Subgroups — C₂×#13123203 #16068904

Order 3328.

2838 conjugacy classes of subgroups.

The subgroup lattice has 236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88130	C₂	1	2	yes	maximal, complemented
2	#13123203	C₂	1	16	yes	maximal, direct product factor
3	C₂×#11718600	C₂	1	3	yes	maximal
4	C₂×#11718589	C₂	1	3	yes	maximal, complemented
5	C₂×#11718601	C₂	1	6	yes	maximal, complemented
6	C₂×C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₅₂	C₂²	1	1	yes	characteristic
8	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
9	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
10	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×#6103	C₂²	1	6	yes	—
12	C₂²×#6103	C₂²	1	6	yes	—
13	C₂²×C₄⋊Dic₁₃	C₂²	1	3	yes	—
14	C₂²×#6101	C₂²	1	6	yes	—
15	C₂×#88130	—	2	16	no	—
16	C₂×#88130	C₂²	1	16	yes	complemented
17	C₄³×C₁₃	C₂²	1	8	yes	complemented
18	C₂×#88071	C₂²	1	6	yes	—
19	#11718601	C₂²	1	48	yes	complemented
20	#11718600	C₂²	1	24	yes	—
21	#11718589	C₂²	1	24	yes	complemented
22	C₂⁴×D₁₃	C₂³	1	2	yes	—
23	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
24	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
25	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
26	C₂³×Dic₁₃	C₂³	1	6	yes	—
27	C₂²×D₅₂	—	2	12	no	—
28	C₂²×D₅₂	C₂³	1	4	yes	—
29	C₂×C₄²×C₁₃	—	2	12	no	—
30	C₂×C₄²×C₁₃	—	2	12	no	—
31	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
32	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
33	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
34	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
35	C₂×#6103	—	2	24	no	—
36	C₂×#6103	—	2	24	no	—
37	C₂×#6103	C₂³	1	24	yes	—
38	C₂×#6103	C₂³	1	24	yes	—
39	C₂×C₄⋊Dic₁₃	—	2	12	no	—
40	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	—
41	C₂×#6101	—	2	24	no	—
42	C₂×#6101	C₂³	1	24	yes	—
43	#88130	—	2	64	no	—
44	#88071	C₂³	1	24	yes	—
45	C₂×#2860	—	13	1	no	maximal, Sylow
46	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
47	C₂³×D₁₃	—	2	4	no	—
48	C₂³×D₁₃	—	2	12	no	—
49	C₂³×D₁₃	—	2	12	no	—
50	C₂³×D₁₃	C₂⁴	1	4	yes	—
51	C₂²×C₄×C₁₃	—	2	6	no	—
52	C₂²×C₄×C₁₃	—	2	6	no	—
53	C₂²×C₄×C₁₃	—	2	6	no	—
54	C₂²×C₄×C₁₃	—	2	6	no	—
55	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	—
56	C₂²×C₄×C₁₃	#41	1	12	yes	—
57	C₂²×C₄×C₁₃	#41	1	12	yes	—
58	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
59	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
60	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
61	C₂²×Dic₁₃	—	2	12	no	—
62	C₂²×Dic₁₃	—	2	12	no	—
63	C₂²×Dic₁₃	—	2	12	no	—
64	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
65	C₂×D₅₂	—	2	24	no	—
66	C₂×D₅₂	—	4	16	no	—
67	C₄²×C₁₃	—	2	24	no	—
68	C₄²×C₁₃	—	2	24	no	—
69	C₄²×C₁₃	C₂×D₄	1	16	yes	complemented
70	#6103	—	2	48	no	—
71	#6103	—	2	48	no	—
72	C₄⋊Dic₁₃	—	2	24	no	—
73	#6101	—	2	48	no	—
74	C₂²×#126	—	13	2	no	—
75	#2860	—	13	16	no	—
76	C₂×#390	—	13	3	no	—
77	C₂×#389	—	13	3	no	—
