Subgroups — #15779000

Order 3328.

410 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13116592	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718157	C₂	1	2	yes	maximal
3	#13115008	C₂	1	1	yes	maximal, characteristic
4	#13112944	C₂	1	2	yes	maximal
5	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
8	C₄×C₁₃×Q₁₆	—	2	1	no	—
9	C₄×C₁₃×Q₁₆	—	2	1	no	—
10	C₄×C₁₃×Q₁₆	C₄	1	2	yes	—
11	C₄×C₁₃×Q₁₆	C₄	1	2	yes	—
12	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#103	—	2	1	no	—
14	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×#88059	—	2	1	no	—
16	C₂×#88059	C₂²	1	2	yes	—
17	C₂×#88052	C₂²	1	2	yes	—
18	#11718585	—	2	1	no	—
19	#11718157	—	2	4	no	—
20	C₄⋊#6090	—	2	1	no	—
21	C₄⋊#6090	—	2	1	no	—
22	C₂²×Q₈×C₁₃	—	2	1	no	—
23	C₂×C₁₃×Q₁₆	—	2	1	no	—
24	C₂×C₁₃×Q₁₆	—	2	1	no	—
25	C₂×C₁₃×Q₁₆	—	2	1	no	—
26	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
27	C₂×C₁₃×Q₁₆	D₄	1	2	yes	—
28	C₂×C₁₃×Q₁₆	Q₈	1	2	yes	—
29	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
31	C₄×Q₈×C₁₃	—	2	2	no	—
32	C₄×Q₈×C₁₃	—	2	2	no	—
33	C₄×Q₈×C₁₃	—	4	1	no	—
34	C₄×Q₈×C₁₃	—	4	1	no	—
35	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
36	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
37	C₂×C₄²×C₁₃	—	4	1	no	—
38	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
39	C₂×#6099	—	2	2	no	—
40	C₁₃×#107	—	2	1	no	—
41	C₁₃×#107	C₂×C₄	1	2	yes	—
42	C₁₃×#103	—	2	2	no	—
43	C₁₃×#103	—	2	2	no	—
44	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
47	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
48	#88059	—	2	2	no	—
49	#88059	—	2	2	no	—
50	#88059	—	4	2	no	—
51	#88052	—	2	2	no	—
52	#88052	—	2	2	no	—
53	C₂×#6090	—	2	2	no	—
54	C₄⋊#1055	—	4	1	no	—
55	C₄⋊#1055	—	4	1	no	—
56	#12819	—	13	1	no	maximal, Sylow
57	C₂×Q₈×C₁₃	—	2	2	no	—
58	C₂×Q₈×C₁₃	—	2	2	no	—
59	C₂×Q₈×C₁₃	—	2	2	no	—
60	C₂×Q₈×C₁₃	—	4	1	no	—
61	C₂×Q₈×C₁₃	—	4	1	no	—
62	C₂×Q₈×C₁₃	—	4	1	no	—
63	C₂²×C₄×C₁₃	—	4	1	no	—
64	C₂²×C₄×C₁₃	—	4	1	no	—
65	C₂²×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
68	C₁₃×Q₁₆	—	2	2	no	—
69	C₁₃×Q₁₆	—	2	2	no	—
70	C₁₃×Q₁₆	—	2	2	no	—
71	C₁₃×Q₁₆	C₄⋊C₄	1	4	yes	—
72	C₂×C₈×C₁₃	—	2	1	no	—
73	C₂×C₈×C₁₃	—	2	1	no	—
74	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
78	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
80	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
81	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
82	C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₁₃×C₄⋊C₄	—	4	2	no	—
84	C₁₃×C₄⋊C₄	—	4	2	no	—
85	C₁₃×C₄⋊C₄	—	4	1	no	—
86	C₄²×C₁₃	—	4	2	no	—
87	C₄²×C₁₃	—	4	2	no	—
88	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
90	C₄²×C₁₃	D₈	1	1	yes	characteristic
91	C₄²×C₁₃	D₈	1	1	yes	characteristic
92	#6099	—	4	2	no	—
93	#6099	—	4	2	no	—
94	C₂×#1055	—	4	2	no	—
95	#6090	—	4	2	no	—
96	C₂×C₄×Q₁₆	D₁₃	1	1	yes	characteristic
97	#2150	—	13	1	no	—
98	C₂×#362	—	13	2	no	—
99	#1848	—	13	1	no	—
100	#1387	—	13	2	no	—
101	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
102	Q₈×C₁₃	—	2	4	no	—
103	Q₈×C₁₃	—	4	2	no	—
104	Q₈×C₁₃	—	4	2	no	—
105	Q₈×C₁₃	—	4	2	no	—
106	C₂×C₄×C₁₃	—	2	2	no	—
107	C₂×C₄×C₁₃	—	4	1	no	—
108	C₂×C₄×C₁₃	—	4	2	no	—
109	C₂×C₄×C₁₃	—	4	2	no	—
110	C₂×C₄×C₁₃	—	4	2	no	—
111	C₂×C₄×C₁₃	—	4	2	no	—
