Finite Group Databasebeta

← #14647357

Subgroups — #14647357

Order 2816.

378 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 99 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#13071583C211yesmaximal, characteristic
2#13068609C211yesmaximal, characteristic
3#13066939C211yesmaximal, characteristic
4#13066518C211yesmaximal, characteristic
5#13066517C211yesmaximal, characteristic
6#13066474C211yesmaximal, characteristic
7C11×#1286C211yesmaximal, characteristic
8C2×C4×Dic22C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#382C2211yescharacteristic
12C2×#66888—21no—
13C4⋊C4×Dic11—21no—
14#10622587—21no—
15C4×C4⋊Dic11C2211yescharacteristic
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18#10622268—22no—
19#10622264C412yes—
20#10622261C412yes—
21#10622192—21no—
22#10622107—22no—
23C22×Dic22D411yescharacteristic
24C2×C11×M16—21no—
25C2×C11×C4⋊C4—21no—
26C2×C42×C11C2311yescharacteristic
27C2×C4⋊Dic11—21no—
28C2×C4⋊Dic11D411yescharacteristic
29C2×Dic11⋊C4D412yes—
30C2×C4×Dic11—21no—
31C2×C4×Dic11—22no—
32C2×C4×Dic11C2×C412yes—
33C2×#4318—21no—
34C4×Dic22—21no—
35C4×Dic22—21no—
36C4×Dic22—21no—
37C4×Dic22—21no—
38C11×C4⋊C8—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8—21no—
41C11×C22⋊C8—21no—
42C4×C8×C11—21no—
43C11×#95—21no—
44C11×#95C2×C412yes—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C11⋊#95C2×C411yescharacteristic
49C11⋊#95C2×C411yescharacteristic
50C22⋊(C11⋊C8)—21no—
51#66888—42no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4×C11⋊C8—21no—
56#8768—111nomaximal, Sylow
57C22×C4×C11—22no—
58C22×C4×C11C22×C411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×Dic11—21no—
62C22×Dic11—21no—
63C22×Dic11C22⋊C412yes—
64C22×Dic11C22⋊C412yes—
65C2×Dic22—21no—
66C2×Dic22—21no—
67C2×Dic22—21no—
68C2×Dic22—21no—
69C2×Dic22—21no—
70C2×Dic22—21no—
71C11×M16—41no—
72C11×M16—41no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C42×C11#4111yescharacteristic
78C42×C11#4111yescharacteristic
79C42×C11#4111yescharacteristic
80C42×C11#4111yescharacteristic
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11—42no—
84Dic11⋊C4—22no—
85Dic11⋊C4—22no—
86C4×Dic11—22no—
87C4×Dic11—22no—
88C4×Dic11—44no—
89C4×Dic11—41no—
90C4×Dic11—41no—
91#4318—41no—
92#4318—41no—
93C2×C11⋊C8—41no—
94C2×C11⋊C8—41no—
95#2356—111no—
96#1801—111no—
97#1461—111no—
98#1303—111no—
99#1303—111no—
100#1286—111no—
101#1286D1111yescharacteristic
102C23×C11C2×C22⋊C411yescharacteristic
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11#11711yescharacteristic
109C2×C4×C11#11711yescharacteristic
110C2×C4×C11#12311yescharacteristic
111C2×C4×C11#12311yescharacteristic
112C2×C4×C11#12311yescharacteristic
113C2×C4×C11#12311yescharacteristic
114C2×C4×C11#13511yescharacteristic
115C2×C4×C11#13511yescharacteristic
116C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C11#13711yescharacteristic
118C2×Dic11—22no—
119C2×Dic11—22no—
120C2×Dic11—22no—
121C2×Dic11—22no—
122C2×Dic11—22no—
123C2×Dic11—41no—
124C2×Dic11—41no—
125C2×Dic11—42no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129Dic22—41no—
130Dic22—41no—
131Dic22—41no—
132Dic22—41no—
133C8×C11—81no—
134C8×C11—81no—
135C11⋊C8—81no—
136C11⋊C8—81no—
137C2×C4×Q8—111no—
138#431—111no—
139#431C2×D1111yescharacteristic
140#423—111no—
141#423C2×D1111yescharacteristic
142C2×#101—221no—
143#391—221no—
144#387—222no—
145#383—112no—
146#382C2×D1111yescharacteristic
147C4×C4⋊C4—111no—
148C4×C4⋊C4—221no—
149#376—112no—
150#343—221no—
