Finite Group Databasebeta

← #14726068

Subgroups — #14726068

Order 2816.

928 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082021C211yesmaximal, characteristic
2#13078655C212yesmaximal, complemented
3#13067657C212yesmaximal, complemented
4#13067640C212yesmaximal
5#13067589C212yesmaximal, complemented
6#13067572C212yesmaximal
7#13067114C212yesmaximal, complemented
8#13066930C211yesmaximal, characteristic
9C11×#2396C211yesmaximal, characteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979—21no—
13#10623050—22no—
14#10623050—22no—
15#10623048—24no—
16#10623031—21no—
17#10623031C2212yes—
18#10623014—21no—
19#10623014C2212yes—
20#10623001—21no—
21#10623001C2212yes—
22C11×#400C2211yescharacteristic
23C11×#399C2211yescharacteristic
24C11×#398—21no—
25C11×#396—21no—
26C11×#395C2211yescharacteristic
27C11×#393C2211yescharacteristic
28C4×C11×C4⋊C4—21no—
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C22⋊C4—21no—
31#10622841C2214yes—
32#10622644—22no—
33C4×#4326—24no—
34#10622634—22no—
35#10622583C2214yes—
36#10622538C2212yes—
37#10622166C2212yes—
38#10622163C2212yes—
39#10622090C2214yes—
40#10622090C2214yes—
41C22×Q8×C11C2311yescharacteristic
42C23×C4×C11D411yescharacteristic
43C4×Q8×C11—22no—
44C4×Q8×C11—22no—
45C11×#117—22no—
46C11×#117—22no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4D411yescharacteristic
57C2×C11×C22⋊C4C2311yescharacteristic
58C2×C42×C11—21no—
59C2×C42×C11—21no—
60C2×C42×C11D411yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—22no—
63C2×#4326—24no—
64#66979—22no—
65#66979—22no—
66#66979—22no—
67#66979—22no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70#66977—22no—
71#66977—22no—
72#66977—22no—
73#66977C2314yes—
74C2×C4×Dic11—22no—
75#66943—24no—
76#66943—24no—
77#66941—24no—
78#66941—24no—
79#66931—24no—
80#66931—24no—
81#66931—24no—
82#66931—24no—
83#66923—22no—
84#66923—22no—
85#66922—21no—
86#66922—21no—
87#66922D412yes—
88#66922D412yes—
89C4×Dic22—22no—
90C4×Dic22—22no—
91C4×Dic22—22no—
92C4×Dic22D414yes—
93C11×#95—21no—
94C11×#95—21no—
95C11×#95—21no—
96C11×#95—21no—
97C11×#95C2311yescharacteristic
98C11×#95C2311yescharacteristic
99#66899—24no—
100C22⋊(C11⋊C8)C2314yes—
101#66874—24no—
102#66871—24no—
103C4⋊(C11⋊C8)—22no—
104C4×C11⋊C8—22no—
105#18125—111nomaximal, Sylow
106C24×C11C2×D411yescharacteristic
107C2×Q8×C11—22no—
108C2×Q8×C11—42no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11Q1614yescomplemented
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—22no—
124C22×Dic11—22no—
125C2×Dic22—22no—
126C2×Dic22—22no—
127C2×Dic22—22no—
128C2×Dic22C2×D414yes—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—42no—
136C11×C22⋊C4—22no—
137C11×C22⋊C4—22no—
138C11×C22⋊C4—42no—
139C11×C22⋊C4—42no—
140C42×C11—21no—
141C42×C11—21no—
142C42×C11—41no—
143C42×C11—41no—
144C42×C11—42no—
145C42×C11C2×D412yes—
146C42×C11C2×D412yes—
147C22⋊Dic11—24no—
148C22⋊Dic11—24no—
149#4326—48no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11C2×D414yes—
