Finite Group Databasebeta

← #14803651

Subgroups — #14803651

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622683C211yesmaximal, characteristic, complemented
2#13073789C211yesmaximal, characteristic, complemented
3#13071681C211yesmaximal, characteristic, complemented
4#13070032C212yesmaximal, complemented
5#13069924C212yesmaximal, complemented
6#13069563C211yesmaximal, characteristic, complemented
7#13069332C211yesmaximal, characteristic, complemented
8#13068966C212yesmaximal, complemented
9#13068624C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C2×C11×#459C211yesmaximal, characteristic
12C22×C11×D8C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×D4×Dic11—21no—
16C2×D4×Dic11C2212yes—
17C2×#66922C2211yescharacteristic
18C11×#459—24no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#102C2212yes—
21#10622834—21no—
22#10622834C2212yes—
23#10622834C2212yes—
24#10622833—22no—
25C2×#66896C2212yes—
26C2×#66896C2211yescharacteristic
27C2×#66896C2212yes—
28C2×#66896C2211yescharacteristic
29#10622825—21no—
30#10622825—21no—
31C2×Dic11⋊C8C2212yes—
32#10622683—24no—
33#10622590C2212yes—
34#10622560—22no—
35C4×C4⋊Dic11C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622189C2212yes—
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11C2312yes—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×Dic11—22no—
49C22×Dic22—21no—
50C2×C11×D8—24no—
51C2×C11×D8—24no—
52C2×C11×D8—42no—
53C22×C8×C11C2312yes—
54C11×#127—22no—
55C11×#127D414yes—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64C2×C22⋊Dic11—22no—
65C2×C22⋊Dic11—22no—
66D4×Dic11—24no—
67D4×Dic11—42no—
68D4×Dic11—44no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11D411yescharacteristic
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4×Dic11—21no—
76C2×C4×Dic11C2312yes—
77C22×C11⋊C8C2311yescharacteristic
78C22×C11⋊C8C2311yescharacteristic
79#66922—22no—
80#66922—22no—
81C11×C4⋊C8—22no—
82C11×#102—24no—
83#66896—24no—
84#66896—24no—
85#66896—22no—
86#66896—22no—
87C11⋊#95—21no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95D412yes—
91Dic11⋊C8—42no—
92C4×C11⋊C8—22no—
93#25321—111nomaximal, Sylow
94C24×C11—21no—
95C24×C11—22no—
96C2×D4×C11—24no—
97C2×D4×C11—24no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—22no—
101C2×D4×C11—21no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—21no—
106C2×D4×C11—22no—
107C2×D4×C11—21no—
108C2×D4×C11—42no—
109C2×D4×C11—42no—
110C2×D4×C11—81no—
111C2×D4×C11—81no—
112C2×D4×C11C2×D414yes—
113C2×D4×C11#4112yes—
114C22×C4×C11—21no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—21no—
122C22×Dic11—22no—
123C22×Dic11—21no—
124C22×Dic11—44no—
125C22×Dic11—44no—
126C22×Dic11—82no—
127C22×Dic11C2×D412yes—
128C22×Dic11C2×D412yes—
129C2×Dic22—42no—
130C2×Dic22—81no—
131C2×Dic22—81no—
132C11×D8—48no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C22⋊C4—42no—
139C42×C11C2×D412yes—
140C42×C11#4112yes—
141C22⋊Dic11—44no—
142C22⋊Dic11—44no—
143C22⋊Dic11—82no—
144C22⋊Dic11—82no—
145C22⋊Dic11—82no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—22no—
149C4⋊Dic11—21no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—42no—
154C4⋊Dic11#4112yes—
155C4×Dic11—22no—
156C4×Dic11—22no—
157C4×Dic11—42no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×#486—111no—
165C2×#459D1111yescharacteristic
166#2563—111no—
167#2366—111no—
168#2073—112no—
169#2054—112no—
170#1987—111no—
171#1939—111no—
172#1879—112no—
173#1804—112no—
174C4×#102—111no—
175C23×C11—24no—
