Finite Group Databasebeta

← #14736241

Subgroups — #14736241

Order 2816.

664 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078670C212yesmaximal, complemented
2C8×#4339C211yesmaximal, characteristic, complemented
3#13068029C212yesmaximal, complemented
4#13068022C212yesmaximal, complemented
5#13068017C211yesmaximal, characteristic, complemented
6#13068012C211yesmaximal, characteristic, complemented
7#13067973C211yesmaximal, characteristic, complemented
8#13067968C211yesmaximal, characteristic, complemented
9#13067364C211yesmaximal, characteristic, complemented
10#13067278C212yesmaximal, complemented
11C11×#3169C211yesmaximal, characteristic, complemented
12C11×#532C2212yes—
13C4×#4339C2211yescharacteristic
14C11×#500C2211yescharacteristic
15C11×#493C2211yescharacteristic
16C11×#486C2212yes—
17C11×#466—21no—
18C11×#466—21no—
19C4×C11×D8—21no—
20C4×C11×D8—21no—
21C2×C4×C8×C11C2211yescharacteristic
22C8×C22⋊D11—21no—
23C8×C22⋊D11—21no—
24#10622704C2212yes—
25#10622697C2212yes—
26#10622688C2212yes—
27#10622685C2212yes—
28#10622650—22no—
29#10622648—22no—
30C4×#4324—22no—
31C4×#4323—22no—
32#10622538C2211yescharacteristic
33#10622538C2212yes—
34C8×D44C2211yescharacteristic
35C8×D44C2211yescharacteristic
36#10622298—21no—
37C4×C8×D11—21no—
38C8×Dic22C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40#10622184C2212yes—
41#10622184C2212yes—
42#10622182C2212yes—
43#10622182C2212yes—
44#10622096C2211yescharacteristic
45#10622096C2211yescharacteristic
46#10622095C2212yes—
47C2×C11×#41—22no—
48C2×#4339D411yescharacteristic
49C2×C11×D8—21no—
50C2×C11×D8—21no—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11D411yescharacteristic
53C11×C4⋊Q8C2312yes—
54C11×#127C2312yes—
55C11×#124—22no—
56C11×#121—22no—
57C11×#121—22no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C2×C42×C11C2311yescharacteristic
61C2×#4324—22no—
62C2×#4323—22no—
63C4×C22⋊D11—21no—
64C4×C22⋊D11—21no—
65#66979D411yescharacteristic
66C2×C8×D11—21no—
67C2×C8×D11—21no—
68C4×D44D411yescharacteristic
69C4×D44C2311yescharacteristic
70#66925—21no—
71C42×D11—21no—
72C4×Dic22D411yescharacteristic
73C4×Dic22C2311yescharacteristic
74C11×#107—21no—
75C11×#107—21no—
76C11×#102—22no—
77C11×#102—22no—
78C4×C8×C11D411yescharacteristic
79C4×C8×C11D411yescharacteristic
80C4×C8×C11C2311yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66896—22no—
83#66896—22no—
84C22⋊(C11⋊C8)—21no—
85C22⋊(C11⋊C8)—22no—
86(C2×D11)⋊C8—21no—
87(C2×D11)⋊C8—21no—
88Dic11⋊C8—21no—
89Dic11⋊C8—21no—
90C8×Dic11—21no—
91C8×Dic11—21no—
92#66874—22no—
93#66873—22no—
94#66872—22no—
95#66871—22no—
96C4⋊(C11⋊C8)C2311yescharacteristic
97C4⋊(C11⋊C8)C2311yescharacteristic
98C4⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)C2312yes—
100C4×C11⋊C8—21no—
101C4×C11⋊C8—22no—
102#19128—111nomaximal, Sylow
103C11×#41—84no—
104C2×Q8×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C2×C22⋊D11—21no—
114#4339—22no—
115#4339—22no—
116C2×D44C2×D411yescharacteristic
117C2×C4×D11—21no—
118C2×C4×D11—21no—
119C2×C4×D11—21no—
120C2×Dic22C2×D411yescharacteristic
121C11×D8—42no—
122C11×D8—42no—
123C2×C8×C11—22no—
124C2×C8×C11—41no—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C22⋊C4—42no—
132C11×C22⋊C4—42no—
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11#4111yescharacteristic
