Finite Group Databasebeta

← #16781904

Subgroups — #16781904

Order 3328.

550 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 106 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#13130697C212yesmaximal
3#13129699C212yesmaximal, complemented
4C2×#11718495C211yesmaximal, characteristic
5C22×C8×D13C411yescharacteristic, complemented
6C22×C8×D13C2211yescharacteristic
7C2×C4×D52C2211yescharacteristic
8#11719136C2214yes—
9C2×#88107—22no—
10C2×#88102—22no—
11C2×C13×C4⋊C8C411yescharacteristic, complemented
12C2×#88060C411yescharacteristic, complemented
13C2×#88060C2211yescharacteristic
14C2×C4×#1055C411yescharacteristic, complemented
15#11718495—22no—
16#11718495—22no—
17#11718289—22no—
18#11718265—22no—
19C22×D52D411yescharacteristic
20C22×C4×D13C2×C411yescharacteristic
21C22×C4×D13C2311yescharacteristic
22C2×C22⋊#261—24no—
23C2×C4⋊#261—24no—
24C22×C8×C13C2×C411yescharacteristic
25C22×C8×C13C2×C411yescharacteristic
26C2×C42×C13C2×C411yescharacteristic
27C2×#6103D411yescharacteristic
28C2×#6103Q811yescharacteristic
29C2×C4⋊Dic13Q811yescharacteristic
30C22×#1055C2×C411yescharacteristic
31C22×#1055C2×C411yescharacteristic
32C2×C8×D13—21no—
33C2×C8×D13—21no—
34C2×C8×D13—42no—
35C2×C8×D13—42no—
36C2×C8×D13D412yes—
37C2×C8×D13D412yes—
38C4×D52—22no—
39C4×D52—22no—
40(C2×#261)⋊C4—24no—
41#88107—44no—
42#88102—44no—
43C13×C4⋊C8—22no—
44#88060—22no—
45#88060—22no—
46C4×#1055—21no—
47C4×#1055—21no—
48#8609—131nomaximal, Sylow
49C23×D13C4⋊C411yescharacteristic
50C23×D13C2×D411yescharacteristic
51C22×#261—44no—
52C22×C4×C13C4⋊C411yescharacteristic
53C22×C4×C13C4⋊C411yescharacteristic
54C22×C4×C13C22×C411yescharacteristic
55C22×Dic13C4⋊C411yescharacteristic
56C22×Dic13C2×Q811yescharacteristic
57C2×D52—22no—
58C2×D52—22no—
59C2×D52D812yes—
60C2×D52Q1612yes—
61C2×C4×D13—21no—
62C2×C4×D13—21no—
63C2×C4×D13—41no—
64C2×C4×D13—41no—
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—21no—
74C2×C8×C13—41no—
75C2×C8×C13—41no—
76C2×C8×C13C22⋊C412yes—
77C42×C13—21no—
78C42×C13—21no—
79#6103—22no—
80#6103—22no—
81C4⋊Dic13—22no—
82C2×#1055—22no—
83C2×#1055—21no—
84C2×#1055—41no—
85C2×#1055C22⋊C411yescharacteristic
86C2×#1055C22⋊C411yescharacteristic
87C8×D13—24no—
88C8×D13—42no—
89C8×D13—42no—
90C8×D13—42no—
91C2×C8×D4—131no—
92#1808—132no—
93#1799—132no—
94#1289—132no—
95C23×C13C2×C4⋊C411yescharacteristic
96C22×D13—21no—
97C22×D13—21no—
98C22×D13—41no—
99C22×D13—41no—
100C22×D13—41no—
101C22×D13—41no—
102C22×D13#10712yescomplemented
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—21no—
114C2×C4×C13—21no—
115C2×C4×C13—41no—
116C2×C4×C13#10712yescomplemented
117C2×C4×C13C2×C22⋊C411yescharacteristic
118C2×C4×C13#11711yescharacteristic
119C2×Dic13—21no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13C22⋊Q812yes—
123D52—24no—
124D52—24no—
125C4×D13—22no—
126C4×D13—22no—
127C4×D13—42no—
128C4×D13—42no—
129C4×D13—41no—
130C4×D13—41no—
131C8×C13—22no—
132C8×C13—41no—
133#1055—21no—
134#1055—41no—
135#1055#9912yescomplemented
136C23×C8—131no—
137C23×C8—131no—
138C2×C4×D4—131no—
139C8×D4—262no—
140C8×D4—262no—
141C2×#107—262no—
142C2×C4⋊C8#26111yescharacteristic, complemented
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#38011yescharacteristic
153C22×C13C2×#10711yescharacteristic
154C22×C13#42711yescharacteristic
155C2×D13—22no—
156C2×D13—22no—
157C2×D13—22no—
158C2×D13—41no—
159C2×D13—41no—
160C2×D13—42no—
161C2×D13—42no—
162C2×D13—41no—
163C2×D13—41no—
