Finite Group Databasebeta

← #14731266

Subgroups — #14731266

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079538C211yesmaximal, characteristic, complemented
2C2×#10622691C211yesmaximal, characteristic, complemented
3#13078431C211yesmaximal, characteristic, complemented
4#13067872C214yesmaximal, complemented
5#13067851C214yesmaximal, complemented
6#13067301C211yesmaximal, characteristic, complemented
7#13067067C211yesmaximal, characteristic, complemented
8#13066998C211yesmaximal, characteristic, complemented
9C11×#3511C211yesmaximal, characteristic
10C11×#556C2212yes—
11C11×#555—21no—
12C11×#554—21no—
13C11×#553—22no—
14C11×#548—22no—
15C11×#547C2212yes—
16C11×#542—22no—
17C11×#537—21no—
18C11×#533—21no—
19C11×#532—21no—
20C11×#532C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C11×#520—21no—
23C4×C11×#41C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25#10622845—21no—
26#10622706—21no—
27#10622691—22no—
28#10622691C2214yes—
29#10622689—21no—
30#10622653—22no—
31#10622634—21no—
32#10622633C2212yes—
33#10622632C2214yes—
34#10622621—21no—
35#10622620C2212yes—
36#10622608—21no—
37C2×#66871—22no—
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622185C2214yes—
42Q8⋊(C11⋊C8)C2212yes—
43D4⋊(C11⋊C8)C2214yes—
44D4⋊(C11⋊C8)C2212yes—
45C2×C11×#41—22no—
46C2×C11×#41—21no—
47C2×C11×#41D411yescharacteristic
48C22×Q8×C11—21no—
49C22×Dic22—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8D412yes—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8C2312yes—
55C11×#127D411yescharacteristic
56C11×#126—24no—
57C11×#125—22no—
58C11×#124—24no—
59C11×#124—22no—
60C11×#124—21no—
61C11×#123—24no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C11×#121—22no—
67C11×#121—22no—
68C11×#121—24no—
69C11×#121—22no—
70C11×#121—21no—
71C11×#121D412yes—
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C4×Q8×C11D411yescharacteristic
75C4×Q8×C11C2311yescharacteristic
76C4×D4×C11—22no—
77C4×D4×C11—24no—
78C4×D4×C11—22no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11D411yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C4×D4×C11C2312yes—
85C11×#117—22no—
86C11×#117—22no—
87C11×#117—21no—
88C11×#117D411yescharacteristic
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4D412yes—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94C2×#4324—24no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×#4318—21no—
98C22×C11⋊C8—21no—
99#66922—21no—
100#66922—21no—
101#66922—21no—
102#66922C2312yes—
103#66899—22no—
104#66896—22no—
105C22⋊(C11⋊C8)—21no—
106#66874—24no—
107#66872—22no—
108#66871—28no—
109#66871—22no—
110C4⋊(C11⋊C8)—21no—
111C4⋊(C11⋊C8)C2312yes—
112C4⋊(C11⋊C8)C2312yes—
113C4×C11⋊C8—21no—
114C4×C11⋊C8—21no—
115C4×C11⋊C8C2312yes—
116#18657—111nomaximal, Sylow
117C11×#41—22no—
118C11×#41—22no—
119C11×#41—42no—
120C11×#41—42no—
121C11×#41—84no—
122C2×Q8×C11—21no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—82no—
126C2×Q8×C11C2×D411yescharacteristic
127C2×D4×C11—21no—
128C2×D4×C11—22no—
129C2×D4×C11—24no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11C2×D411yescharacteristic
133C2×D4×C11C2×D412yes—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×Dic11—41no—
144C2×Dic22—22no—
145C2×Dic22—41no—
146C2×Dic22—82no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4C2×D411yescharacteristic
156C11×C4⋊C4C2×D414yes—
157C11×C4⋊C4C2×D411yescharacteristic
158C11×C4⋊C4C2×D412yes—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—21no—
163C11×C22⋊C4—21no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—21no—
