Subgroups — #15768750

Order 3328.

774 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718585	C₂	1	1	yes	maximal, characteristic
2	C₂²×#88043	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718150	C₂	1	4	yes	maximal
4	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×#6099	C₂²	1	2	yes	—
8	C₂³×#1055	C₂²	1	2	yes	—
9	C₁₃×#423	—	2	2	no	—
10	C₁₃×#423	C₄	1	4	yes	—
11	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
12	#11718585	—	2	2	no	—
13	#11718585	C₄	1	4	yes	—
14	C₂×C₄⋊#1055	—	2	2	no	—
15	C₂×#88043	—	2	2	no	—
16	C₂×#88043	—	2	2	no	—
17	C₂×#88043	C₄	1	4	yes	—
18	#11718150	—	2	8	no	—
19	C₂³×C₄×C₁₃	Q₈	1	2	yes	—
20	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
21	C₂×C₁₃×M₁₆	—	2	2	no	—
22	C₂×C₁₃×M₁₆	—	2	4	no	—
23	C₂×C₁₃×M₁₆	—	2	4	no	—
24	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
25	C₂²×C₈×C₁₃	—	2	2	no	—
26	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₃	D₄	1	2	yes	—
30	C₂×C₄²×C₁₃	D₄	1	2	yes	—
31	C₂×C₄²×C₁₃	D₄	1	2	yes	—
32	C₂×#6099	—	2	2	no	—
33	C₂×#6099	—	2	4	no	—
34	C₂×#6099	—	2	4	no	—
35	C₂×#6099	C₂×C₄	1	4	yes	—
36	C₂²×#1055	—	2	2	no	—
37	C₂²×#1055	—	2	2	no	—
38	C₂²×#1055	—	2	2	no	—
39	C₂²×#1055	—	2	2	no	—
40	C₂²×#1055	—	2	2	no	—
41	C₂²×#1055	C₂×C₄	1	4	yes	—
42	C₂²×#1055	D₄	1	4	yes	—
43	C₂²×#1055	Q₈	1	4	yes	—
44	C₁₃×C₄⋊C₈	—	2	8	no	—
45	C₄⋊#1055	—	2	8	no	—
46	#88043	—	2	8	no	—
47	#10845	—	13	1	no	maximal, Sylow
48	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	—	4	4	no	—
50	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
51	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
52	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
53	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
58	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
61	C₂²×C₄×C₁₃	#41	1	2	yes	—
62	C₂²×C₄×C₁₃	#41	1	2	yes	—
63	C₁₃×M₁₆	—	2	8	no	—
64	C₁₃×M₁₆	—	4	4	no	—
65	C₂×C₈×C₁₃	—	2	4	no	—
66	C₂×C₈×C₁₃	—	4	2	no	—
67	C₂×C₈×C₁₃	—	4	2	no	—
68	C₄²×C₁₃	C₄²	1	4	yes	—
69	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
70	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
71	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
72	#6099	—	2	8	no	—
73	#6099	—	4	4	no	—
74	C₂×#1055	—	2	4	no	—
75	C₂×#1055	—	2	4	no	—
76	C₂×#1055	—	2	4	no	—
77	C₂×#1055	—	2	4	no	—
78	C₂×#1055	—	2	4	no	—
79	C₂×#1055	—	2	4	no	—
80	C₂×#1055	—	2	4	no	—
81	C₂×#1055	—	4	2	no	—
82	C₂×#1055	—	4	2	no	—
83	C₂×#1055	C₄⋊C₄	1	8	yes	—
84	C₂×#423	—	13	1	no	—
85	C₂×#423	D₁₃	1	1	yes	characteristic
86	C₂²×#97	—	13	1	no	—
87	C₂×#341	—	13	4	no	—
88	C₂³×C₁₃	—	2	4	no	—
89	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
91	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
92	C₂³×C₁₃	#125	1	2	yes	—
93	C₂³×C₁₃	C₄⋊Q₈	1	2	yes	—
94	C₂×C₄×C₁₃	—	2	8	no	—
95	C₂×C₄×C₁₃	—	4	4	no	—
96	C₂×C₄×C₁₃	—	4	4	no	—
97	C₂×C₄×C₁₃	#95	1	8	yes	—
98	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
103	C₂×C₄×C₁₃	#117	1	2	yes	—
104	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
