Finite Group Databasebeta

← C2×#11718437 #13124019

Subgroups — C2×#11718437 #13124019

Order 1664.

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

normal subgroups only

This group has 996 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
2C22×#6105C211yesmaximal, characteristic, complemented
3C22×#6095C211yesmaximal, characteristic, complemented
4C2×#88151C211yesmaximal, characteristic, complemented
5C2×C13×#102C211yesmaximal, characteristic, complemented
6C2×#88060C211yesmaximal, characteristic, complemented
7C2×#88049C211yesmaximal, characteristic, complemented
8#11718437C218yesmaximal, direct product factor
9C24×D13—21no—
10C22×D4×C13C2211yescharacteristic
11C22×C22⋊D13—21no—
12C2×D4×D13—24no—
13C2×D4×D13—24no—
14C2×D4×D13—22no—
15C2×D4×D13C2214yes—
16C22×D52C2211yescharacteristic
17C22×C4×D13C2211yescharacteristic
18C22×Dic26C2211yescharacteristic, complemented
19C22×C8×C13C2211yescharacteristic, complemented
20C2×C13×C4⋊C4C2211yescharacteristic, complemented
21C2×#6105—24no—
22C2×#6105C2214yescomplemented
23C2×#6103—21no—
24C2×C4⋊Dic13—21no—
25C22×#1055C2211yescharacteristic, complemented
26C2×#6095—24no—
27C2×#6095C2214yescomplemented
28#88151—22no—
29#88151C2214yescomplemented
30C13×#102C2214yescomplemented
31#88060C2214yescomplemented
32#88049C2214yescomplemented
33C24×C13—21no—
34C23×D13—28no—
35C23×D13—21no—
36C23×D13—24no—
37C23×D13—44no—
38C23×D13—44no—
39C23×D13D411yescharacteristic
40C2×D4×C13—21no—
41C2×D4×C13—22no—
42C2×D4×C13D414yes—
43C2×D4×C13C2312yes—
44C22×C4×C13—21no—
45C22×C4×C13C2311yescharacteristic
46C2×C22⋊D13—28no—
47C2×C22⋊D13—24no—
48C22×Dic13—21no—
49C22×Dic13D411yescharacteristic
50D4×D13—216no—
51D4×D13—28no—
52D4×D13—28no—
53C2×D52—21no—
54C2×D52—22no—
55C2×D52D414yes—
56C2×D52C2312yes—
57C2×C4×D13—22no—
58C2×C4×D13—22no—
59C2×C4×D13D412yes—
60C2×C4×D13C2312yes—
61C2×Dic26—22no—
62C2×Dic26—22no—
63C2×Dic26—21no—
64C2×Dic26C2312yescomplemented
65C2×C8×C13—22no—
66C2×C8×C13C2312yescomplemented
67C13×C4⋊C4—21no—
68C13×C4⋊C4C2312yescomplemented
69#6105—28no—
70#6103—24no—
71C4⋊Dic13—24no—
72C2×#1055—22no—
73C2×#1055C2312yescomplemented
74#6095—28no—
75C2×#450—131nomaximal, Sylow
76C23×C13—24no—
77C23×C13—22no—
78C23×C13—42no—
79C23×C13—42no—
80C23×C13C2×D411yescharacteristic
81C22×D13—22no—
82C22×D13—22no—
83C22×D13—216no—
84C22×D13—24no—
85C22×D13—22no—
86C22×D13—48no—
87C22×D13—432no—
88C22×D13—42no—
89C22×D13—42no—
90C22×D13—48no—
91C22×D13SD1614yescomplemented
92C22×D13C2×D412yes—
93D4×C13—24no—
94D4×C13—22no—
95D4×C13C2×D414yes—
96C2×C4×C13—22no—
97C2×C4×C13—42no—
98C2×C4×C13C2×D411yescharacteristic
99C2×C4×C13C2×D412yes—
100C2×C4×C13C2×D412yes—
101C2×C4×C13C2411yescharacteristic
102C22⋊D13—216no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—42no—
106C2×Dic13C2×D412yes—
107D52—24no—
108D52—22no—
109D52C2×D414yes—
110C4×D13—24no—
111C4×D13—22no—
112C4×D13—22no—
113Dic26—22no—
114Dic26—22no—
115Dic26—42no—
116C8×C13—22no—
117#1055—22no—
118C23×D4—131no—
119C22×SD16—131no—
120C22×SD16—131no—
121C2×C22⋊Q8—131no—
122#450—138no—
123C2×#102—131no—
124C2×#102D1311yescharacteristic, complemented
125C2×C22⋊C8—131no—
126C22×C13—24no—
127C22×C13—42no—
128C22×C13—42no—
129C22×C13—48no—
130C22×C13#12012yes—
131C22×C13C2×SD1612yes—
132C22×C13AGL(1,ℤ/8)12yes—
133C22×C13C22×D411yescharacteristic
134C2×D13—22no—
135C2×D13—22no—
136C2×D13—28no—
137C2×D13—24no—
138C2×D13—432no—
139C2×D13—42no—
140C2×D13—42no—
141C2×D13—48no—
142C2×D13C2×SD1614yescomplemented
143C4×C13—42no—
144C4×C13#12012yes—
145C4×C13C22×D411yescharacteristic
146C4×C13C22×D411yescharacteristic
147Dic13—22no—
148Dic13—42no—
149C25—261no—
150C22×Q8—131no—
151C22×D4—134no—
152C22×D4—131no—
153C22×D4—262no—
154C22×D4—261no—
155C22×D4—264no—
156C22×D4—264no—
157C22×D4C2×D1311yescharacteristic
