Subgroups — C₂³×(C₂×#261)⋊C₄ #16807441

Order 3328.

14334 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×#261	C₂	1	2	yes	maximal
2	C₂²×(C₂×#261)⋊C₄	C₂	1	28	yes	maximal, direct product factor
3	C₂⁴×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂⁵×D₁₃	C₂²	1	1	yes	characteristic
5	C₂⁴×#261	—	2	16	no	—
6	C₂⁴×#261	—	2	16	no	—
7	C₂⁴×#261	C₄	1	32	yes	complemented
8	C₂⁴×#261	C₂²	1	28	yes	—
9	C₂⁴×C₄×C₁₃	C₄	1	1	yes	characteristic, complemented
10	C₂⁴×Dic₁₃	C₄	1	1	yes	characteristic, complemented
11	C₂³×C₄×D₁₃	—	2	16	no	—
12	C₂³×C₄×D₁₃	C₄	1	14	yes	complemented
13	C₂³×C₄×D₁₃	C₂²	1	14	yes	—
14	C₂×(C₂×#261)⋊C₄	C₂²	1	112	yes	direct product factor
15	C₂⁵×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂⁴×D₁₃	C₂×C₄	1	7	yes	—
17	C₂⁴×D₁₃	C₂×C₄	1	16	yes	—
18	C₂⁴×D₁₃	D₄	1	8	yes	—
19	C₂⁴×D₁₃	D₄	1	16	yes	—
20	C₂⁴×D₁₃	Q₈	1	8	yes	—
21	C₂⁴×D₁₃	C₂³	1	7	yes	—
22	C₂³×#261	—	2	256	no	—
23	C₂³×#261	—	2	112	no	—
24	C₂³×#261	—	2	112	no	—
25	C₂³×#261	C₂×C₄	1	224	yes	complemented
26	C₂³×#261	C₂³	1	56	yes	—
27	C₂³×C₄×C₁₃	—	2	8	no	—
28	C₂³×C₄×C₁₃	C₂×C₄	1	14	yes	complemented
29	C₂³×Dic₁₃	—	2	8	no	—
30	C₂³×Dic₁₃	C₂×C₄	1	14	yes	complemented
31	C₂²×C₄×D₁₃	—	2	112	no	—
32	C₂²×C₄×D₁₃	—	2	112	no	—
33	C₂²×C₄×D₁₃	C₂×C₄	1	84	yes	complemented
34	C₂²×C₄×D₁₃	C₂³	1	28	yes	—
35	(C₂×#261)⋊C₄	C₂³	1	64	yes	direct product factor
36	C₂³×#95	—	13	1	no	maximal, Sylow
37	C₂⁴×C₁₃	C₄²	1	8	yes	—
38	C₂⁴×C₁₃	C₂²⋊C₄	1	8	yes	—
39	C₂⁴×C₁₃	C₄⋊C₄	1	8	yes	—
40	C₂⁴×C₁₃	C₂²×C₄	1	7	yes	—
41	C₂³×D₁₃	C₄²	1	56	yes	—
42	C₂³×D₁₃	C₂²⋊C₄	1	56	yes	—
43	C₂³×D₁₃	C₂²⋊C₄	1	128	yes	—
44	C₂³×D₁₃	C₄⋊C₄	1	56	yes	—
45	C₂³×D₁₃	C₄⋊C₄	1	128	yes	—
46	C₂³×D₁₃	C₂²×C₄	1	21	yes	—
47	C₂³×D₁₃	C₂²×C₄	1	56	yes	—
48	C₂³×D₁₃	C₂×D₄	1	28	yes	—
49	C₂³×D₁₃	C₂×D₄	1	56	yes	—
50	C₂³×D₁₃	C₂×Q₈	1	28	yes	—
51	C₂³×D₁₃	C₂⁴	1	7	yes	—
52	C₂²×#261	—	2	896	no	—
53	C₂²×#261	—	2	112	no	—
54	C₂²×#261	—	2	112	no	—
55	C₂²×#261	C₂²×C₄	1	224	yes	complemented
56	C₂²×#261	C₂⁴	1	16	yes	—
57	C₂²×C₄×C₁₃	—	2	56	no	—
58	C₂²×C₄×C₁₃	C₂²×C₄	1	28	yes	complemented
59	C₂²×Dic₁₃	—	2	56	no	—
60	C₂²×Dic₁₃	C₂²×C₄	1	28	yes	complemented
61	C₂×C₄×D₁₃	—	2	336	no	—
62	C₂×C₄×D₁₃	—	2	112	no	—
