Finite Group Databasebeta

← #14727879

Subgroups — #14727879

Order 2816.

1516 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1516 conjugacy classes of subgroups — too many to draw. Only its 183 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#13079413C212yesmaximal, complemented
2#13073547C211yesmaximal, characteristic, complemented
3#13067636C214yesmaximal, complemented
4#13067534C214yesmaximal, complemented
5#13067132C212yesmaximal, complemented
6#13066943C211yesmaximal, characteristic, complemented
7C2×C11×#534C211yesmaximal, characteristic, complemented
8C23×D4×C11—21no—
9C11×#534—24no—
10C11×#534—22no—
11C11×#534C2214yes—
12C2×C11×#123—22no—
13C2×C11×#121—21no—
14C2×C11×#121C2212yes—
15C2×C11×#120—22no—
16C22×C11×C22⋊C4C2211yescharacteristic
17C2×#67006—21no—
18C2×#66983C2211yescharacteristic, complemented
19C2×#66982—21no—
20#10622830—22no—
21C4×C22⋊Dic11C2211yescharacteristic, complemented
22#10622820C2212yescomplemented
23#10622652—24no—
24#10622649C2214yescomplemented
25#10622647C2214yescomplemented
26#10622581—22no—
27#10622573C2212yescomplemented
28#10622570—22no—
29#10622562C2212yescomplemented
30#10622175C2218yescomplemented
31#10622163C2214yescomplemented
32C25×C11—21no—
33C25×C11D411yescharacteristic
34C22×D4×C11—22no—
35C22×D4×C11—24no—
36C22×D4×C11—22no—
37C22×D4×C11—24no—
38C22×D4×C11—21no—
39C22×D4×C11—48no—
40C22×D4×C11D412yescomplemented
41C23×C4×C11—21no—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—21no—
45C22×C22⋊D11—22no—
46C22×D44C2311yescharacteristic, complemented
47C11×#123—28no—
48C11×#123—28no—
49C11×#121—24no—
50C11×#121—24no—
51C11×#121—22no—
52C11×#121—22no—
53C11×#121D414yescomplemented
54C11×#121C2314yes—
55C11×#120—28no—
56C11×#120—28no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4D412yescomplemented
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4D412yes—
64C2×C11×C22⋊C4C2312yes—
65#67006—44no—
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—22no—
68C2×#4323—24no—
69#66983—22no—
70#66983—22no—
71#66982—44no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—21no—
74C2×C4⋊Dic11C2311yescharacteristic, complemented
75C2×Dic11⋊C4—22no—
76C2×C4×Dic11—21no—
77C2×#4318—22no—
78#66896—24no—
79C11⋊#95C2312yescomplemented
80C22⋊(C11⋊C8)—22no—
81C22⋊(C11⋊C8)C2314yescomplemented
82#66873—24no—
83#66872—24no—
84#18316—111nomaximal, Sylow
85C24×C11—21no—
86C24×C11—21no—
87C24×C11—24no—
88C24×C11—24no—
89C24×C11—22no—
90C24×C11—44no—
91C24×C11—42no—
92C24×C11—81no—
93C24×C11—82no—
94C24×C11—82no—
95C24×C11C2×D411yescharacteristic
96C24×C11C2×D412yes—
97C23×D11—21no—
98C2×D4×C11—28no—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—24no—
102C2×D4×C11—22no—
103C2×D4×C11—48no—
104C2×D4×C11—416no—
105C2×D4×C11—48no—
106C2×D4×C11—48no—
107C2×D4×C11—48no—
108C2×D4×C11—82no—
109C2×D4×C11—82no—
110C2×D4×C11C2×D414yes—
111C22×C4×C11—24no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—44no—
116C22×C4×C11—42no—
117C22×C4×C11—81no—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—42no—
124C2×C22⋊D11—42no—
125C2×C22⋊D11—44no—
126C2×C22⋊D11—41no—
127C2×C22⋊D11—41no—
128C2×C22⋊D11—44no—
129C2×C22⋊D11—82no—
130C22×Dic11—22no—
131C22×Dic11—21no—
132C2×D44—22no—
133C2×D44—81no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4C2×D414yes—
137C11×C22⋊C4—28no—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—24no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—24no—
142C22⋊Dic11—24no—
143C22⋊Dic11—44no—
144#4323—84no—
145(C2×D11)⋊C4—44no—
146(C2×D11)⋊C4—42no—
147C4⋊Dic11—22no—
148Dic11⋊C4—44no—
149C4×Dic11—81no—
150#4318—82no—
