Subgroups — #15763013

Order 3328.

468 conjugacy classes of subgroups.

The subgroup lattice has 266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123199	C₂	1	1	yes	maximal, characteristic
2	C₄×#88043	C₂	1	1	yes	maximal, characteristic
3	#13112718	C₂	1	4	yes	maximal
4	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic
5	C₂×#88124	C₄	1	2	yes	—
6	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
7	C₂×C₁₃×#97	C₂²	1	2	yes	—
8	C₄³×C₁₃	C₂²	1	1	yes	characteristic
9	#11718597	C₂²	1	2	yes	—
10	#11718596	C₄	1	1	yes	characteristic
11	#11718596	C₄	1	1	yes	characteristic
12	#11718589	—	2	1	no	—
13	#11718589	—	2	1	no	—
14	#11718589	—	2	1	no	—
15	#11718589	—	2	1	no	—
16	C₂×#88043	—	2	1	no	—
17	C₂×#88043	C₂²	1	2	yes	—
18	C₂×C₄×#1055	—	2	1	no	—
19	C₁₃×#336	—	2	1	no	—
20	C₂²×C₈×C₁₃	—	2	2	no	—
21	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₃	—	2	1	no	—
29	C₂×C₄⋊Dic₁₃	—	2	1	no	—
30	C₂×C₄⋊Dic₁₃	—	2	1	no	—
31	C₂×C₄⋊Dic₁₃	—	2	1	no	—
32	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
33	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
34	C₂×#6101	—	2	2	no	—
35	C₂×#6101	—	2	2	no	—
36	C₂²×#1055	—	2	2	no	—
37	#88124	—	4	4	no	—
38	C₁₃×C₄⋊C₈	—	2	4	no	—
39	C₁₃×#97	—	2	4	no	—
40	#88071	—	2	2	no	—
41	#88071	—	2	2	no	—
42	#88043	—	2	4	no	—
43	#88043	—	2	2	no	—
44	#88043	Q₈	1	4	yes	—
45	C₄×#1055	—	2	4	no	—
46	#9891	—	13	1	no	maximal, Sylow
47	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
54	C₂²×Dic₁₃	—	2	2	no	—
55	C₂²×Dic₁₃	—	2	2	no	—
56	C₂×C₈×C₁₃	—	2	4	no	—
57	C₂×C₈×C₁₃	—	4	2	no	—
58	C₂×C₈×C₁₃	—	4	2	no	—
59	C₄²×C₁₃	—	2	2	no	—
60	C₄²×C₁₃	—	2	2	no	—
61	C₄²×C₁₃	—	2	2	no	—
62	C₄²×C₁₃	—	2	2	no	—
63	C₄²×C₁₃	—	2	2	no	—
64	C₄²×C₁₃	—	4	1	no	—
65	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
66	C₄²×C₁₃	#41	1	2	yes	—
67	C₄⋊Dic₁₃	—	4	2	no	—
68	C₄⋊Dic₁₃	—	4	2	no	—
69	C₄⋊Dic₁₃	—	4	2	no	—
70	C₄⋊Dic₁₃	—	4	2	no	—
71	C₄⋊Dic₁₃	—	4	2	no	—
72	C₄⋊Dic₁₃	—	4	2	no	—
73	#6101	—	4	4	no	—
74	#6101	—	4	4	no	—
75	C₂×#1055	—	2	4	no	—
76	C₂×#1055	—	2	4	no	—
77	C₂×#1055	—	2	4	no	—
78	#2859	—	13	1	no	—
79	#1767	D₁₃	1	1	yes	characteristic
80	C₄×#97	—	13	1	no	—
81	#1295	—	13	4	no	—
82	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₃	—	2	1	no	—
84	C₂×C₄×C₁₃	—	2	1	no	—
85	C₂×C₄×C₁₃	—	2	1	no	—
86	C₂×C₄×C₁₃	—	2	1	no	—
87	C₂×C₄×C₁₃	—	2	1	no	—
88	C₂×C₄×C₁₃	—	2	1	no	—
89	C₂×C₄×C₁₃	—	2	1	no	—
90	C₂×C₄×C₁₃	—	2	1	no	—
91	C₂×C₄×C₁₃	—	2	1	no	—
92	C₂×C₄×C₁₃	—	2	1	no	—
93	C₂×C₄×C₁₃	—	2	1	no	—
94	C₂×C₄×C₁₃	—	2	1	no	—
95	C₂×C₄×C₁₃	—	2	1	no	—
96	C₂×C₄×C₁₃	#100	1	2	yes	—
97	C₂×C₄×C₁₃	#101	1	2	yes	—
98	C₂×C₄×C₁₃	#104	1	2	yes	—
99	C₂×C₄×C₁₃	#104	1	2	yes	—