63	C₂×C₄×D₁₃	C₂²×C₄	1	56	yes	complemented
64	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
65	C₂⁵×C₄	—	13	2	no	—
66	C₂⁵×C₄	—	13	1	no	—
67	C₂²×#95	—	13	28	no	—
68	C₂³×C₁₃	#95	1	64	yes	complemented
69	C₂³×C₁₃	C₂×C₄²	1	28	yes	—
70	C₂³×C₁₃	C₂×C₂²⋊C₄	1	28	yes	—
71	C₂³×C₁₃	C₂×C₄⋊C₄	1	28	yes	—
72	C₂³×C₁₃	C₂³×C₄	1	7	yes	—
73	C₂²×D₁₃	#95	1	448	yes	complemented
74	C₂²×D₁₃	C₂×C₄²	1	84	yes	—
75	C₂²×D₁₃	C₂×C₂²⋊C₄	1	224	yes	—
76	C₂²×D₁₃	C₂×C₂²⋊C₄	1	84	yes	—
77	C₂²×D₁₃	C₂×C₄⋊C₄	1	224	yes	—
78	C₂²×D₁₃	C₂×C₄⋊C₄	1	84	yes	—
79	C₂²×D₁₃	C₂³×C₄	1	28	yes	—
80	C₂²×D₁₃	C₂³×C₄	1	7	yes	—
81	C₂²×D₁₃	C₂²×D₄	1	14	yes	—
82	C₂²×D₁₃	C₂²×D₄	1	28	yes	—
83	C₂²×D₁₃	C₂²×Q₈	1	14	yes	—
84	C₂²×D₁₃	C₂⁵	1	1	yes	characteristic
85	C₂×#261	—	2	448	no	—
86	C₂×#261	—	2	16	no	—
87	C₂×#261	—	2	16	no	—
88	C₂×#261	C₂³×C₄	1	32	yes	complemented
89	C₂×C₄×C₁₃	—	2	56	no	—
90	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	complemented
91	C₂×Dic₁₃	—	2	56	no	—
92	C₂×Dic₁₃	C₂³×C₄	1	8	yes	complemented
93	C₄×D₁₃	—	2	112	no	—
94	C₄×D₁₃	—	2	16	no	—
95	C₂⁶	—	13	1	no	—
96	C₂⁴×C₄	—	13	28	no	—
97	C₂⁴×C₄	—	13	32	no	—
98	C₂⁴×C₄	—	13	1	no	—
99	C₂⁴×C₄	—	13	14	no	—
100	C₂⁴×C₄	—	13	14	no	—
101	C₂⁴×C₄	—	26	16	no	—
102	C₂⁴×C₄	—	26	16	no	—
103	C₂⁴×C₄	—	26	16	no	—
104	C₂⁴×C₄	#261	1	1	yes	characteristic, complemented
105	C₂×#95	—	13	112	no	—
106	C₂²×C₁₃	C₂×#95	1	112	yes	complemented
107	C₂²×C₁₃	C₂²×C₄²	1	14	yes	—
108	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	14	yes	—
109	C₂²×C₁₃	C₂²×C₄⋊C₄	1	14	yes	—
110	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
111	C₂×D₁₃	C₂×#95	1	336	yes	complemented
112	C₂×D₁₃	C₂²×C₄²	1	14	yes	—
113	C₂×D₁₃	C₂²×C₂²⋊C₄	1	56	yes	—
114	C₂×D₁₃	C₂²×C₂²⋊C₄	1	14	yes	—
115	C₂×D₁₃	C₂²×C₄⋊C₄	1	56	yes	—
116	C₂×D₁₃	C₂²×C₄⋊C₄	1	14	yes	—
117	C₂×D₁₃	C₂⁴×C₄	1	2	yes	—
118	C₂×D₁₃	C₂³×D₄	1	1	yes	characteristic
119	C₂×D₁₃	C₂³×D₄	1	2	yes	—
120	C₂×D₁₃	C₂³×Q₈	1	1	yes	characteristic
121	#261	—	2	32	no	—
122	C₄×C₁₃	—	2	8	no	—
123	Dic₁₃	—	2	8	no	—
124	C₂⁵	—	13	16	no	—
125	C₂⁵	—	13	8	no	—
126	C₂⁵	—	13	8	no	—
127	C₂⁵	—	13	16	no	—
128	C₂⁵	—	13	7	no	—
129	C₂⁵	—	13	7	no	—
130	C₂⁵	C₂×#261	1	1	yes	characteristic
131	C₂³×C₄	—	2	8	no	—
