Finite Group Databasebeta

← #14736513

Subgroups — #14736513

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078670C212yesmaximal, complemented
2#13077582C211yesmaximal, characteristic, complemented
3#13068153C212yesmaximal, complemented
4#13068146C212yesmaximal, complemented
5#13068141C211yesmaximal, characteristic, complemented
6#13068136C211yesmaximal, characteristic, complemented
7#13068097C211yesmaximal, characteristic, complemented
8#13068092C211yesmaximal, 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
22#10622724—21no—
23#10622724—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—
34#10622301C2211yescharacteristic
35#10622301C2211yescharacteristic
36C4×#4313—21no—
37#10622298—21no—
38#10622292C2211yescharacteristic
39#10622292C2211yescharacteristic
40#10622184C2212yes—
41#10622184C2212yes—
42#10622182C2212yes—
43#10622182C2212yes—
44#10622096C2212yes—
45#10622095C2211yescharacteristic
46#10622095C2211yescharacteristic
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×#4313—21no—
67C2×#4313—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—
88#66879—21no—
89#66879—21no—
90Dic11⋊C8—21no—
91Dic11⋊C8—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#19160—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—42no—
115C2×D44C2×D411yescharacteristic
116C2×C4×D11—21no—
117C2×C4×D11—21no—
118C2×C4×D11—21no—
119C2×Dic22C2×D411yescharacteristic
120C11×D8—42no—
121C11×D8—42no—
122C2×C8×C11—22no—
123C2×C8×C11—41no—
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C22⋊C4—42no—
131C11×C22⋊C4—42no—
132C42×C11C2×D411yescharacteristic
133C42×C11C2×D411yescharacteristic
134C42×C11#4111yescharacteristic
135C42×C11C2411yescharacteristic
136C22⋊Dic11—21no—
137#4324—44no—
138#4323—44no—
139(C2×D11)⋊C4—21no—
140(C2×D11)⋊C4—21no—
141C4⋊Dic11C2×D411yescharacteristic
142C4⋊Dic11C2×D411yescharacteristic
143Dic11⋊C4—21no—
144Dic11⋊C4—21no—
145C4×Dic11—21no—
146C4×Dic11—21no—
147C4×Dic11—21no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152#4313—42no—
153#4313—42no—
154#3169D1111yescharacteristic, complemented
155#3106—112no—
156#2965—111no—
157#1698—112no—
158#1697—112no—
159#1696—111no—
160#1695—111no—
161#1688—111no—
162#1687—111no—
163#1564—111no—
164#1543—112no—
165C23×C11—42no—
166C23×C11#12111yescharacteristic
167C22×D11—21no—
168Q8×C11—82no—
169D4×C11—42no—
170D4×C11—42no—
171D4×C11—42no—
172D4×C11—42no—
173D4×C11—82no—
174D4×C11—84no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—42no—
180C2×C4×C11—84no—
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C22⋊D11—42no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191D44—22no—
192C4×D11—42no—
193C4×D11—41no—
194C4×D11—41no—
195C4×D11—42no—
196Dic22—22no—
197C8×C11—21no—
198C8×C11—21no—
199C8×C11—21no—
200C8×C11#13512yes—
201C11⋊C8—41no—
202C11⋊C8—41no—
203C11⋊C8—42no—
204C11⋊C8—42no—
205#532C2×D1112yes—
206C4×#41—111no—
207#500C2×D1111yescharacteristic
208#493C2×D1111yescharacteristic
209#486C2×D1112yes—
210#482—222no—
211#477—112no—
212#476—112no—
213#466—21no—
214#466—21no—
215#460—112no—
216#459—112no—
217#449—222no—
218#446—111no—
219#446—111no—
220C4×SD16—222no—
221C4×D8—21no—
222C4×D8—21no—
223C4×D8—222no—
224#436—111no—
225#436—111no—
226#435—221no—
227#435—221no—
228#431—111no—
229#431—112no—
230#431—221no—
231C4×M16—221no—
232C2×C4×C8C2×D1111yescharacteristic
233#335—112no—
234#334—111no—
235#334—111no—
236#333—112no—
237#333—112no—
238#331—112no—
239#331—112no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—82no—
244C22×C11—82no—
245C22×C11—82no—
246C22×C11C2×#12111yescharacteristic
247C2×D11—41no—
248C2×D11—41no—
249C2×D11—41no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—82no—
254C4×C11#47212yes—
255C4×C11C2×#13511yescharacteristic
256C4×C11#57512yes—
257C4×C11#57511yescharacteristic
258Dic11—41no—
259Dic11—41no—
260Dic11—41no—
261C2×#41—22no—
262C2×#41—111no—
263C2×SD16—222no—
264C2×D8—21no—
265C2×D8—21no—
266C2×D8—222no—
267C2×M16—221no—
268C2×M16—221no—
269C22×C8C22⋊D1111yescharacteristic
