Finite Group Databasebeta

← #15617188

Subgroups — #15617188

Order 2816.

3250 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623281C212yesmaximal
2C4×#41×D11C211yesmaximal, characteristic
3#13077045C213yesmaximal, complemented
4#13077044C211yesmaximal, characteristic, complemented
5#13077041C213yesmaximal, complemented
6#13077038C216yesmaximal, complemented
7#131×Dic11C212yesmaximal, complemented
8#13077032C216yesmaximal, complemented
9C2×#10622320C213yesmaximal, complemented
10C4×M16×D11C213yesmaximal, complemented
11C11×#2875C211yesmaximal, characteristic, complemented
12C2×#41×D11C2211yescharacteristic
13C2×C11×#131C2212yes—
14C4×C11×#41C2211yescharacteristic
15#41×Dic11C2211yescharacteristic
16C2×#67001C2212yes—
17#10623281C4132yescomplemented
18C2×#66960C2216yes—
19C2×M16×D11C2216yes—
20C2×#66954C2216yes—
21C22×#4313C2216yes—
22C4×#4343C412yes—
23C4×Q8×D11C412yes—
24C4×D4×D11C416yes—
25C4×#4341C416yes—
26#10623053C2213yes—
27D11×#117C2213yes—
28C4×#4339C2213yes—
29C2×C42×D11C2213yes—
30C11×#405C2216yescomplemented
31C4×C11×M16C2213yescomplemented
32C2×C11×#97C2213yescomplemented
33#10622735C2216yescomplemented
34M16×Dic11C2216yescomplemented
35#10622714C2216yescomplemented
36C2×C8×Dic11C2216yescomplemented
37#10622610C2216yescomplemented
38C4×#4318C2213yescomplemented
39C2×#66867C2213yescomplemented
40#10622321C22112yescomplemented
41#10622320C2213yes—
42#10622320C2211yescharacteristic
43#10622320C2216yes—
44#10622320C2216yescomplemented
45#10622320C2213yescomplemented
46#10622320C2213yescomplemented
47D11×#97C2216yescomplemented
48#10622302C22112yescomplemented
49C4×#4313C2216yes—
50C4×C8×D11C2216yescomplemented
51C2×C11×#41C2311yescharacteristic
52#41×D11C2×C4116yes—
53C2×#4343C2×C411yescharacteristic
54C2×Q8×D11C2×C411yescharacteristic
55C2×#4341C2×C413yes—
56C2×D4×D11C2×C413yes—
57C2×#4339C2313yes—
58C22×C4×D11C2×C416yes—
59C22×C4×D11C2313yes—
60C11×#131C2×C4116yescomplemented
61C2×C11×M16C2316yes—
62C22×C8×C11C2316yes—
63C4×Q8×C11C2×C412yes—
64C4×D4×C11C2×C416yes—
65C11×#117C2313yes—
66C2×C42×C11C2313yes—
67#67001C2×C4116yescomplemented
68Q8×Dic11C2×C412yes—
69D4×Dic11C2×C416yes—
70C4×C22⋊D11C2×C4112yes—
71#66979C2313yes—
72C2×C4×Dic11C2×C416yes—
73C2×C4×Dic11C2313yes—
74C2×#4318C2316yes—
75C22×C11⋊C8C2316yes—
76#66960C2×C4148yescomplemented
77M16×D11C2×C4148yescomplemented
78#66954C2×C4148yescomplemented
79C2×#4313C2×C4148yescomplemented
80C2×#4313C2312yes—
81C2×#4313C2316yes—
82C2×#4313C2316yes—
83C2×#4313C2316yes—
84C2×C8×D11C23112yes—
85#66946C2×C416yes—
86#66945C2×C416yes—
87C4⋊C4×D11C2×C416yes—
88#66940C2×C416yes—
89(C22⋊D11)⋊C4C2×C4112yes—
90C22⋊C4×D11C2×C416yes—
91#66930C2×C416yes—
92C4×D44C2×C416yes—
93#66925C2316yes—
94C42×D11C2×C416yes—
95C42×D11C2×C416yes—
96C42×D11C2311yescharacteristic
97C42×D11C2313yes—
98C42×D11C2313yes—
99C42×D11C2313yes—
100C4×Dic22C2×C416yes—
101C11×#97C2313yes—
102C11×#97C2311yescharacteristic
103C11×#97C2316yes—
104C4×C8×C11C2316yes—
105#66879C23112yes—
106C8×Dic11C2316yes—
107C8×Dic11C2316yes—
108C8×Dic11C2312yes—
109C8×Dic11C2316yes—
110#66867C2311yescharacteristic
111#66867C2313yes—
112#66867C2316yes—
113C4×C11⋊C8C2316yes—
114C4×#568—111nomaximal, Sylow
