Finite Group Databasebeta

← #16790017

Subgroups — #16790017

Order 3328.

524 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 86 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×#11718300C212yesmaximal
2#13130697C212yesmaximal
3#13129931C212yesmaximal
4#13117543C211yesmaximal, characteristic
5C2×C4×Q8×C13C411yescharacteristic, complemented
6C2×#88201C2211yescharacteristic
7C2×C4×D52C2211yescharacteristic
8#11719136—22no—
9C2×#88107C2214yes—
10#11718891C411yescharacteristic, complemented
11#11718650—22no—
12#11718649C2211yescharacteristic
13#11718637C411yescharacteristic, complemented
14#11718601—22no—
15#11718593C411yescharacteristic, complemented
16#11718300—24no—
17#11718289—22no—
18C22×Q8×C13C2×C411yescharacteristic
19C22×D52C2311yescharacteristic
20C22×C4×D13D412yes—
21C2×C22⋊#261—24no—
22C2×C4⋊#261—42no—
23C4×Q8×C13—42no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C42×C13—21no—
27C2×C42×C13C2×C411yescharacteristic
28#88201—22no—
29#88201D412yes—
30#88201Q812yes—
31C2×#6103—22no—
32C2×#6103—22no—
33C2×#6103D412yes—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×#6101—22no—
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13C2×C411yescharacteristic
38C4×D52—42no—
39(C2×#261)⋊C4—42no—
40#88107—24no—
41#88107—24no—
42#88071—21no—
43#88071—21no—
44#88071—22no—
45#12800—131nomaximal, Sylow
46C23×D13C2×D412yes—
47C22×#261—44no—
48C2×Q8×C13—21no—
49C2×Q8×C13—41no—
50C2×Q8×C13—41no—
51C2×Q8×C13C4⋊C412yescomplemented
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22×C411yescharacteristic
57C22×Dic13—21no—
58C22×Dic13—21no—
59C22×Dic13C22⋊C412yes—
60C2×D52—41no—
61C2×D52—41no—
62C2×D52C2×D411yescharacteristic
63C2×D52C2×Q811yescharacteristic
64C2×D52#4112yes—
65C2×C4×D13—22no—
66C2×C4×D13—22no—
67C2×C4×D13—82no—
68C22⋊#261—44no—
69C22⋊#261—44no—
70C4⋊#261—84no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—42no—
73C42×C13—22no—
74C42×C13—42no—
75#6103—24no—
76#6103—24no—
77#6103—42no—
78#6103—82no—
79C4⋊Dic13—41no—
80#6101—82no—
81C4×Dic13—21no—
82C4×Dic13—41no—
83C4×Dic13C4⋊C412yescomplemented
84#2326—131no—
85C2×#354—132no—
86#1799—132no—
87#1393—132no—
88C23×C13C2×C22⋊C411yescharacteristic
89C22×D13—22no—
90C22×D13—22no—
91C22×D13—42no—
92C22×D13—42no—
93C22×D13#12112yes—
94C22×D13C22⋊Q812yes—
95C2×#261—84no—
96C2×#261—84no—
97C2×#261—84no—
98Q8×C13—42no—
99Q8×C13—42no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—22no—
103C2×C4×C13—21no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—42no—
109C2×C4×C13—41no—
110C2×C4×C13#9912yes—
111C2×C4×C13C2×C4⋊C411yescharacteristic
112C2×C4×C13#11711yescharacteristic
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—41no—
116C2×Dic13—41no—
117C2×Dic13—42no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121D52—41no—
122D52—41no—
123D52—42no—
124C4×D13—44no—
125C4×D13—82no—
126C2×#124—131no—
127C2×C4×Q8#26111yescharacteristic, complemented
128C2×C4×D4—131no—
129C2×#99—134no—
130#391—131no—
131#390—131no—
132#388—262no—
133#385—262no—
134#384—131no—
135#380—262no—
136#376—131no—
137#354—264no—
138#342—262no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13#38011yescharacteristic
142C22×C13C2×#9911yescharacteristic
143C22×C13#41011yescharacteristic
144C2×D13—22no—
145C2×D13—22no—
146C2×D13—42no—
147C2×D13—42no—
148C2×D13—42no—
