Finite Group Databasebeta

← #14654151

Subgroups — #14654151

Order 2816.

768 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 85 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#13078556C211yesmaximal, characteristic, complemented
2#13073547C211yesmaximal, characteristic
3#13068715C211yesmaximal, characteristic, complemented
4#13067144C211yesmaximal, characteristic, complemented
5#13066943C211yesmaximal, characteristic, complemented
6#13066468C211yesmaximal, characteristic, complemented
7C11×#2482C211yesmaximal, characteristic, complemented
8C2×C11×#117C2211yescharacteristic
9C22×C11×C22⋊C4C2211yescharacteristic
10C2×#67006—21no—
11C2×#66983C2211yescharacteristic
12C2×#66982—21no—
13C11×#399—21no—
14C11×#397—21no—
15C11×#388—22no—
16C11×#385—21no—
17C11×#381C2211yescharacteristic
18C11×#379—21no—
19C4×C22⋊Dic11C2211yescharacteristic
20#10622820C2211yescharacteristic
21#10622820C2211yescharacteristic
22#10622616—22no—
23#10622614—21no—
24#10622608—21no—
25#10622581—21no—
26#10622580—21no—
27#10622573—21no—
28#10622570—22no—
29#10622562—21no—
30#10622170—22no—
31#10622163—22no—
32#10622089—22no—
33C25×C11D411yescharacteristic
34C23×C4×C11D411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C22×C22⋊D11—21no—
37C22×C22⋊D11—22no—
38C22×D44D411yescharacteristic
39C11×#117—21no—
40C11×#117—21no—
41C11×#117—21no—
42C11×#117—21no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4D411yescharacteristic, complemented
45C2×C11×C4⋊C4D411yescharacteristic, complemented
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—21no—
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—22no—
56C2×C42×C11—21no—
57#67006—44no—
58C2×C22⋊Dic11—21no—
59C2×C22⋊Dic11—22no—
60#66983—21no—
61#66983—21no—
62#66983—21no—
63#66983—21no—
64#66982—44no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—21no—
67C2×C4⋊Dic11D411yescharacteristic
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11D412yes—
70C2×#4318—21no—
71C2×#4318—21no—
72C11×#95—22no—
73C11×#95—21no—
74C11×#95D412yescomplemented
75C11⋊#95—21no—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)—21no—
78C22⋊(C11⋊C8)—21no—
79C22⋊(C11⋊C8)D412yescomplemented
80#66873—22no—
81#66873—22no—
82#66872—22no—
83#66871—22no—
84#9940—111nomaximal, Sylow
85C24×C11—21no—
86C24×C11—21no—
87C24×C11—21no—
88C24×C11—42no—
89C24×C11—42no—
90C24×C11—42no—
91C24×C11C2×D411yescharacteristic
92C23×D11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C2×C22⋊D11—42no—
108C2×C22⋊D11—42no—
109C2×C22⋊D11—44no—
110C2×C22⋊D11—44no—
111C2×C22⋊D11—41no—
112C2×C22⋊D11—41no—
113C2×C22⋊D11—82no—
114C22×Dic11—22no—
115C22×Dic11—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44—42no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—82no—
124C11×C22⋊C4—42no—
125C11×C22⋊C4—44no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—82no—
133C42×C11—41no—
134C42×C11—41no—
135C22⋊Dic11—24no—
136C22⋊Dic11—44no—
137(C2×D11)⋊C4—44no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142Dic11⋊C4—44no—
143C4×Dic11—42no—
144#4318—42no—
145#4318—42no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—41no—
148#3094—111no—
149#2539—111no—
150#2482D1111yescharacteristic, complemented
151#1826—111no—
152#1510—111no—
153#1462—111no—
154#1284—111no—
155C23×C11—22no—
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—22no—
160C23×C11—41no—
161C23×C11—42no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—42no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—81no—
170C23×C11—81no—
171C23×C11—88no—
172C23×C11#12011yescharacteristic
173C23×C11#12011yescharacteristic
174C23×C11#12111yescharacteristic
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—42no—
178C22×D11—41no—
179C22×D11—42no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—81no—
197C2×C4×C11#12011yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12711yescharacteristic
201C22⋊D11—88no—
202C22⋊D11—82no—
203C22⋊D11—82no—
204C2×Dic11—24no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210D44—42no—
211D44—81no—
212C11⋊C8—42no—
213C11⋊C8—81no—
214C2×#123—221no—
215C2×#121—111no—
216C2×#120—221no—
217C2×#117C2×D1111yescharacteristic
218C22×C22⋊C4C2×D1111yescharacteristic
219#482—222no—
220#481—221no—
221#480—221no—
222#428—221no—
223#418—221no—
224#407—111no—
225#407—111no—
226#399—21no—
227#399—221no—
228#397—21no—
229#392—221no—
230#390—222no—
231#388—22no—
232#385—21no—
233#381C2×D1111yescharacteristic
234#379—21no—
235C4×C22⋊C4—111no—
236#339—222no—
237#327—222no—
238#323—222no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—44no—
247C22×C11—44no—
248C22×C11—44no—
249C22×C11—42no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11—82no—
