Subgroups — C₄×Q₁₆×D₂₉ #16828253

Order 3712.

488 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×D₂₉	C₂	1	2	yes	maximal
3	C₄×Dic₁₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₁₆×Dic₂₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#14271257	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#90785	C₂	1	2	yes	maximal, complemented
7	#14271255	C₂	1	2	yes	maximal, complemented
8	#107×D₂₉	C₂	1	1	yes	maximal, characteristic
9	#103×D₂₉	C₂	1	2	yes	maximal
10	C₄×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
11	C₄×Q₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₈×D₂₉	C₂²	1	2	yes	—
13	C₂×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
14	C₄×Q₈×C₂₉	C₂²	1	2	yes	—
15	Q₈×Dic₂₉	C₂²	1	2	yes	—
16	C₂×#90785	C₂²	1	2	yes	—
17	Q₁₆×D₂₉	C₄	1	8	yes	direct product factor
18	C₂×Dic₁₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
20	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
21	C₄⋊C₄×D₂₉	—	2	2	no	—
22	C₄⋊C₄×D₂₉	C₂²	1	2	yes	—
23	#11745249	—	2	2	no	—
24	#11745249	C₂²	1	2	yes	—
25	C₄²×D₂₉	—	2	2	no	—
26	C₄²×D₂₉	C₂²	1	1	yes	characteristic
27	C₄×Dic₅₈	—	2	2	no	—
28	C₄×Dic₅₈	C₂²	1	2	yes	—
29	C₂₉×#107	C₂²	1	1	yes	characteristic
30	C₂₉×#103	C₂²	1	2	yes	—
31	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
32	#11745183	C₂²	1	2	yes	—
33	#11745166	C₂²	1	1	yes	characteristic
34	#11745164	C₂²	1	2	yes	—
35	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
36	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
37	#11745158	C₂²	1	2	yes	—
38	#11745155	C₂²	1	2	yes	—
39	C₄×#6597	C₂²	1	1	yes	characteristic
40	C₂×Q₈×C₂₉	C₂³	1	2	yes	—
41	Q₈×D₂₉	—	2	4	no	—
42	Q₈×D₂₉	C₂×C₄	1	8	yes	—
43	C₂×C₄×D₂₉	—	2	2	no	—
44	C₂×C₄×D₂₉	—	2	2	no	—
45	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
46	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
47	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
48	C₂×Dic₅₈	—	2	2	no	—
49	C₂×Dic₅₈	C₂³	1	2	yes	—
50	Q₁₆×C₂₉	C₂×C₄	1	4	yes	complemented
51	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
52	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
53	C₄⋊C₄×C₂₉	—	2	2	no	—
54	C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
55	C₄²×C₂₉	—	2	2	no	—
56	C₄²×C₂₉	C₂³	1	1	yes	characteristic
57	#90785	C₂×C₄	1	8	yes	complemented
58	C₄⋊Dic₂₉	—	2	2	no	—
59	C₄⋊Dic₂₉	C₂³	1	2	yes	—
60	#90779	—	2	2	no	—
61	#90779	—	2	2	no	—
62	#90779	—	2	2	no	—
63	C₄×Dic₂₉	—	2	2	no	—
64	C₄×Dic₂₉	—	2	2	no	—
65	C₄×Dic₂₉	—	2	2	no	—
66	C₄×Dic₂₉	D₄	1	1	yes	characteristic
67	C₄×Dic₂₉	D₄	1	1	yes	characteristic
68	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
69	C₂×#6597	C₂³	1	1	yes	characteristic
70	C₂×#6597	C₂³	1	1	yes	characteristic
71	Dic₁₁₆	C₂×C₄	1	4	yes	complemented
72	C₈×D₂₉	—	2	2	no	—
73	C₈×D₂₉	C₂×C₄	1	4	yes	—
74	C₂²×D₂₉	C₂×D₄	1	1	yes	characteristic
75	Q₈×C₂₉	—	2	2	no	—
