Finite Group Databasebeta

← #14721526

Subgroups — #14721526

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082421C211yesmaximal, characteristic
2#13077696C211yesmaximal, characteristic
3#13071533C211yesmaximal, characteristic
4#13067179C211yesmaximal, characteristic
5#13067178C214yesmaximal
6#13067116C211yesmaximal, characteristic
7#13067115C211yesmaximal, characteristic
8#13067113C214yesmaximal
9C11×#1518C211yesmaximal, characteristic
10C11×#533C2211yescharacteristic
11#10623253C412yescomplemented
12#10623252C412yescomplemented
13#10623216—22no—
14#10623154—22no—
15#10623153C2214yes—
16#10623098—22no—
17#10623098C412yescomplemented
18Q8×Dic22C412yescomplemented
19#10623050—21no—
20#10623047—21no—
21C2×#66940—21no—
22#10623001C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C11×#431C2211yescharacteristic
25C11×#382C2211yescharacteristic
26#10622586—21no—
27C4×C4⋊Dic11C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622443—22no—
30#10622331C2214yes—
31C8×Dic22—22no—
32#10622263C2212yes—
33#10622262C2212yes—
34#10622260—22no—
35C11×#328C2214yes—
36#10622176C2212yes—
37#10622176C2212yes—
38#10622105C2212yes—
39#10622105C2212yes—
40#10622090C2214yes—
41C22×Dic22D411yescharacteristic
42C11×C4⋊Q8C2×C411yescharacteristic
43C11×C4⋊Q8C2×C411yescharacteristic
44C11×#125—21no—
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8C2312yes—
47C4×Q8×C11—21no—
48C4×Q8×C11C2×C412yes—
49C11×#117—21no—
50C2×C11×C4⋊C4—21no—
51C2×C42×C11C2311yescharacteristic
52Q8×Dic11C2×C414yes—
53#66997—24no—
54#66997C2×C414yes—
55#66979—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11D411yescharacteristic
58#66977—21no—
59#66977C2312yes—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4D412yes—
63C2×C4×Dic11—21no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11C2312yes—
66#66943—22no—
67#66942—24no—
68#66942—24no—
69#66942—24no—
70#66941—22no—
71#66941—24no—
72#66941C2×C414yes—
73#66940—22no—
74#66940—22no—
75#66940—24no—
76#66940—44no—
77#66940C2×C414yes—
78#66931—24no—
79#66930—24no—
80#66923—21no—
81#66923—22no—
82#66922—22no—
83#66922C2×C411yescharacteristic
84#66922C2×C411yescharacteristic
85C4×Dic22—22no—
86C4×Dic22—22no—
87C4×Dic22—21no—
88C4×Dic22C2×C412yes—
89C4×Dic22C2×C412yes—
90C4×Dic22C2×C412yes—
91C4×Dic22D412yes—
92C4×Dic22D412yes—
93C11×C4⋊C8—21no—
94C11×C22⋊C8C2312yes—
95C4×C8×C11—21no—
96C11×#95—21no—
97C11×#95C2312yes—
98C11⋊#95—22no—
99C11⋊#95C2311yescharacteristic
100C11⋊#95C2311yescharacteristic
101C22⋊(C11⋊C8)C2312yes—
102Dic11⋊C8—24no—
103C8×Dic11—24no—
104C4⋊(C11⋊C8)—21no—
105C4×C11⋊C8—21no—
106#17619—111nomaximal, Sylow
107C2×Q8×C11—21no—
108C2×Q8×C11C22×C412yes—
109C22×C4×C11—22no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11C2×D412yes—
116C22×Dic11C2×D412yes—
117C2×Dic22—24no—
118C2×Dic22—21no—
119C2×Dic22C22⋊C412yes—
120C2×Dic22C22⋊C412yes—
121C2×Dic22SD1614yes—
122C2×Dic22Q1614yes—
123C2×Dic22C22×C412yes—
124C2×C8×C11—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4C22×C412yes—
132C11×C22⋊C4—22no—
133C42×C11—22no—
134C42×C11C22×C411yescharacteristic
135C42×C11C22×C411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C22⋊Dic11—22no—
