Finite Group Databasebeta

← #14646754

Subgroups — #14646754

Order 2816.

456 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 97 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#13077306C211yesmaximal, characteristic
2#13068652C211yesmaximal, characteristic, complemented
3#13068643C211yesmaximal, characteristic, complemented
4#13067160C211yesmaximal, characteristic
5#13067157C211yesmaximal, characteristic
6#13066521C211yesmaximal, characteristic, complemented
7C11×#1305C211yesmaximal, characteristic, complemented
8#10623322C2211yescharacteristic
9C23×C11⋊C8C2211yescharacteristic
10C2×#66960C411yescharacteristic, complemented
11C11×#407C2211yescharacteristic
12C11×#407C2211yescharacteristic
13C11×#380C2211yescharacteristic
14#10622825C2211yescharacteristic
15#10622820C2211yescharacteristic
16#10622742C411yescharacteristic, complemented
17C2×#66886—21no—
18#10622735C411yescharacteristic, complemented
19#10622732C411yescharacteristic, complemented
20C2×#66871—21no—
21#10622343—21no—
22#10622343—21no—
23(C22⋊D11)⋊C8—21no—
24(C22⋊D11)⋊C8—21no—
25#10622196—21no—
26#10622167—21no—
27#10622108—21no—
28#10622105—21no—
29#10622090—21no—
30#10622089—21no—
31C23×C4×C11C2311yescharacteristic
32C2×#4339C2×C411yescharacteristic
33C2×C11×M16—21no—
34C2×C11×M16C2×C411yescharacteristic
35C2×C11×M16C2×C411yescharacteristic
36C2×C11×C4⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38#67006—21no—
39C2×C22⋊Dic11—21no—
40#66983D411yescharacteristic
41#66983Q811yescharacteristic
42#66982—21no—
43C4×C22⋊D11—21no—
44C4×C22⋊D11—21no—
45#66979C2×C411yescharacteristic
46C2×C4⋊Dic11—21no—
47#66977D411yescharacteristic
48#66977Q811yescharacteristic
49C2×#4318—21no—
50C22×C11⋊C8—42no—
51C22×C11⋊C8C2×C411yescharacteristic
52C22×C11⋊C8C2×C411yescharacteristic
53C22×C11⋊C8D411yescharacteristic
54C22×C11⋊C8D411yescharacteristic
55C22×C11⋊C8D411yescharacteristic
56C22×C11⋊C8D411yescharacteristic
57#66960—42no—
58C2×#4313—21no—
59C2×C8×D11—21no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×#95—21no—
65C11⋊#95—21no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68#66886—42no—
69(C2×D11)⋊C8—21no—
70(C2×D11)⋊C8—21no—
71#66879—21no—
72Dic11⋊C8—21no—
73Dic11⋊C8—21no—
74C8×Dic11—21no—
75#66871—42no—
76#8628—111nomaximal, Sylow
77C24×C11#4111yescharacteristic
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×Q811yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C2×C22⋊D11—21no—
88C2×C22⋊D11—21no—
89C2×C22⋊D11—21no—
90C22×Dic11—41no—
91#4339—41no—
92#4339—41no—
93C2×D44C4⋊C411yescharacteristic
94C2×C4×D11—21no—
95C2×Dic22C4⋊C411yescharacteristic
96C11×M16—41no—
97C11×M16—41no—
98C11×M16—41no—
99C11×M16—41no—
100C2×C8×C11—21no—
101C2×C8×C11—21no—
102C2×C8×C11—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—81no—
106C22⋊Dic11—21no—
107C22⋊Dic11—21no—
108C22⋊Dic11—21no—
109C22⋊Dic11—81no—
110(C2×D11)⋊C4—21no—
111(C2×D11)⋊C4—21no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11C4⋊C411yescharacteristic
115C4⋊Dic11C4⋊C411yescharacteristic
116Dic11⋊C4—21no—
117Dic11⋊C4—21no—
118C4×Dic11—21no—
119#4318—41no—
120#4318—41no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8C22⋊C411yescharacteristic
129C2×C11⋊C8C22⋊C411yescharacteristic
130C2×C11⋊C8C22⋊C411yescharacteristic
131C2×C11⋊C8C22⋊C411yescharacteristic
132#4313—42no—
133C8×D11—42no—
134#2929—111no—
135#1810—111no—
136#1808—111no—
137#1513—111no—
138#1513—111no—
139#1305—111no—
140#1305D1111yescharacteristic, complemented
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11#11711yescharacteristic
146C23×C11#12111yescharacteristic
147C23×C11C22⋊Q811yescharacteristic
148C22×D11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11C2×C22⋊C411yescharacteristic
162C2×C4×C11C2×C4⋊C411yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11C22⋊Q811yescharacteristic
165C22⋊D11—42no—
166C22⋊D11—42no—
167C22⋊D11—41no—
168C22⋊D11—41no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—81no—
173C2×Dic11—81no—
174C2×Dic11—81no—
175D44—41no—
176C4×D11—41no—
177C4×D11—41no—
178Dic22—41no—
179C8×C11—41no—
180C8×C11—41no—
181C8×C11—81no—
182C11⋊C8—21no—
183C11⋊C8—21no—
184C11⋊C8—21no—
185C11⋊C8—81no—
186C11⋊C8#9912yes—
187C2×#131—111no—
188C23×C8—111no—
189#525—111no—
190#435—221no—
191#435—221no—
192C8×D4—221no—
193C8×D4—221no—
194C2×#108—221no—
195C2×#107—221no—
196#424—111no—
197#408—111no—
198#407—111no—
199#407C2×D1111yescharacteristic
200#407C2×D1111yescharacteristic
201#405—111no—
202#380—111no—
203#380C2×D1111yescharacteristic
