Subgroups — #16015494

Order 3328.

1006 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718535	C₂	1	4	yes	maximal
2	#13123233	C₂	1	2	yes	maximal
3	#13114996	C₂	1	1	yes	maximal, characteristic
4	#13114995	C₂	1	2	yes	maximal
5	#13114994	C₂	1	4	yes	maximal
6	C₄×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic
8	C₂×#88142	—	2	4	no	—
9	C₂×#88142	C₂²	1	4	yes	—
10	C₂×C₁₃×#107	C₂²	1	4	yes	—
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#384	C₂²	1	2	yes	—
13	C₂×#88058	C₂²	1	4	yes	—
14	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
15	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
16	#11718637	—	2	4	no	—
17	#11718637	C₂²	1	4	yes	—
18	C₂×#88047	C₂²	1	8	yes	—
19	#11718596	C₂²	1	2	yes	—
20	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
22	#11718535	—	2	16	no	—
23	C₂²×Dic₂₆	—	2	4	no	—
24	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
26	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
27	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₃	—	2	4	no	—
29	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
30	C₂×#6101	—	2	8	no	—
31	C₂×#6101	—	2	4	no	—
32	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
33	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
34	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
35	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
36	C₂²×#1055	C₂³	1	2	yes	—
37	#88142	—	2	16	no	—
38	#88142	—	4	16	no	—
39	C₁₃×#107	—	2	8	no	—
40	C₄×C₈×C₁₃	Q₈	1	4	yes	complemented
41	#88058	—	2	8	no	—
42	C₈×Dic₁₃	D₄	1	8	yes	—
43	C₈×Dic₁₃	Q₈	1	8	yes	complemented
44	#88047	—	2	16	no	—
45	C₄×#1055	Q₈	1	4	yes	complemented
46	#33312	—	13	1	no	maximal, Sylow
47	C₂²×C₄×C₁₃	—	2	4	no	—
48	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
49	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
50	C₂²×Dic₁₃	—	2	4	no	—
51	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
53	C₂²×Dic₁₃	C₂×D₄	1	2	yes	—
54	C₂×Dic₂₆	—	4	8	no	—
55	C₂×Dic₂₆	—	4	16	no	—
56	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
57	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
58	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
59	C₁₃×C₄⋊C₄	—	2	8	no	—
60	C₁₃×C₄⋊C₄	—	4	8	no	—
61	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
62	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
63	C₄⋊Dic₁₃	—	2	8	no	—
64	C₄⋊Dic₁₃	—	4	8	no	—
65	#6101	—	4	8	no	—
66	#6101	—	4	16	no	—
67	C₄×Dic₁₃	D₈	1	8	yes	—
68	C₄×Dic₁₃	Q₁₆	1	8	yes	—
69	C₄×Dic₁₃	C₂×D₄	1	4	yes	—
70	C₄×Dic₁₃	C₂×Q₈	1	4	yes	—
71	C₂×#1055	C₂×D₄	1	4	yes	—
72	C₂×#1055	C₂×Q₈	1	4	yes	—
73	C₂×#1055	C₂×Q₈	1	4	yes	—
74	C₂×#500	—	13	4	no	—
75	#2868	—	13	2	no	—
76	#1845	—	13	4	no	—
77	#1845	—	13	1	no	—
