Subgroups — C₂₉×#28732 #20323632

Order 7424.

698 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3141	C₂	1	2	yes	maximal
3	C₂₉×#2931	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2079	C₂	1	4	yes	maximal, complemented
5	C₂₉×#1997	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1815	C₂	1	4	yes	maximal, complemented
7	C₄×C₂₉×#108	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₉×#131	C₂²	1	2	yes	—
9	C₂₉×#532	C₂²	1	1	yes	characteristic
10	C₂×C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
11	C₂₉×#498	—	2	2	no	—
12	C₂₉×#498	—	2	2	no	—
13	C₂₉×#489	—	2	4	no	—
14	C₂₉×#487	—	2	2	no	—
15	C₂₉×#486	—	2	2	no	—
16	C₂₉×#436	—	2	2	no	—
17	C₈×D₄×C₂₉	—	2	2	no	—
18	C₂×C₂₉×#108	C₂²	1	2	yes	—
19	C₂×C₂₉×#106	C₂²	1	2	yes	—
20	C₂×C₂₉×#106	C₂²	1	2	yes	—
21	C₂₉×#423	C₂²	1	1	yes	characteristic
22	C₂₉×#417	C₂²	1	8	yes	—
23	C₂₉×#408	C₂²	1	2	yes	—
24	C₄×M₁₆×C₂₉	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
26	C₂₉×#343	C₂²	1	8	yes	—
27	C₂₉×#341	C₂²	1	2	yes	—
28	C₂×#41×C₂₉	C₂³	1	2	yes	—
29	C₂²×Q₈×C₂₉	—	2	2	no	—
30	C₂₉×#131	—	2	8	no	—
31	C₂×M₁₆×C₂₉	—	2	2	no	—
32	C₂×M₁₆×C₂₉	C₂³	1	4	yes	—
33	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
34	C₂²×C₈×C₂₉	—	2	2	no	—
35	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
37	C₂₉×C₄⋊Q₈	—	2	2	no	—
38	C₂₉×C₄⋊Q₈	—	2	2	no	—
39	C₂₉×C₄⋊Q₈	—	2	2	no	—
40	C₂₉×C₄⋊Q₈	—	2	2	no	—
41	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
42	C₂₉×#127	D₄	1	1	yes	characteristic
43	C₂₉×#124	D₄	1	2	yes	—
44	C₂₉×#121	—	2	2	no	—
45	C₄×D₄×C₂₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
48	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
49	C₂₉×#108	—	2	4	no	—
50	C₂₉×#106	—	2	4	no	—
51	C₂₉×#106	—	2	2	no	—
52	C₂₉×#106	—	2	2	no	—
53	C₂₉×C₄⋊C₈	—	2	2	no	—
54	C₂₉×#103	—	2	8	no	—
55	C₂₉×#102	—	2	8	no	—
56	C₂₉×C₂²⋊C₈	—	2	4	no	—
57	C₂₉×#97	—	2	2	no	—
58	C₄×C₈×C₂₉	—	2	2	no	—
59	C₄×C₈×C₂₉	D₄	1	2	yes	—
60	C₄×C₈×C₂₉	D₄	1	2	yes	—
61	#41×C₂₉	—	2	4	no	—
62	#41×C₂₉	—	2	4	no	—
63	C₂×Q₈×C₂₉	—	4	2	no	—
64	C₂×Q₈×C₂₉	—	4	2	no	—
65	C₂×Q₈×C₂₉	—	8	4	no	—
66	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
67	C₂×D₄×C₂₉	—	2	2	no	—
68	C₂×D₄×C₂₉	—	2	2	no	—
69	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
70	C₂²×C₄×C₂₉	—	2	2	no	—
71	C₂²×C₄×C₂₉	—	2	4	no	—
72	C₂²×C₄×C₂₉	#41	1	2	yes	—
73	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
74	M₁₆×C₂₉	—	2	4	no	—
75	M₁₆×C₂₉	—	2	4	no	—
76	M₁₆×C₂₉	—	2	4	no	—
77	M₁₆×C₂₉	—	4	4	no	—
78	C₂×C₈×C₂₉	—	2	2	no	—
79	C₂×C₈×C₂₉	—	2	2	no	—
80	C₂×C₈×C₂₉	—	2	4	no	—
81	C₂×C₈×C₂₉	—	4	4	no	—
82	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
83	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
84	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
85	C₂×C₈×C₂₉	#41	1	4	yes	—
86	C₄⋊C₄×C₂₉	—	2	2	no	—
87	C₄⋊C₄×C₂₉	—	2	4	no	—
88	C₄⋊C₄×C₂₉	—	2	4	no	—
89	C₄⋊C₄×C₂₉	—	4	2	no	—
90	C₄⋊C₄×C₂₉	—	4	2	no	—
91	C₂²⋊C₄×C₂₉	—	2	4	no	—
92	C₄²×C₂₉	C₂×D₄	1	2	yes	—
93	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
94	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
