Finite Group Databasebeta

← #15759516

Subgroups — #15759516

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#13125995C211yesmaximal, characteristic
2#13123930C211yesmaximal, characteristic
3#13113349C211yesmaximal, characteristic
4#13113348C211yesmaximal, characteristic
5#13112697C211yesmaximal, characteristic
6#13112664C211yesmaximal, characteristic
7C13×#1497C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9#11719175C2211yescharacteristic
10C13×#432C2211yescharacteristic
11C13×#431C2211yescharacteristic
12#11718754C411yescharacteristic, complemented
13#11718754C411yescharacteristic, complemented
14#11718740C411yescharacteristic, complemented
15#11718739C411yescharacteristic, complemented
16#11718724—22no—
17#11718657—22no—
18#11718593C2211yescharacteristic
19#11718587C2211yescharacteristic
20#11718586C2211yescharacteristic
21#11718489—22no—
22#11718381—22no—
23#11718340—21no—
24C8×Dic26—21no—
25C13×Q8⋊C8—21no—
26C13×Q8⋊C8—21no—
27#11718130—22no—
28#11718059—22no—
29C13×C4⋊Q8C2×C411yescharacteristic
30C13×C4⋊Q8C2×C411yescharacteristic
31C13×#125—21no—
32C13×C22⋊Q8—21no—
33C13×C22⋊Q8—21no—
34C4×Q8×C13—21no—
35C4×Q8×C13—21no—
36C13×#117—21no—
37C2×C42×C13C2311yescharacteristic
38#88180—21no—
39#88178—21no—
40#88178D412yes—
41C2×C4×Dic13—21no—
42#88124—21no—
43#88123C2×C411yescharacteristic
44#88123C2×C411yescharacteristic
45C4×Dic26—21no—
46C4×Dic26D412yes—
47C13×C4⋊C8—21no—
48C13×C4⋊C8—21no—
49C13×C22⋊C8—21no—
50C13×C22⋊C8—21no—
51C13×#97—21no—
52C4×C8×C13D411yescharacteristic
53C4×C8×C13D411yescharacteristic
54#88071—21no—
55#88071—21no—
56C22⋊#1055—21no—
57C22⋊#1055D412yes—
58#88055—22no—
59#88054—22no—
60#88054—22no—
61C8×Dic13—22no—
62#88050—22no—
63#88050—22no—
64#88048—22no—
65#88047—22no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68#88043—21no—
69C4×#1055C2×C411yescharacteristic
70C4×#1055C2×C411yescharacteristic
71#9280—131nomaximal, Sylow
72C2×Q8×C13—21no—
73C2×Q8×C13—21no—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13#4111yescharacteristic
77C22×Dic13—41no—
78C2×Dic26—21no—
79C2×Dic26C22⋊C412yes—
80C2×C8×C13—21no—
81C2×C8×C13—21no—
82C2×C8×C13—41no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C22⋊C4—41no—
90C42×C13—41no—
91C42×C13C22×C411yescharacteristic
92C42×C13C2×D411yescharacteristic
93C42×C13C2×D411yescharacteristic
94C42×C13#4111yescharacteristic
95C22⋊Dic13—22no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13C22⋊C412yes—
100#6101—22no—
101#6101—22no—
102C4×Dic13—22no—
103C4×Dic13—22no—
104C4×Dic13—41no—
105C2×#1055—21no—
106C2×#1055—21no—
107C2×#1055—22no—
108#3231—131no—
109#2985—131no—
110#1506—131no—
111#1506—131no—
112#1497D1311yescharacteristic
113#1287—131no—
114#1274—131no—
115C23×C13#12111yescharacteristic
116Q8×C13—41no—
117Q8×C13—41no—
118Q8×C13—81no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13C2×C22⋊C411yescharacteristic
126C2×C4×C13C4×D411yescharacteristic
127C2×C4×C13C4×D411yescharacteristic
128C2×C4×C13#12011yescharacteristic
129C2×C4×C13#12111yescharacteristic
130C2×C4×C13#12311yescharacteristic
131C2×Dic13—22no—
132C2×Dic13—22no—
133C2×Dic13—42no—
134C2×Dic13—81no—
135C2×Dic13—81no—
136Dic26—41no—
137Dic26—41no—
138Dic26—42no—
139C8×C13—41no—
140C8×C13—41no—
141C8×C13—81no—
142#1055—42no—
