Finite Group Databasebeta

← #14655203

Subgroups — #14655203

Order 2816.

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

normal subgroups only

This group has 474 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#13079818C211yesmaximal, characteristic
2#13074736C211yesmaximal, characteristic
3#13067333C211yesmaximal, characteristic
4#13067217C211yesmaximal, characteristic
5#13067128C211yesmaximal, characteristic
6#13066510C211yesmaximal, characteristic
7C11×#3165C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66923C2211yescharacteristic
11C11×#501—22no—
12C11×#500—21no—
13C11×#498—21no—
14C11×#428—22no—
15C4×C11×M16C2211yescharacteristic
16#10622842—22no—
17#10622695—21no—
18#10622693—21no—
19#10622657—21no—
20#10622656—21no—
21#10622635—22no—
22#10622593—22no—
23#10622590—21no—
24#10622589—21no—
25#10622545C2211yescharacteristic
26#10622539C2211yescharacteristic
27#10622539C2211yescharacteristic
28#10622185—22no—
29#10622176—22no—
30#10622103—22no—
31C22×Q8×C11—21no—
32C2×C11×M16—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D411yescharacteristic
39C11×#125—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C11×#117—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D412yes—
47C2×C42×C11C2311yescharacteristic
48C2×C4⋊Dic11D411yescharacteristic
49C2×C4⋊Dic11D411yescharacteristic
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C2×Dic11⋊C4—24no—
53C2×C4×Dic11—21no—
54#66923—21no—
55#66923—21no—
56#66923—21no—
57#66923—21no—
58C11×#107—24no—
59C11×#106—24no—
60C11×#97D412yes—
61C4×C8×C11—21no—
62#66899—22no—
63#66899—22no—
64C11⋊#95—24no—
65C11⋊#95—21no—
66C11⋊#95D412yes—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#66872—22no—
70#66871—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73#66867—21no—
74#66867—21no—
75#10101—111nomaximal, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—82no—
81C22×C4×C11—22no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—22no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C11×M16—24no—
89C2×C8×C11—22no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C22⋊C4—41no—
101C42×C11—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110Dic11⋊C4—41no—
111Dic11⋊C4—41no—
112Dic11⋊C4—41no—
113Dic11⋊C4—41no—
114Dic11⋊C4—84no—
115C4×Dic11—24no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—41no—
118#3236—111no—
119#3165D1111yescharacteristic
120#2660—111no—
121#1556—111no—
122#1528—111no—
123#1506—111no—
124#1300—111no—
125C23×C11#12011yescharacteristic
126Q8×C11—42no—
127Q8×C11—81no—
128Q8×C11—82no—
129Q8×C11—82no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—41no—
133C2×C4×C11—44no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12711yescharacteristic
143C2×Dic11—24no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—42no—
150C8×C11—24no—
151C11⋊C8—42no—
152C11⋊C8—81no—
153#533C2×D1111yescharacteristic
154C2×C4⋊Q8C2×D1111yescharacteristic
155C2×#125—111no—
156#501—22no—
157#501—221no—
158#500—21no—
159#498—21no—
160#491—221no—
161#484—221no—
162#483—221no—
163#479—222no—
164#432—111no—
165#432—111no—
166#428—22no—
167C4×M16C2×D1111yescharacteristic
168#398—222no—
169#395—222no—
170#384—221no—
171#382—221no—
172#376—111no—
173#332—222no—
174#330—222no—
175#328—222no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11#39211yescharacteristic
179C22×C11#45612yes—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—81no—
186C4×C11—82no—
187C4×C11—81no—
188C4×C11#45612yes—
189Dic11—44no—
190Dic11—81no—
191Dic11—81no—
192C22×Q8—21no—
193C2×M16—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8C22⋊D1111yescharacteristic
199C4⋊Q8C22⋊D1111yescharacteristic
200#125—21no—
201#125—221no—
202#125—221no—
203#125—221no—
204#125—221no—
205C22⋊Q8—21no—
206C22⋊Q8—21no—
207C4×Q8—21no—
208C4×Q8—21no—
209#117—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—224no—
216C2×C4⋊C4C22⋊D1112yes—
217C2×C42—221no—
218C2×C42C22×D1111yescharacteristic
219#107—24no—
220#107—222no—
221#106—24no—
222#106—222no—
223C4⋊C8—112no—
224C4⋊C8—221no—
225#103—222no—
226#103—222no—
227C22⋊C8—221no—
228C22⋊C8—221no—
229#97—221no—
230#97—221no—
231#97C22⋊D1112yes—
232C4×C8—21no—
233#95—112no—
234#95—224no—
235#95—221no—
236C2×C11—22no—
237C2×C11#200511yescharacteristic
238C2×C11#200511yescharacteristic
239C2×C11#200811yescharacteristic
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—82no—
245C22×C4—22no—
246C22×C4—222no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4D4×D1111yescharacteristic
250C22×C4D4×D1111yescharacteristic
251C22×C4C2×C22⋊D1111yescharacteristic
252M16—24no—
253C2×C8—22no—
254C2×C8—222no—
255C2×C8—441no—
256C4⋊C4—21no—
257C4⋊C4—22no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—22no—
261C4⋊C4—21no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C4⋊C4—884no—
275C22⋊C4—41no—
276C42—41no—
277C42—224no—
278C42D4×D1111yescharacteristic
279C42#434111yescharacteristic
280C42C2×C22⋊D1111yescharacteristic
281C42C2×C22⋊D1111yescharacteristic
282C11#1010111yescharacteristic, complemented, Sylow
283C23#6699011yescharacteristic
284Q8—42no—
285Q8—81no—
286Q8—82no—
287Q8—82no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—44no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—224no—
296C2×C4—442no—
297C2×C4—442no—
298C2×C4—442no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—442no—
302C2×C4#6699011yescharacteristic
303C2×C4#6699111yescharacteristic
304C2×C4#6699211yescharacteristic
305C2×C4#6699211yescharacteristic
306C2×C4#6699311yescharacteristic
307C2×C4#6700611yescharacteristic
308C8—24no—
309C8—442no—
310C8—881no—
311C22—21no—
312C22—21no—
313C22#1062270812yes—
314C22#1062283611yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—81no—
321C4—82no—
322C4—81no—
323C4—444no—
324C4—881no—
325C4—881no—
326C4#1062281812yes—
327C2—22no—
328C2#1306964911yescharacteristic
329C2#1306965211yescharacteristic
330C2#1306966711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3165C2
socleC22×C11#392
prime radicalC23×C11#120
hypercenter#3165D11
hypocenterC11#10101
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
282. C11#10101semidirect

Maximal subgroups

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

subgroupindex
#130798182
#130747362
#130673332
#130672172
#130671282
#130665102
C11×#31652
#1010111