Finite Group Databasebeta

← #15773109

Subgroups — #15773109

Order 3328.

468 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 107 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#13120602C211yesmaximal, characteristic
2#13114569C211yesmaximal, characteristic
3#13112837C214yesmaximal
4C13×#1458C211yesmaximal, characteristic
5C2×C13×#117C2211yescharacteristic
6C2×#88180—21no—
7C2×#88178—21no—
8C2×#88123C411yescharacteristic, complemented
9C13×#431—21no—
10#11718644—21no—
11#11718644C412yescomplemented
12#11718614—21no—
13#11718614C2212yes—
14#11718597C411yescharacteristic, complemented
15#11718590—21no—
16C13×#324—21no—
17C13×#323C2212yes—
18#11718118—21no—
19#11718118C2212yes—
20C23×C4×C13D411yescharacteristic
21C22×Dic26—21no—
22C13×#117—41no—
23C13×#117—41no—
24C2×C13×C4⋊C4C2×C411yescharacteristic
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C13×C22⋊C4D411yescharacteristic
27C2×C13×C22⋊C4C2311yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C22⋊Dic13—22no—
31C2×C22⋊Dic13—22no—
32#88180—24no—
33#88180—42no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—41no—
37C2×C4⋊Dic13C2×C412yes—
38#88178—42no—
39#88178—42no—
40C2×#6101—22no—
41C2×C4×Dic13—41no—
42#88123—41no—
43#88123—41no—
44C13×C4⋊C8—41no—
45C13×C22⋊C8—22no—
46C4×C8×C13—41no—
47#88071—22no—
48#88071—21no—
49#88071—22no—
50#88071C2×C412yes—
51#11694—131nomaximal, Sylow
52C24×C13C2×D411yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—22no—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13D812yes—
61C22×C4×C13SD1612yes—
62C22×C4×C13C22×C411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×Dic13—22no—
65C22×Dic13—22no—
66C22×Dic13—42no—
67C2×Dic26—41no—
68C2×Dic26—41no—
69C2×Dic26—42no—
70C2×Dic26—42no—
71C2×C8×C13—42no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—41no—
74C13×C22⋊C4—41no—
75C13×C22⋊C4—41no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—21no—
80C22⋊Dic13—24no—
81C22⋊Dic13—42no—
82C22⋊Dic13—42no—
83C22⋊Dic13—42no—
84C4⋊Dic13—42no—
85C4⋊Dic13—44no—
86C4⋊Dic13—42no—
87C4⋊Dic13—42no—
88#6101—44no—
89C4×Dic13—44no—
90#2621—131no—
91#1740—131no—
92#1458D1311yescharacteristic
93#1344—134no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13C2×C22⋊C411yescharacteristic
99C23×C13C2×D811yescharacteristic
100C23×C13C2×SD1611yescharacteristic
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13#9911yescharacteristic
116C2×C4×C13#9911yescharacteristic
117C2×C4×C13#10212yes—
118C2×C4×C13#10212yes—
119C2×C4×C13#10412yes—
120C2×Dic13—44no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13—42no—
127C2×Dic13—82no—
128C2×Dic13—82no—
129Dic26—82no—
130Dic26—82no—
131C8×C13—82no—
132C2×C4⋊Q8—131no—
133C2×C22⋊Q8—261no—
134C2×#117—261no—
135C2×#117C2×D1311yescharacteristic
136#431—21no—
137#398—132no—
138#398—261no—
139#397—132no—
140#397—261no—
141#391—261no—
142#382—131no—
143#342—132no—
144#342—261no—
145#324—21no—
146#323C2×D1312yes—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—81no—
156C22×C13C2×#9911yescharacteristic
157C22×C13C2×#10211yescharacteristic
158C22×C13C2×#10411yescharacteristic
159C4×C13—22no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13#32712yes—
