Finite Group Databasebeta

← #14682535

Subgroups — #14682535

Order 2816.

1254 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622587C211yesmaximal, characteristic
2#13066886C212yesmaximal
3#13066874C212yesmaximal
4#13066871C212yesmaximal
5#13066849C212yesmaximal
6#13066848C211yesmaximal, characteristic
7#13066847C212yesmaximal
8Dic11⋊#95C212yesmaximal
9C11×#1436C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×Dic11⋊C4C2212yes—
14C22×Dic11⋊C4C2212yes—
15C22×C4×Dic11C2211yescharacteristic
16C22×C4×Dic11C2211yescharacteristic
17C2×C11×#95C2212yes—
18C2×C11×#95C2212yes—
19C2×C11×#95C2211yescharacteristic
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622587C418yescomplemented
32C23×C4×C11C2312yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C22×Dic22—24no—
42C22×Dic22—42no—
43C22×Dic22—41no—
44C22×Dic22—41no—
45C22×Dic22C2×C414yes—
46C2×C11×C4⋊C4—41no—
47C2×C11×C4⋊C4—41no—
48C2×C11×C4⋊C4C2×C414yes—
49C2×C42×C11—41no—
50C2×C42×C11—42no—
51C2×Dic11⋊C4—24no—
52C2×Dic11⋊C4—42no—
53C2×Dic11⋊C4—42no—
54C2×Dic11⋊C4—42no—
55C2×Dic11⋊C4—42no—
56C2×Dic11⋊C4Q818yescomplemented
57C2×C4×Dic11—42no—
58C2×C4×Dic11—41no—
59C2×C4×Dic11—42no—
60C2×C4×Dic11C2×C414yes—
61C11×#95—24no—
62C11×#95—42no—
63C11×#95—41no—
64C11⋊#95—24no—
65C11⋊#95—24no—
66C11⋊#95—24no—
67C11⋊#95—42no—
68C11⋊#95—42no—
69C11⋊#95—42no—
70C11⋊#95—42no—
71C11⋊#95—42no—
72C11⋊#95—41no—
73C11⋊#95C2×C418yes—
74C11⋊#95C2×C418yes—
75#14471—111nomaximal, Sylow
76C24×C11C2411yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—21no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
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×C11C22×C412yes—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C22×C412yes—
104C22×C4×C11C2×Q814yes—
105C22×C4×C11#4114yes—
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×Dic11C22×C414yes—
130C22×Dic11C22×C414yes—
131C22×Dic11C2×Q814yes—
132C22×Dic11C2×Q814yes—
133C22×Dic11#4114yes—
134C2×Dic22—28no—
135C2×Dic22—44no—
136C2×Dic22—44no—
137C2×Dic22—48no—
138C2×Dic22—48no—
139C11×C4⋊C4—44no—
140C42×C11—44no—
141Dic11⋊C4—48no—
142Dic11⋊C4—48no—
143C4×Dic11—44no—
144C4×Dic11—44no—
145C2×#391—111no—
146#1446—112no—
147#1442—112no—
148#1442—112no—
149#1436—112no—
150#1436—112no—
151#1436—111no—
152#1436D1111yescharacteristic
153C4⋊#95—112no—
154C23×C11C23×C411yescharacteristic
155C23×C11C22×Q812yes—
156C23×C11C2×#4112yes—
157C23×C11C2×#4112yes—
158C23×C11H(5,𝔽2)11yescharacteristic
159C23×C11H(5,𝔽2)11yescharacteristic
160C23×C11H(5,𝔽2)12yes—
161C23×C11H(5,𝔽2)12yes—
162C23×C112−1+412yes—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11#11714yes—
192C2×Dic11—24no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—24no—
202C2×Dic11—24no—
203C2×Dic11—24no—
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—
218C2×Dic11—42no—
219C2×Dic11C4×Q818yes—
220Dic22—416no—
221C23×Q8—111no—
222C22×C4⋊C4—112no—
223C22×C4⋊C4—112no—
224C22×C4⋊C4C2×D1111yescharacteristic
225C22×C42—111no—
226C22×C42—111no—
227C22×C42C2×D1111yescharacteristic
228#391—118no—
229C2×#95—112no—
230C2×#95—112no—
231C2×#95—112no—
232C2×#95—112no—
233C2×#95—112no—
234C2×#95—112no—
235C2×#95—112no—
236C2×#95—111no—
237C2×#95—112no—
238C2×#95—112no—
239C2×#95—112no—
240C2×#95C2×D1112yes—
241C2×#95C2×D1112yes—
242C2×#95C2×D1111yescharacteristic
243C22×C11C2×#11711yescharacteristic
244C22×C11C2×C4×Q812yes—
245C22×C11#51811yescharacteristic
246C22×C11#51811yescharacteristic
247C22×C11#52012yes—
248C22×C11#53812yes—
249C22×C11#53812yes—
250C22×C11#53812yes—
251C22×C11#53912yes—
252C22×C11#54312yes—
253C22×C11#54412yes—
254C22×C11#55412yes—
255C22×C11#55412yes—
256C22×C11#55511yescharacteristic
257C22×C11#55612yes—
258C22×C11#55712yes—
259C22×C11Q8211yescharacteristic