100	C₂×C₄×C₁₃	#104	1	2	yes	—
101	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
102	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
103	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
104	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
105	C₂×Dic₁₃	—	4	2	no	—
106	C₂×Dic₁₃	—	4	2	no	—
107	C₂×Dic₁₃	—	4	2	no	—
108	C₂×Dic₁₃	—	4	2	no	—
109	C₂×Dic₁₃	—	4	2	no	—
110	C₂×Dic₁₃	—	4	2	no	—
111	C₈×C₁₃	—	4	4	no	—
112	#1055	—	2	8	no	—
113	C₂×#125	—	13	2	no	—
114	C₂×C₄⋊C₈	—	2	1	no	—
115	C₂×#97	—	13	2	no	—
116	C₂×#97	—	26	1	no	—
117	C₂×#97	C₂×D₁₃	1	2	yes	—
118	C₂×C₄×C₈	—	26	1	no	—
119	#389	—	26	1	no	—
120	#389	—	26	1	no	—
121	#389	—	26	1	no	—
122	#389	—	26	1	no	—
123	#384	—	13	1	no	—
124	#384	—	13	1	no	—
125	#382	—	13	2	no	—
126	C₄³	C₂×D₁₃	1	1	yes	characteristic
127	#336	—	2	1	no	—
128	C₂²×C₁₃	#391	1	1	yes	characteristic
129	C₂²×C₁₃	C₂×#100	1	1	yes	characteristic
130	C₂²×C₁₃	C₂×#101	1	1	yes	characteristic
131	C₂²×C₁₃	C₂×#104	1	1	yes	characteristic
132	C₂²×C₁₃	C₂×#104	1	1	yes	characteristic
133	C₂²×C₁₃	C₂×#104	1	1	yes	characteristic
134	C₂²×C₁₃	#421	1	1	yes	characteristic
135	C₄×C₁₃	—	2	1	no	—
136	C₄×C₁₃	—	2	1	no	—
137	C₄×C₁₃	—	2	2	no	—
138	C₄×C₁₃	—	2	2	no	—
139	C₄×C₁₃	—	2	2	no	—
140	C₄×C₁₃	—	2	2	no	—
141	C₄×C₁₃	—	4	1	no	—
142	C₄×C₁₃	#330	1	4	yes	—
143	Dic₁₃	—	8	2	no	—
144	Dic₁₃	—	8	2	no	—
145	C₂²×C₈	—	2	2	no	—
146	C₂²×C₈	—	26	2	no	—
147	#125	—	52	4	no	—
148	C₂×C₄⋊C₄	—	13	2	no	—
149	C₂×C₄⋊C₄	—	13	2	no	—
150	C₂×C₄⋊C₄	—	26	2	no	—
151	C₂×C₄⋊C₄	—	26	2	no	—
152	C₂×C₄⋊C₄	—	26	1	no	—
153	C₂×C₄⋊C₄	—	26	1	no	—
154	C₂×C₄⋊C₄	—	26	1	no	—
155	C₂×C₄⋊C₄	—	26	1	no	—
156	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
157	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
158	C₂×C₄²	D₅₂	1	1	yes	characteristic
159	C₂×C₄²	D₅₂	1	1	yes	characteristic
160	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
161	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
162	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
163	C₄⋊C₈	—	2	4	no	—
164	#97	—	2	4	no	—
165	#97	—	13	4	no	—
166	#97	—	26	4	no	—
167	#97	—	26	2	no	—
168	C₄×C₈	—	26	4	no	—
169	#95	—	26	2	no	—
170	#95	—	26	2	no	—
171	C₂×C₁₃	C₂×#330	1	1	yes	characteristic
172	C₂×C₁₃	#1525	1	1	yes	characteristic
173	C₂×C₁₃	#1528	1	1	yes	characteristic
174	C₂×C₁₃	#1530	1	1	yes	characteristic
175	C₂×C₁₃	#1986	1	1	yes	characteristic
176	C₂×C₁₃	#1994	1	1	yes	characteristic
177	C₂×C₁₃	#1997	1	1	yes	characteristic
178	C₂²×C₄	—	26	2	no	—
179	C₂²×C₄	—	26	2	no	—
180	C₂²×C₄	#6103	1	1	yes	characteristic
181	C₂²×C₄	#6103	1	1	yes	characteristic
182	C₂²×C₄	#6103	1	1	yes	characteristic
