Finite Group Databasebeta

← #14656938

Subgroups — #14656938

Order 2816.

464 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 89 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#13073840C211yesmaximal, characteristic, complemented
2#13069451C211yesmaximal, characteristic
3#13067185C211yesmaximal, characteristic
4C2×#10622089C211yesmaximal, characteristic
5#13066483C211yesmaximal, characteristic, complemented
6#13066463C211yesmaximal, characteristic, complemented
7C11×#1294C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C2×C11×C22⋊C8C2211yescharacteristic
10C11×#380C2211yescharacteristic
11C2×C11×#95C2211yescharacteristic
12#10622825—21no—
13#10622825C2211yescharacteristic
14#10622823—21no—
15C4×C22⋊Dic11C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×#66870—21no—
18C2×#66870—21no—
19#10622274—21no—
20#10622273—21no—
21#10622268—21no—
22#10622267—21no—
23#10622108—21no—
24#10622108—21no—
25#10622089—21no—
26#10622089—21no—
27C23×C4×C11—21no—
28C23×C4×C11C2311yescharacteristic
29C22×C22⋊D11—21no—
30C22×D44Q811yescharacteristic
31C22×C8×C11—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11D411yescharacteristic
36C2×C22⋊Dic11D411yescharacteristic
37#66983—21no—
38#66983—21no—
39#66983—21no—
40#66983—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11Q811yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11—21no—
49C22×C11⋊C8—21no—
50C11×C22⋊C8—21no—
51C11×C22⋊C8—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95D411yescharacteristic
55C11×#95D411yescharacteristic
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95D411yescharacteristic
62C11⋊#95D411yescharacteristic
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65#66870—42no—
66#66870—42no—
67#10376—111nomaximal, Sylow
68C24×C11C2×D411yescharacteristic
69C23×D11—21no—
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×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×Q811yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C2×C22⋊D11—41no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—81no—
98C2×C8×C11—41no—
99C2×C8×C11—81no—
100C11×C4⋊C4—81no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C22⋊Dic11—21no—
104C22⋊Dic11—21no—
105C22⋊Dic11—21no—
106C22⋊Dic11—21no—
107C22⋊Dic11—41no—
108C22⋊Dic11—41no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—42no—
114C4⋊Dic11—81no—
115C4⋊Dic11—81no—
116Dic11⋊C4—42no—
117Dic11⋊C4—81no—
118C4×Dic11—81no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—81no—
121#2569—111no—
122#1964—111no—
123#1519—111no—
124C2×#327—111no—
125#1294D1111yescharacteristic, complemented
126#1289—111no—
127#1282—111no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11#12011yescharacteristic
131C23×C11C22⋊Q811yescharacteristic
132C23×C11#12411yescharacteristic
133C23×C11#13511yescharacteristic
134C23×C11#13511yescharacteristic
135C23×C11AGL(1,ℤ/8)11yescharacteristic
136C23×C11AGL(1,ℤ/8)11yescharacteristic
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—81no—
141C22×D11—81no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
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—82no—
155C2×C4×C11—82no—
156C2×C4×C11—81no—
157C2×C4×C11—81no—
158C2×C4×C11—81no—
159C2×C4×C11C22⋊Q811yescharacteristic
160C2×C4×C11C22⋊Q811yescharacteristic
161C2×C4×C11#12411yescharacteristic
162C2×C4×C11#12411yescharacteristic
163C22⋊D11—81no—
164C22⋊D11—81no—
165C22⋊D11—81no—
166C22⋊D11—81no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182D44—81no—
183D44—81no—
184C8×C11—81no—
185C11⋊C8—81no—
186C2×#121—111no—
187C2×#99—221no—
188C2×#99—221no—
189C2×C22⋊C8—111no—
190C2×C22⋊C8C2×D1111yescharacteristic
191#400—221no—
192#398—221no—
193#387—221no—
194#387—221no—
195#385—221no—
196#380—111no—
197#380—221no—
198#380C2×D1111yescharacteristic
199C4×C22⋊C4—111no—
200C2×#95C2×D1111yescharacteristic
201#327—221no—
202#327—221no—
203#327—221no—
204#327—221no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11#39311yescharacteristic
216C22×C11#44911yescharacteristic
217C22×C11#44911yescharacteristic
218C22×C11#47811yescharacteristic
219C22×C11#47811yescharacteristic
220C22×C11#48811yescharacteristic
221C22×C11#49011yescharacteristic
