Finite Group Databasebeta

← C2×#11718817 #13124010

Subgroups — C2×#11718817 #13124010

Order 1664.

1048 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D13C211yesmaximal, characteristic, complemented
2C22×C13×D8C211yesmaximal, characteristic, complemented
3C2×#88192C211yesmaximal, characteristic, complemented
4C22×#6104C211yesmaximal, characteristic, complemented
5C2×#88072C211yesmaximal, characteristic, complemented
6#11718817C218yesmaximal, direct product factor
7C2×#88061C211yesmaximal, characteristic, complemented
8C2×#88060C211yesmaximal, characteristic, complemented
9C24×D13—21no—
10C22×D4×C13C2211yescharacteristic
11C22×D4×C13C2211yescharacteristic, complemented
12C22×C22⋊D13—21no—
13C22×C22⋊D13—21no—
14C2×D4×D13—24no—
15C2×D4×D13—24no—
16C2×D4×D13—22no—
17C2×D4×D13C2214yescomplemented
18C22×D52C2211yescharacteristic
19C22×C4×D13C2211yescharacteristic
20C2×C13×D8—24no—
21C2×C13×D8C2214yescomplemented
22C22×C8×C13C2211yescharacteristic, complemented
23C2×C22⋊Dic13—21no—
24#88192—22no—
25#88192C2214yescomplemented
26C2×#6104—24no—
27C2×#6104C2214yescomplemented
28C2×C4⋊Dic13C2211yescharacteristic, complemented
29C22×#1055C2211yescharacteristic, complemented
30#88072C2214yescomplemented
31#88061C2214yescomplemented
32#88060C2214yescomplemented
33C24×C13—21no—
34C24×C13—21no—
35C23×D13—28no—
36C23×D13—21no—
37C23×D13—24no—
38C23×D13—44no—
39C23×D13—44no—
40C23×D13D411yescharacteristic
41C2×D4×C13—21no—
42C2×D4×C13—22no—
43C2×D4×C13—22no—
44C2×D4×C13—22no—
45C2×D4×C13—21no—
46C2×D4×C13D414yescomplemented
47C2×D4×C13C2312yes—
48C2×D4×C13C2312yescomplemented
49C22×C4×C13C2311yescharacteristic
50C2×C22⋊D13—28no—
51C2×C22⋊D13—24no—
52C2×C22⋊D13—24no—
53C2×C22⋊D13—44no—
54C22×Dic13—21no—
55C22×Dic13D411yescharacteristic
56D4×D13—216no—
57D4×D13—28no—
58D4×D13—28no—
59C2×D52—21no—
60C2×D52—22no—
61C2×D52D414yescomplemented
62C2×D52C2312yes—
63C2×C4×D13—22no—
64C2×C4×D13—22no—
65C2×C4×D13D412yes—
66C2×C4×D13C2312yes—
67C13×D8—28no—
68C2×C8×C13—22no—
69C2×C8×C13C2312yescomplemented
70C22⋊Dic13—24no—
71#6104—28no—
72C4⋊Dic13—21no—
73C4⋊Dic13C2312yescomplemented
74C2×#1055—22no—
75C2×#1055C2312yescomplemented
76C2×#447—131nomaximal, Sylow
77C23×C13—24no—
78C23×C13—22no—
79C23×C13—22no—
80C23×C13—42no—
81C23×C13—42no—
82C23×C13—42no—
83C23×C13—42no—
84C23×C13—42no—
85C23×C13C2×D411yescharacteristic
86C22×D13—22no—
87C22×D13—22no—
88C22×D13—216no—
89C22×D13—24no—
90C22×D13—22no—
91C22×D13—48no—
92C22×D13—432no—
93C22×D13—42no—
94C22×D13—42no—
95C22×D13—48no—
96C22×D13D814yescomplemented
97C22×D13C2×D412yes—
98D4×C13—24no—
99D4×C13—22no—
100D4×C13—22no—
101D4×C13—22no—
102D4×C13—42no—
103D4×C13C2×D414yescomplemented
