Finite Group Databasebeta

← #14664267

Subgroups — #14664267

Order 2816.

484 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 83 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#13074182C211yesmaximal, characteristic
2#13066950C211yesmaximal, characteristic, complemented
3#13066642C212yesmaximal, complemented
4#13066618C212yesmaximal, complemented
5C11×#1742C211yesmaximal, characteristic, complemented
6C22×C11×M16—21no—
7C2×C11×#117C2211yescharacteristic
8C2×C4×D44C411yescharacteristic
9#10622826—21no—
10#10622604C2211yescharacteristic
11#10622602—21no—
12#10622599C2211yescharacteristic
13#10622573C411yescharacteristic
14#10622569—21no—
15#10622562C411yescharacteristic
16#10622553—21no—
17#10622550C411yescharacteristic
18#10622539—21no—
19C11×#343—21no—
20C11×#343C2212yes—
21#10622166C2212yes—
22#10622163—21no—
23C23×C4×C11D411yescharacteristic
24C22×C22⋊D11—21no—
25C22×D44C2×C411yescharacteristic
26C22×C4×D11—21no—
27C2×C11×M16—24no—
28C2×C11×M16—22no—
29C2×C11×M16—41no—
30C2×C11×M16—42no—
31C22×C8×C11—41no—
32C11×#117—41no—
33C11×#117—41no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×C11×C22⋊C4C2×C411yescharacteristic
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C42×C11C2×C411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C22⋊Dic11—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×Dic11⋊C4—21no—
47C4×D44—41no—
48C4×D44—41no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95C2×C411yescharacteristic
54C11⋊#95C2×C411yescharacteristic
55C22⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)—41no—
57#66867—41no—
58#11761—111nomaximal, Sylow
59C24×C11C22⋊C411yescharacteristic
60C23×D11—21no—
61C22×C4×C11—22no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C2×C22⋊D11—42no—
73C2×C22⋊D11—42no—
74C2×C22⋊D11—81no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C2×D44—41no—
79C2×D44—42no—
80C2×C4×D11—42no—
81C2×C4×D11—81no—
82C2×C4×D11—81no—
83C11×M16—24no—
84C11×M16—44no—
85C11×M16—42no—
86C2×C8×C11—44no—
87C2×C8×C11—42no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C42×C11—21no—
93C42×C11—21no—
94C42×C11—21no—
95C42×C11—21no—
96C22⋊Dic11—81no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—81no—
103C4⋊Dic11—41no—
104Dic11⋊C4—81no—
105C2×C11⋊C8—42no—
106#2598—111no—
107#1742D1111yescharacteristic, complemented
108#1464—111no—
109#1353—112no—
110#1345—112no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11#10412yes—
116C23×C11C2×C22⋊C411yescharacteristic
117C22×D11—22no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11#9911yescharacteristic
141C2×C4×C11#9911yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C22⋊D11—84no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154D44—42no—
155D44—42no—
156C4×D11—84no—
157C8×C11—44no—
158C11⋊C8—82no—
159C22×M16—21no—
160C2×C4×D4—111no—
161C2×#117C2×D1111yescharacteristic
162#432—221no—
163#400—111no—
164#399—111no—
165#394—111no—
166#392—111no—
167#388—221no—
168#386—221no—
169#386—221no—
170#385—221no—
171#383—111no—
172#343—21no—
173#343C2×D1112yes—
174#324—112no—
175#323—221no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—22no—
179C22×C11—42no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—81no—
183C22×C11C2×#9911yescharacteristic
184C22×C11#41711yescharacteristic
185C22×C11C2×#10411yescharacteristic
186C2×D11—42no—
187C2×D11—42no—
188C2×D11—42no—
189C2×D11—81no—
190C2×D11—81no—
191C2×D11—81no—
192C2×D11—81no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—41no—