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—161no—
226C2×D11—161no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—42no—
232C4×C11—81no—
233C4×C11—161no—
234Dic11—81no—
235Dic11—81no—
236Dic11—81no—
237Dic11—81no—
238Dic11—81no—
239C22×D4—111no—
240C22×D4—221no—
241C23×C4—21no—
242C23×C4C22×D1111yescharacteristic
243C22×C8—21no—
244C22×C8—221no—
245#121—221no—
246#121—221no—
247#121—221no—
248#121—221no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4—221no—
253C2×C4⋊C4—221no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—221no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—111no—
258C2×C22⋊C4—111no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—221no—
261C2×C42—221no—
262#99—442no—
263#99—442no—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C22⋊C8—221no—
267C22⋊C8—221no—
268#95—21no—
269#95—21no—
270#95—111no—
271#95—111no—
272#95—221no—
273#95—221no—
274#95—221no—
275#95—221no—
276#95—221no—
277#95D4411yescharacteristic
278#95D4411yescharacteristic
279C2×C11—21no—
280C2×C11—21no—
281C2×C11—21no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—21no—
285C2×C11#202511yescharacteristic
286C2×C11#203111yescharacteristic
287C2×C11#203211yescharacteristic
288D11—161no—
289C24—221no—
290C24D4×D1111yescharacteristic
291C2×D4—221no—
292C2×D4—221no—
293C2×D4—441no—
294C2×D4—441no—
295C2×D4—441no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—881no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—42no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—81no—
307C22×C4—81no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—221no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4C2×D4411yescharacteristic
314C22×C4#433911yescharacteristic
315C22×C4#433911yescharacteristic
316C22×C4D4×D1111yescharacteristic
317C22×C4#434111yescharacteristic
318C22×C4Q8×D1111yescharacteristic
319C2×C8—41no—
320C2×C8—81no—
321C2×C8—441no—
322C2×C8—881no—
323C4⋊C4—81no—
324C4⋊C4—221no—
325C4⋊C4—221no—
326C4⋊C4—442no—
327C4⋊C4—442no—
328C4⋊C4—881no—
329C4⋊C4—881no—
330C4⋊C4—881no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—221no—
334C22⋊C4—221no—
335C22⋊C4—221no—
336C22⋊C4—221no—
337C22⋊C4—441no—
338C22⋊C4—441no—
339C22⋊C4—441no—
340C22⋊C4—441no—
341C42—881no—
342C11#1037611yescharacteristic, complemented, Sylow
343C23—41no—
344C23—41no—
345C23—441no—
346C23—441no—
347C23—441no—
348C23—881no—
349C23—881no—
350C23#6693511yescharacteristic
351C23#6693811yescharacteristic
352C23#6694911yescharacteristic
353C23#6696411yescharacteristic
354C23#6696711yescharacteristic
355C23#6696911yescharacteristic
356C23#6697211yescharacteristic
357D4—881no—
358D4—881no—
359D4—881no—
360D4—881no—
361D4—881no—
362D4—881no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4#6692811yescharacteristic
396C2×C4#6693811yescharacteristic
397C2×C4#6694911yescharacteristic
398C2×C4#6695011yescharacteristic
399C8—81no—
400C8—881no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—881no—
412C22—881no—
413C22—881no—
414C22—1761no—
415C22—1761no—
416C22#1062228611yescharacteristic
417C22#1062237711yescharacteristic
418C22#1062239411yescharacteristic
419C22#1062241311yescharacteristic
420C22#1062242411yescharacteristic
421C22#1062248411yescharacteristic
422C22#1062250411yescharacteristic
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—42no—
428C4—81no—
429C4—161no—
430C4—881no—
431C4—881no—
432C4—881no—
433C4—881no—
434C4—881no—
435C2—21no—
436C2—21no—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—21no—
441C2—1761no—
442C2#1306976111yescharacteristic
443C2#1306978911yescharacteristic
444C2#1306979411yescharacteristic
subgroupG/H
centerC22#10622286
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC22×C11#393
prime radicalC2×#66983C22
hypercenter#1294D11
hypocenterC11#10376
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
1. #13073840C2semidirect
5. #13066483C2semidirect
6. #13066463C2semidirect
7. C11×#1294C2semidirect
125. #1294D11semidirect
342. C11#10376semidirect

Maximal subgroups

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

subgroupindex
#130738402
#130694512
#130671852
C2×#106220892
#130664832
#130664632
C11×#12942
#1037611