136C42×C11C2411yescharacteristic
137C22⋊Dic11—21no—
138#4324—44no—
139#4323—44no—
140(C2×D11)⋊C4—21no—
141(C2×D11)⋊C4—21no—
142C4⋊Dic11C2×D411yescharacteristic
143C4⋊Dic11C2×D411yescharacteristic
144Dic11⋊C4—21no—
145Dic11⋊C4—21no—
146C4×Dic11—21no—
147C4×Dic11—21no—
148C4×Dic11—21no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C8×D11—42no—
154C8×D11—42no—
155#3169D1111yescharacteristic, complemented
156#3106—112no—
157C8×#41—111no—
158#1678—112no—
159#1677—112no—
160#1676—111no—
161#1675—111no—
162#1668—111no—
163#1667—111no—
164#1564—111no—
165#1543—112no—
166C23×C11—42no—
167C23×C11#12111yescharacteristic
168C22×D11—21no—
169Q8×C11—82no—
170D4×C11—42no—
171D4×C11—42no—
172D4×C11—42no—
173D4×C11—42no—
174D4×C11—82no—
175D4×C11—84no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—42no—
182C2×C4×C11—84no—
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C22⋊D11—24no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193D44—21no—
194D44#13512yes—
195C4×D11—24no—
196C4×D11—41no—
197C4×D11—41no—
198C4×D11—42no—
199Dic22—21no—
200Dic22#13512yes—
201C8×C11—21no—
202C8×C11—21no—
203C8×C11—21no—
204C8×C11#13512yes—
205C11⋊C8—41no—
206C11⋊C8—42no—
207C11⋊C8—42no—
208C11⋊C8—41no—
209#532C2×D1112yes—
210C4×#41—111no—
211#500C2×D1111yescharacteristic
212#493C2×D1111yescharacteristic
213#486C2×D1112yes—
214#482—222no—
215#477—112no—
216#476—112no—
217#466—21no—
218#466—21no—
219#460—112no—
220#459—112no—
221#449—222no—
222C8×Q8—111no—
223C8×Q8—111no—
224C4×SD16—222no—
225C4×D8—21no—
226C4×D8—21no—
227C4×D8—222no—
228C8×D4—111no—
229C8×D4—111no—
230C8×D4—221no—
231C8×D4—221no—
232#431—111no—
233#431—112no—
234#431—221no—
235C2×C4×C8—221no—
236C2×C4×C8C2×D1111yescharacteristic
237#335—111no—
238#335—111no—
239#334—112no—
240#333—112no—
241#333—112no—
242#331—112no—
243#331—112no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—82no—
248C22×C11—82no—
249C22×C11—82no—
250C22×C11C2×#12111yescharacteristic
251C2×D11—22no—
252C2×D11—41no—
253C2×D11—41no—
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—82no—
258C4×C11#47212yes—
259C4×C11C2×#13511yescharacteristic
260C4×C11C2×#13511yescharacteristic
261C4×C11C2×#13511yescharacteristic
262C4×C11#57511yescharacteristic
263Dic11—22no—
264Dic11—41no—
265Dic11—41no—
266C2×#41—22no—
267C2×#41—111no—
268C2×SD16—222no—
269C2×D8—21no—
270C2×D8—21no—
271C2×D8—222no—
272C22×C8—221no—
273C22×C8—221no—
274C22×C8C22⋊D1111yescharacteristic
275C22×C8C22⋊D1111yescharacteristic
276C4⋊Q8C22×D1112yes—
277#127C22×D1112yes—
278#124—22no—
279#121—22no—
280#121—22no—
281C4×Q8—111no—
282C4×Q8—111no—
283C4×D4—22no—
284C4×D4—22no—
285C4×D4—111no—
286C4×D4—111no—
287C4×D4—221no—
288C4×D4—221no—
289#117—111no—
290#117—221no—
291C2×C42—221no—
292C2×C42C22×D1111yescharacteristic
293#107—21no—
294#107—21no—
295#107—222no—
296#106—222no—
297C4⋊C8—111no—
298C4⋊C8—111no—
299C4⋊C8—112no—
300C4⋊C8—112no—
301C4⋊C8—221no—
302C4⋊C8—221no—
303#103—222no—
304#102—22no—
305#102—22no—
306#102—222no—
307#102—222no—
308#102—222no—
309C22⋊C8—222no—
310C22⋊C8—221no—
311C22⋊C8—221no—
312C22⋊C8—221no—
313C4×C8—221no—
314C4×C8—221no—
315C4×C8—222no—
316C4×C8—221no—
317C4×C8C22⋊D1111yescharacteristic
318C4×C8C22⋊D1111yescharacteristic
319C4×C8C22×D1111yescharacteristic
320C4×C8C22×D1111yescharacteristic