270C22×C8C22⋊D1111yescharacteristic
271C4⋊Q8C22×D1112yes—
272#127C22×D1112yes—
273#124—22no—
274#121—22no—
275#121—22no—
276C4×Q8—111no—
277C4×Q8—111no—
278C4×D4—22no—
279C4×D4—22no—
280C4×D4—111no—
281C4×D4—111no—
282C4×D4—221no—
283C4×D4—221no—
284#117—111no—
285#117—221no—
286C2×C42—221no—
287C2×C42C22×D1111yescharacteristic
288#107—21no—
289#107—21no—
290#107—222no—
291#106—222no—
292C4⋊C8—111no—
293C4⋊C8—111no—
294C4⋊C8—112no—
295C4⋊C8—112no—
296C4⋊C8—221no—
297C4⋊C8—221no—
298#103—222no—
299#102—22no—
300#102—22no—
301#102—222no—
302#102—222no—
303#102—222no—
304C22⋊C8—222no—
305C22⋊C8—221no—
306C22⋊C8—221no—
307C22⋊C8—221no—
308#97—221no—
309#97—221no—
310C4×C8—222no—
311C4×C8—221no—
312C4×C8C22⋊D1111yescharacteristic
313C4×C8C22⋊D1111yescharacteristic
314C4×C8C22×D1111yescharacteristic
315C4×C8C22×D1111yescharacteristic
316C2×C11—41no—
317C2×C11—162no—
318C2×C11#303511yescharacteristic
319C2×C11#305411yescharacteristic
320C2×C11C2×#47211yescharacteristic
321D11—81no—
322#41—84no—
323#41—442no—
324C2×Q8—22no—
325C2×Q8—111no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—42no—
330C2×D4—111no—
331C2×D4—221no—
332C22×C4—42no—
333C22×C4—221no—
334C22×C4—221no—
335C22×C4—221no—
336C22×C4D4×D1111yescharacteristic
337C22×C4#434111yescharacteristic
338C22×C4C2×C22⋊D1111yescharacteristic
339SD16—444no—
340D8—42no—
341D8—42no—
342D8—444no—
343M16—442no—
344M16—442no—
345C2×C8—22no—
346C2×C8—41no—
347C2×C8—222no—
348C2×C8—222no—
349C2×C8—221no—
350C2×C8—221no—
351C2×C8C2×C22⋊D1111yescharacteristic
352C2×C8C2×C22⋊D1111yescharacteristic
353C2×C8C2×C22⋊D1111yescharacteristic
354C2×C8C2×C22⋊D1111yescharacteristic
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—111no—
358C4⋊C4—111no—
359C4⋊C4—221no—
360C4⋊C4—221no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C22⋊C4—221no—
364C22⋊C4—221no—
365C22⋊C4—221no—
366C42—221no—
367C42—221no—
368C42—221no—
369C42D4×D1111yescharacteristic
370C42#434111yescharacteristic
371C42C2×C22⋊D1111yescharacteristic
372C42C23×D1111yescharacteristic
373C11#1916011yescharacteristic, complemented, Sylow
374C23—42no—
375C23—221no—
376C23#6699111yescharacteristic
377Q8—82no—
378Q8—222no—
379D4—42no—
380D4—42no—
381D4—42no—
382D4—42no—
383D4—82no—
384D4—84no—
385D4—222no—
386D4—442no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—42no—
392C2×C4—84no—
393C2×C4—221no—
394C2×C4—221no—
395C2×C4—221no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4#6699111yescharacteristic
401C2×C4#6699111yescharacteristic
402C2×C4#6699111yescharacteristic
403C2×C4C2×D4×D1111yescharacteristic
404C2×C4C2×#434111yescharacteristic
405C2×C4C22×C22⋊D1111yescharacteristic
406C8—21no—
407C8—21no—
408C8—21no—
409C8—442no—
410C8—442no—
411C8—441no—
412C8—441no—
413C8#6700312yes—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—82no—
418C22—82no—
419C22—82no—
420C22—441no—
421C22—441no—
422C22—441no—
423C22C2×#6699111yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—82no—
428C4—441no—
429C4—441no—
430C4—441no—
431C4#1062277312yes—
432C4#1062329912yes—
433C4C2×#6700311yescharacteristic
434C4#1062335311yescharacteristic
435C2—41no—
436C2—162no—
437C2—881no—
438C2#1307806511yescharacteristic
439C2#1307822111yescharacteristic
440C2C2×#1062277311yescharacteristic
subgroupG/H
centerC2×C4#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3169C2
socleC22×C11C2×#121
hypercenter#3169D11
hypocenterC11#19160
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. #13077582C2semidirect
3. #13068153C2semidirect
4. #13068146C2semidirect
5. #13068141C2semidirect
6. #13068136C2semidirect
7. #13068097C2semidirect
8. #13068092C2semidirect
9. #13067364C2semidirect
10. #13067278C2semidirect
11. C11×#3169C2semidirect
154. #3169D11semidirect
373. C11#19160semidirect

Maximal subgroups

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

subgroupindex
#130786702
#130775822
#130681532
#130681462
#130681412
#130681362
#130680972
#130680922
#130673642
#130672782
C11×#31692
#1916011