Finite Group Databasebeta

← #15773863

Subgroups — #15773863

Order 3328.

334 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 89 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#13125417C211yesmaximal, characteristic
2#13116632C211yesmaximal, characteristic
3#13114962C211yesmaximal, characteristic
4#13112849C211yesmaximal, characteristic
5#13112848C211yesmaximal, characteristic
6#13112847C211yesmaximal, characteristic
7C13×#1348C211yesmaximal, characteristic
8#11719327—21no—
9C13×#467C2211yescharacteristic
10Q16×Dic13C411yescharacteristic, complemented
11#11718842C411yescharacteristic, complemented
12#11718777C2211yescharacteristic
13C2×C8×Dic13C2211yescharacteristic
14#11718712—21no—
15#11718637—21no—
16#11718535C411yescharacteristic, complemented
17#11718534C411yescharacteristic, complemented
18#11718453—21no—
19#11718451—21no—
20C13×C22⋊C16C2211yescharacteristic
21C13×#340C2211yescharacteristic
22#11718143C2211yescharacteristic
23C22⋊#6090C2211yescharacteristic
24#11718121—21no—
25#11718093—21no—
26C16×Dic13—21no—
27C2×C13×Q16C2×C411yescharacteristic
28C22×C8×C13C2311yescharacteristic
29C13×C22⋊Q8—21no—
30C2×C13×C4⋊C4—21no—
31Q8×Dic13—21no—
32#88198—21no—
33C2×#6107—21no—
34C2×C4⋊Dic13—21no—
35#88178—21no—
36C2×#6101—41no—
37C2×#6101—41no—
38C2×C4×Dic13D411yescharacteristic
39C22×#1055D411yescharacteristic
40C2×Dic52C2×C411yescharacteristic
41#88143—41no—
42#88142—21no—
43#88141—21no—
44#88141—41no—
45#88132—41no—
46#88131—41no—
47C2×C13×C16—21no—
48C13×#107C2×C411yescharacteristic
49C13×#103—21no—
50#88075—21no—
51#88058C2×C411yescharacteristic
52#88056—21no—
53C8×Dic13C2×C411yescharacteristic
54C8×Dic13C2×C411yescharacteristic
55C8×Dic13D411yescharacteristic
56C8×Dic13D411yescharacteristic
57C2×#6090—21no—
58#88050—21no—
59#88047—21no—
60#11857—131nomaximal, Sylow
61C2×Q8×C13—21no—
62C22×C4×C13—41no—
63C22×C4×C13C2×D411yescharacteristic
64C22×Dic13—41no—
65C22×Dic13D811yescharacteristic
66C22×Dic13D811yescharacteristic
67C2×Dic26—21no—
68C2×Dic26—41no—
69C13×Q16—41no—
70C2×C8×C13—41no—
71C2×C8×C13C22×C411yescharacteristic
72C2×C8×C13C2×D411yescharacteristic
73C13×C4⋊C4—21no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C22⋊C4—41no—
78C22⋊Dic13—41no—
79#6107—42no—
80C4⋊Dic13—21no—
81C4⋊Dic13—41no—
82C4⋊Dic13—41no—
83C4⋊Dic13—41no—
84#6101—41no—
85#6101—41no—
86#6101—41no—
87#6101—41no—
88#6101—41no—
89#6101—82no—
90#6101—82no—
91C4×Dic13—41no—
92C4×Dic13—41no—
93C4×Dic13C22⋊C411yescharacteristic
94C4×Dic13C22⋊C411yescharacteristic
95C4×Dic13SD1611yescharacteristic
96C4×Dic13SD1611yescharacteristic
97C2×#1055—41no—
98C2×#1055C22⋊C411yescharacteristic
99C2×#1055C22⋊C411yescharacteristic
100Dic52—41no—
101C13×C16—41no—
102#6090—41no—
103#3170—131no—
104#2162—131no—
105#1834—131no—
106#1348—131no—
107#1348—131no—
108#1348—131no—
109#1348D1311yescharacteristic
110C23×C13C2×D811yescharacteristic
111Q8×C13—41no—
112Q8×C13—41no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—81no—
118C2×C4×C13—81no—
119C2×C4×C13—81no—
120C2×C4×C13C2×C22⋊C411yescharacteristic
121C2×C4×C13C2×SD1611yescharacteristic
122C2×Dic13—22no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—81no—
126C2×Dic13—81no—
127C2×Dic13—81no—
128C2×Dic13#10211yescharacteristic
129C2×Dic13#10211yescharacteristic
130C2×Dic13#10211yescharacteristic
131C2×Dic13#10211yescharacteristic
132C2×Dic13SD3212yes—
133C2×Dic13Q3212yes—
134Dic26—41no—
135Dic26—41no—
136Dic26—82no—
137C8×C13—21no—
138C8×C13—21no—
139#1055—21no—
140#1055—21no—
141#533—261no—
142#500—131no—
143#494—131no—
144#487—261no—
145#467—131no—
146#467—261no—
147#467C2×D1311yescharacteristic
148C4×Q16—131no—
149C4×Q16—131no—
150C4×Q16—261no—
