Finite Group Databasebeta

← #14736554

Subgroups — #14736554

Order 2816.

760 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079076C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic, complemented
3D4×#4318C211yesmaximal, characteristic, complemented
4#13068103C212yesmaximal, complemented
5#13068079C212yesmaximal, complemented
6#13067979C212yesmaximal, complemented
7#13067955C212yesmaximal, complemented
8#13067369C211yesmaximal, characteristic, complemented
9#13067293C211yesmaximal, characteristic, complemented
10#13067287C211yesmaximal, characteristic, complemented
11C11×#3100C211yesmaximal, characteristic
12C11×#532C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×#67004—21no—
15C2×#67004—21no—
16C22×#4318—21no—
17C2×#66922C2211yescharacteristic
18C11×#480—21no—
19C11×#474C2211yescharacteristic
20C11×#474C2211yescharacteristic
21C11×#459C2211yescharacteristic
22C11×#459C2211yescharacteristic
23C11×#447—21no—
24C4×C11×D8—21no—
25C4×C11×D8—21no—
26C11×#431C2211yescharacteristic
27C2×#66896—21no—
28#10622820—21no—
29#10622705C2212yescomplemented
30#10622689C2212yescomplemented
31#10622673—22no—
32#10622625C2212yes—
33#10622624—22no—
34D4×C11⋊C8C2212yes—
35#10622620—21no—
36#10622620—21no—
37#10622620C2212yes—
38#10622620C2212yes—
39C2×#66871—21no—
40#10622537C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622185C2212yescomplemented
44#10622182C2212yescomplemented
45#10622124C2212yescomplemented
46#10622124C2212yescomplemented
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
71#67004—44no—
72#67004—44no—
73C2×#4326—22no—
74C2×#4326—22no—
75C2×#4324—22no—
76C2×#4324—22no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×#4318—21no—
80C2×#4318—22no—
81C2×#4318—44no—
82C2×#4318D411yescharacteristic
83C2×#4318D411yescharacteristic
84C22×C11⋊C8—21no—
85C22×C11⋊C8—22no—
86#66922—21no—
87#66922—21no—
88#66922—21no—
89#66922C2312yes—
90C11×#107—21no—
91C11×#107—21no—
92C11×C4⋊C8C2311yescharacteristic
93C11×C4⋊C8C2311yescharacteristic
94C11×#102—21no—
95C11×#102—21no—
96C11×#102—21no—
97C11×#102—21no—
98C11×C22⋊C8—21no—
99C4×C8×C11—21no—
100#66896—22no—
101#66896—22no—
102C22⋊(C11⋊C8)—22no—
103C22⋊(C11⋊C8)—22no—
104#66871—22no—
105#66871—22no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)C2312yes—
109C4⋊(C11⋊C8)C2312yes—
110#66867D412yes—
111C4×C11⋊C8C2312yes—
112#19163—111nomaximal, Sylow
113C24×C11—21no—
114C11×#41—42no—
115C11×#41—42no—
116C2×Q8×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11C2×D411yescharacteristic
125C2×D4×C11C2×D411yescharacteristic
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—41no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11#4111yescharacteristic
137C22×Dic11—41no—
138C2×Dic22—22no—
139C2×Dic22—41no—
140C2×Dic22—42no—
141C2×Dic22—42no—
142C11×D8—42no—
143C11×D8—42no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4C2×D411yescharacteristic
150C11×C4⋊C4C2×D411yescharacteristic
151C11×C22⋊C4—21no—
152C11×C22⋊C4—21no—
153C11×C22⋊C4—21no—
154C11×C22⋊C4—21no—
155C11×C22⋊C4—41no—
156C11×C22⋊C4—41no—
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11#4111yescharacteristic
160C42×C11C2411yescharacteristic
161#4326—44no—
162#4326—44no—
163#4324—44no—
164#4324—44no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11—41no—
168C4⋊Dic11—41no—
169#4318—22no—
170#4318—44no—
171#4318—42no—
172#4318D814yescomplemented
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—42no—
176C2×C11⋊C8—44no—
177C2×C11⋊C8C2×D412yes—
178C2×C11⋊C8C2×D412yes—
179#3152—111no—