78	C₂×#388	—	13	6	no	—
79	C₂×C₄³	D₁₃	1	1	yes	characteristic, complemented
80	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
81	C₂³×C₁₃	C₂×#41	1	6	yes	—
82	C₂³×C₁₃	C₂×#41	1	6	yes	—
83	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
84	C₂²×D₁₃	—	2	4	no	—
85	C₂²×D₁₃	—	2	12	no	—
86	C₂²×D₁₃	—	2	12	no	—
87	C₂²×D₁₃	—	4	8	no	—
88	C₂²×D₁₃	—	4	24	no	—
89	C₂²×D₁₃	—	4	24	no	—
90	C₂×C₄×C₁₃	—	2	24	no	—
91	C₂×C₄×C₁₃	—	2	24	no	—
92	C₂×C₄×C₁₃	—	2	6	no	—
93	C₂×C₄×C₁₃	—	2	6	no	—
94	C₂×C₄×C₁₃	—	2	6	no	—
95	C₂×C₄×C₁₃	—	2	6	no	—
96	C₂×C₄×C₁₃	#126	1	16	yes	complemented
97	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
98	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
99	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
100	C₂×Dic₁₃	—	2	12	no	—
101	C₂×Dic₁₃	—	2	12	no	—
102	C₂×Dic₁₃	—	2	12	no	—
103	C₂×Dic₁₃	—	4	24	no	—
104	D₅₂	—	4	16	no	—
105	C₂³×D₄	—	13	1	no	—
106	C₂×#126	—	13	16	no	—
107	C₂×#126	—	26	16	no	—
108	C₂²×C₄⋊C₄	—	13	6	no	—
109	C₂²×C₄⋊C₄	—	13	3	no	—
110	C₂²×C₂²⋊C₄	—	13	6	no	—
111	C₂²×C₂²⋊C₄	—	13	6	no	—
112	C₂²×C₄²	C₂×D₁₃	1	3	yes	—
113	C₂²×C₄²	C₂×D₁₃	1	3	yes	—
114	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
115	#390	—	13	24	no	—
116	#389	—	13	24	no	—
117	#388	—	13	48	no	—
118	C₂×#95	—	13	6	no	—
119	C₄³	C₂×D₁₃	1	8	yes	complemented
120	C₂²×C₁₃	C₂×#126	1	4	yes	—
121	C₂²×C₁₃	#529	1	12	yes	—
122	C₂²×C₁₃	#532	1	12	yes	—
123	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
124	C₂²×C₁₃	C₂²×#41	1	3	yes	—
125	C₂²×C₁₃	C₂²×#41	1	3	yes	—
126	C₂×D₁₃	—	4	4	no	—
127	C₂×D₁₃	—	4	12	no	—
128	C₂×D₁₃	—	4	12	no	—
129	C₂×D₁₃	—	8	16	no	—
130	C₄×C₁₃	—	2	12	no	—
131	C₄×C₁₃	—	2	12	no	—
132	C₄×C₁₃	C₂×#126	1	8	yes	complemented
133	Dic₁₃	—	4	12	no	—
134	C₂⁵	—	13	2	no	—
135	C₂²×D₄	—	13	4	no	—
136	C₂²×D₄	—	26	12	no	—
137	C₂³×C₄	—	13	6	no	—
138	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
139	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
140	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
141	#126	—	26	64	no	—
142	C₂×C₄⋊C₄	—	13	24	no	—
143	C₂×C₄⋊C₄	—	13	12	no	—
144	C₂×C₄⋊C₄	—	26	24	no	—
145	C₂×C₄⋊C₄	—	26	12	no	—
146	C₂×C₂²⋊C₄	—	13	24	no	—
147	C₂×C₂²⋊C₄	—	13	24	no	—
148	C₂×C₂²⋊C₄	—	26	24	no	—
149	C₂×C₂²⋊C₄	—	26	24	no	—
150	C₂×C₄²	—	2	12	no	—
151	C₂×C₄²	—	2	12	no	—
152	C₂×C₄²	D₅₂	1	8	yes	complemented
153	C₂×C₄²	C₂²×D₁₃	1	12	yes	—
154	C₂×C₄²	C₂²×D₁₃	1	12	yes	—
155	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
156	#95	—	13	24	no	—
157	C₂×C₁₃	#2860	1	8	yes	complemented
158	C₂×C₁₃	C₂²×#126	1	1	yes	characteristic
159	C₂×C₁₃	C₂×#529	1	3	yes	—
160	C₂×C₁₃	C₂×#532	1	3	yes	—
161	D₁₃	—	8	4	no	—
162	C₂⁴	—	13	4	no	—
163	C₂⁴	—	26	4	no	—
164	C₂⁴	—	26	12	no	—
165	C₂⁴	—	26	12	no	—
166	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
167	C₂×D₄	—	26	24	no	—
168	C₂×D₄	—	52	16	no	—
169	C₂²×C₄	—	2	6	no	—
170	C₂²×C₄	—	2	6	no	—
171	C₂²×C₄	—	2	6	no	—
172	C₂²×C₄	—	2	6	no	—
173	C₂²×C₄	—	13	12	no	—
