Finite Group Databasebeta

← #14911530

Subgroups — #14911530

Order 2816.

494 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081484C211yesmaximal, characteristic, complemented
2#13070857C211yesmaximal, characteristic, complemented
3#13070852C211yesmaximal, characteristic, complemented
4#13070847C211yesmaximal, characteristic, complemented
5#13070780C211yesmaximal, characteristic, complemented
6#13070773C211yesmaximal, characteristic, complemented
7#13070753C211yesmaximal, characteristic, complemented
8#13070668C211yesmaximal, characteristic, complemented
9#13070668C211yesmaximal, characteristic, complemented
10#13070648C211yesmaximal, characteristic
11#13070525C211yesmaximal, characteristic, complemented
12#13070490C211yesmaximal, characteristic, complemented
13#13070478C211yesmaximal, characteristic, complemented
14C4×#66890C211yesmaximal, characteristic, complemented
15C11×#3396C211yesmaximal, characteristic, complemented
16C11×#559—21no—
17#10623110—21no—
18C11×#495C2211yescharacteristic
19C11×#495C2211yescharacteristic
20C11×#493C2211yescharacteristic
21C11×#463—21no—
22C11×#463—21no—
23C11×#460—21no—
24C8×Q8×C11C2211yescharacteristic
25C4×C11×Q16C2211yescharacteristic
26C4×C11×D8C2211yescharacteristic
27C4×C11×D8C2211yescharacteristic
28C2×#66892C2211yescharacteristic
29C2×#66890C2211yescharacteristic
30C2×#66890C2211yescharacteristic
31#10622460—21no—
32#10622460—21no—
33#10622455—21no—
34C4×D88C2211yescharacteristic
35C4×D88C2211yescharacteristic
36C4×D88C2211yescharacteristic
37#10622296C2211yescharacteristic
38#10622296C2211yescharacteristic
39#10622295C2211yescharacteristic
40#10622202C2211yescharacteristic
41#10622202C2211yescharacteristic
42#10622202C2211yescharacteristic
43#10622200C2211yescharacteristic
44#10622200C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622200C2211yescharacteristic
49#10622129C2211yescharacteristic
50#10622128C2211yescharacteristic
51#10622127C2211yescharacteristic
52#10622127C2211yescharacteristic
53C4⋊(C11⋊C16)C2211yescharacteristic
54C4⋊(C11⋊C16)C2211yescharacteristic
55C4⋊(C11⋊C16)C2211yescharacteristic
56#10622099C2211yescharacteristic
57#10622099C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×SD16—21no—
61C2×C11×SD16—21no—
62C2×C11×D8—21no—
63C2×C11×D8C2311yescharacteristic
64C2×C11×D8C2311yescharacteristic
65C11×#127—21no—
66C11×#124—21no—
67C11×#124—21no—
68C11×#124—41no—
69C11×#123—41no—
70C11×#123—41no—
71C4×Q8×C11—21no—
72C4×Q8×C11D411yescharacteristic
73C4×D4×C11—21no—
74C4×D4×C11—21no—
75C4×D4×C11—41no—
76#66999—41no—
77C2×D88C2311yescharacteristic
78#66949—41no—
79#66949—41no—
80C4⋊C4×D11—41no—
81C4×D44—21no—
82C4×D44—21no—
83C4×D44—21no—
84#66923—21no—
85#66923—21no—
86#66922—21no—
87C11×#107C2311yescharacteristic
88C11×C4⋊C8D411yescharacteristic
89C11×C4⋊C8D411yescharacteristic
90C11×C4⋊C8D411yescharacteristic
91C11×#103—21no—
92C11×#102—21no—
93C11×#102—21no—
94C4×C8×C11C2311yescharacteristic
95C4×C8×C11C2311yescharacteristic
96C4×C8×C11C2311yescharacteristic
97#66892—22no—
98#66890—22no—
99#66890—22no—
100#66885—21no—
101#66885—21no—
102#66885—21no—
103#66882—21no—
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66881—21no—
108#66881—21no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#33937—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×Q8×C11D811yescharacteristic
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—41no—
119C2×D4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11—41no—
122C2×D44—21no—
123C2×C4×D11—41no—
124C2×C4×D11—41no—
125C2×C4×D11—41no—
