Finite Group Databasebeta

← #14767696

Subgroups — #14767696

Order 2816.

772 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079105C211yesmaximal, characteristic
2#13077532C211yesmaximal, characteristic
3#13077484C211yesmaximal, characteristic, complemented
4#13069514C211yesmaximal, characteristic
5#13069151C212yesmaximal, complemented
6#13069135C212yesmaximal, complemented
7#13069108C212yesmaximal, complemented
8#13069092C212yesmaximal, complemented
9#13068741C211yesmaximal, characteristic, complemented
10#13068371C211yesmaximal, characteristic, complemented
11C11×#1979C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13#10623347C2212yes—
14#10623343C2212yes—
15C2×#66995C2212yes—
16#10623276C2212yes—
17C2×#66957C2211yescharacteristic
18C2×C11×#108C2211yescharacteristic
19C11×#419C2212yes—
20C2×C11×#101C2212yes—
21C11×#405C2211yescharacteristic
22#10622838C2212yes—
23#10622804C412yescomplemented
24#10622803C414yescomplemented
25#10622797—22no—
26Q16×Dic11—22no—
27#10622794C412yescomplemented
28#10622752C2212yes—
29#10622752C2212yes—
30#10622719C2211yescharacteristic
31#10622714C2211yescharacteristic
32#10622714C2211yescharacteristic
33#10622619C2212yes—
34#10622508—22no—
35#10622507—22no—
36C11⋊#338C2211yescharacteristic
37#10622197C2212yes—
38#10622195C2212yes—
39#10622195C2211yescharacteristic
40#10622169C2211yescharacteristic
41#10622169C2211yescharacteristic
42C22×Q8×C11C2312yes—
43C2×#4339C2312yes—
44C2×C11×Q16—21no—
45C2×C11×Q16—21no—
46C2×C11×Q16—21no—
47C2×C11×Q16—21no—
48C2×C11×Q16C2×C412yes—
49C2×C11×Q16C2×C412yes—
50C2×C11×M16C2311yescharacteristic
51C2×C11×M16C2312yes—
52C22×C8×C11C2311yescharacteristic
53C11×#117C2311yescharacteristic
54#67000C2×C414yes—
55#66999—42no—
56Q8×Dic11—24no—
57Q8×Dic11—42no—
58#66997C2×C414yes—
59C2×#4326C2×C414yes—
60#66995—42no—
61#66995—42no—
62C2×#4325C2×C414yes—
63#66982—42no—
64#66979—42no—
65#66979C2312yes—
66#66979C2311yescharacteristic
67#66979C2311yescharacteristic
68C2×#4318C2311yescharacteristic
69C2×#4318C2311yescharacteristic
70#66960—24no—
71M16×D11—42no—
72C2×Dic44C2×C411yescharacteristic
73#66957—21no—
74#66957—21no—
75#66957—21no—
76#66957—21no—
77C2×D88C2×C411yescharacteristic
78C2×#4314C2×C412yes—
79#66954—42no—
80C11×#108—21no—
81C11×#108—21no—
82C11×#103—42no—
83C11×#101—42no—
84C11×#97—21no—
85C4×C8×C11—21no—
86#66899—24no—
87#66889—24no—
88#66889—42no—
89#66882—21no—
90#66881—21no—
91#66879C2×C412yes—
92#66879D412yes—
93C8×Dic11C2×C412yes—
94C8×Dic11D412yes—
95#66870—42no—
96#22285—111nomaximal, Sylow
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11C22×C414yes—
103C22×C4×C11—22no—
104C22×C4×C11C2411yescharacteristic
105C2×C22⋊D11—22no—
106#4339—22no—
107#4339—22no—
108#4339—22no—
109#4339—22no—
110C2×D44C22×C412yes—
111C2×C4×D11—22no—
112C2×Dic22C22×C412yes—
113C11×Q16—22no—
114C11×Q16—22no—
115C11×Q16—22no—
116C11×Q16—22no—
117C11×M16—22no—
118C11×M16—21no—
119C11×M16—21no—
120C11×M16—22no—
121C2×C8×C11—21no—
122C2×C8×C11—22no—
123C2×C8×C11C22×C411yescharacteristic
124C2×C8×C11C22×C411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11#4111yescharacteristic
128C2×C8×C11#4111yescharacteristic
129C11×C4⋊C4—21no—
130C11×C22⋊C4—21no—
131C42×C11—21no—
132C22⋊Dic11—21no—
133C22⋊Dic11—21no—
134C22⋊Dic11—22no—
135#4326—44no—
