Subgroups — C₂²×#11718143 #15860315

Order 3328.

3006 conjugacy classes of subgroups.

The subgroup lattice has 222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊Dic₁₃	C₂	1	2	yes	maximal
2	C₂×#11718143	C₂	1	12	yes	maximal, direct product factor
3	C₂⁴×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
5	C₂⁴×Dic₁₃	—	2	2	no	—
6	C₂³×C₈×C₁₃	—	2	8	no	—
7	C₂³×C₈×C₁₃	C₄	1	8	yes	complemented
8	C₂³×C₈×C₁₃	C₂²	1	6	yes	—
9	C₂²×C₄⋊Dic₁₃	—	2	6	no	—
10	C₂²×C₄⋊Dic₁₃	—	2	8	no	—
11	C₂²×C₄⋊Dic₁₃	C₄	1	16	yes	complemented
12	C₂²×C₄⋊Dic₁₃	C₂²	1	12	yes	—
13	#11718143	C₂²	1	16	yes	direct product factor
14	C₂⁵×C₁₃	D₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	—
16	C₂³×C₄×C₁₃	C₂×C₄	1	4	yes	—
17	C₂³×C₄×C₁₃	D₄	1	3	yes	—
18	C₂³×C₄×C₁₃	D₄	1	8	yes	—
19	C₂³×C₄×C₁₃	Q₈	1	4	yes	—
20	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
21	C₂³×Dic₁₃	—	2	16	no	—
22	C₂³×Dic₁₃	—	2	12	no	—
23	C₂³×Dic₁₃	—	4	8	no	—
24	C₂³×Dic₁₃	—	4	8	no	—
25	C₂²×C₈×C₁₃	—	2	32	no	—
26	C₂²×C₈×C₁₃	—	2	24	no	—
27	C₂²×C₈×C₁₃	C₂×C₄	1	24	yes	complemented
28	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
29	C₂×C₄⋊Dic₁₃	—	2	48	no	—
30	C₂×C₄⋊Dic₁₃	—	2	12	no	—
31	C₂×C₄⋊Dic₁₃	—	2	24	no	—
32	C₂×C₄⋊Dic₁₃	C₂×C₄	1	48	yes	complemented
33	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
34	C₂²×#340	—	13	1	no	maximal, Sylow
35	C₂⁴×C₁₃	C₂²⋊C₄	1	8	yes	—
36	C₂⁴×C₁₃	C₄⋊C₄	1	4	yes	—
37	C₂⁴×C₁₃	D₈	1	4	yes	—
38	C₂⁴×C₁₃	SD₁₆	1	8	yes	—
39	C₂⁴×C₁₃	Q₁₆	1	4	yes	—
40	C₂⁴×C₁₃	C₂×D₄	1	3	yes	—
41	C₂²×C₄×C₁₃	C₄²	1	16	yes	—
42	C₂²×C₄×C₁₃	C₂²⋊C₄	1	24	yes	—
43	C₂²×C₄×C₁₃	C₂²⋊C₄	1	16	yes	—
44	C₂²×C₄×C₁₃	C₄⋊C₄	1	32	yes	—
45	C₂²×C₄×C₁₃	C₄⋊C₄	1	12	yes	—
46	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	—
47	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
48	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
49	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	—
50	C₂²×C₄×C₁₃	C₂×Q₈	1	6	yes	—
51	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
52	C₂²×Dic₁₃	—	2	48	no	—
53	C₂²×Dic₁₃	—	2	8	no	—
54	C₂²×Dic₁₃	—	4	64	no	—
55	C₂²×Dic₁₃	—	4	24	no	—
56	C₂²×Dic₁₃	—	4	24	no	—
57	C₂×C₈×C₁₃	—	2	48	no	—
58	C₂×C₈×C₁₃	—	2	8	no	—
59	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	complemented
60	C₄⋊Dic₁₃	—	2	48	no	—
61	C₄⋊Dic₁₃	—	2	8	no	—
62	C₄⋊Dic₁₃	C₂²×C₄	1	16	yes	complemented
63	C₂⁴×C₈	D₁₃	1	1	yes	characteristic
64	C₂³×C₄⋊C₄	—	13	2	no	—
65	C₂×#340	—	13	12	no	—
66	C₂³×C₁₃	#95	1	16	yes	—
67	C₂³×C₁₃	#102	1	32	yes	—
68	C₂³×C₁₃	#103	1	32	yes	—
69	C₂³×C₁₃	#106	1	16	yes	—
70	C₂³×C₁₃	#107	1	16	yes	—
71	C₂³×C₁₃	C₂×C₂²⋊C₄	1	12	yes	—
72	C₂³×C₁₃	C₂×C₄⋊C₄	1	6	yes	—
73	C₂³×C₁₃	C₂×D₈	1	6	yes	—
74	C₂³×C₁₃	C₂×SD₁₆	1	12	yes	—
75	C₂³×C₁₃	C₂×Q₁₆	1	6	yes	—
76	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
77	C₂×C₄×C₁₃	#95	1	48	yes	—
78	C₂×C₄×C₁₃	C₂×C₄²	1	12	yes	—
79	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	12	yes	—
80	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	12	yes	—