126C2×Dic22—41no—
127C11×Q16—21no—
128C11×Q16—21no—
129C11×SD16—81no—
130C11×SD16—81no—
131C11×D8—21no—
132C11×D8—21no—
133C11×D8—21no—
134C11×D8—21no—
135C11×D8—81no—
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2411yescharacteristic
140C11×C4⋊C4—21no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4D811yescharacteristic
143C11×C4⋊C4D811yescharacteristic
144C11×C4⋊C4D811yescharacteristic
145C11×C22⋊C4—41no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4—41no—
151C42×C11—41no—
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—41no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165Dic11⋊C4—41no—
166D88—21no—
167D88#4112yes—
168C11⋊C16—21no—
169C11⋊C16—21no—
170C11⋊C16—21no—
171C11⋊C16—21no—
172#3396D1111yescharacteristic, complemented
173#3380—111no—
174#2244—111no—
175#2243—111no—
176#2242—111no—
177#2229—111no—
178#2228—111no—
179#2224—111no—
180#2210—111no—
181#2210—111no—
182#2206—111no—
183#2183—111no—
184#2177—111no—
185#2175—111no—
186C4×D16—111no—
187C23×C11—41no—
188C23×C11—41no—
189C22×D11—41no—
190Q8×C11—41no—
191Q8×C11—41no—
192Q8×C11—41no—
193D4×C11—41no—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—41no—
197D4×C11—82no—
198D4×C11—161no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—161no—
202C2×C4×C11—161no—
203C2×C4×C11C2×D811yescharacteristic
204C2×C4×C11C2×D811yescharacteristic
205C2×C4×C11C2×D811yescharacteristic
206C2×C4×C11C2×D811yescharacteristic
207C2×C4×C11C2×D811yescharacteristic
208C2×C4×C11C2×D811yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213D44—22no—
214D44—41no—
215C4×D11—82no—
216C4×D11—161no—
217C4×D11—161no—
218Dic22—161no—
219C8×C11—21no—
220C8×C11—21no—
221C8×C11—21no—
222C8×C11C2×#4111yescharacteristic
223C8×C112−1+411yescharacteristic
224#559—21no—
225#554—221no—
226C2×SD32—111no—
227C2×D16—111no—
228C2×D16—111no—
229#500—111no—
230#499—111no—
231#499—111no—
232#495C2×D1111yescharacteristic
233#495C2×D1111yescharacteristic
234#493C2×D1111yescharacteristic
235#478—221no—
236#478—221no—
237#476—221no—
238#463—21no—
239#463—21no—
240#460—21no—
241C8×Q8C2×D1111yescharacteristic
242C4×Q16C2×D1111yescharacteristic
243C4×D8—111no—
244C4×D8—111no—
245C4×D8—111no—
246C4×D8C2×D1111yescharacteristic
247C4×D8C2×D1111yescharacteristic
248#367—111no—
249#366—111no—
250#366—111no—
251C4⋊C16—111no—
252C4⋊C16—111no—
253C4⋊C16—111no—
254#358—111no—
255#358—111no—
256#358—111no—
257#357—111no—
258#357—111no—
259#357—111no—
260#357—111no—
261#357—111no—
262#357—111no—
263#357—111no—
264#346—111no—
265#346—111no—
266C4×C16—111no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11C22×D811yescharacteristic
274C2×D11—42no—
275C2×D11—81no—
276C2×D11—81no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—81no—
284C4×C11—81no—
285C4×C11#54811yescharacteristic
286C4×C11#57711yescharacteristic
287Dic11—81no—
288Dic11—81no—
289Dic11—81no—
290C2×Q16C22×D1111yescharacteristic
291C2×SD16—21no—
292C2×SD16—21no—
293C2×D8—21no—
294C2×D8—111no—
295C2×D8C22×D1111yescharacteristic
296C2×D8C22×D1111yescharacteristic
297C4⋊Q8—221no—
298#127—21no—
299#125—221no—
300#125—221no—
301#124—21no—
302#124—21no—
303#124—41no—
304#123—41no—
305#123—41no—
306C22⋊Q8—441no—
307C22⋊Q8—441no—
308C22⋊Q8—441no—
309C4×Q8—21no—
310C4×Q8C22⋊D1111yescharacteristic
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—41no—
314C4×D4—221no—
315C4×D4—221no—
316C4×D4—221no—
317C2×C4⋊C4—441no—
318SD32—222no—
319D16—222no—
320D16—222no—
321C2×C16—111no—
322C2×C16—111no—
323C2×C16—111no—
324C2×C16—111no—
325#107—111no—
326#107—111no—
327#107—111no—