166C11×C22⋊C4—22no—
167C42×C11—24no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11C2×D411yescharacteristic
172C42×C11C2×D411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11C2411yescharacteristic
175#4324—84no—
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11—41no—
179C4⋊Dic11—41no—
180#4318—42no—
181C2×C11⋊C8—24no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185#3511D1111yescharacteristic
186#3206—111no—
187C2×#500—111no—
188#3079—111no—
189#1650—114no—
190#1647—114no—
191#1549—111no—
192#1492—111no—
193#1476—111no—
194C23×C11—21no—
195C23×C11—22no—
196C23×C11#12011yescharacteristic
197Q8×C11—21no—
198Q8×C11—21no—
199Q8×C11—44no—
200Q8×C11—42no—
201Q8×C11—82no—
202D4×C11—21no—
203D4×C11—21no—
204D4×C11—24no—
205D4×C11—42no—
206D4×C11—44no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—84no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—22no—
215C2×C4×C11—21no—
216C2×C4×C11—24no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—82no—
223C2×C4×C11—84no—
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11#12011yescharacteristic
226C2×C4×C11#12011yescharacteristic
227C2×C4×C11#13512yes—
228C2×C4×C11#13712yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×Dic11—42no—
233C2×Dic11—82no—
234Dic22—44no—
235Dic22—82no—
236C11⋊C8—24no—
237C11⋊C8—42no—
238C11⋊C8—42no—
239#556C2×D1112yes—
240#555—21no—
241#554—21no—
242#553—22no—
243#548—22no—
244#547C2×D1112yes—
245#542—22no—
246#537—21no—
247#533—21no—
248#532—21no—
249#532C2×D1111yescharacteristic
250C2×C4⋊Q8—111no—
251C2×C4⋊Q8C2×D1111yescharacteristic
252#520—21no—
253C4×#41C2×D1111yescharacteristic
254#500—114no—
255#500—222no—
256#492—221no—
257#487—221no—
258#477—221no—
259#476—221no—
260#475—112no—
261#474—112no—
262#461—114no—
263#448—222no—
264#431—111no—
265#428—221no—
266C2×#107—222no—
267#423—111no—
268#417—221no—
269C2×C4×C8—111no—
270#332—114no—
271Q8⋊C8—112no—
272D4⋊C8—112no—
273D4⋊C8—114no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—41no—
277C22×C11—42no—
278C22×C11—41no—
279C22×C11—42no—
280C22×C11—41no—
281C22×C11—42no—
282C22×C11#45212yes—
283C22×C11C2×#12011yescharacteristic
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—41no—
287C4×C11—42no—
288C4×C11—41no—
289C4×C11—44no—
290C4×C11—41no—
291C4×C11#45212yes—
292C4×C11#45612yes—
293C4×C11C2×#13511yescharacteristic
294C4×C11C2×#13711yescharacteristic
295C4×C11#57612yes—
296Dic11—82no—
297C2×#41—22no—
298C2×#41—21no—
299C2×#41C22⋊D1111yescharacteristic
300C22×Q8—21no—
301C22×Q8—221no—
302C2×SD16—224no—
303C2×M16—221no—
304C22×C8—221no—
305C4⋊Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8—112no—
308C4⋊Q8—221no—
309C4⋊Q8—221no—
310C4⋊Q8—221no—
311C4⋊Q8C22⋊D1112yes—
312C4⋊Q8C22⋊D1111yescharacteristic
313C4⋊Q8C22×D1112yes—
314#127C22⋊D1111yescharacteristic
315#126—24no—
316#125—22no—
317#124—24no—
318#124—22no—
319#124—21no—
320#123—24no—
321C22⋊Q8—22no—
322C22⋊Q8—24no—
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325#121—22no—
326#121—22no—
327#121—24no—
328#121—22no—
329#121—21no—
330#121C22⋊D1112yes—
331C4×Q8—22no—
332C4×Q8—22no—
333C4×Q8C22⋊D1111yescharacteristic
334C4×Q8C22×D1111yescharacteristic
335C4×D4—22no—
336C4×D4—24no—
337C4×D4—22no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—21no—
341C4×D4C22⋊D1111yescharacteristic
342C4×D4C22×D1111yescharacteristic
343C4×D4C22×D1112yes—
344#117—22no—
345#117—22no—
346#117—21no—
347#117C22⋊D1111yescharacteristic
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4C22⋊D1112yes—
353C2×C42—21no—
354C2×C42C22×D1111yescharacteristic
