Subgroups — C₂₉×#33242 #20328142

Order 7424.

926 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#500	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#494	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#487	C₂	1	2	yes	maximal
4	C₂₉×#2862	C₂	1	2	yes	maximal
5	C₂₉×#1969	C₂	1	8	yes	maximal
6	C₄²×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₁₆×C₂₉	C₂²	1	4	yes	—
8	C₂×C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
9	C₂×C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
10	C₂₉×#500	—	2	4	no	—
11	C₂₉×#494	—	2	4	no	—
12	C₂₉×#487	—	2	8	no	—
13	C₂×C₂₉×#107	C₂²	1	4	yes	—
14	C₂×C₂₉×#103	C₂²	1	8	yes	—
15	C₂×C₄×C₈×C₂₉	C₂²	1	4	yes	—
16	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
18	C₂₉×#391	—	2	4	no	—
19	C₂₉×#391	C₂²	1	8	yes	—
20	C₂₉×#382	—	2	4	no	—
21	C₄³×C₂₉	C₂²	1	1	yes	characteristic
22	C₂²×Q₈×C₂₉	—	2	2	no	—
23	C₂²×Q₈×C₂₉	C₂³	1	4	yes	—
24	C₂×Q₁₆×C₂₉	—	2	8	no	—
25	C₂×Q₁₆×C₂₉	—	2	16	no	—
26	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
27	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
28	C₂₉×C₄⋊Q₈	—	2	4	no	—
29	C₂₉×C₄⋊Q₈	—	2	4	no	—
30	C₂₉×C₄⋊Q₈	—	2	4	no	—
31	C₂₉×C₄⋊Q₈	—	2	4	no	—
32	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
36	C₂×C₄²×C₂₉	D₄	1	2	yes	—
37	C₂×C₄²×C₂₉	D₄	1	2	yes	—
38	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
39	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
40	C₂₉×#107	—	2	8	no	—
41	C₂₉×#103	—	2	16	no	—
42	C₄×C₈×C₂₉	—	2	8	no	—
43	C₄×C₈×C₂₉	D₄	1	4	yes	—
44	C₄×C₈×C₂₉	D₄	1	4	yes	—
45	C₂₉×#95	—	2	16	no	—
46	C₂×Q₈×C₂₉	—	2	4	no	—
47	C₂×Q₈×C₂₉	—	2	4	no	—
48	C₂×Q₈×C₂₉	—	2	16	no	—
49	C₂×Q₈×C₂₉	—	4	4	no	—
50	C₂×Q₈×C₂₉	—	4	8	no	—
51	C₂²×C₄×C₂₉	—	2	4	no	—
52	C₂²×C₄×C₂₉	—	2	4	no	—
53	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
54	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
57	Q₁₆×C₂₉	—	4	16	no	—
58	C₂×C₈×C₂₉	—	2	4	no	—
59	C₂×C₈×C₂₉	C₂×D₄	1	4	yes	—
60	C₂×C₈×C₂₉	C₂×D₄	1	4	yes	—
61	C₂×C₈×C₂₉	#41	1	8	yes	—
62	C₄⋊C₄×C₂₉	—	2	4	no	—
63	C₄⋊C₄×C₂₉	—	2	4	no	—
64	C₄⋊C₄×C₂₉	—	4	4	no	—
65	C₄⋊C₄×C₂₉	—	4	4	no	—
66	C₄⋊C₄×C₂₉	—	4	4	no	—
67	C₄²×C₂₉	—	2	4	no	—
68	C₄²×C₂₉	—	2	4	no	—
69	C₄²×C₂₉	Q₁₆	1	8	yes	complemented
70	C₄²×C₂₉	C₂×D₄	1	2	yes	—
71	C₄²×C₂₉	C₂×D₄	1	2	yes	—
72	#33242	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
74	Q₈×C₂₉	—	4	8	no	—
75	Q₈×C₂₉	—	4	8	no	—
76	Q₈×C₂₉	—	8	8	no	—