76	Q₈×C₂₉	C₂²×C₄	1	4	yes	—
77	C₂×C₄×C₂₉	—	2	2	no	—
78	C₂×C₄×C₂₉	—	2	2	no	—
79	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
82	C₂×Dic₂₉	—	2	2	no	—
83	C₂×Dic₂₉	—	2	2	no	—
84	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
85	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
86	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
87	C₄×D₂₉	—	2	8	no	—
88	C₄×D₂₉	—	2	2	no	—
89	C₄×D₂₉	—	4	4	no	—
90	C₄×D₂₉	Q₁₆	1	4	yes	direct product factor
91	C₄×D₂₉	C₂²×C₄	1	2	yes	—
92	C₄×D₂₉	#41	1	2	yes	—
93	Dic₅₈	—	2	2	no	—
94	Dic₅₈	—	2	8	no	—
95	Dic₅₈	C₂²×C₄	1	4	yes	—
96	C₈×C₂₉	—	2	1	no	—
97	C₈×C₂₉	C₂²×C₄	1	2	yes	—
98	#6597	—	2	1	no	—
99	#6597	C₂²×C₄	1	2	yes	—
100	C₂×C₄×Q₁₆	—	29	1	no	maximal, Sylow
101	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
102	C₂×D₂₉	C₄×D₄	1	2	yes	—
103	C₂×D₂₉	C₂×Q₁₆	1	2	yes	—
104	C₂×D₂₉	#135	1	2	yes	—
105	C₄×C₂₉	—	2	4	no	—
106	C₄×C₂₉	—	2	1	no	—
107	C₄×C₂₉	—	4	2	no	—
108	C₄×C₂₉	C₂×Q₁₆	1	2	yes	complemented
109	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
110	C₄×C₂₉	C₂×#41	1	1	yes	characteristic
111	Dic₂₉	—	2	4	no	—
112	Dic₂₉	—	2	1	no	—
113	Dic₂₉	—	4	2	no	—
114	Dic₂₉	C₄×D₄	1	2	yes	—
115	Dic₂₉	C₂×Q₁₆	1	2	yes	complemented
116	C₂²×Q₁₆	—	29	1	no	—
117	C₂×C₄×Q₈	—	29	2	no	—
118	C₄×Q₁₆	—	29	1	no	—
119	C₄×Q₁₆	—	29	2	no	—
120	C₄×Q₁₆	—	29	1	no	—
121	C₄×Q₁₆	—	29	2	no	—
122	C₄×Q₁₆	—	29	1	no	—
123	C₄×Q₁₆	D₂₉	1	1	yes	characteristic, direct product factor
124	C₂×#107	—	29	1	no	—
125	C₂×#103	—	29	2	no	—
126	C₂×C₄×C₈	—	29	1	no	—
127	C₂×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
128	C₂×C₂₉	C₂²×Q₁₆	1	1	yes	characteristic
129	C₂×C₂₉	C₂×#135	1	1	yes	characteristic
130	D₂₉	C₄×Q₁₆	1	4	yes	direct product factor
131	C₂²×Q₈	—	29	2	no	—
132	C₂×Q₁₆	—	29	2	no	—
133	C₂×Q₁₆	—	29	8	no	—
134	C₂×Q₁₆	—	29	1	no	—
135	C₂×Q₁₆	C₂×D₂₉	1	1	yes	characteristic
136	C₂²×C₈	—	29	1	no	—
137	C₂²×C₈	—	29	1	no	—
138	C₄×Q₈	—	29	2	no	—
139	C₄×Q₈	—	29	2	no	—
140	C₄×Q₈	—	29	2	no	—
141	C₄×Q₈	—	58	2	no	—
142	C₄×Q₈	—	58	2	no	—
143	C₄×Q₈	C₂×D₂₉	1	2	yes	—
144	C₂×C₄⋊C₄	—	29	2	no	—
145	C₂×C₄⋊C₄	—	58	2	no	—
146	C₂×C₄²	—	29	1	no	—
147	C₂×C₄²	—	58	2	no	—
148	#107	—	29	1	no	—
149	#107	—	29	2	no	—
150	#107	C₂×D₂₉	1	1	yes	characteristic
151	#103	—	29	2	no	—
152	#103	—	29	2	no	—
153	#103	—	29	2	no	—
154	#103	C₂×D₂₉	1	2	yes	—
155	C₄×C₈	—	29	1	no	—
156	C₄×C₈	—	29	1	no	—
157	C₄×C₈	—	29	1	no	—
158	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
159	C₂₉	C₂×C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
160	C₂×Q₈	—	29	8	no	—
161	C₂×Q₈	—	29	2	no	—
162	C₂×Q₈	—	58	2	no	—
163	C₂×Q₈	—	58	4	no	—
164	C₂×Q₈	C₂²×D₂₉	1	2	yes	—
165	C₂²×C₄	—	29	1	no	—
166	C₂²×C₄	—	29	1	no	—
167	C₂²×C₄	—	29	1	no	—
168	C₂²×C₄	—	58	2	no	—
169	C₂²×C₄	—	58	2	no	—
170	Q₁₆	—	29	8	no	—
171	Q₁₆	—	29	4	no	—
172	Q₁₆	C₄×D₂₉	1	4	yes	direct product factor