78	#1845	—	13	2	no	—
79	#1845	D₁₃	1	1	yes	characteristic
80	C₄²×C₈	—	13	1	no	—
81	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
82	C₂×C₄×C₁₃	—	4	4	no	—
83	C₂×C₄×C₁₃	—	4	8	no	—
84	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
85	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
86	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
87	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
88	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
89	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
91	C₂×Dic₁₃	—	4	4	no	—
92	C₂×Dic₁₃	—	4	8	no	—
93	C₂×Dic₁₃	#127	1	2	yes	—
94	C₂×Dic₁₃	#127	1	2	yes	—
95	C₂×Dic₁₃	C₄⋊Q₈	1	4	yes	—
96	C₂×Dic₁₃	C₂×D₈	1	4	yes	—
97	C₂×Dic₁₃	C₂×D₈	1	4	yes	—
98	C₂×Dic₁₃	C₂×Q₁₆	1	4	yes	—
99	C₂×Dic₁₃	C₂×Q₁₆	1	4	yes	—
100	Dic₂₆	—	8	16	no	—
101	C₈×C₁₃	C₄⋊Q₈	1	8	yes	complemented
102	#1055	C₄⋊Q₈	1	8	yes	complemented
103	C₂×C₄⋊Q₈	—	13	4	no	—
104	C₂×C₄⋊Q₈	—	26	4	no	—
105	#500	—	26	16	no	—
106	C₂×#107	—	13	4	no	—
107	C₂×#107	—	13	8	no	—
108	C₂×#107	C₂×D₁₃	1	4	yes	—
109	C₂×C₄×C₈	—	13	2	no	—
110	C₂×C₄×C₈	—	13	2	no	—
111	C₂×C₄×C₈	—	13	1	no	—
112	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
113	#384	—	13	4	no	—
114	#384	—	13	2	no	—
115	#384	—	26	4	no	—
116	#384	C₂×D₁₃	1	2	yes	—
117	C₄³	—	13	1	no	—
118	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
119	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
120	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
121	C₂²×C₁₃	C₂²×D₈	1	2	yes	—
122	C₂²×C₁₃	C₂²×Q₁₆	1	2	yes	—
123	C₄×C₁₃	—	8	4	no	—
124	C₄×C₁₃	#500	1	8	yes	complemented
125	C₄×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
126	C₄×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
127	Dic₁₃	—	8	4	no	—
128	Dic₁₃	#493	1	4	yes	—
129	Dic₁₃	#494	1	4	yes	—
130	Dic₁₃	#500	1	8	yes	complemented
131	C₂²×Q₈	—	26	4	no	—
132	C₂²×C₈	—	13	2	no	—
133	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
134	C₄⋊Q₈	—	26	16	no	—
135	C₄⋊Q₈	—	52	16	no	—
136	C₂×C₄⋊C₄	—	2	4	no	—
137	C₂×C₄⋊C₄	—	13	4	no	—
138	C₂×C₄⋊C₄	—	26	4	no	—
139	C₂×C₄⋊C₄	—	26	8	no	—
140	C₂×C₄⋊C₄	—	26	4	no	—
141	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
142	C₂×C₄²	—	13	2	no	—
143	C₂×C₄²	—	13	2	no	—
144	C₂×C₄²	—	13	1	no	—
145	C₂×C₄²	—	13	1	no	—
146	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
147	#107	—	2	8	no	—
148	#107	—	26	16	no	—
149	#107	—	26	8	no	—
150	C₄×C₈	—	13	8	no	—
151	C₄×C₈	—	13	8	no	—
152	C₄×C₈	—	13	4	no	—
153	C₄×C₈	Dic₂₆	1	4	yes	complemented
154	C₂×C₁₃	#2868	1	1	yes	characteristic
155	C₂×C₁₃	C₂×#493	1	1	yes	characteristic
156	C₂×C₁₃	C₂×#494	1	1	yes	characteristic
157	C₂×C₁₃	C₂×#500	1	2	yes	—
158	C₂×C₁₃	C₂×#500	1	2	yes	—
159	C₂×Q₈	—	52	8	no	—
160	C₂×Q₈	—	52	16	no	—
