Finite Group Databasebeta

← #14651881

Subgroups — #14651881

Order 2816.

444 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 91 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#13078750C211yesmaximal, characteristic
2#13077603C211yesmaximal, characteristic, complemented
3#13067058C211yesmaximal, characteristic, complemented
4#13066956C211yesmaximal, characteristic, complemented
5C11⋊#1308C211yesmaximal, characteristic, complemented
6#13066487C211yesmaximal, characteristic, complemented
7C11×#1535C211yesmaximal, characteristic, complemented
8C11×#529C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12#10622679—21no—
13#10622670—21no—
14#10622659C411yescharacteristic
15#10622656C411yescharacteristic
16#10622649C411yescharacteristic
17#10622646C411yescharacteristic
18#10622639—21no—
19#10622637—21no—
20#10622627—21no—
21#10622625—21no—
22#10622624—21no—
23#10622624—21no—
24#10622613—21no—
25#10622610—21no—
26#10622539C2211yescharacteristic
27#10622539C2211yescharacteristic
28C4×#4318C2211yescharacteristic
29C11×#330—21no—
30C11×#329—21no—
31#10622121—21no—
32#10622121—21no—
33#10622106—21no—
34#10622106—21no—
35C22×D44C2×C411yescharacteristic
36C22×C4×D11—21no—
37C11×#126—21no—
38C11×#125D411yescharacteristic
39C11×#124D411yescharacteristic
40C11×#123—21no—
41C11×C22⋊Q8C2×C411yescharacteristic
42C11×#121C2×C411yescharacteristic
43C4×Q8×C11D411yescharacteristic
44C4×D4×C11—21no—
45C4×D4×C11D411yescharacteristic
46C11×#117—21no—
47C2×C42×C11C2311yescharacteristic
48C2×#4325—21no—
49C2×#4323—21no—
50C2×(C2×D11)⋊C4—21no—
51C2×C4⋊Dic11C2×C411yescharacteristic
52C2×#4318—21no—
53C2×#4318—21no—
54C22×C11⋊C8—21no—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44—21no—
58C4×D44—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×#97—21no—
64C11×#97—21no—
65#66899—21no—
66#66896—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)C2×C411yescharacteristic
70C22⋊(C11⋊C8)C2×C411yescharacteristic
71C22⋊(C11⋊C8)D411yescharacteristic
72C22⋊(C11⋊C8)D411yescharacteristic
73#66873—21no—
74#66873—21no—
75#66872—21no—
76#66871—21no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)—21no—
81#66867—21no—
82#66867—21no—
83#66867—21no—
84#66867—21no—
85C4×C11⋊C8—21no—
86C4×C11⋊C8D411yescharacteristic
87C4×C11⋊C8D411yescharacteristic
88#9532—111nomaximal, Sylow
89C23×D11—21no—
90C2×Q8×C11C22⋊C411yescharacteristic
91C2×D4×C11—21no—
92C2×D4×C11C22⋊C411yescharacteristic
93C22×C4×C11—21no—
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C22×Dic11—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—42no—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11—82no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4C22⋊C411yescharacteristic
111C11×C4⋊C4C22⋊C411yescharacteristic
112C11×C22⋊C4—21no—
113C11×C22⋊C4—21no—
114C11×C22⋊C4—21no—
115C11×C22⋊C4—21no—
116C11×C22⋊C4—21no—
117C42×C11—21no—
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122#4325—42no—
123#4323—42no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128#4318—42no—
129#4318—42no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8—21no—
136C2×C11⋊C8—42no—
137#3114—111no—
138#2967—111no—
139#1535D1111yescharacteristic, complemented
140#1490—111no—
141#1466—111no—
142#1308—111no—
143#1291—111no—
144C23×C11—21no—
145C23×C11C4×D411yescharacteristic
146C22×D11—22no—
147C22×D11—41no—
148C22×D11—41no—
149C22×D11—81no—
150C22×D11—81no—
151Q8×C11—41no—
152D4×C11—41no—
153D4×C11—81no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11C2×C22⋊C411yescharacteristic
163C2×C4×C11C4×D411yescharacteristic
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12311yescharacteristic
168C2×Dic11—41no—
169C2×Dic11—81no—
170D44—22no—
171D44—22no—
172D44—41no—
173D44—41no—
174C4×D11—82no—
175C4×D11—82no—
176C8×C11—81no—
177C8×C11—81no—
178C11⋊C8—22no—
179C11⋊C8—41no—
180C11⋊C8—41no—
181C11⋊C8—41no—
182C11⋊C8—41no—
183C11⋊C8—41no—
184#529C2×D1111yescharacteristic
185C2×C4×D4—111no—
186#483—111no—
187#480—111no—
188#478—221no—
189#463—221no—
190#450—111no—
191#447—111no—
192#446—221no—
193#442—221no—
194#440—221no—
195#436—221no—
196#435—221no—
197#435—221no—
198#433—221no—
199#432—111no—
200#432—111no—
201#432C2×D1111yescharacteristic