77	C₂×C₄×C₂₉	—	2	4	no	—
78	C₂×C₄×C₂₉	—	2	4	no	—
79	C₂×C₄×C₂₉	—	4	4	no	—
80	C₂×C₄×C₂₉	—	4	4	no	—
81	C₂×C₄×C₂₉	—	4	8	no	—
82	C₂×C₄×C₂₉	—	4	8	no	—
83	C₂×C₄×C₂₉	#127	1	2	yes	—
84	C₂×C₄×C₂₉	#127	1	2	yes	—
85	C₂×C₄×C₂₉	C₂×Q₁₆	1	8	yes	—
86	C₂×C₄×C₂₉	C₂×Q₁₆	1	4	yes	—
87	C₂×C₄×C₂₉	#135	1	4	yes	—
88	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
89	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
90	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
91	C₈×C₂₉	—	2	4	no	—
92	C₈×C₂₉	#124	1	8	yes	—
93	C₂×#500	C₂×C₂₉	1	1	yes	characteristic
94	C₂×#494	C₂×C₂₉	1	1	yes	characteristic
95	C₂×#487	C₂×C₂₉	1	2	yes	—
96	#2862	C₂×C₂₉	1	2	yes	—
97	#1969	C₂×C₂₉	1	8	yes	—
98	C₄²×C₈	C₂×C₂₉	1	1	yes	characteristic
99	C₂²×C₂₉	C₂×#127	1	1	yes	characteristic
100	C₂²×C₂₉	#532	1	2	yes	—
101	C₂²×C₂₉	C₂²×Q₁₆	1	2	yes	—
102	C₂²×C₂₉	C₂×#135	1	2	yes	—
103	C₄×C₂₉	—	2	8	no	—
104	C₄×C₂₉	—	8	4	no	—
105	C₄×C₂₉	—	8	4	no	—
106	C₄×C₂₉	#494	1	4	yes	—
107	C₄×C₂₉	#495	1	4	yes	—
108	C₄×C₂₉	C₂×#124	1	2	yes	—
109	C₄×C₂₉	#532	1	2	yes	—
110	C₂²×Q₁₆	C₂²×C₂₉	1	4	yes	—
111	C₂×C₄⋊Q₈	C₂²×C₂₉	1	2	yes	—
112	C₂×C₄⋊Q₈	C₂²×C₂₉	1	2	yes	—
113	#500	—	2	4	no	—
114	#494	—	2	4	no	—
115	#487	—	2	8	no	—
116	C₂×#107	C₂²×C₂₉	1	4	yes	—
117	C₂×#103	C₂²×C₂₉	1	8	yes	—
118	C₂×C₄×C₈	C₂²×C₂₉	1	4	yes	—
119	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
120	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
121	#391	—	2	4	no	—
122	#391	C₂²×C₂₉	1	8	yes	—
123	#382	—	2	4	no	—
124	C₄³	C₂²×C₂₉	1	1	yes	characteristic
125	C₂×C₂₉	#2858	1	1	yes	characteristic
126	C₂×C₂₉	C₂×#494	1	1	yes	characteristic
127	C₂×C₂₉	C₂×#495	1	1	yes	characteristic
128	C₂×C₂₉	#3170	1	4	yes	—
129	C₂²×Q₈	—	2	2	no	—
130	C₂²×Q₈	C₂³×C₂₉	1	4	yes	—
131	C₂×Q₁₆	—	2	8	no	—
132	C₂×Q₁₆	—	2	16	no	—
133	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
134	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
135	C₄⋊Q₈	—	2	4	no	—
136	C₄⋊Q₈	—	2	4	no	—
137	C₄⋊Q₈	—	2	4	no	—
138	C₄⋊Q₈	—	2	4	no	—
139	C₂×C₄⋊C₄	—	2	2	no	—
140	C₂×C₄⋊C₄	—	2	2	no	—
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
143	C₂×C₄²	D₄×C₂₉	1	2	yes	—
144	C₂×C₄²	D₄×C₂₉	1	2	yes	—
145	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
146	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
147	#107	—	2	8	no	—
148	#103	—	2	16	no	—
149	C₄×C₈	—	2	8	no	—
150	C₄×C₈	D₄×C₂₉	1	4	yes	—
151	C₄×C₈	D₄×C₂₉	1	4	yes	—
152	#95	—	2	16	no	—
