Finite Group Databasebeta

← #14911135

Subgroups — #14911135

Order 2816.

516 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081005C211yesmaximal, characteristic, complemented
2#13080960C211yesmaximal, characteristic
3#13070897C211yesmaximal, characteristic, complemented
4#13070812C211yesmaximal, characteristic, complemented
5#13070811C211yesmaximal, characteristic, complemented
6#13070800C211yesmaximal, characteristic, complemented
7#13070799C211yesmaximal, characteristic, complemented
8#13070761C211yesmaximal, characteristic, complemented
9#13070756C211yesmaximal, characteristic, complemented
10#13070709C211yesmaximal, characteristic, complemented
11SD32×Dic11C211yesmaximal, characteristic, complemented
12C16×C22⋊D11C211yesmaximal, characteristic, complemented
13C2×#10622143C211yesmaximal, characteristic, complemented
14D11×#367C211yesmaximal, characteristic, complemented
15C11×#2217C211yesmaximal, characteristic, complemented
16#10623166—21no—
17#10623142—21no—
18C2×C11×SD32C2211yescharacteristic
19C22×C11×C16C2211yescharacteristic
20C11×#467C2211yescharacteristic
21C11×#466C2211yescharacteristic
22#10622801C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic
24#10622770C2211yescharacteristic
25D8×Dic11C2211yescharacteristic
26C8×C22⋊D11C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29#10622657—21no—
30#10622646—21no—
31C2×C16×D11C2211yescharacteristic
32D11×#107C2211yescharacteristic
33D11×#107C2211yescharacteristic
34#10622487C2211yescharacteristic
35#10622487C2211yescharacteristic
36#10622422—21no—
37#10622407—21no—
38#10622387—21no—
39#10622372—21no—
40C11×#367C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47C22⋊(C11⋊C16)C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622143C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622128C2211yescharacteristic
59C2×#4341—41no—
60C2×C11×Q16C2311yescharacteristic
61C2×C11×D8C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×C22⋊Q8—21no—
64C11×#121—21no—
65#66999—21no—
66Q8×Dic11—21no—
67#66991—21no—
68#66988—41no—
69D4×Dic11—21no—
70C4×C22⋊D11D411yescharacteristic
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C8×D11C2311yescharacteristic
74#66950—41no—
75C4⋊C4×D11—21no—
76C4⋊C4×D11—21no—
77#66942—41no—
78#66941—21no—
79#66941—21no—
80#66936—41no—
81(C22⋊D11)⋊C4—41no—
82#66931—41no—
83#66931—41no—
84C11×SD32—22no—
85C2×C11×C16—22no—
86C2×C11×C16C2311yescharacteristic
87C2×C11×C16C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#103—21no—
91C11×#102—21no—
92#66899—21no—
93#66899—21no—
94#66896—21no—
95#66896—21no—
96C22⋊(C11⋊C8)D411yescharacteristic
97(C2×D11)⋊C8D411yescharacteristic
98#66882—21no—
99#66882—21no—
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104Dic11⋊C8D411yescharacteristic
105C8×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66871—21no—
109#66871—21no—
110#66871—21no—
111#66871—21no—
112C16×D11—22no—
113#33902—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—41no—
117C22×C4×C11C2×D411yescharacteristic
118C2×C22⋊D11—41no—
119C2×C22⋊D11D811yescharacteristic
120C22×Dic11—41no—
121C22×Dic11—41no—
122C22×Dic11—41no—
123#4341—84no—
124C2×C4×D11—41no—
125C2×C4×D11—41no—
126C2×C4×D11C2×D411yescharacteristic
127C2×Dic22—41no—
128C2×Dic22—41no—
129C11×Q16—21no—
130C11×Q16—21no—
131C11×D8—21no—
132C11×D8—21no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2411yescharacteristic
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—41no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—41no—
