Subgroups — #16018845

Order 3328.

582 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125422	C₂	1	1	yes	maximal, characteristic
2	#13117088	C₂	1	2	yes	maximal, complemented
3	#13117063	C₂	1	2	yes	maximal, complemented
4	#13116883	C₂	1	4	yes	maximal, complemented
5	#13116770	C₂	1	4	yes	maximal
6	#13116635	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₁₃×Q₁₆	—	2	1	no	—
9	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
10	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
11	#11719175	—	2	1	no	—
12	C₁₃×#494	—	2	1	no	—
13	C₁₃×#494	—	2	1	no	—
14	C₁₃×#494	C₂²	1	2	yes	—
15	C₁₃×#494	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×#88069	C₂²	1	8	yes	—
18	#11718777	—	2	1	no	—
19	#11718777	C₂²	1	2	yes	—
20	#11718360	C₂²	1	1	yes	characteristic
21	C₄×Dic₅₂	—	2	1	no	—
22	C₄×Dic₅₂	C₂²	1	2	yes	—
23	#11718343	C₂²	1	1	yes	characteristic
24	#11718342	—	2	1	no	—
25	#11718156	C₂²	1	8	yes	—
26	C₂²⋊#6090	C₂²	1	2	yes	—
27	C₄⋊#6090	C₂²	1	2	yes	—
28	C₄×#6090	C₂²	1	2	yes	—
29	C₂²×Q₈×C₁₃	—	2	2	no	—
30	C₂×C₁₃×Q₁₆	—	2	2	no	—
31	C₂×C₁₃×Q₁₆	—	2	2	no	—
32	C₂×C₁₃×Q₁₆	—	2	2	no	—
33	C₂×C₁₃×Q₁₆	—	4	4	no	—
34	C₂×C₁₃×Q₁₆	—	4	4	no	—
35	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
36	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
38	C₁₃×C₄⋊Q₈	—	2	2	no	—
39	C₁₃×C₄⋊Q₈	—	2	2	no	—
40	C₁₃×C₄⋊Q₈	—	4	1	no	—
41	C₁₃×C₄⋊Q₈	—	4	1	no	—
42	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
43	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
44	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
45	#88180	—	4	1	no	—
46	#88178	—	2	2	no	—
47	#88178	—	4	1	no	—
48	C₂×Dic₅₂	—	2	1	no	—
49	C₂×Dic₅₂	C₂³	1	2	yes	—
50	#88124	—	4	1	no	—
51	#88123	—	2	1	no	—
52	#88123	—	2	1	no	—
53	C₄×Dic₂₆	—	2	2	no	—
54	C₄×Dic₂₆	—	4	1	no	—
55	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
56	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
57	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	#88069	—	4	8	no	—
60	#88058	—	2	1	no	—
61	#88058	C₂³	1	2	yes	—
62	#88056	—	2	2	no	—
63	#88056	—	2	2	no	—
64	C₂×#6090	C₂³	1	4	yes	—
65	#33775	—	13	1	no	maximal, Sylow
66	C₂×Q₈×C₁₃	—	2	4	no	—
67	C₂×Q₈×C₁₃	—	4	4	no	—
68	C₂×Q₈×C₁₃	—	4	4	no	—
69	C₂×Q₈×C₁₃	—	4	2	no	—
70	C₂²×C₄×C₁₃	—	4	2	no	—
71	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
74	C₂×Dic₂₆	—	2	2	no	—
75	C₂×Dic₂₆	—	4	1	no	—
76	C₁₃×Q₁₆	—	2	8	no	—
77	C₁₃×Q₁₆	—	4	4	no	—
78	C₁₃×Q₁₆	—	4	4	no	—
79	C₁₃×Q₁₆	—	4	4	no	—
80	C₂×C₈×C₁₃	—	2	2	no	—
81	C₂×C₈×C₁₃	—	2	2	no	—
82	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
83	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
84	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
85	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
86	C₁₃×C₄⋊C₄	—	4	2	no	—
87	C₁₃×C₄⋊C₄	—	4	2	no	—
88	C₁₃×C₄⋊C₄	—	4	2	no	—
89	C₁₃×C₄⋊C₄	—	4	2	no	—
90	C₄²×C₁₃	D₈	1	1	yes	characteristic
91	C₄²×C₁₃	D₈	1	1	yes	characteristic
92	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
93	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂²⋊Dic₁₃	—	4	2	no	—
95	C₄⋊Dic₁₃	—	2	2	no	—
96	C₄⋊Dic₁₃	—	4	1	no	—
97	C₄⋊Dic₁₃	—	4	1	no	—
98	C₄⋊Dic₁₃	—	4	1	no	—
99	#6101	—	4	2	no	—
100	#6101	—	4	2	no	—
101	C₄×Dic₁₃	—	4	2	no	—
102	Dic₅₂	—	2	4	no	—
