Finite Group Databasebeta

← #14680322

Subgroups — #14680322

Order 2816.

1406 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622598C211yesmaximal, characteristic
2C2×#10622586C211yesmaximal, characteristic
3C2×#10622589C211yesmaximal, characteristic
4C2×#10622590C211yesmaximal, characteristic
5C2×#10622545C211yesmaximal, characteristic
6#13066870C214yesmaximal
7#13066867C214yesmaximal
8#13066846C211yesmaximal, characteristic
9C11×C4⋊#95C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2212yes—
16C22×Dic11⋊C4C2212yes—
17C22×Dic11⋊C4C2214yes—
18C22×C4×Dic11C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C2×C11×#95C2214yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2214yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2214yes—
27#10622598—24no—
28#10622590—24no—
29#10622589C418yescomplemented
30#10622586—24no—
31#10622545—24no—
32C23×C4×C11C2312yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C23×Dic11C2312yes—
37C23×Dic11C2312yes—
38C23×Dic11C2311yescharacteristic
39C23×Dic11C2311yescharacteristic
40C23×Dic11C2312yes—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4C2×C414yes—
47C2×C42×C11—22no—
48C2×C42×C11—22no—
49C2×C42×C11Q814yes—
50C2×C4⋊Dic11—22no—
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11—24no—
56C2×C4⋊Dic11—44no—
57C2×C4⋊Dic11C2×C414yes—
58C2×Dic11⋊C4—24no—
59C2×Dic11⋊C4—44no—
60C2×Dic11⋊C4—44no—
61C2×Dic11⋊C4—44no—
62C2×Dic11⋊C4C2×C4116yes—
63C2×C4×Dic11—22no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11C2×C414yes—
66C2×C4×Dic11D414yes—
67C2×C4×Dic11D414yes—
68C2×C4×Dic11Q814yes—
69C11×#95—44no—
70C11⋊#95—24no—
71C11⋊#95—24no—
72C11⋊#95—24no—
73C11⋊#95—28no—
74C11⋊#95—24no—
75C11⋊#95—44no—
76#14276—111nomaximal, Sylow
77C24×C11C2411yescharacteristic
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—24no—
85C22×C4×C11—24no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—24no—
92C22×C4×C11—24no—
93C22×C4×C11C22×C414yes—
94C22×C4×C11C22×C412yes—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×Q814yes—
98C22×C4×C11C2×Q812yes—
99C22×C4×C11C2×Q812yes—
100C22×C4×C11#4112yes—
101C22×C4×C11#4112yes—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11—22no—
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—24no—
114C22×Dic11—24no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—24no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—24no—
123C22×Dic11C22×C414yes—
124C22×Dic11C22×C414yes—
125C22×Dic11C2×D412yes—
126C22×Dic11C2×D412yes—
127C22×Dic11C2×D414yes—
128C22×Dic11C2×Q814yes—
129C11×C4⋊C4—28no—
130C11×C4⋊C4—44no—
131C42×C11—28no—
132C4⋊Dic11—28no—
133C4⋊Dic11—48no—
134C4⋊Dic11—44no—
135Dic11⋊C4—416no—
136Dic11⋊C4—48no—
137C4×Dic11—28no—
138C4×Dic11C4⋊C4116yescomplemented
139C2×#389—111no—
140C2×#389—111no—
141C2×#384—111no—
142C2×#382—111no—
143C2×#376—111no—
144#1441—114no—
145#1441—114no—
146C4⋊#95—111no—
147C4⋊#95D1111yescharacteristic
148C23×C11C23×C411yescharacteristic
149C23×C11C22×D411yescharacteristic
150C23×C11C22×D411yescharacteristic
151C23×C11C22×Q811yescharacteristic
152C23×C11C22×Q811yescharacteristic
153C23×C11C2×#4111yescharacteristic
154C23×C11C2×#4111yescharacteristic
155C23×C11H(5,𝔽2)12yes—
156C23×C11H(5,𝔽2)12yes—
157C23×C112−1+412yes—
158C23×C112−1+412yes—
159C2×C4×C11—24no—
