Finite Group Databasebeta

← #14647333

Subgroups — #14647333

Order 2816.

472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 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#13071552C211yesmaximal, characteristic
2#13068601C211yesmaximal, characteristic
3#13066932C211yesmaximal, characteristic
4#13066495C211yesmaximal, characteristic, complemented
5#13066484C211yesmaximal, characteristic, complemented
6#13066483C211yesmaximal, characteristic, complemented
7C11×#1294C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D11C2211yescharacteristic
9C2×C11×C22⋊C8C2211yescharacteristic
10C11×#380C2211yescharacteristic
11C2×C11×#95C2211yescharacteristic
12#10622826—21no—
13#10622825C2211yescharacteristic
14#10622825C2211yescharacteristic
15C4×C22⋊Dic11—21no—
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×#66870—21no—
18#10622283—21no—
19#10622279C411yescharacteristic, complemented
20#10622277C411yescharacteristic, complemented
21#10622268—21no—
22#10622264C411yescharacteristic, complemented
23#10622261C411yescharacteristic, complemented
24#10622165—21no—
25#10622107—21no—
26#10622106—21no—
27C23×C4×C11—21no—
28C23×C4×C11C2311yescharacteristic
29C22×C22⋊D11D411yescharacteristic
30C22×C4×D11C2×C411yescharacteristic
31C22×C8×C11—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11D411yescharacteristic
37C4×C22⋊D11—21no—
38C4×C22⋊D11—21no—
39C4×C22⋊D11—21no—
40C4×C22⋊D11—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4D411yescharacteristic
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×Dic11⋊C4D411yescharacteristic
47C2×C4×Dic11—21no—
48C2×C4×Dic11—21no—
49C2×C4×Dic11C2×C411yescharacteristic
50C22×C11⋊C8—21no—
51C11×C22⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95C2×C411yescharacteristic
56C11×#95C2×C411yescharacteristic
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95C2×C411yescharacteristic
63C11⋊#95C2×C411yescharacteristic
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66#66870—42no—
67#8763—111nomaximal, Sylow
68C24×C11C2×D411yescharacteristic
69C23×D11C22⋊C411yescharacteristic
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—42no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—81no—
77C22×C4×C11—81no—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C2×C22⋊D11—21no—
85C2×C22⋊D11—21no—
86C2×C22⋊D11—21no—
87C2×C22⋊D11—21no—
88C2×C22⋊D11—21no—
89C2×C22⋊D11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—41no—
93C22×Dic11C22⋊C411yescharacteristic
94C22×Dic11C22⋊C411yescharacteristic
95C22×Dic11C22⋊C411yescharacteristic
96C2×C4×D11—21no—
97C2×C4×D11—21no—
98C2×C4×D11—81no—
99C2×C8×C11—41no—
100C2×C8×C11—81no—
101C11×C4⋊C4—81no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C22⋊Dic11—21no—
105C22⋊Dic11—21no—
106C22⋊Dic11—41no—
107C22⋊Dic11—41no—
108C22⋊Dic11—41no—
109C22⋊Dic11—41no—
110(C2×D11)⋊C4—21no—
111(C2×D11)⋊C4—21no—
112(C2×D11)⋊C4—42no—
113(C2×D11)⋊C4—81no—
114C4⋊Dic11—81no—
115C4⋊Dic11—81no—
116Dic11⋊C4—21no—
117Dic11⋊C4—21no—
118C4×Dic11—21no—
119C4×Dic11—21no—
120C4×Dic11—42no—
121C4×Dic11—81no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—81no—
124#2353—111no—
125#1799—111no—
126#1459—111no—
127#1294—111no—
128#1294D1111yescharacteristic, complemented
129#1289—111no—
130#1289—111no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11C2×C22⋊C411yescharacteristic
134C23×C11#12311yescharacteristic
135C23×C11#12311yescharacteristic
136C23×C11#13511yescharacteristic
137C23×C11#13511yescharacteristic
138C23×C11AGL(1,ℤ/8)11yescharacteristic
139C23×C11#13711yescharacteristic
140C22×D11—21no—
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—41no—
144C22×D11—41no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—82no—
158C2×C4×C11—82no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11#11711yescharacteristic
163C2×C4×C11#11711yescharacteristic
164C2×C4×C11#12311yescharacteristic
165C2×C4×C11#12311yescharacteristic
166C22⋊D11—41no—
167C22⋊D11—41no—
168C22⋊D11—41no—
169C22⋊D11—41no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—81no—
184C2×Dic11—81no—
185C2×Dic11—81no—
186C4×D11—81no—
187C4×D11—81no—
188C8×C11—81no—
189C11⋊C8—81no—
190C2×C4×D4—111no—
191C2×#99—221no—
192C2×C22⋊C8—111no—
193C2×C22⋊C8C2×D1111yescharacteristic
194#388—221no—
195#387—221no—
196#386—221no—
197#383—111no—
198#381—111no—
199#380—111no—
200#380—111no—
201#380C2×D1111yescharacteristic
202C4×C22⋊C4—111no—
203C4×C22⋊C4—221no—
204#376—111no—
205C2×#95C2×D1111yescharacteristic
206#342—221no—
207#324—221no—
208#323—221no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11#38111yescharacteristic
220C22×C11#41611yescharacteristic
