Finite Group Databasebeta

← #14651582

Subgroups — #14651582

Order 2816.

734 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 111 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#13072890C211yesmaximal, characteristic
2#13068716C212yesmaximal, complemented
3#13066943C211yesmaximal, characteristic
4#13066469C212yesmaximal, complemented
5C11×#2273C211yesmaximal, characteristic
6C22×C11×C22⋊C4—21no—
7C22×C11×C22⋊C4C2211yescharacteristic
8C2×#66979C2211yescharacteristic
9C4×C11×C22⋊C4—21no—
10C4×C11×C22⋊C4—24no—
11C4×C11×C22⋊C4C2212yes—
12#10622860—21no—
13#10622824C2211yescharacteristic
14#10622823—21no—
15#10622820C2212yes—
16#10622566C412yescomplemented
17#10622562C412yescomplemented
18#10622557—22no—
19#10622163—22no—
20#10622161—24no—
21C25×C11D411yescharacteristic
22C23×C4×C11—22no—
23C23×C4×C11D411yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C2×C11×C22⋊C4—28no—
26C2×C11×C22⋊C4—22no—
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4C2×C412yes—
31C2×C11×C22⋊C4D412yes—
32C2×C42×C11—22no—
33C2×C42×C11D414yes—
34C2×C22⋊Dic11—22no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—22no—
38#66979—22no—
39#66979—22no—
40C2×C4⋊Dic11C2×C411yescharacteristic, complemented
41C2×C4⋊Dic11C2×C411yescharacteristic, complemented
42C2×Dic11⋊C4—22no—
43C2×C4×Dic11—21no—
44C2×#4318—22no—
45C11×#95—22no—
46C11×#95—22no—
47C11⋊#95—22no—
48C11⋊#95—21no—
49C11⋊#95C2×C412yescomplemented
50C22⋊(C11⋊C8)—22no—
51C22⋊(C11⋊C8)—22no—
52#9477—111nomaximal, Sylow
53C24×C11—21no—
54C24×C11—24no—
55C24×C11—21no—
56C24×C11—42no—
57C24×C11—81no—
58C24×C11C22⋊C412yes—
59C24×C11C2×D411yescharacteristic
60C22×C4×C11—21no—
61C22×C4×C11—24no—
62C22×C4×C11—28no—
63C22×C4×C11—21no—
64C22×C4×C11—42no—
65C22×C4×C11—81no—
66C22×C4×C11—82no—
67C22×C4×C11—82no—
68C22×C4×C11C22⋊C412yes—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D412yes—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4112yes—
73C22×Dic11—22no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C11×C22⋊C4—28no—
77C11×C22⋊C4—28no—
78C11×C22⋊C4—24no—
79C11×C22⋊C4—24no—
80C42×C11—44no—
81C42×C11—82no—
82C22⋊Dic11—42no—
83C22⋊Dic11—44no—
84C22⋊Dic11—41no—
85C22⋊Dic11—41no—
86C22⋊Dic11—82no—
87C4⋊Dic11—22no—
88C4⋊Dic11—22no—
89Dic11⋊C4—82no—
90C4×Dic11—42no—
91#4318—44no—
92C2×C11⋊C8—42no—
93#2482—111no—
94#2273D1111yescharacteristic
95#1826—112no—
96#1462—111no—
97#1284—112no—
98C23×C11—22no—
99C23×C11—22no—
100C23×C11—24no—
101C23×C11—22no—
102C23×C11—22no—
103C23×C11—22no—
104C23×C11—22no—
105C23×C11—41no—
106C23×C11—42no—
107C23×C11—42no—
108C23×C11—42no—
109C23×C11—42no—
110C23×C11—81no—
111C23×C11—81no—
112C23×C11—88no—
113C23×C11#10414yes—
114C23×C11C2×C22⋊C411yescharacteristic
115C23×C11#12011yescharacteristic
116C23×C11#12311yescharacteristic
117C2×C4×C11—24no—
118C2×C4×C11—28no—
119C2×C4×C11—22no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—44no—
124C2×C4×C11—42no—
125C2×C4×C11—44no—
126C2×C4×C11—42no—
127C2×C4×C11—81no—
128C2×C4×C11—88no—
129C2×C4×C11C4×D412yes—
130C2×C4×C11#12112yes—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—42no—
137C2×Dic11—42no—
138C11⋊C8—82no—
139C2×#117—111no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4C2×D1111yescharacteristic
142#407—112no—
143#399—112no—
144#397—112no—
145#388—222no—
146#385—221no—
147#381—111no—
148#379—221no—
149C4×C22⋊C4—21no—
150C4×C22⋊C4—24no—
151C4×C22⋊C4C2×D1112yes—
152#339—224no—
153#323—222no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—24no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—44no—
163C22×C11—44no—
164C22×C11—44no—
165C22×C11—44no—
166C22×C11—42no—
167C22×C11—42no—
168C22×C11—82no—
