Finite Group Databasebeta

← #14736614

Subgroups — #14736614

Order 2816.

728 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
1#13079009C211yesmaximal, characteristic, complemented
2C2×#10622632C211yesmaximal, characteristic, complemented
3D4×#4318C211yesmaximal, characteristic, complemented
4#13068175C212yesmaximal, complemented
5#13068161C212yesmaximal, complemented
6#13068051C212yesmaximal, complemented
7#13068037C212yesmaximal, complemented
8#13067369C211yesmaximal, characteristic, complemented
9#13067300C211yesmaximal, characteristic, complemented
10#13067293C211yesmaximal, characteristic, complemented
11C11×#3100C211yesmaximal, characteristic
12C11×#532C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C22×#4324—21no—
15C22×#4318—21no—
16C2×#66922C2211yescharacteristic
17C11×#480—21no—
18C11×#474C2211yescharacteristic
19C11×#474C2211yescharacteristic
20C11×#459C2211yescharacteristic
21C11×#459C2211yescharacteristic
22C11×#447—21no—
23C4×C11×D8—21no—
24C4×C11×D8—21no—
25C11×#431C2211yescharacteristic
26#10622845—21no—
27#10622845—21no—
28#10622820—21no—
29#10622694C2212yescomplemented
30#10622683C2212yescomplemented
31#10622668—22no—
32#10622632—21no—
33#10622632—21no—
34#10622632C2212yes—
35#10622632C2212yes—
36#10622625C2212yes—
37#10622624—22no—
38D4×C11⋊C8C2212yes—
39C2×#66874—21no—
40#10622537C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622185C2212yescomplemented
44#10622182C2212yescomplemented
45#10622120C2212yescomplemented
46#10622120C2212yescomplemented
47#10622118C2212yescomplemented
48#10622117C2212yescomplemented
49C2×C11×#41—21no—
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—21no—
52C22×Dic22—21no—
53C2×C11×D8—21no—
54C2×C11×D8—21no—
55C11×C4⋊Q8C2311yescharacteristic
56C11×#127C2311yescharacteristic
57C11×#124—21no—
58C11×#121—21no—
59C11×#121—21no—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11D411yescharacteristic
65C4×D4×C11D411yescharacteristic
66C4×D4×C11C2311yescharacteristic
67C4×D4×C11C2311yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C42×C11C2311yescharacteristic
71C2×#4324—22no—
72C2×#4324—22no—
73C2×#4324—44no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×#4318—21no—
77C2×#4318—22no—
78C2×#4318—44no—
79C2×#4318D411yescharacteristic
80C2×#4318D411yescharacteristic
81C22×C11⋊C8—21no—
82C22×C11⋊C8—22no—
83#66922—21no—
84#66922—21no—
85#66922—21no—
86#66922C2312yes—
87C11×#107—21no—
88C11×#107—21no—
89C11×C4⋊C8C2311yescharacteristic
90C11×C4⋊C8C2311yescharacteristic
91C11×#102—21no—
92C11×#102—21no—
93C11×#102—21no—
94C11×#102—21no—
95C11×C22⋊C8—21no—
96C4×C8×C11—21no—
97#66899—22no—
98#66899—22no—
99#66896—22no—
100#66896—22no—
101C22⋊(C11⋊C8)—22no—
102C22⋊(C11⋊C8)—22no—
103#66874—22no—
104#66874—22no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2312yes—
109#66867D412yes—
110C4×C11⋊C8C2312yes—
111#19169—111nomaximal, Sylow
112C24×C11—21no—
113C11×#41—42no—
114C11×#41—42no—
115C2×Q8×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11C2×D411yescharacteristic
124C2×D4×C11C2×D411yescharacteristic
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—41no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11#4111yescharacteristic
136C22×Dic11—41no—
137C2×Dic22—22no—
138C2×Dic22—42no—
139C2×Dic22—42no—
140C2×Dic22—41no—
141C11×D8—42no—
142C11×D8—42no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4C2×D411yescharacteristic
149C11×C4⋊C4C2×D411yescharacteristic
150C11×C22⋊C4—21no—
151C11×C22⋊C4—21no—
152C11×C22⋊C4—21no—
153C11×C22⋊C4—21no—
154C11×C22⋊C4—41no—
155C11×C22⋊C4—41no—
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11#4111yescharacteristic