180#3100D1111yescharacteristic
181C2×#474—111no—
182D4×M16—111no—
183#1689—112no—
184#1685—112no—
185#1669—112no—
186#1665—112no—
187#1565—111no—
188#1547—111no—
189#1546—111no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—41no—
195C23×C11—81no—
196C23×C11#12111yescharacteristic
197Q8×C11—41no—
198Q8×C11—41no—
199D4×C11—21no—
200D4×C11—21no—
201D4×C11—21no—
202D4×C11—42no—
203D4×C11—41no—
204D4×C11—41no—
205D4×C11—41no—
206D4×C11—41no—
207D4×C11—81no—
208D4×C11—82no—
209D4×C11#13712yescomplemented
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—41no—
223C2×C4×C11—82no—
224C2×C4×C11#12111yescharacteristic
225C2×C4×C11#12111yescharacteristic
226C2×C4×C11#12111yescharacteristic
227C2×C4×C11C2×D812yes—
228C2×C4×C11AGL(1,ℤ/8)12yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×Dic11—42no—
233C2×Dic11—82no—
234Dic22—42no—
235Dic22—42no—
236Dic22—82no—
237C8×C11—41no—
238C8×C11—41no—
239C11⋊C8—22no—
240C11⋊C8—42no—
241C11⋊C8—42no—
242C11⋊C8C2×D814yes—
243C2×#137—221no—
244C2×#137—221no—
245C22×M16—221no—
246#532C2×D1111yescharacteristic
247C2×C4⋊Q8—111no—
248C2×C4×D4C2×D1111yescharacteristic
249#497—222no—
250#494—112no—
251#492—112no—
252#480—21no—
253#474—112no—
254#474—112no—
255#474—221no—
256#474—221no—
257#474C2×D1111yescharacteristic
258#474C2×D1111yescharacteristic
259#459C2×D1111yescharacteristic
260#459C2×D1111yescharacteristic
261#447—21no—
262C4×D8—21no—
263C4×D8—21no—
264#436—112no—
265#435—222no—
266C8×D4—112no—
267#431C2×D1111yescharacteristic
268C2×#107—221no—
269#423—111no—
270C2×C4⋊C8—111no—
271C2×#102—221no—
272#407—221no—
273C4×M16—111no—
274#335—112no—
275#334—112no—
276#332—112no—
277#332—112no—
278#332—112no—
279#331—112no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—22no—
283C22×C11—41no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—84no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11#45912yes—
293C22×C11C2×#12111yescharacteristic
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11—81no—
300C4×C11#45912yes—
301C4×C11C22×D811yescharacteristic
302C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
303C4×C11C2×#13711yescharacteristic
304C4×C11#57511yescharacteristic
305Dic11—82no—
306C2×#41—21no—
307C22×Q8—221no—
308C22×D4C22⋊D1111yescharacteristic
309C23×C4—21no—
310#137—444no—
311#137—444no—
312C2×Q16—222no—
313C2×Q16—222no—
314C2×SD16—222no—
315C2×SD16—222no—
316C2×D8—21no—
317C2×D8—21no—
318C2×M16—111no—
319C2×M16—111no—
320C2×M16—222no—
321C2×M16—221no—
322C2×M16—444no—
323C22×C8—222no—
324C22×C8—221no—
325C4⋊Q8—112no—
326C4⋊Q8—221no—
327C4⋊Q8—221no—
328C4⋊Q8—221no—
329C4⋊Q8C22×D1111yescharacteristic
330#127C22×D1111yescharacteristic
331#124—21no—
332#121—21no—
333#121—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4C22⋊D1111yescharacteristic
339C4×D4C22⋊D1111yescharacteristic
340C4×D4C22×D1111yescharacteristic
341C4×D4C22×D1111yescharacteristic
342C2×C4⋊C4—221no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4C22⋊D1111yescharacteristic
345C2×C22⋊C4—21no—
346C2×C42C22×D1111yescharacteristic
347#107—21no—
348#107—21no—
349#107—222no—
350#107—222no—
351C4⋊C8—112no—
352C4⋊C8—112no—
353C4⋊C8—221no—
354C4⋊C8—221no—
355C4⋊C8C22×D1111yescharacteristic
356C4⋊C8C22×D1111yescharacteristic
357#102—21no—
358#102—21no—
359#102—21no—
360#102—21no—
361#102—222no—
362#102—222no—
363C22⋊C8—21no—
364C22⋊C8—222no—
365C22⋊C8—222no—
366#97—112no—
367C4×C8—21no—
368C4×C8—112no—
369C2×C11—22no—
370C2×C11—42no—
371C2×C11—81no—
372C2×C11—161no—
373C2×C11C2×#45911yescharacteristic
