Subgroups — C₂×#13123218 #16068937

Order 3328.

2142 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123218	C₂	1	16	yes	maximal, direct product factor
2	C₂×#11718590	C₂	1	3	yes	maximal
3	C₂×#11718589	C₂	1	3	yes	maximal
4	C₂×#11718594	C₂	1	6	yes	maximal
5	C₂×#11718598	C₂	1	2	yes	maximal
6	C₂×C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic
7	C₂³×Dic₂₆	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×C₄⋊Dic₁₃	C₂²	1	3	yes	—
12	C₂²×#6101	C₂²	1	6	yes	—
13	C₄³×C₁₃	C₂²	1	8	yes	—
14	C₂×#88071	C₂²	1	6	yes	—
15	C₂×#88071	C₂²	1	6	yes	—
16	C₂×#88071	C₂²	1	6	yes	—
17	#11718598	C₂²	1	16	yes	—
18	#11718594	C₂²	1	48	yes	—
19	#11718590	C₂²	1	24	yes	—
20	#11718589	C₂²	1	24	yes	—
21	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
22	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
23	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₂³×Dic₁₃	C₂³	1	6	yes	—
25	C₂³×Dic₁₃	C₂³	1	2	yes	—
26	C₂²×Dic₂₆	—	2	12	no	—
27	C₂²×Dic₂₆	C₂³	1	4	yes	—
28	C₂×C₄²×C₁₃	—	2	12	no	—
29	C₂×C₄²×C₁₃	—	2	12	no	—
30	C₂×C₄²×C₁₃	Q₈	1	8	yes	complemented
31	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
32	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
33	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
34	C₂×C₄⋊Dic₁₃	—	2	12	no	—
35	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	—
36	C₂×#6101	—	2	24	no	—
37	C₂×#6101	C₂³	1	24	yes	—
38	#88071	C₂³	1	24	yes	—
39	#88071	C₂³	1	24	yes	—
40	#88071	C₂³	1	24	yes	—
41	C₂×#2863	—	13	1	no	maximal, Sylow
42	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	—	2	6	no	—
44	C₂²×C₄×C₁₃	—	2	6	no	—
45	C₂²×C₄×C₁₃	—	2	6	no	—
46	C₂²×C₄×C₁₃	—	2	6	no	—
47	C₂²×C₄×C₁₃	C₂×Q₈	1	12	yes	—
48	C₂²×C₄×C₁₃	#41	1	12	yes	—
49	C₂²×C₄×C₁₃	#41	1	12	yes	—
50	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
51	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
52	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
53	C₂²×Dic₁₃	—	2	24	no	—
54	C₂²×Dic₁₃	—	2	12	no	—
55	C₂²×Dic₁₃	—	2	12	no	—
56	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
57	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
58	C₂×Dic₂₆	—	2	24	no	—
59	C₂×Dic₂₆	—	4	16	no	—
60	C₄²×C₁₃	—	2	24	no	—
61	C₄²×C₁₃	—	2	24	no	—
62	C₄²×C₁₃	C₂×Q₈	1	16	yes	complemented
63	C₄⋊Dic₁₃	—	2	24	no	—
64	#6101	—	2	48	no	—
65	#2863	—	13	16	no	—
66	C₂×#391	—	13	3	no	—
67	C₂×#389	—	13	3	no	—
68	C₂×#387	—	13	6	no	—
69	C₂×#383	—	13	2	no	—
70	C₂×C₄³	D₁₃	1	1	yes	characteristic
71	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
72	C₂³×C₁₃	C₂×#41	1	6	yes	—
73	C₂³×C₁₃	C₂×#41	1	6	yes	—
74	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
75	C₂×C₄×C₁₃	—	2	24	no	—
76	C₂×C₄×C₁₃	—	2	24	no	—
77	C₂×C₄×C₁₃	—	2	6	no	—
78	C₂×C₄×C₁₃	—	2	6	no	—
79	C₂×C₄×C₁₃	—	2	6	no	—
80	C₂×C₄×C₁₃	—	2	6	no	—
81	C₂×C₄×C₁₃	#126	1	16	yes	—
82	C₂×C₄×C₁₃	C₂²×Q₈	1	12	yes	—
83	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
84	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
85	C₂×Dic₁₃	—	2	24	no	—
86	C₂×Dic₁₃	—	2	12	no	—
87	C₂×Dic₁₃	—	2	12	no	—
88	C₂×Dic₁₃	—	4	8	no	—
89	C₂×Dic₁₃	—	4	24	no	—
90	Dic₂₆	—	4	16	no	—
91	C₂³×Q₈	—	13	1	no	—
92	C₂²×C₄⋊C₄	—	13	6	no	—
93	C₂²×C₄⋊C₄	—	13	3	no	—
94	C₂²×C₄²	C₂×D₁₃	1	3	yes	—
95	C₂²×C₄²	C₂×D₁₃	1	3	yes	—
96	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
97	#391	—	13	24	no	—
98	#389	—	13	24	no	—
99	#387	—	13	48	no	—
100	#383	—	13	16	no	—
101	C₂×#95	—	13	6	no	—
102	C₂×#95	—	13	6	no	—
103	C₂×#95	—	13	6	no	—
104	C₄³	C₂×D₁₃	1	8	yes	—
105	C₂²×C₁₃	C₂×#126	1	4	yes	—
106	C₂²×C₁₃	#529	1	12	yes	—
107	C₂²×C₁₃	#533	1	12	yes	—