139C4⋊Dic11—24no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—42no—
144C4⋊Dic11C22⋊C412yes—
145C4⋊Dic11C22⋊C412yes—
146C4⋊Dic11C22×C412yes—
147Dic11⋊C4—24no—
148Dic11⋊C4—24no—
149Dic11⋊C4—24no—
150Dic11⋊C4—24no—
151Dic11⋊C4—22no—
152Dic11⋊C4—22no—
153Dic11⋊C4—44no—
154Dic11⋊C4—44no—
155Dic11⋊C4C22⋊C414yes—
156Dic11⋊C4C22⋊C414yes—
157C4×Dic11—24no—
158C4×Dic11—24no—
159C4×Dic11—22no—
160C4×Dic11—44no—
161C4×Dic11—42no—
162C4×Dic11C22×C414yes—
163C4×Dic11C2×D414yes—
164C2×C11⋊C8—22no—
165#3502—111no—
166#2982—111no—
167#2351—111no—
168#1518—111no—
169#1518—114no—
170#1518D1111yescharacteristic
171#1503—111no—
172#1503—114no—
173#1503—111no—
174C23×C11C22×D411yescharacteristic
175Q8×C11—42no—
176Q8×C11—81no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11C2×C22⋊C411yescharacteristic
185C2×C4×C11C2×C22⋊C411yescharacteristic
186C2×C4×C11C2×C22⋊C411yescharacteristic
187C2×C4×C11C2×C22⋊C411yescharacteristic
188C2×C4×C11C2×SD1612yes—
189C2×C4×C11C2×Q1612yes—
190C2×C4×C11C23×C411yescharacteristic
191C2×C4×C11C22×D411yescharacteristic
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—42no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11C2×C22⋊C414yes—
202C2×Dic11C2×C22⋊C414yes—
203C2×Dic11C2×SD1614yes—
204C2×Dic11C2×Q1614yes—
205Dic22—42no—
206Dic22—84no—
207Dic22—81no—
208Dic22#10318yes—
209Dic22#10318yes—
210C8×C11—42no—
211C11⋊C8—42no—
212Q82—112no—
213Q82—112no—
214#557—112no—
215#557—112no—
216#557—222no—
217#557—222no—
218#544—221no—
219#544—222no—
220#533—114no—
221#533—111no—
222#533C2×D1111yescharacteristic
223#519—221no—
224C2×C4×Q8—111no—
225C2×C4×Q8—221no—
226C8×Q8—222no—
227C8×Q8—222no—
228#431—111no—
229#431—114no—
230#431C2×D1111yescharacteristic
231#389—222no—
232#389—221no—
233#382—112no—
234#382C2×D1111yescharacteristic
235C4×C4⋊C4—111no—
236C4×C4⋊C4—112no—
237#328—112no—
238#328—112no—
239#328—112no—
240#328—112no—
241#328—114no—
242#328C2×D1114yes—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11C22×C22⋊C411yescharacteristic
246C22×C11C22×SD1611yescharacteristic
247C22×C11C22×Q1611yescharacteristic
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—42no—
253C4×C11—42no—
254C4×C11—82no—
255C4×C11C2×#10312yes—
256C4×C11C2×#10312yes—
257Dic11—24no—
258Dic11—42no—
259Dic11—42no—
260Dic11—42no—
261Dic11—81no—
262Dic11C2×#10318yes—
263C22×Q8—111no—
264C4⋊Q8—114no—
265C4⋊Q8—114no—
266C4⋊Q8—111no—
267C4⋊Q8—111no—
268C4⋊Q8—222no—
269C4⋊Q8—224no—
270C4⋊Q8—222no—
271C4⋊Q8—224no—
272C4⋊Q8C4×D1111yescharacteristic
273C4⋊Q8C4×D1111yescharacteristic
274#125—21no—
275#125—222no—
276#125—224no—
277#125—224no—
278#125—224no—
279#125—222no—
280#125—221no—
281C22⋊Q8—21no—
282C22⋊Q8—112no—
283C22⋊Q8—224no—
284C22⋊Q8—221no—
285C22⋊Q8C22×D1112yes—
286C4×Q8—21no—
287C4×Q8—112no—
288C4×Q8—112no—
289C4×Q8—112no—
290C4×Q8—112no—
291C4×Q8—114no—
292C4×Q8—114no—
293C4×Q8—112no—
294C4×Q8—222no—
295C4×Q8—222no—
296C4×Q8—224no—
297C4×Q8—222no—
298C4×Q8—222no—
299C4×Q8—221no—
300C4×Q8—444no—
301C4×Q8C4×D1112yes—
302#117—21no—
303#117—224no—
304#117—221no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—112no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—221no—
