Finite Group Databasebeta

← #14911265

Subgroups — #14911265

Order 2816.

484 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081020C211yesmaximal, characteristic
2#13081008C211yesmaximal, characteristic, complemented
3#13070899C211yesmaximal, characteristic, complemented
4#13070826C211yesmaximal, characteristic, complemented
5#13070820C211yesmaximal, characteristic, complemented
6#13070800C211yesmaximal, characteristic, complemented
7#13070795C211yesmaximal, characteristic, complemented
8#13070781C211yesmaximal, characteristic, complemented
9#13070728C211yesmaximal, characteristic, complemented
10#13070711C211yesmaximal, characteristic, complemented
11#13070480C211yesmaximal, characteristic, complemented
12#13070440C211yesmaximal, characteristic, complemented
13#13070401C211yesmaximal, characteristic, complemented
14D11×#366C211yesmaximal, characteristic, complemented
15C11×#2224C211yesmaximal, characteristic, complemented
16#10623261—21no—
17#10623089—21no—
18C11×#500C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20#10622770C2211yescharacteristic
21#10622770C2211yescharacteristic
22C2×#66891C2211yescharacteristic
23#10622704—21no—
24#10622622—21no—
25C2×#66862C2211yescharacteristic
26C2×C16×D11C2211yescharacteristic
27#10622500C2211yescharacteristic
28#10622500C2211yescharacteristic
29#10622497—21no—
30#10622497—21no—
31#10622493C2211yescharacteristic
32D11×#107C2211yescharacteristic
33D11×#107C2211yescharacteristic
34D11×#107C2211yescharacteristic
35#10622392—21no—
36#10622390—21no—
37C4×Dic44C2211yescharacteristic
38C8×D44C2211yescharacteristic
39#10622296C2211yescharacteristic
40C11×#366C2211yescharacteristic
41C11×#366C2211yescharacteristic
42C11×C4⋊C16C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C11×#357C2211yescharacteristic
45#10622200C2211yescharacteristic
46(C2×D11)⋊C16C2211yescharacteristic
47(C2×D11)⋊C16C2211yescharacteristic
48#10622143C2211yescharacteristic
49#10622142C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622128C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×C11×D8C2311yescharacteristic
60C11×C4⋊Q8—21no—
61C4×D4×C11—21no—
62#66999—41no—
63#66999—41no—
64#66991—21no—
65#66991—21no—
66#66982—41no—
67C4×C22⋊D11—41no—
68C2×Dic44C2311yescharacteristic
69C2×C8×D11C2311yescharacteristic
70C2×C8×D11C2311yescharacteristic
71#66950—21no—
72#66950—21no—
73#66946—41no—
74#66945—21no—
75C4⋊C4×D11—21no—
76C4⋊C4×D11—21no—
77C4⋊C4×D11—21no—
78#66943—41no—
79#66937—41no—
80#66932—41no—
81C4×D44D411yescharacteristic
82#66923—21no—
83C4×Dic22—21no—
84C2×C11×C16C2311yescharacteristic
85C2×C11×C16C2311yescharacteristic
86C11×#107—21no—
87C11×#107C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#102—21no—
91C4×C8×C11C2311yescharacteristic
92#66896—21no—
93#66896—21no—
94#66891—22no—
95(C2×D11)⋊C8D411yescharacteristic
96(C2×D11)⋊C8D411yescharacteristic
97#66882C2311yescharacteristic
98#66882C2311yescharacteristic
99#66882C2311yescharacteristic
100#66881—21no—
101#66880—21no—
102C2×C11⋊C16C2311yescharacteristic
103C2×C11⋊C16C2311yescharacteristic
104#66874—21no—
105#66874—21no—
106#66872—21no—
107#66871—21no—
108#66871—21no—
109#66871—21no—
110C4⋊(C11⋊C8)D411yescharacteristic
111#66862—22no—
112C16×D11—22no—
113#33913—111nomaximal, Sylow
114C2×Q8×C11—41no—
115C2×D4×C11—21no—
116C22×C4×C11—41no—
117C2×C22⋊D11—41no—
118C2×C22⋊D11—41no—
119C2×D44D811yescharacteristic
120C2×C4×D11—41no—
121C2×C4×D11—41no—
122C2×C4×D11—41no—
123C2×C4×D11C2×D411yescharacteristic
