Finite Group Databasebeta

← #14651302

Subgroups — #14651302

Order 2816.

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

normal subgroups only

This group has 436 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#13078990C211yesmaximal, characteristic
2#13077721C211yesmaximal, characteristic, complemented
3#13067330C211yesmaximal, characteristic
4#13067253C211yesmaximal, characteristic, complemented
5#13066489C211yesmaximal, characteristic, complemented
6#13066487C211yesmaximal, characteristic, complemented
7C11×#1555C211yesmaximal, characteristic
8C2×C11×#127C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12#10622828—22no—
13#10622684—22no—
14#10622683C412yes—
15#10622683C412yes—
16#10622539C2211yescharacteristic
17#10622539C2211yescharacteristic
18C4×#4318C2211yescharacteristic
19#10622441—22no—
20#10622333—22no—
21#10622314—22no—
22C11×#331—22no—
23#10622182—22no—
24#10622103—22no—
25C22×D4×C11—21no—
26C22×D4×C11—21no—
27C22×D4×C11—21no—
28C11×#127—21no—
29C11×#127—21no—
30C11×#127—21no—
31C11×#127C2×C412yes—
32C2×C42×C11C2311yescharacteristic
33#66979D412yes—
34#66977—21no—
35#66977—21no—
36C2×#4318—21no—
37#66923D412yes—
38#66922C2×C411yescharacteristic
39#66922C2×C411yescharacteristic
40C4×Dic22—21no—
41C4×Dic22—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8D412yes—
44C11×C22⋊C8—21no—
45C11×C22⋊C8—21no—
46C11×#97—21no—
47C11×#97—21no—
48#66896—24no—
49#66896—24no—
50C22⋊(C11⋊C8)—21no—
51C22⋊(C11⋊C8)—21no—
52#66879—22no—
53Dic11⋊C8—24no—
54C8×Dic11—22no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)D412yes—
57#66867—21no—
58#66867—21no—
59#66867—21no—
60C4×C11⋊C8C2×C412yes—
61#9424—111nomaximal, Sylow
62C24×C11—41no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—22no—
66C2×D4×C11—44no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—82no—
71C2×D4×C11—82no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×C8×C11—22no—
78C2×C8×C11—41no—
79C42×C11C22×C411yescharacteristic
80C42×C11C2×D411yescharacteristic
81C42×C11C2×D411yescharacteristic
82C42×C11C2×D411yescharacteristic
83C22⋊Dic11—22no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11C22⋊C412yes—
87C4⋊Dic11C22⋊C412yes—
88Dic11⋊C4—22no—
89Dic11⋊C4—22no—
90C4×Dic11—22no—
91#4318—42no—
92C2×C11⋊C8—22no—
93C2×C11⋊C8—22no—
94C2×C11⋊C8—41no—
95#3138—111no—
96#2987—111no—
97#1555—111no—
98#1555D1111yescharacteristic
99#1537—111no—
100#1291—111no—
101#1291—111no—
102C23×C11—42no—
103C23×C11—82no—
104C23×C11—82no—
105C23×C11—82no—
106C23×C11#12311yescharacteristic
107D4×C11—44no—
108D4×C11—82no—
109D4×C11—82no—
110D4×C11—82no—
111D4×C11—82no—
112D4×C11—82no—
113C2×C4×C11—22no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11C2×C22⋊C411yescharacteristic
117C2×C4×C11C4×D411yescharacteristic
118C2×C4×C11C4×D411yescharacteristic
119C2×C4×C11#12011yescharacteristic
120C2×C4×C11#12111yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×Dic11—22no—
123C2×Dic11—22no—
124Dic22—81no—
125Dic22—81no—
126C8×C11—42no—
127C8×C11—81no—
128C11⋊C8—42no—
129C11⋊C8—42no—
130C11⋊C8—81no—
131#533—111no—
132C2×#127C2×D1111yescharacteristic
133#490—222no—
134#486—112no—
135#486—112no—
136#446—222no—
137#446—222no—
138#433—222no—
139#432—111no—
140#432—111no—
141#432C2×D1111yescharacteristic
142#432C2×D1111yescharacteristic