95	#28732	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂³×C₂₉	—	2	2	no	—
97	C₂³×C₂₉	C₂×#41	1	1	yes	characteristic
98	Q₈×C₂₉	—	2	4	no	—
99	Q₈×C₂₉	—	8	4	no	—
100	Q₈×C₂₉	—	8	4	no	—
101	D₄×C₂₉	—	2	4	no	—
102	D₄×C₂₉	—	4	4	no	—
103	D₄×C₂₉	—	4	4	no	—
104	C₂×C₄×C₂₉	—	2	4	no	—
105	C₂×C₄×C₂₉	—	2	2	no	—
106	C₂×C₄×C₂₉	—	4	2	no	—
107	C₂×C₄×C₂₉	—	4	2	no	—
108	C₂×C₄×C₂₉	—	4	4	no	—
109	C₂×C₄×C₂₉	—	8	4	no	—
110	C₂×C₄×C₂₉	#121	1	2	yes	—
111	C₂×C₄×C₂₉	#121	1	2	yes	—
112	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
113	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
114	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
115	C₂×C₄×C₂₉	2₋¹⁺⁴	1	2	yes	—
116	C₈×C₂₉	—	2	2	no	—
117	C₈×C₂₉	—	4	2	no	—
118	C₈×C₂₉	—	4	4	no	—
119	C₈×C₂₉	#124	1	2	yes	—
120	C₈×C₂₉	#124	1	2	yes	—
121	C₂×#498	C₂×C₂₉	1	1	yes	characteristic, complemented
122	#3141	C₂×C₂₉	1	2	yes	—
123	#2931	C₂×C₂₉	1	1	yes	characteristic
124	#2079	C₂×C₂₉	1	4	yes	complemented
125	#1997	C₂×C₂₉	1	2	yes	complemented
126	#1815	C₂×C₂₉	1	4	yes	complemented
127	C₄×#108	C₂×C₂₉	1	1	yes	characteristic, complemented
128	C₂²×C₂₉	—	2	2	no	—
129	C₂²×C₂₉	—	4	2	no	—
130	C₂²×C₂₉	—	4	4	no	—
131	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
132	C₂²×C₂₉	#556	1	2	yes	—
133	C₄×C₂₉	—	2	2	no	—
134	C₄×C₂₉	—	4	2	no	—
135	C₄×C₂₉	—	8	4	no	—
136	C₄×C₂₉	#471	1	4	yes	—
137	C₄×C₂₉	C₂×#124	1	1	yes	characteristic
138	C₄×C₂₉	#536	1	1	yes	characteristic
139	C₄×C₂₉	#547	1	2	yes	—
140	C₂×#131	C₂²×C₂₉	1	2	yes	—
141	#532	C₂²×C₂₉	1	1	yes	characteristic
142	C₂×C₄⋊Q₈	C₂²×C₂₉	1	2	yes	—
143	#498	—	2	2	no	—
144	#498	—	2	2	no	—
145	#489	—	2	4	no	—
146	#487	—	2	2	no	—
147	#486	—	2	2	no	—
148	#436	—	2	2	no	—
149	C₈×D₄	—	2	2	no	—
150	C₂×#108	C₂²×C₂₉	1	2	yes	—
151	C₂×#106	C₂²×C₂₉	1	2	yes	—
152	C₂×#106	C₂²×C₂₉	1	2	yes	—
153	#423	C₂²×C₂₉	1	1	yes	characteristic
154	#417	C₂²×C₂₉	1	8	yes	—
155	#408	C₂²×C₂₉	1	2	yes	—
156	C₄×M₁₆	C₂²×C₂₉	1	2	yes	—
157	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
158	#343	C₂²×C₂₉	1	8	yes	—
159	#341	C₂²×C₂₉	1	2	yes	—
160	C₂×C₂₉	—	2	2	no	—
161	C₂×C₂₉	—	8	2	no	—
162	C₂×C₂₉	#2547	1	1	yes	characteristic
163	C₂×C₂₉	C₂×#471	1	2	yes	—
164	C₂×#41	C₂³×C₂₉	1	2	yes	—
165	C₂²×Q₈	—	2	2	no	—
166	#131	—	2	8	no	—
167	C₂×M₁₆	—	2	2	no	—
168	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
169	C₂×M₁₆	C₂³×C₂₉	1	4	yes	—
170	C₂²×C₈	—	2	2	no	—
171	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
172	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
173	C₄⋊Q₈	—	2	2	no	—
174	C₄⋊Q₈	—	2	2	no	—
175	C₄⋊Q₈	—	2	2	no	—
176	C₄⋊Q₈	—	2	2	no	—
177	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
178	#127	D₄×C₂₉	1	1	yes	characteristic
179	#124	D₄×C₂₉	1	2	yes	—
180	#121	—	2	2	no	—
181	C₄×D₄	—	2	2	no	—
182	C₂×C₄⋊C₄	—	2	2	no	—
183	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
184	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
185	#108	—	2	4	no	—
186	#106	—	2	4	no	—
187	#106	—	2	2	no	—
188	#106	—	2	2	no	—
189	C₄⋊C₈	—	2	2	no	—
190	#103	—	2	8	no	—
191	#102	—	2	8	no	—
192	C₂²⋊C₈	—	2	4	no	—
