Finite Group Databasebeta

← #15759512

Subgroups — #15759512

Order 3328.

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

normal subgroups only

This group has 382 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#13125997C211yesmaximal, characteristic
2#13123930C211yesmaximal, characteristic
3#13113347C211yesmaximal, characteristic
4#13113347C211yesmaximal, characteristic
5#13113310C211yesmaximal, characteristic
6#13112698C211yesmaximal, characteristic
7C13×#1274C211yesmaximal, characteristic
8#11719175C2211yescharacteristic
9#11719175C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C13×#376C2211yescharacteristic
13#11718587C2211yescharacteristic
14#11718587C2211yescharacteristic
15#11718490—22no—
16#11718489—22no—
17#11718384—22no—
18#11718381—22no—
19#11718343C411yescharacteristic, complemented
20#11718342C411yescharacteristic, complemented
21#11718342C411yescharacteristic, complemented
22#11718341C411yescharacteristic, complemented
23#11718340—21no—
24C8×Dic26—21no—
25#11718048—21no—
26#11718048—21no—
27#11718044—22no—
28#11718044—22no—
29C2×C42×C13—21no—
30C2×C42×C13C2311yescharacteristic
31#88180—21no—
32#88180—21no—
33#88178—21no—
34#88178—21no—
35#88178—21no—
36#88178D412yes—
37#88124—21no—
38#88124—21no—
39#88123C2×C411yescharacteristic
40#88123C2×C411yescharacteristic
41#88123C2×C411yescharacteristic
42#88123C2×C411yescharacteristic
43C4×Dic26—21no—
44C4×Dic26—21no—
45C4×Dic26—21no—
46C4×Dic26D412yes—
47C13×C4⋊C8—21no—
48C13×C4⋊C8—21no—
49C13×C22⋊C8—21no—
50C13×C22⋊C8—21no—
51C4×C8×C13C2×C411yescharacteristic
52C4×C8×C13C2×C411yescharacteristic
53C4×C8×C13D411yescharacteristic
54C4×C8×C13D411yescharacteristic
55C13×#95—21no—
56C13×#95—21no—
57C22⋊#1055—21no—
58C22⋊#1055D412yes—
59#88058—22no—
60#88057—22no—
61#88056—22no—
62#88056—22no—
63#88055—22no—
64#88054—22no—
65#88054—22no—
66C8×Dic13—22no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69#88043—21no—
70#88043—21no—
71#9280—131nomaximal, Sylow
72C22×C4×C13—41no—
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13#4111yescharacteristic
76C2×Dic26—21no—
77C2×Dic26—21no—
78C2×Dic26—21no—
79C2×Dic26C22⋊C412yes—
80C2×C8×C13—21no—
81C2×C8×C13—21no—
82C2×C8×C13—21no—
83C2×C8×C13—21no—
84C42×C13—22no—
85C42×C13—41no—
86C42×C13C22×C411yescharacteristic
87C42×C13C2×D411yescharacteristic
88C42×C13C2×D411yescharacteristic
89C42×C13#4111yescharacteristic
90C22⋊Dic13—22no—
91C22⋊Dic13—41no—
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13C22⋊C412yes—
100#6101—22no—
101#6101—22no—
102#6101—41no—
103#6101—41no—
104C4×Dic13—22no—
105C4×Dic13—41no—
106C2×#1055—22no—
107C2×#1055—41no—
108#3231—131no—
109#2985—131no—
110#1506—131no—
111#1506—131no—
112#1497—131no—
113#1287—131no—
114#1274D1311yescharacteristic
115C23×C13#12111yescharacteristic
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—42no—
121C2×C4×C13—81no—
122C2×C4×C13—81no—
123C2×C4×C13C2×C22⋊C411yescharacteristic
124C2×C4×C13C4×D411yescharacteristic
125C2×C4×C13C4×D411yescharacteristic
126C2×C4×C13#12011yescharacteristic
127C2×C4×C13#12111yescharacteristic
128C2×C4×C13#12311yescharacteristic
129C2×Dic13—22no—
130C2×Dic13—22no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133Dic26—41no—
134Dic26—41no—
135Dic26—42no—
136Dic26—41no—
137Dic26—41no—
138Dic26—81no—
139C8×C13—41no—
140C8×C13—41no—
141C8×C13—41no—
142C8×C13—41no—
143#1055—42no—
144#1055—81no—
145#533—131no—
146#533—131no—
147#500—131no—
148#498—131no—
149#487—131no—
150#487—131no—
151#485—262no—
152#479—262no—
153#446—262no—