311C2×C42—112no—
312C2×C42—222no—
313C2×C42—221no—
314C2×C42C22×D1111yescharacteristic
315C4⋊C8—21no—
316C4⋊C8—224no—
317C4⋊C8—221no—
318C22⋊C8—112no—
319C22⋊C8C22×D1112yes—
320C4×C8—21no—
321C4×C8—224no—
322C4×C8—221no—
323#95—21no—
324#95—111no—
325#95—111no—
326#95—222no—
327#95C22×D1112yes—
328C2×C11—21no—
329C2×C11—21no—
330C2×C11#288411yescharacteristic
331C2×C11C22×#10311yescharacteristic
332C2×C11#290111yescharacteristic
333C2×Q8—21no—
334C2×Q8—112no—
335C2×Q8—112no—
336C2×Q8—114no—
337C2×Q8—114no—
338C2×Q8—112no—
339C2×Q8—224no—
340C2×Q8—221no—
341C2×Q8C2×C4×D1112yes—
342C22×C4—22no—
343C22×C4—112no—
344C22×C4—112no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4D4×D1111yescharacteristic
348C22×C4D4×D1111yescharacteristic
349C22×C4C23×D1111yescharacteristic
350C2×C8—22no—
351C2×C8—222no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—42no—
358C4⋊C4—114no—
359C4⋊C4—114no—
360C4⋊C4—112no—
361C4⋊C4—112no—
362C4⋊C4—112no—
363C4⋊C4—224no—
364C4⋊C4—224no—
365C4⋊C4—224no—
366C4⋊C4—224no—
367C4⋊C4—224no—
368C4⋊C4—221no—
369C4⋊C4—221no—
370C4⋊C4—222no—
371C4⋊C4—221no—
372C4⋊C4—222no—
373C4⋊C4—444no—
374C4⋊C4—444no—
375C4⋊C4—442no—
376C4⋊C4C2×C4×D1112yes—
377C22⋊C4—22no—
378C22⋊C4—222no—
379C42—22no—
380C42—114no—
381C42—114no—
382C42—224no—
383C42—224no—
384C42—222no—
385C42—444no—
386C42—442no—
387C42C2×C4×D1111yescharacteristic
388C42C2×C4×D1111yescharacteristic
389C42D4×D1111yescharacteristic
390C42D4×D1111yescharacteristic
391C11#1761911yescharacteristic, complemented, Sylow
392C23C2×D4×D1111yescharacteristic
393Q8—42no—
394Q8—81no—
395Q8—118no—
396Q8—118no—
397Q8—442no—
398Q8—881no—
399Q8—884no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—114no—
408C2×C4—114no—
409C2×C4—114no—
410C2×C4—114no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—442no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4C22⋊C4×D1111yescharacteristic
421C2×C4C22⋊C4×D1111yescharacteristic
422C2×C4C22⋊C4×D1111yescharacteristic
423C2×C4C22⋊C4×D1111yescharacteristic
424C2×C4SD16×D1112yes—
425C2×C4Q16×D1112yes—
426C2×C4C22×C4×D1111yescharacteristic
427C2×C4C2×D4×D1111yescharacteristic
428C8—42no—
429C8—442no—
430C22—21no—
431C22—21no—
432C22C2×C22⋊C4×D1111yescharacteristic
433C22C2×SD16×D1111yescharacteristic
434C22C2×Q16×D1111yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—42no—
440C4—42no—
441C4—82no—
442C4—118no—
443C4—224no—
444C4—442no—
445C4—442no—
446C4—442no—
447C4—881no—
448C4D11×#10312yes—
449C4D11×#10312yes—
450C2—21no—
451C2—21no—
452C2#1307707811yescharacteristic
453C2C2×D11×#10311yescharacteristic
454C2#1307716211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1518C2
socleC22×C11C22×C22⋊C4
prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#1518D11
hypocenterC11#17619
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
11. #10623253C4semidirect
12. #10623252C4semidirect
17. #10623098C4semidirect
18. Q8×Dic22C4semidirect
391. C11#17619semidirect

Maximal subgroups

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

subgroupindex
#130824212
#130776962
#130715332
#130671792
#130671782
#130671162
#130671152
#130671132
C11×#15182
#1761911