Finite Group Databasebeta

← #14911444

Subgroups — #14911444

Order 2816.

498 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#13081628C211yesmaximal, characteristic, complemented
2#13081483C211yesmaximal, characteristic, complemented
3#13070848C211yesmaximal, characteristic, complemented
4#13070846C211yesmaximal, characteristic, complemented
5#13070838C211yesmaximal, characteristic, complemented
6#13070776C211yesmaximal, characteristic, complemented
7#13070773C211yesmaximal, characteristic, complemented
8#13070767C211yesmaximal, characteristic, complemented
9#13070671C211yesmaximal, characteristic, complemented
10#13070669C211yesmaximal, characteristic, complemented
11#13070649C211yesmaximal, characteristic
12C16×Dic22C211yesmaximal, characteristic, complemented
13#13070471C211yesmaximal, characteristic, complemented
14#13070460C211yesmaximal, characteristic, complemented
15C4×C11×D16C211yesmaximal, characteristic, complemented
16#10623090—21no—
17#10623070—21no—
18C2×C11×D16C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21#10622768C2211yescharacteristic
22#10622764C2211yescharacteristic
23D8×Dic11C2211yescharacteristic
24D8×Dic11C2211yescharacteristic
25C2×#66891C2211yescharacteristic
26C2×#66890C2211yescharacteristic
27#10622629—21no—
28#10622622—21no—
29#10622491C2211yescharacteristic
30#10622487C2211yescharacteristic
31#10622486C2211yescharacteristic
32#10622485C2211yescharacteristic
33#10622400—21no—
34#10622376—21no—
35#10622375—21no—
36#10622374—21no—
37#10622309C2211yescharacteristic
38#10622296C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40C11×#366C2211yescharacteristic
41C11×#357C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C4×C11×C16C2211yescharacteristic
44#10622200C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622141C2211yescharacteristic
49#10622141C2211yescharacteristic
50Dic11⋊C16C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52C16×Dic11C2211yescharacteristic
53C16×Dic11C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×C11×D8C2311yescharacteristic
60C2×C11×D8C2311yescharacteristic
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63#66993—21no—
64#66989—21no—
65D4×Dic11—21no—
66D4×Dic11—21no—
67C2×#4324—21no—
68C2×#4323—21no—
69#66982—41no—
70C4×C22⋊D11—41no—
71#66977—41no—
72C2×Dic11⋊C4—41no—
73C2×Dic44C2311yescharacteristic
74C2×D88C2311yescharacteristic
75C2×#4314—21no—
76#66946—21no—
77#66943—21no—
78#66941—21no—
79#66940—21no—
80#66938—41no—
81#66936—41no—
82#66931—41no—
83#66931—41no—
84#66928—21no—
85#66923—21no—
86C4×Dic22D411yescharacteristic
87C11×D16—22no—
88C2×C11×C16C2311yescharacteristic
89C2×C11×C16C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#102—21no—
93C11×#102—21no—
94C4×C8×C11C2311yescharacteristic
95#66896—21no—
96#66896—21no—
97#66891—22no—
98#66890—22no—
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66881—21no—
102Dic11⋊C8D411yescharacteristic
103Dic11⋊C8D411yescharacteristic
104C8×Dic11C2311yescharacteristic
105C8×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66874—21no—
109#66873—21no—
110#66872—21no—
111#66871—21no—
112C4⋊(C11⋊C8)D411yescharacteristic
113#33928—111nomaximal, Sylow
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C22×C4×C11—41no—
117C22×C4×C11—41no—
118C2×C22⋊D11—41no—
119C2×C22⋊D11—41no—
120C22×Dic11—41no—
121C22×Dic11—41no—
122C2×D44—21no—
123C2×C4×D11—41no—
124C2×Dic22—21no—
125C2×Dic22—41no—
126C2×Dic22D811yescharacteristic
127C11×D8—21no—
128C11×D8—21no—
129C11×D8—21no—
130C11×D8#4112yes—
