Finite Group Databasebeta

← #14649607

Subgroups — #14649607

Order 2816.

486 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 95 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#13078711C211yesmaximal, characteristic
2#13077653C211yesmaximal, characteristic
3#13068442C211yesmaximal, characteristic
4#13067115C211yesmaximal, characteristic, complemented
5#13066515C211yesmaximal, characteristic, complemented
6#13066471C211yesmaximal, characteristic, complemented
7C11×#1531C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C2×C11×#97C2211yescharacteristic
12C2×#66885—21no—
13#10622700C411yescharacteristic, complemented
14#10622700C411yescharacteristic, complemented
15#10622696C411yescharacteristic, complemented
16#10622696C411yescharacteristic, complemented
17#10622659—21no—
18#10622657—21no—
19#10622639—21no—
20#10622639—21no—
21C4×C4⋊Dic11C2211yescharacteristic
22#10622539C2211yescharacteristic
23#10622538C2211yescharacteristic
24#10622451—21no—
25#10622447—21no—
26#10622339—21no—
27D11×C22⋊C8—21no—
28#10622319—22no—
29C11×#330—22no—
30#10622189—21no—
31#10622176—21no—
32#10622176—21no—
33C22×D44D411yescharacteristic
34C22×C4×D11—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8C2×C411yescharacteristic
37C11×C4⋊Q8C2×C411yescharacteristic
38C11×#125—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C11×#117—21no—
44C2×C42×C11C2311yescharacteristic
45C2×#4325—21no—
46C2×#4325—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11D411yescharacteristic
50C2×C4×Dic11—21no—
51C2×#4313—22no—
52C2×C8×D11—22no—
53C4×D44—21no—
54C4×D44—21no—
55C4×D44C2×C411yescharacteristic
56C4×D44C2×C411yescharacteristic
57C4×D44D411yescharacteristic
58C4×D44D411yescharacteristic
59C11×C4⋊C8—21no—
60C11×C22⋊C8—21no—
61C11×#97—21no—
62C11×#97—21no—
63C11×#97D412yes—
64#66899—21no—
65#66899—21no—
66C11⋊#95—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)D411yescharacteristic
69C22⋊(C11⋊C8)D411yescharacteristic
70#66885—24no—
71(C2×D11)⋊C8—22no—
72(C2×D11)⋊C8—22no—
73#66873—21no—
74#66873—21no—
75#66871—21no—
76#66871—21no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)C2×C411yescharacteristic
79C4⋊(C11⋊C8)C2×C411yescharacteristic
80#66867—21no—
81C4×C11⋊C8—21no—
82#9165—111nomaximal, Sylow
83C23×D11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×Dic11—21no—
90C22×Dic11—41no—
91C2×D44—22no—
92C2×D44—21no—
93C2×D44—41no—
94C2×D44C22⋊C411yescharacteristic
95C2×D44C22⋊C411yescharacteristic
96C2×C4×D11—21no—
97C2×C4×D11—21no—
98C2×C4×D11—21no—
99C2×C4×D11—21no—
100C2×C4×D11—82no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11—41no—
113C42×C11C22×C411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117#4325—42no—
118#4325—42no—
119(C2×D11)⋊C4—21no—
120(C2×D11)⋊C4—21no—
121(C2×D11)⋊C4—21no—
122(C2×D11)⋊C4—21no—
123C4⋊Dic11—22no—
124C4⋊Dic11—21no—
125C4⋊Dic11—41no—
126C4⋊Dic11C22⋊C411yescharacteristic
127C4⋊Dic11C22⋊C411yescharacteristic
128C4×Dic11—81no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8—21no—
133#4313—82no—
134C8×D11—82no—
135#3110—111no—
136#2974—111no—
137#1762—111no—
138#1531D1111yescharacteristic, complemented
139#1503—111no—
140#1302—111no—
141#1285—111no—
142C23×C11#12111yescharacteristic
143C22×D11—21no—
144C22×D11—21no—
145C22×D11—42no—
146C22×D11—41no—
147C22×D11—41no—
148C22×D11—81no—
149Q8×C11—41no—
150Q8×C11—41no—
151Q8×C11—81no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11C2×C22⋊C411yescharacteristic
160C2×C4×C11C4×D411yescharacteristic
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12311yescharacteristic
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—42no—
168C2×Dic11—81no—
169C2×Dic11—81no—
170C2×Dic11—81no—
171D44—21no—
172D44—21no—
173D44—21no—
174D44—42no—
175D44#10412yes—
176C4×D11—42no—
177C4×D11—42no—
178C4×D11—81no—
179C4×D11—81no—
180C8×C11—42no—
181C8×C11—42no—
182C11⋊C8—41no—
183C11⋊C8—41no—
184C11⋊C8—41no—
185C11⋊C8—41no—
186#533C2×D1111yescharacteristic
187C2×C4×D4—111no—
188#484—221no—
189#474—111no—
190#474—111no—
191#461—111no—
192#461—111no—
193#450—221no—
194#440—221no—
195#440—221no—
196#436—221no—
197#435—222no—
198C8×D4—221no—
199#432—111no—
200#432C2×D1111yescharacteristic
201#431—111no—
202C2×#102—221no—
203#407—221no—
204C2×C22⋊C8—221no—
205C2×#97C2×D1111yescharacteristic
206C4×C4⋊C4—111no—
207#340—221no—
208#330—22no—
209#328—221no—