149C2×D13—42no—
150C2×D13—82no—
151#261—164no—
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—22no—
155C4×C13—42no—
156C4×C13—41no—
157C4×C13—81no—
158Dic13—42no—
159Dic13—42no—
160Dic13—81no—
161C22×Q8C2×#26111yescharacteristic
162C22×D4—131no—
163C23×C4—132no—
164#124—132no—
165#124—132no—
166#124—262no—
167C4×Q8—42no—
168C4×D4—522no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—131no—
171C2×C4⋊C4—262no—
172C2×C4⋊C4—522no—
173C2×C4⋊C4C2×#26111yescharacteristic
174C2×C22⋊C4—132no—
175C2×C22⋊C4—262no—
176C2×C22⋊C4—264no—
177C2×C22⋊C4—262no—
178C2×C42—21no—
179C2×C42—131no—
180C2×C42—131no—
181C2×C42C2×#26111yescharacteristic
182#99—264no—
183#99—264no—
184#95—262no—
185#95—261no—
186#95—261no—
187#95—522no—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13#179911yescharacteristic
191C2×C13#212711yescharacteristic
192C2×C13#212911yescharacteristic
193D13—42no—
194D13—42no—
195C24—132no—
196C2×Q8—21no—
197C2×Q8—41no—
198C2×Q8—41no—
199C2×Q8C4⋊#26112yescomplemented
200C2×D4—131no—
201C2×D4—131no—
202C2×D4—132no—
203C2×D4—521no—
204C2×D4—521no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—132no—
208C22×C4—261no—
209C22×C4—262no—
210C22×C4—262no—
211C22×C4—261no—
212C22×C4—524no—
213C22×C4—1042no—
214C22×C4C22⋊#26111yescharacteristic
215C22×C4C22⋊#26111yescharacteristic
216C22×C4C22×#26111yescharacteristic
217C4⋊C4—41no—
218C4⋊C4—42no—
219C4⋊C4—521no—
220C4⋊C4—1042no—
221C4⋊C4—1044no—
222C22⋊C4—264no—
223C22⋊C4—264no—
224C22⋊C4—522no—
225C22⋊C4—524no—
226C22⋊C4—524no—
227C22⋊C4—1042no—
228C42—22no—
229C42—42no—
230C42—132no—
231C42—261no—
232C42—521no—
233C13#1280011yescharacteristic, complemented, Sylow
234C23—132no—
235C23—132no—
236C23—262no—
237C23—262no—
238C23—522no—
239C23—522no—
240C23C2×C22⋊#26111yescharacteristic
241Q8—42no—
242Q8—42no—
243D4—521no—
244D4—521no—
245D4—522no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—262no—
257C2×C4—262no—
258C2×C4—524no—
259C2×C4—521no—
260C2×C4—521no—
261C2×C4—522no—
262C2×C4—521no—
263C2×C4—521no—
264C2×C4—521no—
265C2×C4—1042no—
266C2×C4—1044no—
267C2×C4—1044no—
268C2×C4—1044no—
269C2×C4#8811912yes—
270C2×C4C2×C4⋊#26111yescharacteristic
271C2×C4#8823711yescharacteristic
272C22—21no—
273C22—21no—
274C22—262no—
275C22—262no—
276C22—522no—
277C22—522no—
278C22—522no—
279C22—522no—
280C22—1042no—
281C22#1171911611yescharacteristic
282C22#1171913611yescharacteristic
283C22C2×#8811911yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—41no—
288C4—42no—
289C4—81no—
290C4—522no—
291C4—522no—
292C4—1041no—
293C4—2084no—
294C2—21no—
295C2—21no—
296C2—522no—
297C2—522no—
298C2#1313069611yescharacteristic
299C2#1313111111yescharacteristic
300C2#1313111811yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C4×Q8×C13C4
socleC22×C13C2×#99
prime radical, cosocleC22×D52C23
hypercenterC2×C4×Q8#261
hypocenterC13#12800
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
5. C2×C4×Q8×C13C4semidirect
10. #11718891C4semidirect
13. #11718637C4semidirect
15. #11718593C4semidirect
51. C2×Q8×C13C4⋊C4semidirect
83. C4×Dic13C4⋊C4semidirect
127. C2×C4×Q8#261semidirect
199. C2×Q8C4⋊#261semidirect
233. C13#12800semidirect

Maximal subgroups

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

subgroupindex
C2×#117183002
#131306972
#131299312
#131175432
#1280013