151C2×C11⋊C8—24no—
152C2×#534D1111yescharacteristic, complemented
153#3192—112no—
154#2539—111no—
155#1613—114no—
156#1595—114no—
157#1507—112no—
158#1462—111no—
159C23×C11—24no—
160C23×C11—24no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—24no—
166C23×C11—41no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—44no—
171C23×C11—48no—
172C23×C11—44no—
173C23×C11—42no—
174C23×C11—44no—
175C23×C11—81no—
176C23×C11—81no—
177C23×C11—88no—
178C23×C11—84no—
179C23×C11—84no—
180C23×C11—816no—
181C23×C11#12011yescharacteristic
182C23×C11#12011yescharacteristic
183C23×C11AGL(1,ℤ/8)14yes—
184C23×C11C22×D411yescharacteristic
185C22×D11—41no—
186C22×D11—42no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—42no—
190D4×C11—44no—
191D4×C11—416no—
192D4×C11—48no—
193D4×C11—48no—
194D4×C11—82no—
195D4×C11—84no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—42no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—44no—
203C2×C4×C11—48no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—81no—
207C2×C4×C11#12012yes—
208C2×C4×C11C22×D412yes—
209C22⋊D11—88no—
210C22⋊D11—82no—
211C22⋊D11—82no—
212C2×Dic11—24no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218D44—44no—
219C11⋊C8—44no—
220C23×D4—21no—
221#534—24no—
222#534—22no—
223#534C2×D1114yes—
224C2×#123—22no—
225C2×#123—221no—
226C2×#121—21no—
227C2×#121—111no—
228C2×#121C2×D1112yes—
229C2×#120—22no—
230C2×#120—221no—
231C22×C22⋊C4C2×D1111yescharacteristic
232#481—114no—
233#481—222no—
234#469—224no—
235#447—114no—
236#447—222no—
237#407—112no—
238#399—112no—
239#392—112no—
240#390—222no—
241C4×C22⋊C4—111no—
242#327—118no—
243#323—114no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—24no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—44no—
253C22×C11—44no—
254C22×C11—48no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—44no—
258C22×C11—44no—
259C22×C11—44no—
260C22×C11—82no—
261C22×C11—88no—
262C22×C11—84no—
263C22×C11—816no—
264C22×C11#45312yes—
265C22×C11C2×#12011yescharacteristic
266C22×C11C2×AGL(1,ℤ/8)12yes—
267C2×D11—82no—
268C2×D11—82no—
269C2×D11—81no—
270C2×D11—81no—
271C2×D11—81no—
272C4×C11—22no—
273C4×C11—22no—
274C4×C11—44no—
275C4×C11—42no—
276Dic11—44no—
277Dic11—81no—
278C25—21no—
279C25C22⋊D1111yescharacteristic
280C22×D4—22no—
281C22×D4—24no—
282C22×D4—22no—
283C22×D4—24no—
284C22×D4—21no—
285C22×D4—48no—
286C22×D4—111no—
287C22×D4—221no—
288C22×D4—222no—
289C22×D4C22⋊D1112yescomplemented
290C23×C4—21no—
291C23×C4C22⋊D1111yescharacteristic
292C23×C4C22×D1111yescharacteristic
293C2×D8—224no—
294C2×M16—222no—
295#123—28no—
296#123—28no—
297#123—444no—
298#121—24no—
299#121—24no—
300#121—22no—
301#121—22no—
302#121—222no—
303#121—222no—
304#121C22⋊D1114yescomplemented
305#121C22×D1114yes—
306#120—28no—
307#120—28no—
308#120—444no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4C22⋊D1112yescomplemented
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—221no—
318C2×C22⋊C4—222no—
319C2×C22⋊C4—221no—
320C2×C22⋊C4—222no—
321C2×C22⋊C4C22⋊D1112yes—
322C2×C22⋊C4C22×D1112yes—
323C2×C42—221no—
324#106—224no—
325#102—224no—
326#102—224no—
327C22⋊C8—114no—
328C22⋊C8—222no—
329#95—112no—
330C2×C11—22no—
331C2×C11—22no—
332C2×C11—41no—
333C2×C11—44no—
334C2×C11—84no—
335C2×C11#300311yescharacteristic
336C2×C11C2×#45311yescharacteristic
337C2×C11#302611yescharacteristic
338D11—161no—
339C24—21no—
340C24—24no—
341C24—21no—
342C24—24no—
343C24—22no—
344C24—44no—
345C24—42no—
346C24—81no—
347C24—82no—
348C24—82no—
349C24—221no—
350C24C2×C22⋊D1111yescharacteristic
351C24C2×C22⋊D1112yes—
352C2×D4—28no—