154#446—261no—
155C8×Q8—261no—
156#433—262no—
157#432—131no—
158#432—131no—
159#431C2×D1311yescharacteristic
160#431C2×D1311yescharacteristic
161#376C2×D1311yescharacteristic
162#328—262no—
163#328—262no—
164Q8⋊C8—261no—
165Q8⋊C8—261no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13#38611yescharacteristic
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—82no—
176C4×C13#44311yescharacteristic
177C4×C13#44411yescharacteristic
178Dic13—42no—
179Dic13—42no—
180Dic13—81no—
181Dic13—81no—
182C4⋊Q8—131no—
183C4⋊Q8—131no—
184C4⋊Q8—131no—
185C4⋊Q8—131no—
186#125—261no—
187#125—261no—
188C22⋊Q8—132no—
189C22⋊Q8—261no—
190C22⋊Q8—261no—
191C22⋊Q8—261no—
192C4×Q8—132no—
193C4×Q8—261no—
194C4×Q8—261no—
195C4×Q8—261no—
196#117—261no—
197#117—261no—
198C2×C42—21no—
199C2×C42C22×D1311yescharacteristic
200#107—262no—
201#106—262no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—262no—
205C4⋊C8—262no—
206C4⋊C8—261no—
207C4⋊C8—261no—
208#103—262no—
209#103—262no—
210C22⋊C8—21no—
211C22⋊C8—21no—
212C22⋊C8—132no—
213C22⋊C8—261no—
214#97—262no—
215#97—261no—
216#97—261no—
217C4×C8—262no—
218C4×C8C4×D1311yescharacteristic
219C4×C8C4×D1311yescharacteristic
220C4×C8D5211yescharacteristic
221C4×C8D5211yescharacteristic
222#95—21no—
223#95—21no—
224C2×C13—41no—
225C2×C13#187611yescharacteristic
226C2×C13#190511yescharacteristic
227C2×C13#190911yescharacteristic
228C2×Q8—132no—
229C2×Q8—261no—
230C2×Q8—261no—
231C2×Q8—261no—
232C22×C4—41no—
233C22×C4#612711yescharacteristic
234C22×C4D4×D1311yescharacteristic
235C22×C4D4×D1311yescharacteristic
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—262no—
241C2×C8—521no—
242C4⋊C4—132no—
243C4⋊C4—261no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4—262no—
247C4⋊C4—262no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—521no—
253C4⋊C4—521no—
254C22⋊C4—262no—
255C22⋊C4—521no—
256C42—22no—
257C42—41no—
258C42—262no—
259C42—521no—
260C42C2×C4×D1311yescharacteristic
261C42C2×D5211yescharacteristic
262C42D4×D1311yescharacteristic
263C42#613111yescharacteristic
264C13#928011yescharacteristic, complemented, Sylow
265C23#8813811yescharacteristic
266Q8—522no—
267Q8—521no—
268Q8—521no—
269Q8—521no—
270Q8—521no—
271Q8—1041no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—262no—
280C2×C4—262no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4C4×D5211yescharacteristic
284C2×C4C22⋊C4×D1311yescharacteristic
285C2×C4#8813611yescharacteristic
286C2×C4#8814711yescharacteristic
287C2×C4#8814811yescharacteristic
288C2×C4#8814911yescharacteristic
289C8—41no—
290C8—41no—
291C8—41no—
292C8—41no—
293C8—522no—
294C8—1041no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22#1171832611yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—82no—
305C4—522no—
306C4—522no—
307C4—1041no—
308C4—1041no—
309C4#1171836111yescharacteristic
310C4#1171837811yescharacteristic
311C2—41no—
312C2#1311516211yescharacteristic
313C2#1311533111yescharacteristic
314C2#1311535711yescharacteristic
subgroupG/H
centerC22#11718326
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1274C2
socleC22×C13#386
prime radicalC23×C13#121
cosocleC2×C42×C13C23
hypercenter#1274D13
hypocenterC13#9280
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
19. #11718343C4semidirect
20. #11718342C4semidirect
21. #11718342C4semidirect
22. #11718341C4semidirect
264. C13#9280semidirect

Maximal subgroups

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

subgroupindex
#131259972
#131239302
#131133472
#131133102
#131126982
C13×#12742
#928013