108	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
109	C₂²×C₁₃	C₂²×#41	1	3	yes	—
110	C₂²×C₁₃	C₂²×#41	1	3	yes	—
111	C₄×C₁₃	—	2	12	no	—
112	C₄×C₁₃	—	2	12	no	—
113	C₄×C₁₃	C₂×#126	1	8	yes	—
114	Dic₁₃	—	4	4	no	—
115	Dic₁₃	—	4	12	no	—
116	C₂²×Q₈	—	13	4	no	—
117	C₂²×Q₈	—	26	12	no	—
118	C₂³×C₄	—	13	6	no	—
119	C₂³×C₄	—	13	2	no	—
120	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
121	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
122	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
123	C₂×C₄⋊C₄	—	13	24	no	—
124	C₂×C₄⋊C₄	—	13	12	no	—
125	C₂×C₄⋊C₄	—	26	24	no	—
126	C₂×C₄⋊C₄	—	26	12	no	—
127	C₂×C₄²	—	2	12	no	—
128	C₂×C₄²	—	2	12	no	—
129	C₂×C₄²	Dic₂₆	1	8	yes	complemented
130	C₂×C₄²	C₂²×D₁₃	1	12	yes	—
131	C₂×C₄²	C₂²×D₁₃	1	12	yes	—
132	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
133	#95	—	13	24	no	—
134	#95	—	13	24	no	—
135	#95	—	13	24	no	—
136	C₂×C₁₃	#2863	1	8	yes	complemented
137	C₂×C₁₃	C₂²×#126	1	1	yes	characteristic
138	C₂×C₁₃	C₂×#529	1	3	yes	—
139	C₂×C₁₃	C₂×#533	1	3	yes	—
140	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
141	C₂×Q₈	—	26	24	no	—
142	C₂×Q₈	—	52	16	no	—
143	C₂²×C₄	—	2	6	no	—
144	C₂²×C₄	—	2	6	no	—
145	C₂²×C₄	—	2	6	no	—
146	C₂²×C₄	—	2	6	no	—
147	C₂²×C₄	—	13	4	no	—
148	C₂²×C₄	—	13	12	no	—
149	C₂²×C₄	—	26	12	no	—
150	C₂²×C₄	—	26	24	no	—
151	C₂²×C₄	—	26	12	no	—
152	C₂²×C₄	C₂×Dic₂₆	1	12	yes	—
153	C₂²×C₄	#6127	1	12	yes	—
154	C₂²×C₄	#6127	1	12	yes	—
155	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
156	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
157	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
158	C₄⋊C₄	—	26	48	no	—
159	C₄⋊C₄	—	26	24	no	—
160	C₄²	—	2	24	no	—
161	C₄²	—	2	24	no	—
162	C₄²	C₂×Dic₂₆	1	16	yes	complemented
163	C₁₃	C₂×#2863	1	1	yes	characteristic, complemented, Sylow
164	C₂³	C₂²×Dic₂₆	1	2	yes	—
165	C₂³	C₂×#6127	1	6	yes	—
166	C₂³	C₂×#6127	1	6	yes	—
167	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
168	Q₈	—	52	16	no	—
169	C₂×C₄	—	2	24	no	—
170	C₂×C₄	—	2	24	no	—
171	C₂×C₄	—	2	6	no	—
172	C₂×C₄	—	2	6	no	—
173	C₂×C₄	—	2	6	no	—
174	C₂×C₄	—	2	6	no	—
175	C₂×C₄	—	26	12	no	—
176	C₂×C₄	—	26	24	no	—
177	C₂×C₄	—	26	12	no	—
178	C₂×C₄	—	52	8	no	—
179	C₂×C₄	—	52	24	no	—
180	C₂×C₄	#88130	1	16	yes	—
181	C₂×C₄	C₂²×Dic₂₆	1	12	yes	—
182	C₂×C₄	C₂×#6127	1	12	yes	—
183	C₂×C₄	C₂×#6127	1	12	yes	—
184	C₂²	#11719175	1	12	yes	—
185	C₂²	C₂×#88130	1	4	yes	—
186	C₂²	#11719184	1	12	yes	—
187	C₂²	C₂³×Dic₂₆	1	1	yes	characteristic
188	C₂²	C₂²×#6127	1	3	yes	—
189	C₂²	C₂²×#6127	1	3	yes	—
190	C₄	—	2	12	no	—
191	C₄	—	2	12	no	—
192	C₄	—	52	4	no	—
193	C₄	—	52	12	no	—
194	C₄	C₂×#88130	1	8	yes	—
195	C₂	#13123218	1	8	yes	direct product factor
196	C₂	C₂²×#88130	1	1	yes	characteristic
197	C₂	C₂×#11719184	1	3	yes	—
198	C₂	C₂×#11719175	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, prime radical	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂×C₄³	D₁₃
hypocenter	C₁₃	C₂×#2863
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. #13123218	C₂	direct (N × H)
30. C₂×C₄²×C₁₃	Q₈	semidirect
62. C₄²×C₁₃	C₂×Q₈	semidirect
129. C₂×C₄²	Dic₂₆	semidirect
136. C₂×C₁₃	#2863	semidirect
162. C₄²	C₂×Dic₂₆	semidirect
163. C₁₃	C₂×#2863	semidirect
195. C₂	#13123218	direct (N × H)

Maximal subgroups

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

subgroup	index
#13123218	2
C₂×#11718590	2
C₂×#11718589	2
C₂×#11718594	2
C₂×#11718598	2
C₂×C₄³×C₁₃	2
C₂×#2863	13

Subgroups — C2×#13123218 #16068937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13123218 #16068937