104C2×C4×C13C2×D411yescharacteristic
105C2×C4×C13C2×D412yes—
106C2×C4×C13C2×D412yes—
107C2×C4×C13C2411yescharacteristic
108C22⋊D13—216no—
109C22⋊D13—48no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—42no—
113C2×Dic13C2×D412yes—
114D52—24no—
115D52—22no—
116D52C2×D414yescomplemented
117C4×D13—24no—
118C4×D13—22no—
119C4×D13—22no—
120C8×C13—22no—
121#1055—22no—
122C23×D4—131no—
123C22×D8—131no—
124C22×D8D1311yescharacteristic, complemented
125C2×#121—131no—
126#447—138no—
127C2×#102—131no—
128C2×#102—131no—
129C2×C22⋊C8—131no—
130C22×C13—24no—
131C22×C13—42no—
132C22×C13—42no—
133C22×C13—48no—
134C22×C13—42no—
135C22×C13—42no—
136C22×C13—42no—
137C22×C13—84no—
138C22×C13#12012yes—
139C22×C13C2×D812yes—
140C22×C13AGL(1,ℤ/8)12yes—
141C22×C13C22×D411yescharacteristic
142C2×D13—22no—
143C2×D13—22no—
144C2×D13—28no—
145C2×D13—24no—
146C2×D13—432no—
147C2×D13—42no—
148C2×D13—42no—
149C2×D13—48no—
150C2×D13C2×D814yescomplemented
151C4×C13#12012yes—
152C4×C13C22×D411yescharacteristic
153C4×C13C22×D411yescharacteristic
154Dic13—22no—
155Dic13—42no—
156C25—261no—
157C22×D4—134no—
158C22×D4—131no—
159C22×D4—262no—
160C22×D4—261no—
161C22×D4—264no—
162C22×D4—264no—
163C22×D4—261no—
164C22×D4C2×D1311yescharacteristic
165C22×D4C2×D1311yescharacteristic, complemented
166C23×C4—131no—
167C2×D8—24no—
168C2×D8—134no—
169C2×D8—264no—
170C2×D8C2×D1314yescomplemented
171C22×C8—131no—
172C22×C8C2×D1311yescharacteristic, complemented
173#121—134no—
174#121—262no—
175C2×C4⋊C4—131no—
176C2×C22⋊C4—261no—
177#102—134no—
178#102—134no—
179C22⋊C8—134no—
180C2×C13—44no—
181C2×C13—82no—
182C2×C13#44714yescomplemented
183C2×C13C2×#12011yescharacteristic
184C2×C13C22×D811yescharacteristic
185C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
186D13—24no—
187D13—44no—
188C24—21no—
189C24—21no—
190C24—131no—
191C24—264no—
192C24—268no—
193C24—261no—
194C24—524no—
195C24—524no—
196C2×D4—21no—
197C2×D4—22no—
198C2×D4—22no—
199C2×D4—21no—
200C2×D4—22no—
201C2×D4—134no—
202C2×D4—132no—
203C2×D4—264no—
204C2×D4—268no—
205C2×D4—2616no—
206C2×D4—268no—
207C2×D4—268no—
208C2×D4—264no—
209C2×D4—261no—
210C2×D4—262no—
211C2×D4—524no—
212C2×D4C22⋊D1314yescomplemented
213C2×D4C22×D1312yes—
214C2×D4C22×D1312yescomplemented
215C22×C4—131no—
216C22×C4—132no—
217C22×C4—132no—
218C22×C4—262no—
219C22×C4—262no—
220C22×C4—261no—
221C22×C4C22×D1311yescharacteristic
222D8—28no—
223D8—268no—
224C2×C8—22no—
225C2×C8—132no—
226C2×C8—262no—
227C2×C8C22×D1312yescomplemented
228C4⋊C4—132no—
229C4⋊C4—261no—
230C22⋊C4—264no—
231C13C2×#44711yescharacteristic, complemented, Sylow
232C23—24no—
233C23—22no—
234C23—22no—
235C23—42no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23—42no—