160C2×C4×C11—28no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—44no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—44no—
175C2×C4×C11—44no—
176C2×C4×C11C2×C4⋊C414yes—
177C2×C4×C11C4×D414yes—
178C2×C4×C11C4×Q814yes—
179C2×C4×C11#12114yes—
180C2×C4×C11C22⋊Q814yes—
181C2×C4×C11#12514yes—
182C2×C4×C11C4⋊Q814yes—
183C2×Dic11—24no—
184C2×Dic11—24no—
185C2×Dic11—24no—
186C2×Dic11—24no—
187C2×Dic11—24no—
188C2×Dic11—24no—
189C2×Dic11—24no—
190C2×Dic11—28no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—44no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—44no—
208C2×Dic11—44no—
209C2×Dic11C2×C4⋊C418yes—
210C22×C4⋊C4—111no—
211C22×C4⋊C4—114no—
212C22×C4⋊C4—111no—
213C22×C4⋊C4—112no—
214C22×C4⋊C4—112no—
215C22×C4⋊C4C2×D1111yescharacteristic
216C22×C4⋊C4C2×D1111yescharacteristic
217C22×C42—111no—
218C22×C42—111no—
219C22×C42C2×D1111yescharacteristic
220#389—224no—
221#389—224no—
222#384—118no—
223#382—224no—
224#376—224no—
225C2×#95—112no—
226C2×#95—112no—
227C2×#95—114no—
228C2×#95—112no—
229C2×#95—112no—
230C2×#95—114no—
231C2×#95C2×D1114yes—
232C22×C11C22×C4⋊C411yescharacteristic
233C22×C11C2×C4×D411yescharacteristic
234C22×C11C2×C4×Q811yescharacteristic
235C22×C11#51812yes—
236C22×C11#51912yes—
237C22×C11C2×#12111yescharacteristic
238C22×C11C2×C22⋊Q811yescharacteristic
239C22×C11C2×#12511yescharacteristic
240C22×C11C2×C4⋊Q811yescharacteristic
241C22×C11#53511yescharacteristic
242C22×C11#53511yescharacteristic
243C22×C11#53611yescharacteristic
244C22×C11#53611yescharacteristic
245C22×C11#53712yes—
246C22×C11#53712yes—
247C22×C11#54012yes—
248C22×C11#54112yes—
249C22×C11#54212yes—
250C22×C11#54212yes—
251C22×C11#54412yes—
252C22×C11#54412yes—
253C22×C11#54412yes—
254C22×C11#54412yes—
255C4×C11—44no—
256C4×C11—44no—
257C4×C11—82no—
258C4×C11#38918yes—
259Dic11—28no—
260Dic11—44no—
261Dic11—42no—
262Dic11—42no—
263Dic11—82no—
264C23×C4—112no—
265C23×C4—112no—
266C23×C4—111no—
267C23×C4—111no—
268C23×C4—112no—
269C23×C4C22×D1112yes—
270C23×C4C22×D1112yes—
271C23×C4C22×D1112yes—
272C23×C4C22×D1111yescharacteristic
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—114no—
279C2×C4⋊C4—1116no—
280C2×C4⋊C4—222no—
281C2×C4⋊C4—222no—
282C2×C4⋊C4—224no—
283C2×C4⋊C4—224no—
284C2×C4⋊C4—222no—
285C2×C4⋊C4—222no—
286C2×C4⋊C4—222no—
287C2×C4⋊C4—444no—
288C2×C4⋊C4—444no—
289C2×C4⋊C4—444no—
290C2×C4⋊C4—444no—
291C2×C4⋊C4C4×D1114yes—
292C2×C42—22no—
293C2×C42—22no—
294C2×C42—114no—
295C2×C42—114no—
296C2×C42—114no—
297C2×C42—114no—
298C2×C42—222no—
299C2×C42—222no—
300C2×C42Dic2214yes—
301#95—44no—
302#95—224no—
303#95—224no—
304#95—228no—
305#95—224no—
306#95—224no—
307#95—444no—
308C2×C11C2×#38911yescharacteristic
309C2×C11#231612yes—
310C2×C11#232711yescharacteristic
311C2×C11#232811yescharacteristic
312C2×C11#233112yes—
313C2×C11#262011yescharacteristic
314C2×C11#262011yescharacteristic
315C2×C11#262912yes—
316C2×C11#264712yes—
317C2×C11#266011yescharacteristic
318C2×C11#266011yescharacteristic
319C24C23×D1111yescharacteristic
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—24no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—24no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—114no—
336C22×C4—114no—
337C22×C4—114no—
338C22×C4—114no—
339C22×C4—112no—
340C22×C4—112no—
