Finite Group Databasebeta

← #14682284

Subgroups — #14682284

Order 2816.

1614 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66922C211yesmaximal, characteristic
2C2×#10622259C212yesmaximal
3#13066886C212yesmaximal
4#13066868C212yesmaximal
5#13066868C212yesmaximal
6#13066850C212yesmaximal
7#13066850C212yesmaximal
8#13066843C211yesmaximal, characteristic
9C11×#1434C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×C4⋊Dic11C2212yes—
14C22×C4⋊Dic11C2212yes—
15C22×Dic11⋊C4C2212yes—
16C22×C4×Dic11C2212yes—
17C2×#66922—28no—
18C2×#66922C418yescomplemented
19C2×C11×#95C2212yes—
20C2×C11×#95C2211yescharacteristic
21C2×C11×#95C2212yes—
22C2×C11×#95C2211yescharacteristic
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33#10622259—28no—
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C22×Dic22—24no—
44C22×Dic22—41no—
45C22×Dic22—42no—
46C22×Dic22—41no—
47C22×Dic22—42no—
48C22×Dic22—41no—
49C22×Dic22—41no—
50C22×Dic22C2×C414yes—
51C22×Dic22C2×C414yes—
52C22×Dic22D418yes—
53C2×C42×C11—24no—
54C2×C42×C11C2×C414yes—
55C2×C4⋊Dic11—24no—
56C2×C4⋊Dic11—24no—
57C2×C4⋊Dic11—24no—
58C2×C4⋊Dic11—24no—
59C2×C4⋊Dic11C2×C418yes—
60C2×C4⋊Dic11C2×C418yes—
61C2×Dic11⋊C4—24no—
62C2×Dic11⋊C4—42no—
63C2×Dic11⋊C4—42no—
64C2×C4×Dic11—24no—
65C2×C4×Dic11—42no—
66C2×C4×Dic11—42no—
67#66922—232no—
68C11×#95—24no—
69C11×#95—22no—
70C11×#95—24no—
71C11×#95Q814yescomplemented
72C11⋊#95—24no—
73C11⋊#95—24no—
74C11⋊#95—22no—
75C11⋊#95—24no—
76C11⋊#95—24no—
77C11⋊#95—42no—
78C11⋊#95—42no—
79C11⋊#95—42no—
80C11⋊#95—42no—
81C11⋊#95Q814yescomplemented
82#14450—111nomaximal, Sylow
83C24×C11C2411yescharacteristic
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C22×C412yes—
107C22×C4×C11C2×D414yes—
108C22×C4×C11C2×Q814yes—
109C22×C4×C11C2×Q812yes—
110C22×C4×C11C2×Q812yes—
111C22×C4×C11#4112yes—
112C22×C4×C11#4112yes—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11C22×C414yes—
137C22×Dic11C22×C414yes—
138C22×Dic11C2×D414yes—
139C22×Dic11C2×D414yes—
140C22×Dic11C2×Q814yes—
141C2×Dic22—28no—
142C2×Dic22—44no—
143C2×Dic22—44no—
144C2×Dic22—44no—
145C2×Dic22—44no—
146C2×Dic22—48no—
147C2×Dic22—48no—
148C2×Dic22—48no—
149C2×Dic22—48no—
150C2×Dic22C22⋊C4116yes—
151C42×C11—28no—
152C4⋊Dic11—216no—
153C4⋊Dic11—216no—
154Dic11⋊C4—48no—
155C4×Dic11—48no—
156C22×C4⋊Q8—111no—
157C2×#391—112no—
158#1446—112no—
159#1441—112no—
160#1441—112no—
161#1436—112no—
162#1436—112no—
163#1434—111no—
164#1434D1111yescharacteristic
165C23×C11C23×C411yescharacteristic
166C23×C11C22×D412yes—
167C23×C11C22×Q811yescharacteristic
168C23×C11C22×Q811yescharacteristic
169C23×C11C2×#4111yescharacteristic
170C23×C11C2×#4111yescharacteristic
171C23×C11H(5,𝔽2)12yes—
172C23×C11H(5,𝔽2)11yescharacteristic
173C23×C11H(5,𝔽2)11yescharacteristic
174C23×C112−1+412yes—
175C23×C112−1+412yes—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—24no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11C2×C22⋊C414yes—
203C2×C4×C11C4×Q814yes—
204C2×C4×C11C4×Q814yes—
205C2×Dic11—24no—
206C2×Dic11—24no—