136#4325—44no—
137(C2×D11)⋊C4—44no—
138C4⋊Dic11—22no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11—44no—
142Dic11⋊C4—44no—
143C4×Dic11—22no—
144C4×Dic11—44no—
145C4×Dic11C22×C412yes—
146C4×Dic11C2×D412yes—
147#4318—21no—
148#4318—21no—
149#4318—21no—
150#4318—21no—
151C2×C11⋊C8C22×C412yes—
152C2×C11⋊C8C2×D412yes—
153Dic44—21no—
154Dic44—21no—
155D88—21no—
156D88—21no—
157#4314—22no—
158#4314—22no—
159#4313—44no—
160C8×D11—44no—
161#3156—111no—
162#2957—111no—
163#2950—111no—
164#1979D1111yescharacteristic, complemented
165#1976—111no—
166#1912—112no—
167#1909—112no—
168#1905—112no—
169#1902—112no—
170#1833—111no—
171#1747—111no—
172C23×C11H(5,𝔽2)11yescharacteristic
173C22×D11—22no—
174Q8×C11—24no—
175Q8×C11—24no—
176Q8×C11—42no—
177Q8×C11—42no—
178C2×C4×C11—24no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11C23×C411yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×C4×C11H(5,𝔽2)11yescharacteristic
186C2×C4×C11H(5,𝔽2)11yescharacteristic
187C2×C4×C11H(5,𝔽2)11yescharacteristic
188C22⋊D11—42no—
189C22⋊D11—42no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—42no—
194D44—22no—
195D44—22no—
196C4×D11—42no—
197C4×D11—42no—
198Dic22—22no—
199Dic22—22no—
200C8×C11—42no—
201C8×C11—41no—
202C8×C11C4×D411yescharacteristic
203C8×C11C4×D411yescharacteristic
204C8×C11C4×D411yescharacteristic
205C8×C11C4×D411yescharacteristic
206C11⋊C8—22no—
207C11⋊C8—22no—
208C2×#137—112no—
209C2×#135—111no—
210C22×Q16C2×D1111yescharacteristic
211#568—112no—
212#536—112no—
213#519—112no—
214#497—114no—
215#495—112no—
216#494—112no—
217#444—222no—
218#443—222no—
219#441—222no—
220C4×Q16—222no—
221C2×#108C2×D1111yescharacteristic
222#427—111no—
223#421—112no—
224#421—112no—
225#419—112no—
226#419C2×D1112yes—
227C2×#101C2×D1112yes—
228#410—112no—
229#405—111no—
230#405—111no—
231#405C2×D1111yescharacteristic
232#344—112no—
233#338—111no—
234H(3,ℤ/4)—112no—
235H(3,ℤ/4)—111no—
236H(3,ℤ/4)—111no—
237H(3,ℤ/4)—111no—
238C22×C11—41no—
239C22×C11#51811yescharacteristic
240C22×C11#53511yescharacteristic
241C22×C11#54011yescharacteristic
242C2×D11—42no—
243C2×D11—82no—
244C4×C11—44no—
245C4×C11—81no—
246C4×C11C2×C4×D411yescharacteristic
247C4×C11#51811yescharacteristic
248C4×C11#53511yescharacteristic
249C4×C11#54011yescharacteristic
250Dic11—42no—
251Dic11—42no—
252Dic11—42no—
253Dic11—82no—
254C2×#41—112no—
255C22×Q8C22×D1112yes—
256#137—442no—
257#137—442no—
258#135—221no—
259#135—221no—
260#135—221no—
261#135—221no—
262C2×Q16—21no—
263C2×Q16—21no—
264C2×Q16—21no—
265C2×Q16—21no—
266C2×Q16—114no—
267C2×Q16—111no—
268C2×Q16C4×D1112yes—
269C2×Q16C4×D1112yes—
270C2×SD16—114no—
271C2×SD16—112no—
272C2×D8—111no—
273#131—224no—
274#131—442no—
275C2×M16—111no—
276C2×M16—111no—
277C2×M16—442no—
278C2×M16C22×D1112yes—
279C2×M16C22×D1111yescharacteristic
280C22×C8C22×D1111yescharacteristic
281C4⋊Q8—114no—
282#124—114no—
283#123—442no—
284C22⋊Q8—442no—
285C4×Q8—224no—
286C4×Q8—442no—
287#117—111no—
288#117—111no—
289#117—112no—
290#117—442no—
291#117C22×D1111yescharacteristic
292#108—21no—
293#108—21no—
294#107—221no—
295#106—221no—
296#104—224no—
297#104—442no—
298#103—42no—
299#103—224no—
300#101—42no—
301#99—442no—
302#97—21no—
303#97—112no—
304#97—112no—
305C4×C8—21no—
306C4×C8—112no—
307C4×C8—112no—
308C2×C11—21no—
