Subgroups — C₂₉×#11936 #20306836

Order 7424.

310 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3160	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2150	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#334	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1363	C₂	1	4	yes	maximal, complemented
5	C₂₉×#533	—	2	1	no	—
6	C₂×C₂₉×M₃₂	—	2	1	no	—
7	C₂₉×#500	C₄	1	1	yes	characteristic
8	C₂₉×#500	C₄	1	1	yes	characteristic
9	C₂₉×#499	—	2	1	no	—
10	C₂₉×#499	C₂²	1	2	yes	—
11	C₂₉×#498	—	2	1	no	—
12	C₂₉×#427	—	2	1	no	—
13	C₂₉×#427	C₄	1	2	yes	—
14	C₂×C₂₉×C₄⋊C₈	—	2	1	no	—
15	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
16	C₂₉×C₄⋊C₁₆	—	2	1	no	—
17	C₂₉×C₄⋊C₁₆	C₂²	1	2	yes	—
18	C₂₉×#334	—	2	1	no	—
19	C₂₉×#334	C₂²	1	2	yes	—
20	C₂²×C₈×C₂₉	—	4	1	no	—
21	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
23	C₂₉×C₄⋊Q₈	—	2	1	no	—
24	C₂₉×C₄⋊Q₈	—	2	1	no	—
25	C₂₉×#125	—	2	2	no	—
26	C₂₉×C₂²⋊Q₈	—	4	1	no	—
27	C₂₉×C₂²⋊Q₈	—	4	1	no	—
28	C₄×Q₈×C₂₉	—	4	1	no	—
29	C₄×Q₈×C₂₉	—	4	1	no	—
30	C₂₉×#117	—	2	2	no	—
31	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
32	C₂₉×M₃₂	—	4	2	no	—
33	C₂×C₁₆×C₂₉	—	2	2	no	—
34	C₂₉×#107	—	2	1	no	—
35	C₂₉×#107	—	2	1	no	—
36	C₂₉×#107	C₂×C₄	1	2	yes	—
37	C₂₉×#107	C₂×C₄	1	2	yes	—
38	C₂₉×#106	—	2	2	no	—
39	C₂₉×#106	—	2	2	no	—
40	C₂₉×C₄⋊C₈	—	2	2	no	—
41	C₂₉×C₄⋊C₈	—	4	1	no	—
42	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
44	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
45	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
46	C₂×Q₈×C₂₉	—	4	1	no	—
47	C₂×Q₈×C₂₉	—	4	1	no	—
48	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₂₉	D₈	1	1	yes	characteristic
50	C₂²×C₄×C₂₉	SD₁₆	1	1	yes	characteristic
51	C₂×C₈×C₂₉	—	2	2	no	—
52	C₂×C₈×C₂₉	—	4	2	no	—
53	C₂×C₈×C₂₉	—	8	2	no	—
54	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₂₉	SD₁₆	1	2	yes	—
57	C₂×C₈×C₂₉	Q₁₆	1	2	yes	—
58	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
60	C₄⋊C₄×C₂₉	—	2	2	no	—
61	C₄⋊C₄×C₂₉	—	2	2	no	—
62	C₄⋊C₄×C₂₉	—	4	1	no	—
63	C₄⋊C₄×C₂₉	—	4	1	no	—
64	C₄⋊C₄×C₂₉	—	4	2	no	—
65	C₄⋊C₄×C₂₉	—	4	2	no	—
66	C₂²⋊C₄×C₂₉	—	4	2	no	—
67	C₄²×C₂₉	—	4	2	no	—
68	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₄²×C₂₉	D₈	1	1	yes	characteristic
70	C₄²×C₂₉	SD₁₆	1	1	yes	characteristic
71	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
72	C₁₆×C₂₉	—	4	2	no	—
73	#11936	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂³×C₂₉	#102	1	1	yes	characteristic
75	Q₈×C₂₉	—	8	2	no	—
76	Q₈×C₂₉	—	8	2	no	—
77	C₂×C₄×C₂₉	—	2	2	no	—
78	C₂×C₄×C₂₉	—	4	1	no	—
79	C₂×C₄×C₂₉	—	4	2	no	—
80	C₂×C₄×C₂₉	—	4	2	no	—
