Finite Group Databasebeta

← #14675211

Subgroups — #14675211

Order 2816.

1838 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622589C211yesmaximal, characteristic
2C2×C4×Dic11⋊C4C212yesmaximal
3C2×#10622262C212yesmaximal
4C2×#10622262C212yesmaximal
5#13066850C212yesmaximal
6#13066848C211yesmaximal, characteristic
7Dic11⋊#95C212yesmaximal
8Dic11⋊#95C212yesmaximal
9C11×#1436C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×Dic11⋊C4C2212yes—
14C22×Dic11⋊C4C2212yes—
15C22×Dic11⋊C4C2212yes—
16C22×Dic11⋊C4C2212yes—
17C22×C4×Dic11C2211yescharacteristic
18C22×C4×Dic11C2212yes—
19C22×C4×Dic11C2212yes—
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622589C418yescomplemented
32C4×Dic11⋊C4—28no—
33#10622262—28no—
34#10622262C4116yescomplemented
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C2×C11×C4⋊C4—41no—
45C2×C11×C4⋊C4—41no—
46C2×C11×C4⋊C4C2×C414yes—
47C2×C42×C11—24no—
48C2×C42×C11—41no—
49C2×C4⋊Dic11—41no—
50C2×C4⋊Dic11—41no—
51C2×C4⋊Dic11C2×C414yes—
52C2×Dic11⋊C4—24no—
53C2×Dic11⋊C4—24no—
54C2×Dic11⋊C4—24no—
55C2×Dic11⋊C4—24no—
56C2×Dic11⋊C4—24no—
57C2×Dic11⋊C4—24no—
58C2×Dic11⋊C4C2×C418yes—
59C2×Dic11⋊C4C2×C418yes—
60C2×Dic11⋊C4C2×C418yes—
61C2×Dic11⋊C4C2×C418yes—
62C2×Dic11⋊C4D418yes—
63C2×Dic11⋊C4Q818yes—
64C2×C4×Dic11—24no—
65C2×C4×Dic11—24no—
66C2×C4×Dic11—24no—
67C2×C4×Dic11—24no—
68C2×C4×Dic11—24no—
69C2×C4×Dic11—24no—
70C2×C4×Dic11—24no—
71C2×C4×Dic11—42no—
72C2×C4×Dic11—41no—
73C2×C4×Dic11C2×C418yes—
74C2×C4×Dic11C2×C418yes—
75C2×C4×Dic11C2×C418yes—
76C2×C4×Dic11C2×C414yes—
77C11×#95—24no—
78C11×#95—41no—
79C11×#95C2×C418yes—
80C11⋊#95—24no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—41no—
84C11⋊#95—42no—
85C11⋊#95C2×C418yes—
86C4⋊C42—111nomaximal, Sylow
87C24×C11C2411yescharacteristic
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
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×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11C22×C414yes—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C22×C414yes—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C22×C414yes—
115C22×C4×C11C2×D414yes—
116C22×C4×C11C2×Q814yes—
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×Dic11C22×C414yes—
134C22×Dic11C22×C414yes—
135C22×Dic11C22×C414yes—
136C22×Dic11C22×C414yes—
137C22×Dic11C22×C414yes—
138C22×Dic11C22×C414yes—
139C22×Dic11C2×D414yes—
140C22×Dic11C2×D414yes—
141C22×Dic11C2×Q814yes—
142C22×Dic11C2×Q814yes—
143C22×Dic11#4114yes—
144C22×Dic11#4114yes—
145C11×C4⋊C4—44no—
146C42×C11—44no—
147C4⋊Dic11—44no—
148Dic11⋊C4—216no—
149Dic11⋊C4—216no—
150Dic11⋊C4—216no—
151Dic11⋊C4C4⋊C4132yescomplemented
152C4×Dic11—216no—
153C4×Dic11—216no—
154C4×Dic11—48no—
155C4×Dic11—44no—
156C4×Dic11C42116yescomplemented
157C2×#384—111no—
158C2×C4×C4⋊C4—112no—
159C2×C4×C4⋊C4—112no—
160C2×C4×C4⋊C4—112no—
161#1436—112no—
162#1436—111no—
163#1436D1111yescharacteristic
164C4⋊#95—112no—
165C4⋊#95—112no—
166C23×C11C23×C412yes—
167C23×C11C23×C411yescharacteristic
168C23×C11C22×D412yes—
169C23×C11C22×Q812yes—
170C23×C11C2×#4112yes—
171C23×C11C2×#4112yes—