164C2×D13—42no—
165C2×D13#46612yes—
166C2×D13#46712yes—
167#261—164no—
168C4×C13—21no—
169C4×C13—22no—
170C4×C13—41no—
171C4×C13C2×#9911yescharacteristic
172C4×C13#41011yescharacteristic
173Dic13—22no—
174Dic13—41no—
175C22×D4—131no—
176C23×C4—131no—
177C23×C4—131no—
178C22×C8—131no—
179C22×C8—132no—
180C22×C8—132no—
181C22×C8—131no—
182C22×C8—261no—
183C22×C8—261no—
184C22×C8—522no—
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×C42C2×#26111yescharacteristic
196#107—524no—
197C4⋊C8—22no—
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#179911yescharacteristic
207C2×C13#180811yescharacteristic
208C2×C13#181211yescharacteristic
209D13—22no—
210D13—22no—
211D13—42no—
212C24—131no—
213C24—131no—
214C2×D4—132no—
215C2×D4—132no—
216C2×D4—262no—
217C2×D4—262no—
218C22×C4—131no—
219C22×C4—132no—
220C22×C4—132no—
221C22×C4—131no—
222C22×C4—261no—
223C22×C4—261no—
224C22×C4—521no—
225C22×C4—521no—
226C22×C4—521no—
227C22×C4—521no—
228C22×C4—524no—
229C22×C4C4⋊#26111yescharacteristic
230C22×C4C4⋊#26111yescharacteristic
231C22×C4C22×#26111yescharacteristic
232C2×C8—21no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—131no—
236C2×C8—131no—
237C2×C8—264no—
238C2×C8—262no—
239C2×C8—261no—
240C2×C8—522no—
241C2×C8—522no—
242C2×C8—522no—
243C2×C8—521no—
244C2×C8C22⋊#26112yes—
245C4⋊C4—262no—
246C4⋊C4—524no—
247C4⋊C4—524no—
248C22⋊C4—262no—
249C22⋊C4—262no—
250C22⋊C4—524no—
251C22⋊C4—524no—
252C42—21no—
253C42—21no—
254C13#860911yescharacteristic, complemented, Sylow
255C23—132no—
256C23—131no—
257C23—131no—
258C23—132no—
259C23—132no—
260C23—261no—
261C23—261no—
262C23—521no—
263C23—521no—
264C23—521no—
265C23—521no—
266C23C2×C4⋊#26111yescharacteristic
267D4—264no—
268D4—264no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—132no—
276C2×C4—262no—
277C2×C4—262no—
278C2×C4—261no—
279C2×C4—522no—
280C2×C4—522no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—1044no—
286C2×C4—1044no—
287C2×C4—1044no—
288C2×C4#8810212yescomplemented
289C2×C4#8823711yescharacteristic
290C2×C4C2×C22⋊#26111yescharacteristic
291C8—22no—
292C8—41no—
293C8—132no—
294C8—261no—
295C8—521no—
296C22—21no—
297C22—21no—
298C22—132no—
299C22—132no—
300C22—262no—
301C22—262no—
302C22—262no—
303C22—521no—
304C22—521no—
305C22—522no—
306C22—522no—
307C22—522no—
308C22—521no—
309C22—521no—
310C22C2×#8810211yescharacteristic
311C22#1171909211yescharacteristic
312C22#1171913611yescharacteristic
313C4—21no—
314C4—22no—
315C4—41no—
316C4—262no—
317C4—521no—
318C4—2084no—
319C4D13⋊#9911yescharacteristic
320C4#1171915611yescharacteristic
321C2—21no—
322C2—21no—
323C2—262no—
324C2—262no—
325C2—522no—
326C2#1313069911yescharacteristic
327C2#1313071311yescharacteristic
328C2#1313071911yescharacteristic
subgroupG/H
centerC22#11719136
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊C8C4
socleC22×C13#380
prime radicalC22×D52D4
cosocleC22×C4×D13C23
hypercenterC2×C4⋊C8#261
hypocenterC13#8609
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #13130713C2semidirect
3. #13129699C2semidirect
5. C22×C8×D13C4semidirect
11. C2×C13×C4⋊C8C4semidirect
12. C2×#88060C4semidirect
14. C2×C4×#1055C4semidirect
102. C22×D13#107semidirect
116. C2×C4×C13#107semidirect
135. #1055#99semidirect
142. C2×C4⋊C8#261semidirect
254. C13#8609semidirect
288. C2×C4#88102semidirect

Maximal subgroups

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

subgroupindex
#131307132
#131306972
#131296992
C2×#117184952
#860913