Finite Group Databasebeta

← #14676047

Subgroups — #14676047

Order 2816.

1774 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622585C214yesmaximal
2C2×#10622589C211yesmaximal, characteristic
3C2×#10622589C211yesmaximal, characteristic
4C2×C4⋊C4×Dic11C211yesmaximal, characteristic
5C2×C4×Dic11⋊C4C211yesmaximal, characteristic
6#13066879C214yesmaximal
7#13066846C211yesmaximal, characteristic
8#13066845C211yesmaximal, characteristic
9C2×C11×#384C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C11×C4⋊C4C2214yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×Dic11⋊C4C2212yes—
17C22×Dic11⋊C4C2214yes—
18C22×Dic11⋊C4C2212yes—
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C11×#384—24no—
24C2×C11⋊#95C2214yes—
25C2×C11⋊#95C2214yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28#10622589—24no—
29#10622589—24no—
30C4⋊C4×Dic11—24no—
31#10622585—216no—
32C4×Dic11⋊C4C418yescomplemented
33C23×C4×C11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2311yescharacteristic
41C23×Dic11C2311yescharacteristic
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—28no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—28no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—44no—
50C2×C11×C4⋊C4D414yes—
51C2×C42×C11—22no—
52C2×C42×C11—22no—
53C2×C42×C11C2×C414yes—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11Q814yes—
60C2×Dic11⋊C4—28no—
61C2×Dic11⋊C4—28no—
62C2×Dic11⋊C4—28no—
63C2×Dic11⋊C4—24no—
64C2×Dic11⋊C4—24no—
65C2×Dic11⋊C4—44no—
66C2×Dic11⋊C4—44no—
67C2×Dic11⋊C4C2×C418yes—
68C2×Dic11⋊C4D418yes—
69C2×Dic11⋊C4Q818yes—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—28no—
73C2×C4×Dic11—24no—
74C2×C4×Dic11C2×C414yes—
75C2×C4×Dic11C2×C414yes—
76C2×C4×Dic11D414yes—
77C2×C4×Dic11Q814yes—
78C11⋊#95—28no—
79C11⋊#95—28no—
80C11⋊#95—24no—
81C11⋊#95C2×C418yes—
82#13910—111nomaximal, Sylow
83C24×C11C2411yescharacteristic
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—24no—
90C22×C4×C11—22no—
91C22×C4×C11—24no—
92C22×C4×C11—24no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—24no—
97C22×C4×C11C22×C414yes—
98C22×C4×C11C22×C412yes—
99C22×C4×C11C2×D414yes—
100C22×C4×C11C2×D414yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×Q814yes—
104C22×C4×C11C2×Q812yes—
105C22×C4×C11C2×Q812yes—
106C22×C4×C11#4112yes—
107C22×C4×C11#4112yes—
108C22×Dic11—22no—
109C22×Dic11—24no—
110C22×Dic11—22no—
111C22×Dic11—24no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—24no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—24no—
123C22×Dic11C22×C412yes—
124C22×Dic11C22×C414yes—
125C22×Dic11C22×C412yes—
126C22×Dic11C2×D412yes—
127C22×Dic11C2×D414yes—
128C22×Dic11C2×D412yes—
129C22×Dic11C2×D414yes—
130C22×Dic11C2×Q814yes—
131C22×Dic11C2×Q812yes—
132C22×Dic11C2×Q814yes—
133C22×Dic11C2×Q812yes—
134C22×Dic11C2×Q814yes—
135C11×C4⋊C4—28no—
136C11×C4⋊C4—416no—
137C11×C4⋊C4—44no—
138C42×C11—28no—
139C4⋊Dic11—28no—
140C4⋊Dic11—44no—
141Dic11⋊C4—416no—
142Dic11⋊C4—48no—
143Dic11⋊C4—48no—
144Dic11⋊C4C4⋊C4132yescomplemented
145C4×Dic11—28no—
146C4×Dic11—48no—
147C4×Dic11C4⋊C4116yescomplemented
148C2×#389—114no—
149C2×#384—111no—
150C2×#384—111no—
151C2×#384D1111yescharacteristic
152C2×C4×C4⋊C4—111no—
153C2×C4×C4⋊C4—111no—
154#1444—114no—
155C4⋊#95—111no—
156C4⋊#95—111no—
157C23×C11C23×C411yescharacteristic
158C23×C11C22×D411yescharacteristic
159C23×C11C22×D412yes—
160C23×C11C22×D411yescharacteristic
161C23×C11C22×Q811yescharacteristic
162C23×C11C22×Q812yes—
163C23×C11C22×Q811yescharacteristic
164C23×C11C2×#4111yescharacteristic
165C23×C11C2×#4111yescharacteristic
166C23×C11H(5,𝔽2)12yes—