374C2×C11#305611yescharacteristic
375C2×C11#306911yescharacteristic
376C24—21no—
377#41—42no—
378#41—42no—
379C2×Q8—21no—
380C2×Q8—222no—
381C2×Q8—441no—
382C2×Q8—442no—
383C2×Q8—442no—
384C2×D4—22no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4C2×C22⋊D1111yescharacteristic
392C2×D4C2×C22⋊D1111yescharacteristic
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—41no—
401C22×C4—441no—
402C22×C4D4×D1111yescharacteristic
403C22×C4#434111yescharacteristic
404C22×C4C2×C22⋊D1111yescharacteristic
405Q16—444no—
406Q16—444no—
407SD16—444no—
408SD16—444no—
409D8—42no—
410D8—42no—
411M16—114no—
412M16—222no—
413M16—444no—
414M16—442no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—112no—
418C2×C8—112no—
419C2×C8—222no—
420C2×C8—222no—
421C2×C8—444no—
422C2×C8—442no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—222no—
427C4⋊C4—222no—
428C4⋊C4—441no—
429C4⋊C4—441no—
430C4⋊C4C2×C22⋊D1111yescharacteristic
431C4⋊C4C2×C22⋊D1111yescharacteristic
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C42D4×D1111yescharacteristic
439C42#434111yescharacteristic
440C42C2×C22⋊D1111yescharacteristic
441C42C23×D1111yescharacteristic
442C11#1916311yescharacteristic, complemented, Sylow
443C23—21no—
444C23—21no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—81no—
449C23#6699211yescharacteristic
450Q8—41no—
451Q8—41no—
452Q8—442no—
453Q8—442no—
454Q8—882no—
455D4—21no—
456D4—21no—
457D4—21no—
458D4—42no—
459D4—41no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—81no—
464D4—82no—
465D4#6700412yescomplemented
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—82no—
480C2×C4—442no—
481C2×C4—882no—
482C2×C4D8×D1112yes—
483C2×C4#6696412yes—
484C2×C4#6699211yescharacteristic
485C2×C4#6699211yescharacteristic
486C2×C4#6699211yescharacteristic
487C2×C4C2×D4×D1111yescharacteristic
488C2×C4C2×#434111yescharacteristic
489C2×C4C22×C22⋊D1111yescharacteristic
490C8—41no—
491C8—41no—
492C8—114no—
493C8—222no—
494C8—442no—
495C8—442no—
496C22—21no—
497C22—21no—
498C22—22no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—84no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22#1062276312yes—
509C22C2×#6699211yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—41no—
514C4—41no—
515C4—81no—
516C4—882no—
517C4#1062276312yes—
518C4C2×D8×D1111yescharacteristic
519C4C2×#6696411yescharacteristic
520C4#1062335311yescharacteristic
521C4C2×#6700411yescharacteristic
522C2—22no—
523C2—42no—
524C2—81no—
525C2—161no—
526C2C2×#1062276311yescharacteristic
527C2#1307824811yescharacteristic
528C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3100C2
socleC22×C11C2×#121
hypercenter#3100D11
hypocenterC11#19163
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. #13079076C2semidirect
2. C2×#10622620C2semidirect
3. D4×#4318C2semidirect
4. #13068103C2semidirect
5. #13068079C2semidirect
6. #13067979C2semidirect
7. #13067955C2semidirect
8. #13067369C2semidirect
9. #13067293C2semidirect
10. #13067287C2semidirect
29. #10622705C22semidirect
30. #10622689C22semidirect
43. #10622185C22semidirect
44. #10622182C22semidirect
45. #10622124C22semidirect
46. #10622124C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
172. #4318D8semidirect
209. D4×C11#137semidirect
442. C11#19163semidirect
465. D4#67004semidirect

Maximal subgroups

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

subgroupindex
#130790762
C2×#106226202
D4×#43182
#130681032
#130680792
#130679792
#130679552
#130673692
#130672932
#130672872
C11×#31002
#1916311