105	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
106	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
107	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
108	C₂×C₄×C₁₃	#121	1	2	yes	—
109	C₂×C₄×C₁₃	#121	1	2	yes	—
110	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
111	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
112	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
113	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
114	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
115	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
116	C₈×C₁₃	—	4	4	no	—
117	#1055	—	2	8	no	—
118	#1055	—	4	4	no	—
119	C₂²×M₁₆	—	13	2	no	—
120	C₂²×M₁₆	C₂×D₁₃	1	2	yes	—
121	C₂³×C₈	—	13	2	no	—
122	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
123	#423	—	2	2	no	—
124	#423	—	13	4	no	—
125	#423	—	26	2	no	—
126	#423	Dic₁₃	1	4	yes	—
127	C₂×C₄⋊C₈	—	2	2	no	—
128	C₂×C₄⋊C₈	—	26	2	no	—
129	C₂×#97	—	13	4	no	—
130	C₂×#97	—	26	2	no	—
131	C₂×#97	—	26	2	no	—
132	#341	—	26	8	no	—
133	C₂²×C₁₃	—	2	4	no	—
134	C₂²×C₁₃	—	2	4	no	—
135	C₂²×C₁₃	—	2	2	no	—
136	C₂²×C₁₃	—	2	2	no	—
137	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
138	C₂²×C₁₃	#382	1	1	yes	characteristic
139	C₂²×C₁₃	#384	1	1	yes	characteristic
140	C₂²×C₁₃	#389	1	2	yes	—
141	C₂²×C₁₃	#389	1	2	yes	—
142	C₂²×C₁₃	#430	1	4	yes	—
143	C₄×C₁₃	—	2	8	no	—
144	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
145	C₄×C₁₃	#380	1	2	yes	—
146	C₄×C₁₃	#390	1	1	yes	characteristic
147	C₄×C₁₃	#390	1	1	yes	characteristic
148	C₄×C₁₃	#391	1	1	yes	characteristic
149	C₄×C₁₃	#391	1	1	yes	characteristic
150	C₂³×C₄	Dic₂₆	1	2	yes	—
151	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
152	C₂×M₁₆	—	2	2	no	—
153	C₂×M₁₆	—	2	4	no	—
154	C₂×M₁₆	—	2	4	no	—
155	C₂×M₁₆	—	13	4	no	—
156	C₂×M₁₆	—	26	2	no	—
157	C₂×M₁₆	—	26	4	no	—
158	C₂×M₁₆	—	26	4	no	—
159	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
160	C₂²×C₈	—	2	2	no	—
161	C₂²×C₈	—	13	4	no	—
162	C₂²×C₈	—	13	4	no	—
163	C₂²×C₈	—	13	4	no	—
164	C₂²×C₈	—	26	2	no	—
165	C₂²×C₈	—	26	2	no	—
166	C₂²×C₈	—	26	2	no	—
167	C₂²×C₈	—	26	2	no	—
168	C₂²×C₈	—	26	2	no	—
169	C₂×C₄²	C₄×D₁₃	1	2	yes	—
170	C₂×C₄²	C₄×D₁₃	1	2	yes	—
171	C₂×C₄²	D₅₂	1	2	yes	—
172	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
173	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
174	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
175	C₄⋊C₈	—	2	8	no	—
176	C₄⋊C₈	—	26	8	no	—
177	#97	—	26	8	no	—
178	C₂×C₁₃	—	2	2	no	—
179	C₂×C₁₃	—	2	2	no	—
180	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
181	C₂×C₁₃	#1738	1	2	yes	—
182	C₂×C₁₃	#1838	1	2	yes	—
183	C₂×C₁₃	#1849	1	2	yes	—
184	C₂⁴	C₂×Dic₂₆	1	1	yes	characteristic
185	C₂²×C₄	—	4	4	no	—
186	C₂²×C₄	#6101	1	4	yes	—
187	C₂²×C₄	#6101	1	4	yes	—
188	C₂²×C₄	C₄⋊Dic₁₃	1	4	yes	—
189	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
190	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
191	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
192	C₂²×C₄	D₄×D₁₃	1	2	yes	—
193	C₂²×C₄	#6129	1	2	yes	—
