Finite Group Databasebeta

← #16778618

Subgroups — #16778618

Order 3328.

568 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 126 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#13130691C211yesmaximal, characteristic
2#13130497C211yesmaximal, characteristic
3#13129655C214yesmaximal, complemented
4#13123183C211yesmaximal, characteristic
5C22×D13⋊C8—21no—
6C2×C13×C4⋊Q8C411yescharacteristic
7C2×#88200—21no—
8C2×C42×D13C2211yescharacteristic
9C2×#88111—21no—
10C2×C4⋊#1057—21no—
11#11718891—21no—
12#11718648—21no—
13#11718648C412yes—
14#11718634—21no—
15#11718634C2212yes—
16#11718596C411yescharacteristic
17#11718290—21no—
18#11718290C2212yes—
19#11718290C2212yes—
20C22×Q8×C13—21no—
21C22×C4×D13C2×C411yescharacteristic
22C22×C4×D13D411yescharacteristic
23C22×C4×D13D411yescharacteristic
24C22×#1057—22no—
25C22×#1057—22no—
26C2×D13⋊C8—24no—
27C2×D13⋊C8—42no—
28C2×D13⋊C8—42no—
29C13×C4⋊Q8—42no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C412yes—
32C2×C42×C13C2×C411yescharacteristic
33#88200—42no—
34#88200—42no—
35C2×#6103—22no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13C2×C412yes—
39C2×#6101—22no—
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13C2311yescharacteristic
43C42×D13—42no—
44#88111—42no—
45C4⋊#1057—42no—
46#88071—22no—
47#88071—22no—
48#7668—131nomaximal, Sylow
49C23×D13C22⋊C411yescharacteristic
50C2×Q8×C13—42no—
51C2×Q8×C13—42no—
52C2×Q8×C13—42no—
53C22×C4×C13—22no—
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22×C411yescharacteristic
57C22×Dic13—22no—
58C22×Dic13C22⋊C411yescharacteristic
59C22×Dic13C2×D411yescharacteristic
60C22×Dic13C2×D411yescharacteristic
61C2×C4×D13—22no—
62C2×C4×D13—22no—
63C2×C4×D13—22no—
64C2×C4×D13—22no—
65C2×C4×D13—41no—
66C2×C4×D13—41no—
67C2×C4×D13—41no—
68C2×C4×D13D812yes—
69C2×C4×D13SD1612yes—
70C2×C4×D13SD1612yes—
71C2×C4×D13Q1612yes—
72C2×#1057—24no—
73C2×#1057—42no—
74C2×#1057—42no—
75C2×#1057—42no—
76C2×#1057—42no—
77C2×#1057—42no—
78D13⋊C8—48no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C42×C13—22no—
82#6103—44no—
83C4⋊Dic13—24no—
84C4⋊Dic13—42no—
85C4⋊Dic13—42no—
86#6101—42no—
87#6101—42no—
88C4×Dic13—22no—
89C4×Dic13—41no—
90C4×Dic13—41no—
91#2857—131no—
92#1797—131no—
93C2×#336—131no—
94#1271—134no—
95C23×C13C2×C22⋊C411yescharacteristic
96C22×D13—21no—
97C22×D13—21no—
98C22×D13—21no—
99C22×D13—21no—
100C22×D13#10112yes—
101C22×D13#10212yes—
102C22×D13#10312yes—
103Q8×C13—84no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13#9912yes—
112C2×C4×C13#10212yes—
113C2×C4×C13#10312yes—
114C2×C4×C13#10412yes—
115C2×C4×C13#13112yes—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—42no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13C2×D811yescharacteristic
127C2×Dic13C2×SD1611yescharacteristic
128C2×Dic13C2×SD1611yescharacteristic
129C2×Dic13C2×Q1611yescharacteristic
130C4×D13—24no—
131C4×D13—24no—
132C4×D13—42no—
133C4×D13—42no—
134C4×D13—44no—
135#1057—44no—
136#1057—82no—
137C23×C8—261no—
138C2×C4⋊Q8#26111yescharacteristic
139C2×C22⋊Q8—261no—
140C22×C42—131no—
141C2×C4⋊C8—261no—
142C2×C22⋊C8—261no—
143#391—261no—
144#389—132no—
145#389—261no—
146#384—131no—
147#380—132no—
148#380—261no—
149#336—132no—
150#336—132no—
151#336—261no—
152C22×C13#40811yescharacteristic
153C22×C13C2×#9911yescharacteristic
154C22×C13C2×#10111yescharacteristic
155C22×C13C2×#10211yescharacteristic
156C22×C13C2×#10311yescharacteristic
157C22×C13C2×#10411yescharacteristic
158C22×C13#42111yescharacteristic
159C2×D13—22no—