176C23×C11—22no—
177C23×C11—41no—
178C23×C11—42no—
179C23×C11—41no—
180C23×C11—42no—
181C23×C11—41no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11C22×D411yescharacteristic
190D4×C11—22no—
191D4×C11—22no—
192D4×C11—24no—
193D4×C11—24no—
194D4×C11—42no—
195D4×C11—41no—
196D4×C11—42no—
197D4×C11—41no—
198D4×C11—48no—
199D4×C11—84no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—84no—
206C2×C4×C11#12112yes—
207C2×C4×C11#12112yes—
208C2×C4×C11#13512yes—
209C2×C4×C11AGL(1,ℤ/8)12yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11H(5,𝔽2)11yescharacteristic
215C2×C4×C112−1+411yescharacteristic
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—42no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—88no—
232Dic22—84no—
233C8×C11—42no—
234C11⋊C8—41no—
235C11⋊C8—41no—
236C22×D8C2×D1112yes—
237C2×C4⋊Q8—111no—
238C2×#127C2×D1111yescharacteristic
239C2×C4×D4—112no—
240C2×C4×D4—221no—
241C2×C4×D4C2×D1111yescharacteristic
242#486—224no—
243#459—24no—
244C2×C4⋊C8—112no—
245C2×C4⋊C8C2×D1111yescharacteristic
246C2×#102—111no—
247C2×#102—112no—
248C2×#102—112no—
249C2×#102—111no—
250C2×#102C2×D1112yes—
251C2×C4×C8—111no—
252#393—222no—
253#390—112no—
254#390—112no—
255#390—221no—
256#386—222no—
257#382—112no—
258#380—221no—
259#380—221no—
260C4×C4⋊C4—111no—
261C4×C4⋊C4—111no—
262#340—112no—
263#340—112no—
264#340—111no—
265#340—111no—
266#336—112no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—44no—
271C22×C11—44no—
272C22×C11—44no—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11—82no—
278C22×C11—81no—
279C22×C11—81no—
280C22×C11—82no—
281C22×C11C2×#12111yescharacteristic
282C22×C11#54611yescharacteristic
283C22×C11#54811yescharacteristic
284C22×C11C2×#13511yescharacteristic
285C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C11#57611yescharacteristic
287C22×C11#57611yescharacteristic
288C4×C11—22no—
289C4×C11—81no—
290C4×C11#46314yes—
291C4×C11#52911yescharacteristic
292C4×C11#54211yescharacteristic
293C4×C11#54611yescharacteristic
294C4×C11#54711yescharacteristic
295Dic11—42no—
296Dic11—42no—
297Dic11—42no—
298Dic11—81no—
299Dic11—82no—
300C22×Q8—221no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4C22×D1111yescharacteristic
304C22×D4C22×D1112yes—
305C23×C4—21no—
306C23×C4—222no—
307C2×D8—24no—
308C2×D8—24no—
309C2×D8—42no—
310C22×C8—111no—
311C22×C8—111no—
312C22×C8C22×D1112yes—
313C4⋊Q8—222no—
314C4⋊Q8—222no—
315#127—22no—
316#127C22⋊D1114yes—
317C4×D4—22no—
318C4×D4—22no—
319C4×D4—224no—
320C4×D4—442no—
321C4×D4—444no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—112no—
326C2×C4⋊C4—111no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4C22×D1111yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—222no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4—222no—
335C2×C42—112no—
336C2×C42—221no—
337C2×C42C22×D1111yescharacteristic
338C4⋊C8—22no—
339C4⋊C8—442no—
340#102—24no—
341#102—222no—
342#102—222no—
343#102—224no—
344#102—224no—
345C4×C8—222no—
346#95—112no—
347#95—222no—
348#95—222no—
349#95—221no—
350C2×C11—82no—
351C2×C11—84no—
352C2×C11#242711yescharacteristic
353C2×C11C2×#46311yescharacteristic
354C2×C11#304111yescharacteristic
355C2×C11#330511yescharacteristic
356C2×C11#332511yescharacteristic
357C2×C11#336111yescharacteristic
358C2×C11#336611yescharacteristic
359C24—21no—
360C24—22no—
361C2×Q8—442no—
362C2×Q8—881no—
363C2×Q8—881no—
364C2×D4—24no—
365C2×D4—24no—
366C2×D4—21no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—81no—