183	C₂²×C₄	#6103	1	1	yes	characteristic
184	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
185	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
186	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
187	C₂×C₈	—	2	4	no	—
188	C₂×C₈	—	4	2	no	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	—	26	4	no	—
191	C₂×C₈	—	26	4	no	—
192	C₂×C₈	—	26	4	no	—
193	C₄⋊C₄	—	52	2	no	—
194	C₄⋊C₄	—	52	2	no	—
195	C₄⋊C₄	—	52	4	no	—
196	C₄⋊C₄	—	52	2	no	—
197	C₄⋊C₄	—	52	2	no	—
198	C₄⋊C₄	—	52	2	no	—
199	C₄⋊C₄	—	52	2	no	—
200	C₄⋊C₄	—	52	4	no	—
201	C₄²	—	2	2	no	—
202	C₄²	—	2	2	no	—
203	C₄²	—	2	2	no	—
204	C₄²	—	2	2	no	—
205	C₄²	—	2	2	no	—
206	C₄²	—	4	1	no	—
207	C₄²	#6129	1	2	yes	—
208	C₄²	Q₈×D₁₃	1	2	yes	—
209	C₁₃	#9891	1	1	yes	characteristic, complemented, Sylow
210	C₂³	C₂×#6103	1	1	yes	characteristic
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	52	2	no	—
225	C₂×C₄	—	52	2	no	—
226	C₂×C₄	—	52	2	no	—
227	C₂×C₄	—	52	2	no	—
228	C₂×C₄	—	52	2	no	—
229	C₂×C₄	—	52	2	no	—
230	C₂×C₄	#88045	1	2	yes	—
231	C₂×C₄	#88063	1	2	yes	—
232	C₂×C₄	#88064	1	2	yes	—
233	C₂×C₄	#88065	1	2	yes	—
234	C₂×C₄	#88065	1	2	yes	—
235	C₂×C₄	#88141	1	2	yes	—
236	C₂×C₄	#88151	1	2	yes	—
237	C₂×C₄	#88190	1	1	yes	characteristic
238	C₂×C₄	#88198	1	1	yes	characteristic
239	C₈	—	4	4	no	—
240	C₈	—	26	8	no	—
241	C₂²	C₂×#88045	1	1	yes	characteristic
242	C₂²	#11718635	1	1	yes	characteristic
243	C₂²	#11718666	1	1	yes	characteristic
244	C₂²	C₂×#88063	1	1	yes	characteristic
245	C₂²	C₂×#88064	1	1	yes	characteristic
246	C₂²	C₂×#88065	1	1	yes	characteristic
247	C₂²	C₂×#88065	1	1	yes	characteristic
248	C₄	—	2	2	no	—
249	C₄	—	2	2	no	—
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	2	2	no	—
253	C₄	—	2	2	no	—
254	C₄	—	4	1	no	—
255	C₄	—	104	2	no	—
256	C₄	—	104	2	no	—
257	C₄	#11718057	1	4	yes	—
258	C₂	C₂×#11718057	1	1	yes	characteristic
259	C₂	#13113427	1	1	yes	characteristic
260	C₂	#13113439	1	1	yes	characteristic
261	C₂	#13113448	1	1	yes	characteristic
262	C₂	#13115779	1	1	yes	characteristic
263	C₂	#13115812	1	1	yes	characteristic
264	C₂	#13115824	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#6103
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1767	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1767	D₁₃
hypocenter	C₁₃	#9891
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1767

Complements

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

N	H ≅ G/N	type
209. C₁₃	#9891	semidirect

Maximal subgroups

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

subgroup	index
#13123199	2
C₄×#88043	2
#13112718	2
C₁₃×#1767	2
#9891	13