Finite Group Databasebeta

← #14656974

Subgroups — #14656974

Order 2816.

446 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 77 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#13069451C211yesmaximal, characteristic
2#13067144C211yesmaximal, characteristic
3#13067131C211yesmaximal, characteristic
4#13066522C211yesmaximal, characteristic, complemented
5#13066502C211yesmaximal, characteristic, complemented
6#13066468C211yesmaximal, characteristic, complemented
7C11×#2665C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C11×#400—21no—
10C11×#396—21no—
11C11×#395—21no—
12C11×#393—21no—
13C11×#391—21no—
14C11×#387—21no—
15C11×#381C2211yescharacteristic
16C11×#380C2211yescharacteristic
17C4×C11×C22⋊C4C2211yescharacteristic
18C4×C22⋊Dic11C2211yescharacteristic
19#10622820C2211yescharacteristic
20#10622820C2211yescharacteristic
21C2×#66870—21no—
22C2×#66870—21no—
23#10622089—21no—
24#10622089—21no—
25#10622089—21no—
26#10622089—21no—
27C22×Q8×C11—21no—
28C23×C4×C11C2311yescharacteristic
29C22×C22⋊D11—21no—
30C22×D44Q811yescharacteristic, complemented
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C42×C11—21no—
40C2×C22⋊Dic11—21no—
41#66983—21no—
42#66983—21no—
43#66983—21no—
44#66983—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11Q811yescharacteristic, complemented
47C2×C4×Dic11—21no—
48C2×#4318—21no—
49C2×#4318—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95D411yescharacteristic
57C11×#95D411yescharacteristic
58C11×#95D411yescharacteristic
59C11×#95D411yescharacteristic
60C11⋊#95—21no—
61C22⋊(C11⋊C8)—21no—
62C22⋊(C11⋊C8)—21no—
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65#66870—42no—
66#66870—42no—
67#10382—111nomaximal, Sylow
68C24×C11C2×D411yescharacteristic
69C23×D11—21no—
70C2×Q8×C11—42no—
71C2×Q8×C11—81no—
72C2×Q8×C11—81no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—81no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×Q811yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C2×C22⋊D11—41no—
90C2×C22⋊D11—41no—
91C2×C22⋊D11—41no—
92C22×Dic11—21no—
93C22×Dic11—41no—
94C2×D44—21no—
95C2×D44—21no—
96C2×D44—81no—
97C11×C4⋊C4—42no—
98C11×C4⋊C4—81no—
99C11×C4⋊C4—81no—
100C11×C4⋊C4—81no—
101C11×C22⋊C4—42no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—81no—
105C42×C11—81no—
106C22⋊Dic11—22no—
107C22⋊Dic11—41no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4×Dic11—81no—
113#4318—81no—
114#4318—81no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117#2665D1111yescharacteristic, complemented
118#1964—111no—
119#1510—111no—
120#1507—111no—
121#1305—111no—
122#1297—111no—
123#1284—111no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11#12011yescharacteristic
129C23×C11C22⋊Q811yescharacteristic
130C23×C11#12411yescharacteristic
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—81no—
135C22×D11—81no—
136Q8×C11—84no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
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—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11C22⋊Q811yescharacteristic
162C2×C4×C11C22⋊Q811yescharacteristic
163C2×C4×C11#12411yescharacteristic
164C2×C4×C11#12411yescharacteristic
165C22⋊D11—81no—
166C22⋊D11—81no—
167C22⋊D11—81no—
168C22⋊D11—81no—
169C2×Dic11—42no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—81no—
174C2×Dic11—81no—
175D44—81no—
176D44—81no—
177C11⋊C8—81no—
178C11⋊C8—81no—
179C2×#121—111no—
180C2×#99—221no—
181C2×#99—221no—
182#407—111no—
183#407—111no—
184#400—21no—
185#396—21no—
186#395—21no—
187#393—21no—
188#391—21no—
189#387—21no—
190#381C2×D1111yescharacteristic
191#380C2×D1111yescharacteristic
192C4×C22⋊C4—111no—
193C4×C22⋊C4C2×D1111yescharacteristic
194#327—221no—
195#327—221no—
196#327—221no—
197#327—221no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11#39311yescharacteristic
209C22×C11#45311yescharacteristic
210C22×C11#45411yescharacteristic
211C2×D11—81no—