353C2×D4—24no—
354C2×D4—24no—
355C2×D4—24no—
356C2×D4—22no—
357C2×D4—48no—
358C2×D4—416no—
359C2×D4—48no—
360C2×D4—48no—
361C2×D4—48no—
362C2×D4—82no—
363C2×D4—82no—
364C2×D4—222no—
365C2×D4—444no—
366C2×D4—442no—
367C2×D4—442no—
368C2×D4—444no—
369C2×D4—441no—
370C2×D4—441no—
371C2×D4—881no—
372C2×D4—882no—
373C2×D4C2×C22⋊D1114yes—
374C22×C4—24no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—44no—
379C22×C4—42no—
380C22×C4—81no—
381C22×C4—222no—
382C22×C4—221no—
383C22×C4C2×C22⋊D1112yes—
384C22×C4C2×C22⋊D1111yescharacteristic
385C22×C4C2×C22⋊D1112yes—
386C22×C4C2×C22⋊D1112yes—
387C22×C4C23×D1111yescharacteristic
388D8—884no—
389M16—882no—
390C2×C8—224no—
391C4⋊C4—24no—
392C4⋊C4—22no—
393C4⋊C4—222no—
394C4⋊C4—444no—
395C4⋊C4C2×C22⋊D1114yes—
396C22⋊C4—28no—
397C22⋊C4—24no—
398C22⋊C4—24no—
399C22⋊C4—24no—
400C22⋊C4—24no—
401C22⋊C4—224no—
402C22⋊C4—444no—
403C22⋊C4—444no—
404C22⋊C4—442no—
405C42—881no—
406C11#1831611yescharacteristic, complemented, Sylow
407C23—24no—
408C23—24no—
409C23—22no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—24no—
414C23—41no—
415C23—42no—
416C23—42no—
417C23—42no—
418C23—44no—
419C23—48no—
420C23—44no—
421C23—42no—
422C23—44no—
423C23—81no—
424C23—81no—
425C23—88no—
426C23—84no—
427C23—84no—
428C23—816no—
429C23—441no—
430C23—441no—
431C23—442no—
432C23—442no—
433C23—441no—
434C23#6698514yes—
435C23#6700611yescharacteristic
436C23#6700611yescharacteristic
437C23C22×C22⋊D1111yescharacteristic
438D4—44no—
439D4—416no—
440D4—48no—
441D4—48no—
442D4—82no—
443D4—84no—
444D4—444no—
445D4—888no—
446D4—882no—
447D4—882no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—44no—
455C2×C4—48no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—81no—
459C2×C4—224no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4#6700612yes—
466C2×C4C22×C22⋊D1112yes—
467C8—444no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—24no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—44no—
477C22—44no—
478C22—48no—
479C22—42no—
480C22—42no—
481C22—44no—
482C22—44no—
483C22—44no—
484C22—82no—
485C22—88no—
486C22—84no—
487C22—816no—
488C22—882no—
489C22—882no—
490C22—881no—
491C22—881no—
492C22—881no—
493C22#1062285412yes—
494C22C2×#6698512yes—
495C22C2×#6700611yescharacteristic
496C4—22no—
497C4—22no—
498C4—44no—
499C4—42no—
500C4—444no—
501C4—881no—
502C2—22no—
503C2—22no—
504C2—41no—
505C2—44no—
506C2—84no—
507C2—1761no—
508C2#1307784311yescharacteristic
509C2C2×#1062285411yescharacteristic
510C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#534C2
socleC22×C11C2×#120
hypercenterC2×#534D11
hypocenterC11#18316
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. #13079413C2semidirect
2. #13073547C2semidirect
3. #13067636C2semidirect
4. #13067534C2semidirect
5. #13067132C2semidirect
6. #13066943C2semidirect
7. C2×C11×#534C2semidirect
18. C2×#66983C22semidirect
21. C4×C22⋊Dic11C22semidirect
22. #10622820C22semidirect
24. #10622649C22semidirect
25. #10622647C22semidirect
27. #10622573C22semidirect
29. #10622562C22semidirect
30. #10622175C22semidirect
31. #10622163C22semidirect
40. C22×D4×C11D4semidirect
46. C22×D44C23semidirect
53. C11×#121D4semidirect
58. C2×C11×C4⋊C4D4semidirect
74. C2×C4⋊Dic11C23semidirect
79. C11⋊#95C23semidirect
81. C22⋊(C11⋊C8)C23semidirect
152. C2×#534D11semidirect
289. C22×D4C22⋊D11semidirect
304. #121C22⋊D11semidirect
312. C2×C4⋊C4C22⋊D11semidirect
406. C11#18316semidirect

Maximal subgroups

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

subgroupindex
#130794132
#130735472
#130676362
#130675342
#130671322
#130669432
C2×C11×#5342
#1831611