81	C₂×C₄×C₂₉	#101	1	2	yes	—
82	C₂×C₄×C₂₉	#102	1	1	yes	characteristic
83	C₂×C₄×C₂₉	#102	1	1	yes	characteristic
84	C₂×C₄×C₂₉	#102	1	1	yes	characteristic
85	C₂×C₄×C₂₉	#103	1	2	yes	—
86	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
88	C₂×C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
89	C₈×C₂₉	—	2	1	no	—
90	C₈×C₂₉	—	2	1	no	—
91	C₈×C₂₉	—	8	2	no	—
92	C₈×C₂₉	#103	1	2	yes	—
93	C₈×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
94	C₈×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
95	#3160	C₂×C₂₉	1	1	yes	characteristic
96	#2150	C₂×C₂₉	1	1	yes	characteristic
97	C₂×#334	C₂×C₂₉	1	1	yes	characteristic
98	#1363	C₂×C₂₉	1	4	yes	complemented
99	C₂²×C₂₉	—	2	1	no	—
100	C₂²×C₂₉	—	2	1	no	—
101	C₂²×C₂₉	#332	1	2	yes	—
102	C₂²×C₂₉	C₂×#102	1	1	yes	characteristic
103	C₄×C₂₉	—	2	1	no	—
104	C₄×C₂₉	—	2	1	no	—
105	C₄×C₂₉	—	2	1	no	—
106	C₄×C₂₉	—	8	2	no	—
107	C₄×C₂₉	—	8	2	no	—
108	C₄×C₂₉	#332	1	2	yes	—
109	C₄×C₂₉	#360	1	2	yes	—
110	C₄×C₂₉	C₂×#101	1	1	yes	characteristic
111	C₄×C₂₉	C₂×#103	1	1	yes	characteristic
112	#533	—	2	1	no	—
113	C₂×M₃₂	—	2	1	no	—
114	#500	C₄×C₂₉	1	1	yes	characteristic
115	#500	C₄×C₂₉	1	1	yes	characteristic
116	#499	—	2	1	no	—
117	#499	C₂²×C₂₉	1	2	yes	—
118	#498	—	2	1	no	—
119	#427	—	2	1	no	—
120	#427	C₄×C₂₉	1	2	yes	—
121	C₂×C₄⋊C₈	—	2	1	no	—
122	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
123	C₄⋊C₁₆	—	2	1	no	—
124	C₄⋊C₁₆	C₂²×C₂₉	1	2	yes	—
125	#334	—	2	1	no	—
126	#334	C₂²×C₂₉	1	2	yes	—
127	C₂×C₂₉	—	2	2	no	—
128	C₂×C₂₉	C₂×#332	1	1	yes	characteristic
129	C₂×C₂₉	#2143	1	1	yes	characteristic
130	C₂×C₂₉	C₂×#360	1	1	yes	characteristic
131	C₂²×C₈	—	4	1	no	—
132	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
133	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
134	C₄⋊Q₈	—	2	1	no	—
135	C₄⋊Q₈	—	2	1	no	—
136	#125	—	2	2	no	—
137	C₂²⋊Q₈	—	4	1	no	—
138	C₂²⋊Q₈	—	4	1	no	—
139	C₄×Q₈	—	4	1	no	—
140	C₄×Q₈	—	4	1	no	—
141	#117	—	2	2	no	—
142	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
143	M₃₂	—	4	2	no	—
144	C₂×C₁₆	—	2	2	no	—
145	#107	—	2	1	no	—
146	#107	—	2	1	no	—
147	#107	C₂×C₄×C₂₉	1	2	yes	—
148	#107	C₂×C₄×C₂₉	1	2	yes	—
149	#106	—	2	2	no	—
150	#106	—	2	2	no	—
151	C₄⋊C₈	—	2	2	no	—
152	C₄⋊C₈	—	4	1	no	—
153	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
154	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
155	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
156	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
157	C₂₉	#11936	1	1	yes	characteristic, direct product factor, Sylow
158	C₂×Q₈	—	4	1	no	—
159	C₂×Q₈	—	4	1	no	—
160	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