173	C₂×C₈	—	29	1	no	—
174	C₂×C₈	—	29	4	no	—
175	C₂×C₈	—	29	1	no	—
176	C₂×C₈	—	58	2	no	—
177	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
178	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	29	2	no	—
181	C₄⋊C₄	—	58	2	no	—
182	C₄⋊C₄	—	58	2	no	—
183	C₄⋊C₄	—	58	2	no	—
184	C₄⋊C₄	—	58	2	no	—
185	C₄⋊C₄	C₂²×D₂₉	1	2	yes	—
186	C₄²	—	2	2	no	—
187	C₄²	—	29	1	no	—
188	C₄²	—	29	1	no	—
189	C₄²	—	29	1	no	—
190	C₄²	—	58	2	no	—
191	C₄²	—	58	2	no	—
192	C₄²	—	58	2	no	—
193	C₄²	C₂²×D₂₉	1	1	yes	characteristic
194	C₂³	—	29	1	no	—
195	Q₈	—	2	2	no	—
196	Q₈	—	29	4	no	—
197	Q₈	—	58	8	no	—
198	Q₈	—	58	2	no	—
199	Q₈	C₂×C₄×D₂₉	1	4	yes	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	29	1	no	—
203	C₂×C₄	—	29	1	no	—
204	C₂×C₄	—	29	2	no	—
205	C₂×C₄	—	29	2	no	—
206	C₂×C₄	—	29	4	no	—
207	C₂×C₄	—	29	1	no	—
208	C₂×C₄	—	58	2	no	—
209	C₂×C₄	—	58	8	no	—
210	C₂×C₄	—	58	2	no	—
211	C₂×C₄	—	58	2	no	—
212	C₂×C₄	—	116	4	no	—
213	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
214	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
215	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
216	C₈	—	2	1	no	—
217	C₈	—	29	2	no	—
218	C₈	—	58	1	no	—
219	C₈	C₂×C₄×D₂₉	1	2	yes	—
220	C₂²	—	29	2	no	—
221	C₂²	—	29	2	no	—
222	C₂²	—	29	2	no	—
223	C₂²	C₂×D₄×D₂₉	1	1	yes	characteristic
224	C₄	—	2	4	no	—
225	C₄	—	2	1	no	—
226	C₄	—	4	2	no	—
227	C₄	—	29	2	no	—
228	C₄	—	29	2	no	—
229	C₄	—	58	4	no	—
230	C₄	—	58	1	no	—
231	C₄	—	116	2	no	—
232	C₄	Q₁₆×D₂₉	1	2	yes	direct product factor
233	C₄	C₂²×C₄×D₂₉	1	1	yes	characteristic
234	C₄	#41×D₂₉	1	1	yes	characteristic
235	C₂	—	29	4	no	—
236	C₂	C₄×D₄×D₂₉	1	1	yes	characteristic
237	C₂	C₂×Q₁₆×D₂₉	1	1	yes	characteristic
238	C₂	#135×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₂₉
commutator	C₄×C₂₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₄×Q₁₆×C₂₉	C₂
socle	C₂²×C₂₉	C₂²×D₄
prime radical	C₂²×D₂₉	C₂×D₄
cosocle	C₂×C₄×C₂₉	C₂⁴
hypercenter	C₄×Q₁₆	D₂₉
hypocenter	C₂₉	C₂×C₄×Q₁₆
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
3. C₄×Dic₁₁₆	C₂	semidirect
4. Q₁₆×Dic₂₉	C₂	semidirect
5. #14271257	C₂	semidirect
6. C₄×#90785	C₂	semidirect
7. #14271255	C₂	semidirect
11. C₄×Q₁₆×C₂₉	C₂	semidirect
17. Q₁₆×D₂₉	C₄	direct (N × H)
50. Q₁₆×C₂₉	C₂×C₄	semidirect
57. #90785	C₂×C₄	semidirect
71. Dic₁₁₆	C₂×C₄	semidirect
90. C₄×D₂₉	Q₁₆	direct (N × H)
108. C₄×C₂₉	C₂×Q₁₆	semidirect
115. Dic₂₉	C₂×Q₁₆	semidirect
123. C₄×Q₁₆	D₂₉	direct (N × H)
130. D₂₉	C₄×Q₁₆	direct (N × H)
159. C₂₉	C₂×C₄×Q₁₆	semidirect
172. Q₁₆	C₄×D₂₉	direct (N × H)
232. C₄	Q₁₆×D₂₉	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×Q₁₆×D₂₉	2
C₄×Q₈×D₂₉	2
C₄×Dic₁₁₆	2
Q₁₆×Dic₂₉	2
#14271257	2
C₄×#90785	2
#14271255	2
#107×D₂₉	2
#103×D₂₉	2
C₄×C₈×D₂₉	2
C₄×Q₁₆×C₂₉	2
C₂×C₄×Q₁₆	29

Subgroups — C4×Q16×D29 #16828253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Q₁₆×D₂₉ #16828253