Finite Group Databasebeta

← #14732269

Subgroups — #14732269

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079564C211yesmaximal, characteristic, complemented
2#13078655C211yesmaximal, characteristic, complemented
3#13078413C211yesmaximal, characteristic
4#13067830C214yesmaximal, complemented
5#13067750C214yesmaximal, complemented
6#13067297C211yesmaximal, characteristic, complemented
7#13067045C211yesmaximal, characteristic, complemented
8#13067007C211yesmaximal, characteristic
9C2×C11×#554C211yesmaximal, characteristic
10C11×#554—22no—
11C11×#554—22no—
12C11×#554—22no—
13C11×#554C2214yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125—21no—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8—22no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4—21no—
22#10623001C2211yescharacteristic
23#10622841—22no—
24#10622841—21no—
25#10622828—21no—
26#10622705C2212yescomplemented
27#10622703—22no—
28#10622694C2212yescomplemented
29#10622644C2212yescomplemented
30C4×#4326—22no—
31#10622634C2212yescomplemented
32#10622622—22no—
33#10622621C2212yes—
34#10622620C2212yes—
35#10622583—21no—
36#10622577—21no—
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40#10622184C2214yescomplemented
41Q8⋊(C11⋊C8)C2214yescomplemented
42D4⋊(C11⋊C8)C2214yes—
43C22×Q8×C11D411yescharacteristic
44C22×Q8×C11D412yes—
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8D412yes—
51C11×C4⋊Q8C2312yes—
52C11×#125—24no—
53C11×#125—24no—
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8—28no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—28no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11D412yes—
61C4×Q8×C11C2312yes—
62C4×D4×C11—24no—
63C4×D4×C11—24no—
64C4×D4×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11D412yes—
67C4×D4×C11C2312yes—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×#4326—22no—
82C2×#4326—24no—
83#66979—21no—
84#66977—21no—
85#66977—21no—
86C2×#4318—21no—
87#66923—21no—
88#66922C2311yescharacteristic
89#66922C2311yescharacteristic
90C4×Dic22—21no—
91C4×Dic22—21no—
92#66899—22no—
93#66899—24no—
94#66896—22no—
95#66896—22no—
96C22⋊(C11⋊C8)—21no—
97C22⋊(C11⋊C8)—21no—
98#66874—22no—
99#66872—22no—
100#66871—22no—
101#66871—22no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)C2312yes—
105C4⋊(C11⋊C8)C2312yes—
106C4×C11⋊C8—21no—
107C4×C11⋊C8C2312yes—
108#18749—111nomaximal, Sylow
109C24×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—22no—
112C2×Q8×C11—42no—
113C2×Q8×C11—82no—
114C2×Q8×C11C2×D412yes—
115C2×Q8×C11C2×D414yes—
116C2×D4×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11Q1614yescomplemented
119C2×D4×C11C2×D412yes—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—28no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—44no—
128C22×C4×C11—84no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C2×Dic22—21no—
133C2×Dic22—21no—
134C11×C4⋊C4—28no—
135C11×C4⋊C4—28no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4C2×D412yes—
145C11×C4⋊C4C2×D412yes—
146C11×C22⋊C4—28no—
147C11×C22⋊C4—22no—
148C11×C22⋊C4—22no—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11C2411yescharacteristic
155C22⋊Dic11—41no—
156#4326—44no—
157#4326—84no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164C4×Dic11—41no—
165#4318—42no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×#554D1111yescharacteristic
170#3209—111no—
171#3104—111no—
172#3077—111no—
173#1644—114no—
174#1632—114no—
175#1548—111no—
176#1487—111no—
177#1478—111no—
178C23×C11—22no—
179C23×C11—24no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11#12011yescharacteristic
183Q8×C11—22no—
184Q8×C11—22no—
185Q8×C11—44no—
186Q8×C11—42no—
187Q8×C11—82no—
188D4×C11—22no—
189D4×C11—24no—
190D4×C11C2×Q1614yes—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—41no—
197C2×C4×C11—44no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—44no—
201C2×C4×C11—42no—
202C2×C4×C11—44no—
203C2×C4×C11—88no—
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11C2×Q1612yes—
208C2×C4×C11#13712yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×Dic11—41no—
213C2×Dic11—41no—
214Dic22—42no—
215Dic22—42no—
216C11⋊C8—42no—
217C11⋊C8—42no—
218C11⋊C8—42no—
219#554—22no—
220#554—22no—
221#554—22no—
222#554C2×D1114yes—
223#533—111no—
224C2×C4⋊Q8C2×D1111yescharacteristic
225C2×#125—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—22no—
228C2×C4×Q8C2×D1111yescharacteristic
229C2×C4×D4—21no—
230C2×C4×D4C2×D1111yescharacteristic
231C22×C4⋊C4—21no—
232#494—112no—
233#487—112no—
234#484—221no—
235#478—222no—
236#477—112no—
237#476—112no—
238#474—112no—
239#462—112no—
240#462—222no—
241#451—221no—
242#451—222no—
243C4×Q16—222no—
244#431—111no—
245#431—111no—
246#428—221no—
247#423—111no—
248#418—221no—
249#333—114no—
