Subgroups — C₂×#11718646 #13117288

Order 1664.

800 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄⋊Dic₁₃	C₂	1	2	yes	maximal
4	C₂²×C₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#88071	C₂	1	2	yes	maximal
6	#11718646	C₂	1	8	yes	maximal, direct product factor
7	C₂³×C₄×C₁₃	C₂²	1	2	yes	—
8	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂³×Dic₁₃	C₂²	1	2	yes	—
10	C₂³×Dic₁₃	C₂²	1	1	yes	characteristic
11	C₂³×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×C₄⋊C₄	C₄	1	8	yes	complemented
13	C₂×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
14	C₂×C₄⋊Dic₁₃	—	2	4	no	—
15	C₂×C₄⋊Dic₁₃	—	2	8	no	—
16	C₂×C₄⋊Dic₁₃	C₂²	1	4	yes	—
17	C₂×C₄⋊Dic₁₃	C₂²	1	8	yes	—
18	C₂×C₄×Dic₁₃	—	2	4	no	—
19	C₂×C₄×Dic₁₃	C₂²	1	4	yes	—
20	#88071	C₂²	1	8	yes	—
21	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₁₃	—	2	4	no	—
23	C₂²×C₄×C₁₃	—	2	4	no	—
24	C₂²×C₄×C₁₃	C₂×C₄	1	8	yes	—
25	C₂²×C₄×C₁₃	C₂×C₄	1	4	yes	—
26	C₂²×C₄×C₁₃	D₄	1	4	yes	—
27	C₂²×C₄×C₁₃	Q₈	1	4	yes	—
28	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
29	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
30	C₂²×Dic₁₃	—	2	2	no	—
31	C₂²×Dic₁₃	—	2	2	no	—
32	C₂²×Dic₁₃	—	2	2	no	—
33	C₂²×Dic₁₃	—	2	2	no	—
34	C₂²×Dic₁₃	—	2	4	no	—
35	C₂²×Dic₁₃	—	2	4	no	—
36	C₂²×Dic₁₃	—	2	4	no	—
37	C₂²×Dic₁₃	D₄	1	4	yes	—
38	C₂²×Dic₁₃	Q₈	1	4	yes	—
39	C₂²×Dic₁₃	C₂³	1	4	yes	—
40	C₂²×Dic₁₃	C₂³	1	2	yes	—
41	C₂²×Dic₁₃	C₂³	1	2	yes	—
42	C₁₃×C₄⋊C₄	C₂×C₄	1	16	yes	complemented
43	C₄⋊Dic₁₃	—	2	8	no	—
44	C₄⋊Dic₁₃	—	2	16	no	—
45	C₄×Dic₁₃	—	2	8	no	—
46	C₂×#389	—	13	1	no	maximal, Sylow
47	C₂³×C₁₃	C₂²×C₄	1	2	yes	—
48	C₂³×C₁₃	C₂×D₄	1	2	yes	—
49	C₂³×C₁₃	C₂×D₄	1	2	yes	—
50	C₂³×C₁₃	C₂×Q₈	1	2	yes	—
51	C₂³×C₁₃	C₂×Q₈	1	2	yes	—
52	C₂³×C₁₃	#41	1	2	yes	—
53	C₂³×C₁₃	#41	1	2	yes	—
54	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
55	C₂×C₄×C₁₃	—	2	16	no	—
56	C₂×C₄×C₁₃	—	2	4	no	—
57	C₂×C₄×C₁₃	—	2	4	no	—
58	C₂×C₄×C₁₃	C₄⋊C₄	1	16	yes	complemented
59	C₂×C₄×C₁₃	C₂²×C₄	1	8	yes	—
60	C₂×C₄×C₁₃	C₂²×C₄	1	4	yes	—
61	C₂×C₄×C₁₃	C₂×D₄	1	4	yes	—
62	C₂×C₄×C₁₃	C₂×Q₈	1	4	yes	—
63	C₂×Dic₁₃	—	2	8	no	—
64	C₂×Dic₁₃	—	2	8	no	—
65	C₂×Dic₁₃	—	2	2	no	—
66	C₂×Dic₁₃	—	2	2	no	—
67	C₂×Dic₁₃	—	2	2	no	—
68	C₂×Dic₁₃	—	2	2	no	—
69	C₂×Dic₁₃	—	2	4	no	—
70	C₂×Dic₁₃	—	2	4	no	—
71	C₂×Dic₁₃	—	2	4	no	—
72	C₂×Dic₁₃	—	4	8	no	—
73	C₂×Dic₁₃	C₂×D₄	1	4	yes	—
74	C₂×Dic₁₃	C₂×Q₈	1	4	yes	—
75	C₂²×C₄⋊C₄	—	13	2	no	—
76	C₂²×C₄⋊C₄	—	13	1	no	—
77	C₂²×C₄⋊C₄	D₁₃	1	1	yes	characteristic
