Finite Group Databasebeta

← #14727892

Subgroups — #14727892

Order 2816.

1172 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1172 conjugacy classes of subgroups — too many to draw. Only its 167 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
1C2×#10623014C211yesmaximal, characteristic, complemented
2#13079422C212yesmaximal, complemented
3#13067640C214yesmaximal, complemented
4#13067538C214yesmaximal, complemented
5#13067135C212yesmaximal, complemented
6#13066943C211yesmaximal, characteristic, complemented
7C11×#2539C211yesmaximal, characteristic
8C2×C11×#123—21no—
9C2×C11×#121C2211yescharacteristic
10C2×C11×#120—21no—
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×C22⋊Dic11—21no—
13C2×#66977—21no—
14C2×#66977C2212yes—
15#10623014—22no—
16#10623014—24no—
17#10623014C2214yes—
18C2×#66931—22no—
19C2×#66931—22no—
20C11×#399C2212yes—
21C11×#392C2212yes—
22C11×#390—22no—
23C4×C11×C22⋊C4C2211yescharacteristic
24#10622831C2214yescomplemented
25#10622820C2212yes—
26#10622655—24no—
27#10622653—22no—
28#10622646—22no—
29#10622583C2214yescomplemented
30#10622163C2214yes—
31#10622090C2218yescomplemented
32C25×C11D411yescharacteristic
33C22×D4×C11—21no—
34C22×D4×C11—22no—
35C22×D4×C11C2311yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×Dic11—21no—
39C23×Dic11—21no—
40C22×Dic22—21no—
41C22×Dic22D412yescomplemented
42C11×#123—44no—
43C11×#121—22no—
44C11×#121—22no—
45C11×#120—44no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4C2311yescharacteristic
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4D412yes—
55C2×C11×C22⋊C4C2312yes—
56C2×C42×C11—21no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—24no—
59C2×C22⋊Dic11—24no—
60C2×C22⋊Dic11—22no—
61C2×#4324—24no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11D412yescomplemented
64#66977—24no—
65#66977—22no—
66#66977—22no—
67#66977—24no—
68#66977D414yescomplemented
69#66977C2314yes—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×#4318—22no—
73#66931—28no—
74#66931—28no—
75#66931—28no—
76#66931—28no—
77C11×#95C2312yes—
78#66896—24no—
79C22⋊(C11⋊C8)—22no—
80C22⋊(C11⋊C8)C2314yes—
81#66874—24no—
82#66871—24no—
83#18318—111nomaximal, Sylow
84C24×C11—21no—
85C24×C11—21no—
86C24×C11—24no—
87C24×C11—21no—
88C24×C11—42no—
89C24×C11—81no—
90C24×C11C2×D411yescharacteristic
91C24×C11C2×D412yes—
92C2×D4×C11—22no—
93C2×D4×C11—44no—
94C2×D4×C11—42no—
95C2×D4×C11—42no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—44no—
99C2×D4×C11—81no—
100C2×D4×C11—82no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—42no—
106C22×C4×C11—81no—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2411yescharacteristic
112C22×Dic11—24no—
113C22×Dic11—24no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—82no—
117C22×Dic11—82no—
118C2×Dic22—24no—
119C2×Dic22—22no—
120C2×Dic22—82no—
121C2×Dic22—82no—
122C2×Dic22C2×D414yes—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—44no—
125C11×C22⋊C4—24no—
126C11×C22⋊C4—24no—
127C11×C22⋊C4—24no—
128C11×C22⋊C4—44no—
129C11×C22⋊C4—44no—
130C11×C22⋊C4—42no—
131C42×C11—81no—
132C22⋊Dic11—28no—
133C22⋊Dic11—24no—
134C22⋊Dic11—24no—