159C42×C11C2411yescharacteristic
160#4324—44no—
161#4324—44no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11—41no—
165C4⋊Dic11—41no—
166#4318—22no—
167#4318—22no—
168#4318—44no—
169#4318—42no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—42no—
173C2×C11⋊C8—44no—
174C2×C11⋊C8C2×D412yes—
175C2×C11⋊C8C2×D412yes—
176#3141—111no—
177#3100D1111yescharacteristic
178C2×#461—111no—
179D4×M16—111no—
180#1701—112no—
181#1699—112no—
182#1681—112no—
183#1679—112no—
184#1565—111no—
185#1549—111no—
186#1547—111no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—41no—
192C23×C11—81no—
193C23×C11#12111yescharacteristic
194Q8×C11—41no—
195Q8×C11—41no—
196D4×C11—21no—
197D4×C11—21no—
198D4×C11—21no—
199D4×C11—42no—
200D4×C11—41no—
201D4×C11—41no—
202D4×C11—41no—
203D4×C11—41no—
204D4×C11—81no—
205D4×C11—82no—
206D4×C11AGL(1,ℤ/8)12yes—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—82no—
221C2×C4×C11#12111yescharacteristic
222C2×C4×C11#12111yescharacteristic
223C2×C4×C11#12111yescharacteristic
224C2×C4×C11#13512yes—
225C2×C4×C11AGL(1,ℤ/8)12yes—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×Dic11—42no—
230C2×Dic11—82no—
231Dic22—42no—
232Dic22—42no—
233Dic22—82no—
234C8×C11—41no—
235C8×C11—41no—
236C11⋊C8—22no—
237C11⋊C8—22no—
238C11⋊C8—42no—
239C11⋊C8—42no—
240C22×SD16—221no—
241C22×M16—221no—
242#532C2×D1111yescharacteristic
243C2×C4⋊Q8—111no—
244C2×C4×D4C2×D1111yescharacteristic
245#489—222no—
246#487—112no—
247#486—112no—
248#480—21no—
249#474C2×D1111yescharacteristic
250#474C2×D1111yescharacteristic
251#461—112no—
252#461—112no—
253#461—221no—
254#461—221no—
255#459C2×D1111yescharacteristic
256#459C2×D1111yescharacteristic
257#447—21no—
258C4×D8—21no—
259C4×D8—21no—
260#436—112no—
261#435—222no—
262C8×D4—112no—
263#431C2×D1111yescharacteristic
264#423—111no—
265C2×C4⋊C8—111no—
266#417—221no—
267#417—221no—
268C2×#103—221no—
269#407—221no—
270C4×M16—111no—
271#335—112no—
272#334—112no—
273#332—112no—
274#332—112no—
275#332—112no—
276#331—112no—
277C22×C11—21no—
278C22×C11—21no—
279C22×C11—22no—
280C22×C11—41no—
281C22×C11—41no—
282C22×C11—41no—
283C22×C11—41no—
284C22×C11—41no—
285C22×C11—84no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11#46312yes—
290C22×C11C2×#12111yescharacteristic
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—41no—
295C4×C11—41no—
296C4×C11—81no—
297C4×C11#46312yes—
298C4×C11C2×#13511yescharacteristic
299C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
301C4×C11#57511yescharacteristic
302Dic11—82no—
303C2×#41—21no—
304C22×Q8—221no—
305C22×D4C22⋊D1111yescharacteristic
306C23×C4—21no—
307C2×SD16—222no—
308C2×SD16—222no—
309C2×SD16—444no—
310C2×D8—21no—
311C2×D8—21no—
312C2×M16—111no—
313C2×M16—111no—
314C2×M16—222no—
315C2×M16—221no—
316C2×M16—444no—
317C22×C8—222no—
318C22×C8—221no—
319C4⋊Q8—112no—
320C4⋊Q8—221no—
321C4⋊Q8—221no—
322C4⋊Q8—221no—
323C4⋊Q8C22×D1111yescharacteristic
324#127C22×D1111yescharacteristic
325#124—21no—
326#121—21no—
327#121—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4C22⋊D1111yescharacteristic
333C4×D4C22⋊D1111yescharacteristic
334C4×D4C22×D1111yescharacteristic
335C4×D4C22×D1111yescharacteristic
336C2×C4⋊C4—221no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4C22⋊D1111yescharacteristic
339C2×C22⋊C4—21no—
340C2×C42C22×D1111yescharacteristic
341#107—21no—
342#107—21no—
343C4⋊C8—112no—
344C4⋊C8—112no—
345C4⋊C8—221no—
346C4⋊C8—221no—
347C4⋊C8C22×D1111yescharacteristic
348C4⋊C8C22×D1111yescharacteristic
349#103—222no—
350#103—222no—
351#103—222no—
352#103—222no—
353#102—21no—
354#102—21no—
355#102—21no—
356#102—21no—