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2411yescharacteristic
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C42×C11C2×D411yescharacteristic
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141C22⋊Dic11—41no—
142#4324—81no—
143#4323—81no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—41no—
150C4⋊Dic11D811yescharacteristic
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4D811yescharacteristic
157Dic11⋊C4D811yescharacteristic
158C4×Dic11—41no—
159C4×Dic11C2×D411yescharacteristic
160C4×Dic11C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163Dic44—21no—
164Dic44—21no—
165D88—21no—
166D88—21no—
167#4314—81no—
168C11×C16—21no—
169C11×C16—21no—
170C11⋊C16—21no—
171C11⋊C16—21no—
172#3396—111no—
173#3380—111no—
174#2242—111no—
175#2242—111no—
176#2240—111no—
177#2228—111no—
178#2228—111no—
179#2227—111no—
180#2210—111no—
181#2210—111no—
182#2206—111no—
183Q8×C16—111no—
184C4×SD32—111no—
185C4×D16—111no—
186C4×D16D1111yescharacteristic, complemented
187C23×C11—41no—
188C23×C11—41no—
189C22×D11—41no—
190D4×C11—22no—
191D4×C11—41no—
192D4×C11—41no—
193D4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—161no—
197C2×C4×C11—161no—
198C2×C4×C11C2×D811yescharacteristic
199C2×C4×C11C2×D811yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C22⋊D11—82no—
202C22⋊D11—161no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—82no—
207C2×Dic11—161no—
208C2×Dic11C2×D811yescharacteristic
209C2×Dic11C2×D811yescharacteristic
210C2×Dic11C2×D811yescharacteristic
211C2×Dic11C2×D811yescharacteristic
212D44—41no—
213D44—41no—
214C4×D11—161no—
215Dic22—22no—
216Dic22—41no—
217Dic22—41no—
218Dic22—161no—
219C8×C11—21no—
220C8×C11C2×#4111yescharacteristic
221C8×C112−1+411yescharacteristic
222C11⋊C8—21no—
223C11⋊C8—21no—
224#559—221no—
225#554—221no—
226C2×SD32—111no—
227C2×D16—111no—
228C2×D16C2×D1111yescharacteristic
229#500—111no—
230#499—111no—
231#499—111no—
232#495—111no—
233#495—111no—
234#493—111no—
235#478—221no—
236#478—221no—
237#476—221no—
238#463—221no—
239#463—221no—
240#460—221no—
241C8×Q8—111no—
242C4×Q16—111no—
243C4×D8—111no—
244C4×D8—111no—
245C4×D8—111no—
246C4×D8C2×D1111yescharacteristic
247C4×D8C2×D1111yescharacteristic
248#367—111no—
249#366—111no—
250#366C2×D1111yescharacteristic
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#357C2×D1111yescharacteristic
263#357C2×D1111yescharacteristic
264C4×C16—111no—
265C4×C16—111no—
266C4×C16C2×D1111yescharacteristic
267C22×C11—42no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11C22×D811yescharacteristic
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—81no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—81no—
280C4×C11—81no—
281C4×C11#54811yescharacteristic
282C4×C11#57711yescharacteristic
283Dic11—21no—
284Dic11—21no—
285Dic11—21no—
286Dic11—81no—
287Dic11—81no—
288Dic11—81no—
289Dic11#50812yes—
290C2×Q16—111no—
291C2×SD16—221no—
292C2×SD16—221no—
293C2×D8—111no—
294C2×D8—221no—
295C2×D8C22×D1111yescharacteristic
296C2×D8C22×D1111yescharacteristic
297C4⋊Q8—221no—
298#127—221no—
299#125—221no—
300#125—221no—
301#124—221no—
302#124—221no—
303#124—441no—
304#123—441no—
305#123—441no—
306C22⋊Q8—441no—
307C22⋊Q8—441no—
308C22⋊Q8—441no—
309C4×Q8—111no—
310C4×Q8—221no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—221no—
314C4×D4—221no—
315C4×D4—221no—
316C4×D4—441no—
317C2×C4⋊C4—441no—
318SD32—222no—
319D16—22no—
320D16—222no—
321C2×C16—111no—
322C2×C16—111no—
323C2×C16C22×D1111yescharacteristic
324C2×C16C22×D1111yescharacteristic
