Finite Group Databasebeta

← #14655220

Subgroups — #14655220

Order 2816.

458 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079822C211yesmaximal, characteristic
2#13079158C211yesmaximal, characteristic
3#13067333C211yesmaximal, characteristic
4#13067218C211yesmaximal, characteristic
5#13067127C211yesmaximal, characteristic
6#13066509C211yesmaximal, characteristic
7C11×#2642C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#400—22no—
12C11×#400—22no—
13C11×#391—21no—
14C11×#391—21no—
15C11×#376C2211yescharacteristic
16#10622693—22no—
17#10622692—21no—
18#10622691—21no—
19#10622682—21no—
20#10622678—21no—
21#10622676—22no—
22#10622584—21no—
23#10622583—21no—
24#10622577—22no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622185—22no—
29#10622181—22no—
30#10622090—22no—
31C22×Q8×C11—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×#125—21no—
37C11×#125—21no—
38C11×#125—21no—
39C11×#125—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4D412yes—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C42×C11—21no—
47C2×C42×C11C2311yescharacteristic
48#66979—21no—
49#66977—21no—
50#66977—21no—
51C2×#4318—21no—
52#66923—21no—
53#66922D411yescharacteristic
54#66922D411yescharacteristic
55C4×Dic22—21no—
56C4×Dic22—21no—
57C11×#95—24no—
58C11×#95—24no—
59C11×#95—21no—
60C11×#95D412yes—
61C22⋊(C11⋊C8)—21no—
62C22⋊(C11⋊C8)—21no—
63#66874—22no—
64#66874—22no—
65#66872—24no—
66#66872—22no—
67#66871—24no—
68#66871—22no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)D412yes—
71#66867—21no—
72#66867—21no—
73#66867D412yes—
74C4×C11⋊C8—21no—
75#10103—111nomaximal, Sylow
76C2×Q8×C11—44no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C22×C4×C11—22no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C2×Dic22—21no—
87C2×Dic22—21no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C42×C11—42no—
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11#4111yescharacteristic
105C22⋊Dic11—41no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110Dic11⋊C4—41no—
111Dic11⋊C4—41no—
112C4×Dic11—41no—
113#4318—24no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—41no—
117#3236—111no—
118#3165—111no—
119#2642D1111yescharacteristic
120#1556—111no—
121#1528—111no—
122#1506—111no—
123#1300—111no—
124C23×C11#12011yescharacteristic
125Q8×C11—82no—
126Q8×C11—82no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—44no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12711yescharacteristic
145C2×Dic11—41no—
146C2×Dic11—41no—
147Dic22—42no—
148Dic22—81no—
149C11⋊C8—24no—
150C11⋊C8—42no—
151C11⋊C8—81no—
152#533—111no—
153C2×C4⋊Q8C2×D1111yescharacteristic
154C2×#125C2×D1111yescharacteristic
155#501—222no—
156#501—221no—
157#500—221no—
158#498—221no—
159#491—221no—
160#484—221no—
161#483—221no—
162#479—222no—
163#432—111no—
164#432—111no—
165#428—222no—
166C4×M16—111no—
167#400—22no—
168#400—22no—
169#391—21no—
170#391—21no—
171#376C2×D1111yescharacteristic
172#332—222no—
173#330—222no—
174#328—222no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#39211yescharacteristic
178C22×C11#45612yes—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—82no—
185C4×C11—82no—
186C4×C11—81no—
187C4×C11—81no—
188C4×C11#45412yes—
189Dic11—81no—
190Dic11—81no—
191C22×Q8—21no—
192C2×M16—221no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—111no—
198C4⋊Q8—111no—
199#125—21no—
200#125—21no—
201#125—21no—
202#125—21no—
203#125—221no—
204C22⋊Q8—221no—
205C22⋊Q8—221no—
206C4×Q8—221no—
207C4×Q8—221no—
208#117—221no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4C22⋊D1111yescharacteristic
213C2×C4⋊C4C22⋊D1111yescharacteristic
214C2×C4⋊C4C22⋊D1112yes—
215C2×C42—21no—
216C2×C42C22×D1111yescharacteristic
217#107—224no—
218#107—222no—
219#106—224no—
220#106—222no—
221C4⋊C8—112no—
222C4⋊C8—221no—
223#103—222no—
224#103—222no—
225C22⋊C8—221no—
226C22⋊C8—221no—
227#97—112no—
228#97—221no—
229#97—221no—
230C4×C8—221no—
231#95—24no—
232#95—24no—
233#95—21no—
234#95C22⋊D1112yes—
235C2×C11—22no—
236C2×C11#200311yescharacteristic
237C2×C11#200511yescharacteristic
238C2×C11#200911yescharacteristic
239C2×Q8—44no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—221no—
243C2×Q8—221no—
244C22×C4—22no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4C2×C22⋊D1111yescharacteristic
249C22×C4C2×C22⋊D1111yescharacteristic
250C22×C4C2×C22⋊D1111yescharacteristic
251M16—224no—
252C2×C8—222no—
253C2×C8—222no—
254C2×C8—441no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—22no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C22⋊C4—441no—
274C42—42no—
275C42—441no—
276C42D4×D1111yescharacteristic
277C42D4×D1111yescharacteristic
278C42D4×D1111yescharacteristic
279C42#434111yescharacteristic
280C11#1010311yescharacteristic, complemented, Sylow
281C23#6700611yescharacteristic
282Q8—82no—
283Q8—82no—
284Q8—442no—
285Q8—881no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—44no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4#6699011yescharacteristic
301C2×C4#6699011yescharacteristic
302C2×C4#6699111yescharacteristic
303C2×C4#6699211yescharacteristic
304C2×C4#6699211yescharacteristic
305C2×C4#6699311yescharacteristic
306C8—224no—
307C8—442no—
308C8—881no—
309C22—21no—
310C22—21no—
311C22#1062283611yescharacteristic
312C22#1062285912yes—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—82no—
319C4—82no—
320C4—81no—
321C4—81no—
322C4—881no—
323C4—881no—
324C4#1062267512yes—
325C2—22no—
326C2#1306963811yescharacteristic
327C2#1306965011yescharacteristic
328C2#1306967611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2642C2
socleC22×C11#392
prime radicalC23×C11#120
hypercenter#2642D11
hypocenterC11#10103
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2642

Complements

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

NH ≅ G/Ntype
280. C11#10103semidirect

Maximal subgroups

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

subgroupindex
#130798222
#130791582
#130673332
#130672182
#130671272
#130665092
C11×#26422
#1010311