Finite Group Databasebeta

← #14682323

Subgroups — #14682323

Order 2816.

1190 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622548C211yesmaximal, characteristic
2#13066868C212yesmaximal
3#13066868C212yesmaximal
4#13066868C212yesmaximal
5#13066850C212yesmaximal
6#13066850C212yesmaximal
7#13066850C212yesmaximal
8#13066843C211yesmaximal, characteristic
9C11×#1434C211yesmaximal, characteristic
10C22×C42×C11C2211yescharacteristic
11C22×C4⋊Dic11C2211yescharacteristic
12C22×C4⋊Dic11C2212yes—
13C22×C4⋊Dic11C2212yes—
14C22×C4⋊Dic11C2211yescharacteristic
15C22×Dic11⋊C4C2212yes—
16C22×C4×Dic11C2212yes—
17C2×C11×#95C2212yes—
18C2×C11×#95C2212yes—
19C2×C11×#95C2211yescharacteristic
20C2×C11×#95C2211yescharacteristic
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2211yescharacteristic
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31#10622548C418yescomplemented
32C23×C4×C11C2312yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C2×C42×C11—24no—
42C2×C42×C11C2×C414yes—
43C2×C4⋊Dic11—41no—
44C2×C4⋊Dic11—42no—
45C2×C4⋊Dic11—42no—
46C2×C4⋊Dic11—41no—
47C2×C4⋊Dic11—41no—
48C2×C4⋊Dic11—42no—
49C2×C4⋊Dic11—42no—
50C2×C4⋊Dic11—41no—
51C2×C4⋊Dic11C2×C414yes—
52C2×C4⋊Dic11C2×C414yes—
53C2×C4⋊Dic11C2×C418yes—
54C2×C4⋊Dic11C2×C418yes—
55C2×Dic11⋊C4—42no—
56C2×Dic11⋊C4—42no—
57C2×Dic11⋊C4—42no—
58C2×C4×Dic11—42no—
59C2×C4×Dic11—42no—
60C2×C4×Dic11—42no—
61C11×#95—22no—
62C11×#95—24no—
63C11×#95—24no—
64C11×#95Q814yes—
65C11⋊#95—24no—
66C11⋊#95—24no—
67C11⋊#95—22no—
68C11⋊#95—42no—
69C11⋊#95—42no—
70C11⋊#95—42no—
71C11⋊#95—42no—
72C11⋊#95—42no—
73C11⋊#95—42no—
74C11⋊#95Q814yes—
75#14454—111nomaximal, Sylow
76C24×C11C2411yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
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×C11C22×C412yes—
98C22×C4×C11C22×C412yes—
99C22×C4×C11C22×C412yes—
100C22×C4×C11C2×Q814yes—
101C22×C4×C11C2×Q812yes—
102C22×C4×C11C2×Q812yes—
103C22×C4×C11#4114yes—
104C22×C4×C11#4112yes—
105C22×C4×C11#4112yes—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11—22no—
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×Dic11C22×C414yes—
132C22×Dic11C22×C414yes—
133C22×Dic11C2×Q814yes—
134C42×C11—28no—
135C4⋊Dic11—44no—
136C4⋊Dic11—44no—
137C4⋊Dic11—48no—
138C4⋊Dic11—48no—
139Dic11⋊C4—48no—
140C4×Dic11—48no—
141C2×#384—111no—
142#1441—112no—
143#1441—112no—
144#1441—112no—
145#1436—112no—
146#1436—112no—
147#1436—112no—
148#1434—111no—
149#1434D1111yescharacteristic
150C23×C11C23×C411yescharacteristic
151C23×C11C22×Q811yescharacteristic
152C23×C11C22×Q811yescharacteristic
153C23×C11C2×#4111yescharacteristic
154C23×C11C2×#4112yes—
155C23×C11C2×#4111yescharacteristic
156C23×C11H(5,𝔽2)11yescharacteristic
157C23×C11H(5,𝔽2)11yescharacteristic
158C23×C11H(5,𝔽2)12yes—
159C23×C11H(5,𝔽2)12yes—
160C23×C112−1+412yes—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—24no—
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—24no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11#11714yes—
188C2×C4×C11C4×Q814yes—
189C2×C4×C11C4×Q814yes—
190C2×Dic11—24no—
191C2×Dic11—24no—
192C2×Dic11—24no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C22×C4⋊C4—111no—
219C22×C4⋊C4—112no—
220C22×C4⋊C4—112no—
221C22×C4⋊C4—111no—
222C22×C4⋊C4—112no—
223C22×C42—112no—
224C22×C42C2×D1111yescharacteristic
225#384—118no—
226C2×#95—111no—
227C2×#95—112no—
228C2×#95—112no—
229C2×#95—111no—
230C2×#95—112no—
231C2×#95—112no—
232C2×#95—112no—
233C2×#95—112no—
234C2×#95—112no—
235C2×#95—112no—
236C2×#95C2×D1112yes—
237C2×#95C2×D1112yes—
238C2×#95C2×D1111yescharacteristic
239C2×#95C2×D1111yescharacteristic
240C22×C11C2×#11711yescharacteristic
241C22×C11C2×C4×Q811yescharacteristic
242C22×C11C2×C4×Q811yescharacteristic
243C22×C11#51811yescharacteristic
244C22×C11#51811yescharacteristic
245C22×C11#51811yescharacteristic
246C22×C11#51911yescharacteristic
247C22×C11#53912yes—
248C22×C11#53912yes—
249C22×C11#54212yes—
250C22×C11#54212yes—
251C22×C11#54412yes—
252C22×C11#54412yes—
253C22×C11#55312yes—
254C22×C11#55312yes—
255C22×C11#55412yes—