321C2×C11—41no—
322C2×C11—162no—
323C2×C11#303511yescharacteristic
324C2×C11#305011yescharacteristic
325C2×C11C2×#47211yescharacteristic
326D11—42no—
327#41—84no—
328#41—222no—
329#41—222no—
330C2×Q8—22no—
331C2×Q8—111no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—42no—
336C2×D4—111no—
337C2×D4—221no—
338C22×C4—42no—
339C22×C4—221no—
340C22×C4—221no—
341C22×C4—221no—
342C22×C4D4×D1111yescharacteristic
343C22×C4#434111yescharacteristic
344C22×C4C2×C22⋊D1111yescharacteristic
345SD16—444no—
346D8—42no—
347D8—42no—
348D8—444no—
349C2×C8—22no—
350C2×C8—41no—
351C2×C8—222no—
352C2×C8—222no—
353C2×C8—221no—
354C2×C8—221no—
355C2×C8—442no—
356C2×C8—442no—
357C2×C8C2×C22⋊D1111yescharacteristic
358C2×C8C2×C22⋊D1111yescharacteristic
359C2×C8C2×C22⋊D1111yescharacteristic
360C2×C8C2×C22⋊D1111yescharacteristic
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—111no—
364C4⋊C4—111no—
365C4⋊C4—221no—
366C4⋊C4—221no—
367C22⋊C4—42no—
368C22⋊C4—42no—
369C22⋊C4—221no—
370C22⋊C4—221no—
371C22⋊C4—221no—
372C42—221no—
373C42—221no—
374C42—221no—
375C42D4×D1111yescharacteristic
376C42#434111yescharacteristic
377C42C2×C22⋊D1111yescharacteristic
378C42C23×D1111yescharacteristic
379C11#1912811yescharacteristic, complemented, Sylow
380C23—42no—
381C23—221no—
382C23#6699111yescharacteristic
383Q8—82no—
384Q8—112no—
385Q8—221no—
386D4—42no—
387D4—42no—
388D4—42no—
389D4—42no—
390D4—82no—
391D4—84no—
392D4—112no—
393D4—224no—
394D4—221no—
395C2×C4—22no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—42no—
401C2×C4—84no—
402C2×C4—224no—
403C2×C4—221no—
404C2×C4—221no—
405C2×C4—221no—
406C2×C4—442no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4#6699111yescharacteristic
410C2×C4#6699111yescharacteristic
411C2×C4#6699111yescharacteristic
412C2×C4C2×D4×D1111yescharacteristic
413C2×C4C2×#434111yescharacteristic
414C2×C4C22×C22⋊D1111yescharacteristic
415C8—21no—
416C8—21no—
417C8—21no—
418C8—442no—
419C8—442no—
420C8—441no—
421C8—441no—
422C8#6700312yes—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—82no—
427C22—82no—
428C22—82no—
429C22—222no—
430C22—441no—
431C22—441no—
432C22C2×#6699111yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—82no—
437C4—222no—
438C4—441no—
439C4—441no—
440C4#1062277312yes—
441C4D11×#13511yescharacteristic
442C4D11×#13511yescharacteristic
443C4C2×#6700311yescharacteristic
444C4#1062335311yescharacteristic
445C2—41no—
446C2—162no—
447C2—442no—
448C2#1307806511yescharacteristic
449C2#1307819311yescharacteristic
450C2C2×#1062277311yescharacteristic
subgroupG/H
centerC2×C4#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3169C2
socleC22×C11C2×#121
hypercenter#3169D11
hypocenterC11#19128
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #13078670C2semidirect
2. C8×#4339C2semidirect
3. #13068029C2semidirect
4. #13068022C2semidirect
5. #13068017C2semidirect
6. #13068012C2semidirect
7. #13067973C2semidirect
8. #13067968C2semidirect
9. #13067364C2semidirect
10. #13067278C2semidirect
11. C11×#3169C2semidirect
155. #3169D11semidirect
379. C11#19128semidirect

Maximal subgroups

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

subgroupindex
#130786702
C8×#43392
#130680292
#130680222
#130680172
#130680122
#130679732
#130679682
#130673642
#130672782
C11×#31692
#1912811