167C23×C112−1+412yes—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—28no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—44no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—44no—
183C2×C4×C11—44no—
184C2×C4×C11C2×C4⋊C418yes—
185C2×C4×C11C2×C4⋊C414yes—
186C2×C4×C11C4×D414yes—
187C2×C4×C11C4×Q814yes—
188C2×C4×C11#12114yes—
189C2×C4×C11C22⋊Q814yes—
190C2×C4×C11#12514yes—
191C2×C4×C11C4⋊Q814yes—
192C2×Dic11—24no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—24no—
202C2×Dic11—24no—
203C2×Dic11—28no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—44no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—44no—
211C2×Dic11—44no—
212C2×Dic11C2×C4⋊C414yes—
213C2×Dic11C2×C4⋊C418yes—
214C2×Dic11C2×C4⋊C414yes—
215C2×Dic11C2×C4⋊C418yes—
216C2×Dic11#12714yes—
217C2×Dic11C4⋊Q814yes—
218C2×Dic11C4⋊Q818yes—
219C22×C4⋊C4—112no—
220C22×C4⋊C4—111no—
221C22×C4⋊C4—112no—
222C22×C4⋊C4—111no—
223C22×C4⋊C4—114no—
224C22×C4⋊C4—112no—
225C22×C4⋊C4C2×D1111yescharacteristic
226C22×C4⋊C4C2×D1114yes—
227C22×C4⋊C4C2×D1111yescharacteristic
228C22×C42—111no—
229C22×C42—111no—
230C22×C42—112no—
231C22×C42C2×D1111yescharacteristic
232#389—2216no—
233#384—24no—
234#384—224no—
235#384—224no—
236C4×C4⋊C4—118no—
237C4×C4⋊C4—224no—
238C2×#95—112no—
239C2×#95—114no—
240C2×#95—114no—
241C2×#95—112no—
242C22×C11C22×C4⋊C411yescharacteristic
243C22×C11C22×C4⋊C412yes—
244C22×C11C2×C4×D411yescharacteristic
245C22×C11C2×C4×Q811yescharacteristic
246C22×C11#52012yes—
247C22×C11C2×#12111yescharacteristic
248C22×C11C2×C22⋊Q811yescharacteristic
249C22×C11C2×#12511yescharacteristic
250C22×C11C2×#12711yescharacteristic
251C22×C11C2×C4⋊Q811yescharacteristic
252C22×C11C2×C4⋊Q812yes—
253C22×C11C2×C4⋊Q811yescharacteristic
254C22×C11#53511yescharacteristic
255C22×C11#53611yescharacteristic
256C22×C11#54412yes—
257C22×C11D4212yes—
258C22×C11#54712yes—
259C22×C11D4×Q812yes—
260C22×C11D4×Q812yes—
261C22×C11#55012yes—
262C22×C11#55412yes—
263C22×C11#55712yes—
264C22×C11Q8212yes—
265C4×C11—28no—
266C4×C11—44no—
267C4×C11—82no—
268C4×C11#38918yescomplemented
269Dic11—24no—
270Dic11—28no—
271Dic11—44no—
272Dic11—82no—
273Dic11#38418yescomplemented
274C23×C4—111no—
275C23×C4—112no—
276C23×C4—111no—
277C23×C4—112no—
278C23×C4—112no—
279C23×C4C22×D1112yes—
280C23×C4C22×D1112yes—
281C23×C4C22×D1112yes—
282C23×C4C22×D1111yescharacteristic
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—118no—
292C2×C4⋊C4—118no—
293C2×C4⋊C4—118no—
294C2×C4⋊C4—114no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—224no—
298C2×C4⋊C4—224no—
299C2×C4⋊C4—228no—
300C2×C4⋊C4—228no—
301C2×C4⋊C4—222no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—228no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—444no—
306C2×C4⋊C4—444no—
307C2×C4⋊C4C22⋊D1114yes—
308C2×C42—22no—
309C2×C42—22no—
310C2×C42—114no—
311C2×C42—114no—
312C2×C42—114no—
313C2×C42—114no—
314C2×C42—222no—
315C2×C42—222no—
316C2×C42—224no—
317C2×C42—228no—
318C2×C42C4×D1114yes—
319#95—118no—
320#95—224no—
321#95—228no—
322#95—228no—
323C2×C11C2×#38411yescharacteristic
324C2×C11C2×#38911yescharacteristic
325C2×C11#231711yescharacteristic
326C2×C11D4×C4⋊C412yes—
327C2×C11Q8×C4⋊C412yes—
328C2×C11#254111yescharacteristic
329C2×C11#254211yescharacteristic
330C2×C11#254611yescharacteristic
331C2×C11#255112yes—
332C2×C11#255212yes—
333C2×C11#256711yescharacteristic
334C24C23×D1111yescharacteristic
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—24no—
347C22×C4—22no—
348C22×C4—112no—
349C22×C4—112no—
350C22×C4—114no—
351C22×C4—112no—
352C22×C4—114no—
353C22×C4—112no—
354C22×C4—114no—
355C22×C4—112no—
356C22×C4—114no—