135#4324—84no—
136C4⋊Dic11—24no—
137C4⋊Dic11—22no—
138C4⋊Dic11C2×D414yes—
139Dic11⋊C4—28no—
140Dic11⋊C4—24no—
141Dic11⋊C4—24no—
142#4318—82no—
143C2×C11⋊C8—24no—
144C2×#543—111no—
145#3193—112no—
146#2539D1111yescharacteristic
147#1614—114no—
148#1596—114no—
149#1508—112no—
150#1462—111no—
151C23×C11—24no—
152C23×C11—24no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—22no—
157C23×C11—41no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—41no—
166C23×C11—42no—
167C23×C11—81no—
168C23×C11—81no—
169C23×C11—88no—
170C23×C11#12011yescharacteristic
171C23×C11#12011yescharacteristic
172C23×C11#13714yes—
173C23×C11C22×D411yescharacteristic
174D4×C11—44no—
175D4×C11—88no—
176D4×C11—82no—
177D4×C11—82no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—81no—
192C2×C4×C11#12012yes—
193C2×C4×C11C22×D412yes—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—44no—
197C2×Dic11—44no—
198C2×Dic11—84no—
199C2×Dic11—84no—
200Dic22—44no—
201Dic22—82no—
202Dic22—84no—
203C11⋊C8—44no—
204#543—114no—
205#543—224no—
206#543—222no—
207C2×#123—21no—
208C2×C22⋊Q8—112no—
209C2×C22⋊Q8—222no—
210C2×C22⋊Q8—222no—
211C2×C22⋊Q8—221no—
212C2×#121C2×D1111yescharacteristic
213C2×#120—21no—
214C22×C22⋊C4—221no—
215C22×C22⋊C4C2×D1111yescharacteristic
216#484—114no—
217#480—222no—
218#468—224no—
219#450—114no—
220#448—222no—
221#407—112no—
222#399C2×D1112yes—
223#392C2×D1112yes—
224#390—22no—
225C4×C22⋊C4C2×D1111yescharacteristic
226#328—118no—
227#323—114no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—24no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—44no—
237C22×C11—44no—
238C22×C11—48no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—82no—
242C22×C11—82no—
243C22×C11—82no—
244C22×C11—84no—
245C22×C11—81no—
246C22×C11—81no—
247C22×C11—81no—
248C22×C11#45312yes—
249C22×C11C2×#12011yescharacteristic
250C22×C11C2×#13712yes—
251C4×C11—22no—
252C4×C11—22no—
253C4×C11—44no—
254C4×C11—42no—
255C4×C11—81no—
256Dic11—44no—
257Dic11—44no—
258C25C22⋊D1111yescharacteristic
259C22×Q8—112no—
260C22×Q8—221no—
261C22×D4—21no—
262C22×D4—22no—
263C22×D4C22×D1111yescharacteristic
264C23×C4—221no—
265C23×C4—221no—
266C23×C4C22⋊D1111yescharacteristic
267C23×C4C22×D1111yescharacteristic
268C2×SD16—224no—
269C2×M16—222no—
270#123—44no—
271C22⋊Q8—114no—
272C22⋊Q8—114no—
273C22⋊Q8—228no—
274C22⋊Q8—228no—
275C22⋊Q8—228no—
276C22⋊Q8—228no—
277C22⋊Q8—224no—
278C22⋊Q8—222no—
279C22⋊Q8—222no—
280C22⋊Q8—224no—
281#121—22no—
282#121—22no—
283#120—44no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—112no—
286C2×C4⋊C4—222no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4C22×D1111yescharacteristic
290C2×C22⋊C4—21no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—222no—
297C2×C22⋊C4—224no—
298C2×C22⋊C4—222no—
299C2×C22⋊C4—224no—
300C2×C22⋊C4C22⋊D1112yes—
301C2×C22⋊C4C22×D1112yes—
302C2×C42—21no—
303#107—224no—
304#103—224no—
305#102—224no—
306C22⋊C8—114no—
307C22⋊C8—222no—
308#95C22×D1112yes—
309C2×C11—22no—
310C2×C11—22no—
311C2×C11—41no—
312C2×C11—44no—
313C2×C11—161no—
314C2×C11#300411yescharacteristic
315C2×C11C2×#45311yescharacteristic
316C2×C11#302611yescharacteristic
