	1	2	yes	complemented
184	C₂²⋊C₄	—	2	1	no	—
185	C₂²⋊C₄	—	58	2	no	—
186	C₂²⋊C₄	—	58	1	no	—
187	C₄²	—	2	1	no	—
188	C₄²	—	2	1	no	—
189	C₄²	—	29	2	no	—
190	C₄²	—	58	4	no	—
191	C₄²	—	58	2	no	—
192	C₄²	—	58	1	no	—
193	C₄²	—	58	1	no	—
194	C₄²	C₄×D₂₉	1	2	yes	complemented
195	C₂³	—	29	1	no	—
196	C₂³	—	29	1	no	—
197	C₂³	—	29	2	no	—
198	C₂³	—	29	2	no	—
199	C₂³	—	58	4	no	—
200	C₂³	D₄×D₂₉	1	1	yes	characteristic
201	C₂×C₄	—	2	4	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	29	2	no	—
205	C₂×C₄	—	29	1	no	—
206	C₂×C₄	—	29	1	no	—
207	C₂×C₄	—	29	2	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	2	no	—
213	C₂×C₄	—	29	2	no	—
214	C₂×C₄	—	29	2	no	—
215	C₂×C₄	—	29	2	no	—
216	C₂×C₄	—	58	16	no	—
217	C₂×C₄	—	58	4	no	—
218	C₂×C₄	—	58	2	no	—
219	C₂×C₄	—	58	2	no	—
220	C₂×C₄	—	116	4	no	—
221	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
222	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
223	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
224	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
225	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
226	C₂×C₄	Q₈×D₂₉	1	1	yes	characteristic
227	C₈	—	2	2	no	—
228	C₈	—	58	2	no	—
229	C₂²	—	2	2	no	—
230	C₂²	—	29	2	no	—
231	C₂²	—	29	4	no	—
232	C₂²	—	29	2	no	—
233	C₂²	—	58	4	no	—
234	C₂²	—	58	4	no	—
235	C₂²	—	58	2	no	—
236	C₂²	C₂²⋊C₄×D₂₉	1	1	yes	characteristic
237	C₂²	C₂²⋊C₄×D₂₉	1	1	yes	characteristic
238	C₂²	C₄⋊C₄×D₂₉	1	1	yes	characteristic
239	C₄	—	2	4	no	—
240	C₄	—	4	2	no	—
241	C₄	—	29	2	no	—
242	C₄	—	29	2	no	—
243	C₄	—	58	4	no	—
244	C₄	—	116	2	no	—
245	C₄	C₄²×D₂₉	1	1	yes	characteristic
246	C₄	C₂²⋊C₄×D₂₉	1	1	yes	characteristic
247	C₄	C₄⋊C₄×D₂₉	1	1	yes	characteristic
248	C₄	C₄⋊C₄×D₂₉	1	1	yes	characteristic
249	C₂	—	2	1	no	—
250	C₂	—	2	1	no	—
251	C₂	—	29	4	no	—
252	C₂	—	58	2	no	—
253	C₂	#95×D₂₉	1	1	yes	characteristic
254	C₂	#104×D₂₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₄×D₂₉
commutator	C₄×C₂₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#339	C₂
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₂₉	D₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#339	D₂₉
hypocenter	C₂₉	C₂×#339
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #339

Complements

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

N	H ≅ G/N	type
4. #14270924	C₂	semidirect
5. #14270923	C₂	semidirect
6. #14270922	C₂	semidirect
7. C₂₉×#339	C₂	semidirect
18. M₁₆×D₂₉	C₄	semidirect
21. #11745254	C₄	semidirect
22. C₄⋊C₄×D₂₉	C₄	semidirect
28. C₄²×D₂₉	C₄	semidirect
46. M₁₆×C₂₉	C₂×C₄	semidirect
48. C₄⋊C₄×C₂₉	C₂×C₄	semidirect
52. C₄²×C₂₉	C₂×C₄	semidirect
55. C₄⋊Dic₂₉	C₂×C₄	semidirect
61. C₄×Dic₂₉	C₂×C₄	semidirect
63. #90777	C₂×C₄	semidirect
128. #339	D₂₉	direct (N × H)
134. D₂₉	#339	direct (N × H)
156. C₂₉	C₂×#339	semidirect
177. M₁₆	C₄×D₂₉	semidirect
183. C₄⋊C₄	C₄×D₂₉	semidirect
194. C₄²	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
#117×D₂₉	2
C₂×C₄²×D₂₉	2
#14270924	2
#14270923	2
#14270922	2
C₂₉×#339	2
C₂×#339	29

Subgroups — D29×#339 #16819196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉×#339 #16819196