165C4×C13#32712yes—
166Dic13—82no—
167Dic13—84no—
168Dic13—82no—
169C22×Q8—261no—
170C23×C4D5211yescharacteristic
171C4⋊Q8—521no—
172C4⋊Q8—521no—
173C22⋊Q8—522no—
174C22⋊Q8—522no—
175#117—41no—
176#117—41no—
177#117—264no—
178#117—522no—
179C2×C4⋊C4—132no—
180C2×C4⋊C4—262no—
181C2×C4⋊C4—261no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—521no—
184C2×C4⋊C4C4×D1311yescharacteristic
185C2×C4⋊C4C22⋊D1311yescharacteristic
186C2×C22⋊C4—262no—
187C2×C22⋊C4—262no—
188C2×C22⋊C4D5211yescharacteristic
189C2×C22⋊C4C22×D1311yescharacteristic
190C2×C42—521no—
191C2×C42C4×D1311yescharacteristic
192C2×C42C22⋊D1311yescharacteristic
193C4⋊C8—41no—
194C22⋊C8—22no—
195C4×C8—41no—
196#95—132no—
197#95—261no—
198#95—262no—
199#95—262no—
200C2×C13—21no—
201C2×C13—21no—
202C2×C13—41no—
203C2×C13—41no—
204C2×C13C2×#32711yescharacteristic
205C2×C13#212311yescharacteristic
206C2×C13#212911yescharacteristic
207C24C2×D5211yescharacteristic
208C2×Q8—522no—
209C2×Q8—521no—
210C2×Q8—521no—
211C2×Q8—522no—
212C22×C4—22no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—262no—
216C22×C4—262no—
217C22×C4—522no—
218C22×C4#609512yes—
219C22×C4D10412yes—
220C22×C4#610311yescharacteristic
221C22×C4#610311yescharacteristic
222C22×C4#610311yescharacteristic
223C22×C4#610311yescharacteristic
224C22×C4C2×C4×D1311yescharacteristic
225C22×C4C2×C22⋊D1311yescharacteristic
226C2×C8—42no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—522no—
230C4⋊C4—522no—
231C4⋊C4—524no—
232C4⋊C4—524no—
233C4⋊C4—522no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C22⋊C4—264no—
237C22⋊C4—522no—
238C22⋊C4—522no—
239C22⋊C4—522no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—524no—
245C13#1169411yescharacteristic, complemented, Sylow
246C23—21no—
247C23—21no—
248C23—41no—
249C23—41no—
250C23C2×#609511yescharacteristic
251C23C2×D10411yescharacteristic
252C23C2×#610311yescharacteristic
253Q8—1042no—
254Q8—1042no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—524no—
270C2×C4—522no—
271C2×C4—522no—
272C2×C4—522no—
273C2×C4—522no—
274C2×C4—522no—
275C2×C4—522no—
276C2×C4—1042no—
277C2×C4—1042no—
278C2×C4#8804611yescharacteristic
279C2×C4#8804611yescharacteristic
280C2×C4#8806112yes—
281C2×C4#8806112yes—
282C2×C4#8806512yes—
283C8—82no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22C2×#8804611yescharacteristic
294C22C2×#8806111yescharacteristic
295C22C2×#8806511yescharacteristic
296C4—22no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—41no—
301C4—1042no—
302C4—1044no—
303C4—1042no—
304C4#1171806212yes—
305C4#1171806212yes—
306C2—21no—
307C2—21no—
308C2—41no—
309C2—41no—
310C2C2×#1171806211yescharacteristic
311C2#1311649111yescharacteristic
312C2#1311651011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1458C2
socleC22×C13C2×#99
prime radicalC24×C13C2×D4
cosocleC2×C13×C22⋊C4C23
hypercenter#1458D13
hypocenterC13#11694
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
8. C2×#88123C4semidirect
11. #11718644C4semidirect
14. #11718597C4semidirect
245. C13#11694semidirect

Maximal subgroups

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

subgroupindex
#131206022
#131145692
#131128372
C13×#14582
#1169413