317C24—21no—
318C24—21no—
319C24—24no—
320C24—21no—
321C24—42no—
322C24—81no—
323C24C2×C22⋊D1111yescharacteristic
324C24C2×C22⋊D1112yes—
325C2×Q8—114no—
326C2×Q8—224no—
327C2×Q8—222no—
328C2×Q8—882no—
329C2×Q8—882no—
330C2×D4—22no—
331C2×D4—44no—
332C2×D4—42no—
333C2×D4—42no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—44no—
337C2×D4—81no—
338C2×D4—82no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—42no—
344C22×C4—81no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—224no—
348C22×C4—224no—
349C22×C4—882no—
350C22×C4—882no—
351C22×C4D4×D1112yes—
352C22×C4D4×D1112yes—
353C22×C4C2×C22⋊D1112yes—
354C22×C4C2×C22⋊D1111yescharacteristic
355C22×C4C23×D1111yescharacteristic
356SD16—884no—
357M16—882no—
358C2×C8—224no—
359C4⋊C4—22no—
360C4⋊C4—44no—
361C4⋊C4—114no—
362C4⋊C4—228no—
363C4⋊C4—224no—
364C4⋊C4—222no—
365C4⋊C4—224no—
366C4⋊C4—224no—
367C22⋊C4—24no—
368C22⋊C4—24no—
369C22⋊C4—24no—
370C22⋊C4—44no—
371C22⋊C4—44no—
372C22⋊C4—42no—
373C22⋊C4—228no—
374C22⋊C4—224no—
375C22⋊C4—224no—
376C42—81no—
377C11#1831811yescharacteristic, complemented, Sylow
378C23—24no—
379C23—24no—
380C23—22no—
381C23—22no—
382C23—22no—
383C23—22no—
384C23—41no—
385C23—42no—
386C23—42no—
387C23—42no—
388C23—41no—
389C23—41no—
390C23—42no—
391C23—42no—
392C23—41no—
393C23—42no—
394C23—81no—
395C23—81no—
396C23—88no—
397C23#6699011yescharacteristic
398C23#6699011yescharacteristic
399C23#6700414yes—
400C23C22×C22⋊D1111yescharacteristic
401Q8—444no—
402Q8—882no—
403Q8—884no—
404D4—44no—
405D4—88no—
406D4—82no—
407D4—82no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—81no—
422C2×C4—224no—
423C2×C4—224no—
424C2×C4—444no—
425C2×C4—444no—
426C2×C4—884no—
427C2×C4—884no—
428C2×C4#6699012yes—
429C2×C4C2×D4×D1112yes—
430C8—444no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—24no—
437C22—21no—
438C22—21no—
439C22—44no—
440C22—44no—
441C22—48no—
442C22—42no—
443C22—42no—
444C22—82no—
445C22—82no—
446C22—82no—
447C22—84no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22#1062269012yes—
452C22C2×#6699011yescharacteristic
453C22C2×#6700412yes—
454C4—22no—
455C4—22no—
456C4—44no—
457C4—42no—
458C4—81no—
459C4—444no—
460C4—444no—
461C2—22no—
462C2—22no—
463C2—41no—
464C2—44no—
465C2—161no—
466C2#1307784911yescharacteristic
467C2C2×#1062269011yescharacteristic
468C2#1307801211yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2539C2
socleC22×C11C2×#120
hypercenter#2539D11
hypocenterC11#18318
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2539

Complements

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

NH ≅ G/Ntype
1. C2×#10623014C2semidirect
2. #13079422C2semidirect
3. #13067640C2semidirect
4. #13067538C2semidirect
5. #13067135C2semidirect
6. #13066943C2semidirect
24. #10622831C22semidirect
29. #10622583C22semidirect
31. #10622090C22semidirect
41. C22×Dic22D4semidirect
63. C2×C4⋊Dic11D4semidirect
68. #66977D4semidirect
377. C11#18318semidirect

Maximal subgroups

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

subgroupindex
C2×#106230142
#130794222
#130676402
#130675382
#130671352
#130669432
C11×#25392
#1831811