Finite Group Databasebeta

← #14730960

Subgroups — #14730960

Order 2816.

992 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079741C211yesmaximal, characteristic, complemented
2C2×#10622705C211yesmaximal, characteristic, complemented
3#13078431C211yesmaximal, characteristic, complemented
4#13067761C214yesmaximal, complemented
5#13067750C214yesmaximal, complemented
6#13067297C211yesmaximal, characteristic, complemented
7#13067067C211yesmaximal, characteristic, complemented
8#13066998C211yesmaximal, characteristic, complemented
9C11×#3511C211yesmaximal, characteristic
10C11×#556—21no—
11C11×#555C2212yes—
12C11×#554C2212yes—
13C11×#553—22no—
14C11×#548—22no—
15C11×#547—21no—
16C11×#542—22no—
17C11×#537—21no—
18C11×#533—21no—
19C11×#532—21no—
20C11×#532C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C11×#520—21no—
23C4×C11×#41C2211yescharacteristic
24C22×#4326—22no—
25C2×#66922C2211yescharacteristic
26#10622845—21no—
27#10622705—22no—
28#10622705C2214yes—
29#10622692—21no—
30#10622683—21no—
31#10622647—22no—
32#10622634C2212yes—
33#10622633—21no—
34#10622621C2212yes—
35#10622621C2214yes—
36#10622620—21no—
37#10622608—21no—
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622184C2214yes—
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×C11D412yes—
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—22no—
59C11×#124—24no—
60C11×#124—21no—
61C11×#123—24no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—24no—
66C11×#121—22no—
67C11×#121—24no—
68C11×#121—22no—
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—21no—
91C2×C11×C4⋊C4—22no—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94C2×#4326—28no—
95C2×#4326—48no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×#4318—21no—
99C22×C11⋊C8—21no—
100#66922—21no—
101#66922—21no—
102#66922—21no—
103#66922C2312yes—
104#66899—22no—
105#66896—22no—
106#66896—24no—
107C22⋊(C11⋊C8)—21no—
108#66872—22no—
109#66872—24no—
110#66871—22no—
111C4⋊(C11⋊C8)—21no—
112C4⋊(C11⋊C8)C2312yes—
113C4⋊(C11⋊C8)C2312yes—
114C4×C11⋊C8—21no—
115C4×C11⋊C8—21no—
116C4×C11⋊C8C2312yes—
117#18627—111nomaximal, Sylow
118C11×#41—22no—
119C11×#41—22no—
120C11×#41—42no—
121C11×#41—42no—
122C11×#41—84no—
123C2×Q8×C11—21no—
124C2×Q8×C11—22no—
125C2×Q8×C11—44no—
126C2×Q8×C11C2×D411yescharacteristic
127C2×Q8×C11C2×D414yes—
128C2×D4×C11—21no—
129C2×D4×C11—22no—
130C2×D4×C11—24no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11C2×D412yes—
134C2×D4×C11C2×D411yescharacteristic
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×Dic11—41no—
145C2×Dic22—22no—
146C2×Dic22—44no—
147C2×Dic22—41no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4C2×D411yescharacteristic
158C11×C4⋊C4C2×D411yescharacteristic
159C11×C4⋊C4C2×D412yes—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—21no—
164C11×C22⋊C4—21no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—21no—
167C11×C22⋊C4—22no—
168C42×C11—24no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11C2×D411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11C2×D411yescharacteristic
175C42×C11C2411yescharacteristic
176#4326—416no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—41no—
180C4⋊Dic11—41no—
181#4318—42no—
182C2×C11⋊C8—24no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186#3511D1111yescharacteristic