256C22×C11#55411yescharacteristic
257C22×C11#55411yescharacteristic
258C22×C11#55412yes—
259C22×C11#55511yescharacteristic
260C22×C11Q8211yescharacteristic
261C22×C11#56012yes—
262C22×C11#56012yes—
263C4×C11—24no—
264C4×C11—24no—
265C4×C11—24no—
266C4×C11—44no—
267C4×C11—82no—
268Dic11—44no—
269Dic11—44no—
270Dic11—44no—
271Dic11—82no—
272C23×C4—112no—
273C23×C4—112no—
274C23×C4—112no—
275C23×C4—112no—
276C23×C4C22×D1112yes—
277C23×C4C22×D1112yes—
278C23×C4C22×D1111yescharacteristic
279C23×C4C22×D1111yescharacteristic
280C23×C4C22×D1111yescharacteristic
281C2×C4⋊C4—118no—
282C2×C4⋊C4—114no—
283C2×C4⋊C4—114no—
284C2×C4⋊C4—118no—
285C2×C4⋊C4—442no—
286C2×C4⋊C4—442no—
287C2×C4⋊C4—442no—
288C2×C4⋊C4—441no—
289C2×C4⋊C4—442no—
290C2×C4⋊C4—442no—
291C2×C4⋊C4—441no—
292C2×C4⋊C4—441no—
293C2×C4⋊C4—442no—
294C2×C4⋊C4—442no—
295C2×C4⋊C4—441no—
296C2×C42—24no—
297C2×C42—442no—
298C2×C42—442no—
299C2×C42—442no—
300C2×C42C4×D1114yes—
301#95—22no—
302#95—24no—
303#95—24no—
304#95—114no—
305#95—224no—
306#95—224no—
307#95—222no—
308#95—442no—
309#95—442no—
310#95—442no—
311#95—442no—
312#95—442no—
313#95—442no—
314#95Dic2214yes—
315C2×C11#231311yescharacteristic
316C2×C11#233111yescharacteristic
317C2×C11#233111yescharacteristic
318C2×C11#234511yescharacteristic
319C2×C11#234511yescharacteristic
320C2×C11#236911yescharacteristic
321C2×C11#238011yescharacteristic
322C2×C11#279012yes—
323C2×C11#279012yes—
324C2×C11#279212yes—
325C2×C11#279512yes—
326C24C23×D1111yescharacteristic
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—114no—
348C22×C4—114no—
349C22×C4—114no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4C2×Dic2214yes—
376C22×C4C2×Dic2212yes—
377C22×C4C2×C4×D1112yes—
378C22×C4C2×C4×D1112yes—
379C22×C4C2×C4×D1112yes—
380C22×C4#433912yes—
381C22×C4#434114yes—
382C22×C4#434112yes—
383C22×C4Q8×D1112yes—
384C4⋊C4—444no—
385C4⋊C4—444no—
386C4⋊C4—448no—
387C4⋊C4—448no—
388C4⋊C4—448no—
389C42—28no—
390C42—448no—
391C11#1445411yescharacteristic, complemented, Sylow
392C23C22×Dic2211yescharacteristic
393C23C22×C4×D1111yescharacteristic
394C23C2×#433911yescharacteristic
395C23C2×#434112yes—
396C23C2×#434111yescharacteristic
397C23C2×Q8×D1111yescharacteristic
398C23#6704212yes—
399C23#6704212yes—
400C23#6704211yescharacteristic
401C23#6704211yescharacteristic
402C23#6704312yes—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—224no—
430C2×C4—224no—
431C2×C4—224no—
432C2×C4—224no—
433C2×C4—224no—
434C2×C4—224no—
435C2×C4—224no—
436C2×C4—224no—
437C2×C4—224no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4C4×Dic2214yes—
458C2×C4#6693014yes—
459C2×C4#6694014yes—
460C22C2×C4×Dic2211yescharacteristic
461C22C2×#6693011yescharacteristic
462C22C2×#6694011yescharacteristic
463C22#1062304711yescharacteristic
464C22#1062305012yes—
465C22#1062305211yescharacteristic
466C22#1062305211yescharacteristic
467C22#1062305211yescharacteristic
468C22#1062306512yes—
469C22#1062307411yescharacteristic
470C22#1062307412yes—
471C22#1062309411yescharacteristic
472C22#1062309612yes—
473C22Q8×Dic2211yescharacteristic
474C22#1062311011yescharacteristic
475C22#1062314912yes—
476C22#1062316612yes—
477C22#1062319612yes—
478C22#1062319612yes—
479C22#1062321312yes—
480C22#1062322012yes—
481C22#1062324212yes—
482C22#1062324212yes—
483C4—24no—
484C4—24no—
485C4—24no—
486C4—44no—
487C4—82no—
488C4—444no—
489C4—444no—
490C4—444no—
491C4—882no—
492C2#1307121711yescharacteristic
493C2#1307136211yescharacteristic
494C2#1307136411yescharacteristic
495C2#1307149111yescharacteristic
496C2#1307149511yescharacteristic
497C2#1307170511yescharacteristic
498C2#1307179211yescharacteristic
499C2#1307638612yes—
500C2#1307639012yes—
501C2#1307641512yes—
502C2#1307644812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1434D11
hypocenterC11#14454
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
31. #10622548C4semidirect
391. C11#14454semidirect

Maximal subgroups

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

subgroupindex
C2×#106225482
#130668682
#130668502
#130668432
C11×#14342
#1445411