Finite Group Databasebeta

← #14651432

Subgroups — #14651432

Order 2816.

568 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 103 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#13073583C211yesmaximal, characteristic
2#13067239C212yesmaximal, complemented
3#13066957C211yesmaximal, characteristic, complemented
4#13066471C212yesmaximal, complemented
5C11×#2973C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66993C411yescharacteristic
8C2×#66989C411yescharacteristic
9C2×#66928C2211yescharacteristic
10C11×#435—24no—
11C11×#432C2212yes—
12C11×#407—21no—
13C2×C11×C22⋊C8—21no—
14#10622826—21no—
15#10622826—21no—
16#10622601C411yescharacteristic
17#10622587C411yescharacteristic
18#10622574—21no—
19#10622574—21no—
20C4×C4⋊Dic11C2211yescharacteristic
21#10622539C2212yes—
22#10622163—21no—
23#10622163—21no—
24#10622102—24no—
25C22×D4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C22×C22⋊D11—21no—
29C22×C22⋊D11—21no—
30C22×D44C2×C411yescharacteristic
31C22×Dic22C2×C411yescharacteristic
32C2×C11×M16—22no—
33C22×C8×C11—22no—
34C4×D4×C11—22no—
35C4×D4×C11—22no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C42×C11C2311yescharacteristic
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42#66993—42no—
43#66989—42no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×C4⋊Dic11—21no—
49C2×C4×Dic11C2×C411yescharacteristic
50C2×C4×Dic11C2×C411yescharacteristic
51#66928—22no—
52#66928—22no—
53C11×C4⋊C8—22no—
54C11×C22⋊C8—22no—
55C11×C22⋊C8—22no—
56C11×C22⋊C8—22no—
57C11×#97D414yescomplemented
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C22⋊(C11⋊C8)—22no—
62C4⋊(C11⋊C8)—22no—
63#66867—22no—
64#9447—111nomaximal, Sylow
65C24×C11C22⋊C411yescharacteristic
66C24×C11C22⋊C411yescharacteristic
67C23×D11—21no—
68C2×D4×C11—22no—
69C2×D4×C11—22no—
70C2×D4×C11—41no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—81no—
76C22×C4×C11—81no—
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C2×C22⋊D11—42no—
83C2×C22⋊D11—42no—
84C2×C22⋊D11—42no—
85C2×C22⋊D11—42no—
86C2×C22⋊D11—81no—
87C2×C22⋊D11—81no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C2×D44—22no—
92C2×D44—41no—
93C2×D44—41no—
94C2×Dic22—22no—
95C2×Dic22—41no—
96C2×Dic22—41no—
97C11×M16—82no—
98C2×C8×C11—24no—
99C2×C8×C11—82no—
100C11×C4⋊C4—22no—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—22no—
103C42×C11C2×D412yes—
104C42×C11#4112yes—
105C22⋊Dic11—42no—
106C22⋊Dic11—42no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—81no—
111(C2×D11)⋊C4—81no—
112C4⋊Dic11—42no—
113C4×Dic11—41no—
114C4×Dic11—41no—
115C2×C11⋊C8—42no—
116#2973D1111yescharacteristic, complemented
117#2544—111no—
118#1533—112no—
119#1466—111no—
120#1285—112no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11#10012yes—
131C23×C11C2×C22⋊C411yescharacteristic
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139D4×C11—44no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—81no—
151C2×C4×C11—81no—
152C2×C4×C11C4×D412yes—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12112yes—
155C2×C4×C11#12311yescharacteristic
156C22⋊D11—84no—
157C22⋊D11—84no—
158C2×Dic11—22no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167D44—82no—
168Dic22—82no—
169C8×C11—44no—
170C11⋊C8—82no—
171C2×#127—111no—
172C2×#124—111no—
173C2×#124—111no—
174C2×C4×D4C2×D1111yescharacteristic
175#435—24no—
176#432—112no—
177#432C2×D1112yes—
178#407—21no—
179C2×C22⋊C8—21no—
180#394—221no—
181#394—221no—
182#391—111no—
183#390—111no—
184#386—221no—
185#386—221no—
186C4×C4⋊C4—111no—
187#329—224no—
188#323—221no—
189#323—221no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—22no—
193C22×C11—42no—
194C22×C11—42no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11#38611yescharacteristic
203C22×C11C2×#10011yescharacteristic
204C22×C11#41311yescharacteristic