174	C₂²×C₄	—	26	12	no	—
175	C₂²×C₄	—	26	12	no	—
176	C₂²×C₄	—	26	12	no	—
177	C₂²×C₄	C₂×D₅₂	1	12	yes	—
178	C₂²×C₄	#6127	1	12	yes	—
179	C₂²×C₄	#6127	1	12	yes	—
180	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
181	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
182	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
183	C₄⋊C₄	—	26	48	no	—
184	C₄⋊C₄	—	26	24	no	—
185	C₂²⋊C₄	—	26	48	no	—
186	C₂²⋊C₄	—	26	48	no	—
187	C₄²	—	2	24	no	—
188	C₄²	—	2	24	no	—
189	C₄²	C₂×D₅₂	1	16	yes	complemented
190	C₁₃	C₂×#2860	1	1	yes	characteristic, complemented, Sylow
191	C₂³	—	26	4	no	—
192	C₂³	—	26	12	no	—
193	C₂³	—	26	12	no	—
194	C₂³	—	52	24	no	—
195	C₂³	—	52	8	no	—
196	C₂³	—	52	24	no	—
197	C₂³	C₂²×D₅₂	1	2	yes	—
198	C₂³	C₂×#6127	1	6	yes	—
199	C₂³	C₂×#6127	1	6	yes	—
200	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
201	D₄	—	52	16	no	—
202	C₂×C₄	—	2	24	no	—
203	C₂×C₄	—	2	24	no	—
204	C₂×C₄	—	2	6	no	—
205	C₂×C₄	—	2	6	no	—
206	C₂×C₄	—	2	6	no	—
207	C₂×C₄	—	2	6	no	—
208	C₂×C₄	—	26	12	no	—
209	C₂×C₄	—	26	12	no	—
210	C₂×C₄	—	26	12	no	—
211	C₂×C₄	—	52	24	no	—
212	C₂×C₄	#88130	1	16	yes	complemented
213	C₂×C₄	C₂²×D₅₂	1	12	yes	—
214	C₂×C₄	C₂×#6127	1	12	yes	—
215	C₂×C₄	C₂×#6127	1	12	yes	—
216	C₂²	—	52	4	no	—
217	C₂²	—	52	12	no	—
218	C₂²	—	52	12	no	—
219	C₂²	—	104	16	no	—
220	C₂²	#11719182	1	12	yes	—
221	C₂²	C₂×#88130	1	4	yes	—
222	C₂²	#11719184	1	12	yes	—
223	C₂²	C₂³×D₅₂	1	1	yes	characteristic
224	C₂²	C₂²×#6127	1	3	yes	—
225	C₂²	C₂²×#6127	1	3	yes	—
226	C₄	—	2	12	no	—
227	C₄	—	2	12	no	—
228	C₄	—	52	12	no	—
229	C₄	C₂×#88130	1	8	yes	complemented
230	C₂	—	104	4	no	—
231	C₂	#13123203	1	8	yes	direct product factor
232	C₂	C₂²×#88130	1	1	yes	characteristic
233	C₂	C₂×#11719184	1	3	yes	—
234	C₂	C₂×#11719182	1	3	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂³×C₁₃	C₂⁵
Frattini	C₂³	C₂⁴×D₁₃
Fitting	C₂×C₄³×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂³×D₅₂	C₂²
hypercenter	C₂×C₄³	D₁₃
hypocenter	C₁₃	C₂×#2860
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
1. C₂²×#88130	C₂	semidirect
2. #13123203	C₂	direct (N × H)
4. C₂×#11718589	C₂	semidirect
5. C₂×#11718601	C₂	semidirect
6. C₂×C₄³×C₁₃	C₂	semidirect
16. C₂×#88130	C₂²	semidirect
17. C₄³×C₁₃	C₂²	semidirect
19. #11718601	C₂²	semidirect
21. #11718589	C₂²	semidirect
31. C₂×C₄²×C₁₃	D₄	semidirect
69. C₄²×C₁₃	C₂×D₄	semidirect
79. C₂×C₄³	D₁₃	semidirect
96. C₂×C₄×C₁₃	#126	semidirect
119. C₄³	C₂×D₁₃	semidirect
132. C₄×C₁₃	C₂×#126	semidirect
152. C₂×C₄²	D₅₂	semidirect
157. C₂×C₁₃	#2860	semidirect
189. C₄²	C₂×D₅₂	semidirect
190. C₁₃	C₂×#2860	semidirect
212. C₂×C₄	#88130	semidirect
229. C₄	C₂×#88130	semidirect
231. C₂	#13123203	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#88130	2
#13123203	2
C₂×#11718600	2
C₂×#11718589	2
C₂×#11718601	2
C₂×C₄³×C₁₃	2
C₂×#2860	13

Subgroups — C2×#13123203 #16068904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13123203 #16068904