81	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	24	yes	—
82	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	6	yes	—
83	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
85	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
86	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
87	C₂×Dic₁₃	—	2	16	no	—
88	C₂×Dic₁₃	—	4	8	no	—
89	C₂×Dic₁₃	—	4	8	no	—
90	C₂×Dic₁₃	—	4	96	no	—
91	C₈×C₁₃	—	2	8	no	—
92	C₂⁴×C₄	—	26	2	no	—
93	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
94	C₂³×C₈	—	2	8	no	—
95	C₂³×C₈	Dic₁₃	1	8	yes	complemented
96	C₂³×C₈	C₂×D₁₃	1	6	yes	—
97	C₂²×C₄⋊C₄	—	13	16	no	—
98	C₂²×C₄⋊C₄	—	13	12	no	—
99	C₂²×C₄⋊C₄	—	26	6	no	—
100	C₂²×C₄⋊C₄	—	26	8	no	—
101	#340	—	13	16	no	—
102	C₂²×C₁₃	#340	1	64	yes	complemented
103	C₂²×C₁₃	C₂×#95	1	12	yes	—
104	C₂²×C₁₃	C₂×#102	1	24	yes	—
105	C₂²×C₁₃	C₂×#103	1	24	yes	—
106	C₂²×C₁₃	C₂×#106	1	12	yes	—
107	C₂²×C₁₃	C₂×#107	1	12	yes	—
108	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	2	yes	—
109	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
110	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
111	C₂²×C₁₃	C₂²×SD₁₆	1	2	yes	—
112	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
113	C₄×C₁₃	C₂×#95	1	12	yes	—
114	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
115	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
116	C₄×C₁₃	C₂²×C₄⋊C₄	1	2	yes	—
117	Dic₁₃	—	4	16	no	—
118	C₂⁵	D₅₂	1	1	yes	characteristic
119	C₂³×C₄	—	26	16	no	—
120	C₂³×C₄	—	26	12	no	—
121	C₂³×C₄	—	52	8	no	—
122	C₂³×C₄	—	52	8	no	—
123	C₂³×C₄	Dic₂₆	1	4	yes	—
124	C₂³×C₄	C₄×D₁₃	1	8	yes	—
125	C₂³×C₄	D₅₂	1	3	yes	—
126	C₂³×C₄	C₂×Dic₁₃	1	4	yes	—
127	C₂³×C₄	C₂²⋊D₁₃	1	8	yes	—
128	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
129	C₂²×C₈	—	2	32	no	—
130	C₂²×C₈	—	2	24	no	—
131	C₂²×C₈	C₂×Dic₁₃	1	24	yes	complemented
132	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
133	C₂×C₄⋊C₄	—	13	48	no	—
134	C₂×C₄⋊C₄	—	13	8	no	—
135	C₂×C₄⋊C₄	—	26	48	no	—
136	C₂×C₄⋊C₄	—	26	12	no	—
137	C₂×C₄⋊C₄	—	26	24	no	—
138	C₂×C₁₃	C₂×#340	1	24	yes	complemented
139	C₂×C₁₃	C₂²×#95	1	1	yes	characteristic
140	C₂×C₁₃	C₂²×#102	1	2	yes	—
141	C₂×C₁₃	C₂²×#103	1	2	yes	—
142	C₂×C₁₃	C₂²×#106	1	1	yes	characteristic
143	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
144	C₂⁴	#6095	1	8	yes	—
145	C₂⁴	D₁₀₄	1	4	yes	—
146	C₂⁴	Dic₅₂	1	4	yes	—
147	C₂⁴	C₄⋊Dic₁₃	1	4	yes	—
148	C₂⁴	#6103	1	8	yes	—
149	C₂⁴	C₂×D₅₂	1	3	yes	—
150	C₂²×C₄	—	26	48	no	—
151	C₂²×C₄	—	26	8	no	—
152	C₂²×C₄	—	52	24	no	—
153	C₂²×C₄	—	52	24	no	—
154	C₂²×C₄	—	52	64	no	—
155	C₂²×C₄	C₄×Dic₁₃	1	16	yes	—
156	C₂²×C₄	#6101	1	32	yes	—
157	C₂²×C₄	C₄⋊Dic₁₃	1	12	yes	—
158	C₂²×C₄	#6103	1	24	yes	—
159	C₂²×C₄	C₂²⋊Dic₁₃	1	16	yes	—
160	C₂²×C₄	C₂×Dic₂₆	1	6	yes	—
161	C₂²×C₄	C₂×C₄×D₁₃	1	12	yes	—
162	C₂²×C₄	C₂×D₅₂	1	3	yes	—
163	C₂²×C₄	C₂²×Dic₁₃	1	6	yes	—
164	C₂²×C₄	C₂×C₂²⋊D₁₃	1	12	yes	—
165	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
166	C₂×C₈	—	2	48	no	—
