Finite Group Databasebeta

← #14664232

Subgroups — #14664232

Order 2816.

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

normal subgroups only

This group has 500 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#13066639C212yesmaximal, complemented
4#13066612C212yesmaximal
5C11×#1740C211yesmaximal, characteristic, complemented
6C2×C11×#117—21no—
7C2×C11×#117C2211yescharacteristic
8C2×C4×D44C411yescharacteristic, complemented
9#10622826—21no—
10#10622604C411yescharacteristic, complemented
11#10622602—21no—
12#10622599C411yescharacteristic, complemented
13#10622573C2211yescharacteristic
14#10622569—21no—
15#10622562C2211yescharacteristic
16#10622553—21no—
17#10622550C411yescharacteristic, complemented
18#10622539—21no—
19C11×#342—21no—
20C11×#342C2212yes—
21#10622166—21no—
22#10622163C2212yes—
23C23×C4×C11D411yescharacteristic
24C22×C22⋊D11—21no—
25C22×D44C2×C411yescharacteristic
26C22×C4×D11—21no—
27C11×#117—24no—
28C11×#117—41no—
29C11×#117—41no—
30C11×#117—42no—
31C2×C11×C4⋊C4—41no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4D411yescharacteristic
36C2×C11×C22⋊C4C2311yescharacteristic
37C2×C42×C11—41no—
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#11754—111nomaximal, Sylow
59C24×C11C2×D411yescharacteristic
60C23×D11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—22no—
66C22×C4×C11—42no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—42no—
74C2×C22⋊D11—41no—
75C2×C22⋊D11—41no—
76C2×C22⋊D11—81no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C2×D44—41no—
81C2×D44—42no—
82C2×C4×D11—42no—
83C2×C4×D11—81no—
84C2×C4×D11—81no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—44no—
88C11×C22⋊C4—24no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—42no—
92C42×C11—21no—
93C42×C11—21no—
94C42×C11—21no—
95C42×C11—21no—
96C42×C11—44no—
97C22⋊Dic11—81no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—81no—
103C4⋊Dic11—41no—
104Dic11⋊C4—81no—
105C2×C11⋊C8—42no—
106#2598—111no—
107#1740D1111yescharacteristic, complemented
108#1464—111no—
109#1352—112no—
110#1343—112no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11C2×C22⋊C411yescharacteristic
116C23×C11AGL(1,ℤ/8)11yescharacteristic
117C23×C11#13711yescharacteristic
118C22×D11—22no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
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—21no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—44no—
142C2×C4×C11—82no—
143C2×C4×C11—82no—
144C2×C4×C11#9911yescharacteristic
145C2×C4×C11#9911yescharacteristic
146C2×C4×C11#10412yes—
147C22⋊D11—82no—
148C22⋊D11—82no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158D44—42no—
159D44—42no—
160C4×D11—84no—
161C11⋊C8—82no—
162C2×C4×D4—111no—
163C2×#117—21no—
164C2×#117C2×D1111yescharacteristic
165#432—221no—
166#400—111no—
167#399—111no—
168#394—111no—
169#392—111no—
170#388—221no—
171#386—221no—
172#386—221no—
173#385—221no—
174#383—111no—
175#342—21no—
176#342C2×D1112yes—
177#324—221no—
178#323—112no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—81no—
188C22×C11C2×#9911yescharacteristic
189C22×C11#41711yescharacteristic
190C22×C11C2×#10411yescharacteristic
191C2×D11—42no—
192C2×D11—42no—
193C2×D11—42no—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—22no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11—84no—
206Dic11—81no—
207Dic11—81no—
208Dic11—81no—
209C22×D4—111no—
210C22×D4—221no—
211C23×C4—221no—
212C23×C4C22⋊D1111yescharacteristic
213C4×D4—441no—
214C4×D4—441no—
215#117—24no—
216#117—41no—
217#117—41no—
218#117—42no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4C4×D1111yescharacteristic
223C2×C4⋊C4D4411yescharacteristic
224C2×C22⋊C4—22no—
225C2×C22⋊C4—221no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4C22⋊D1111yescharacteristic
231C2×C22⋊C4C22×D1111yescharacteristic
232C2×C42—41no—
233C2×C42C4×D1111yescharacteristic
234C2×C42D4411yescharacteristic
235C4⋊C8—441no—
236C22⋊C8—222no—
237#97—441no—
238#95—111no—
239#95—111no—
240#95—221no—
241#95—221no—
242#95—221no—
243#95—221no—
244C2×C11—21no—
245C2×C11—21no—
246C2×C11—41no—
247C2×C11—41no—
248C2×C11#150411yescharacteristic
249C2×C11#212011yescharacteristic
250C2×C11#212811yescharacteristic
251D11—82no—
252C24—221no—
253C24C2×C22⋊D1111yescharacteristic
254C2×D4—441no—
255C2×D4—442no—
256C2×D4—442no—
257C2×D4—441no—
258C2×D4—441no—
259C2×D4—881no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—42no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—442no—
270C22×C4—881no—
271C22×C4—881no—
272C22×C4(C2×D11)⋊C411yescharacteristic
273C22×C4(C2×D11)⋊C411yescharacteristic
274C22×C4(C2×D11)⋊C411yescharacteristic
275C22×C4(C2×D11)⋊C411yescharacteristic
276C22×C4C2×C4×D1111yescharacteristic
277C22×C4C2×D4411yescharacteristic
278C2×C8—442no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—44no—
282C4⋊C4—441no—
283C4⋊C4—881no—
284C22⋊C4—24no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—42no—
288C22⋊C4—442no—
289C22⋊C4—442no—
290C22⋊C4—441no—
291C22⋊C4—441no—
292C22⋊C4—881no—
293C22⋊C4—881no—
294C42—21no—
295C42—21no—
296C42—21no—
297C42—21no—
298C42—44no—
299C11#1175411yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—222no—
305C23—441no—
306C23—441no—
307C23—441no—
308C23—441no—
309C23—441no—
310C23—441no—
311C23C2×(C2×D11)⋊C411yescharacteristic
312C23#6698511yescharacteristic
313C23#6699511yescharacteristic
314D4—442no—
315D4—442no—
316D4—882no—
317D4—882no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—44no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—884no—
347C2×C4#6686912yes—
348C2×C4#6687011yescharacteristic
349C2×C4#6687011yescharacteristic
350C8—882no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—81no—
360C22—442no—
361C22—442no—
362C22—442no—
363C22—881no—
364C22—881no—
365C22—881no—
366C22—881no—
367C22C2×#6686911yescharacteristic
368C22C2×#6687011yescharacteristic
369C22#1062257911yescharacteristic
370C4—22no—
371C4—21no—
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—84no—
378C4—881no—
379C4—881no—
380C4—881no—
381C2—21no—
382C2—21no—
383C2—41no—
384C2—41no—
385C2—882no—
386C2#1306711811yescharacteristic
387C2#1307025511yescharacteristic
388C2#1307028711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1740C2
socleC22×C11C2×#99
prime radical#10622573C22
cosocleC2×C11×C22⋊C4C23
hypercenter#1740D11
hypocenterC11#11754
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1740

Complements

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

NH ≅ G/Ntype
2. #13066950C2semidirect
3. #13066639C2semidirect
5. C11×#1740C2semidirect
8. C2×C4×D44C4semidirect
10. #10622604C4semidirect
12. #10622599C4semidirect
17. #10622550C4semidirect
107. #1740D11semidirect
299. C11#11754semidirect

Maximal subgroups

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

subgroupindex
#130741822
#130669502
#130666392
#130666122
C11×#17402
#1175411