Finite Group Databasebeta

← #14726069

Subgroups — #14726069

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#13078651C212yesmaximal, complemented
2#13071884C211yesmaximal, characteristic
3#13067658C212yesmaximal, complemented
4#13067641C212yesmaximal
5#13067590C212yesmaximal, complemented
6#13067573C212yesmaximal
7#13067115C212yesmaximal, complemented
8#13066930C211yesmaximal, characteristic
9C11×#3458C211yesmaximal, characteristic
10C11×#544—22no—
11C11×#544—22no—
12C11×#544—21no—
13C11×#544C2212yes—
14C11×#543—21no—
15C11×#543C2212yes—
16C11×#533—24no—
17C11×#533—21no—
18C11×#533C2212yes—
19C2×C11×#117—21no—
20C2×C11×#117C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C4×C22⋊Dic11—21no—
23#10622704—22no—
24#10622703—22no—
25#10622663C2214yes—
26#10622657C2214yes—
27C4×#4326—24no—
28#10622599C2211yescharacteristic
29#10622597—21no—
30#10622592C2211yescharacteristic
31#10622562C2211yescharacteristic
32#10622561—21no—
33#10622560C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35C4×Dic11⋊C4—21no—
36#10622538C2212yes—
37#10622176C2214yes—
38#10622176C2214yes—
39#10622166C2212yes—
40#10622163C2212yes—
41C23×C4×C11D411yescharacteristic
42C22×Dic22C2311yescharacteristic
43C11×C4⋊Q8—24no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—24no—
47C11×C4⋊Q8D412yes—
48C11×C4⋊Q8D412yes—
49C11×#125—24no—
50C11×#125—22no—
51C11×#125—24no—
52C11×#125—22no—
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8—22no—
57C11×C22⋊Q8—22no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8C2314yes—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×Q8×C11—22no—
64C4×Q8×C11D414yes—
65C11×#117—22no—
66C11×#117—22no—
67C11×#117—22no—
68C11×#117—22no—
69C11×#117—22no—
70C11×#117—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C11×C22⋊C4C2311yescharacteristic
78C2×C42×C11—22no—
79C2×C42×C11D411yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×#4326—24no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C4×Dic22—22no—
92C4×Dic22—22no—
93#66899—24no—
94C11⋊#95—21no—
95C11⋊#95—21no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98C11⋊#95C2311yescharacteristic
99C11⋊#95C2311yescharacteristic
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—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11C2×D414yes—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
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—21no—
124C22×Dic11—21no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C2×Dic22—22no—
128C2×Dic22—42no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4C2×D414yes—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—24no—
145C11×C22⋊C4—22no—
146C11×C22⋊C4—22no—
147C42×C11—24no—
148C42×C11—24no—
149C42×C11—21no—
150C42×C11—21no—
151C42×C11C2×D412yes—
152C42×C11C2×D412yes—
153C22⋊Dic11—42no—
154C22⋊Dic11—42no—
155#4326—48no—
156C4⋊Dic11—22no—
157C4⋊Dic11—42no—
158Dic11⋊C4—42no—
159Dic11⋊C4—42no—
160Dic11⋊C4—42no—
161C4×Dic11—41no—
162C4×Dic11—41no—
163C4×Dic11—42no—
164C2×C11⋊C8—24no—
165#3458D1111yescharacteristic
166#3104—112no—
167#2396—111no—
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—44no—
181Q8×C11—82no—
182Q8×C11—82no—
183Q8×C11—82no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—24no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—82no—
197C2×C4×C11—82no—
198C2×C4×C11#12012yes—
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11#12011yescharacteristic
201C2×C4×C11C2×Q1612yes—
202C2×C4×C11C2×Q1612yes—
203C2×C4×C11#13712yes—
204C2×C4×C11C22×D412yes—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217Dic22—24no—
218Dic22—42no—
219C11⋊C8—44no—
220#544—22no—
221#544—22no—
222#544—21no—
223#544C2×D1112yes—
224#543—21no—
225#543C2×D1112yes—
226#533—24no—
227#533—21no—
228#533C2×D1112yes—
229C2×C4×Q8—111no—
230C2×#117—21no—
231C2×#117C2×D1111yescharacteristic
232#484—114no—
233#477—222no—