221C22×C11#41711yescharacteristic
222C22×C11#48211yescharacteristic
223C22×C11#48211yescharacteristic
224C22×C11#48511yescharacteristic
225C22×C11#48511yescharacteristic
226C2×D11—41no—
227C2×D11—41no—
228C2×D11—41no—
229C2×D11—81no—
230C2×D11—81no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—42no—
236C4×C11—81no—
237C4×C11—161no—
238Dic11—41no—
239Dic11—41no—
240Dic11—41no—
241Dic11—81no—
242Dic11—81no—
243Dic11—161no—
244C22×D4—111no—
245C23×C4—21no—
246C23×C4—111no—
247C23×C4C22×D1111yescharacteristic
248C22×C8—21no—
249C22×C8—221no—
250C4×D4—221no—
251C4×D4—221no—
252C4×D4—221no—
253C4×D4—221no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—221no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—111no—
260C2×C22⋊C4—111no—
261C2×C22⋊C4—221no—
262C2×C22⋊C4—221no—
263C2×C22⋊C4—221no—
264C2×C22⋊C4—221no—
265C2×C42—111no—
266C2×C42—221no—
267C2×C42—221no—
268#99—442no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271C22⋊C8—221no—
272C22⋊C8—221no—
273#95—21no—
274#95—21no—
275#95—111no—
276#95—111no—
277#95—221no—
278#95—221no—
279#95—221no—
280#95—221no—
281#95—221no—
282#95C4×D1111yescharacteristic
283#95C4×D1111yescharacteristic
284C2×C11—21no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11—21no—
290C2×C11#182511yescharacteristic
291C2×C11#182711yescharacteristic
292C2×C11#182811yescharacteristic
293D11—81no—
294C24—111no—
295C24D4×D1111yescharacteristic
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—221no—
299C2×D4—221no—
300C2×D4—221no—
301C2×D4—221no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—42no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—81no—
309C22×C4—81no—
310C22×C4—111no—
311C22×C4—111no—
312C22×C4—111no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—441no—
318C22×C4—881no—
319C22×C4C2×C4×D1111yescharacteristic
320C22×C4#433911yescharacteristic
321C22×C4#433911yescharacteristic
322C22×C4D4×D1111yescharacteristic
323C22×C4#434111yescharacteristic
324C22×C4#434311yescharacteristic
325C2×C8—41no—
326C2×C8—81no—
327C2×C8—441no—
328C2×C8—881no—
329C4⋊C4—81no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4—881no—
333C4⋊C4—881no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—221no—
337C22⋊C4—221no—
338C22⋊C4—221no—
339C22⋊C4—221no—
340C22⋊C4—442no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C22⋊C4—441no—
345C22⋊C4—881no—
346C42—221no—
347C42—221no—
348C42—442no—
349C42—881no—
350C11#876311yescharacteristic, complemented, Sylow
351C23—41no—
352C23—41no—
353C23—221no—
354C23—221no—
355C23—221no—
356C23—441no—
357C23—441no—
358C23C22⋊C4×D1111yescharacteristic
359C23#6693611yescharacteristic
360C23#6694711yescharacteristic
361C23#6696511yescharacteristic
362C23#6696711yescharacteristic
363C23#6696911yescharacteristic
364C23#6697111yescharacteristic
365D4—441no—
366D4—441no—
367D4—441no—
368D4—441no—
369C2×C4—22no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—221no—
389C2×C4—221no—
390C2×C4—221no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—881no—
400C2×C4—881no—
401C2×C4—881no—
402C2×C4—881no—
403C2×C4—881no—
404C2×C4#6692511yescharacteristic
405C2×C4#6693611yescharacteristic
406C2×C4#6694511yescharacteristic
407C2×C4#6694711yescharacteristic
408C8—81no—
409C8—881no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—441no—
421C22—441no—
422C22—441no—
423C22—881no—
424C22—881no—
425C22#1062227711yescharacteristic
426C22#1062238511yescharacteristic
427C22#1062239711yescharacteristic
428C22#1062241611yescharacteristic
429C22#1062242811yescharacteristic
430C22#1062247911yescharacteristic
431C22#1062250111yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—42no—
437C4—81no—
438C4—161no—
439C4—441no—
440C4—441no—
441C4—441no—
442C4—881no—
443C4—881no—
444C4—1761no—
445C2—21no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—881no—
452C2#1306870911yescharacteristic
453C2#1306871911yescharacteristic
454C2#1306872311yescharacteristic
subgroupG/H
centerC22#10622277
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC22×C11#381
prime radicalC22×C22⋊D11D4
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#8763
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
4. #13066495C2semidirect
5. #13066484C2semidirect
6. #13066483C2semidirect
7. C11×#1294C2semidirect
19. #10622279C4semidirect
20. #10622277C4semidirect
22. #10622264C4semidirect
23. #10622261C4semidirect
128. #1294D11semidirect
350. C11#8763semidirect

Maximal subgroups

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

subgroupindex
#130715522
#130686012
#130669322
#130664952
#130664842
#130664832
C11×#12942
#876311