167	C₂×C₈	—	2	8	no	—
168	C₂×C₈	C₂²×Dic₁₃	1	8	yes	complemented
169	C₄⋊C₄	—	13	16	no	—
170	C₄⋊C₄	—	26	48	no	—
171	C₄⋊C₄	—	26	8	no	—
172	C₁₃	C₂²×#340	1	1	yes	characteristic, complemented, Sylow
173	C₂³	#88056	1	32	yes	—
174	C₂³	#88057	1	16	yes	—
175	C₂³	#88058	1	16	yes	—
176	C₂³	#88061	1	32	yes	—
177	C₂³	#88071	1	16	yes	—
178	C₂³	C₂×#6095	1	12	yes	—
179	C₂³	C₂×D₁₀₄	1	6	yes	—
180	C₂³	C₂×Dic₅₂	1	6	yes	—
181	C₂³	C₂×C₄⋊Dic₁₃	1	6	yes	—
182	C₂³	C₂×#6103	1	12	yes	—
183	C₂³	C₂²×D₅₂	1	1	yes	characteristic
184	C₂×C₄	—	26	16	no	—
185	C₂×C₄	—	52	8	no	—
186	C₂×C₄	—	52	8	no	—
187	C₂×C₄	—	52	96	no	—
188	C₂×C₄	#88071	1	48	yes	—
189	C₂×C₄	C₂×C₄×Dic₁₃	1	12	yes	—
190	C₂×C₄	C₂×#6101	1	24	yes	—
191	C₂×C₄	C₂×C₄⋊Dic₁₃	1	6	yes	—
192	C₂×C₄	C₂×#6103	1	12	yes	—
193	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	12	yes	—
194	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
195	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
196	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
197	C₂×C₄	C₂²×C₂²⋊D₁₃	1	2	yes	—
198	C₈	—	2	8	no	—
199	C₂²	#11718143	1	64	yes	direct product factor
200	C₂²	C₂×#88056	1	24	yes	—
201	C₂²	C₂×#88057	1	12	yes	—
202	C₂²	C₂×#88058	1	12	yes	—
203	C₂²	C₂×#88061	1	24	yes	—
204	C₂²	C₂×#88071	1	12	yes	—
205	C₂²	C₂²×#6095	1	2	yes	—
206	C₂²	C₂²×D₁₀₄	1	1	yes	characteristic
207	C₂²	C₂²×Dic₅₂	1	1	yes	characteristic
208	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
209	C₂²	C₂²×#6103	1	2	yes	—
210	C₄	—	52	16	no	—
211	C₄	C₂×#88071	1	12	yes	—
212	C₄	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
213	C₄	C₂²×#6101	1	2	yes	—
214	C₄	C₂²×C₂²⋊Dic₁₃	1	1	yes	characteristic
215	C₂	C₂×#11718143	1	24	yes	direct product factor
216	C₂	C₂²×#88071	1	1	yes	characteristic
217	C₂	C₂²×#88061	1	2	yes	—
218	C₂	C₂²×#88056	1	2	yes	—
219	C₂	C₂²×#88057	1	1	yes	characteristic
220	C₂	C₂²×#88058	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁵	D₅₂
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂⁴×C₈×C₁₃	C₂
socle, prime radical	C₂⁵×C₁₃	D₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂⁴×C₈	D₁₃
hypocenter	C₁₃	C₂²×#340
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×C₄ ◁ C₂⁴×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#11718143	C₂	direct (N × H)
7. C₂³×C₈×C₁₃	C₄	semidirect
11. C₂²×C₄⋊Dic₁₃	C₄	semidirect
13. #11718143	C₂²	direct (N × H)
27. C₂²×C₈×C₁₃	C₂×C₄	semidirect
32. C₂×C₄⋊Dic₁₃	C₂×C₄	semidirect
59. C₂×C₈×C₁₃	C₂²×C₄	semidirect
62. C₄⋊Dic₁₃	C₂²×C₄	semidirect
95. C₂³×C₈	Dic₁₃	semidirect
102. C₂²×C₁₃	#340	semidirect
131. C₂²×C₈	C₂×Dic₁₃	semidirect
138. C₂×C₁₃	C₂×#340	semidirect
168. C₂×C₈	C₂²×Dic₁₃	semidirect
172. C₁₃	C₂²×#340	semidirect
199. C₂²	#11718143	direct (N × H)
215. C₂	C₂×#11718143	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊Dic₁₃	2
C₂×#11718143	2
C₂⁴×C₈×C₁₃	2
C₂²×#340	13

Subgroups — C22×#11718143 #15860315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11718143 #15860315