142C22⋊Dic11—41no—
143C22⋊Dic11—41no—
144C22⋊Dic11D811yescharacteristic
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4D811yescharacteristic
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—41no—
152C4⋊Dic11—41no—
153C4⋊Dic11—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4D811yescharacteristic
160C4×Dic11—41no—
161C4×Dic11C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164C8×D11—21no—
165C8×D11—21no—
166C11×C16—21no—
167C11×C16#4112yescomplemented
168C11⋊C16—21no—
169C11⋊C16—21no—
170#3338—111no—
171#3334—111no—
172#2254—111no—
173#2235—111no—
174#2235—111no—
175#2233—111no—
176#2233—111no—
177#2226—111no—
178#2225—111no—
179#2217—111no—
180#2217D1111yescharacteristic, complemented
181C4×SD32—111no—
182D4×C16—111no—
183C2×#367—111no—
184C2×#367—111no—
185C23×C11—41no—
186C23×C11C2×D811yescharacteristic
187C22×D11C2×D811yescharacteristic
188Q8×C11—41no—
189Q8×C11—41no—
190D4×C11—41no—
191D4×C11—41no—
192D4×C11—82no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11C2×D811yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C22⋊D11—82no—
201C22⋊D11SD3214yescomplemented
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—82no—
207C2×Dic11—82no—
208C2×Dic11—161no—
209C2×Dic11C2×D811yescharacteristic
210C2×Dic11C2×D811yescharacteristic
211C2×Dic11C2×D811yescharacteristic
212C4×D11—21no—
213C4×D11—21no—
214C4×D11—82no—
215C4×D11—161no—
216Dic22—82no—
217Dic22—161no—
218C8×C11—21no—
219C8×C11C2×#4111yescharacteristic
220C8×C112−1+411yescharacteristic
221C11⋊C8—21no—
222C11⋊C8—21no—
223#554—221no—
224#547—221no—
225C2×SD32C2×D1111yescharacteristic
226C22×C16—111no—
227C22×C16C2×D1111yescharacteristic
228#500—111no—
229#500—111no—
230#484—221no—
231#484—221no—
232#480—221no—
233#480—221no—
234#477—221no—
235#474—221no—
236#467—111no—
237#467C2×D1111yescharacteristic
238#466—111no—
239#466C2×D1111yescharacteristic
240C4×Q16—111no—
241C4×D8—111no—
242C8×D4—111no—
243C2×#107—111no—
244C2×#107—111no—
245C2×#107—111no—
246C2×#107—111no—
247#367—111no—
248#367—111no—
249#367—111no—
250#367—111no—
251#367—111no—
252#367—111no—
253#367—111no—
254#367—111no—
255#367C2×D1111yescharacteristic
256C4⋊C16—111no—
257#358—111no—
258#358—111no—
259#358C2×D1111yescharacteristic
260#357—111no—
261#357—111no—
262#357C2×D1111yescharacteristic
263C22⋊C16—111no—
264C22⋊C16—111no—
265C4×C16—111no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11C2×SD3212yes—
272C22×C11C22×D811yescharacteristic
273C2×D11—21no—
274C2×D11—21no—
275C2×D11C2×SD3212yes—
276C4×C11—21no—
277C4×C11—81no—
278C4×C11—81no—
279C4×C11—81no—
280C4×C11#54711yescharacteristic
281C4×C11#57811yescharacteristic
282Dic11—21no—
283Dic11—21no—
284Dic11—81no—
285Dic11—81no—
286Dic11—81no—
287Dic11—81no—
288Dic11C2×SD3212yes—
289C2×#41—441no—
290C2×Q16C22×D1111yescharacteristic
291C2×D8C22×D1111yescharacteristic
292C22×C8—111no—
293C22×C8C22×D1111yescharacteristic
294C4⋊Q8—221no—
295C4⋊Q8—221no—
296#125—441no—
297#123—441no—
298#123—441no—
299C22⋊Q8—21no—
300C22⋊Q8—221no—
301C22⋊Q8—441no—
302C22⋊Q8—441no—
303C22⋊Q8—441no—
304#121—21no—
305#121—221no—
306C4×Q8—221no—
307C4×D4—111no—
308C4×D4—221no—
309C4×D4—441no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—221no—
314SD32—22no—
315C2×C16—22no—
316C2×C16—111no—
317C2×C16—111no—
318C2×C16—222no—
319C2×C16C22×D1111yescharacteristic
320C2×C16C22×D1111yescharacteristic
321#107—111no—
322#107—111no—
323#107—111no—
