Finite Group Databasebeta

← C4×#11718133 #15778085

Subgroups — C4×#11718133 #15778085

Order 3328.

584 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×#11718133C212yesmaximal
2C4×#88074C212yesmaximal
3#13112961C212yesmaximal
4C4×C13×#124C211yesmaximal, characteristic
5C2×C13×#124C2211yescharacteristic
6C2×C4×Q8×C13C411yescharacteristic, complemented
7C2×C4×D4×C13C2211yescharacteristic
8C13×#391C411yescharacteristic, complemented
9C13×#390C2211yescharacteristic
10C13×#388—22no—
11C13×#382C411yescharacteristic, complemented
12C4×C13×C22⋊C4—22no—
13C43×C13C411yescharacteristic, complemented
14C2×#88074C2214yes—
15C4×C22⋊Dic13—22no—
16#11718133C418yesdirect product factor
17#11718118—22no—
18C22×Q8×C13C2×C411yescharacteristic
19C22×D4×C13C2311yescharacteristic
20C23×C4×C13D412yes—
21C13×#124—22no—
22C13×#124C2×C414yes—
23C4×Q8×C13—41no—
24C4×Q8×C13—41no—
25C4×D4×C13—41no—
26C4×D4×C13—41no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4D412yes—
33C2×C42×C13—21no—
34C2×C42×C13—21no—
35C2×C42×C13—21no—
36C2×C42×C13C2×C411yescharacteristic
37C2×C42×C13C2×C411yescharacteristic
38C2×C42×C13C2×C411yescharacteristic
39C2×C22⋊Dic13—24no—
40C2×C4×Dic13—42no—
41C13×#95—22no—
42C13×#95—22no—
43#88074—24no—
44#88074C2×C418yes—
45#88071—42no—
46C4×#354—131nomaximal, Sylow
47C24×C13C2×D412yes—
48C2×Q8×C13—21no—
49C2×Q8×C13—41no—
50C2×Q8×C13—41no—
51C2×Q8×C13C4212yescomplemented
52C2×D4×C13—41no—
53C2×D4×C13—41no—
54C2×D4×C13C22×C412yes—
55C2×D4×C13#4112yes—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—21no—
62C22×C4×C13—44no—
63C22×C4×C13C22⋊C412yes—
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22×C411yescharacteristic
67C22×Dic13—44no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—42no—
71C13×C22⋊C4—28no—
72C13×C22⋊C4—42no—
73C13×C22⋊C4—44no—
74C42×C13—21no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—41no—
78C42×C13—42no—
79C42×C13—42no—
80C42×C13—41no—
81C42×C13—41no—
82C42×C13C4212yescomplemented
83C22⋊Dic13—28no—
84C22⋊Dic13—44no—
85C4×Dic13—84no—
86C4×#124D1311yescharacteristic
87C2×#354—132no—
88C4×#99—132no—
89#1393—132no—
90C23×C13—22no—
91C23×C13—22no—
92C23×C13—42no—
93C23×C13—42no—
94C23×C13C2×C22⋊C411yescharacteristic
95C23×C13C4×D414yes—
96Q8×C13—42no—
97Q8×C13—42no—
98D4×C13—42no—
99D4×C13—42no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—44no—
115C2×C4×C13—41no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—41no—
119C2×C4×C13—82no—
120C2×C4×C13#9911yescharacteristic
121C2×C4×C13#9911yescharacteristic
122C2×C4×C13C2×C4211yescharacteristic
123C2×C4×C13#11711yescharacteristic
124C2×Dic13—48no—
125C2×Dic13—84no—
126C2×Dic13—84no—
127C2×#124C2×D1311yescharacteristic
128C2×C4×Q8Dic1311yescharacteristic, complemented
129C2×C4×D4C2×D1311yescharacteristic
130C2×#99—134no—
131#391Dic1311yescharacteristic, complemented
132#390C2×D1311yescharacteristic
133#388—22no—
134#382Dic1311yescharacteristic, complemented
135C4×C22⋊C4—22no—
136C4×C22⋊C4—262no—
137C43Dic1311yescharacteristic, complemented
138#354—138no—
139#342—262no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—24no—
143C22×C13—44no—
144C22×C13—42no—
145C22×C13—42no—
146C22×C13—82no—
147C22×C13C4×C22⋊C411yescharacteristic
148C22×C13C2×#9911yescharacteristic
149C22×C13#41011yescharacteristic
150C4×C13—21no—
151C4×C13—21no—
152C4×C13—21no—
153C4×C13—42no—
154C4×C13—42no—
155C4×C13—42no—