210#328—221no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11#38611yescharacteristic
214C22×C11#47111yescharacteristic
215C22×C11#47311yescharacteristic
216C2×D11—22no—
217C2×D11—41no—
218C2×D11—41no—
219C2×D11—41no—
220C2×D11—41no—
221C2×D11—41no—
222C2×D11—82no—
223C2×D11—82no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—81no—
230C4×C11—81no—
231C4×C11C2×#10411yescharacteristic
232C4×C11#42111yescharacteristic
233Dic11—41no—
234Dic11—41no—
235Dic11—82no—
236C22×D4—111no—
237C23×C4—221no—
238C2×SD16—221no—
239C2×SD16—221no—
240C2×M16—222no—
241C22×C8—21no—
242C22×C8—222no—
243C4⋊Q8C4×D1111yescharacteristic
244C4⋊Q8C4×D1111yescharacteristic
245#125—21no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×D4—111no—
251C4×D4—111no—
252C4×D4—111no—
253C4×D4—111no—
254C4×D4—221no—
255C4×D4—221no—
256#117—21no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C42—221no—
261C2×C42C22×D1111yescharacteristic
262#107—221no—
263#107—221no—
264C4⋊C8—21no—
265C4⋊C8—111no—
266C4⋊C8—111no—
267C4⋊C8—221no—
268#103—221no—
269#103—221no—
270#102—221no—
271#102—221no—
272#102—224no—
273C22⋊C8—21no—
274C22⋊C8—111no—
275C22⋊C8—111no—
276C22⋊C8—222no—
277C22⋊C8—222no—
278C22⋊C8—221no—
279#97—21no—
280#97—21no—
281#97—221no—
282#97C22⋊D1112yes—
283C4×C8—221no—
284#95—221no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11#187111yescharacteristic
288C2×C11#190411yescharacteristic
289C2×C11#190811yescharacteristic
290D11—42no—
291D11—81no—
292C24—221no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×D4—111no—
296C2×D4—111no—
297C2×D4—222no—
298C2×D4—221no—
299C2×D4—441no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4—441no—
306C22×C4—882no—
307C22×C4#433911yescharacteristic
308C22×C4D4×D1111yescharacteristic
309C22×C4D4×D1111yescharacteristic
310SD16—442no—
311SD16—442no—
312M16—882no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—221no—
318C2×C8—221no—
319C2×C8—221no—
320C2×C8—221no—
321C2×C8—882no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—111no—
329C4⋊C4—111no—
330C4⋊C4—222no—
331C4⋊C4—221no—
332C4⋊C4—441no—
333C22⋊C4—41no—
334C22⋊C4—221no—
335C22⋊C4—221no—
336C22⋊C4—221no—
337C22⋊C4—221no—
338C42—41no—
339C42—881no—
340C42C2×C4×D1111yescharacteristic
341C42D4×D1111yescharacteristic
342C42#434111yescharacteristic
343C42C2×C22⋊D1111yescharacteristic
344C11#916511yescharacteristic, complemented, Sylow
345C23—221no—
346C23—221no—
347C23—442no—
348C23—441no—
349C23—441no—
350C23—881no—
351C23#6693711yescharacteristic
352Q8—41no—
353Q8—41no—
354Q8—81no—
355D4—112no—
356D4—221no—
357D4—221no—
358D4—221no—
359D4—442no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—442no—
370C2×C4—442no—
371C2×C4—442no—
372C2×C4—881no—
373C2×C4—881no—
374C2×C4—881no—
375C2×C4—881no—
376C2×C4—881no—
377C2×C4C22⋊C4×D1111yescharacteristic
378C2×C4(C22⋊D11)⋊C411yescharacteristic
379C2×C4#6693611yescharacteristic
380C2×C4C4×C22⋊D1111yescharacteristic
381C2×C4#6699011yescharacteristic
382C2×C4#6699111yescharacteristic
383C8—42no—
384C8—42no—
385C8—441no—
386C8—441no—
387C8—441no—
388C8—441no—
389C22—21no—
390C22—21no—
391C22—222no—
392C22—441no—
393C22—441no—
394C22—441no—
395C22—441no—
396C22—441no—
397C22—882no—
398C22—882no—
399C22#1062236711yescharacteristic
400C22#1062236811yescharacteristic
401C22#1062256911yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—81no—
408C4—81no—
409C4—441no—
410C4—441no—
411C4—882no—
412C4D11×#10411yescharacteristic
413C4#1062243411yescharacteristic
414C2—21no—
415C2—21no—
416C2—442no—
417C2—881no—
418C2#1306891511yescharacteristic
419C2#1306910011yescharacteristic
420C2#1306912811yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1531C2
socleC22×C11#386
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1531D11
hypocenterC11#9165
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1531

Complements

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

NH ≅ G/Ntype
4. #13067115C2semidirect
5. #13066515C2semidirect
6. #13066471C2semidirect
7. C11×#1531C2semidirect
13. #10622700C4semidirect
14. #10622700C4semidirect
15. #10622696C4semidirect
16. #10622696C4semidirect
138. #1531D11semidirect
344. C11#9165semidirect

Maximal subgroups

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

subgroupindex
#130787112
#130776532
#130684422
#130671152
#130665152
#130664712
C11×#15312
#916511