158Dic11⋊C4—24no—
159Dic11⋊C4—24no—
160Dic11⋊C4—24no—
161Dic11⋊C4—24no—
162C4×Dic11—24no—
163C4×Dic11—24no—
164C2×C11⋊C8—24no—
165#3458—111no—
166#3104—112no—
167#2396D1111yescharacteristic
168#1617—112no—
169#1614—112no—
170#1605—112no—
171#1602—112no—
172#1503—112no—
173#1458—111no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11C2×Q1612yes—
179C23×C11C22×D411yescharacteristic
180Q8×C11—24no—
181Q8×C11—42no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11#12012yes—
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11C2×Q1612yes—
208C2×C4×C11C2×Q1612yes—
209C2×C4×C11#13712yes—
210C2×C4×C11C22×D412yes—
211C2×Dic11—24no—
212C2×Dic11—24no—
213C2×Dic11—82no—
214C2×Dic11—82no—
215Dic22—44no—
216Dic22—82no—
217Dic22—82no—
218Dic22—82no—
219C11⋊C8—44no—
220#544—112no—
221#544—222no—
222#544—222no—
223#544—221no—
224#543—112no—
225#543—221no—
226#533—112no—
227#533—224no—
228#533—221no—
229C2×C4×Q8C2×D1111yescharacteristic
230C2×#117—221no—
231C2×#117C2×D1111yescharacteristic
232#484—114no—
233#477—222no—
234#462—222no—
235#451—114no—
236C4×Q16—224no—
237#431—112no—
238#400C2×D1111yescharacteristic
239#399C2×D1111yescharacteristic
240#398—21no—
241#396—21no—
242#395C2×D1111yescharacteristic
243#393C2×D1111yescharacteristic
244C4×C4⋊C4—21no—
245C4×C4⋊C4C2×D1111yescharacteristic
246C4×C22⋊C4—21no—
247#328—114no—
248#328—114no—
249#324—112no—
250#323—112no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—22no—
254C22×C11—42no—
255C22×C11—41no—
256C22×C11—41no—
257C22×C11—81no—
258C22×C11C2×#12011yescharacteristic
259C22×C11C22×Q1611yescharacteristic
260C22×C11C2×#13711yescharacteristic
261C4×C11—22no—
262C4×C11—22no—
263C4×C11—22no—
264C4×C11—42no—
265C4×C11—41no—
266C4×C11—42no—
267C4×C11—41no—
268C4×C11—81no—
269C4×C11—81no—
270C4×C11#45112yes—
271C4×C11#45112yes—
272Dic11—44no—
273Dic11—44no—
274C22×Q8C22×D1111yescharacteristic
275C23×C4C22⋊D1111yescharacteristic
276C2×Q16—224no—
277C4⋊Q8—112no—
278C4⋊Q8—112no—
279C4⋊Q8—221no—
280C4⋊Q8—221no—
281C4⋊Q8—224no—
282C4⋊Q8—224no—
283#125—222no—
284#125—224no—
285#125—224no—
286#125—222no—
287C22⋊Q8—114no—
288C22⋊Q8—224no—
289C22⋊Q8—224no—
290C22⋊Q8—224no—
291C22⋊Q8—224no—
292C22⋊Q8—222no—
293C22⋊Q8—222no—
294C22⋊Q8—222no—
295C4×Q8—22no—
296C4×Q8—22no—
297C4×Q8—114no—
298C4×Q8—222no—
299C4×Q8—222no—
300C4×Q8—222no—
301#117—22no—
302#117—22no—
303#117—222no—
304#117—222no—
305#117—222no—
306#117—222no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4C22⋊D1111yescharacteristic
314C2×C4⋊C4C22×D1111yescharacteristic
315C2×C4⋊C4C22×D1111yescharacteristic
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—222no—
319C2×C22⋊C4C22⋊D1111yescharacteristic
320C2×C22⋊C4C22×D1111yescharacteristic
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—222no—
324C2×C42C22⋊D1111yescharacteristic
325C2×C42C22×D1111yescharacteristic
326#107—224no—
327C4⋊C8—222no—
328#103—224no—
329#103—224no—
330C22⋊C8—114no—
331C4×C8—222no—
332#95—21no—
333#95—21no—
334#95—21no—
335#95—21no—