151C2×C4×C8—131no—
152#384—261no—
153C4⋊C16—261no—
154C22⋊C16—131no—
155C22⋊C16C2×D1311yescharacteristic
156C4×C16—261no—
157#340—131no—
158#340—261no—
159#340C2×D1311yescharacteristic
160C22×C13—21no—
161C22×C13—21no—
162C22×C13C2×#10211yescharacteristic
163C22×C13C2×SD3211yescharacteristic
164C22×C13C2×Q3211yescharacteristic
165C4×C13—21no—
166C4×C13—81no—
167C4×C13—81no—
168C4×C13—161no—
169C4×C13#41011yescharacteristic
170C4×C13#42111yescharacteristic
171Dic13—21no—
172Dic13—81no—
173Dic13—81no—
174Dic13—161no—
175Dic13#35812yes—
176Dic13#35812yes—
177Dic13#36012yes—
178C2×Q16—131no—
179C2×Q16—261no—
180C2×Q16C4×D1311yescharacteristic
181C22×C8—131no—
182C22×C8C22×D1311yescharacteristic
183C4⋊Q8—261no—
184C4⋊Q8—261no—
185#125—521no—
186C22⋊Q8—21no—
187C22⋊Q8—261no—
188C22⋊Q8—521no—
189C4×Q8—261no—
190C4×Q8—261no—
191C4×Q8—521no—
192#117—521no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—261no—
195C2×C4⋊C4—521no—
196C2×C4⋊C4—521no—
197C2×C42—131no—
198C2×C16—21no—
199C2×C16—261no—
200#107—131no—
201#107—261no—
202#107C4×D1311yescharacteristic
203#103—21no—
204#103—261no—
205#103—261no—
206#103—261no—
207C4×C8—131no—
208C4×C8—131no—
209C4×C8—131no—
210C4×C8—131no—
211C2×C13—21no—
212C2×C13—21no—
213C2×C13#151711yescharacteristic
214C2×C13C2×#35811yescharacteristic
215C2×C13C2×#36011yescharacteristic
216C2×Q8—21no—
217C2×Q8—261no—
218C2×Q8—521no—
219C22×C4—41no—
220C22×C4—131no—
221C22×C4—131no—
222C22×C4—521no—
223C22×C4D4×D1311yescharacteristic
224Q16—41no—
225Q16—521no—
226Q16—522no—
227C2×C8—41no—
228C2×C8—131no—
229C2×C8—131no—
230C2×C8—521no—
231C2×C8C2×C4×D1311yescharacteristic
232C2×C8D4×D1311yescharacteristic
233C4⋊C4—21no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—261no—
238C4⋊C4—521no—
239C4⋊C4—521no—
240C4⋊C4—521no—
241C4⋊C4—521no—
242C4⋊C4—521no—
243C4⋊C4—521no—
244C4⋊C4—521no—
245C4⋊C4—521no—
246C4⋊C4—1042no—
247C4⋊C4—1042no—
248C22⋊C4—41no—
249C22⋊C4—521no—
250C42—131no—
251C42—131no—
252C42—131no—
253C42—131no—
254C42—521no—
255C42—521no—
256C16—41no—
257C16—521no—
258C13#1185711yescharacteristic, complemented, Sylow
259C23D8×D1311yescharacteristic
260Q8—41no—
261Q8—41no—
262Q8—521no—
263Q8—521no—
264Q8—1042no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—131no—
273C2×C4—131no—
274C2×C4—131no—
275C2×C4—132no—
276C2×C4—132no—
277C2×C4—131no—
278C2×C4—262no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4—1041no—
282C2×C4—1041no—
283C2×C4—1041no—
284C2×C4C22⋊C4×D1311yescharacteristic
285C2×C4SD16×D1311yescharacteristic
286C8—21no—
287C8—21no—
288C8—261no—
289C8—261no—
290C22—21no—
291C22—21no—
292C22D13×#10211yescharacteristic
293C22D13×SD3211yescharacteristic
294C22D13×Q3211yescharacteristic
295C4—21no—
296C4—81no—
297C4—81no—
298C4—132no—
299C4—132no—
300C4—132no—
301C4—161no—
302C4—261no—
303C4—1041no—
304C4—1041no—
305C4—2081no—
306C4#1171840111yescharacteristic
307C4#1171848211yescharacteristic
308C2—21no—
309C2—21no—
310C2#1311339411yescharacteristic
311C2D13×#35811yescharacteristic
312C2D13×#36011yescharacteristic
subgroupG/H
centerC22D13×#102
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1348C2
socleC22×C13C2×#102
prime radicalC23×C13C2×D8
cosocleC22×C8×C13C23
hypercenter#1348D13
hypocenterC13#11857
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1348

Complements

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

NH ≅ G/Ntype
10. Q16×Dic13C4semidirect
11. #11718842C4semidirect
16. #11718535C4semidirect
17. #11718534C4semidirect
258. C13#11857semidirect

Maximal subgroups

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

subgroupindex
#131254172
#131166322
#131149622
#131128492
#131128482
#131128472
C13×#13482
#1185713