158C23×C4—131no—
159C2×SD16—134no—
160C2×SD16—134no—
161C2×SD16—264no—
162C2×SD16—264no—
163C22×C8—131no—
164C22×C8C2×D1311yescharacteristic, complemented
165C22⋊Q8—134no—
166C22⋊Q8—262no—
167C2×C4⋊C4—261no—
168C2×C4⋊C4C2×D1311yescharacteristic, complemented
169C2×C22⋊C4—261no—
170#102—134no—
171#102C2×D1314yescomplemented
172C22⋊C8—134no—
173C2×C13—44no—
174C2×C13#45014yescomplemented
175C2×C13C2×#12011yescharacteristic
176C2×C13C22×SD1611yescharacteristic
177C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
178D13—24no—
179D13—44no—
180C24—21no—
181C24—131no—
182C24—264no—
183C24—268no—
184C24—261no—
185C24—524no—
186C24—524no—
187C2×Q8—132no—
188C2×Q8—261no—
189C2×Q8—262no—
190C2×Q8—262no—
191C2×D4—21no—
192C2×D4—22no—
193C2×D4—134no—
194C2×D4—132no—
195C2×D4—264no—
196C2×D4—268no—
197C2×D4—2616no—
198C2×D4—268no—
199C2×D4—268no—
200C2×D4—262no—
201C2×D4—261no—
202C2×D4D5214yes—
203C2×D4C22×D1312yes—
204C22×C4—21no—
205C22×C4—131no—
206C22×C4—132no—
207C22×C4—132no—
208C22×C4—262no—
209C22×C4—262no—
210C22×C4—261no—
211C22×C4C22×D1311yescharacteristic
212SD16—268no—
213SD16—268no—
214C2×C8—22no—
215C2×C8—132no—
216C2×C8—262no—
217C2×C8C22×D1312yescomplemented
218C4⋊C4—21no—
219C4⋊C4—264no—
220C4⋊C4C22×D1312yescomplemented
221C22⋊C4—264no—
222C13C2×#45011yescharacteristic, complemented, Sylow
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—134no—
228C23—132no—
229C23—2616no—
230C23—262no—
231C23—262no—
232C23—264no—
233C23—262no—
234C23—528no—
235C23—528no—
236C23—5232no—
237C23—522no—
238C23—522no—
239C23D4×D1311yescharacteristic
240Q8—262no—
241Q8—262no—
242Q8—522no—
243D4—24no—
244D4—22no—
245D4—134no—
246D4—2616no—
247D4—264no—
248D4—262no—
249D4C2×D5214yes—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—132no—
253C2×C4—262no—
254C2×C4—264no—
255C2×C4—262no—
256C2×C4—262no—
257C2×C4—262no—
258C2×C4—522no—
259C2×C4C2×D5212yes—
260C2×C4D4×D1311yescharacteristic
261C2×C4D4×D1312yes—
262C2×C4C23×D1311yescharacteristic
263C8—22no—
264C8—262no—
265C22—24no—
266C22—42no—
267C22—48no—
268C22—42no—
269C22—134no—
270C22—262no—
271C22—262no—
272C22—268no—
273C22—264no—
274C22—5232no—
275C22—522no—
276C22—528no—
277C22—522no—
278C22#8813612yes—
279C22#8816512yes—
280C22SD16×D1312yes—
281C22C2×D4×D1311yescharacteristic
282C4—42no—
283C4—262no—
284C4—522no—
285C4#8813612yes—
286C4C22×D5211yescharacteristic
287C4C2×D4×D1311yescharacteristic
288C2—44no—
289C2—264no—
290C2—524no—
291C2#1171843714yesdirect product factor
292C2C2×#8813611yescharacteristic
293C2C2×#8816511yescharacteristic
294C2C2×SD16×D1311yescharacteristic
subgroupG/H
centerC23D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#102C2
socleC23×C13C2×D4
prime radicalC22×D4×D13C2
hypercenterC2×#102D13
hypocenterC13C2×#450
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C22×#6105C2semidirect
3. C22×#6095C2semidirect
4. C2×#88151C2semidirect
5. C2×C13×#102C2semidirect
6. C2×#88060C2semidirect
7. C2×#88049C2semidirect
8. #11718437C2direct (N × H)
18. C22×Dic26C22semidirect
19. C22×C8×C13C22semidirect
20. C2×C13×C4⋊C4C22semidirect
22. C2×#6105C22semidirect
25. C22×#1055C22semidirect
27. C2×#6095C22semidirect
29. #88151C22semidirect
30. C13×#102C22semidirect
31. #88060C22semidirect
32. #88049C22semidirect
64. C2×Dic26C23semidirect
66. C2×C8×C13C23semidirect
68. C13×C4⋊C4C23semidirect
73. C2×#1055C23semidirect
91. C22×D13SD16semidirect
124. C2×#102D13semidirect
142. C2×D13C2×SD16semidirect
164. C22×C8C2×D13semidirect
168. C2×C4⋊C4C2×D13semidirect
171. #102C2×D13semidirect
174. C2×C13#450semidirect
217. C2×C8C22×D13semidirect
220. C4⋊C4C22×D13semidirect
222. C13C2×#450semidirect
291. C2#11718437direct (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×#61052
C22×#60952
C2×#881512
C2×C13×#1022
C2×#880602
C2×#880492
#117184372
C2×#45013