328#107—221no—
329#107C22×D1111yescharacteristic
330#106—221no—
331#106—221no—
332C4⋊C8C22⋊D1111yescharacteristic
333C4⋊C8C22⋊D1111yescharacteristic
334C4⋊C8C22⋊D1111yescharacteristic
335#103—21no—
336#102—21no—
337#102—21no—
338#102—221no—
339#102—221no—
340#102—221no—
341C4×C8C22×D1111yescharacteristic
342C4×C8C22×D1111yescharacteristic
343C4×C8C22×D1111yescharacteristic
344C2×C11—161no—
345C2×C11—161no—
346C2×C11#335811yescharacteristic
347C2×C11#341411yescharacteristic
348C2×C11#341511yescharacteristic
349D11—82no—
350C2×Q8—21no—
351C2×Q8—441no—
352C2×Q8#432311yescharacteristic
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—221no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—441no—
361C22×C4—441no—
362C22×C4—441no—
363Q16—21no—
364Q16—21no—
365SD16—81no—
366SD16—81no—
367D8—21no—
368D8—21no—
369D8—21no—
370D8—21no—
371D8—81no—
372D8—112no—
373D8—221no—
374C2×C8C2×C22⋊D1111yescharacteristic
375C2×C8C2×C22⋊D1111yescharacteristic
376C2×C8C2×C22⋊D1111yescharacteristic
377C2×C8C23×D1111yescharacteristic
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C4⋊C4#432311yescharacteristic
389C4⋊C4#432311yescharacteristic
390C4⋊C4#432311yescharacteristic
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C42—41no—
401C42C2×C22⋊D1111yescharacteristic
402C42C2×C22⋊D1111yescharacteristic
403C42C2×C22⋊D1111yescharacteristic
404C16—221no—
405C16—221no—
406C16—221no—
407C16—221no—
408C11#3393711yescharacteristic, complemented, Sylow
409C23—41no—
410C23—41no—
411C23—441no—
412Q8—41no—
413Q8—41no—
414Q8—41no—
415Q8—1761no—
416D4—41no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—82no—
421D4—161no—
422D4—222no—
423D4—441no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—161no—
427C2×C4—161no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—882no—
432C2×C4—1761no—
433C2×C4—1761no—
434C2×C4C2×#432311yescharacteristic
435C2×C4C2×#432311yescharacteristic
436C2×C4C2×#432311yescharacteristic
437C2×C4C2×#432311yescharacteristic
438C2×C4C2×#432311yescharacteristic
439C2×C4C2×#432311yescharacteristic
440C2×C4C22×C22⋊D1111yescharacteristic
441C8—21no—
442C8—21no—
443C8—21no—
444C8#41×D1111yescharacteristic
445C8#6704311yescharacteristic
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—442no—
453C22—881no—
454C22—881no—
455C22C22×#432311yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—81no—
463C4—81no—
464C4—881no—
465C4—881no—
466C4—881no—
467C4#1062336211yescharacteristic
468C4#1062336711yescharacteristic
469C2—161no—
470C2—161no—
471C2—882no—
472C2#1308124711yescharacteristic
473C2#1308175011yescharacteristic
474C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3396C2
socleC22×C11C22×D8
prime radical#13070648C2
hypercenter#3396D11
hypocenterC11#33937
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3396

Complements

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

NH ≅ G/Ntype
1. #13081484C2semidirect
2. #13070857C2semidirect
3. #13070852C2semidirect
4. #13070847C2semidirect
5. #13070780C2semidirect
6. #13070773C2semidirect
7. #13070753C2semidirect
8. #13070668C2semidirect
9. #13070668C2semidirect
11. #13070525C2semidirect
12. #13070490C2semidirect
13. #13070478C2semidirect
14. C4×#66890C2semidirect
15. C11×#3396C2semidirect
172. #3396D11semidirect
408. C11#33937semidirect

Maximal subgroups

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

subgroupindex
#130814842
#130708572
#130708522
#130708472
#130707802
#130707732
#130707532
#130706682
#130706482
#130705252
#130704902
#130704782
C4×#668902
C11×#33962
#3393711