379C2×D4—81no—
380C2×D4#434112yes—
381C2×D4C2×C22⋊D1114yes—
382C22×C4—21no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—112no—
387C22×C4—112no—
388C22×C4—221no—
389C22×C4—222no—
390C22×C4—221no—
391C22×C4—444no—
392C22×C4—444no—
393C22×C4—882no—
394C22×C4D4×D1111yescharacteristic
395C22×C4D4×D1111yescharacteristic
396C22×C4C23×D1111yescharacteristic
397D8—48no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—221no—
402C2×C8—221no—
403C2×C8—221no—
404C2×C8—221no—
405C2×C8—221no—
406C2×C8—221no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—112no—
410C4⋊C4—222no—
411C4⋊C4—222no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—222no—
415C4⋊C4—221no—
416C4⋊C4—222no—
417C4⋊C4—442no—
418C22⋊C4—42no—
419C22⋊C4—444no—
420C22⋊C4—444no—
421C22⋊C4—882no—
422C22⋊C4—882no—
423C22⋊C4—882no—
424C42—222no—
425C42—222no—
426C42—442no—
427C42#434112yes—
428C42C2×C22⋊D1112yes—
429C11#2532111yescharacteristic, complemented, Sylow
430C23—24no—
431C23—22no—
432C23—42no—
433C23—41no—
434C23—41no—
435C23—42no—
436C23—41no—
437C23—41no—
438C23—42no—
439C23—42no—
440C23—41no—
441C23—42no—
442C23—42no—
443C23—41no—
444C23C2×D4×D1111yescharacteristic
445Q8—884no—
446D4—22no—
447D4—24no—
448D4—24no—
449D4—22no—
450D4—48no—
451D4—41no—
452D4—42no—
453D4—41no—
454D4—42no—
455D4—84no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—84no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4—222no—
468C2×C4—222no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—441no—
477C2×C4—888no—
478C2×C4#6696412yes—
479C2×C4#6696512yes—
480C2×C4#6699212yes—
481C2×C4#6699212yes—
482C2×C4C2×#434111yescharacteristic
483C2×C4C2×#434111yescharacteristic
484C2×C4#6703711yescharacteristic
485C2×C4#41×D1111yescharacteristic
486C2×C4#6704311yescharacteristic
487C2×C4C22×C22⋊D1111yescharacteristic
488C8—42no—
489C8—441no—
490C8—441no—
491C22—44no—
492C22—42no—
493C22—44no—
494C22—44no—
495C22—42no—
496C22—42no—
497C22—81no—
498C22—82no—
499C22—81no—
500C22—81no—
501C22—82no—
502C22—82no—
503C22—81no—
504C22—82no—
505C22#1062312911yescharacteristic
506C22#1062314311yescharacteristic
507C22C2×#6696411yescharacteristic
508C22C2×#6696511yescharacteristic
509C22#1062330511yescharacteristic
510C22#1062330511yescharacteristic
511C22C2×#6699211yescharacteristic
512C4—22no—
513C4—81no—
514C4—442no—
515C4—442no—
516C4—442no—
517C4—882no—
518C4—881no—
519C4#1062276614yes—
520C4#1062313111yescharacteristic
521C4#1062313411yescharacteristic
522C4#1062333711yescharacteristic
523C4#1062335511yescharacteristic
524C2—84no—
525C2—82no—
526C2#1307219511yescharacteristic
527C2C2×#1062276611yescharacteristic
528C2#1307812111yescharacteristic
529C2#1308056911yescharacteristic
530C2#1308086111yescharacteristic
531C2#1308128011yescharacteristic
532C2#1308132711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#459C2
socleC23×C11C22×D4
hypercenterC2×#459D11
hypocenterC11#25321
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10622683C2semidirect
2. #13073789C2semidirect
3. #13071681C2semidirect
4. #13070032C2semidirect
5. #13069924C2semidirect
6. #13069563C2semidirect
7. #13069332C2semidirect
8. #13068966C2semidirect
9. #13068624C2semidirect
10. C4×#66896C2semidirect
429. C11#25321semidirect

Maximal subgroups

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

subgroupindex
C2×#106226832
#130737892
#130716812
#130700322
#130699242
#130695632
#130693322
#130689662
#130686242
C4×#668962
C2×C11×#4592
#2532111