78	C₂²×C₄²	—	13	1	no	—
79	#389	—	13	8	no	—
80	C₂×#95	—	13	2	no	—
81	C₂²×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
82	C₂²×C₁₃	C₄×D₄	1	4	yes	—
83	C₂²×C₁₃	C₄×Q₈	1	4	yes	—
84	C₂²×C₁₃	#121	1	4	yes	—
85	C₂²×C₁₃	C₂²⋊Q₈	1	4	yes	—
86	C₂²×C₁₃	#125	1	4	yes	—
87	C₂²×C₁₃	C₄⋊Q₈	1	4	yes	—
88	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
89	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
90	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
91	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
92	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
93	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
94	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
95	C₄×C₁₃	—	2	8	no	—
96	C₄×C₁₃	C₂×C₄⋊C₄	1	8	yes	complemented
97	Dic₁₃	—	2	4	no	—
98	Dic₁₃	—	2	4	no	—
99	Dic₁₃	—	4	4	no	—
100	C₂³×C₄	—	13	1	no	—
101	C₂³×C₄	—	13	1	no	—
102	C₂³×C₄	—	13	2	no	—
103	C₂³×C₄	C₂×D₁₃	1	2	yes	—
104	C₂³×C₄	C₂×D₁₃	1	1	yes	characteristic
105	C₂×C₄⋊C₄	—	13	8	no	—
106	C₂×C₄⋊C₄	—	13	4	no	—
107	C₂×C₄⋊C₄	—	26	8	no	—
108	C₂×C₄⋊C₄	—	26	4	no	—
109	C₂×C₄⋊C₄	Dic₁₃	1	8	yes	complemented
110	C₂×C₄⋊C₄	C₂×D₁₃	1	4	yes	—
111	C₂×C₄²	—	13	4	no	—
112	C₂×C₄²	—	26	4	no	—
113	#95	—	13	8	no	—
114	C₂×C₁₃	#389	1	8	yes	complemented
115	C₂×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
117	C₂×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
118	C₂×C₁₃	C₂×#121	1	1	yes	characteristic
119	C₂×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
120	C₂×C₁₃	C₂×#125	1	1	yes	characteristic
121	C₂×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
122	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
123	C₂²×C₄	—	2	4	no	—
124	C₂²×C₄	—	2	4	no	—
125	C₂²×C₄	—	13	4	no	—
126	C₂²×C₄	—	13	4	no	—
127	C₂²×C₄	—	13	2	no	—
128	C₂²×C₄	—	13	2	no	—
129	C₂²×C₄	—	13	4	no	—
130	C₂²×C₄	—	26	2	no	—
131	C₂²×C₄	—	26	2	no	—
132	C₂²×C₄	—	26	2	no	—
133	C₂²×C₄	—	26	2	no	—
134	C₂²×C₄	—	26	4	no	—
135	C₂²×C₄	—	26	4	no	—
136	C₂²×C₄	—	26	4	no	—
137	C₂²×C₄	Dic₂₆	1	4	yes	—
138	C₂²×C₄	D₅₂	1	4	yes	—
139	C₂²×C₄	C₂×Dic₁₃	1	8	yes	—
140	C₂²×C₄	C₂×Dic₁₃	1	4	yes	—
141	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
142	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
143	C₄⋊C₄	—	26	16	no	—
144	C₄⋊C₄	—	26	8	no	—
145	C₄⋊C₄	C₂×Dic₁₃	1	16	yes	complemented
146	C₄²	—	26	8	no	—
147	C₁₃	C₂×#389	1	1	yes	characteristic, complemented, Sylow
148	C₂³	C₂×Dic₂₆	1	2	yes	—
149	C₂³	C₂×D₅₂	1	2	yes	—
150	C₂³	D₄×D₁₃	1	2	yes	—