202#432C2×D1111yescharacteristic
203#405—221no—
204C4×M16—111no—
205#330—21no—
206#329—21no—
207D4⋊C8—221no—
208D4⋊C8—221no—
209#323—221no—
210#323—221no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11#38611yescharacteristic
218C2×D11—42no—
219C2×D11—82no—
220C2×D11—81no—
221C2×D11—81no—
222C2×D11—82no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—41no—
230C4×C11—41no—
231C4×C11—41no—
232Dic11—81no—
233C22×D4—111no—
234C23×C4—221no—
235C2×SD16—221no—
236C2×D8—221no—
237C2×M16—221no—
238C2×M16—221no—
239C22×C8—221no—
240#126—21no—
241#125C22⋊D1111yescharacteristic
242#124C22⋊D1111yescharacteristic
243#123—21no—
244C22⋊Q8C4×D1111yescharacteristic
245#121C4×D1111yescharacteristic
246C4×Q8D4411yescharacteristic
247C4×D4—21no—
248C4×D4—221no—
249C4×D4—221no—
250C4×D4—221no—
251C4×D4—221no—
252C4×D4D4411yescharacteristic
253#117—21no—
254C2×C4⋊C4—111no—
255C2×C22⋊C4—221no—
256C2×C42C22×D1111yescharacteristic
257#107—221no—
258#106—221no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—221no—
262C4⋊C8—221no—
263C4⋊C8—221no—
264C4⋊C8—221no—
265#103—221no—
266#102—221no—
267#102—221no—
268#102—221no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271C22⋊C8—111no—
272C22⋊C8—111no—
273C22⋊C8—111no—
274C22⋊C8—111no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277#97—21no—
278#97—21no—
279#97—221no—
280#97—221no—
281#97—221no—
282#97—221no—
283C4×C8—111no—
284C4×C8—111no—
285C4×C8—221no—
286C2×C11—41no—
287C2×C11—81no—
288C2×C11#189111yescharacteristic
289C2×C11#190311yescharacteristic
290C2×C11#190611yescharacteristic
291D11—82no—
292C24—221no—
293C2×Q8(C2×D11)⋊C411yescharacteristic
294C2×D4—21no—
295C2×D4—221no—
296C2×D4—221no—
297C2×D4—442no—
298C2×D4(C2×D11)⋊C411yescharacteristic
299C22×C4—21no—
300C22×C4—221no—
301C22×C4—441no—
302C22×C4—441no—
303C22×C4—882no—
304C22×C4C2×C4×D1111yescharacteristic
305C22×C4D4×D1111yescharacteristic
306C22×C4#434111yescharacteristic
307SD16—442no—
308D8—442no—
309M16—442no—
310M16—442no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—221no—
314C2×C8—221no—
315C2×C8—221no—
316C2×C8—221no—
317C2×C8—221no—
318C2×C8—221no—
319C2×C8—442no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—221no—
325C4⋊C4—221no—
326C4⋊C4(C2×D11)⋊C411yescharacteristic
327C4⋊C4(C2×D11)⋊C411yescharacteristic
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—441no—
334C22⋊C4—441no—
335C42—21no—
336C42C2×D4411yescharacteristic
337C42D4×D1111yescharacteristic
338C42#434111yescharacteristic
339C42C2×C22⋊D1111yescharacteristic
340C11#953211yescharacteristic, complemented, Sylow
341C23—21no—
342C23—222no—
343C23—441no—
344C23—441no—
345C23—881no—
346C23—881no—
347C23(C22⋊D11)⋊C411yescharacteristic
348Q8—41no—
349D4—41no—
350D4—81no—
351D4—222no—
352D4—222no—
353D4—441no—
354D4—441no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—441no—
364C2×C4—882no—
365C2×C4—882no—
366C2×C4—881no—
367C2×C4(C22⋊D11)⋊C411yescharacteristic
368C2×C4#6693511yescharacteristic
369C2×C4#6693911yescharacteristic
370C2×C4C2×(C2×D11)⋊C411yescharacteristic
371C2×C4#6699211yescharacteristic
372C2×C4#6699211yescharacteristic
373C8—81no—
374C8—81no—
375C8—222no—
376C8—441no—
377C8—441no—
378C8—441no—
379C8—441no—
380C8—441no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—442no—
388C22—882no—
389C22—882no—
390C22—881no—
391C22—881no—
392C22#1062257111yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—881no—
403C2—41no—
404C2—81no—
405C2—882no—
406C2#1306903211yescharacteristic
407C2#1306909411yescharacteristic
408C2#1306911511yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1535C2
socleC22×C11#386
prime radical#10622649C4
cosocleC2×C42×C11C23
hypercenter#1535D11
hypocenterC11#9532
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1535

Complements

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

NH ≅ G/Ntype
2. #13077603C2semidirect
3. #13067058C2semidirect
4. #13066956C2semidirect
5. C11⋊#1308C2semidirect
6. #13066487C2semidirect
7. C11×#1535C2semidirect
139. #1535D11semidirect
340. C11#9532semidirect

Maximal subgroups

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

subgroupindex
#130787502
#130776032
#130670582
#130669562
C11⋊#13082
#130664872
C11×#15352
#953211