112	C₂×C₄×C₁₃	—	8	2	no	—
113	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
114	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
115	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
116	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
117	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
119	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
120	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
121	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
122	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
123	C₈×C₁₃	—	2	1	no	—
124	C₈×C₁₃	—	2	1	no	—
125	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₈×C₁₃	#117	1	1	yes	characteristic
127	C₈×C₁₃	#121	1	1	yes	characteristic
128	C₈×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
129	#1055	—	8	2	no	—
130	C₂²×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
131	C₂×C₄×Q₈	—	2	1	no	—
132	C₂×M₃₂	—	13	2	no	—
133	C₄×Q₁₆	—	2	1	no	—
134	C₄×Q₁₆	—	2	1	no	—
135	C₄×Q₁₆	Dic₁₃	1	2	yes	—
136	C₄×Q₁₆	Dic₁₃	1	2	yes	—
137	C₂×#108	—	13	2	no	—
138	C₂×#108	—	26	1	no	—
139	C₂×#107	C₂×D₁₃	1	1	yes	characteristic
140	#423	—	26	1	no	—
141	C₂×#103	—	2	1	no	—
142	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
143	C₄⋊C₁₆	—	26	1	no	—
144	C₄⋊C₁₆	—	26	1	no	—
145	#362	—	26	4	no	—
146	C₂²×C₁₃	—	2	1	no	—
147	C₂²×C₁₃	—	2	1	no	—
148	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
149	C₂²×C₁₃	#461	1	1	yes	characteristic
150	C₂²×C₁₃	#476	1	1	yes	characteristic
151	C₄×C₁₃	—	2	1	no	—
152	C₄×C₁₃	—	2	1	no	—
153	C₄×C₁₃	—	2	1	no	—
154	C₄×C₁₃	—	4	4	no	—
155	C₄×C₁₃	—	8	2	no	—
156	C₄×C₁₃	#362	1	2	yes	complemented
157	C₄×C₁₃	#380	1	1	yes	characteristic
158	C₄×C₁₃	#417	1	1	yes	characteristic
159	C₄×C₁₃	#459	1	1	yes	characteristic
160	C₄×C₁₃	#474	1	1	yes	characteristic
161	C₂²×Q₈	—	2	1	no	—
162	C₂×Q₁₆	—	2	1	no	—
163	C₂×Q₁₆	—	2	1	no	—
164	C₂×Q₁₆	—	2	1	no	—
165	C₂×Q₁₆	Dic₂₆	1	2	yes	—
166	C₂×Q₁₆	D₅₂	1	2	yes	—
167	C₂×Q₁₆	C₂×Dic₁₃	1	2	yes	—
168	C₂×M₁₆	—	26	2	no	—
169	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
170	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
171	C₄×Q₈	—	2	2	no	—
172	C₄×Q₈	—	2	2	no	—
173	C₄×Q₈	—	4	1	no	—
174	C₄×Q₈	—	4	1	no	—
175	C₂×C₄⋊C₄	—	2	1	no	—
176	C₂×C₄⋊C₄	—	4	1	no	—
177	C₂×C₄²	—	4	1	no	—
178	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
179	M₃₂	—	26	2	no	—
180	M₃₂	—	26	2	no	—
181	C₂×C₁₆	—	26	2	no	—
182	#108	—	26	2	no	—
183	#108	—	26	2	no	—
184	#108	—	52	2	no	—
185	#107	—	2	1	no	—
186	#107	C₂×Dic₁₃	1	2	yes	—
187	C₄⋊C₈	—	52	1	no	—
188	C₄⋊C₈	—	52	1	no	—
189	#103	—	2	2	no	—
190	#103	—	2	2	no	—
191	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
192	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
193	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
194	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
195	C₂×C₁₃	—	2	1	no	—
196	C₂×C₁₃	—	2	1	no	—
197	C₂×C₁₃	#1802	1	1	yes	characteristic
198	C₂×C₁₃	C₂×#362	1	1	yes	characteristic
199	C₂×C₁₃	#2148	1	1	yes	characteristic
200	C₂×Q₈	—	2	2	no	—
201	C₂×Q₈	—	2	2	no	—
202	C₂×Q₈	—	2	2	no	—
203	C₂×Q₈	—	4	1	no	—
204	C₂×Q₈	—	4	1	no	—
205	C₂×Q₈	—	4	1	no	—
206	C₂²×C₄	—	4	1	no	—
207	C₂²×C₄	—	4	1	no	—
208	C₂²×C₄	#6105	1	1	yes	characteristic