324#107—111no—
325#107—221no—
326#107—221no—
327#107—221no—
328#107—221no—
329#107—221no—
330#107—221no—
331#107C22×D1111yescharacteristic
332#107C22×D1111yescharacteristic
333C4⋊C8—111no—
334#103—21no—
335#103—221no—
336#103—221no—
337#102—21no—
338#102—221no—
339#102—221no—
340C22⋊C8—111no—
341C22⋊C8—111no—
342C4×C8—111no—
343C2×C11—22no—
344C2×C11—161no—
345C2×C11#333411yescharacteristic
346C2×C11C22×SD3211yescharacteristic
347C2×C11#341611yescharacteristic
348D11—22no—
349#41—884no—
350C2×Q8—21no—
351C2×Q8—441no—
352C2×Q8—441no—
353C2×D4—21no—
354C2×D4—41no—
355C2×D4—111no—
356C2×D4—441no—
357C22×C4—111no—
358C22×C4—441no—
359C22×C4—441no—
360C22×C4—441no—
361C22×C4—441no—
362C22×C4—441no—
363C22×C4D4×D1111yescharacteristic
364Q16—21no—
365Q16—21no—
366D8—21no—
367D8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—111no—
371C2×C8—111no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8D4×D1111yescharacteristic
375C2×C8C23×D1111yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—41no—
379C4⋊C4—111no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C4⋊C4—441no—
391C4⋊C4—441no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—111no—
395C22⋊C4—111no—
396C22⋊C4—441no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C42—111no—
400C42—441no—
401C16—21no—
402C16—221no—
403C16—221no—
404C16#434112yescomplemented
405C11#3390211yescharacteristic, complemented, Sylow
406C23—41no—
407C23—111no—
408C23D8×D1111yescharacteristic
409Q8—41no—
410Q8—41no—
411Q8—882no—
412Q8—1761no—
413D4—41no—
414D4—41no—
415D4—82no—
416D4—114no—
417D4—882no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—111no—
424C2×C4—111no—
425C2×C4—111no—
426C2×C4—221no—
427C2×C4—221no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—882no—
433C2×C4—882no—
434C2×C4—882no—
435C2×C4—1761no—
436C2×C4—1761no—
437C2×C4D8×D1111yescharacteristic
438C2×C4C2×D4×D1111yescharacteristic
439C8—21no—
440C8—221no—
441C8—221no—
442C8C2×#434111yescharacteristic
443C8#6704311yescharacteristic
444C22—21no—
445C22—21no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—112no—
450C22—221no—
451C22—221no—
452C22D11×SD3212yes—
453C22C2×D8×D1111yescharacteristic
454C4—21no—
455C4—81no—
456C4—81no—
457C4—81no—
458C4—112no—
459C4—221no—
460C4—221no—
461C4—881no—
462C4—881no—
463C4—881no—
464C4—881no—
465C4#1062314211yescharacteristic
466C4#1062330211yescharacteristic
467C2—22no—
468C2—161no—
469C2—222no—
470C2#1308096011yescharacteristic
471C2C2×D11×SD3211yescharacteristic
472C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2217C2
socleC22×C11C22×D8
prime radical#13080960C2
hypercenter#2217D11
hypocenterC11#33902
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. #13081005C2semidirect
3. #13070897C2semidirect
4. #13070812C2semidirect
5. #13070811C2semidirect
6. #13070800C2semidirect
7. #13070799C2semidirect
8. #13070761C2semidirect
9. #13070756C2semidirect
10. #13070709C2semidirect
11. SD32×Dic11C2semidirect
12. C16×C22⋊D11C2semidirect
13. C2×#10622143C2semidirect
14. D11×#367C2semidirect
15. C11×#2217C2semidirect
167. C11×C16#41semidirect
180. #2217D11semidirect
201. C22⋊D11SD32semidirect
404. C16#4341semidirect
405. C11#33902semidirect

Maximal subgroups

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

subgroupindex
#130810052
#130809602
#130708972
#130708122
#130708112
#130708002
#130707992
#130707612
#130707562
#130707092
SD32×Dic112
C16×C22⋊D112
C2×#106221432
D11×#3672
C11×#22172
#3390211