250Q8⋊C8—114no—
251D4⋊C8—114no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—24no—
255C22×C11—48no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11#45112yes—
259C22×C11C2×#12011yescharacteristic
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—42no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—44no—
267C4×C11#45112yes—
268C4×C11C22×Q1611yescharacteristic
269C4×C11C2×#13711yescharacteristic
270C4×C11#57512yes—
271Dic11—81no—
272Dic11—81no—
273C22×Q8C22⋊D1111yescharacteristic
274C22×Q8C22⋊D1112yes—
275C22×D4C22⋊D1111yescharacteristic
276C23×C4—22no—
277C23×C4—21no—
278C2×Q16—222no—
279C2×Q16—224no—
280C2×M16—221no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—111no—
284C4⋊Q8—111no—
285C4⋊Q8C22⋊D1112yes—
286C4⋊Q8C22×D1112yes—
287#125—24no—
288#125—24no—
289#125—221no—
290C22⋊Q8—24no—
291C22⋊Q8—28no—
292C22⋊Q8—24no—
293C22⋊Q8—28no—
294C22⋊Q8—221no—
295C22⋊Q8—221no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×Q8—221no—
299C4×Q8—221no—
300C4×Q8C22⋊D1112yes—
301C4×Q8C22×D1112yes—
302C4×D4—24no—
303C4×D4—24no—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4C22⋊D1112yes—
307C4×D4C22×D1112yes—
308#117—221no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4C22⋊D1111yescharacteristic
317C2×C4⋊C4C22⋊D1111yescharacteristic
318C2×C22⋊C4—22no—
319C2×C22⋊C4—21no—
320C2×C42—21no—
321C2×C42C22×D1111yescharacteristic
322#107—222no—
323#107—222no—
324#106—222no—
325C4⋊C8—112no—
326C4⋊C8—112no—
327C4⋊C8—221no—
328C4⋊C8—221no—
329#103—222no—
330#103—224no—
331#103—222no—
332#102—222no—
333#102—222no—
334C22⋊C8—221no—
335C22⋊C8—221no—
336C4×C8—112no—
337C4×C8—221no—
338C2×C11—22no—
339C2×C11—44no—
340C2×C11C2×#45111yescharacteristic
341C2×C11#300511yescharacteristic
342C2×C11#301911yescharacteristic
343C24—21no—
344C2×Q8—21no—
345C2×Q8—22no—
346C2×Q8—42no—
347C2×Q8—82no—
348C2×Q8—221no—
349C2×Q8—221no—
350C2×Q8C2×C22⋊D1112yes—
351C2×Q8C2×C22⋊D1114yes—
352C2×D4—22no—
353C2×D4—21no—
354C2×D4#432614yescomplemented
355C2×D4C2×C22⋊D1112yes—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—28no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—44no—
364C22×C4—84no—
365C22×C4C2×C22⋊D1111yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367C22×C4C2×C22⋊D1111yescharacteristic
368Q16—444no—
369Q16—884no—
370M16—442no—
371C2×C8—222no—
372C2×C8—222no—
373C2×C8—222no—
374C4⋊C4—28no—
375C4⋊C4—28no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C4⋊C4C2×C22⋊D1112yes—
391C4⋊C4C2×C22⋊D1112yes—
392C22⋊C4—28no—
393C22⋊C4—22no—
394C22⋊C4—22no—
395C22⋊C4—441no—
396C42—22no—
397C42—22no—
398C42—441no—
399C42C2×C22⋊D1111yescharacteristic
400C42C2×C22⋊D1111yescharacteristic
401C42C2×C22⋊D1111yescharacteristic
402C42C23×D1111yescharacteristic
403C11#1874911yescharacteristic, complemented, Sylow
404C23—24no—
405C23—22no—
406C23—42no—
407C23—42no—
408C23#6700611yescharacteristic
409Q8—22no—
410Q8—22no—
411Q8—44no—
412Q8—42no—
413Q8—82no—
414Q8—442no—
415Q8—442no—
416D4—22no—
417D4—24no—
418D4C2×#432614yes—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—41no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—44no—
431C2×C4—88no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4#6699512yes—
435C2×C4C2×#432612yes—
436C2×C4#6700611yescharacteristic
437C2×C4#6700611yescharacteristic
438C2×C4#6700611yescharacteristic
439C2×C4C22×C22⋊D1111yescharacteristic
440C2×C4C22×C22⋊D1111yescharacteristic
441C2×C4C22×C22⋊D1111yescharacteristic
442C8—442no—
443C8—442no—
444C8—442no—
445C22—21no—
446C22—21no—
447C22—24no—
448C22—48no—
449C22—42no—
450C22—42no—
451C22#1062284112yes—
452C22C2×#6700611yescharacteristic
453C4—21no—
454C4—21no—
455C4—21no—
456C4—42no—
457C4—42no—
458C4—42no—
459C4—44no—
460C4—881no—
461C4—881no—
462C4#1062284112yes—
463C4C2×#6699511yescharacteristic
464C4C22×#432611yescharacteristic
465C4#1062335312yes—
466C2—22no—
467C2—44no—
468C2C2×#1062284111yescharacteristic
469C2#1307785811yescharacteristic
470C2#1307797311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#554C2
socleC22×C11C2×#120
prime radicalC22×D4×C11D4
hypercenterC2×#554D11
hypocenterC11#18749
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #13079564C2semidirect
2. #13078655C2semidirect
4. #13067830C2semidirect
5. #13067750C2semidirect
6. #13067297C2semidirect
7. #13067045C2semidirect
26. #10622705C22semidirect
28. #10622694C22semidirect
29. #10622644C22semidirect
31. #10622634C22semidirect
40. #10622184C22semidirect
41. Q8⋊(C11⋊C8)C22semidirect
118. C2×D4×C11Q16semidirect
354. C2×D4#4326semidirect
403. C11#18749semidirect

Maximal subgroups

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

subgroupindex
#130795642
#130786552
#130784132
#130678302
#130677502
#130672972
#130670452
#130670072
C2×C11×#5542
#1874911