172C23×C11H(5,𝔽2)11yescharacteristic
173C23×C11H(5,𝔽2)11yescharacteristic
174C23×C112−1+412yes—
175C2×C4×C11—24no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
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—22no—
190C2×C4×C11—22no—
191C2×C4×C11—24no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
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—41no—
201C2×C4×C11—41no—
202C2×C4×C11C2×C4214yes—
203C2×C4×C11C2×C4⋊C418yes—
204C2×Dic11—24no—
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—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11C2×C4218yes—
225C2×Dic11C2×C4⋊C418yes—
226C2×Dic11C2×C4⋊C418yes—
227C2×Dic11#11718yes—
228C2×Dic11C4×D418yes—
229C2×Dic11C4×D418yes—
230C2×Dic11C4×Q818yes—
231C2×Dic11C4×Q818yes—
232C22×C4⋊C4—112no—
233C22×C4⋊C4—112no—
234C22×C4⋊C4—112no—
235C22×C4⋊C4—112no—
236C22×C4⋊C4—111no—
237C22×C4⋊C4C2×D1111yescharacteristic
238C22×C42—111no—
239C22×C42—112no—
240C22×C42—112no—
241C22×C42—111no—
242C22×C42—112no—
243C22×C42C2×D1111yescharacteristic
244#384—118no—
245C4×C4⋊C4—1116no—
246C4×C4⋊C4—228no—
247C4×C4⋊C4—228no—
248C2×#95—112no—
249C2×#95—112no—
250C2×#95—112no—
251C2×#95—112no—
252C2×#95—112no—
253C2×#95—111no—
254C2×#95C2×D1112yes—
255C2×#95C2×D1111yescharacteristic
256C2×#95C2×D1112yes—
257C22×C11C22×C4211yescharacteristic
258C22×C11C22×C4⋊C412yes—
259C22×C11C2×#11712yes—
260C22×C11C2×C4×D412yes—
261C22×C11C2×C4×D412yes—
262C22×C11C2×C4×Q812yes—
263C22×C11C2×C4×Q812yes—
264C22×C11#51811yescharacteristic
265C22×C11#51911yescharacteristic
266C22×C11#52012yes—
267C22×C11#52012yes—
268C22×C11D4211yescharacteristic
269C22×C11#54712yes—
270C22×C11D4×Q812yes—
271C22×C11#55012yes—
272C22×C11#55412yes—
273C22×C11#55511yescharacteristic
274C22×C11#55612yes—
275C22×C11#55712yes—
276C22×C11Q8211yescharacteristic
277C22×C11#55911yescharacteristic
278C4×C11—28no—
279C4×C11—24no—
280C4×C11—44no—
281C4×C11—42no—
282C4×C11—42no—
283Dic11—28no—
284Dic11—44no—
285Dic11—44no—
286Dic11C4×C4⋊C4116yescomplemented
287C23×C4—112no—
288C23×C4—112no—
289C23×C4—112no—
290C23×C4—112no—
291C23×C4C22×D1111yescharacteristic
292C23×C4C22×D1111yescharacteristic
293C23×C4C22×D1112yes—
294C23×C4C22×D1111yescharacteristic
295C23×C4C22×D1112yes—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—118no—
299C2×C4⋊C4—118no—
300C2×C4⋊C4—118no—
301C2×C4⋊C4—118no—
302C2×C4⋊C4—118no—
303C2×C4⋊C4—118no—
304C2×C4⋊C4—114no—
305C2×C4⋊C4—224no—
306C2×C4⋊C4—224no—
307C2×C4⋊C4—224no—
308C2×C4⋊C4—224no—
309C2×C4⋊C4—224no—
310C2×C4⋊C4—224no—
311C2×C4⋊C4—441no—
312C2×C4⋊C4—441no—
313C2×C4⋊C4C4×D1114yes—
314C2×C42—24no—
315C2×C42—41no—
316C2×C42—118no—
317C2×C42—114no—
318C2×C42—118no—
319C2×C42—118no—
320C2×C42—224no—
321C2×C42—224no—
322C2×C42—224no—
323C2×C42—224no—
324C2×C42—224no—
325C2×C42—224no—
326C2×C42—224no—
327C2×C42—442no—
328C2×C42—441no—
329#95—24no—
330#95—41no—
331#95—118no—
332#95—224no—
333#95—224no—
334#95—224no—
335#95—442no—
336#95—441no—
337#95C4×D1118yes—
338C2×C11C2×C4×C4⋊C412yes—
339C2×C11#227411yescharacteristic