103	Dic₅₂	—	4	2	no	—
104	#6090	—	2	4	no	—
105	#3170	—	13	1	no	—
106	C₂×#494	D₁₃	1	1	yes	characteristic
107	#2247	—	13	2	no	—
108	#2241	—	13	2	no	—
109	#2209	—	13	4	no	—
110	#2188	—	13	4	no	—
111	#2162	—	13	1	no	—
112	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
113	Q₈×C₁₃	—	4	4	no	—
114	Q₈×C₁₃	—	4	4	no	—
115	Q₈×C₁₃	—	8	4	no	—
116	C₂×C₄×C₁₃	—	2	1	no	—
117	C₂×C₄×C₁₃	—	2	1	no	—
118	C₂×C₄×C₁₃	—	2	2	no	—
119	C₂×C₄×C₁₃	—	4	4	no	—
120	C₂×C₄×C₁₃	—	8	4	no	—
121	C₂×C₄×C₁₃	Q₃₂	1	4	yes	complemented
122	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
123	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
124	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
125	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
126	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
127	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
128	C₂×Dic₁₃	—	4	2	no	—
129	C₂×Dic₁₃	—	4	2	no	—
130	Dic₂₆	—	4	2	no	—
131	Dic₂₆	—	4	2	no	—
132	Dic₂₆	—	8	2	no	—
133	C₈×C₁₃	—	2	1	no	—
134	C₈×C₁₃	—	2	1	no	—
135	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
136	C₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
137	C₂²×Q₁₆	—	2	1	no	—
138	C₂²×Q₁₆	C₂×D₁₃	1	2	yes	—
139	#533	—	26	1	no	—
140	C₂×C₄⋊Q₈	—	2	1	no	—
141	C₂×Q₃₂	—	13	8	no	—
142	#500	—	13	1	no	—
143	#494	—	2	1	no	—
144	#494	—	2	1	no	—
145	#494	—	13	1	no	—
146	#494	C₂×D₁₃	1	2	yes	—
147	#494	C₂×D₁₃	1	2	yes	—
148	#487	—	26	1	no	—
149	#467	—	13	2	no	—
150	#467	—	26	1	no	—
151	C₄×Q₁₆	—	13	2	no	—
152	C₄×Q₁₆	—	26	1	no	—
153	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
154	C₄⋊C₁₆	—	13	2	no	—
155	#358	—	13	8	no	—
156	C₂²⋊C₁₆	—	13	2	no	—
157	C₄×C₁₆	—	13	2	no	—
158	C₂²×C₁₃	—	2	1	no	—
159	C₂²×C₁₃	—	2	1	no	—
160	C₂²×C₁₃	C₂×Q₃₂	1	2	yes	—
161	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
162	C₄×C₁₃	—	2	1	no	—
163	C₄×C₁₃	—	2	1	no	—
164	C₄×C₁₃	—	8	4	no	—
165	C₄×C₁₃	C₂×Q₃₂	1	2	yes	—
166	C₄×C₁₃	C₂×Q₃₂	1	2	yes	—
167	C₄×C₁₃	#510	1	2	yes	—
168	C₄×C₁₃	#535	1	1	yes	characteristic
169	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
170	Dic₁₃	—	8	2	no	—
171	Dic₁₃	—	8	2	no	—
172	C₂²×Q₈	—	2	2	no	—
173	C₂×Q₁₆	—	2	2	no	—
174	C₂×Q₁₆	—	2	2	no	—
175	C₂×Q₁₆	—	2	2	no	—
176	C₂×Q₁₆	—	4	4	no	—
177	C₂×Q₁₆	—	4	4	no	—
178	C₂×Q₁₆	—	13	2	no	—
179	C₂×Q₁₆	—	26	1	no	—
180	C₂×Q₁₆	C₂²×D₁₃	1	4	yes	—
181	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
182	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
183	C₄⋊Q₈	—	2	2	no	—
184	C₄⋊Q₈	—	2	2	no	—
185	C₄⋊Q₈	—	4	1	no	—
186	C₄⋊Q₈	—	4	1	no	—
187	C₄⋊Q₈	—	26	1	no	—
188	C₄⋊Q₈	—	26	1	no	—
189	#125	—	52	1	no	—
190	C₂²⋊Q₈	—	26	2	no	—
191	C₂²⋊Q₈	—	52	1	no	—
192	C₄×Q₈	—	26	2	no	—
193	C₄×Q₈	—	52	1	no	—
194	#117	—	52	1	no	—
195	C₂×C₄⋊C₄	—	4	1	no	—
196	C₂×C₄⋊C₄	—	4	1	no	—
197	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
198	Q₃₂	—	52	8	no	—
199	C₂×C₁₆	—	13	4	no	—
200	#107	—	13	2	no	—
201	#107	—	26	1	no	—
202	#103	—	26	2	no	—
203	#103	—	26	2	no	—
204	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
205	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
206	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
207	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
208	C₂×C₁₃	—	2	2	no	—
209	C₂×C₁₃	#3205	1	1	yes	characteristic