124C2×C4×D11C2×D411yescharacteristic
125C2×Dic22—21no—
126C11×D8—21no—
127C11×D8—21no—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2411yescharacteristic
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—41no—
134C11×C22⋊C4—41no—
135C42×C11C2×D411yescharacteristic
136C22⋊Dic11—41no—
137C22⋊Dic11—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4D811yescharacteristic
142(C2×D11)⋊C4D811yescharacteristic
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—41no—
147C4⋊Dic11—41no—
148C4⋊Dic11D811yescharacteristic
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155C4×Dic11—41no—
156C4×Dic11—41no—
157C2×C11⋊C8C2×D411yescharacteristic
158C2×C11⋊C8C2×D411yescharacteristic
159Dic44—21no—
160Dic44—21no—
161C8×D11—21no—
162C8×D11—21no—
163C8×D11—21no—
164C8×D11—21no—
165C11×C16—21no—
166C11×C16—21no—
167C11⋊C16—21no—
168C11⋊C16#4112yes—
169#3339—111no—
170#3338—111no—
171#2255—111no—
172#2237—111no—
173#2236—111no—
174#2233—111no—
175#2232—111no—
176#2229—111no—
177#2224D1111yescharacteristic, complemented
178#2220—111no—
179#2217—111no—
180#2175—111no—
181#2168—111no—
182#2159—111no—
183C2×#366—111no—
184C23×C11—41no—
185C22×D11C2×D811yescharacteristic
186C22×D11C2×D811yescharacteristic
187Q8×C11—161no—
188D4×C11—41no—
189D4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—161no—
194C2×C4×C11C2×D811yescharacteristic
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C22⋊D11—82no—
198C22⋊D11—161no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11C2×D811yescharacteristic
204C2×Dic11C2×D811yescharacteristic
205D44—22no—
206C4×D11—21no—
207C4×D11—21no—
208C4×D11—21no—
209C4×D11—21no—
210C4×D11—161no—
211C4×D11—161no—
212C4×D11—161no—
213Dic22—41no—
214Dic22—41no—
215C8×C11—21no—
216C8×C11C2×#4111yescharacteristic
217C8×C112−1+411yescharacteristic
218C11⋊C8—21no—
219C11⋊C8—21no—
220#554—221no—
221#553—221no—
222C2×SD32—111no—
223C2×M32—111no—
224C22×C16—111no—
225#500C2×D1111yescharacteristic
226#499—111no—
227#484—221no—
228#484—221no—
229#482—221no—
230#481—221no—
231#478—221no—
232#477—221no—
233#467—111no—
234#467—111no—
235#466—111no—
236#466—111no—
237C4×Q16—111no—
238C4×D8C2×D1111yescharacteristic
239C8×D4—111no—
240#427—111no—
241C2×#107—111no—
242C2×#107—111no—
243C2×#107—111no—
244#367—111no—
245#367—111no—
246#367—111no—
247#366—111no—
248#366—111no—
249#366—111no—
250#366—111no—
251#366C2×D1111yescharacteristic
252#366C2×D1111yescharacteristic
253C4⋊C16C2×D1111yescharacteristic
254#358—111no—
255#358—111no—
256#358—111no—
257#357—111no—
258#357C2×D1111yescharacteristic
259#357C2×D1111yescharacteristic
260C22⋊C16—111no—
261C22⋊C16—111no—
262#346—111no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11C22×D811yescharacteristic
267C2×D11—21no—
268C2×D11—21no—
269C2×D11—21no—
270C2×D11—21no—
271C2×D11—21no—
272C2×D11#51012yes—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11—81no—
278C4×C11#54711yescharacteristic
279C4×C11#57811yescharacteristic
280Dic11—21no—
281Dic11—21no—
282Dic11—81no—
283Dic11—81no—
284Dic11—81no—
285Dic11—81no—
286C2×Q16—111no—
287C2×D8C22×D1111yescharacteristic
288C22×C8—111no—
289C22×C8—111no—
290C4⋊Q8—21no—
291#126—441no—
292#125—221no—
293#125—441no—
294#123—441no—
295C22⋊Q8—221no—
296C22⋊Q8—221no—
297C22⋊Q8—441no—
298C22⋊Q8—441no—
299#121—221no—
300#121—221no—
301#121—441no—
302C4×Q8—221no—
303C4×D4—21no—
304C4×D4—111no—
305C4×D4—441no—
306C4×D4—441no—
307#117—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—221no—
311SD32—222no—
312M32—222no—
313C2×C16—111no—