207C2×Dic11—24no—
208C2×Dic11—24no—
209C2×Dic11—24no—
210C2×Dic11—24no—
211C2×Dic11—24no—
212C2×Dic11—24no—
213C2×Dic11—24no—
214C2×Dic11—24no—
215C2×Dic11—24no—
216C2×Dic11—24no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11C2×C22⋊C418yes—
233Dic22—416no—
234Dic22—416no—
235C23×Q8—111no—
236C23×Q8—111no—
237C2×C4⋊Q8—118no—
238C2×C4⋊Q8—228no—
239C22×C4⋊C4—112no—
240C22×C4⋊C4—112no—
241C22×C4⋊C4—112no—
242C22×C42—112no—
243C22×C42C2×D1111yescharacteristic
244#391—228no—
245C2×#95—111no—
246C2×#95—112no—
247C2×#95—111no—
248C2×#95—112no—
249C2×#95—112no—
250C2×#95—112no—
251C2×#95—112no—
252C2×#95—112no—
253C2×#95—112no—
254C2×#95—112no—
255C2×#95C2×D1112yes—
256C2×#95C2×D1111yescharacteristic
257C2×#95C2×D1112yes—
258C2×#95C2×D1111yescharacteristic
259C22×C11C22×C22⋊C411yescharacteristic
260C22×C11C2×C4×Q811yescharacteristic
261C22×C11C2×C4×Q811yescharacteristic
262C22×C11#51811yescharacteristic
263C22×C11#51811yescharacteristic
264C22×C11#51911yescharacteristic
265C22×C11#51911yescharacteristic
266C22×C11#53412yes—
267C22×C11#53412yes—
268C22×C11#54212yes—
269C22×C11#54212yes—
270C22×C11#54412yes—
271C22×C11#54412yes—
272C22×C11#54812yes—
273C22×C11#54812yes—
274C22×C11D4×Q812yes—
275C22×C11D4×Q812yes—
276C22×C11#55411yescharacteristic
277C22×C11#55411yescharacteristic
278C22×C11#55511yescharacteristic
279C22×C11Q8211yescharacteristic
280C22×C11#56312yes—
281C22×C11#56312yes—
282C4×C11—24no—
283C4×C11—24no—
284C4×C11—24no—
285C4×C11—44no—
286C4×C11—82no—
287Dic11—28no—
288Dic11—44no—
289Dic11—44no—
290Dic11—82no—
291C22×Q8—114no—
292C22×Q8—114no—
293C22×Q8—118no—
294C22×Q8—224no—
295C22×Q8—441no—
296C22×Q8—442no—
297C22×Q8—441no—
298C22×Q8—441no—
299C22×Q8—441no—
300C22×Q8—442no—
301C23×C4—112no—
302C23×C4—112no—
303C23×C4—112no—
304C23×C4—112no—
305C23×C4C22×D1112yes—
306C23×C4C22×D1112yes—
307C23×C4C22×D1111yescharacteristic
308C23×C4C22×D1111yescharacteristic
309C23×C4C22×D1111yescharacteristic
310C4⋊Q8—2232no—
311C2×C4⋊C4—118no—
312C2×C4⋊C4—118no—
313C2×C4⋊C4—224no—
314C2×C4⋊C4—224no—
315C2×C4⋊C4—224no—
316C2×C4⋊C4—224no—
317C2×C4⋊C4—224no—
318C2×C4⋊C4—442no—
319C2×C4⋊C4—442no—
320C2×C42—24no—
321C2×C42—224no—
322C2×C42—442no—
323C2×C42—442no—
324C2×C42C4×D1114yes—
325#95—22no—
326#95—24no—
327#95—24no—
328#95—114no—
329#95—224no—
330#95—224no—
331#95—224no—
332#95—224no—
333#95—222no—
334#95—442no—
335#95—442no—
336#95—442no—
337#95—442no—
338#95Dic2214yescomplemented
339C2×C11#230811yescharacteristic
340C2×C11#233111yescharacteristic
341C2×C11#233111yescharacteristic
342C2×C11Q8×C22⋊C411yescharacteristic
343C2×C11Q8×C22⋊C411yescharacteristic
344C2×C11#236911yescharacteristic
345C2×C11#238111yescharacteristic
346C2×C11#272912yes—
347C2×C11#272912yes—
348C2×C11#273112yes—
349C2×C11#273412yes—
350C24C23×D1111yescharacteristic
351C2×Q8—1116no—
352C2×Q8—228no—
353C2×Q8—444no—
354C2×Q8—444no—
355C2×Q8—444no—
356C2×Q8—444no—
357C2×Q8—448no—
358C2×Q8—448no—
359C2×Q8—448no—
360C2×Q8—448no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—114no—