156C4×C13—41no—
157C4×C13—42no—
158C4×C13—81no—
159C4×C13#35412yescomplemented
160Dic13—88no—
161C22×Q8C2×Dic1311yescharacteristic
162C22×D4C22×D1311yescharacteristic
163C23×C4C22⋊D1312yes—
164#124—22no—
165#124C4×D1314yes—
166C4×Q8—41no—
167C4×Q8—41no—
168C4×D4—41no—
169C4×D4—41no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4C2×Dic1311yescharacteristic
172C2×C4⋊C4C2×Dic1311yescharacteristic
173C2×C22⋊C4—22no—
174C2×C22⋊C4—22no—
175C2×C22⋊C4—264no—
176C2×C22⋊C4C22⋊D1312yes—
177C2×C42—21no—
178C2×C42—21no—
179C2×C42—21no—
180C2×C42—522no—
181C2×C42C2×Dic1311yescharacteristic
182C2×C42C2×Dic1311yescharacteristic
183C2×C42C2×Dic1311yescharacteristic
184#99—138no—
185#99—264no—
186#95—22no—
187#95—22no—
188#95—522no—
189C2×C13—21no—
190C2×C13—21no—
191C2×C13—44no—
192C2×C13C4×#9911yescharacteristic
193C2×C13C2×#35411yescharacteristic
194C2×C13#212611yescharacteristic
195C24C2×C22⋊D1312yes—
196C2×Q8—21no—
197C2×Q8—41no—
198C2×Q8—41no—
199C2×Q8C4×Dic1312yescomplemented
200C2×D4—41no—
201C2×D4—41no—
202C2×D4C2×C4×D1312yes—
203C2×D4#612712yes—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—44no—
211C22×C4—524no—
212C22×C4C22⋊Dic1312yes—
213C22×C4C22⋊Dic1311yescharacteristic
214C22×C4C22⋊Dic1311yescharacteristic
215C22×C4C22×Dic1311yescharacteristic
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—42no—
219C22⋊C4—28no—
220C22⋊C4—42no—
221C22⋊C4—44no—
222C22⋊C4—268no—
223C22⋊C4—524no—
224C42—21no—
225C42—21no—
226C42—21no—
227C42—41no—
228C42—42no—
229C42—42no—
230C42—41no—
231C42—41no—
232C42—1044no—
233C42C4×Dic1312yescomplemented
234C13C4×#35411yescharacteristic, complemented, Sylow
235C23—22no—
236C23—22no—
237C23—42no—
238C23—42no—
239C23C4×C22⋊D1314yes—
240C23C2×C22⋊Dic1311yescharacteristic
241Q8—42no—
242Q8—42no—
243D4—42no—
244D4—42no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—44no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—82no—
265C2×C4—528no—
266C2×C4—1044no—
267C2×C4—1044no—
268C2×C4#8807411yescharacteristic
269C2×C4#8807411yescharacteristic
270C2×C4C2×C4×Dic1311yescharacteristic
271C2×C4#8818011yescharacteristic
272C22—21no—
273C22—21no—
274C22—24no—
275C22—44no—
276C22—42no—
277C22—42no—
278C22—82no—
279C22C4×C22⋊Dic1311yescharacteristic
280C22C2×#8807411yescharacteristic
281C22#1171890111yescharacteristic
282C4—21no—
283C4—21no—
284C4—21no—
285C4—42no—
286C4—42no—
287C4—42no—
288C4—42no—
289C4—41no—
290C4—81no—
291C4—1048no—
292C4#1171813312yesdirect product factor
293C2—21no—
294C2—21no—
295C2—44no—
296C2C4×#8807411yescharacteristic
297C2C2×#1171813311yescharacteristic
298C2#1311650111yescharacteristic
subgroupG/H
centerC2×C4#88074
commutatorC2×C4×C13C2×C42
FrattiniC22×D4C22×D13
FittingC4×C13×#124C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenterC4×#124D13
hypocenterC13C4×#354
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
6. C2×C4×Q8×C13C4semidirect
8. C13×#391C4semidirect
11. C13×#382C4semidirect
13. C43×C13C4semidirect
16. #11718133C4direct (N × H)
51. C2×Q8×C13C42semidirect
82. C42×C13C42semidirect
128. C2×C4×Q8Dic13semidirect
131. #391Dic13semidirect
134. #382Dic13semidirect
137. C43Dic13semidirect
159. C4×C13#354semidirect
199. C2×Q8C4×Dic13semidirect
233. C42C4×Dic13semidirect
234. C13C4×#354semidirect
292. C4#11718133direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117181332
C4×#880742
#131129612
C4×C13×#1242
C4×#35413