314C2×C16—111no—
315C2×C16—222no—
316C2×C16C22×D1111yescharacteristic
317C2×C16C22×D1111yescharacteristic
318#107—21no—
319#107—111no—
320#107—111no—
321#107—111no—
322#107—221no—
323#107—221no—
324#107—221no—
325#107C22×D1111yescharacteristic
326#107C22×D1111yescharacteristic
327#107C22×D1111yescharacteristic
328#106—221no—
329#106—221no—
330C4⋊C8—111no—
331#103—221no—
332#103—221no—
333#103—221no—
334#102—21no—
335#102—221no—
336#102—221no—
337C22⋊C8—111no—
338C22⋊C8—111no—
339C4×C8C22×D1111yescharacteristic
340C2×C11—161no—
341C2×C11#333411yescharacteristic
342C2×C11C2×#51011yescharacteristic
343C2×C11#341511yescharacteristic
344D11—22no—
345D11—41no—
346C2×Q8—41no—
347C2×Q8—221no—
348C2×D4—21no—
349C2×D4—111no—
350C2×D4—441no—
351C2×D4—441no—
352C22×C4—41no—
353C22×C4—111no—
354C22×C4—111no—
355C22×C4—441no—
356C22×C4—441no—
357C22×C4—441no—
358Q16—221no—
359Q16—221no—
360D8—21no—
361D8—21no—
362C2×C8—111no—
363C2×C8—111no—
364C2×C8—221no—
365C2×C8—221no—
366C2×C8—221no—
367C2×C8—221no—
368C2×C8D4×D1111yescharacteristic
369C2×C8C23×D1111yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—111no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C22⋊C4—41no—
387C22⋊C4—111no—
388C22⋊C4—111no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C42—441no—
395C42—441no—
396C42D4×D1111yescharacteristic
397C16—21no—
398C16—21no—
399C16—112no—
400C16—221no—
401C11#3391311yescharacteristic, complemented, Sylow
402C23—41no—
403C23—111no—
404C23—111no—
405Q8—161no—
406Q8—441no—
407Q8—441no—
408D4—41no—
409D4—41no—
410D4—222no—
411D4—882no—
412D4—1761no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—111no—
417C2×C4—111no—
418C2×C4—161no—
419C2×C4—221no—
420C2×C4—221no—
421C2×C4—221no—
422C2×C4—221no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—1761no—
428C2×C4—1761no—
429C2×C4—1761no—
430C2×C4D8×D1111yescharacteristic
431C2×C4D8×D1111yescharacteristic
432C2×C4C2×D4×D1111yescharacteristic
433C8—21no—
434C8—221no—
435C8—221no—
436C8#6704011yescharacteristic
437C8#41×D1111yescharacteristic
438C22—81no—
439C22—81no—
440C22—81no—
441C22—112no—
442C22—221no—
443C22—221no—
444C22—221no—
445C22—221no—
446C22—221no—
447C22C2×D8×D1111yescharacteristic
448C4—21no—
449C4—21no—
450C4—81no—
451C4—81no—
452C4—81no—
453C4—221no—
454C4—221no—
455C4—881no—
456C4—881no—
457C4—881no—
458C4—881no—
459C4#1062316211yescharacteristic
460C4#1062331011yescharacteristic
461C2—161no—
462C2—222no—
463C2—441no—
464C2#1308096211yescharacteristic
465C2D11×#51011yescharacteristic
466C2#1308175311yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2224C2
socleC22×C11C22×D8
prime radical#13081020C2
hypercenter#2224D11
hypocenterC11#33913
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2224

Complements

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

NH ≅ G/Ntype
2. #13081008C2semidirect
3. #13070899C2semidirect
4. #13070826C2semidirect
5. #13070820C2semidirect
6. #13070800C2semidirect
7. #13070795C2semidirect
8. #13070781C2semidirect
9. #13070728C2semidirect
10. #13070711C2semidirect
11. #13070480C2semidirect
12. #13070440C2semidirect
13. #13070401C2semidirect
14. D11×#366C2semidirect
15. C11×#2224C2semidirect
177. #2224D11semidirect
401. C11#33913semidirect

Maximal subgroups

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

subgroupindex
#130810202
#130810082
#130708992
#130708262
#130708202
#130708002
#130707952
#130707812
#130707282
#130707112
#130704802
#130704402
#130704012
D11×#3662
C11×#22242
#3391311