187#3227—111no—
188C2×#494—111no—
189#3079—111no—
190#1634—114no—
191#1632—114no—
192#1548—111no—
193#1492—111no—
194#1476—111no—
195C23×C11—21no—
196C23×C11—22no—
197C23×C11#12011yescharacteristic
198Q8×C11—21no—
199Q8×C11—21no—
200Q8×C11—44no—
201Q8×C11—42no—
202Q8×C11—44no—
203D4×C11—21no—
204D4×C11—21no—
205D4×C11—24no—
206D4×C11—42no—
207D4×C11—44no—
208D4×C11—42no—
209D4×C11—42no—
210D4×C11—84no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—21no—
217C2×C4×C11—24no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—82no—
224C2×C4×C11—84no—
225C2×C4×C11#12011yescharacteristic
226C2×C4×C11#12011yescharacteristic
227C2×C4×C11#12011yescharacteristic
228C2×C4×C11#13512yes—
229C2×C4×C11#13712yes—
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×Dic11—42no—
234C2×Dic11—82no—
235Dic22—44no—
236Dic22—82no—
237C11⋊C8—24no—
238C11⋊C8—42no—
239C11⋊C8—42no—
240C22×Q16—222no—
241#556—21no—
242#555C2×D1112yes—
243#554C2×D1112yes—
244#553—22no—
245#548—22no—
246#547—21no—
247#542—22no—
248#537—21no—
249#533—21no—
250#532—21no—
251#532C2×D1111yescharacteristic
252C2×C4⋊Q8—111no—
253C2×C4⋊Q8C2×D1111yescharacteristic
254#520—21no—
255C4×#41C2×D1111yescharacteristic
256#498—221no—
257#494—114no—
258#494—222no—
259#486—221no—
260#481—222no—
261#477—112no—
262#476—112no—
263#476—114no—
264#475—221no—
265#474—221no—
266#431—111no—
267#428—221no—
268#423—111no—
269#417—221no—
270C2×C4×C8—111no—
271#333—114no—
272Q8⋊C8—112no—
273D4⋊C8—114no—
274D4⋊C8—112no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—41no—
278C22×C11—42no—
279C22×C11—41no—
280C22×C11—42no—
281C22×C11—41no—
282C22×C11—42no—
283C22×C11#45212yes—
284C22×C11C2×#12011yescharacteristic
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—41no—
288C4×C11—42no—
289C4×C11—41no—
290C4×C11—41no—
291C4×C11—44no—
292C4×C11#45212yes—
293C4×C11#45312yes—
294C4×C11C2×#13511yescharacteristic
295C4×C11C2×#13711yescharacteristic
296C4×C11#57812yes—
297Dic11—82no—
298C2×#41—22no—
299C2×#41—21no—
300C2×#41C22⋊D1111yescharacteristic
301C22×Q8—221no—
302C22×Q8C22⋊D1112yes—
303C2×Q16—228no—
304C2×Q16—448no—
305C2×M16—221no—
306C22×C8—221no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—112no—
310C4⋊Q8—221no—
311C4⋊Q8—221no—
312C4⋊Q8—221no—
313C4⋊Q8C22⋊D1112yes—
314C4⋊Q8C22⋊D1111yescharacteristic
315C4⋊Q8C22×D1112yes—
316#127C22⋊D1111yescharacteristic
317#126—24no—
318#125—22no—
319#124—22no—
320#124—24no—
321#124—21no—
322#123—24no—
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325C22⋊Q8—22no—
326C22⋊Q8—24no—
327#121—22no—
328#121—24no—
329#121—22no—
330#121—22no—
331#121—21no—
332#121C22⋊D1112yes—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8C22⋊D1111yescharacteristic
336C4×Q8C22×D1111yescharacteristic
337C4×D4—22no—
338C4×D4—24no—
339C4×D4—22no—
340C4×D4—21no—
341C4×D4—21no—
342C4×D4—21no—
343C4×D4C22⋊D1111yescharacteristic
344C4×D4C22×D1111yescharacteristic
345C4×D4C22×D1112yes—
346#117—22no—
347#117—22no—
348#117—21no—
349#117C22⋊D1111yescharacteristic
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4—221no—
355C2×C42—21no—
356C2×C42C22×D1111yescharacteristic
357#107—222no—
358#106—222no—
359#106—224no—
360C4⋊C8—112no—
361C4⋊C8—112no—
362C4⋊C8—221no—
363#103—222no—
364#102—222no—
365#102—224no—
366C22⋊C8—221no—
367C4×C8—112no—
