Finite Group Databasebeta

← #16778752

Subgroups — #16778752

Order 3328.

500 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 94 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#13130728C211yesmaximal, characteristic
2#13130563C211yesmaximal, characteristic
3#13129655C214yesmaximal, complemented
4#13123183C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×#88200—21no—
7C2×C42×D13C2211yescharacteristic
8C2×#88111—21no—
9C2×#88111—21no—
10C2×#88110—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—
26C13×C4⋊Q8—42no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4C2×C412yes—
29C2×C42×C13C2×C411yescharacteristic
30#88200—44no—
31C2×#6103—22no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13C2×C412yes—
35C2×#6101—22no—
36C2×C4×Dic13D411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13C2311yescharacteristic
39C42×D13—42no—
40#88111—24no—
41#88111—42no—
42#88110—42no—
43#88071—22no—
44#88071—22no—
45#7705—131nomaximal, Sylow
46C23×D13C22⋊C411yescharacteristic
47C2×Q8×C13—42no—
48C2×Q8×C13—42no—
49C2×Q8×C13—42no—
50C22×C4×C13—22no—
51C22×C4×C13C22⋊C411yescharacteristic
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22×C411yescharacteristic
54C22×Dic13—22no—
55C22×Dic13C22⋊C411yescharacteristic
56C22×Dic13C2×D411yescharacteristic
57C22×Dic13C2×D411yescharacteristic
58C2×C4×D13—22no—
59C2×C4×D13—22no—
60C2×C4×D13—22no—
61C2×C4×D13—22no—
62C2×C4×D13—22no—
63C2×C4×D13—22no—
64C2×C4×D13—41no—
65C2×C4×D13—41no—
66C2×C4×D13—41no—
67C2×#1057—24no—
68C2×#1057—42no—
69C2×#1057—42no—
70C2×#1057—42no—
71C2×#1057—42no—
72C2×#1057—42no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—42no—
75C42×C13—22no—
76#6103—44no—
77C4⋊Dic13—24no—
78C4⋊Dic13—42no—
79C4⋊Dic13—42no—
80#6101—44no—
81C4×Dic13—22no—
82C4×Dic13—41no—
83C4×Dic13—41no—
84#2857—131no—
85#1817—131no—
86#1749—131no—
87#1271—134no—
88C23×C13C2×C22⋊C411yescharacteristic
89C22×D13—21no—
90C22×D13—21no—
91C22×D13—21no—
92C22×D13—21no—
93C22×D13—21no—
94C22×D13—21no—
95C22×D13#10112yes—
96Q8×C13—84no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13#9912yes—
107C2×C4×C13#10412yes—
108C2×C4×C13#13112yes—
109C2×Dic13—21no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13AGL(1,ℤ/8)12yes—
120C2×Dic13#13712yes—
121C4×D13—44no—
122C4×D13—44no—
123C4×D13—44no—
124#1057—44no—
125#1057—82no—
126C2×C4⋊Q8#26111yescharacteristic
127C2×C22⋊Q8—261no—
128C22×C42—131no—
129C2×C22⋊C8—261no—
130C2×C22⋊C8—261no—
131C2×#97—261no—
132#391—261no—
133#389—132no—
134#389—261no—
135#384—131no—
136#380—132no—
137#380—261no—
138#336—132no—
139#336—132no—
140#336—261no—
141C22×C13#40811yescharacteristic
142C22×C13C2×#9911yescharacteristic
143C22×C13C2×#10111yescharacteristic
144C22×C13#41811yescharacteristic
145C22×C13#41911yescharacteristic
146C22×C13C2×#10411yescharacteristic
147C22×C13#42111yescharacteristic
148C2×D13—22no—
149C2×D13—22no—
150C2×D13—22no—
151C2×D13—41no—
152C2×D13—41no—
153C2×D13—41no—
154C2×D13—41no—
155C4×C13—22no—
156C4×C13—22no—
157C4×C13—22no—
158C4×C13—82no—
159Dic13—22no—