357C22×C4—112no—
358C22×C4—114no—
359C22×C4—114no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—224no—
368C22×C4—222no—
369C22×C4—224no—
370C22×C4—224no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—224no—
374C22×C4—222no—
375C22×C4C2×C4×D1114yes—
376C22×C4C2×C4×D1112yes—
377C22×C4#433912yes—
378C22×C4D4×D1114yes—
379C22×C4D4×D1112yes—
380C22×C4#434112yes—
381C22×C4Q8×D1114yes—
382C22×C4Q8×D1112yes—
383C22×C4Q8×D1112yes—
384C22×C4C2×C22⋊D1114yes—
385C22×C4C2×C22⋊D1112yes—
386C4⋊C4—28no—
387C4⋊C4—416no—
388C4⋊C4—44no—
389C4⋊C4—1132no—
390C4⋊C4—228no—
391C4⋊C4—4416no—
392C4⋊C4—448no—
393C4⋊C4—448no—
394C4⋊C4—444no—
395C42—28no—
396C42—1116no—
397C42—228no—
398C42—448no—
399C11#1391011yescharacteristic, complemented, Sylow
400C23C22×C4×D1111yescharacteristic
401C23C2×#433911yescharacteristic
402C23C2×D4×D1111yescharacteristic
403C23C2×D4×D1112yes—
404C23C2×#434111yescharacteristic
405C23#6703712yes—
406C23C2×Q8×D1112yes—
407C23C2×Q8×D1111yescharacteristic
408C23C2×Q8×D1111yescharacteristic
409C23#6704012yes—
410C23C22×C22⋊D1111yescharacteristic
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—28no—
418C2×C4—24no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—44no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—114no—
428C2×C4—114no—
429C2×C4—118no—
430C2×C4—114no—
431C2×C4—118no—
432C2×C4—114no—
433C2×C4—118no—
434C2×C4—222no—
435C2×C4—222no—
436C2×C4—224no—
437C2×C4—224no—
438C2×C4—224no—
439C2×C4—224no—
440C2×C4—224no—
441C2×C4—224no—
442C2×C4—224no—
443C2×C4—224no—
444C2×C4—228no—
445C2×C4—224no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—444no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—444no—
452C2×C4—444no—
453C2×C4—442no—
454C2×C4#6694014yes—
455C2×C4#6694214yes—
456C2×C4C4⋊C4×D1118yes—
457C2×C4C4⋊C4×D1114yes—
458C2×C4#6694914yes—
459C2×C4C4×C22⋊D1114yes—
460C2×C4#6699214yes—
461C2×C4#6699714yes—
462C22C2×#6694011yescharacteristic
463C22C2×#6694211yescharacteristic
464C22C2×C4⋊C4×D1111yescharacteristic
465C22C2×C4⋊C4×D1112yes—
466C22#1062303512yes—
467C22#1062303812yes—
468C22C2×#6694911yescharacteristic
469C22#1062304212yes—
470C22D11×#12711yescharacteristic
471C22#1062324611yescharacteristic
472C22#1062324912yes—
473C22#1062325212yes—
474C22#1062325312yes—
475C22D11×C4⋊Q811yescharacteristic
476C22D11×C4⋊Q812yes—
477C22#1062325511yescharacteristic
478C22#1062325812yes—
479C22#1062326012yes—
480C22C2×C4×C22⋊D1111yescharacteristic
481C22D4×C22⋊D1112yes—
482C22C2×#6699211yescharacteristic
483C22C2×#6699711yescharacteristic
484C22Q8×C22⋊D1112yes—
485C4—28no—
486C4—44no—
487C4—82no—
488C4—118no—
489C4—224no—
490C4—228no—
491C4—444no—
492C4—882no—
493C4#1062258518yescomplemented
494C2D11×#38411yescharacteristic
495C2C2×#1062258511yescharacteristic
496C2#1307123711yescharacteristic
497C2C4⋊C4×C22⋊D1112yes—
498C2#1307152812yes—
499C2#1307356011yescharacteristic
500C2#1307356811yescharacteristic
501C2#1307360211yescharacteristic
502C2#1307364312yes—
503C2#1307364912yes—
504C2#1307382211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#384C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#384D11
hypocenterC11#13910
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
32. C4×Dic11⋊C4C4semidirect
144. Dic11⋊C4C4⋊C4semidirect
147. C4×Dic11C4⋊C4semidirect
268. C4×C11#389semidirect
273. Dic11#384semidirect
399. C11#13910semidirect
493. C4#10622585semidirect

Maximal subgroups

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

subgroupindex
C2×#106225852
C2×#106225892
C2×C4⋊C4×Dic112
C2×C4×Dic11⋊C42
#130668792
#130668462
#130668452
C2×C11×#3842
#1391011