209	C₂²×C₄	#6105	1	1	yes	characteristic
210	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
211	Q₁₆	—	2	2	no	—
212	Q₁₆	—	2	2	no	—
213	Q₁₆	—	2	2	no	—
214	Q₁₆	C₄⋊Dic₁₃	1	4	yes	—
215	M₁₆	—	52	2	no	—
216	M₁₆	—	52	2	no	—
217	C₂×C₈	—	2	1	no	—
218	C₂×C₈	—	2	1	no	—
219	C₂×C₈	—	52	2	no	—
220	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
221	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
222	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
223	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
224	C₂×C₈	#6127	1	1	yes	characteristic
225	C₂×C₈	#6127	1	1	yes	characteristic
226	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
227	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
228	C₄⋊C₄	—	2	2	no	—
229	C₄⋊C₄	—	4	2	no	—
230	C₄⋊C₄	—	4	2	no	—
231	C₄⋊C₄	—	4	1	no	—
232	C₄²	—	4	2	no	—
233	C₄²	—	4	2	no	—
234	C₄²	#6104	1	1	yes	characteristic
235	C₄²	#6104	1	1	yes	characteristic
236	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
237	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
238	C₁₆	—	52	2	no	—
239	C₁₃	#12819	1	1	yes	characteristic, complemented, Sylow
240	C₂³	C₂×#6105	1	1	yes	characteristic
241	Q₈	—	2	4	no	—
242	Q₈	—	4	2	no	—
243	Q₈	—	4	2	no	—
244	Q₈	—	4	2	no	—
245	C₂×C₄	—	2	2	no	—
246	C₂×C₄	—	4	1	no	—
247	C₂×C₄	—	4	2	no	—
248	C₂×C₄	—	4	2	no	—
249	C₂×C₄	—	4	2	no	—
250	C₂×C₄	—	4	2	no	—
251	C₂×C₄	—	8	2	no	—
252	C₂×C₄	#88072	1	1	yes	characteristic
253	C₂×C₄	#88072	1	1	yes	characteristic
254	C₂×C₄	#88072	1	1	yes	characteristic
255	C₂×C₄	#88072	1	1	yes	characteristic
256	C₂×C₄	#88178	1	1	yes	characteristic
257	C₂×C₄	#88184	1	1	yes	characteristic
258	C₂×C₄	C₂×#6104	1	1	yes	characteristic
259	C₂×C₄	#88203	1	1	yes	characteristic
260	C₂×C₄	#88205	1	1	yes	characteristic
261	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
262	C₈	—	2	1	no	—
263	C₈	—	2	1	no	—
264	C₈	—	104	2	no	—
265	C₈	#88178	1	1	yes	characteristic
266	C₈	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
267	C₈	#88180	1	1	yes	characteristic
268	C₈	#88184	1	1	yes	characteristic
269	C₂²	—	2	1	no	—
270	C₂²	—	2	1	no	—
271	C₂²	#11718669	1	1	yes	characteristic
272	C₂²	#11718680	1	1	yes	characteristic
273	C₂²	C₂×#88072	1	1	yes	characteristic
274	C₄	—	2	1	no	—
275	C₄	—	2	1	no	—
276	C₄	—	2	1	no	—
277	C₄	—	4	4	no	—
278	C₄	—	8	2	no	—
279	C₄	#11718157	1	2	yes	complemented
280	C₄	#11718668	1	1	yes	characteristic
281	C₄	#11718676	1	1	yes	characteristic
282	C₄	#11718873	1	1	yes	characteristic
283	C₄	#11718893	1	1	yes	characteristic
284	C₂	—	2	1	no	—
285	C₂	—	2	1	no	—
286	C₂	#13114836	1	1	yes	characteristic
287	C₂	C₂×#11718157	1	1	yes	characteristic
288	C₂	#13116585	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#88072
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₄×C₁₃×Q₁₆	C₂
socle	C₂²×C₁₃	C₂×#102
prime radical	C₂³×C₁₃	C₂×SD₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×C₄×Q₁₆	D₁₃
hypocenter	C₁₃	#12819
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
156. C₄×C₁₃	#362	semidirect
239. C₁₃	#12819	semidirect
279. C₄	#11718157	semidirect

Maximal subgroups

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

subgroup	index
#13116592	2
C₂×#11718157	2
#13115008	2
#13112944	2
C₂×C₄×C₁₃×Q₁₆	2
#12819	13