340C2×C11D4×C4⋊C412yes—
341C2×C11Q8×C4⋊C412yes—
342C2×C11#235412yes—
343C2×C11#235512yes—
344C2×C11#236512yes—
345C2×C11#236611yescharacteristic
346C2×C11#236911yescharacteristic
347C24C23×D1111yescharacteristic
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—114no—
370C22×C4—114no—
371C22×C4—114no—
372C22×C4—114no—
373C22×C4—114no—
374C22×C4—114no—
375C22×C4—114no—
376C22×C4—114no—
377C22×C4—114no—
378C22×C4—114no—
379C22×C4—114no—
380C22×C4—114no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—222no—
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×C4C2×C4×D1114yes—
398C22×C4C2×C4×D1112yes—
399C22×C4C2×C4×D1112yes—
400C22×C4C2×C4×D1114yes—
401C22×C4C2×C4×D1112yes—
402C22×C4C2×C4×D1114yes—
403C22×C4D4×D1114yes—
404C22×C4Q8×D1114yes—
405C4⋊C4—44no—
406C4⋊C4—1132no—
407C4⋊C4—2216no—
408C4⋊C4—2216no—
409C4⋊C4—2216no—
410C4⋊C4—444no—
411C42—44no—
412C42—1116no—
413C42—2216no—
414C42—2216no—
415C42—448no—
416C42—444no—
417C11C4⋊C4211yescharacteristic, complemented, Sylow
418C23C22×C4×D1111yescharacteristic
419C23C22×C4×D1112yes—
420C23C2×D4×D1112yes—
421C23#6703711yescharacteristic
422C23#6703711yescharacteristic
423C23C2×Q8×D1112yes—
424C23#41×D1112yes—
425C23#41×D1112yes—
426C23#6704312yes—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—118no—
455C2×C4—118no—
456C2×C4—118no—
457C2×C4—118no—
458C2×C4—118no—
459C2×C4—118no—
460C2×C4—118no—
461C2×C4—118no—
462C2×C4—224no—
463C2×C4—224no—
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—442no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4—442no—
481C2×C4—442no—
482C2×C4C42×D1114yes—
483C2×C4C4⋊C4×D1118yes—
484C22C2×C42×D1111yescharacteristic
485C22#1062301711yescharacteristic
486C22C2×C4⋊C4×D1112yes—
487C22#1062304711yescharacteristic
488C22D11×#11712yes—
489C22C4×D4×D1112yes—
490C22C4×D4×D1112yes—
491C22#1062307712yes—
492C22#1062307712yes—
493C22C4×Q8×D1112yes—
494C22C4×Q8×D1112yes—
495C22#1062312111yescharacteristic
496C22#1062313012yes—
497C22#1062316312yes—
498C22#1062316712yes—
499C22#1062318612yes—
500C22#1062319511yescharacteristic
501C22#1062320111yescharacteristic
502C22#1062321612yes—
503C22#1062323312yes—
504C22#1062325311yescharacteristic
505C4—24no—
506C4—28no—
507C4—42no—
508C4—42no—
509C4—44no—
510C4—1116no—
511C4—228no—
512C4—444no—
513C4—444no—
514C2C4×C4⋊C4×D1112yes—
515C2#1307097111yescharacteristic
516C2#1307151412yes—
517C2#1307153012yes—
518C2#1307156212yes—
519C2#1307157012yes—
520C2#1307167112yes—
521C2#1307167911yescharacteristic
522C2#1307170411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×#1436C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1436D11
hypocenterC11C4⋊C42
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
31. #10622589C4semidirect
34. #10622262C4semidirect
151. Dic11⋊C4C4⋊C4semidirect
156. C4×Dic11C42semidirect
286. Dic11C4×C4⋊C4semidirect
417. C11C4⋊C42semidirect

Maximal subgroups

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

subgroupindex
C2×#106225892
C2×C4×Dic11⋊C42
C2×#106222622
#130668502
#130668482
Dic11⋊#952
C11×#14362
C4⋊C4211