260C22×C11#55912yes—
261C22×C11H(3,𝔽4)11yescharacteristic
262C22×C11#56212yes—
263C22×C11#56311yescharacteristic
264C4×C11—24no—
265C4×C11—42no—
266C4×C11—42no—
267C4×C11—44no—
268C4×C11—82no—
269Dic11—28no—
270Dic11—44no—
271Dic11—44no—
272Dic11—82no—
273C22×Q8—114no—
274C22×Q8—224no—
275C22×Q8—441no—
276C22×Q8—441no—
277C22×Q8—442no—
278C23×C4—112no—
279C23×C4—112no—
280C23×C4—112no—
281C23×C4—112no—
282C23×C4C22×D1112yes—
283C23×C4C22×D1111yescharacteristic
284C23×C4C22×D1111yescharacteristic
285C23×C4C22×D1112yes—
286C23×C4C22×D1111yescharacteristic
287C2×C4⋊C4—41no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4—118no—
290C2×C4⋊C4—224no—
291C2×C4⋊C4—442no—
292C2×C4⋊C4—442no—
293C2×C4⋊C4—442no—
294C2×C4⋊C4—442no—
295C2×C4⋊C4C4×D1114yes—
296C2×C42—42no—
297C2×C42—41no—
298C2×C42—114no—
299C2×C42—442no—
300C2×C42—442no—
301C2×C42—441no—
302#95—24no—
303#95—42no—
304#95—41no—
305#95—118no—
306#95—118no—
307#95—224no—
308#95—224no—
309#95—224no—
310#95—442no—
311#95—442no—
312#95—441no—
313#95—442no—
314#95—442no—
315#95—442no—
316C2×C11#231211yescharacteristic
317C2×C11#232912yes—
318C2×C11#235512yes—
319C2×C11#236911yescharacteristic
320C2×C11#237911yescharacteristic
321C2×C11#280412yes—
322C2×C11#280512yes—
323C2×C11#280612yes—
324C2×C11#280812yes—
325C24C23×D1111yescharacteristic
326C2×Q8—228no—
327C2×Q8—444no—
328C2×Q8—444no—
329C2×Q8—448no—
330C2×Q8—448no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—114no—
356C22×C4—114no—
357C22×C4—114no—
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—222no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4C2×C4×D1112yes—
384C22×C4C2×C4×D1112yes—
385C22×C4C2×C4×D1112yes—
386C22×C4#433914yes—
387C22×C4Q8×D1114yes—
388C4⋊C4—44no—
389C4⋊C4—448no—
390C4⋊C4—448no—
391C42—44no—
392C42—444no—
393C42—444no—
394C11#1447111yescharacteristic, complemented, Sylow
395C23C22×C4×D1111yescharacteristic
396C23C2×#433912yes—
397C23#6703711yescharacteristic
398C23#6703711yescharacteristic
399C23#6703712yes—
400C23C2×Q8×D1112yes—
401C23#41×D1112yes—
402C23#6704212yes—
403C23#6704312yes—
404Q8—4416no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—118no—
434C2×C4—224no—
435C2×C4—224no—
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—224no—
445C2×C4—224no—
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×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4#6692514yes—
462C22C2×#6692511yescharacteristic
463C22#1062301711yescharacteristic
464C22#1062304212yes—
465C22#1062305211yescharacteristic
466C22#1062306412yes—
467C22#1062307712yes—
468C22#1062309012yes—
469C22#1062309112yes—
470C22#1062309112yes—
471C22#1062309812yes—
472C22C4×Q8×D1112yes—
473C22#1062312511yescharacteristic
474C22#1062315212yes—
475C22#1062316512yes—
476C22#1062316712yes—
477C22#1062318211yescharacteristic
478C22#1062318812yes—
479C22#1062320111yescharacteristic
480C22#1062322012yes—
481C22#1062323812yes—
482C22#1062325311yescharacteristic
483C4—24no—
484C4—44no—
485C4—42no—
486C4—42no—
487C4—82no—
488C4—228no—
489C4—444no—
490C4—444no—
491C4—882no—
492C2#1307121111yescharacteristic
493C2#1307134512yes—
494C2#1307156912yes—
495C2#1307170411yescharacteristic
496C2#1307178611yescharacteristic
497C2#1307655812yes—
498C2#1307656712yes—
499C2#1307657312yes—
500C2#1307659412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1436D11
hypocenterC11#14471
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
31. #10622587C4semidirect
56. C2×Dic11⋊C4Q8semidirect
394. C11#14471semidirect

Maximal subgroups

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

subgroupindex
C2×#106225872
#130668862
#130668742
#130668712
#130668492
#130668482
#130668472
Dic11⋊#952
C11×#14362
#1447111