Finite Group Databasebeta

← #16781901

Subgroups — #16781901

Order 3328.

550 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 108 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
1#13130713C212yesmaximal, complemented
2#13130696C212yesmaximal
3#13129699C212yesmaximal, complemented
4C2×C8×C22⋊D13C211yesmaximal, characteristic
5C23×C8×C13C411yescharacteristic, complemented
6C2×C4×C22⋊D13C2211yescharacteristic
7C22×C8×D13C2211yescharacteristic
8C2×#88119—22no—
9#11719136C2214yes—
10C2×#88102—22no—
11C2×C22⋊#1055C411yescharacteristic, complemented
12C8×C22⋊D13—22no—
13C8×C22⋊D13—22no—
14C2×#88060C2211yescharacteristic
15C2×#88054C411yescharacteristic, complemented
16C2×C8×Dic13C411yescharacteristic, complemented
17#11718289—22no—
18#11718265—22no—
19C23×C4×C13C2×C411yescharacteristic
20C22×C22⋊D13D411yescharacteristic
21C22×C4×D13C2311yescharacteristic
22C2×C22⋊#261—24no—
23C2×C4⋊#261—24no—
24C22×C8×C13—21no—
25C22×C8×C13—21no—
26C22×C8×C13—42no—
27C22×C8×C13C2×C411yescharacteristic
28C22×C8×C13C2×C411yescharacteristic
29C2×C22⋊Dic13Q811yescharacteristic
30C4×C22⋊D13—22no—
31C4×C22⋊D13—22no—
32C2×#6103D411yescharacteristic
33C2×#6101Q811yescharacteristic
34C2×C4×Dic13C2×C411yescharacteristic
35C22×#1055C2×C411yescharacteristic
36C22×#1055C2×C411yescharacteristic
37C2×C8×D13—42no—
38C2×C8×D13D412yes—
39C2×C8×D13D412yes—
40#88119—44no—
41(C2×#261)⋊C4—24no—
42#88102—44no—
43C22⋊#1055—22no—
44#88060—22no—
45#88054—22no—
46C8×Dic13—21no—
47C8×Dic13—21no—
48#8609—131nomaximal, Sylow
49C24×C13C4⋊C411yescharacteristic
50C23×D13C2×D411yescharacteristic
51C22×#261—44no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—41no—
55C22×C4×C13—41no—
56C22×C4×C13C4⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C2×C22⋊D13—22no—
59C2×C22⋊D13—22no—
60C2×C22⋊D13D812yes—
61C2×C22⋊D13Q1612yes—
62C22×Dic13C4⋊C411yescharacteristic
63C22×Dic13C4⋊C411yescharacteristic
64C22×Dic13C2×Q811yescharacteristic
65C2×C4×D13—41no—
66C2×C4×D13—41no—
67C2×C4×D13C2×D412yes—
68C2×C4×D13#4112yes—
69C22⋊#261—44no—
70C22⋊#261—44no—
71C4⋊#261—44no—
72C4⋊#261—44no—
73C2×C8×C13—22no—
74C2×C8×C13—21no—
75C2×C8×C13—42no—
76C2×C8×C13—42no—
77C2×C8×C13—41no—
78C2×C8×C13C22⋊C411yescharacteristic
79C2×C8×C13C22⋊C411yescharacteristic
80C22⋊Dic13—22no—
81#6103—22no—
82#6101—22no—
83C4×Dic13—21no—
84C4×Dic13—21no—
85C2×#1055—21no—
86C2×#1055—41no—
87C2×#1055—41no—
88C2×#1055C22⋊C412yes—
89C8×D13—24no—
90C8×D13—42no—
91C2×C8×D4—131no—
92#1808—132no—
93#1799—132no—
94#1289—132no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13#10712yescomplemented
100C23×C13C2×C4⋊C411yescharacteristic
101C22×D13—41no—
102C22×D13—41no—
103C22×D13#12112yes—
104C22×D13C2×D811yescharacteristic
105C22×D13C2×Q1611yescharacteristic
106C22×D13#13512yes—
107C2×#261—84no—
108C2×#261—84no—
109C2×#261—84no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—42no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13C2×C22⋊C411yescharacteristic
118C2×C4×C13#11711yescharacteristic
119C22⋊D13—24no—
120C22⋊D13—24no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13#10712yescomplemented
127C2×Dic13C22⋊Q812yes—
128C4×D13—22no—
129C4×D13—22no—
130C4×D13—42no—
131C8×C13—21no—
132C8×C13—41no—
133C8×C13#9912yescomplemented
134#1055—22no—
135#1055—41no—
136C23×C8—131no—
137C23×C8#26111yescharacteristic, complemented
138C2×C4×D4—131no—
139C8×D4—262no—
140C8×D4—262no—
141C2×#107—262no—
142C2×C4⋊C8—131no—
143C2×#99—262no—
144C2×C22⋊C8—131no—
145C2×C22⋊C8—131no—
146C2×C4×C8—131no—
147#380—134no—
148#342—262no—
149#340—262no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13—22no—
153C22×C13—42no—
154C22×C13—42no—
155C22×C13—41no—
156C22×C13—41no—
157C22×C13#38011yescharacteristic
158C22×C13C2×#10711yescharacteristic
159C22×C13#42711yescharacteristic
160C2×D13—22no—
161C2×D13—22no—