234#462—222no—
235#451—114no—
236C4×Q16—224no—
237#431—112no—
238#400—111no—
239#399—111no—
240#398—221no—
241#396—221no—
242#395—111no—
243#393—111no—
244C4×C4⋊C4—111no—
245C4×C4⋊C4—221no—
246C4×C22⋊C4—221no—
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—41no—
265C4×C11—44no—
266C4×C11—41no—
267C4×C11—44no—
268C4×C11#45112yes—
269C4×C11#45112yes—
270Dic11—42no—
271Dic11—42no—
272Dic11—81no—
273Dic11—81no—
274C22×Q8—111no—
275C23×C4C22⋊D1111yescharacteristic
276C2×Q16—224no—
277C4⋊Q8—24no—
278C4⋊Q8—21no—
279C4⋊Q8—21no—
280C4⋊Q8—24no—
281C4⋊Q8C22⋊D1112yes—
282C4⋊Q8C22⋊D1112yes—
283#125—24no—
284#125—22no—
285#125—24no—
286#125—22no—
287C22⋊Q8—24no—
288C22⋊Q8—24no—
289C22⋊Q8—24no—
290C22⋊Q8—22no—
291C22⋊Q8—22no—
292C22⋊Q8—22no—
293C22⋊Q8—24no—
294C22⋊Q8C22×D1114yes—
295C4×Q8—22no—
296C4×Q8—22no—
297C4×Q8—22no—
298C4×Q8—222no—
299C4×Q8—222no—
300C4×Q8C22⋊D1114yes—
301#117—22no—
302#117—22no—
303#117—22no—
304#117—22no—
305#117—22no—
306#117—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—111no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4C22⋊D1111yescharacteristic
315C2×C4⋊C4C22×D1111yescharacteristic
316C2×C22⋊C4—22no—
317C2×C22⋊C4—221no—
318C2×C22⋊C4—221no—
319C2×C22⋊C4C22⋊D1111yescharacteristic
320C2×C22⋊C4C22×D1111yescharacteristic
321C2×C42—22no—
322C2×C42—221no—
323C2×C42—221no—
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—111no—
333#95—111no—
334#95—221no—
335#95—221no—
336#95—221no—
337#95—221no—
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—22no—
347C2×Q8—22no—
348C2×Q8—222no—
349C2×Q8—442no—
350C2×Q8C2×C22⋊D1114yes—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—221no—
357C22×C4—221no—
358C22×C4—221no—
359C22×C4—221no—
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—24no—
373C4⋊C4—24no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—24no—
380C4⋊C4—22no—
381C4⋊C4—24no—
382C4⋊C4—222no—
383C4⋊C4—442no—
384C4⋊C4—442no—
385C4⋊C4—442no—
386C4⋊C4—442no—
387C4⋊C4C2×C22⋊D1114yes—
388C22⋊C4—24no—
389C22⋊C4—24no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—442no—
393C22⋊C4—442no—
394C42—24no—
395C42—21no—
396C42—24no—
397C42—21no—
398C42—442no—
399C42—441no—
400C42—441no—
401C42C2×C22⋊D1112yes—
402C42C2×C22⋊D1112yes—
403C11#1812511yescharacteristic, complemented, Sylow
404C23—21no—
405C23—21no—
406C23—41no—
407C23—41no—
408C23C2×#432612yes—
409C23C22×C22⋊D1111yescharacteristic
410Q8—44no—
411Q8—82no—
412Q8—82no—
413Q8—82no—
414Q8—224no—
415Q8—442no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—24no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4#6699512yes—
443C2×C4C2×#432612yes—
444C2×C4C2×#432612yes—
445C2×C4#6700612yes—
446C2×C4#6700611yescharacteristic
447C2×C4#6700611yescharacteristic
448C2×C4C22×C22⋊D1112yes—
449C8—444no—
450C22—21no—
451C22—21no—
452C22—22no—
453C22—42no—
454C22—41no—
455C22—41no—
456C22—81no—
457C22C2×#6699511yescharacteristic
458C22C22×#432611yescharacteristic
459C22C2×#6700611yescharacteristic
460C4—22no—
461C4—22no—
462C4—22no—
463C4—41no—
464C4—44no—
465C4—41no—
466C4—44no—
467C4—442no—
468C4—442no—
469C4—881no—
470C4—881no—
471C4#1062284112yes—
472C4#1062284112yes—
473C2—21no—
474C2—21no—
475C2—42no—
476C2C2×#1062284111yescharacteristic
477C2#1307796511yescharacteristic
478C2#1307800811yescharacteristic
subgroupG/H
centerC2×C4#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3458C2
socleC22×C11C2×#120
prime radicalC24×C11C2×D4
hypercenter#3458D11
hypocenterC11#18125
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3458

Complements

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

NH ≅ G/Ntype
1. #13078651C2semidirect
3. #13067658C2semidirect
5. #13067590C2semidirect
7. #13067115C2semidirect
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
#130786512
#130718842
#130676582
#130676412
#130675902
#130675732
#130671152
#130669302
C11×#34582
#1812511