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C2×D11—81no—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—41no—
217C4×C11—41no—
218Dic11—42no—
219Dic11—81no—
220Dic11—81no—
221C22×Q8—111no—
222C22×D4—111no—
223C22×D4—221no—
224C22×D4—221no—
225C22×D4C4×D1111yescharacteristic
226C23×C4C22⋊D1111yescharacteristic
227C23×C4C22⋊D1111yescharacteristic
228C2×M16—22no—
229C22×C8—22no—
230#127—442no—
231#124—222no—
232#124—222no—
233#124—442no—
234C4×D4—22no—
235C4×D4—22no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4C4×D1111yescharacteristic
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4—221no—
244C2×C22⋊C4D4411yescharacteristic
245C2×C22⋊C4D4411yescharacteristic
246C2×C42—111no—
247C2×C42—111no—
248C2×C42C22×D1111yescharacteristic
249C4⋊C8—22no—
250C4⋊C8—222no—
251C22⋊C8—22no—
252C22⋊C8—22no—
253C22⋊C8—22no—
254C22⋊C8—222no—
255#97—222no—
256#97C22⋊D1114yescomplemented
257#95—221no—
258#95—221no—
259#95—221no—
260C2×C11—21no—
261C2×C11—21no—
262C2×C11—42no—
263C2×C11—81no—
264C2×C11#188411yescharacteristic
265C2×C11#190011yescharacteristic
266C2×C11#191111yescharacteristic
267D11—161no—
268C24—221no—
269C24(C2×D11)⋊C411yescharacteristic
270C24(C2×D11)⋊C411yescharacteristic
271C2×Q8—222no—
272C2×Q8—441no—
273C2×Q8—441no—
274C2×D4—22no—
275C2×D4—22no—
276C2×D4—41no—
277C2×D4—222no—
278C2×D4—441no—
279C2×D4—441no—
280C2×D4—442no—
281C2×D4—442no—
282C2×D4—442no—
283C2×D4—442no—
284C2×D4—881no—
285C2×D4—881no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—81no—
291C22×C4—81no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4(C2×D11)⋊C411yescharacteristic
296C22×C4(C2×D11)⋊C411yescharacteristic
297C22×C4C2×C4×D1111yescharacteristic
298C22×C4C2×D4411yescharacteristic
299C22×C4C2×C22⋊D1111yescharacteristic
300M16—82no—
301C2×C8—24no—
302C2×C8—82no—
303C2×C8—442no—
304C4⋊C4—22no—
305C4⋊C4—442no—
306C22⋊C4—22no—
307C22⋊C4—22no—
308C22⋊C4—442no—
309C22⋊C4—442no—
310C22⋊C4—441no—
311C22⋊C4—442no—
312C22⋊C4—441no—
313C22⋊C4—881no—
314C22⋊C4—881no—
315C42—441no—
316C42—441no—
317C42#433912yes—
318C42C2×C22⋊D1112yes—
319C11#944711yescharacteristic, complemented, Sylow
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—441no—
330C23—441no—
331C23—441no—
332C23—441no—
333C23—441no—
334C23—441no—
335C23—441no—
336C23#6688712yes—
337C23C2×(C2×D11)⋊C411yescharacteristic
338Q8—882no—
339D4—44no—
340D4—882no—
341D4—884no—
342D4—884no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—222no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4C4×C22⋊D1112yes—
365C2×C4#6698211yescharacteristic
366C2×C4#6698312yes—
367C2×C4#6700611yescharacteristic
368C8—44no—
369C8—882no—
370C22—21no—
371C22—21no—
372C22—22no—
373C22—42no—
374C22—42no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—81no—
382C22—881no—
383C22—881no—
384C22—881no—
385C22—881no—
386C22—881no—
387C22—881no—
388C22—881no—
389C22C2×#6688711yescharacteristic
390C22#1062274511yescharacteristic
391C22#1062282611yescharacteristic
392C4—22no—
393C4—21no—
394C4—21no—
395C4—22no—
396C4—41no—
397C4—41no—
398C4—442no—
399C4—881no—
400C4—881no—
401C2—21no—
402C2—21no—
403C2—42no—
404C2—81no—
405C2—1761no—
406C2#1306899911yescharacteristic
407C2#1306907911yescharacteristic
408C2#1306914811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2973C2
socleC22×C11#386
prime radicalC2×#66993C4
cosocleC2×C42×C11C23
hypercenter#2973D11
hypocenterC11#9447
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #13067239C2semidirect
3. #13066957C2semidirect
4. #13066471C2semidirect
5. C11×#2973C2semidirect
57. C11×#97D4semidirect
116. #2973D11semidirect
256. #97C22⋊D11semidirect
319. C11#9447semidirect

Maximal subgroups

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

subgroupindex
#130735832
#130672392
#130669572
#130664712
C11×#29732
#944711