Subgroups — #15779379

Order 3328.

462 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	C₂×#11718093	C₂	1	2	yes	maximal, complemented
2	C₂×C₂²⋊#6090	C₂	1	1	yes	maximal, characteristic
3	C₈×C₂²⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	#13112913	C₂	1	2	yes	maximal, complemented
5	C₂³×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×C₁₃×C₁₆	—	2	2	no	—
8	C₂²×C₁₃×C₁₆	—	2	4	no	—
9	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
10	C₄×C₂²⋊Dic₁₃	C₄	1	1	yes	characteristic
11	C₂×C₂²⋊#1055	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
13	C₂²×#6090	C₂²	1	1	yes	characteristic
14	C₂²×#6090	C₂²	1	1	yes	characteristic
15	#11718142	C₄	1	2	yes	—
16	C₂²⋊#6090	—	2	2	no	—
17	#11718093	—	2	4	no	—
18	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	—	2	2	no	—
20	C₂²×C₈×C₁₃	—	2	2	no	—
21	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	D₄	1	2	yes	—
23	C₂²×C₈×C₁₃	Q₈	1	2	yes	—
24	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
25	C₂×C₂²⋊Dic₁₃	C₈	1	1	yes	characteristic
26	C₂×C₂²⋊Dic₁₃	C₈	1	1	yes	characteristic
27	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
28	C₂²×#1055	C₂×C₄	1	2	yes	—
29	C₂×C₁₃×C₁₆	—	2	8	no	—
30	C₂×C₁₃×C₁₆	—	2	2	no	—
31	C₂×C₁₃×C₁₆	—	2	2	no	—
32	C₂×C₁₃×C₁₆	D₄	1	4	yes	—
33	#88071	C₈	1	2	yes	—
34	C₂²⋊#1055	—	2	2	no	—
35	C₈×Dic₁₃	—	2	2	no	—
36	C₈×Dic₁₃	—	2	2	no	—
37	C₂×#6090	—	2	2	no	—
38	C₂×#6090	—	2	1	no	—
39	C₂×#6090	—	2	1	no	—
40	C₂×#6090	—	2	2	no	—
41	#12912	—	13	1	no	maximal, Sylow
42	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	—	2	2	no	—
44	C₂²×C₄×C₁₃	—	2	2	no	—
45	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
46	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
48	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
49	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
50	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
51	C₂×C₈×C₁₃	—	2	2	no	—
52	C₂×C₈×C₁₃	—	2	2	no	—
53	C₂×C₈×C₁₃	—	2	4	no	—
54	C₂×C₈×C₁₃	—	2	2	no	—
55	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
56	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
57	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
58	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
59	C₂×C₈×C₁₃	#41	1	2	yes	—
60	C₂²⋊Dic₁₃	—	2	2	no	—
61	C₂²⋊Dic₁₃	C₁₆	1	4	yes	complemented
62	C₄×Dic₁₃	—	2	2	no	—
63	C₄×Dic₁₃	—	2	2	no	—
64	C₂×#1055	—	2	2	no	—
65	C₂×#1055	—	2	2	no	—
66	C₂×#1055	—	2	2	no	—
67	C₁₃×C₁₆	—	2	4	no	—
68	#6090	—	4	1	no	—
69	#6090	—	4	1	no	—
70	C₂³×C₁₆	D₁₃	1	1	yes	characteristic
71	C₂×C₄⋊C₁₆	—	13	2	no	—
72	C₂×C₂²⋊C₁₆	—	13	1	no	—
73	C₈×C₂²⋊C₄	—	13	1	no	—
74	#1374	—	13	2	no	—
75	C₂³×C₁₃	—	2	2	no	—
76	C₂³×C₁₃	—	2	2	no	—
77	C₂³×C₁₃	C₄⋊C₈	1	2	yes	—