169C22×C11—84no—
170C22×C11#38611yescharacteristic
171C22×C11C2×#10412yes—
172C22×C11#45812yes—
173C4×C11—22no—
174C4×C11—22no—
175C4×C11—48no—
176C4×C11—42no—
177Dic11—82no—
178Dic11—81no—
179Dic11—81no—
180C25C22⋊D1111yescharacteristic
181C23×C4—22no—
182C23×C4C22⋊D1111yescharacteristic
183C23×C4C22×D1111yescharacteristic
184C2×M16—222no—
185#117—222no—
186#117—222no—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—111no—
189C2×C4⋊C4—222no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—28no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—222no—
196C2×C22⋊C4—221no—
197C2×C22⋊C4—221no—
198C2×C22⋊C4—222no—
199C2×C22⋊C4C4×D1112yes—
200C2×C22⋊C4D4412yes—
201C2×C42—22no—
202C2×C42—221no—
203C2×C42C22⋊D1114yes—
204C22⋊C8—222no—
205C22⋊C8—222no—
206#95—22no—
207#95—22no—
208#95—112no—
209#95—222no—
210#95—221no—
211C2×C11—22no—
212C2×C11—22no—
213C2×C11—41no—
214C2×C11—44no—
215C2×C11#189011yescharacteristic
216C2×C11#189611yescharacteristic
217C2×C11#191111yescharacteristic
218C24—21no—
219C24—24no—
220C24—21no—
221C24—42no—
222C24—81no—
223C24(C2×D11)⋊C412yes—
224C24C2×C22⋊D1111yescharacteristic
225C22×C4—21no—
226C22×C4—24no—
227C22×C4—28no—
228C22×C4—21no—
229C22×C4—42no—
230C22×C4—81no—
231C22×C4—82no—
232C22×C4—82no—
233C22×C4—222no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4(C2×D11)⋊C412yes—
237C22×C4C2×C4×D1111yescharacteristic
238C22×C4C2×D4411yescharacteristic
239C22×C4#433912yes—
240C22×C4C2×C22⋊D1112yes—
241M16—444no—
242C2×C8—442no—
243C4⋊C4—222no—
244C4⋊C4—222no—
245C4⋊C4—882no—
246C22⋊C4—28no—
247C22⋊C4—28no—
248C22⋊C4—24no—
249C22⋊C4—24no—
250C22⋊C4—442no—
251C22⋊C4—444no—
252C22⋊C4—441no—
253C22⋊C4—441no—
254C22⋊C4—882no—
255C42—44no—
256C42—82no—
257C42—442no—
258C11#947711yescharacteristic, complemented, Sylow
259C23—22no—
260C23—22no—
261C23—24no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—41no—
267C23—42no—
268C23—42no—
269C23—42no—
270C23—42no—
271C23—81no—
272C23—81no—
273C23—88no—
274C23#6686914yes—
275C23C2×(C2×D11)⋊C411yescharacteristic
276C23#6698211yescharacteristic
277C23#6700611yescharacteristic
278C2×C4—24no—
279C2×C4—28no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—44no—
285C2×C4—42no—
286C2×C4—44no—
287C2×C4—42no—
288C2×C4—81no—
289C2×C4—88no—
290C2×C4—442no—
291C2×C4—442no—
292C2×C4—442no—
293C2×C4—442no—
294C2×C4—442no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4C4×C22⋊D1112yes—
298C2×C4#6698312yes—
299C8—882no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—24no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—44no—
309C22—44no—
310C22—44no—
311C22—44no—
312C22—42no—
313C22—42no—
314C22—82no—
315C22—84no—
316C22C2×#6686912yes—
317C22#1062282611yescharacteristic
318C22#1062285612yes—
319C4—22no—
320C4—22no—
321C4—48no—
322C4—42no—
323C4—882no—
324C4—881no—
325C4—881no—
326C2—22no—
327C2—22no—
328C2—41no—
329C2—44no—
330C2#1306902911yescharacteristic
331C2#1306905911yescharacteristic
332C2#1306914811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2273C2
socleC22×C11#386
prime radicalC25×C11D4
cosocleC23×C4×C11C23
hypercenter#2273D11
hypocenterC11#9477
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2273

Complements

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

NH ≅ G/Ntype
2. #13068716C2semidirect
4. #13066469C2semidirect
16. #10622566C4semidirect
17. #10622562C4semidirect
40. C2×C4⋊Dic11C2×C4semidirect
41. C2×C4⋊Dic11C2×C4semidirect
49. C11⋊#95C2×C4semidirect
258. C11#9477semidirect

Maximal subgroups

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

subgroupindex
#130728902
#130687162
#130669432
#130664692
C11×#22732
#947711