357#102—222no—
358#102—222no—
359C22⋊C8—21no—
360C22⋊C8—222no—
361C22⋊C8—222no—
362#97—112no—
363C4×C8—21no—
364C4×C8—112no—
365C2×C11—22no—
366C2×C11—42no—
367C2×C11—81no—
368C2×C11—161no—
369C2×C11C2×#46311yescharacteristic
370C2×C11#305511yescharacteristic
371C2×C11#306911yescharacteristic
372C24—21no—
373#41—42no—
374#41—42no—
375C2×Q8—21no—
376C2×Q8—222no—
377C2×Q8—442no—
378C2×Q8—442no—
379C2×Q8—441no—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4C2×C22⋊D1111yescharacteristic
388C2×D4C2×C22⋊D1111yescharacteristic
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—41no—
397C22×C4—441no—
398C22×C4D4×D1111yescharacteristic
399C22×C4#434111yescharacteristic
400C22×C4C2×C22⋊D1111yescharacteristic
401SD16—444no—
402SD16—444no—
403D8—42no—
404D8—42no—
405M16—222no—
406M16—222no—
407M16—444no—
408M16—442no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—112no—
412C2×C8—112no—
413C2×C8—222no—
414C2×C8—222no—
415C2×C8—444no—
416C2×C8—442no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—222no—
421C4⋊C4—222no—
422C4⋊C4—441no—
423C4⋊C4—441no—
424C4⋊C4C2×C22⋊D1111yescharacteristic
425C4⋊C4C2×C22⋊D1111yescharacteristic
426C22⋊C4—21no—
427C22⋊C4—21no—
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C42D4×D1111yescharacteristic
433C42#434111yescharacteristic
434C42C2×C22⋊D1111yescharacteristic
435C42C23×D1111yescharacteristic
436C11#1916911yescharacteristic, complemented, Sylow
437C23—21no—
438C23—21no—
439C23—42no—
440C23—42no—
441C23—41no—
442C23—81no—
443C23#6699211yescharacteristic
444Q8—41no—
445Q8—41no—
446Q8—442no—
447Q8—442no—
448Q8—882no—
449D4—21no—
450D4—21no—
451D4—21no—
452D4—42no—
453D4—41no—
454D4—41no—
455D4—41no—
456D4—41no—
457D4—81no—
458D4—82no—
459D4#6700212yes—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—82no—
474C2×C4—442no—
475C2×C4—882no—
476C2×C4#6696412yes—
477C2×C4#6696512yes—
478C2×C4#6699211yescharacteristic
479C2×C4#6699211yescharacteristic
480C2×C4#6699211yescharacteristic
481C2×C4C2×D4×D1111yescharacteristic
482C2×C4C2×#434111yescharacteristic
483C2×C4C22×C22⋊D1111yescharacteristic
484C8—41no—
485C8—41no—
486C8—222no—
487C8—222no—
488C8—442no—
489C8—442no—
490C22—21no—
491C22—21no—
492C22—22no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—84no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22#1062276612yes—
503C22C2×#6699211yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—41no—
508C4—41no—
509C4—81no—
510C4—882no—
511C4#1062276612yes—
512C4C2×#6696411yescharacteristic
513C4C2×#6696511yescharacteristic
514C4C2×#6700211yescharacteristic
515C4#1062335311yescharacteristic
516C2—22no—
517C2—42no—
518C2—81no—
519C2—161no—
520C2C2×#1062276611yescharacteristic
521C2#1307823711yescharacteristic
522C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3100C2
socleC22×C11C2×#121
hypercenter#3100D11
hypocenterC11#19169
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #13079009C2semidirect
2. C2×#10622632C2semidirect
3. D4×#4318C2semidirect
4. #13068175C2semidirect
5. #13068161C2semidirect
6. #13068051C2semidirect
7. #13068037C2semidirect
8. #13067369C2semidirect
9. #13067300C2semidirect
10. #13067293C2semidirect
29. #10622694C22semidirect
30. #10622683C22semidirect
43. #10622185C22semidirect
44. #10622182C22semidirect
45. #10622120C22semidirect
46. #10622120C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
436. C11#19169semidirect

Maximal subgroups

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

subgroupindex
#130790092
C2×#106226322
D4×#43182
#130681752
#130681612
#130680512
#130680372
#130673692
#130673002
#130672932
C11×#31002
#1916911