240C23—134no—
241C23—132no—
242C23—2616no—
243C23—262no—
244C23—262no—
245C23—264no—
246C23—262no—
247C23—528no—
248C23—528no—
249C23—5232no—
250C23—522no—
251C23—522no—
252C23D4×D1311yescharacteristic
253D4—24no—
254D4—22no—
255D4—22no—
256D4—22no—
257D4—42no—
258D4—134no—
259D4—2616no—
260D4—264no—
261D4—262no—
262D4—528no—
263D4C2×C22⋊D1314yescomplemented
264C2×C4—132no—
265C2×C4—262no—
266C2×C4—264no—
267C2×C4—262no—
268C2×C4—262no—
269C2×C4—262no—
270C2×C4—522no—
271C2×C4D4×D1311yescharacteristic
272C2×C4D4×D1312yes—
273C2×C4C2×C22⋊D1312yes—
274C2×C4C23×D1311yescharacteristic
275C8—22no—
276C8—262no—
277C22—24no—
278C22—42no—
279C22—42no—
280C22—48no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—84no—
285C22—134no—
286C22—262no—
287C22—262no—
288C22—268no—
289C22—264no—
290C22—5232no—
291C22—522no—
292C22—522no—
293C22—528no—
294C22D8×D1312yes—
295C22#8816512yes—
296C22#8819112yes—
297C22C2×D4×D1311yescharacteristic
298C4—262no—
299C4—522no—
300C4#8819112yes—
301C4C2×D4×D1311yescharacteristic
302C4C22×C22⋊D1311yescharacteristic
303C2—44no—
304C2—82no—
305C2—264no—
306C2—524no—
307C2#1171881714yesdirect product factor
308C2C2×D8×D1311yescharacteristic
309C2C2×#8816511yescharacteristic
310C2C2×#8819111yescharacteristic
subgroupG/H
centerC23D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC22×C13×D8C2
socleC23×C13C2×D4
hypercenterC22×D8D13
hypocenterC13C2×#447
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×D4×D13C2semidirect
2. C22×C13×D8C2semidirect
3. C2×#88192C2semidirect
4. C22×#6104C2semidirect
5. C2×#88072C2semidirect
6. #11718817C2direct (N × H)
7. C2×#88061C2semidirect
8. C2×#88060C2semidirect
11. C22×D4×C13C22semidirect
17. C2×D4×D13C22semidirect
21. C2×C13×D8C22semidirect
22. C22×C8×C13C22semidirect
25. #88192C22semidirect
27. C2×#6104C22semidirect
28. C2×C4⋊Dic13C22semidirect
29. C22×#1055C22semidirect
30. #88072C22semidirect
31. #88061C22semidirect
32. #88060C22semidirect
46. C2×D4×C13D4semidirect
48. C2×D4×C13C23semidirect
61. C2×D52D4semidirect
69. C2×C8×C13C23semidirect
73. C4⋊Dic13C23semidirect
75. C2×#1055C23semidirect
96. C22×D13D8semidirect
103. D4×C13C2×D4semidirect
116. D52C2×D4semidirect
124. C22×D8D13semidirect
150. C2×D13C2×D8semidirect
165. C22×D4C2×D13semidirect
170. C2×D8C2×D13semidirect
172. C22×C8C2×D13semidirect
182. C2×C13#447semidirect
212. C2×D4C22⋊D13semidirect
214. C2×D4C22×D13semidirect
227. C2×C8C22×D13semidirect
231. C13C2×#447semidirect
263. D4C2×C22⋊D13semidirect
307. C2#11718817direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D132
C22×C13×D82
C2×#881922
C22×#61042
C2×#880722
#117188172
C2×#880612
C2×#880602
C2×#44713