341C22×C4—222no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4—222no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—224no—
353C22×C4—222no—
354C22×C4—224no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—224no—
361C22×C4—224no—
362C22×C4C2×Dic2214yes—
363C22×C4C2×Dic2212yes—
364C22×C4C2×C4×D1114yes—
365C22×C4C2×C4×D1112yes—
366C22×C4#433912yes—
367C22×C4D4×D1112yes—
368C22×C4D4×D1112yes—
369C22×C4#434112yes—
370C22×C4Q8×D1112yes—
371C4⋊C4—28no—
372C4⋊C4—44no—
373C4⋊C4—228no—
374C4⋊C4—4416no—
375C4⋊C4—448no—
376C4⋊C4—448no—
377C4⋊C4—444no—
378C42—28no—
379C42—1116no—
380C42—228no—
381C11#1427611yescharacteristic, complemented, Sylow
382C23C22×Dic2211yescharacteristic
383C23C22×C4×D1111yescharacteristic
384C23C2×#433911yescharacteristic
385C23C2×D4×D1111yescharacteristic
386C23C2×D4×D1111yescharacteristic
387C23C2×#434111yescharacteristic
388C23#6703712yes—
389C23C2×Q8×D1111yescharacteristic
390C23#6704012yes—
391C23#6704212yes—
392C23#6704312yes—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—28no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—44no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—44no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—118no—
411C2×C4—224no—
412C2×C4—224no—
413C2×C4—224no—
414C2×C4—224no—
415C2×C4—224no—
416C2×C4—224no—
417C2×C4—222no—
418C2×C4—222no—
419C2×C4—224no—
420C2×C4—222no—
421C2×C4—222no—
422C2×C4—228no—
423C2×C4—222no—
424C2×C4—222no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4—444no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—444no—
435C2×C4—444no—
436C2×C4—442no—
437C2×C4C4×Dic2214yes—
438C2×C4#6693114yes—
439C2×C4(C22⋊D11)⋊C414yes—
440C2×C4#6693714yes—
441C2×C4#6694114yes—
442C2×C4#6694214yes—
443C2×C4C4⋊C4×D1114yes—
444C22C2×C4×Dic2211yescharacteristic
445C22C2×#6693111yescharacteristic
446C22C2×(C22⋊D11)⋊C411yescharacteristic
447C22C2×#6693711yescharacteristic
448C22C2×#6694111yescharacteristic
449C22C2×#6694211yescharacteristic
450C22#1062303112yes—
451C22C2×C4⋊C4×D1111yescharacteristic
452C22#1062305012yes—
453C22#1062307612yes—
454C22#1062309212yes—
455C22#1062310312yes—
456C22#1062311312yes—
457C22#1062313912yes—
458C22#1062315012yes—
459C22#1062315612yes—
460C22#1062316012yes—
461C22#1062320511yescharacteristic
462C22#1062320611yescharacteristic
463C22#1062322012yes—
464C22#1062324611yescharacteristic
465C22#1062325511yescharacteristic
466C22#1062326012yes—
467C4—44no—
468C4—44no—
469C4—82no—
470C4—228no—
471C4—442no—
472C4—442no—
473C4—444no—
474C4—882no—
475C4#1062226018yes—
476C2C2×#1062226011yescharacteristic
477C2#1307123112yes—
478C2#1307133411yescharacteristic
479C2#1307134011yescharacteristic
480C2#1307136012yes—
481C2#1307437911yescharacteristic
482C2#1307438011yescharacteristic
483C2#1307445012yes—
484C2#1307459212yes—
485C2#1307473811yescharacteristic
486C2#1307474011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, prime radical, cosocleC24×C11C24
hypercenterC4⋊#95D11
hypocenterC11#14276
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
29. #10622589C4semidirect
138. C4×Dic11C4⋊C4semidirect
381. C11#14276semidirect

Maximal subgroups

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

subgroupindex
C2×#106225982
C2×#106225862
C2×#106225892
C2×#106225902
C2×#106225452
#130668702
#130668672
#130668462
C11×C4⋊#952
#1427611