151#324—222no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11#38111yescharacteristic
155C22×C11#41611yescharacteristic
156C22×C11#41711yescharacteristic
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—82no—
162C4×C11#48211yescharacteristic
163C4×C11#48211yescharacteristic
164C4×C11#48511yescharacteristic
165C4×C11#48511yescharacteristic
166Dic11—42no—
167Dic11—42no—
168Dic11—42no—
169Dic11—81no—
170C22×Q8—111no—
171C2×M16—21no—
172C2×M16—221no—
173C4×Q8—221no—
174C4×Q8—221no—
175C4×Q8—221no—
176C4×Q8—221no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—112no—
179C2×C4⋊C4—111no—
180C2×C4⋊C4—221no—
181C2×C42—112no—
182C2×C42—222no—
183C2×C42—221no—
184C2×C42C22×D1111yescharacteristic
185C4⋊C8—21no—
186C4⋊C8—21no—
187C4⋊C8—21no—
188C4⋊C8—221no—
189C4⋊C8—221no—
190C4⋊C8—221no—
191#101—442no—
192C22⋊C8—21no—
193C22⋊C8—221no—
194C4×C8—21no—
195C4×C8—221no—
196#95—21no—
197#95—111no—
198#95—111no—
199#95—222no—
200#95—222no—
201#95—222no—
202#95C4×D1112yes—
203C2×C11—21no—
204C2×C11—21no—
205C2×C11#182511yescharacteristic
206C2×C11#182711yescharacteristic
207C2×C11#183011yescharacteristic
208C2×Q8—221no—
209C2×Q8—221no—
210C2×Q8—221no—
211C2×Q8—221no—
212C2×Q8—221no—
213C2×Q8—221no—
214C22×C4—22no—
215C22×C4—112no—
216C22×C4—112no—
217C22×C4—221no—
218C22×C4—221no—
219C22×C4C2×C4×D1111yescharacteristic
220C22×C4D4×D1111yescharacteristic
221C22×C4D4×D1111yescharacteristic
222M16—41no—
223M16—41no—
224M16—441no—
225M16—441no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—441no—
229C2×C8—441no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—222no—
233C4⋊C4—221no—
234C4⋊C4—222no—
235C4⋊C4—221no—
236C4⋊C4—442no—
237C42—222no—
238C42—222no—
239C42—444no—
240C42—441no—
241C42—441no—
242C42#433911yescharacteristic
243C42#433911yescharacteristic
244C42#434111yescharacteristic
245C42#434311yescharacteristic
246C11#876811yescharacteristic, complemented, Sylow
247C23C22⋊C4×D1111yescharacteristic
248Q8—441no—
249Q8—441no—
250Q8—441no—
251Q8—441no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—222no—
258C2×C4—222no—
259C2×C4—222no—
260C2×C4—222no—
261C2×C4—222no—
262C2×C4—441no—
263C2×C4—441no—
264C2×C4—442no—
265C2×C4—441no—
266C2×C4—441no—
267C2×C4—441no—
268C2×C4#6692511yescharacteristic
269C2×C4#6693611yescharacteristic
270C2×C4#6693611yescharacteristic
271C2×C4#6694511yescharacteristic
272C2×C4#6694711yescharacteristic
273C2×C4#6694711yescharacteristic
274C2×C4#6696511yescharacteristic
275C2×C4#6696711yescharacteristic
276C2×C4#6696911yescharacteristic
277C2×C4#6697111yescharacteristic
278C8—81no—
279C8—81no—
280C8—881no—
281C8—881no—
282C22—21no—
283C22—21no—
284C22#1062227711yescharacteristic
285C22#1062238511yescharacteristic
286C22#1062241611yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—21no—
291C4—82no—
292C4—442no—
293C4—442no—
294C4—442no—
295C4—881no—
296C4#1062239711yescharacteristic
297C4#1062242811yescharacteristic
298C4#1062247911yescharacteristic
299C4#1062250111yescharacteristic
300C2—21no—
301C2—21no—
302C2#1306870911yescharacteristic
303C2#1306871811yescharacteristic
304C2#1306872911yescharacteristic
subgroupG/H
centerC22#10622277
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#381
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1286D11
hypocenterC11#8768
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
246. C11#8768semidirect

Maximal subgroups

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

subgroupindex
#130715832
#130686092
#130669392
#130665182
#130665172
#130664742
C11×#12862
#876811