Finite Group Databasebeta

← #14655724

Subgroups — #14655724

Order 2816.

492 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C2×#10622691C211yesmaximal, characteristic
2#13078998C211yesmaximal, characteristic
3#13069461C211yesmaximal, characteristic
4#13067287C211yesmaximal, characteristic
5#13067071C211yesmaximal, characteristic
6#13066452C211yesmaximal, characteristic
7C11×#3229C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#498—21no—
12C11×#487—21no—
13C11×#483—22no—
14C11×#475—22no—
15C11×#431C2211yescharacteristic
16C2×#66900—22no—
17#10622706—21no—
18#10622706—21no—
19#10622691—22no—
20#10622691—22no—
21#10622682—22no—
22#10622617—22no—
23C2×#66871—22no—
24#10622537C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27Q8⋊(C11⋊C8)—22no—
28#10622124—22no—
29C22×Q8×C11—21no—
30C22×Dic22—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#125—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C11×#117—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D412yes—
45C2×C42×C11C2311yescharacteristic
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×#4318—21no—
49C2×#4318D412yes—
50C22×C11⋊C8—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922D412yes—
55C11×#106—24no—
56C11×C4⋊C8D412yes—
57C11×#103—24no—
58C11×C22⋊C8—21no—
59C4×C8×C11—21no—
60#66900—44no—
61#66874—24no—
62#66874—24no—
63#66871—28no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66#66867—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10175—111nomaximal, Sylow
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C2×Q8×C11—42no—
76C2×Q8×C11—42no—
77C22×C4×C11—22no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×Dic11—41no—
82C2×Dic22—22no—
83C2×Dic22—41no—
84C2×Dic22—42no—
85C2×Dic22—42no—
86C2×C8×C11—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—41no—
98C42×C11—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107#4318—22no—
108#4318—22no—
109#4318—42no—
110C2×C11⋊C8—24no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—41no—
114#3229D1111yescharacteristic
115C2×#500—111no—
116#3139—111no—
117#1966—111no—
118#1546—111no—
119#1493—111no—
120#1278—111no—
121C23×C11#12111yescharacteristic
122Q8×C11—42no—
123Q8×C11—42no—
124Q8×C11—82no—
125Q8×C11—81no—
126Q8×C11—81no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—42no—
132C2×C4×C11—44no—
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12711yescharacteristic
139C2×C4×C11#13512yes—
140C2×C4×C11AGL(1,ℤ/8)12yes—
141C2×Dic11—42no—
142C2×Dic11—82no—
143Dic22—44no—
144Dic22—81no—
145Dic22—81no—
146C8×C11—42no—
147C11⋊C8—24no—
148C11⋊C8—42no—
149C11⋊C8—81no—
150#533C2×D1111yescharacteristic
151C2×C4⋊Q8—111no—
152C2×C4⋊Q8C2×D1111yescharacteristic
153#500—222no—
154#500—222no—
155#498—21no—
156#491—222no—
157#487—21no—
158#487—221no—
159#487—221no—
160#483—22no—
161#475—22no—
162#431C2×D1111yescharacteristic
163C2×#107—222no—
164#423—111no—
165#419—222no—
166C2×#101—222no—
167C4×M16—111no—
168C2×C4×C8—111no—
169#332—222no—
170Q8⋊C8—222no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11#39211yescharacteristic
174C22×C11#46312yes—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—81no—
178C4×C11—82no—
179C4×C11—81no—
180C4×C11#44912yes—
181C4×C11#45612yes—
182C4×C11#47312yes—
183C4×C11#49511yescharacteristic
184C4×C11#49611yescharacteristic
185Dic11—82no—
186C22×Q8—21no—
187C22×Q8—221no—
188C2×M16—112no—
189C2×M16—221no—
190C22×C8—221no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—112no—
196C4⋊Q8—221no—
197C4⋊Q8—221no—
198C4⋊Q8—221no—
199C4⋊Q8C22⋊D1111yescharacteristic
200C4⋊Q8C22⋊D1111yescharacteristic
201#125—21no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204C4×Q8—21no—
205C4×Q8—21no—
206#117—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4C22⋊D1112yes—
211C2×C42C22×D1111yescharacteristic
212#107—228no—
213#106—24no—
214C4⋊C8—221no—
215C4⋊C8—221no—
216C4⋊C8C22⋊D1112yes—
217#103—24no—
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—21no—
232C2×Q8—21no—
233C2×Q8—42no—
234C2×Q8—42no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—222no—
238C2×Q8—441no—
239C2×Q8—442no—
240C2×Q8—442no—
241C22×C4—22no—
242C22×C4—441no—
243C22×C4D4×D1111yescharacteristic
244C22×C4#434111yescharacteristic
245C22×C4C2×C22⋊D1111yescharacteristic
246M16—222no—
247M16—222no—
248M16—442no—
249C2×C8—22no—
250C2×C8—224no—
251C2×C8—222no—
252C2×C8—222no—
253C2×C8—441no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—22no—
257C4⋊C4—21no—
258C4⋊C4—22no—
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—222no—
265C4⋊C4—222no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C22⋊C4—41no—
269C42—41no—
270C42D4×D1111yescharacteristic
271C42D4×D1111yescharacteristic
272C42C2×C22⋊D1111yescharacteristic
273C42C2×C22⋊D1111yescharacteristic
274C11#1017511yescharacteristic, complemented, Sylow
275C23#6699211yescharacteristic
276Q8—42no—
277Q8—42no—
278Q8—81no—
279Q8—82no—
280Q8—81no—
281Q8—444no—
282Q8—881no—
283Q8—881no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—44no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—442no—
291C2×C4—882no—
292C2×C4#6696712yes—
293C2×C4#6696912yes—
294C2×C4#6699011yescharacteristic
295C2×C4#6699011yescharacteristic
296C2×C4#6699111yescharacteristic
297C2×C4#6699211yescharacteristic
298C2×C4#6699311yescharacteristic
299C2×C4#6700611yescharacteristic
300C8—42no—
301C8—224no—
302C8—442no—
303C8—881no—
304C22—21no—
305C22—21no—
306C22#1062277812yes—
307C22#1062283611yescharacteristic
308C4—21no—
309C4—21no—
310C4—81no—
311C4—82no—
312C4—81no—
313C4—882no—
314C4#1062278111yescharacteristic
315C4#1062278512yes—
316C4#1062278911yescharacteristic
317C4#1062281712yes—
318C4#1062285912yes—
319C2—22no—
320C2#1306965011yescharacteristic
321C2#1306969011yescharacteristic
322C2#1306973411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3229C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#3229D11
hypocenterC11#10175
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

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
C2×#106226912
#130789982
#130694612
#130672872
#130670712
#130664522
C11×#32292
#1017511