309C2×C11—21no—
310C2×C11—21no—
311C2×C11#232811yescharacteristic
312D11—82no—
313#41—222no—
314#41—222no—
315#41—222no—
316#41—222no—
317C2×Q8—22no—
318C2×Q8—22no—
319C2×Q8—22no—
320C2×Q8—22no—
321C2×Q8—22no—
322C2×Q8—112no—
323C2×Q8C2×C4×D1114yes—
324C2×D4—112no—
325C2×D4—222no—
326C22×C4—22no—
327C22×C4—222no—
328C22×C4C23×D1111yescharacteristic
329Q16—22no—
330Q16—22no—
331Q16—22no—
332Q16—22no—
333Q16—221no—
334Q16—221no—
335Q16—444no—
336SD16—222no—
337SD16—222no—
338SD16—444no—
339D8—221no—
340D8—221no—
341M16—22no—
342M16—21no—
343M16—22no—
344M16—21no—
345M16—221no—
346M16—221no—
347M16—221no—
348M16—221no—
349M16—444no—
350C2×C8—21no—
351C2×C8—22no—
352C2×C8—112no—
353C2×C8—112no—
354C2×C8—444no—
355C2×C8C2×C4×D1111yescharacteristic
356C2×C8C2×C4×D1111yescharacteristic
357C2×C8D4×D1111yescharacteristic
358C2×C8D4×D1111yescharacteristic
359C2×C8#434111yescharacteristic
360C2×C8#434111yescharacteristic
361C4⋊C4—21no—
362C4⋊C4—221no—
363C4⋊C4—221no—
364C4⋊C4—222no—
365C4⋊C4—444no—
366C4⋊C4—444no—
367C22⋊C4—21no—
368C22⋊C4—221no—
369C22⋊C4—221no—
370C22⋊C4—222no—
371C22⋊C4—444no—
372C42—21no—
373C42—112no—
374C42—112no—
375C42—222no—
376C42—444no—
377C11#2228511yescharacteristic, complemented, Sylow
378C23—222no—
379C23#6704211yescharacteristic
380Q8—24no—
381Q8—24no—
382Q8—42no—
383Q8—42no—
384Q8—222no—
385Q8—222no—
386D4—222no—
387D4—222no—
388D4—442no—
389D4—442no—
390C2×C4—24no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—222no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4C22×C4×D1111yescharacteristic
401C2×C4C2×D4×D1111yescharacteristic
402C2×C4C2×#434111yescharacteristic
403C2×C4#6703711yescharacteristic
404C2×C4#6703711yescharacteristic
405C2×C4#6704211yescharacteristic
406C8—42no—
407C8—41no—
408C8—222no—
409C8—222no—
410C8(C22⋊D11)⋊C411yescharacteristic
411C8(C22⋊D11)⋊C411yescharacteristic
412C8(C22⋊D11)⋊C411yescharacteristic
413C8(C22⋊D11)⋊C411yescharacteristic
414C22—41no—
415C22—442no—
416C22—882no—
417C22#1062307611yescharacteristic
418C22#1062315011yescharacteristic
419C22#1062320511yescharacteristic
420C4—44no—
421C4—81no—
422C4—442no—
423C4—442no—
424C4—442no—
425C4—882no—
426C4C2×(C22⋊D11)⋊C411yescharacteristic
427C4#1062307611yescharacteristic
428C4#1062315011yescharacteristic
429C4#1062324611yescharacteristic
430C2—21no—
431C2—21no—
432C2—21no—
433C2—882no—
434C2#1307134011yescharacteristic
subgroupG/H
centerC2#13071340
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1979C2
socleC2×C11#2328
prime radicalC2×#66957C22
cosocleC22×C4×C11C24
hypercenter#1979D11
hypocenterC11#22285
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1979

Complements

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

NH ≅ G/Ntype
3. #13077484C2semidirect
5. #13069151C2semidirect
6. #13069135C2semidirect
7. #13069108C2semidirect
8. #13069092C2semidirect
9. #13068741C2semidirect
10. #13068371C2semidirect
11. C11×#1979C2semidirect
23. #10622804C4semidirect
24. #10622803C4semidirect
27. #10622794C4semidirect
164. #1979D11semidirect
377. C11#22285semidirect

Maximal subgroups

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

subgroupindex
#130791052
#130775322
#130774842
#130695142
#130691512
#130691352
#130691082
#130690922
#130687412
#130683712
C11×#19792
#2228511