336#95C22×D1111yescharacteristic
337#95C22×D1111yescharacteristic
338C2×C11—21no—
339C2×C11—21no—
340C2×C11—42no—
341C2×C11C2×#45111yescharacteristic
342C2×C11#301811yescharacteristic
343C2×C11#302511yescharacteristic
344C24C2×C22⋊D1111yescharacteristic
345C2×Q8—22no—
346C2×Q8—42no—
347C2×Q8—114no—
348C2×Q8—222no—
349C2×Q8—222no—
350C2×Q8—222no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4#432614yescomplemented
361C22×C4C2×C22⋊D1111yescharacteristic
362C22×C4C2×C22⋊D1111yescharacteristic
363C22×C4C2×C22⋊D1111yescharacteristic
364C22×C4C2×C22⋊D1111yescharacteristic
365C22×C4C2×C22⋊D1111yescharacteristic
366C22×C4C23×D1111yescharacteristic
367Q16—448no—
368C2×C8—224no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—42no—
373C4⋊C4—42no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—114no—
377C4⋊C4—222no—
378C4⋊C4—222no—
379C4⋊C4—224no—
380C4⋊C4—224no—
381C4⋊C4—222no—
382C4⋊C4—222no—
383C4⋊C4—222no—
384C4⋊C4—222no—
385C4⋊C4—224no—
386C4⋊C4—222no—
387C4⋊C4—224no—
388C22⋊C4—22no—
389C22⋊C4—22no—
390C22⋊C4—42no—
391C22⋊C4—42no—
392C22⋊C4—224no—
393C22⋊C4—224no—
394C42—21no—
395C42—21no—
396C42—41no—
397C42—41no—
398C42—42no—
399C42—224no—
400C42—224no—
401C42D4×D1112yes—
402C42D4×D1112yes—
403C11#1812511yescharacteristic, complemented, Sylow
404C23—21no—
405C23—21no—
406C23—41no—
407C23—41no—
408C23C2×#432612yes—
409C23C22×C22⋊D1111yescharacteristic
410Q8—24no—
411Q8—42no—
412Q8—444no—
413Q8—882no—
414Q8—882no—
415Q8—882no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—224no—
439C2×C4—224no—
440C2×C4—882no—
441C2×C4—882no—
442C2×C4#6699012yes—
443C2×C4#6699011yescharacteristic
444C2×C4#6699011yescharacteristic
445C2×C4C2×#432612yes—
446C2×C4C2×#432612yes—
447C2×C4#6700412yes—
448C2×C4C2×D4×D1112yes—
449C8—444no—
450C22—21no—
451C22—21no—
452C22—22no—
453C22—42no—
454C22—41no—
455C22—41no—
456C22—81no—
457C22C2×#6699011yescharacteristic
458C22C22×#432611yescharacteristic
459C22C2×#6700411yescharacteristic
460C4—22no—
461C4—22no—
462C4—22no—
463C4—42no—
464C4—41no—
465C4—42no—
466C4—41no—
467C4—81no—
468C4—81no—
469C4—444no—
470C4—444no—
471C4#1062266312yes—
472C4#1062266312yes—
473C2—21no—
474C2—21no—
475C2—42no—
476C2C2×#1062266311yescharacteristic
477C2#1307796411yescharacteristic
478C2#1307800711yescharacteristic
subgroupG/H
centerC2×C4#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2396C2
socleC22×C11C2×#120
prime radicalC24×C11C2×D4
hypercenter#2396D11
hypocenterC11#18125
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2396

Complements

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

NH ≅ G/Ntype
2. #13078655C2semidirect
3. #13067657C2semidirect
5. #13067589C2semidirect
7. #13067114C2semidirect
116. C22×C4×C11Q16semidirect
360. C22×C4#4326semidirect
403. C11#18125semidirect

Maximal subgroups

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

subgroupindex
#130820212
#130786552
#130676572
#130676402
#130675892
#130675722
#130671142
#130669302
C11×#23962
#1812511