368C4×C8—221no—
369C4×C8—221no—
370C2×C11—22no—
371C2×C11—81no—
372C2×C11—82no—
373C2×C11C2×#45211yescharacteristic
374C2×C11#301111yescharacteristic
375C2×C11C2×#45311yescharacteristic
376#41—22no—
377#41—22no—
378#41—42no—
379#41—42no—
380#41—84no—
381C2×Q8—21no—
382C2×Q8—22no—
383C2×Q8—44no—
384C2×Q8—222no—
385C2×Q8—444no—
386C2×Q8—441no—
387C2×Q8C2×C22⋊D1111yescharacteristic
388C2×Q8C2×C22⋊D1114yes—
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—24no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4C2×C22⋊D1112yes—
395C2×D4C2×C22⋊D1111yescharacteristic
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—441no—
403C22×C4C2×C22⋊D1111yescharacteristic
404C22×C4C2×C22⋊D1111yescharacteristic
405C22×C4C2×C22⋊D1111yescharacteristic
406Q16—4416no—
407M16—442no—
408C2×C8—224no—
409C2×C8—222no—
410C2×C8—222no—
411C2×C8—222no—
412C4⋊C4—24no—
413C4⋊C4—24no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—222no—
422C4⋊C4—222no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4C2×C22⋊D1111yescharacteristic
426C4⋊C4C2×C22⋊D1112yes—
427C4⋊C4C2×C22⋊D1111yescharacteristic
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—22no—
434C22⋊C4—21no—
435C22⋊C4—22no—
436C42—24no—
437C42—21no—
438C42—21no—
439C42—21no—
440C42C2×C22⋊D1111yescharacteristic
441C42C2×C22⋊D1111yescharacteristic
442C42C2×C22⋊D1111yescharacteristic
443C42C23×D1111yescharacteristic
444C11#1862711yescharacteristic, complemented, Sylow
445C23—21no—
446C23—22no—
447C23#6700611yescharacteristic
448Q8—21no—
449Q8—21no—
450Q8—44no—
451Q8—42no—
452Q8—44no—
453Q8—444no—
454Q8—882no—
455D4—21no—
456D4—21no—
457D4—24no—
458D4—42no—
459D4—44no—
460D4—42no—
461D4—42no—
462D4—84no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—21no—
469C2×C4—24no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—82no—
476C2×C4—84no—
477C2×C4—442no—
478C2×C4—882no—
479C2×C4#6700312yes—
480C2×C4#6700412yes—
481C2×C4#6700611yescharacteristic
482C2×C4#6700611yescharacteristic
483C2×C4#6700611yescharacteristic
484C2×C4C22×C22⋊D1111yescharacteristic
485C2×C4C22×C22⋊D1111yescharacteristic
486C2×C4C22×C22⋊D1111yescharacteristic
487C8—224no—
488C8—442no—
489C8—442no—
490C22—21no—
491C22—21no—
492C22—41no—
493C22—42no—
494C22—41no—
495C22—42no—
496C22—41no—
497C22—42no—
498C22#1062285212yes—
499C22C2×#6700611yescharacteristic
500C4—21no—
501C4—21no—
502C4—41no—
503C4—42no—
504C4—41no—
505C4—41no—
506C4—44no—
507C4—882no—
508C4#1062285212yes—
509C4#1062285412yes—
510C4C2×#6700311yescharacteristic
511C4C2×#6700411yescharacteristic
512C4#1062336912yes—
513C2—22no—
514C2—81no—
515C2—82no—
516C2C2×#1062285211yescharacteristic
517C2#1307791111yescharacteristic
518C2C2×#1062285411yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3511C2
socleC22×C11C2×#120
hypercenter#3511D11
hypocenterC11#18627
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. #13079741C2semidirect
2. C2×#10622705C2semidirect
3. #13078431C2semidirect
4. #13067761C2semidirect
5. #13067750C2semidirect
6. #13067297C2semidirect
7. #13067067C2semidirect
8. #13066998C2semidirect
444. C11#18627semidirect

Maximal subgroups

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

subgroupindex
#130797412
C2×#106227052
#130784312
#130677612
#130677502
#130672972
#130670672
#130669982
C11×#35112
#1862711