Finite Group Databasebeta

← #14655723

Subgroups — #14655723

Order 2816.

492 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079762C211yesmaximal, characteristic
2C2×#10622691C211yesmaximal, characteristic
3#13078996C211yesmaximal, characteristic
4#13069459C211yesmaximal, characteristic
5#13067070C211yesmaximal, characteristic
6#13066452C211yesmaximal, characteristic
7C11×#1546C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622838—22no—
14C2×#66888—22no—
15#10622695—22no—
16#10622694—21no—
17#10622694—21no—
18#10622691—22no—
19#10622691—22no—
20C2×#66871—22no—
21C4×#4318C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622464—22no—
24#10622334—22no—
25#10622294—21no—
26#10622293—21no—
27C11×#332—22no—
28#10622122—22no—
29C22×Q8×C11—21no—
30C22×Dic22—21no—
31C2×C11×M16—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8D412yes—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C42×C11C2311yescharacteristic
39#66979—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11D412yes—
42#66977—21no—
43#66977—21no—
44C2×#4318D412yes—
45C22×C11⋊C8—21no—
46#66923—21no—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922—21no—
51#66922D411yescharacteristic
52#66922D411yescharacteristic
53C4×Dic22—21no—
54C4×Dic22—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8D412yes—
58C11×C22⋊C8—21no—
59C4×C8×C11—21no—
60#66899—24no—
61#66899—24no—
62#66888—44no—
63#66881—24no—
64#66880—24no—
65#66871—28no—
66#66867—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10175—111nomaximal, Sylow
71C2×Q8×C11—22no—
72C2×Q8×C11—41no—
73C2×Q8×C11—42no—
74C2×Q8×C11—42no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×Dic11—22no—
80C2×Dic22—21no—
81C2×Dic22—21no—
82C2×Dic22—41no—
83C2×Dic22—41no—
84C2×Dic22—42no—
85C2×Dic22—42no—
86C11×M16—42no—
87C2×C8×C11—22no—
88C2×C8×C11—41no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C22⋊Dic11—41no—
98C4⋊Dic11—22no—
99C4⋊Dic11—22no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108C4×Dic11—41no—
109#4318—22no—
110#4318—22no—
111C2×C11⋊C8—24no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114#3229—111no—
115C2×#500—111no—
116#3139—111no—
117#1966—111no—
118#1546D1111yescharacteristic
119#1493—111no—
120#1278—111no—
121C23×C11#12111yescharacteristic
122Q8×C11—44no—
123Q8×C11—81no—
124Q8×C11—81no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—42no—
128C2×C4×C11—82no—
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12711yescharacteristic
135C2×C4×C11#13512yes—
136C2×C4×C11AGL(1,ℤ/8)12yes—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—42no—
140C2×Dic11—44no—
141Dic22—42no—
142Dic22—42no—
143Dic22—82no—
144Dic22—81no—
145Dic22—81no—
146C8×C11—42no—
147C8×C11—81no—
148C11⋊C8—24no—
149C11⋊C8—42no—
150#533—111no—
151C2×C4⋊Q8—111no—
152C2×C4⋊Q8C2×D1111yescharacteristic
153#500—222no—
154#500—222no—
155#498—221no—
156#491—222no—
157#487—221no—
158#487—221no—
159#487—221no—
160#483—222no—
161#475—222no—
162#431C2×D1111yescharacteristic
163C2×#107—222no—
164#423C2×D1111yescharacteristic
165#419—222no—
166C2×#101—222no—
167C4×M16—111no—
168C2×C4×C8—111no—
169#332—22no—
170Q8⋊C8—222no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11#39211yescharacteristic
174C22×C11#46312yes—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—82no—
178C4×C11#44912yes—
179C4×C11#45612yes—
180C4×C11#47312yes—
181C4×C11#49511yescharacteristic
182C4×C11#49611yescharacteristic
183Dic11—81no—
184Dic11—82no—
185Dic11—81no—
186C22×Q8—21no—
187C22×Q8—221no—
188C2×M16—21no—
189C2×M16—112no—
190C22×C8—221no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—111no—
195C4⋊Q8—111no—
196C4⋊Q8—221no—
197C4⋊Q8—221no—
198C4⋊Q8—221no—
199C4⋊Q8—221no—
200C4⋊Q8D4412yes—
201#125—221no—
202C22⋊Q8—221no—
203C22⋊Q8—221no—
204C4×Q8—221no—
205C4×Q8—221no—
206#117—221no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—112no—
210C2×C4⋊C4—221no—
211C2×C42C22×D1111yescharacteristic
212#107—228no—
213#106—224no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8C22⋊D1112yes—
217#103—224no—
218#103—224no—
219#103—224no—
220#101—444no—
221C22⋊C8—21no—
222#97—221no—
223C4×C8—21no—
224C4×C8—112no—
225C4×C8—221no—
226C4×C8—221no—
227C2×C11—22no—
228C2×C11#200511yescharacteristic
229C2×C11#201211yescharacteristic
230C2×C11#202011yescharacteristic
231C2×Q8—22no—
232C2×Q8—41no—
233C2×Q8—42no—
234C2×Q8—42no—
235C2×Q8—221no—
236C2×Q8—221no—
237C2×Q8—441no—
238C2×Q8—442no—
239C2×Q8—442no—
240C2×Q8—441no—
241C22×C4—41no—
242C22×C4—222no—
243C22×C4#433911yescharacteristic
244C22×C4D4×D1111yescharacteristic
245C22×C4D4×D1111yescharacteristic
246M16—42no—
247M16—222no—
248M16—222no—
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—224no—
252C2×C8—222no—
253C2×C8—222no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—222no—
261C4⋊C4—221no—
262C4⋊C4—222no—
263C4⋊C4—221no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C22⋊C4—441no—
269C42—441no—
270C42C2×D4411yescharacteristic
271C42D4×D1111yescharacteristic
272C42D4×D1111yescharacteristic
273C42C2×C22⋊D1111yescharacteristic
274C11#1017511yescharacteristic, complemented, Sylow
275C23#6693711yescharacteristic
276Q8—44no—
277Q8—81no—
278Q8—81no—
279Q8—442no—
280Q8—442no—
281Q8—881no—
282Q8—881no—
283Q8—882no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—42no—
287C2×C4—82no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—442no—
291C2×C4—444no—
292C2×C4#6693511yescharacteristic
293C2×C4#6693511yescharacteristic
294C2×C4#6693711yescharacteristic
295C2×C4#6696412yes—
296C2×C4#6696912yes—
297C2×C4#6698311yescharacteristic
298C2×C4#6699011yescharacteristic
299C2×C4#6699311yescharacteristic
300C8—42no—
301C8—81no—
302C8—224no—
303C8—442no—
304C22—21no—
305C22—21no—
306C22#1062240012yes—
307C22#1062257311yescharacteristic
308C4—21no—
309C4—21no—
310C4—82no—
311C4—881no—
312C4—882no—
313C4—881no—
314C4#1062236812yes—
315C4#1062239412yes—
316C4#1062276711yescharacteristic
317C4#1062278111yescharacteristic
318C4#1062281812yes—
319C2—22no—
320C2#1306965311yescharacteristic
321C2#1306969511yescharacteristic
322C2#1306973611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1546C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#1546D11
hypocenterC11#10175
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
274. C11#10175semidirect

Maximal subgroups

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

subgroupindex
#130797622
C2×#106226912
#130789962
#130694592
#130670702
#130664522
C11×#15462
#1017511