210	C₂×C₁₃	C₂²×Q₃₂	1	1	yes	characteristic
211	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
212	C₂×Q₈	—	2	4	no	—
213	C₂×Q₈	—	4	4	no	—
214	C₂×Q₈	—	4	4	no	—
215	C₂×Q₈	—	4	2	no	—
216	C₂×Q₈	—	26	2	no	—
217	C₂×Q₈	—	52	1	no	—
218	C₂²×C₄	—	4	2	no	—
219	C₂²×C₄	#6104	1	1	yes	characteristic
220	C₂²×C₄	#6104	1	1	yes	characteristic
221	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
222	Q₁₆	—	2	8	no	—
223	Q₁₆	—	4	4	no	—
224	Q₁₆	—	4	4	no	—
225	Q₁₆	—	4	4	no	—
226	Q₁₆	—	26	4	no	—
227	Q₁₆	—	52	2	no	—
228	C₂×C₈	—	2	2	no	—
229	C₂×C₈	—	2	2	no	—
230	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
231	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
232	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
233	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
234	C₄⋊C₄	—	4	2	no	—
235	C₄⋊C₄	—	4	2	no	—
236	C₄⋊C₄	—	4	2	no	—
237	C₄⋊C₄	—	4	2	no	—
238	C₄⋊C₄	—	26	2	no	—
239	C₄⋊C₄	—	52	1	no	—
240	C₄⋊C₄	—	52	1	no	—
241	C₄⋊C₄	—	52	2	no	—
242	C₄⋊C₄	—	52	2	no	—
243	C₄⋊C₄	—	52	1	no	—
244	C₂²⋊C₄	—	52	2	no	—
245	C₄²	—	52	2	no	—
246	C₄²	#6104	1	1	yes	characteristic
247	C₄²	#6104	1	1	yes	characteristic
248	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
249	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
250	C₁₆	—	26	4	no	—
251	C₁₃	#33775	1	1	yes	characteristic, complemented, Sylow
252	C₂³	C₂×#6104	1	1	yes	characteristic
253	Q₈	—	4	4	no	—
254	Q₈	—	4	4	no	—
255	Q₈	—	8	4	no	—
256	Q₈	—	52	2	no	—
257	Q₈	—	52	2	no	—
258	Q₈	—	104	2	no	—
259	C₂×C₄	—	2	1	no	—
260	C₂×C₄	—	2	1	no	—
261	C₂×C₄	—	2	2	no	—
262	C₂×C₄	—	4	4	no	—
263	C₂×C₄	—	8	4	no	—
264	C₂×C₄	—	52	2	no	—
265	C₂×C₄	—	52	2	no	—
266	C₂×C₄	#88069	1	4	yes	complemented
267	C₂×C₄	C₂×#6104	1	1	yes	characteristic
268	C₂×C₄	C₂×#6104	1	1	yes	characteristic
269	C₂×C₄	C₂×#6104	1	1	yes	characteristic
270	C₂×C₄	C₂×#6104	1	1	yes	characteristic
271	C₂×C₄	C₂×#6104	1	1	yes	characteristic
272	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
273	C₈	—	2	1	no	—
274	C₈	—	2	1	no	—
275	C₈	#88186	1	2	yes	—
276	C₈	#88251	1	2	yes	—
277	C₂²	—	2	1	no	—
278	C₂²	—	2	1	no	—
279	C₂²	C₂×#88069	1	2	yes	—
280	C₂²	C₂²×#6104	1	1	yes	characteristic
281	C₄	—	2	1	no	—
282	C₄	—	2	1	no	—
283	C₄	—	8	4	no	—
284	C₄	—	104	2	no	—
285	C₄	—	104	2	no	—
286	C₄	#11718840	1	2	yes	—
287	C₄	C₂×#88069	1	2	yes	—
288	C₄	C₂×#88069	1	2	yes	—
289	C₄	C₂×#88186	1	1	yes	characteristic
290	C₄	#11719510	1	1	yes	characteristic
291	C₂	—	2	2	no	—
292	C₂	#13125754	1	1	yes	characteristic
293	C₂	C₂²×#88069	1	1	yes	characteristic
294	C₂	C₂×#11718840	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#494	C₂
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₂³×C₁₃	C₂×D₈
hypercenter	C₂×#494	D₁₃
hypocenter	C₁₃	#33775
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#494

Complements

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

N	H ≅ G/N	type
2. #13117088	C₂	semidirect
3. #13117063	C₂	semidirect
4. #13116883	C₂	semidirect
121. C₂×C₄×C₁₃	Q₃₂	semidirect
251. C₁₃	#33775	semidirect
266. C₂×C₄	#88069	semidirect

Maximal subgroups

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

subgroup	index
#13125422	2
#13117088	2
#13117063	2
#13116883	2
#13116770	2
#13116635	2
C₂×C₁₃×#494	2
#33775	13