Finite Group Databasebeta

← #14666837

Subgroups — #14666837

Order 2816.

352 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 59 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#13074324C211yesmaximal, characteristic
2#13067658C211yesmaximal, characteristic
3#13067590C211yesmaximal, characteristic
4#13066645C211yesmaximal, characteristic
5#13066642C211yesmaximal, characteristic
6#13066560C211yesmaximal, characteristic
7C11×#2061C211yesmaximal, characteristic
8C11×#544C2211yescharacteristic
9C11×#428—21no—
10C11×#382C2211yescharacteristic
11#10622663—21no—
12#10622657—21no—
13#10622599C2211yescharacteristic
14#10622597—21no—
15#10622592C2211yescharacteristic
16#10622545—21no—
17#10622268—21no—
18#10622267—21no—
19#10622260—21no—
20#10622259—21no—
21C11×#343C2211yescharacteristic
22C11×#339—21no—
23#10622176—21no—
24#10622176—21no—
25#10622166C2211yescharacteristic
26#10622166C2211yescharacteristic
27C22×Dic22D411yescharacteristic
28C2×C11×M16—21no—
29C11×C4⋊Q8—41no—
30C11×#125—41no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8—21no—
33C11×#117—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×#4326—41no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11D411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44C2×C4×Dic11—21no—
45C11×#107—41no—
46C11×#106—41no—
47C11×#95—21no—
48C11×#95—21no—
49#66899—41no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95D411yescharacteristic
57C11⋊#95D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66874—41no—
61#66871—41no—
62#12258—111nomaximal, Sylow
63C2×Q8×C11—21no—
64C2×Q8×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C2×Dic22—41no—
75C2×Dic22—42no—
76C11×M16—22no—
77C11×M16—41no—
78C2×C8×C11—41no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C22⋊C4—41no—
88C42×C11—21no—
89C42×C11—41no—
90C42×C11Q1612yescomplemented
91#4326—82no—
92C4⋊Dic11—41no—
93C4⋊Dic11—42no—
94Dic11⋊C4—42no—
95Dic11⋊C4—42no—
96Dic11⋊C4—81no—
97C4×Dic11—42no—
98C4×Dic11—42no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101#2612—111no—
102#2061D1111yescharacteristic
103#1617—111no—
104#1605—111no—
105#1354—111no—
106#1353—111no—
107#1324—111no—
108C23×C11#12011yescharacteristic
109Q8×C11—81no—
110Q8×C11—81no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11C2×Q1611yescharacteristic
126C2×C4×C11#13711yescharacteristic
127C2×Dic11—22no—
128C2×Dic11—22no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139Dic22—42no—
140Dic22—81no—
141C8×C11—42no—
142C11⋊C8—81no—
143C11⋊C8—81no—
144#544C2×D1111yescharacteristic
145#484—221no—
146#451—221no—
147#428—21no—
148#400—111no—
149#398—221no—
150#395—111no—
151#391—221no—
152#389—221no—
153#387—221no—
154#387—221no—
155#382C2×D1111yescharacteristic
156#376—221no—
157#343C2×D1111yescharacteristic
158#339—21no—
159#328—221no—
160#328—221no—
161#324—111no—
162#324—111no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11#45111yescharacteristic
166C22×C11#45611yescharacteristic
167C22×C11B(4,𝔽2)11yescharacteristic
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—42no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—81no—
174C4×C11—81no—
175C4×C11—81no—
176Dic11—42no—
177Dic11—42no—
178Dic11—81no—
179Dic11—81no—
180C22×Q8—111no—
181C2×Q16—441no—
182C2×M16—21no—
183C4⋊Q8—41no—
184#125—41no—
185C22⋊Q8—21no—
186C22⋊Q8—21no—
187#117—21no—
188C2×C4⋊C4—111no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—221no—
191C2×C4⋊C4—221no—
192C2×C4⋊C4—221no—
193C2×C4⋊C4C22⋊D1111yescharacteristic
194C2×C4⋊C4C22×D1111yescharacteristic
195C2×C42—221no—
196C2×C42—221no—
197C2×C42C22⋊D1111yescharacteristic
198#107—41no—
199#107—441no—
200#106—41no—
201#103—441no—
202#103—441no—
203C22⋊C8—221no—
204C22⋊C8—221no—
205#95—21no—
206#95—21no—
207#95—111no—
208#95—111no—
209#95—221no—
210#95—221no—
211#95—221no—
212#95—221no—
213#95—221no—
214#95—221no—
215C2×C11—21no—
216C2×C11—21no—
217C2×C11#160511yescharacteristic
218C2×C11#219711yescharacteristic
219C2×C11#220411yescharacteristic
220C2×Q8—21no—
221C2×Q8—21no—
222C2×Q8—441no—
223C2×Q8—442no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—221no—
227C22×C4—221no—
228C22×C4—221no—
229C22×C4—221no—
230C22×C4D4×D1111yescharacteristic
231C22×C4D4×D1111yescharacteristic
232C22×C4C2×C22⋊D1111yescharacteristic
233Q16—882no—
234M16—22no—
235M16—41no—
236C2×C8—41no—
237C2×C8—441no—
238C2×C8—441no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—441no—
248C4⋊C4—442no—
249C4⋊C4—442no—
250C4⋊C4—442no—
251C4⋊C4—881no—
252C22⋊C4—41no—
253C42—21no—
254C42—41no—
255C42—442no—
256C42—442no—
257C42#432612yescomplemented
258C11#1225811yescharacteristic, complemented, Sylow
259C23#6699011yescharacteristic
260Q8—81no—
261Q8—81no—
262Q8—442no—
263Q8—881no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—222no—
279C2×C4—222no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4C2×#432611yescharacteristic
291C2×C4#6700411yescharacteristic
292C8—42no—
293C8—881no—
294C8—881no—
295C22—21no—
296C22—21no—
297C22#1062264511yescharacteristic
298C22#1062266311yescharacteristic
299C22#1062270811yescharacteristic
300C4—21no—
301C4—21no—
302C4—42no—
303C4—41no—
304C4—41no—
305C4—81no—
306C4—81no—
307C4—81no—
308C4—442no—
309C4—442no—
310C4—881no—
311C4—881no—
312C2—21no—
313C2—21no—
314C2#1306758911yescharacteristic
315C2#1307060511yescharacteristic
316C2#1307064011yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2061C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2061D11
hypocenterC11#12258
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2061

Complements

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

NH ≅ G/Ntype
90. C42×C11Q16semidirect
257. C42#4326semidirect
258. C11#12258semidirect

Maximal subgroups

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

subgroupindex
#130743242
#130676582
#130675902
#130666452
#130666422
#130665602
C11×#20612
#1225811