193	#97	—	2	2	no	—
194	C₄×C₈	—	2	2	no	—
195	C₄×C₈	D₄×C₂₉	1	2	yes	—
196	C₄×C₈	D₄×C₂₉	1	2	yes	—
197	C₂₉	#28732	1	1	yes	characteristic, direct product factor, Sylow
198	#41	—	2	4	no	—
199	#41	—	2	4	no	—
200	C₂×Q₈	—	4	2	no	—
201	C₂×Q₈	—	4	2	no	—
202	C₂×Q₈	—	8	4	no	—
203	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
204	C₂×D₄	—	2	2	no	—
205	C₂×D₄	—	2	2	no	—
206	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
207	C₂²×C₄	—	2	2	no	—
208	C₂²×C₄	—	2	4	no	—
209	C₂²×C₄	#41×C₂₉	1	2	yes	—
210	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
211	M₁₆	—	2	4	no	—
212	M₁₆	—	2	4	no	—
213	M₁₆	—	2	4	no	—
214	M₁₆	—	4	4	no	—
215	C₂×C₈	—	2	2	no	—
216	C₂×C₈	—	2	4	no	—
217	C₂×C₈	—	2	2	no	—
218	C₂×C₈	—	4	4	no	—
219	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
220	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
221	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
222	C₂×C₈	#41×C₂₉	1	4	yes	—
223	C₄⋊C₄	—	2	2	no	—
224	C₄⋊C₄	—	2	4	no	—
225	C₄⋊C₄	—	2	4	no	—
226	C₄⋊C₄	—	4	2	no	—
227	C₄⋊C₄	—	4	2	no	—
228	C₂²⋊C₄	—	2	4	no	—
229	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
230	C₄²	C₂×D₄×C₂₉	1	2	yes	—
231	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
232	C₂³	—	2	2	no	—
233	C₂³	C₂×#41×C₂₉	1	1	yes	characteristic
234	Q₈	—	2	4	no	—
235	Q₈	—	8	4	no	—
236	Q₈	—	8	4	no	—
237	D₄	—	2	4	no	—
238	D₄	—	4	4	no	—
239	D₄	—	4	4	no	—
240	C₂×C₄	—	2	4	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	4	2	no	—
243	C₂×C₄	—	4	2	no	—
244	C₂×C₄	—	4	4	no	—
245	C₂×C₄	—	8	4	no	—
246	C₂×C₄	C₂₉×#121	1	2	yes	—
247	C₂×C₄	C₂₉×#121	1	2	yes	—
248	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
249	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
250	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
251	C₂×C₄	C₂₉×2₋¹⁺⁴	1	2	yes	—
252	C₈	—	2	2	no	—
253	C₈	—	4	2	no	—
254	C₈	—	4	4	no	—
255	C₈	C₂₉×#124	1	2	yes	—
256	C₈	C₂₉×#124	1	2	yes	—
257	C₂²	—	2	2	no	—
258	C₂²	—	4	2	no	—
259	C₂²	—	4	4	no	—
260	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
261	C₂²	C₂₉×#556	1	2	yes	—
262	C₄	—	2	2	no	—
263	C₄	—	4	2	no	—
264	C₄	—	8	4	no	—
265	C₄	C₂₉×#471	1	4	yes	—
266	C₄	C₂×C₂₉×#124	1	1	yes	characteristic
267	C₄	C₂₉×#536	1	1	yes	characteristic
268	C₄	C₂₉×#547	1	2	yes	—
269	C₂	—	2	2	no	—
270	C₂	—	8	2	no	—
271	C₂	C₂₉×#2547	1	1	yes	characteristic
272	C₂	C₂×C₂₉×#471	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂₉×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#498	C₂	semidirect
4. C₂₉×#2079	C₂	semidirect
5. C₂₉×#1997	C₂	semidirect
6. C₂₉×#1815	C₂	semidirect
7. C₄×C₂₉×#108	C₂	semidirect
95. #28732	C₂₉	direct (N × H)
121. C₂×#498	C₂×C₂₉	semidirect
124. #2079	C₂×C₂₉	semidirect
125. #1997	C₂×C₂₉	semidirect
126. #1815	C₂×C₂₉	semidirect
127. C₄×#108	C₂×C₂₉	semidirect
197. C₂₉	#28732	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×C₂₉×#498	2
C₂₉×#3141	2
C₂₉×#2931	2
C₂₉×#2079	2
C₂₉×#1997	2
C₂₉×#1815	2
C₄×C₂₉×#108	2
#28732	29

Subgroups — C29×#28732 #20323632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#28732 #20323632