143#418—222no—
144C4×M16—111no—
145#331—22no—
146#331—222no—
147#330—222no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—82no—
152C22×C11—82no—
153C22×C11—82no—
154C22×C11—164no—
155C22×C11#38611yescharacteristic
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—21no—
161C4×C11#45412yes—
162Dic11—42no—
163Dic11—42no—
164C22×D4—21no—
165C22×D4—21no—
166C22×D4—21no—
167C2×M16—221no—
168C4⋊Q8—111no—
169C4⋊Q8—111no—
170#127—21no—
171#127—21no—
172#127—21no—
173#127C4×D1112yes—
174#125—112no—
175C22⋊Q8—221no—
176C22⋊Q8—221no—
177C4×Q8—221no—
178C4×Q8—221no—
179#117—112no—
180C2×C42C22×D1111yescharacteristic
181C4⋊C8—21no—
182C4⋊C8—112no—
183C4⋊C8—224no—
184C4⋊C8—221no—
185C4⋊C8C22⋊D1112yes—
186#102—224no—
187#102—224no—
188C22⋊C8—21no—
189C22⋊C8—21no—
190C22⋊C8—221no—
191C22⋊C8—221no—
192#97—21no—
193#97—21no—
194#97—222no—
195#97—221no—
196#97—221no—
197#97—221no—
198C4×C8—112no—
199C4×C8—222no—
200C2×C11—41no—
201C2×C11—162no—
202C2×C11#188811yescharacteristic
203C2×C11#190311yescharacteristic
204C2×C11#190311yescharacteristic
205C24—41no—
206C2×Q8—221no—
207C2×Q8—221no—
208C2×D4—22no—
209C2×D4—22no—
210C2×D4—22no—
211C2×D4—44no—
212C2×D4—41no—
213C2×D4—41no—
214C2×D4—41no—
215C2×D4—82no—
216C2×D4—82no—
217C22×C4#433911yescharacteristic
218C22×C4D4×D1111yescharacteristic
219C22×C4#434111yescharacteristic
220M16—442no—
221C2×C8—22no—
222C2×C8—41no—
223C2×C8—222no—
224C2×C8—222no—
225C2×C8—441no—
226C4⋊C4—112no—
227C4⋊C4—112no—
228C4⋊C4—221no—
229C4⋊C4—222no—
230C4⋊C4—221no—
231C4⋊C4—222no—
232C22⋊C4—222no—
233C42—222no—
234C42C2×C4×D1111yescharacteristic
235C42D4×D1111yescharacteristic
236C42D4×D1111yescharacteristic
237C42C2×C22⋊D1111yescharacteristic
238C11#942411yescharacteristic, complemented, Sylow
239C23—42no—
240C23—82no—
241C23—82no—
242C23—82no—
243C23#6693611yescharacteristic
244Q8—881no—
245Q8—881no—
246D4—44no—
247D4—82no—
248D4—82no—
249D4—82no—
250D4—82no—
251D4—82no—
252C2×C4—22no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—222no—
256C2×C4—222no—
257C2×C4C22⋊C4×D1111yescharacteristic
258C2×C4(C22⋊D11)⋊C411yescharacteristic
259C2×C4#6693711yescharacteristic
260C2×C4C4×C22⋊D1111yescharacteristic
261C2×C4#6699011yescharacteristic
262C2×C4#6699111yescharacteristic
263C8—42no—
264C8—81no—
265C8—442no—
266C8—442no—
267C8—881no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—82no—
272C22—82no—
273C22—82no—
274C22—164no—
275C22#1062256911yescharacteristic
276C4—21no—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—442no—
282C4—442no—
283C4#1062281412yes—
284C2—41no—
285C2—162no—
286C2#1306901611yescharacteristic
287C2#1306909311yescharacteristic
288C2#1306909911yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1555C2
socleC22×C11#386
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenter#1555D11
hypocenterC11#9424
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1555

Complements

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

NH ≅ G/Ntype
2. #13077721C2semidirect
4. #13067253C2semidirect
5. #13066489C2semidirect
6. #13066487C2semidirect
238. C11#9424semidirect

Maximal subgroups

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

subgroupindex
#130789902
#130777212
#130673302
#130672532
#130664892
#130664872
C11×#15552
#942411