161	C₂²×C₄	—	2	4	no	—
162	C₂²×C₄	—	13	2	no	—
163	C₂²×C₄	—	13	1	no	—
164	C₂²×C₄	—	13	1	no	—
165	C₂²×C₄	—	26	4	no	—
166	C₂²×C₄	D₄×D₁₃	1	2	yes	—
167	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
168	C₂×C₈	—	13	4	no	—
169	C₂×C₈	—	13	4	no	—
170	C₂×C₈	—	13	4	no	—
171	C₂×C₈	C₂×Dic₂₆	1	4	yes	—
172	C₂×C₈	D₄×D₁₃	1	4	yes	—
173	C₂×C₈	Q₈×D₁₃	1	4	yes	—
174	C₄⋊C₄	—	2	8	no	—
175	C₄⋊C₄	—	4	8	no	—
176	C₄⋊C₄	—	26	8	no	—
177	C₄⋊C₄	—	52	8	no	—
178	C₄⋊C₄	—	52	16	no	—
179	C₄⋊C₄	—	52	8	no	—
180	C₄²	—	13	8	no	—
181	C₄²	—	13	8	no	—
182	C₄²	—	13	4	no	—
183	C₄²	—	13	4	no	—
184	C₄²	C₂×Dic₂₆	1	2	yes	—
185	C₄²	Q₈×D₁₃	1	2	yes	—
186	C₁₃	#33312	1	1	yes	characteristic, complemented, Sylow
187	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
188	Q₈	—	104	16	no	—
189	C₂×C₄	—	4	8	no	—
190	C₂×C₄	—	4	4	no	—
191	C₂×C₄	—	13	4	no	—
192	C₂×C₄	—	13	4	no	—
193	C₂×C₄	—	13	4	no	—
194	C₂×C₄	—	13	4	no	—
195	C₂×C₄	—	13	4	no	—
196	C₂×C₄	—	13	2	no	—
197	C₂×C₄	—	13	2	no	—
198	C₂×C₄	—	52	8	no	—
199	C₂×C₄	—	52	4	no	—
200	C₂×C₄	#88142	1	4	yes	—
201	C₂×C₄	D₈×D₁₃	1	4	yes	—
202	C₂×C₄	Q₁₆×D₁₃	1	4	yes	—
203	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
204	C₂×C₄	C₂×D₄×D₁₃	1	2	yes	—
205	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
206	C₂×C₄	C₂×Q₈×D₁₃	1	2	yes	—
207	C₈	—	13	8	no	—
208	C₈	#88142	1	8	yes	complemented
209	C₂²	C₂×#88142	1	1	yes	characteristic
210	C₂²	D₁₃×#127	1	1	yes	characteristic
211	C₂²	D₁₃×C₄⋊Q₈	1	1	yes	characteristic
212	C₂²	C₂×D₈×D₁₃	1	2	yes	—
213	C₂²	C₂×Q₁₆×D₁₃	1	2	yes	—
214	C₄	—	8	4	no	—
215	C₄	—	13	4	no	—
216	C₄	—	13	4	no	—
217	C₄	—	13	8	no	—
218	C₄	—	104	4	no	—
219	C₄	#11718535	1	8	yes	complemented
220	C₄	C₂×#88142	1	2	yes	—
221	C₄	D₁₃×C₄⋊Q₈	1	2	yes	—
222	C₂	#13123233	1	1	yes	characteristic
223	C₂	D₁₃×#493	1	1	yes	characteristic
224	C₂	D₁₃×#494	1	1	yes	characteristic
225	C₂	D₁₃×#500	1	2	yes	—
226	C₂	C₂×#11718535	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₁₃
commutator, cosocle	C₂²×C₄×C₁₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1845	C₂
socle, prime radical	C₂³×C₁₃	C₂²×D₄
hypercenter	#1845	D₁₃
hypocenter	C₁₃	#33312
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

Complements

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

N	H ≅ G/N	type
40. C₄×C₈×C₁₃	Q₈	semidirect
43. C₈×Dic₁₃	Q₈	semidirect
45. C₄×#1055	Q₈	semidirect
101. C₈×C₁₃	C₄⋊Q₈	semidirect
102. #1055	C₄⋊Q₈	semidirect
124. C₄×C₁₃	#500	semidirect
130. Dic₁₃	#500	semidirect
153. C₄×C₈	Dic₂₆	semidirect
186. C₁₃	#33312	semidirect
208. C₈	#88142	semidirect
219. C₄	#11718535	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718535	2
#13123233	2
#13114996	2
#13114995	2
#13114994	2
C₄×C₈×Dic₁₃	2
C₁₃×#1845	2
#33312	13