132	C₂³×C₄	—	13	56	no	—
133	C₂³×C₄	—	13	224	no	—
134	C₂³×C₄	—	13	14	no	—
135	C₂³×C₄	—	13	28	no	—
136	C₂³×C₄	—	13	84	no	—
137	C₂³×C₄	—	26	112	no	—
138	C₂³×C₄	—	26	112	no	—
139	C₂³×C₄	—	26	256	no	—
140	C₂³×C₄	—	26	112	no	—
141	C₂³×C₄	—	26	112	no	—
142	C₂³×C₄	—	26	8	no	—
143	C₂³×C₄	C₂×#261	1	14	yes	complemented
144	#95	—	13	64	no	—
145	C₂×C₁₃	C₂²×#95	1	28	yes	complemented
146	C₂×C₁₃	C₂³×C₄²	1	1	yes	characteristic
147	C₂×C₁₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₁₃	C₂³×C₄⋊C₄	1	1	yes	characteristic
149	D₁₃	C₂²×#95	1	28	yes	complemented
150	D₁₃	C₂³×C₂²⋊C₄	1	2	yes	—
151	D₁₃	C₂³×C₄⋊C₄	1	2	yes	—
152	C₂⁴	—	13	128	no	—
153	C₂⁴	—	13	128	no	—
154	C₂⁴	—	13	56	no	—
155	C₂⁴	—	13	56	no	—
156	C₂⁴	—	13	28	no	—
157	C₂⁴	—	13	56	no	—
158	C₂⁴	—	13	28	no	—
159	C₂⁴	—	13	56	no	—
160	C₂⁴	—	13	56	no	—
161	C₂⁴	—	13	7	no	—
162	C₂⁴	—	13	21	no	—
163	C₂⁴	C₄×#261	1	8	yes	—
164	C₂⁴	C₄⋊#261	1	8	yes	—
165	C₂⁴	C₂²⋊#261	1	8	yes	—
166	C₂⁴	C₂²×#261	1	7	yes	—
167	C₂²×C₄	—	2	56	no	—
168	C₂²×C₄	—	13	16	no	—
169	C₂²×C₄	—	13	224	no	—
170	C₂²×C₄	—	13	28	no	—
171	C₂²×C₄	—	13	8	no	—
172	C₂²×C₄	—	13	56	no	—
173	C₂²×C₄	—	26	112	no	—
174	C₂²×C₄	—	26	336	no	—
175	C₂²×C₄	—	26	112	no	—
176	C₂²×C₄	—	26	112	no	—
177	C₂²×C₄	—	26	896	no	—
178	C₂²×C₄	—	26	56	no	—
179	C₂²×C₄	C₂²×#261	1	28	yes	complemented
180	C₁₃	C₂³×#95	1	1	yes	characteristic, complemented, Sylow
181	C₂³	—	13	28	no	—
182	C₂³	—	13	84	no	—
183	C₂³	—	13	14	no	—
184	C₂³	—	13	84	no	—
185	C₂³	—	13	14	no	—
186	C₂³	—	13	28	no	—
187	C₂³	—	13	84	no	—
188	C₂³	—	13	224	no	—
189	C₂³	—	13	448	no	—
190	C₂³	—	13	224	no	—
191	C₂³	—	13	1	no	—
192	C₂³	—	13	7	no	—
193	C₂³	(C₂×#261)⋊C₄	1	64	yes	direct product factor
194	C₂³	C₂×C₄×#261	1	28	yes	—
195	C₂³	C₂×C₄⋊#261	1	28	yes	—
196	C₂³	C₂×C₂²⋊#261	1	28	yes	—
197	C₂³	C₂³×#261	1	7	yes	—
198	C₂×C₄	—	2	56	no	—
199	C₂×C₄	—	13	32	no	—
200	C₂×C₄	—	13	8	no	—
201	C₂×C₄	—	26	112	no	—
202	C₂×C₄	—	26	16	no	—
203	C₂×C₄	—	26	16	no	—
204	C₂×C₄	—	26	16	no	—
205	C₂×C₄	—	26	448	no	—
206	C₂×C₄	—	26	56	no	—
207	C₂×C₄	C₂³×#261	1	8	yes	complemented
208	C₂²	—	13	2	no	—
209	C₂²	—	13	14	no	—
210	C₂²	—	13	14	no	—
211	C₂²	—	13	2	no	—