253C22×C11—82no—
254C22×C11—81no—
255C22×C11—81no—
256C22×C11#39211yescharacteristic
257C22×C11#45312yes—
258C22×C11#45812yes—
259C2×D11—82no—
260C2×D11—82no—
261C2×D11—81no—
262C2×D11—81no—
263C2×D11—81no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—82no—
269C4×C11—81no—
270C4×C11—81no—
271C4×C11—81no—
272Dic11—44no—
273Dic11—81no—
274C25C22⋊D1111yescharacteristic
275C22×D4—111no—
276C22×D4—221no—
277C22×D4—222no—
278C23×C4C22⋊D1111yescharacteristic
279C23×C4C22×D1111yescharacteristic
280C2×M16—221no—
281C2×M16—221no—
282#123—444no—
283#121—221no—
284#121—221no—
285#121—221no—
286#121—221no—
287#120—444no—
288#117—21no—
289#117—21no—
290#117—21no—
291#117—21no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4C22⋊D1111yescharacteristic, complemented
296C2×C4⋊C4C22⋊D1111yescharacteristic, complemented
297C2×C22⋊C4—22no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—221no—
308C2×C22⋊C4—222no—
309C2×C22⋊C4—222no—
310C2×C22⋊C4—221no—
311C2×C42—21no—
312C2×C42—112no—
313#107—222no—
314#106—222no—
315#102—222no—
316#102—222no—
317C22⋊C8—112no—
318C22⋊C8—221no—
319C22⋊C8—221no—
320C22⋊C8—221no—
321#95—22no—
322#95—21no—
323#95—221no—
324#95C22⋊D1112yescomplemented
325C2×C11—22no—
326C2×C11—22no—
327C2×C11—41no—
328C2×C11—82no—
329C2×C11#200211yescharacteristic
330C2×C11#201011yescharacteristic
331C2×C11#202211yescharacteristic
332D11—161no—
333C24—21no—
334C24—21no—
335C24—21no—
336C24—42no—
337C24—42no—
338C24—42no—
339C24—221no—
340C24C2×C22⋊D1111yescharacteristic
341C2×D4—221no—
342C2×D4—221no—
343C2×D4—442no—
344C2×D4—444no—
345C2×D4—442no—
346C2×D4—442no—
347C2×D4—444no—
348C2×D4—441no—
349C2×D4—441no—
350C2×D4—882no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—222no—
360C22×C4—221no—
361C22×C4D4×D1111yescharacteristic
362C22×C4D4×D1111yescharacteristic
363C22×C4D4×D1111yescharacteristic
364C22×C4#434111yescharacteristic
365C22×C4C2×C22⋊D1111yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367M16—442no—
368M16—442no—
369C2×C8—222no—
370C2×C8—441no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—82no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—444no—
379C22⋊C4—42no—
380C22⋊C4—44no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—82no—
388C22⋊C4—224no—
389C22⋊C4—444no—
390C22⋊C4—444no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C42—41no—
394C42—41no—
395C42—442no—
396C11#994011yescharacteristic, complemented, Sylow
397C23—22no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—22no—
402C23—41no—
403C23—42no—
404C23—41no—
405C23—41no—
406C23—42no—
407C23—41no—
408C23—41no—
409C23—42no—
410C23—42no—
411C23—81no—
412C23—81no—
413C23—88no—
414C23—441no—
415C23—441no—
416C23—442no—
417C23—441no—
418C23—442no—
419C23#6699011yescharacteristic
420C23#6699211yescharacteristic
421C23#6700611yescharacteristic
422D4—442no—
423D4—881no—
424D4—888no—
425D4—882no—
426D4—882no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—81no—
444C2×C4—224no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4#6699011yescharacteristic
451C2×C4#6699111yescharacteristic
452C2×C4#6699211yescharacteristic
453C2×C4#6699311yescharacteristic
454C8—442no—
455C8—881no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—44no—
464C22—44no—
465C22—44no—
466C22—42no—
467C22—82no—
468C22—82no—
469C22—82no—
470C22—82no—
471C22—81no—
472C22—81no—
473C22—882no—
474C22—882no—
475C22—881no—
476C22—881no—
477C22—881no—
478C22#1062266612yes—
479C22#1062283611yescharacteristic
480C22#1062285412yes—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—82no—
486C4—81no—
487C4—81no—
488C4—81no—
489C4—444no—
490C4—881no—
491C2—22no—
492C2—22no—
493C2—41no—
494C2—82no—
495C2—1761no—
496C2#1306962911yescharacteristic
497C2#1306968111yescharacteristic
498C2#1306974411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2482C2
socleC22×C11#392
prime radical#13073547C2
hypercenter#2482D11
hypocenterC11#9940
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2482

Complements

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

NH ≅ G/Ntype
1. #13078556C2semidirect
3. #13068715C2semidirect
4. #13067144C2semidirect
5. #13066943C2semidirect
6. #13066468C2semidirect
7. C11×#2482C2semidirect
44. C2×C11×C4⋊C4D4semidirect
45. C2×C11×C4⋊C4D4semidirect
74. C11×#95D4semidirect
79. C22⋊(C11⋊C8)D4semidirect
150. #2482D11semidirect
295. C2×C4⋊C4C22⋊D11semidirect
296. C2×C4⋊C4C22⋊D11semidirect
324. #95C22⋊D11semidirect
396. C11#9940semidirect

Maximal subgroups

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

subgroupindex
#130785562
#130735472
#130687152
#130671442
#130669432
#130664682
C11×#24822
#994011