160Dic13—22no—
161Dic13—41no—
162Dic13—82no—
163C22×Q8—21no—
164C23×C4—131no—
165C23×C4—131no—
166C23×C4—131no—
167C22×C8—262no—
168C22×C8—262no—
169C4⋊Q8—42no—
170C22⋊Q8—524no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—132no—
173C2×C4⋊C4—262no—
174C2×C4⋊C4—261no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4C2×#26112yes—
177C2×C22⋊C4—262no—
178C2×C42—131no—
179C2×C42—131no—
180C2×C42—131no—
181C2×C42—522no—
182C2×C42C2×#26111yescharacteristic
183C22⋊C8—264no—
184C22⋊C8—522no—
185#97—522no—
186#95—262no—
187#95—262no—
188C2×C13#147211yescharacteristic
189C2×C13#148511yescharacteristic
190C2×C13#149611yescharacteristic
191C2×C13#150711yescharacteristic
192C2×C13#151111yescharacteristic
193C2×C13#153111yescharacteristic
194C2×C13#155611yescharacteristic
195D13—42no—
196C24—131no—
197C2×Q8—42no—
198C2×Q8—42no—
199C2×Q8—42no—
200C22×C4—22no—
201C22×C4—131no—
202C22×C4—131no—
203C22×C4—131no—
204C22×C4—262no—
205C22×C4—262no—
206C22×C4—262no—
207C22×C4—262no—
208C22×C4—262no—
209C22×C4—262no—
210C22×C4—262no—
211C22×C4—521no—
212C22×C4—521no—
213C22×C4—521no—
214C22×C4C22⋊#26111yescharacteristic
215C22×C4C22⋊#26111yescharacteristic
216C22×C4C22×#26111yescharacteristic
217C2×C8—264no—
218C2×C8—522no—
219C2×C8—522no—
220C2×C8—522no—
221C2×C8—522no—
222C2×C8—522no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—264no—
226C4⋊C4—522no—
227C4⋊C4—522no—
228C4⋊C4—524no—
229C22⋊C4—524no—
230C42—22no—
231C42—262no—
232C42—521no—
233C42—521no—
234C13#770511yescharacteristic, complemented, Sylow
235C23—132no—
236C23—261no—
237C23—261no—
238C23—261no—
239C23—261no—
240C23—261no—
241C23—261no—
242C23C2×C22⋊#26111yescharacteristic
243Q8—84no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—132no—
254C2×C4—132no—
255C2×C4—261no—
256C2×C4—261no—
257C2×C4—261no—
258C2×C4—261no—
259C2×C4—261no—
260C2×C4—261no—
261C2×C4—261no—
262C2×C4—524no—
263C2×C4—524no—
264C2×C4—524no—
265C2×C4—522no—
266C2×C4—522no—
267C2×C4—522no—
268C2×C4#8811612yes—
269C2×C4#8811912yes—
270C2×C4#8824012yes—
271C8—524no—
272C8—1042no—
273C22—262no—
274C22—262no—
275C22—262no—
276C22—521no—
277C22—521no—
278C22—521no—
279C22—521no—
280C22#1171913811yescharacteristic
281C22C2×#8811611yescharacteristic
282C22#1171915311yescharacteristic
283C22#1171915511yescharacteristic
284C22#1171915911yescharacteristic
285C22D13⋊#10111yescharacteristic
286C22C2×#8811911yescharacteristic
287C4—22no—
288C4—22no—
289C4—22no—
290C4—82no—
291C4—262no—
292C4—262no—
293C4—521no—
294C4—1042no—
295C2—522no—
296C2#1313011611yescharacteristic
297C2#1313016011yescharacteristic
298C2#1313019711yescharacteristic
299C2#1313023211yescharacteristic
300C2#1313024611yescharacteristic
301C2#1313030911yescharacteristic
302C2#1313036611yescharacteristic
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#7705
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
234. C13#7705semidirect

Maximal subgroups

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

subgroupindex
#131307282
#131305632
#131296552
#131231832
#770513