78	C₂³×C₁₃	C₂×C₁₆	1	2	yes	—
79	C₂³×C₁₃	M₃₂	1	2	yes	—
80	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
81	C₂×C₄×C₁₃	—	2	2	no	—
82	C₂×C₄×C₁₃	—	2	2	no	—
83	C₂×C₄×C₁₃	—	2	2	no	—
84	C₂×C₄×C₁₃	—	2	4	no	—
85	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
86	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
88	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
89	C₂×C₄×C₁₃	#131	1	2	yes	—
90	C₂×Dic₁₃	—	2	2	no	—
91	C₂×Dic₁₃	—	2	2	no	—
92	C₂×Dic₁₃	—	2	2	no	—
93	C₂×Dic₁₃	—	2	2	no	—
94	C₂×Dic₁₃	—	2	2	no	—
95	C₂×Dic₁₃	C₂×C₁₆	1	4	yes	complemented
96	C₈×C₁₃	—	2	2	no	—
97	C₈×C₁₃	#120	1	1	yes	characteristic
98	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
99	C₈×C₁₃	#123	1	1	yes	characteristic
100	#1055	—	4	2	no	—
101	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
102	C₂²×C₁₆	—	2	2	no	—
103	C₂²×C₁₆	—	2	4	no	—
104	C₂²×C₁₆	—	13	1	no	—
105	C₂²×C₁₆	—	13	1	no	—
106	C₂²×C₁₆	C₂×D₁₃	1	2	yes	—
107	C₂×C₂²⋊C₈	—	13	1	no	—
108	C₂×C₄×C₈	—	13	2	no	—
109	C₄×C₂²⋊C₄	—	13	1	no	—
110	C₄⋊C₁₆	—	26	4	no	—
111	C₂²⋊C₁₆	—	26	2	no	—
112	#336	—	13	2	no	—
113	C₂²×C₁₃	—	2	2	no	—
114	C₂²×C₁₃	—	2	2	no	—
115	C₂²×C₁₃	—	2	4	no	—
116	C₂²×C₁₃	—	2	4	no	—
117	C₂²×C₁₃	C₄⋊C₁₆	1	4	yes	complemented
118	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
119	C₂²×C₁₃	C₈×D₄	1	2	yes	—
120	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
121	C₂²×C₁₃	C₂×M₃₂	1	1	yes	characteristic
122	C₂²×C₁₃	#504	1	2	yes	—
123	C₄×C₁₃	—	2	2	no	—
124	C₄×C₁₃	#385	1	1	yes	characteristic
125	C₄×C₁₃	#424	1	1	yes	characteristic
126	C₄×C₁₃	#435	1	2	yes	—
127	Dic₁₃	—	2	4	no	—
128	Dic₁₃	—	4	2	no	—
129	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
130	C₂²×C₈	—	2	2	no	—
131	C₂²×C₈	—	2	2	no	—
132	C₂²×C₈	—	13	2	no	—
133	C₂²×C₈	Dic₂₆	1	2	yes	—
134	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
135	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
136	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
137	C₂×C₂²⋊C₄	—	13	1	no	—
138	C₂×C₂²⋊C₄	—	13	1	no	—
139	C₂×C₄²	—	13	2	no	—
140	C₂×C₁₆	—	2	8	no	—
141	C₂×C₁₆	—	2	2	no	—
142	C₂×C₁₆	—	2	2	no	—
143	C₂×C₁₆	—	26	2	no	—
144	C₂×C₁₆	—	26	1	no	—
145	C₂×C₁₆	—	26	1	no	—
146	C₂×C₁₆	—	26	2	no	—
147	C₂×C₁₆	C₂²⋊D₁₃	1	4	yes	—
148	C₂²⋊C₈	—	26	2	no	—
149	C₄×C₈	—	26	2	no	—
150	C₄×C₈	—	26	2	no	—
151	#95	—	13	2	no	—
152	C₂×C₁₃	—	2	4	no	—
153	C₂×C₁₃	#1850	1	1	yes	characteristic
154	C₂×C₁₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
155	C₂×C₁₃	#2151	1	1	yes	characteristic
156	C₂×C₁₃	D₄×C₁₆	1	2	yes	—
157	C₂×C₁₃	#2168	1	2	yes	—
158	C₂⁴	C₈×D₁₃	1	1	yes	characteristic
159	C₂²×C₄	—	2	2	no	—
160	C₂²×C₄	—	2	2	no	—
161	C₂²×C₄	—	13	2	no	—
162	C₂²×C₄	—	13	2	no	—
163	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