204#341—221no—
205#340—221no—
206#328—221no—
207#328—221no—
208#327—221no—
209#327—221no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—42no—
219C22×C11—42no—
220C22×C11#38011yescharacteristic
221C22×C11#47211yescharacteristic
222C22×C11#47311yescharacteristic
223C2×D11—41no—
224C2×D11—41no—
225C2×D11—41no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—161no—
230C4×C11C2×#9911yescharacteristic
231C4×C11#41011yescharacteristic
232Dic11—41no—
233Dic11—41no—
234Dic11—41no—
235Dic11—161no—
236C2×#41—111no—
237C23×C4C22×D1111yescharacteristic
238#131—442no—
239C2×M16—21no—
240C2×M16—221no—
241C2×M16—221no—
242C2×M16C4×D1111yescharacteristic
243C2×M16C4×D1111yescharacteristic
244C22×C8—111no—
245C22×C8—111no—
246C22×C8—111no—
247C22×C8—111no—
248C22×C8—111no—
249C22×C8—111no—
250C22×C8—221no—
251C22×C8—442no—
252#123—221no—
253C22⋊Q8—111no—
254C22⋊Q8—111no—
255#121—111no—
256#121—111no—
257#120—221no—
258C4×D4—221no—
259C4×D4—221no—
260#117—111no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—221no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—221no—
265#108—442no—
266#107—442no—
267C4⋊C8—221no—
268C4⋊C8—221no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—221no—
274C22⋊C8—221no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277#97—221no—
278C4×C8—221no—
279#95—21no—
280#95—221no—
281C2×C11—21no—
282C2×C11—21no—
283C2×C11—41no—
284C2×C11—41no—
285C2×C11#179911yescharacteristic
286C2×C11#181411yescharacteristic
287C2×C11#181611yescharacteristic
288D11—81no—
289C24#433911yescharacteristic
290#41—441no—
291#41—441no—
292C2×Q8—111no—
293C2×D4—111no—
294C2×D4—221no—
295C2×D4—221no—
296C2×D4—221no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—221no—
301C22×C4—441no—
302C22×C4C2×C4×D1111yescharacteristic
303C22×C4#433911yescharacteristic
304C22×C4D4×D1111yescharacteristic
305C22×C4D4×D1111yescharacteristic
306C22×C4D4×D1111yescharacteristic
307C22×C4Q8×D1111yescharacteristic
308M16—41no—
309M16—41no—
310M16—41no—
311M16—41no—
312M16—442no—
313M16—441no—
314M16—441no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—41no—
318C2×C8—111no—
319C2×C8—111no—
320C2×C8—111no—
321C2×C8—111no—
322C2×C8—222no—
323C2×C8—222no—
324C2×C8—222no—
325C2×C8—442no—
326C2×C8—441no—
327C2×C8—441no—
328C2×C8—441no—
329C2×C8—441no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—111no—
333C4⋊C4—111no—
334C4⋊C4—221no—
335C4⋊C4—221no—
336C4⋊C4—441no—
337C4⋊C4—441no—
338C22⋊C4—81no—
339C22⋊C4—221no—
340C22⋊C4—221no—
341C22⋊C4—221no—
342C22⋊C4—221no—
343C22⋊C4—221no—
344C22⋊C4—881no—
345C42—221no—
346C11#862811yescharacteristic, complemented, Sylow
347C23—21no—
348C23—21no—
349C23—41no—
350C23—41no—
351C23—221no—
352C23#6692511yescharacteristic
353C23#6693711yescharacteristic
354C23#6694911yescharacteristic
355Q8—441no—
356D4—441no—
357D4—442no—
358D4—442no—
359D4—441no—
360D4—441no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—221no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—881no—
379C2×C4—881no—
380C2×C4—881no—
381C2×C4C22⋊C4×D1111yescharacteristic
382C2×C4#6693711yescharacteristic
383C2×C4C4⋊C4×D1111yescharacteristic
384C2×C4#6694911yescharacteristic
385C8—41no—
386C8—41no—
387C8—81no—
388C8—112no—
389C8—221no—
390C8—221no—
391C8—221no—
392C8—881no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—42no—
402C22—42no—
403C22—441no—
404C22—441no—
405C22—441no—
406C22#1062228011yescharacteristic
407C22#1062236211yescharacteristic
408C22#1062236811yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—161no—
413C4—441no—
414C4—441no—
415C4—441no—
416C4—1761no—
417C4#1062235311yescharacteristic
418C4D11×#9911yescharacteristic
419C2—21no—
420C2—21no—
421C2—41no—
422C2—41no—
423C2—881no—
424C2#1306860311yescharacteristic
425C2#1306866911yescharacteristic
426C2#1306867911yescharacteristic
subgroupG/H
centerC22#10622280
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1305C2
socleC22×C11#380
prime radical#10623322C22
cosocleC23×C4×C11C23
hypercenter#1305D11
hypocenterC11#8628
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
2. #13068652C2semidirect
3. #13068643C2semidirect
6. #13066521C2semidirect
7. C11×#1305C2semidirect
10. C2×#66960C4semidirect
16. #10622742C4semidirect
18. #10622735C4semidirect
19. #10622732C4semidirect
140. #1305D11semidirect
346. C11#8628semidirect

Maximal subgroups

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

subgroupindex
#130773062
#130686522
#130686432
#130671602
#130671572
#130665212
C11×#13052
#862811