212	C₂²	—	13	14	no	—
213	C₂²	—	13	1	no	—
214	C₂²	—	13	1	no	—
215	C₂²	—	13	56	no	—
216	C₂²	—	13	56	no	—
217	C₂²	—	13	336	no	—
218	C₂²	C₂×(C₂×#261)⋊C₄	1	112	yes	direct product factor
219	C₂²	C₂²×C₄×#261	1	14	yes	—
220	C₂²	C₂²×C₄⋊#261	1	14	yes	—
221	C₂²	C₂²×C₂²⋊#261	1	14	yes	—
222	C₂²	C₂⁴×#261	1	1	yes	characteristic
223	C₄	—	2	8	no	—
224	C₄	—	26	32	no	—
225	C₄	—	26	8	no	—
226	C₂	—	13	2	no	—
227	C₂	—	13	2	no	—
228	C₂	—	13	28	no	—
229	C₂	C₂²×(C₂×#261)⋊C₄	1	28	yes	direct product factor
230	C₂	C₂³×C₄×#261	1	1	yes	characteristic
231	C₂	C₂³×C₂²⋊#261	1	1	yes	characteristic
232	C₂	C₂³×C₄⋊#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁵	C₂×#261
commutator	C₂×C₁₃	C₂³×C₄²
Frattini	C₂²	C₂⁴×#261
Fitting	C₂⁴×C₄×C₁₃	C₄
socle	C₂⁵×C₁₃	C₂×C₄
prime radical	C₂⁵×D₁₃	C₂²
cosocle	C₂²×D₁₃	C₂⁵
hypercenter	C₂⁴×C₄	#261
hypocenter	C₁₃	C₂³×#95
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×(C₂×#261)⋊C₄	C₂	direct (N × H)
7. C₂⁴×#261	C₄	semidirect
9. C₂⁴×C₄×C₁₃	C₄	semidirect
10. C₂⁴×Dic₁₃	C₄	semidirect
12. C₂³×C₄×D₁₃	C₄	semidirect
14. C₂×(C₂×#261)⋊C₄	C₂²	direct (N × H)
25. C₂³×#261	C₂×C₄	semidirect
28. C₂³×C₄×C₁₃	C₂×C₄	semidirect
30. C₂³×Dic₁₃	C₂×C₄	semidirect
33. C₂²×C₄×D₁₃	C₂×C₄	semidirect
35. (C₂×#261)⋊C₄	C₂³	direct (N × H)
55. C₂²×#261	C₂²×C₄	semidirect
58. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
60. C₂²×Dic₁₃	C₂²×C₄	semidirect
63. C₂×C₄×D₁₃	C₂²×C₄	semidirect
68. C₂³×C₁₃	#95	semidirect
73. C₂²×D₁₃	#95	semidirect
88. C₂×#261	C₂³×C₄	semidirect
90. C₂×C₄×C₁₃	C₂³×C₄	semidirect
92. C₂×Dic₁₃	C₂³×C₄	semidirect
104. C₂⁴×C₄	#261	semidirect
106. C₂²×C₁₃	C₂×#95	semidirect
111. C₂×D₁₃	C₂×#95	semidirect
143. C₂³×C₄	C₂×#261	semidirect
145. C₂×C₁₃	C₂²×#95	semidirect
149. D₁₃	C₂²×#95	semidirect
179. C₂²×C₄	C₂²×#261	semidirect
180. C₁₃	C₂³×#95	semidirect
193. C₂³	(C₂×#261)⋊C₄	direct (N × H)
207. C₂×C₄	C₂³×#261	semidirect
218. C₂²	C₂×(C₂×#261)⋊C₄	direct (N × H)
229. C₂	C₂²×(C₂×#261)⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×#261	2
C₂²×(C₂×#261)⋊C₄	2
C₂⁴×C₄×D₁₃	2
C₂³×#95	13

Subgroups — C23×(C2×#261)⋊C4 #16807441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×(C₂×#261)⋊C₄ #16807441