115C23×D11C22×C413yes—
116C11×#41C22×C418yes—
117C2×Q8×C11C22×C411yescharacteristic
118C2×D4×C11C22×C413yes—
119C22×C4×C11C22×C416yes—
120C22×C4×C11C2413yes—
121C2×C22⋊D11C22×C416yes—
122C22×Dic11C22×C416yes—
123C22×Dic11C22×C413yes—
124#4343C4218yes—
125Q8×D11C4218yes—
126#4341C42124yes—
127D4×D11C42124yes—
128#4339C22×C4124yes—
129C2×D44C22×C413yes—
130C2×C4×D11—412no—
131C2×C4×D11C22×C4124yes—
132C2×C4×D11C22×C412yes—
133C2×C4×D11C22×C416yes—
134C2×C4×D11C22×C416yes—
135C2×C4×D11C22×C416yes—
136C2×C4×D11C22×C413yes—
137C2×C4×D11C22×C413yes—
138C2×C4×D11C2411yescharacteristic
139C2×C4×D11C2413yes—
140C2×Dic22C22×C413yes—
141C11×M16C22×C4124yescomplemented
142C2×C8×C11C22×C4124yescomplemented
143C2×C8×C11C2412yes—
144C2×C8×C11C2416yes—
145C11×C4⋊C4C22×C416yes—
146C11×C22⋊C4C22×C416yes—
147C42×C11C22×C416yes—
148C42×C11C2413yes—
149C42×C11C2411yescharacteristic
150C22⋊Dic11C22×C416yes—
151(C2×D11)⋊C4C22×C4112yes—
152C4⋊Dic11C22×C416yes—
153Dic11⋊C4C22×C4112yes—
154C4×Dic11C22×C416yes—
155C4×Dic11C22×C412yes—
156C4×Dic11C22×C416yes—
157C4×Dic11C22×C416yes—
158C4×Dic11C22×C416yes—
159C4×Dic11C2411yescharacteristic
160C4×Dic11C2413yes—
161#4318C22×C4124yescomplemented
162C2×C11⋊C8C22×C4124yescomplemented
163C2×C11⋊C8C2416yes—
164C2×C11⋊C8C2412yes—
165#4313C22×C418yes—
166#4313C22×C4124yes—
167#4313C22×C4124yescomplemented
168#4313C22×C4124yescomplemented
169C8×D11C22×C4148yescomplemented
170C2×#568—112no—
171C2×C4×#41—111no—
172#2875—113no—
173#2875—113no—
174#2875—111no—
175#2875D1111yescharacteristic, complemented
176C4×#131—116no—
177C4×#131—112no—
178#2873—116no—
179C2×C4×M16—113no—
180C2×C4×M16—113no—
181C23×C11C23×C413yes—
182C22×D11—46no—
183C22×D11C2×C42112yes—
184C22×D11C23×C413yes—
185C22×D11C23×C411yescharacteristic
186Q8×C11C2×C4214yes—
187D4×C11C2×C42112yes—
188C2×C4×C11—46no—
189C2×C4×C11C23×C412yes—
190C2×C4×C11C23×C416yes—
191C2×C4×C11C23×C4112yes—
192C2×C4×C11C23×C413yes—
193C2×C4×C11C2511yescharacteristic
194C22⋊D11C2×C42124yes—
195C2×Dic11—212no—
196C2×Dic11C2×C42112yes—
197C2×Dic11C23×C416yes—
198C2×Dic11C23×C412yes—
199C2×Dic11C23×C411yescharacteristic
200C2×Dic11C23×C413yes—
201D44C2×C42112yes—
202C4×D11—24no—
203C4×D11—212no—
204C4×D11—46no—
205C4×D11—46no—
206C4×D11C2×C42112yes—
207C4×D11C2×C42112yes—
208C4×D11C23×C4112yes—
209C4×D11C23×C414yes—
210Dic22C2×C42112yes—
211C8×C11C23×C4112yes—
212C8×C11C23×C414yes—
213C11⋊C8C23×C4112yes—
214C11⋊C8C23×C414yes—
215C22×#41—111no—
216#568—1132no—
217C2×#131—112no—
218C2×#131—116no—
219C2×#131—116no—
220C2×#131C2×D1112yes—
221C22×M16—116no—
222C22×M16—116no—
223C4×#41—111no—
224C4×#41—112no—
225C4×#41—116no—
226C4×#41—113no—
227C4×#41—113no—
228C4×#41C2×D1111yescharacteristic
229C2×C4×Q8—112no—
230C2×C4×D4—116no—
231C2×#117—113no—
232C22×C42—113no—
233#405—116no—
234#405—116no—
235#405—116no—
236#405—1112no—
237#405—1112no—
238#405C2×D1116yescomplemented
239C4×M16—116no—
240C4×M16—113no—
241C4×M16—113no—
242C4×M16—111no—
243C4×M16—116no—
244C4×M16—116no—
245C4×M16—113no—
246C4×M16—113no—
247C4×M16—116no—
248C4×M16C2×D1113yescomplemented
249C2×#97—113no—
250C2×#97—116no—
251C2×#97C2×D1113yescomplemented
252C2×C4×C8—116no—
253C2×C4×C8—116no—