325#107—111no—
326#107—111no—
327#107—221no—
328#107C22×D1111yescharacteristic
329#107C22×D1111yescharacteristic
330#106—221no—
331#106—221no—
332C4⋊C8—111no—
333C4⋊C8—111no—
334C4⋊C8—111no—
335#103—221no—
336#102—21no—
337#102—21no—
338#102—221no—
339#102—221no—
340#102—221no—
341C4×C8—111no—
342C4×C8—111no—
343C4×C8C22×D1111yescharacteristic
344C2×C11—82no—
345C2×C11—161no—
346C2×C11#335811yescharacteristic
347C2×C11C2×#50811yescharacteristic
348C2×C11#341511yescharacteristic
349D11—161no—
350C2×Q8—111no—
351C2×Q8—221no—
352C2×Q8—441no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—221no—
356C2×D4—441no—
357C2×D4—441no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—441no—
361C22×C4—441no—
362C22×C4—441no—
363Q16—221no—
364Q16—221no—
365SD16—881no—
366SD16—881no—
367D8—21no—
368D8—21no—
369D8—21no—
370D8—221no—
371D8—221no—
372D8—881no—
373D8#433912yes—
374C2×C8—111no—
375C2×C8—111no—
376C2×C8D4×D1111yescharacteristic
377C2×C8C23×D1111yescharacteristic
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—111no—
381C4⋊C4—111no—
382C4⋊C4—111no—
383C4⋊C4—221no—
384C4⋊C4—221no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C4⋊C4—441no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—441no—
394C22⋊C4—441no—
395C22⋊C4—441no—
396C22⋊C4—441no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C42—111no—
401C42—111no—
402C42—441no—
403C42D4×D1111yescharacteristic
404C16—21no—
405C16—21no—
406C16—221no—
407C16—221no—
408C11#3392811yescharacteristic, complemented, Sylow
409C23—41no—
410C23—41no—
411C23—441no—
412Q8—222no—
413Q8—441no—
414Q8—441no—
415Q8—1761no—
416D4—22no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—441no—
421D4—441no—
422D4—882no—
423D4—1761no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—111no—
427C2×C4—111no—
428C2×C4—111no—
429C2×C4—111no—
430C2×C4—161no—
431C2×C4—161no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—882no—
436C2×C4—1761no—
437C2×C4—1761no—
438C2×C4D8×D1111yescharacteristic
439C2×C4D8×D1111yescharacteristic
440C2×C4C2×D4×D1111yescharacteristic
441C8—21no—
442C8—221no—
443C8—221no—
444C8C2×#433911yescharacteristic
445C8#6704311yescharacteristic
446C22—42no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—881no—
453C22—881no—
454C22—881no—
455C22C2×D8×D1111yescharacteristic
456C4—21no—
457C4—21no—
458C4—81no—
459C4—81no—
460C4—112no—
461C4—221no—
462C4—221no—
463C4—221no—
464C4—881no—
465C4—881no—
466C4—881no—
467C4#1062308311yescharacteristic
468C4#1062330111yescharacteristic
469C2—82no—
470C2—161no—
471C2—1761no—
472C2#1308124911yescharacteristic
473C2D11×#50811yescharacteristic
474C2#1308175311yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×D16C2
socleC22×C11C22×D8
prime radical#13070649C2
hypercenterC4×D16D11
hypocenterC11#33928
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
1. #13081628C2semidirect
2. #13081483C2semidirect
3. #13070848C2semidirect
4. #13070846C2semidirect
5. #13070838C2semidirect
6. #13070776C2semidirect
7. #13070773C2semidirect
8. #13070767C2semidirect
9. #13070671C2semidirect
10. #13070669C2semidirect
12. C16×Dic22C2semidirect
13. #13070471C2semidirect
14. #13070460C2semidirect
15. C4×C11×D16C2semidirect
186. C4×D16D11semidirect
408. C11#33928semidirect

Maximal subgroups

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

subgroupindex
#130816282
#130814832
#130708482
#130708462
#130708382
#130707762
#130707732
#130707672
#130706712
#130706692
#130706492
C16×Dic222
#130704712
#130704602
C4×C11×D162
#3392811