194	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
195	C₂²×C₄	#6131	1	2	yes	—
196	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
197	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
198	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
199	M₁₆	—	2	8	no	—
200	M₁₆	—	4	4	no	—
201	M₁₆	—	26	8	no	—
202	M₁₆	—	52	4	no	—
203	C₂×C₈	—	2	4	no	—
204	C₂×C₈	—	4	2	no	—
205	C₂×C₈	—	4	2	no	—
206	C₂×C₈	—	13	8	no	—
207	C₂×C₈	—	26	4	no	—
208	C₂×C₈	—	26	4	no	—
209	C₂×C₈	—	26	4	no	—
210	C₂×C₈	—	26	4	no	—
211	C₂×C₈	—	26	4	no	—
212	C₂×C₈	—	26	4	no	—
213	C₂×C₈	—	26	4	no	—
214	C₂×C₈	—	52	2	no	—
215	C₂×C₈	—	52	2	no	—
216	C₄²	C₄×Dic₁₃	1	4	yes	—
217	C₄²	#6103	1	4	yes	—
218	C₄²	#6103	1	4	yes	—
219	C₄²	C₂²⋊Dic₁₃	1	4	yes	—
220	C₁₃	#10845	1	1	yes	characteristic, complemented, Sylow
221	C₂³	—	2	4	no	—
222	C₂³	#88142	1	2	yes	—
223	C₂³	#88144	1	2	yes	—
224	C₂³	C₂×#6101	1	1	yes	characteristic
225	C₂³	C₂×#6101	1	1	yes	characteristic
226	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
227	C₂×C₄	—	2	8	no	—
228	C₂×C₄	—	4	4	no	—
229	C₂×C₄	—	4	4	no	—
230	C₂×C₄	#88071	1	8	yes	—
231	C₂×C₄	#88141	1	2	yes	—
232	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
233	C₂×C₄	#88146	1	2	yes	—
234	C₂×C₄	#88147	1	2	yes	—
235	C₂×C₄	#88149	1	2	yes	—
236	C₂×C₄	#88151	1	2	yes	—
237	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
238	C₂×C₄	C₂×#6103	1	1	yes	characteristic
239	C₂×C₄	C₂×#6103	1	1	yes	characteristic
240	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
241	C₂×C₄	#88190	1	1	yes	characteristic
242	C₂×C₄	#88192	1	2	yes	—
243	C₂×C₄	#88194	1	1	yes	characteristic
244	C₂×C₄	#88198	1	1	yes	characteristic
245	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
246	C₂×C₄	#88200	1	2	yes	—
247	C₂×C₄	#88201	1	1	yes	characteristic
248	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
249	C₈	—	4	4	no	—
250	C₈	—	26	8	no	—
251	C₈	—	52	4	no	—
252	C₂²	—	2	4	no	—
253	C₂²	—	2	4	no	—
254	C₂²	—	2	2	no	—
255	C₂²	—	2	2	no	—
256	C₂²	#11718634	1	2	yes	—
257	C₂²	#11718637	1	1	yes	characteristic
258	C₂²	#11718638	1	1	yes	characteristic
259	C₂²	#11718646	1	2	yes	—
260	C₂²	#11718785	1	4	yes	—
261	C₂²	C₂×#88071	1	1	yes	characteristic
262	C₄	—	2	8	no	—
263	C₄	#11718635	1	1	yes	characteristic
264	C₄	C₄⋊C₄×Dic₁₃	1	2	yes	—
265	C₄	#11718648	1	2	yes	—
266	C₄	#11718649	1	1	yes	characteristic
267	C₄	#11718882	1	1	yes	characteristic
268	C₄	#11718891	1	1	yes	characteristic
269	C₂	—	2	2	no	—
270	C₂	—	2	2	no	—
271	C₂	#13113065	1	1	yes	characteristic
272	C₂	#13114562	1	2	yes	—
273	C₂	#13114976	1	2	yes	—
274	C₂	#13115010	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#423	C₂
socle	C₂³×C₁₃	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₂×Q₈
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×#423	D₁₃
hypocenter	C₁₃	#10845
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
220. C₁₃	#10845	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718585	2
C₂²×#88043	2
C₂×#11718150	2
C₂×C₁₃×#423	2
#10845	13