151	C₂³	#6129	1	2	yes	—
152	C₂³	Q₈×D₁₃	1	2	yes	—
153	C₂³	#6131	1	2	yes	—
154	C₂³	C₂²×Dic₁₃	1	2	yes	—
155	C₂³	C₂³×D₁₃	1	1	yes	characteristic
156	C₂×C₄	—	2	16	no	—
157	C₂×C₄	—	2	4	no	—
158	C₂×C₄	—	2	4	no	—
159	C₂×C₄	—	13	4	no	—
160	C₂×C₄	—	13	4	no	—
161	C₂×C₄	—	26	8	no	—
162	C₂×C₄	—	26	8	no	—
163	C₂×C₄	—	26	2	no	—
164	C₂×C₄	—	26	2	no	—
165	C₂×C₄	—	26	2	no	—
166	C₂×C₄	—	26	2	no	—
167	C₂×C₄	—	26	4	no	—
168	C₂×C₄	—	26	4	no	—
169	C₂×C₄	—	26	4	no	—
170	C₂×C₄	—	52	8	no	—
171	C₂×C₄	C₄⋊Dic₁₃	1	16	yes	complemented
172	C₂×C₄	C₂×Dic₂₆	1	4	yes	—
173	C₂×C₄	C₂×D₅₂	1	4	yes	—
174	C₂×C₄	C₂²×Dic₁₃	1	8	yes	—
175	C₂×C₄	C₂²×Dic₁₃	1	4	yes	—
176	C₂²	#88142	1	4	yes	—
177	C₂²	#88144	1	4	yes	—
178	C₂²	#88149	1	4	yes	—
179	C₂²	#88151	1	4	yes	—
180	C₂²	C₂×C₄⋊Dic₁₃	1	4	yes	—
181	C₂²	D₄×Dic₁₃	1	4	yes	—
182	C₂²	Q₈×Dic₁₃	1	4	yes	—
183	C₂²	C₂²×Dic₂₆	1	1	yes	characteristic
184	C₂²	C₂²×D₅₂	1	1	yes	characteristic
185	C₂²	C₂×D₄×D₁₃	1	1	yes	characteristic
186	C₂²	C₂×#6129	1	1	yes	characteristic
187	C₂²	C₂×Q₈×D₁₃	1	1	yes	characteristic
188	C₂²	C₂×#6131	1	1	yes	characteristic
189	C₂²	C₂³×Dic₁₃	1	1	yes	characteristic
190	C₄	—	2	8	no	—
191	C₄	—	26	4	no	—
192	C₄	—	26	4	no	—
193	C₄	—	52	4	no	—
194	C₄	C₂×C₄⋊Dic₁₃	1	8	yes	complemented
195	C₂	#11718646	1	8	yes	direct product factor
196	C₂	C₂×#88142	1	1	yes	characteristic
197	C₂	C₂×#88144	1	1	yes	characteristic
198	C₂	C₂×#88149	1	1	yes	characteristic
199	C₂	C₂×#88151	1	1	yes	characteristic
200	C₂	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
201	C₂	C₂×D₄×Dic₁₃	1	1	yes	characteristic
202	C₂	C₂×Q₈×Dic₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂³×C₄
Frattini	C₂³	C₂³×D₁₃
Fitting	C₂²×C₁₃×C₄⋊C₄	C₂
socle, prime radical	C₂⁴×C₁₃	C₂³
cosocle	C₂³×C₁₃	C₂⁴
hypercenter	C₂²×C₄⋊C₄	D₁₃
hypocenter	C₁₃	C₂×#389
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
6. #11718646	C₂	direct (N × H)
12. C₂×C₁₃×C₄⋊C₄	C₄	semidirect
42. C₁₃×C₄⋊C₄	C₂×C₄	semidirect
58. C₂×C₄×C₁₃	C₄⋊C₄	semidirect
96. C₄×C₁₃	C₂×C₄⋊C₄	semidirect
109. C₂×C₄⋊C₄	Dic₁₃	semidirect
114. C₂×C₁₃	#389	semidirect
145. C₄⋊C₄	C₂×Dic₁₃	semidirect
147. C₁₃	C₂×#389	semidirect
171. C₂×C₄	C₄⋊Dic₁₃	semidirect
194. C₄	C₂×C₄⋊Dic₁₃	semidirect
195. C₂	#11718646	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×C₁₃×C₄⋊C₄	2
C₂²×C₄⋊Dic₁₃	2
C₂²×C₄×Dic₁₃	2
C₂×#88071	2
#11718646	2
C₂×#389	13

Subgroups — C2×#11718646 #13117288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11718646 #13117288