212C2×D11—81no—
213C2×D11—81no—
214C2×D11—161no—
215C2×D11—161no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—42no—
221C4×C11—81no—
222C4×C11—81no—
223C4×C11—81no—
224C4×C11—81no—
225C4×C11—81no—
226Dic11—82no—
227Dic11—81no—
228C22×Q8—21no—
229C22×D4—111no—
230C22×D4—221no—
231C23×C4C22×D1111yescharacteristic
232C2×M16—221no—
233C2×M16—221no—
234#121—221no—
235#121—221no—
236#121—221no—
237#121—221no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—111no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—221no—
246C2×C22⋊C4—221no—
247C2×C22⋊C4C22⋊D1111yescharacteristic
248C2×C22⋊C4C22⋊D1111yescharacteristic
249C2×C42—21no—
250C2×C42—221no—
251#99—442no—
252#99—442no—
253C22⋊C8—221no—
254C22⋊C8—221no—
255C22⋊C8—221no—
256C22⋊C8—221no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—221no—
264#95C22⋊D1111yescharacteristic
265#95C22⋊D1111yescharacteristic
266#95C22⋊D1111yescharacteristic
267#95C22⋊D1111yescharacteristic
268C2×C11—21no—
269C2×C11—21no—
270C2×C11—41no—
271C2×C11—41no—
272C2×C11#202711yescharacteristic
273C2×C11#203111yescharacteristic
274C2×C11#203211yescharacteristic
275D11—161no—
276C24—221no—
277C24C2×C22⋊D1111yescharacteristic
278C2×Q8—42no—
279C2×Q8—81no—
280C2×Q8—81no—
281C2×D4—221no—
282C2×D4—221no—
283C2×D4—441no—
284C2×D4—441no—
285C2×D4—441no—
286C2×D4—441no—
287C2×D4—441no—
288C2×D4—441no—
289C2×D4—881no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—81no—
297C22×C4—221no—
298C22×C4—441no—
299C22×C4Q8×D1111yescharacteristic
300C22×C4#434311yescharacteristic
301C22×C4#434311yescharacteristic
302C22×C4#434311yescharacteristic
303C22×C4C2×C22⋊D1111yescharacteristic
304C22×C4C2×C22⋊D1111yescharacteristic
305M16—881no—
306M16—881no—
307C2×C8—441no—
308C2×C8—441no—
309C4⋊C4—42no—
310C4⋊C4—81no—
311C4⋊C4—81no—
312C4⋊C4—81no—
313C4⋊C4—221no—
314C4⋊C4—221no—
315C22⋊C4—42no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—81no—
319C22⋊C4—222no—
320C22⋊C4—441no—
321C22⋊C4—441no—
322C22⋊C4—441no—
323C42—81no—
324C42—881no—
325C11#1038211yescharacteristic, complemented, Sylow
326C23—21no—
327C23—21no—
328C23—41no—
329C23—41no—
330C23—441no—
331C23—441no—
332C23—441no—
333C23—881no—
334C23—881no—
335C23#6699911yescharacteristic
336C23#6700011yescharacteristic
337C23#6700611yescharacteristic
338Q8—84no—
339D4—881no—
340D4—881no—
341D4—881no—
342D4—881no—
343D4—881no—
344D4—881no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—442no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—881no—
374C2×C4—881no—
375C2×C4#6699911yescharacteristic
376C2×C4#6699911yescharacteristic
377C2×C4#6700011yescharacteristic
378C2×C4#6700011yescharacteristic
379C8—881no—
380C8—881no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—81no—
390C22—81no—
391C22—881no—
392C22—881no—
393C22—881no—
394C22—1761no—
395C22—1761no—
396C22#1062284411yescharacteristic
397C22#1062285411yescharacteristic
398C22#1062285811yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—81no—
405C4—81no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—882no—
410C4—881no—
411C2—21no—
412C2—21no—
413C2—41no—
414C2—41no—
415C2—1761no—
416C2#1306976911yescharacteristic
417C2#1306978511yescharacteristic
418C2#1306979211yescharacteristic
subgroupG/H
centerC22#10622844
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2665C2
socleC22×C11#393
prime radicalC2×#66983C22
hypercenter#2665D11
hypocenterC11#10382
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2665

Complements

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

NH ≅ G/Ntype
4. #13066522C2semidirect
5. #13066502C2semidirect
6. #13066468C2semidirect
7. C11×#2665C2semidirect
30. C22×D44Q8semidirect
46. C2×C4⋊Dic11Q8semidirect
117. #2665D11semidirect
325. C11#10382semidirect

Maximal subgroups

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

subgroupindex
#130694512
#130671442
#130671312
#130665222
#130665022
#130664682
C11×#26652
#1038211