200C4×C11—41no—
201Dic11—81no—
202Dic11—81no—
203Dic11—81no—
204C22×D4—111no—
205C22×D4—221no—
206C23×C4—221no—
207C23×C4C22⋊D1111yescharacteristic
208C2×M16—24no—
209C2×M16—22no—
210C2×M16—41no—
211C2×M16—42no—
212C22×C8—41no—
213C4×D4—441no—
214C4×D4—441no—
215#117—41no—
216#117—41no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4C22⋊D1111yescharacteristic
220C2×C4⋊C4C22×D1111yescharacteristic
221C2×C22⋊C4—221no—
222C2×C22⋊C4—221no—
223C2×C22⋊C4—221no—
224C2×C22⋊C4—221no—
225C2×C22⋊C4—221no—
226C2×C22⋊C4C4×D1111yescharacteristic
227C2×C22⋊C4D4411yescharacteristic
228C2×C42C4×D1111yescharacteristic
229C2×C42D4411yescharacteristic
230C4⋊C8—441no—
231C22⋊C8—222no—
232#97—441no—
233#95—111no—
234#95—111no—
235#95—221no—
236#95—221no—
237#95—221no—
238#95—221no—
239C2×C11—21no—
240C2×C11—21no—
241C2×C11—42no—
242C2×C11#150411yescharacteristic
243C2×C11#212011yescharacteristic
244C2×C11#213411yescharacteristic
245D11—82no—
246C24—221no—
247C24(C2×D11)⋊C411yescharacteristic
248C2×D4—441no—
249C2×D4—442no—
250C2×D4—442no—
251C2×D4—442no—
252C2×D4—881no—
253C22×C4—22no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—442no—
262C22×C4—881no—
263C22×C4—881no—
264C22×C4(C2×D11)⋊C411yescharacteristic
265C22×C4(C2×D11)⋊C411yescharacteristic
266C22×C4(C2×D11)⋊C411yescharacteristic
267C22×C4C2×C4×D1111yescharacteristic
268C22×C4C2×D4411yescharacteristic
269C22×C4C2×C22⋊D1111yescharacteristic
270M16—24no—
271M16—44no—
272M16—42no—
273C2×C8—44no—
274C2×C8—42no—
275C2×C8—442no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—441no—
279C4⋊C4—881no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—442no—
283C22⋊C4—441no—
284C22⋊C4—441no—
285C22⋊C4—441no—
286C22⋊C4—441no—
287C22⋊C4—881no—
288C22⋊C4—881no—
289C42—21no—
290C42—21no—
291C42—21no—
292C42—21no—
293C11#1176111yescharacteristic, complemented, Sylow
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—222no—
299C23—441no—
300C23—441no—
301C23—441no—
302C23—441no—
303C23—441no—
304C23—441no—
305C23#6686912yes—
306C23C2×(C2×D11)⋊C411yescharacteristic
307D4—442no—
308D4—442no—
309D4—884no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—884no—
336C2×C4#6687011yescharacteristic
337C2×C4#6687011yescharacteristic
338C2×C4#6698511yescharacteristic
339C2×C4#6699511yescharacteristic
340C8—44no—
341C8—882no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—42no—
346C22—41no—
347C22—41no—
348C22—81no—
349C22—442no—
350C22—442no—
351C22—442no—
352C22—881no—
353C22—881no—
354C22—881no—
355C22—881no—
356C22C2×#6686911yescharacteristic
357C22C2×#6687011yescharacteristic
358C22#1062257911yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—881no—
368C4—881no—
369C4—881no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—882no—
374C2#1306711811yescharacteristic
375C2#1307025811yescharacteristic
376C2#1307030711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1742C2
socleC22×C11C2×#99
prime radical#10622573C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1742D11
hypocenterC11#11761
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1742

Complements

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

NH ≅ G/Ntype
2. #13066950C2semidirect
3. #13066642C2semidirect
4. #13066618C2semidirect
5. C11×#1742C2semidirect
107. #1742D11semidirect
293. C11#11761semidirect

Maximal subgroups

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

subgroupindex
#130741822
#130669502
#130666422
#130666182
C11×#17422
#1176111