160C2×D13—22no—
161C2×D13—22no—
162C2×D13—22no—
163C2×D13—22no—
164C2×D13—22no—
165C2×D13#33214yes—
166C4×C13—22no—
167C4×C13—22no—
168C4×C13—82no—
169C4×C13#32714yes—
170Dic13—21no—
171Dic13—21no—
172Dic13—21no—
173Dic13—21no—
174Dic13—41no—
175Dic13—82no—
176C22×Q8—21no—
177C23×C4—131no—
178C23×C4—131no—
179C23×C4—131no—
180C22×C8—262no—
181C22×C8—264no—
182C22×C8—262no—
183C22×C8—522no—
184C22×C8—522no—
185C4⋊Q8—42no—
186C22⋊Q8—522no—
187C22⋊Q8—522no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—132no—
190C2×C4⋊C4—262no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4C2×#26112yes—
194C2×C22⋊C4—262no—
195C2×C42—131no—
196C2×C42—131no—
197C2×C42—131no—
198C2×C42—522no—
199C2×C42C2×#26111yescharacteristic
200C4⋊C8—522no—
201C22⋊C8—522no—
202#95—262no—
203#95—262no—
204C2×C13#147211yescharacteristic
205C2×C13#148011yescharacteristic
206C2×C13#149311yescharacteristic
207C2×C13C2×#32711yescharacteristic
208C2×C13#152011yescharacteristic
209C2×C13#153111yescharacteristic
210C2×C13C2×#33211yescharacteristic
211D13—24no—
212C24—131no—
213C2×Q8—42no—
214C2×Q8—42no—
215C2×Q8—42no—
216C22×C4—22no—
217C22×C4—131no—
218C22×C4—131no—
219C22×C4—132no—
220C22×C4—132no—
221C22×C4—132no—
222C22×C4—132no—
223C22×C4—131no—
224C22×C4—262no—
225C22×C4—262no—
226C22×C4—262no—
227C22×C4—262no—
228C22×C4—262no—
229C22×C4—521no—
230C22×C4—521no—
231C22×C4—521no—
232C22×C4C22⋊#26111yescharacteristic
233C22×C4C22⋊#26111yescharacteristic
234C22×C4C22×#26111yescharacteristic
235C2×C8—264no—
236C2×C8—522no—
237C2×C8—528no—
238C2×C8—522no—
239C2×C8—522no—
240C2×C8—522no—
241C2×C8—522no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—264no—
245C4⋊C4—522no—
246C4⋊C4—522no—
247C4⋊C4—522no—
248C4⋊C4—522no—
249C22⋊C4—524no—
250C42—22no—
251C42—262no—
252C42—521no—
253C42—521no—
254C13#766811yescharacteristic, complemented, Sylow
255C23—132no—
256C23—132no—
257C23—132no—
258C23—261no—
259C23—261no—
260C23—261no—
261C23—261no—
262C23C2×C22⋊#26111yescharacteristic
263Q8—84no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—131no—
272C2×C4—131no—
273C2×C4—131no—
274C2×C4—131no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—264no—
280C2×C4—264no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—522no—
285C2×C4—522no—
286C2×C4—524no—
287C2×C4—522no—
288C2×C4—522no—
289C2×C4—522no—
290C2×C4#8811512yes—
291C2×C4#8811612yes—
292C2×C4#8811712yes—
293C2×C4#8811912yes—
294C2×C4#8824012yes—
295C8—524no—
296C8—1042no—
297C22—134no—
298C22—262no—
299C22—262no—
300C22—262no—
301C22—262no—
302C22—262no—
303C22—262no—
304C22C2×#8811511yescharacteristic
305C22C2×#8811611yescharacteristic
306C22C2×#8811711yescharacteristic
307C22#1171915511yescharacteristic
308C22#1171915911yescharacteristic
309C22D13⋊#10111yescharacteristic
310C22C2×#8811911yescharacteristic
311C4—22no—
312C4—22no—
313C4—82no—
314C4—261no—
315C4—261no—
316C4—261no—
317C4—261no—
318C4—521no—
319C4—1042no—
320C4#1171829214yes—
321C2—264no—
322C2#1313011611yescharacteristic
323C2#1313014311yescharacteristic
324C2#1313018611yescharacteristic
325C2C2×#1171829211yescharacteristic
326C2#1313027611yescharacteristic
327C2#1313030911yescharacteristic
328C2D13⋊#33211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#7668
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13129655C2semidirect
254. C13#7668semidirect

Maximal subgroups

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

subgroupindex
#131306912
#131304972
#131296552
#131231832
#766813