382C22×C4—114no—
383C22×C4—114no—
384C22×C4—114no—
385C22×C4—114no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4—222no—
394C22×C4—222no—
395C22×C4—222no—
396C22×C4—222no—
397C22×C4—222no—
398C22×C4—222no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4C2×Dic2214yes—
410C22×C4C2×Dic2212yes—
411C22×C4C2×C4×D1112yes—
412C22×C4C2×C4×D1112yes—
413C22×C4C2×C4×D1112yes—
414C22×C4#433912yes—
415C22×C4D4×D1114yes—
416C22×C4#434112yes—
417C22×C4Q8×D1112yes—
418C4⋊C4—2216no—
419C4⋊C4—2216no—
420C4⋊C4—448no—
421C42—28no—
422C42—448no—
423C11#1445011yescharacteristic, complemented, Sylow
424C23C22×Dic2211yescharacteristic
425C23C22×C4×D1111yescharacteristic
426C23C2×#433911yescharacteristic
427C23C2×D4×D1112yes—
428C23C2×#434111yescharacteristic
429C23C2×Q8×D1111yescharacteristic
430C23#6704211yescharacteristic
431C23#6704211yescharacteristic
432C23#6704212yes—
433C23#6704312yes—
434C23#6704312yes—
435Q8—4416no—
436Q8—4416no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—118no—
464C2×C4—224no—
465C2×C4—224no—
466C2×C4—224no—
467C2×C4—224no—
468C2×C4—224no—
469C2×C4—224no—
470C2×C4—224no—
471C2×C4—224no—
472C2×C4—224no—
473C2×C4—224no—
474C2×C4—224no—
475C2×C4—224no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4—442no—
481C2×C4—442no—
482C2×C4—442no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—442no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4C4×Dic2214yes—
492C2×C4C22⋊C4×D1114yes—
493C2×C4#6694014yes—
494C22C2×C4×Dic2211yescharacteristic
495C22C2×C22⋊C4×D1111yescharacteristic
496C22C2×#6694011yescharacteristic
497C22#1062304711yescharacteristic
498C22#1062304711yescharacteristic
499C22#1062305012yes—
500C22#1062305211yescharacteristic
501C22#1062305211yescharacteristic
502C22#1062306512yes—
503C22D4×Dic2212yes—
504C22#1062307411yescharacteristic
505C22#1062308312yes—
506C22#1062309411yescharacteristic
507C22Q8×Dic2211yescharacteristic
508C22#1062311011yescharacteristic
509C22#1062312912yes—
510C22#1062316312yes—
511C22#1062318412yes—
512C22#1062318412yes—
513C22#1062321312yes—
514C22#1062322012yes—
515C22#1062324312yes—
516C22#1062324312yes—
517C4—24no—
518C4—24no—
519C4—24no—
520C4—44no—
521C4—82no—
522C4—228no—
523C4—444no—
524C4—444no—
525C4—882no—
526C2#1307119311yescharacteristic
527C2#1307136211yescharacteristic
528C2#1307136411yescharacteristic
529C2#1307144811yescharacteristic
530C2C22⋊C4×Dic2211yescharacteristic
531C2#1307170511yescharacteristic
532C2#1307179611yescharacteristic
533C2#1307559912yes—
534C2#1307560112yes—
535C2#1307562712yes—
536C2#1307564912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1434D11
hypocenterC11#14450
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
18. C2×#66922C4semidirect
71. C11×#95Q8semidirect
81. C11⋊#95Q8semidirect
338. #95Dic22semidirect
423. C11#14450semidirect

Maximal subgroups

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

subgroupindex
C22×#669222
C2×#106222592
#130668862
#130668682
#130668502
#130668432
C11×#14342
#1445011