164	C₂²×C₄	#6094	1	2	yes	—
165	C₂²×C₄	#6101	1	2	yes	—
166	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	4	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	2	2	no	—
171	C₂×C₈	—	26	2	no	—
172	C₂×C₈	—	26	2	no	—
173	C₂×C₈	—	26	2	no	—
174	C₂×C₈	#6101	1	2	yes	—
175	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
176	C₂×C₈	#6127	1	2	yes	—
177	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
178	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
179	C₂²⋊C₄	—	13	4	no	—
180	C₂²⋊C₄	—	26	2	no	—
181	C₄²	—	26	2	no	—
182	C₄²	—	26	2	no	—
183	C₁₆	—	2	4	no	—
184	C₁₆	—	52	1	no	—
185	C₁₆	—	52	1	no	—
186	C₁₃	#12912	1	1	yes	characteristic, complemented, Sylow
187	C₂³	—	2	2	no	—
188	C₂³	—	2	2	no	—
189	C₂³	C₁₆×D₁₃	1	2	yes	—
190	C₂³	#88038	1	2	yes	—
191	C₂³	#88054	1	2	yes	—
192	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	4	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	13	4	no	—
198	C₂×C₄	—	26	2	no	—
199	C₂×C₄	—	26	2	no	—
200	C₂×C₄	—	26	2	no	—
201	C₂×C₄	—	26	2	no	—
202	C₂×C₄	—	26	2	no	—
203	C₂×C₄	#88054	1	2	yes	—
204	C₂×C₄	C₂×#6094	1	1	yes	characteristic
205	C₂×C₄	#88155	1	2	yes	—
206	C₂×C₄	C₂×#6101	1	1	yes	characteristic
207	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
208	C₈	—	2	2	no	—
209	C₈	—	52	2	no	—
210	C₈	#88178	1	2	yes	—
211	C₈	#88183	1	1	yes	characteristic
212	C₈	#88207	1	1	yes	characteristic
213	C₂²	—	2	2	no	—
214	C₂²	—	2	2	no	—
215	C₂²	—	2	4	no	—
216	C₂²	—	2	4	no	—
217	C₂²	#11718093	1	4	yes	complemented
218	C₂²	C₂×C₁₆×D₁₃	1	1	yes	characteristic
219	C₂²	C₂×#88038	1	1	yes	characteristic
220	C₂²	#11718562	1	2	yes	—
221	C₂²	C₂×#88054	1	1	yes	characteristic
222	C₂²	C₈×C₂²⋊D₁₃	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	26	4	no	—
225	C₄	—	52	2	no	—
226	C₄	#11718763	1	1	yes	characteristic
227	C₄	#11718772	1	2	yes	—
228	C₄	#11718871	1	1	yes	characteristic
229	C₂	—	2	4	no	—
230	C₂	#13115014	1	1	yes	characteristic
231	C₂	C₂×#11718093	1	1	yes	characteristic
232	C₂	#13116594	1	1	yes	characteristic
233	C₂	C₁₆×C₂²⋊D₁₃	1	2	yes	—
234	C₂	#13116661	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂²×C₁₆
Fitting	C₂³×C₁₃×C₁₆	C₂
socle	C₂³×C₁₃	C₂²×C₈
prime radical	C₂⁴×C₁₃	C₂×C₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂³×C₁₆	D₁₃
hypocenter	C₁₃	#12912
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂³×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#11718093	C₂	semidirect
4. #13112913	C₂	semidirect
61. C₂²⋊Dic₁₃	C₁₆	semidirect
95. C₂×Dic₁₃	C₂×C₁₆	semidirect
117. C₂²×C₁₃	C₄⋊C₁₆	semidirect
186. C₁₃	#12912	semidirect
217. C₂²	#11718093	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718093	2
C₂×C₂²⋊#6090	2
C₈×C₂²⋊Dic₁₃	2
#13112913	2
C₂³×C₁₃×C₁₆	2
#12912	13