Finite Group Databasebeta

← #14739310

Subgroups — #14739310

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079557C211yesmaximal, characteristic, complemented
2#13078413C211yesmaximal, characteristic, complemented
3#13077657C211yesmaximal, characteristic, complemented
4#13068147C214yesmaximal, complemented
5#13068079C214yesmaximal, complemented
6#13067390C211yesmaximal, characteristic, complemented
7#13067284C211yesmaximal, characteristic, complemented
8#13067274C211yesmaximal, characteristic, complemented
9C2×C11×#459C211yesmaximal, characteristic
10C22×C11×D8—21no—
11C2×C11×#127C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13#10623001C2211yescharacteristic
14C11×#459—22no—
15C11×#459C2214yes—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#102—21no—
18#10622831—22no—
19#10622828—21no—
20#10622820—22no—
21#10622689C2212yescomplemented
22#10622688—22no—
23#10622683C2212yescomplemented
24#10622625—22no—
25#10622625C2214yescomplemented
26#10622622—22no—
27#10622621C2212yescomplemented
28#10622620C2212yescomplemented
29#10622577—21no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622182C2214yescomplemented
34#10622124C2212yescomplemented
35#10622119C2212yescomplemented
36#10622117C2214yescomplemented
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11D411yescharacteristic
41C23×C4×C11—21no—
42C2×C11×D8—24no—
43C2×C11×D8—44no—
44C22×C8×C11—21no—
45C11×#127—21no—
46C11×#127—21no—
47C11×#127—21no—
48C11×#127C2312yes—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11D412yes—
52C4×D4×C11C2312yes—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C22⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C2×#4324—24no—
57#66979—21no—
58#66977—21no—
59#66977—21no—
60C2×#4318—21no—
61C2×#4318—24no—
62#66923—21no—
63#66922C2311yescharacteristic
64#66922C2311yescharacteristic
65C4×Dic22—21no—
66C4×Dic22—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8C2312yes—
69C11×#102—24no—
70#66896—22no—
71#66896—22no—
72#66896—24no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—24no—
75C22⋊(C11⋊C8)D412yes—
76#66872—22no—
77#66871—22no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)D412yes—
80C4⋊(C11⋊C8)C2312yes—
81C4⋊(C11⋊C8)C2312yes—
82C4×C11⋊C8—21no—
83C4×C11⋊C8C2312yes—
84#19420—111nomaximal, Sylow
85C24×C11—21no—
86C24×C11—41no—
87C2×D4×C11—21no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—42no—
97C2×D4×C11—42no—
98C2×D4×C11—82no—
99C2×D4×C11—82no—
100C2×D4×C11C2×D412yes—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—82no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C2×Dic22—21no—
109C2×Dic22—21no—
110C11×D8—48no—
111C2×C8×C11—22no—
112C2×C8×C11—42no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4C2×D412yes—
115C11×C22⋊C4—22no—
116C11×C22⋊C4—22no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11#4111yescharacteristic
120C42×C11C2411yescharacteristic
121C22⋊Dic11—41no—
122#4324—84no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127Dic11⋊C4—41no—
128Dic11⋊C4—41no—
129C4×Dic11—41no—
130#4318—42no—
131#4318—84no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8C2×D414yes—
135#3208—111no—
136#3077—111no—
137C2×#459D1111yescharacteristic
138#2975—111no—
139#1697—114no—
140#1685—114no—
141#1571—111no—
142#1545—111no—
143#1542—111no—
144C23×C11—22no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—81no—
148C23×C11—81no—
149C23×C11—82no—
150C23×C11—82no—
151C23×C11—82no—
152C23×C11#12111yescharacteristic
153D4×C11—22no—
154D4×C11—22no—
155D4×C11—42no—
156D4×C11—42no—
157D4×C11—44no—
158D4×C11—42no—
159D4×C11—82no—
160D4×C11—82no—
161D4×C11—82no—
162D4×C11—82no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—41no—
166C2×C4×C11—44no—
167C2×C4×C11—82no—
168C2×C4×C11—81no—
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)12yes—
173C2×C4×C11#13712yes—
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C11C2×#4111yescharacteristic
177C2×Dic11—41no—
178C2×Dic11—41no—
179Dic22—42no—
180Dic22—81no—
181C8×C11—42no—
182C11⋊C8—24no—
183C11⋊C8—42no—
184C11⋊C8—42no—
185C22×D8—21no—
186#533—111no—
187C2×#127C2×D1111yescharacteristic
188C2×C4×D4C2×D1111yescharacteristic
189#492—112no—
190#486—112no—
191#478—222no—
192#476—112no—
193#474—112no—
194#460—222no—
195#459—22no—
196#459C2×D1114yes—
197#450—222no—
198#436—114no—
199#436—222no—
200#431—111no—
201#431—111no—
202#428—221no—
203#423—111no—
204C2×C4⋊C8C2×D1111yescharacteristic
205#418—221no—
206C2×#102—21no—
207#407—222no—
208#335—114no—
209#333—112no—