162C2×D13—41no—
163C2×D13—41no—
164C2×D13—42no—
165C2×D13#46612yes—
166C2×D13#46712yes—
167#261—164no—
168C4×C13—21no—
169C4×C13—41no—
170C4×C13C2×#9911yescharacteristic
171C4×C13#41011yescharacteristic
172Dic13—22no—
173Dic13—22no—
174Dic13—41no—
175C22×D4—131no—
176C23×C4—131no—
177C23×C4C2×#26111yescharacteristic
178C22×C8—21no—
179C22×C8—21no—
180C22×C8—42no—
181C22×C8—131no—
182C22×C8—132no—
183C22×C8—132no—
184C22×C8—131no—
185C22×C8—522no—
186C22×C8C2×#26111yescharacteristic
187C22×C8C2×#26111yescharacteristic
188C4×D4—262no—
189C4×D4—262no—
190C2×C4⋊C4—131no—
191C2×C4⋊C4—264no—
192C2×C22⋊C4—131no—
193C2×C22⋊C4—131no—
194C2×C22⋊C4—264no—
195C2×C42—131no—
196#107—524no—
197C4⋊C8—262no—
198#99—524no—
199C22⋊C8—262no—
200C22⋊C8—262no—
201C4×C8—261no—
202C4×C8—261no—
203#95—264no—
204C2×C13—21no—
205C2×C13—21no—
206C2×C13—42no—
207C2×C13#179911yescharacteristic
208C2×C13#180811yescharacteristic
209C2×C13#181211yescharacteristic
210D13—22no—
211D13—22no—
212C24—131no—
213C24C4⋊#26111yescharacteristic
214C2×D4—132no—
215C2×D4—132no—
216C2×D4—262no—
217C2×D4—262no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—131no—
223C22×C4—131no—
224C22×C4—132no—
225C22×C4—132no—
226C22×C4—131no—
227C22×C4—521no—
228C22×C4—521no—
229C22×C4—524no—
230C22×C4C4⋊#26111yescharacteristic
231C22×C4C22×#26111yescharacteristic
232C2×C8—22no—
233C2×C8—21no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—41no—
237C2×C8—132no—
238C2×C8—264no—
239C2×C8—261no—
240C2×C8—522no—
241C2×C8—521no—
242C2×C8—521no—
243C2×C8C22⋊#26111yescharacteristic
244C2×C8C22⋊#26111yescharacteristic
245C4⋊C4—262no—
246C4⋊C4—524no—
247C4⋊C4—524no—
248C22⋊C4—262no—
249C22⋊C4—262no—
250C22⋊C4—524no—
251C22⋊C4—524no—
252C42—261no—
253C42—261no—
254C13#860911yescharacteristic, complemented, Sylow
255C23—21no—
256C23—21no—
257C23—41no—
258C23—41no—
259C23—132no—
260C23—131no—
261C23—131no—
262C23—132no—
263C23—521no—
264C23—521no—
265C23#8810212yescomplemented
266C23C2×C4⋊#26111yescharacteristic
267D4—264no—
268D4—264no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—132no—
277C2×C4—132no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—262no—
281C2×C4—262no—
282C2×C4—261no—
283C2×C4—522no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—1044no—
287C2×C4—1044no—
288C2×C4—1044no—
289C2×C4#8823711yescharacteristic
290C2×C4C2×C22⋊#26111yescharacteristic
291C8—21no—
292C8—41no—
293C8—262no—
294C8—521no—
295C8#8811912yescomplemented
296C22—21no—
297C22—21no—
298C22—22no—
299C22—42no—
300C22—42no—
301C22—41no—
302C22—41no—
303C22—132no—
304C22—132no—
305C22—262no—
306C22—262no—
307C22—521no—
308C22—521no—
309C22—522no—
310C22C2×#8810211yescharacteristic
311C22#1171909211yescharacteristic
312C22#1171913611yescharacteristic
313C4—21no—
314C4—41no—
315C4—262no—
316C4—262no—
317C4—521no—
318C4—2084no—
319C4#1171911611yescharacteristic
320C4C2×#8811911yescharacteristic
321C2—21no—
322C2—21no—
323C2—42no—
324C2—262no—
325C2—262no—
326C2#1313069611yescharacteristic
327C2#1313071311yescharacteristic
328C2#1313071811yescharacteristic
subgroupG/H
centerC22#11719136
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC23×C8×C13C4
socleC22×C13#380
prime radicalC22×C22⋊D13D4
cosocleC22×C4×D13C23
hypercenterC23×C8#261
hypocenterC13#8609
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. #13130713C2semidirect
3. #13129699C2semidirect
5. C23×C8×C13C4semidirect
11. C2×C22⋊#1055C4semidirect
15. C2×#88054C4semidirect
16. C2×C8×Dic13C4semidirect
99. C23×C13#107semidirect
126. C2×Dic13#107semidirect
133. C8×C13#99semidirect
137. C23×C8#261semidirect
254. C13#8609semidirect
265. C23#88102semidirect
295. C8#88119semidirect

Maximal subgroups

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

subgroupindex
#131307132
#131306962
#131296992
C2×C8×C22⋊D132
#860913