355#107—228no—
356#107—222no—
357#106—222no—
358C4⋊C8—112no—
359C4⋊C8—112no—
360C4⋊C8—221no—
361#103—222no—
362#103—224no—
363#102—222no—
364C22⋊C8—221no—
365C4×C8—112no—
366C4×C8—221no—
367C4×C8—221no—
368C2×C11—22no—
369C2×C11—81no—
370C2×C11—82no—
371C2×C11C2×#45211yescharacteristic
372C2×C11#300811yescharacteristic
373C2×C11C2×#45611yescharacteristic
374#41—22no—
375#41—22no—
376#41—42no—
377#41—42no—
378#41—84no—
379C2×Q8—21no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—82no—
383C2×Q8—222no—
384C2×Q8—441no—
385C2×Q8—882no—
386C2×Q8C2×C22⋊D1111yescharacteristic
387C2×D4—21no—
388C2×D4—22no—
389C2×D4—24no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4C2×C22⋊D1111yescharacteristic
393C2×D4C2×C22⋊D1112yes—
394C22×C4—24no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—441no—
401C22×C4C2×C22⋊D1111yescharacteristic
402C22×C4C2×C22⋊D1111yescharacteristic
403C22×C4C2×C22⋊D1111yescharacteristic
404SD16—884no—
405M16—442no—
406C2×C8—224no—
407C2×C8—222no—
408C2×C8—222no—
409C2×C8—222no—
410C4⋊C4—24no—
411C4⋊C4—24no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—22no—
417C4⋊C4—21no—
418C4⋊C4—222no—
419C4⋊C4—222no—
420C4⋊C4—441no—
421C4⋊C4—441no—
422C4⋊C4C2×C22⋊D1112yes—
423C4⋊C4C2×C22⋊D1111yescharacteristic
424C4⋊C4C2×C22⋊D1111yescharacteristic
425C4⋊C4C2×C22⋊D1114yes—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—21no—
430C22⋊C4—21no—
431C22⋊C4—22no—
432C22⋊C4—21no—
433C22⋊C4—22no—
434C42—24no—
435C42—21no—
436C42—21no—
437C42—21no—
438C42C2×C22⋊D1111yescharacteristic
439C42C2×C22⋊D1111yescharacteristic
440C42C2×C22⋊D1111yescharacteristic
441C42C23×D1111yescharacteristic
442C11#1865711yescharacteristic, complemented, Sylow
443C23—21no—
444C23—22no—
445C23#6700611yescharacteristic
446Q8—21no—
447Q8—21no—
448Q8—42no—
449Q8—44no—
450Q8—82no—
451Q8—444no—
452Q8—882no—
453D4—21no—
454D4—21no—
455D4—24no—
456D4—42no—
457D4—44no—
458D4—42no—
459D4—42no—
460D4—84no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—24no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—82no—
474C2×C4—84no—
475C2×C4—442no—
476C2×C4—882no—
477C2×C4#6700312yes—
478C2×C4#6700412yes—
479C2×C4#6700611yescharacteristic
480C2×C4#6700611yescharacteristic
481C2×C4#6700611yescharacteristic
482C2×C4C22×C22⋊D1111yescharacteristic
483C2×C4C22×C22⋊D1111yescharacteristic
484C2×C4C22×C22⋊D1111yescharacteristic
485C8—224no—
486C8—442no—
487C8—442no—
488C22—21no—
489C22—21no—
490C22—41no—
491C22—42no—
492C22—41no—
493C22—42no—
494C22—41no—
495C22—42no—
496C22#1062285212yes—
497C22C2×#6700611yescharacteristic
498C4—21no—
499C4—21no—
500C4—41no—
501C4—42no—
502C4—41no—
503C4—44no—
504C4—41no—
505C4—882no—
506C4#1062285212yes—
507C4#1062285912yes—
508C4C2×#6700311yescharacteristic
509C4C2×#6700411yescharacteristic
510C4#1062336612yes—
511C2—22no—
512C2—81no—
513C2—82no—
514C2C2×#1062285211yescharacteristic
515C2#1307788411yescharacteristic
516C2C2×#1062285911yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3511C2
socleC22×C11C2×#120
hypercenter#3511D11
hypocenterC11#18657
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #13079538C2semidirect
2. C2×#10622691C2semidirect
3. #13078431C2semidirect
4. #13067872C2semidirect
5. #13067851C2semidirect
6. #13067301C2semidirect
7. #13067067C2semidirect
8. #13066998C2semidirect
442. C11#18657semidirect

Maximal subgroups

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

subgroupindex
#130795382
C2×#106226912
#130784312
#130678722
#130678512
#130673012
#130670672
#130669982
C11×#35112
#1865711