143#1055—41no—
144#1055—41no—
145#533—131no—
146#533C2×D1311yescharacteristic
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#432C2×D1311yescharacteristic
159#431—131no—
160#431C2×D1311yescharacteristic
161#376—131no—
162#328—262no—
163#328—262no—
164Q8⋊C8—21no—
165Q8⋊C8—21no—
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—81no—
176C4×C13—81no—
177C4×C13#44311yescharacteristic
178C4×C13#44411yescharacteristic
179Dic13—42no—
180Dic13—42no—
181Dic13—82no—
182C4⋊Q8—131no—
183C4⋊Q8—131no—
184C4⋊Q8C4×D1311yescharacteristic
185C4⋊Q8C4×D1311yescharacteristic
186#125—21no—
187#125—261no—
188C22⋊Q8—21no—
189C22⋊Q8—21no—
190C22⋊Q8—132no—
191C22⋊Q8—261no—
192C4×Q8—21no—
193C4×Q8—21no—
194C4×Q8—132no—
195C4×Q8—261no—
196#117—21no—
197#117—261no—
198C2×C42—261no—
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—21no—
215#97—262no—
216#97—261no—
217C4×C8—131no—
218C4×C8—131no—
219C4×C8—262no—
220C4×C8C22⋊D1311yescharacteristic
221C4×C8C22⋊D1311yescharacteristic
222#95—261no—
223#95—261no—
224C2×C13—41no—
225C2×C13#187611yescharacteristic
226C2×C13#190511yescharacteristic
227C2×C13#190911yescharacteristic
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—132no—
231C2×Q8—261no—
232C22×C4—521no—
233C22×C4#612711yescharacteristic
234C22×C4D4×D1311yescharacteristic
235C22×C4D4×D1311yescharacteristic
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—41no—
239C2×C8—261no—
240C2×C8—261no—
241C2×C8—262no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—132no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—262no—
252C4⋊C4—261no—
253C4⋊C4—262no—
254C22⋊C4—41no—
255C22⋊C4—262no—
256C42—41no—
257C42—262no—
258C42—262no—
259C42—521no—
260C42C2×C4×D1311yescharacteristic
261C42D4×D1311yescharacteristic
262C42#612911yescharacteristic
263C42C2×C22⋊D1311yescharacteristic
264C13#928011yescharacteristic, complemented, Sylow
265C23#8813811yescharacteristic
266Q8—41no—
267Q8—41no—
268Q8—81no—
269Q8—522no—
270Q8—521no—
271Q8—521no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—262no—
279C2×C4—262no—
280C2×C4—522no—
281C2×C4—1041no—
282C2×C4—1041no—
283C2×C4C22⋊C4×D1311yescharacteristic
284C2×C4#8813511yescharacteristic
285C2×C4#8813711yescharacteristic
286C2×C4C4×C22⋊D1311yescharacteristic
287C2×C4#8819111yescharacteristic
288C2×C4#8819211yescharacteristic
289C8—41no—
290C8—41no—
291C8—81no—
292C8—522no—
293C8—521no—
294C8—521no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22#1171861711yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—81no—
305C4—81no—
306C4—522no—
307C4—522no—
308C4—1042no—
309C4#1171880511yescharacteristic
310C4#1171880611yescharacteristic
311C2—41no—
312C2#1311516611yescharacteristic
313C2#1311532711yescharacteristic
314C2#1311535511yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1497C2
socleC22×C13#386
prime radicalC23×C13#121
cosocleC2×C42×C13C23
hypercenter#1497D13
hypocenterC13#9280
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
12. #11718754C4semidirect
13. #11718754C4semidirect
14. #11718740C4semidirect
15. #11718739C4semidirect
264. C13#9280semidirect

Maximal subgroups

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

subgroupindex
#131259952
#131239302
#131133492
#131133482
#131126972
#131126642
C13×#14972
#928013