153	C₂₉	#33242	1	1	yes	characteristic, direct product factor, Sylow
154	C₂×Q₈	—	2	4	no	—
155	C₂×Q₈	—	2	4	no	—
156	C₂×Q₈	—	2	16	no	—
157	C₂×Q₈	—	4	4	no	—
158	C₂×Q₈	—	4	8	no	—
159	C₂²×C₄	—	2	4	no	—
160	C₂²×C₄	—	2	4	no	—
161	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
162	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
163	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
164	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
165	Q₁₆	—	4	16	no	—
166	C₂×C₈	—	2	4	no	—
167	C₂×C₈	C₂×D₄×C₂₉	1	4	yes	—
168	C₂×C₈	C₂×D₄×C₂₉	1	4	yes	—
169	C₂×C₈	#41×C₂₉	1	8	yes	—
170	C₄⋊C₄	—	2	4	no	—
171	C₄⋊C₄	—	2	4	no	—
172	C₄⋊C₄	—	4	4	no	—
173	C₄⋊C₄	—	4	4	no	—
174	C₄⋊C₄	—	4	4	no	—
175	C₄²	—	2	4	no	—
176	C₄²	—	2	4	no	—
177	C₄²	Q₁₆×C₂₉	1	8	yes	complemented
178	C₄²	C₂×D₄×C₂₉	1	2	yes	—
179	C₄²	C₂×D₄×C₂₉	1	2	yes	—
180	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
181	Q₈	—	4	8	no	—
182	Q₈	—	4	8	no	—
183	Q₈	—	8	8	no	—
184	C₂×C₄	—	2	4	no	—
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	—	4	4	no	—
187	C₂×C₄	—	4	4	no	—
188	C₂×C₄	—	4	8	no	—
189	C₂×C₄	—	4	8	no	—
190	C₂×C₄	C₂₉×#127	1	2	yes	—
191	C₂×C₄	C₂₉×#127	1	2	yes	—
192	C₂×C₄	C₂×Q₁₆×C₂₉	1	8	yes	—
193	C₂×C₄	C₂×Q₁₆×C₂₉	1	4	yes	—
194	C₂×C₄	C₂₉×#135	1	4	yes	—
195	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
196	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
197	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
198	C₈	—	2	4	no	—
199	C₈	C₂₉×#124	1	8	yes	—
200	C₂²	C₂×C₂₉×#127	1	1	yes	characteristic
201	C₂²	C₂₉×#532	1	2	yes	—
202	C₂²	C₂²×Q₁₆×C₂₉	1	2	yes	—
203	C₂²	C₂×C₂₉×#135	1	2	yes	—
204	C₄	—	2	8	no	—
205	C₄	—	8	4	no	—
206	C₄	—	8	4	no	—
207	C₄	C₂₉×#494	1	4	yes	—
208	C₄	C₂₉×#495	1	4	yes	—
209	C₄	C₂×C₂₉×#124	1	2	yes	—
210	C₄	C₂₉×#532	1	2	yes	—
211	C₂	C₂₉×#2858	1	1	yes	characteristic
212	C₂	C₂×C₂₉×#494	1	1	yes	characteristic
213	C₂	C₂×C₂₉×#495	1	1	yes	characteristic
214	C₂	C₂₉×#3170	1	4	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₄³×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
69. C₄²×C₂₉	Q₁₆	semidirect
72. #33242	C₂₉	direct (N × H)
153. C₂₉	#33242	direct (N × H)
177. C₄²	Q₁₆×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#500	2
C₂×C₂₉×#494	2
C₂×C₂₉×#487	2
C₂₉×#2862	2
C₂₉×#1969	2
C₄²×C₈×C₂₉	2
#33242	29

Subgroups — C29×#33242 #20328142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#33242 #20328142