161	C₂²×C₄	D₈×C₂₉	1	1	yes	characteristic
162	C₂²×C₄	SD₁₆×C₂₉	1	1	yes	characteristic
163	C₂×C₈	—	2	2	no	—
164	C₂×C₈	—	4	2	no	—
165	C₂×C₈	—	8	2	no	—
166	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
167	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
168	C₂×C₈	SD₁₆×C₂₉	1	2	yes	—
169	C₂×C₈	Q₁₆×C₂₉	1	2	yes	—
170	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
171	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
172	C₄⋊C₄	—	2	2	no	—
173	C₄⋊C₄	—	2	2	no	—
174	C₄⋊C₄	—	4	2	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	4	1	no	—
177	C₄⋊C₄	—	4	1	no	—
178	C₂²⋊C₄	—	4	2	no	—
179	C₄²	—	4	2	no	—
180	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
181	C₄²	D₈×C₂₉	1	1	yes	characteristic
182	C₄²	SD₁₆×C₂₉	1	1	yes	characteristic
183	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
184	C₁₆	—	4	2	no	—
185	C₂³	C₂₉×#102	1	1	yes	characteristic
186	Q₈	—	8	2	no	—
187	Q₈	—	8	2	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	4	1	no	—
190	C₂×C₄	—	4	2	no	—
191	C₂×C₄	—	4	2	no	—
192	C₂×C₄	C₂₉×#101	1	2	yes	—
193	C₂×C₄	C₂₉×#102	1	1	yes	characteristic
194	C₂×C₄	C₂₉×#102	1	1	yes	characteristic
195	C₂×C₄	C₂₉×#102	1	1	yes	characteristic
196	C₂×C₄	C₂₉×#103	1	2	yes	—
197	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
198	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
199	C₂×C₄	C₂×SD₁₆×C₂₉	1	1	yes	characteristic
200	C₈	—	2	1	no	—
201	C₈	—	2	1	no	—
202	C₈	—	8	2	no	—
203	C₈	C₂₉×#103	1	2	yes	—
204	C₈	C₂×SD₁₆×C₂₉	1	1	yes	characteristic
205	C₈	C₂×Q₁₆×C₂₉	1	1	yes	characteristic
206	C₂²	—	2	1	no	—
207	C₂²	—	2	1	no	—
208	C₂²	C₂₉×#332	1	2	yes	—
209	C₂²	C₂×C₂₉×#102	1	1	yes	characteristic
210	C₄	—	2	1	no	—
211	C₄	—	2	1	no	—
212	C₄	—	2	1	no	—
213	C₄	—	8	2	no	—
214	C₄	—	8	2	no	—
215	C₄	C₂₉×#332	1	2	yes	—
216	C₄	C₂₉×#360	1	2	yes	—
217	C₄	C₂×C₂₉×#101	1	1	yes	characteristic
218	C₄	C₂×C₂₉×#103	1	1	yes	characteristic
219	C₂	—	2	2	no	—
220	C₂	C₂×C₂₉×#332	1	1	yes	characteristic
221	C₂	C₂₉×#2143	1	1	yes	characteristic
222	C₂	C₂×C₂₉×#360	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₂₉
Frattini, cosocle	C₄×C₈	C₂³×C₂₉
prime radical	C₂³×C₂₉	#102
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ C₂×C₄×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₉×#1363	C₂	semidirect
73. #11936	C₂₉	direct (N × H)
98. #1363	C₂×C₂₉	semidirect
157. C₂₉	#11936	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#3160	2
C₂₉×#2150	2
C₂×C₂₉×#334	2
C₂₉×#1363	2
#11936	29

Subgroups — C29×#11936 #20306836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#11936 #20306836