210#332—112no—
211#331—114no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—84no—
218C22×C11—82no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11—164no—
222C22×C11#46812yes—
223C22×C11C2×#12111yescharacteristic
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—42no—
228C4×C11#46812yes—
229C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
230C4×C11C2×#13711yescharacteristic
231C4×C11#57612yes—
232Dic11—81no—
233Dic11—81no—
234C22×D4—21no—
235C22×D4—21no—
236C22×D4—21no—
237C22×D4C22⋊D1111yescharacteristic
238C23×C4—21no—
239C2×SD16—224no—
240C2×D8—24no—
241C2×D8—44no—
242C2×M16—224no—
243C2×M16—221no—
244C22×C8—21no—
245C4⋊Q8—111no—
246C4⋊Q8—111no—
247#127—21no—
248#127—21no—
249#127—21no—
250#127C22×D1112yes—
251#125—221no—
252C22⋊Q8—221no—
253C22⋊Q8—221no—
254C4×Q8—221no—
255C4×Q8—221no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4C22⋊D1112yes—
259C4×D4C22×D1112yes—
260#117—221no—
261C2×C4⋊C4C22⋊D1111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C42C22×D1111yescharacteristic
264#107—222no—
265#106—222no—
266C4⋊C8—21no—
267C4⋊C8—112no—
268C4⋊C8—112no—
269C4⋊C8—112no—
270C4⋊C8—221no—
271C4⋊C8C22×D1112yes—
272#102—24no—
273#102—224no—
274#102—222no—
275#102—222no—
276C22⋊C8—112no—
277C22⋊C8—224no—
278C22⋊C8—221no—
279C4×C8—112no—
280C4×C8—221no—
281C2×C11—22no—
282C2×C11—82no—
283C2×C11—162no—
284C2×C11#304111yescharacteristic
285C2×C11C2×#46811yescharacteristic
286C2×C11#306811yescharacteristic
287C24—21no—
288C24—41no—
289C2×Q8—221no—
290C2×Q8—221no—
291C2×D4—22no—
292C2×D4—21no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—42no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—42no—
302C2×D4—82no—
303C2×D4—82no—
304C2×D4C2×C22⋊D1112yes—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—82no—
309C22×C4D4×D1111yescharacteristic
310C22×C4#434111yescharacteristic
311C22×C4C2×C22⋊D1111yescharacteristic
312SD16—884no—
313D8—48no—
314M16—442no—
315M16—884no—
316C2×C8—22no—
317C2×C8—42no—
318C2×C8—114no—
319C2×C8—222no—
320C2×C8—222no—
321C4⋊C4—21no—
322C4⋊C4—221no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C4⋊C4—221no—
326C4⋊C4—441no—
327C4⋊C4—441no—
328C4⋊C4C2×C22⋊D1112yes—
329C22⋊C4—22no—
330C22⋊C4—22no—
331C22⋊C4—441no—
332C42—441no—
333C42D4×D1111yescharacteristic
334C42#434111yescharacteristic
335C42C2×C22⋊D1111yescharacteristic
336C42C23×D1111yescharacteristic
337C11#1942011yescharacteristic, complemented, Sylow
338C23—22no—
339C23—42no—
340C23—42no—
341C23—81no—
342C23—81no—
343C23—82no—
344C23—82no—
345C23—82no—
346C23#6699211yescharacteristic
347Q8—442no—
348Q8—881no—
349D4—22no—
350D4—22no—
351D4—44no—
352D4—42no—
353D4—42no—
354D4—42no—
355D4—82no—
356D4—82no—
357D4—82no—
358D4—82no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—44no—
363C2×C4—82no—
364C2×C4—81no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4#6698512yes—
368C2×C4#6699211yescharacteristic
369C2×C4#6699211yescharacteristic
370C2×C4#6699211yescharacteristic
371C2×C4#6700412yes—
372C2×C4C2×D4×D1111yescharacteristic
373C2×C4C2×#434111yescharacteristic
374C2×C4C22×C22⋊D1111yescharacteristic
375C8—42no—
376C8—224no—
377C8—442no—
378C8—442no—
379C22—21no—
380C22—21no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—84no—
385C22—82no—
386C22—82no—
387C22—82no—
388C22—164no—
389C22#1062265512yes—
390C22C2×#6699211yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—881no—
396C4—881no—
397C4#1062265512yes—
398C4#1062328812yes—
399C4C2×#6698511yescharacteristic
400C4C2×#6700411yescharacteristic
401C2—22no—
402C2—82no—
403C2—162no—
404C2#1307811611yescharacteristic
405C2C2×#1062265511yescharacteristic
406C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC2×C11×#459C2
socleC22×C11C2×#121
hypercenterC2×#459D11
hypocenterC11#19420
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. #13079557C2semidirect
2. #13078413C2semidirect
3. #13077657C2semidirect
4. #13068147C2semidirect
5. #13068079C2semidirect
6. #13067390C2semidirect
7. #13067284C2semidirect
8. #13067274C2semidirect
21. #10622689C22semidirect
23. #10622683C22semidirect
25. #10622625C22semidirect
27. #10622621C22semidirect
28. #10622620C22semidirect
33. #10622182C22semidirect
34. #10622124C22semidirect
35. #10622119C22semidirect
36. #10622117C22semidirect
337. C11#19420semidirect

Maximal subgroups

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

subgroupindex
#130795572
#130784132
#130776572
#130681472
#130680792
#130673902
#130672842
#130672742
C2×C11×#4592
#1942011