254C22×C11—26no—
255C22×C11C22×C4216yes—
256C22×C11C24×C411yescharacteristic
257C2×D11—22no—
258C2×D11—26no—
259C2×D11—412no—
260C2×D11C22×C4212yes—
261C2×D11C22×C4216yes—
262C4×C11—22no—
263C4×C11—26no—
264C4×C11C22×C4216yes—
265C4×C11C24×C412yes—
266Dic11—26no—
267Dic11C22×C4216yes—
268Dic11C22×C4212yes—
269Dic11#56814yescomplemented
270C2×#41—1116no—
271C2×#41—111no—
272C2×#41—113no—
273C2×#41—113no—
274C2×#41C22×D1111yescharacteristic
275C22×Q8—111no—
276C22×D4—113no—
277C23×C4—113no—
278C23×C4—116no—
279#131—1116no—
280#131—1148no—
281#131—1148no—
282#131C4×D11116yescomplemented
283C2×M16—116no—
284C2×M16—1148no—
285C2×M16—1148no—
286C2×M16—112no—
287C2×M16—116no—
288C2×M16—116no—
289C2×M16—116no—
290C2×M16C22×D1116yes—
291C22×C8—116no—
292C22×C8—1112no—
293C22×C8C22×D1116yes—
294C4×Q8—112no—
295C4×Q8—116no—
296C4×Q8—116no—
297C4×Q8C4×D1112yes—
298C4×D4—116no—
299C4×D4—1112no—
300C4×D4—116no—
301C4×D4—1112no—
302C4×D4—116no—
303C4×D4C4×D1116yes—
304#117—113no—
305#117—116no—
306#117—116no—
307#117—116no—
308#117C22×D1113yes—
309C2×C4⋊C4—116no—
310C2×C22⋊C4—116no—
311C2×C42—116no—
312C2×C42—113no—
313C2×C42—116no—
314C2×C42—116no—
315C2×C42—113no—
316C2×C42—113no—
317C2×C42—113no—
318C2×C42—111no—
319C2×C42C22×D1113yes—
320#97—1112no—
321#97—111no—
322#97—113no—
323#97—116no—
324#97C22×D1113yes—
325#97C22×D1111yescharacteristic
326#97C22×D1116yes—
327C4×C8—112no—
328C4×C8—116no—
329C4×C8—116no—
330C4×C8—116no—
331C4×C8—116no—
332C4×C8C22×D1116yes—
333C2×C11—26no—
334C2×C11C23×C4211yescharacteristic
335C2×C11C2×#56812yes—
336D11—22no—
337D11—26no—
338C24—113no—
339#41—118no—
340#41—1124no—
341#41—1124no—
342#41C2×C4×D1118yes—
343C2×Q8—118no—
344C2×Q8—113no—
345C2×Q8C2×C4×D1111yescharacteristic
346C2×D4—116no—
347C2×D4—1124no—
348C2×D4—113no—
349C2×D4C2×C4×D1113yes—
350C22×C4—113no—
351C22×C4—113no—
352C22×C4—113no—
353C22×C4—1124no—
354C22×C4—111no—
355C22×C4—113no—
356C22×C4—116no—
357C22×C4—112no—
358C22×C4—116no—
359C22×C4—116no—
360C22×C4—116no—
361C22×C4—4412no—
362C22×C4C2×C4×D1116yes—
363C22×C4C23×D1113yes—
364M16—1124no—
365M16—1124no—
366M16—118no—
367M16—1124no—
368M16—1124no—
369M16C2×C4×D11124yescomplemented
370C2×C8—1124no—
371C2×C8—112no—
372C2×C8—116no—
373C2×C8—1148no—
374C2×C8C2×C4×D11124yescomplemented
375C2×C8C23×D1112yes—
376C2×C8C23×D1116yes—
377C4⋊C4—1112no—
378C4⋊C4—116no—
379C4⋊C4C2×C4×D1116yes—
380C22⋊C4—116no—
381C22⋊C4—1112no—
382C22⋊C4C2×C4×D1116yes—
383C42—112no—
384C42—116no—
385C42—116no—
386C42—116no—
387C42—116no—
388C42—111no—
389C42—113no—
390C42C2×C4×D1116yes—
391C42C23×D1113yes—
392C42C23×D1111yescharacteristic
393C11C4×#56811yescharacteristic, complemented, Sylow
394C23—113no—
395C23—111no—
396C23—1112no—
397C23—446no—
398C23C22×C4×D1113yes—
399Q8—1112no—
400Q8C42×D1114yes—
401D4—1124no—
402D4—1112no—
403D4C42×D11112yes—
404C2×C4—46no—
405C2×C4—1112no—
406C2×C4—111no—
407C2×C4—112no—
408C2×C4—113no—
409C2×C4—1112no—
410C2×C4—1112no—
411C2×C4—1112no—
412C2×C4—114no—
413C2×C4—116no—
414C2×C4—224no—
415C2×C4—2212no—
416C2×C4—2212no—
417C2×C4—446no—
418C2×C4—446no—
419C2×C4C22×C4×D1112yes—
420C2×C4C22×C4×D1116yes—
421C2×C4C22×C4×D1113yes—
422C2×C4C22×C4×D11112yes—
423C2×C4C24×D1111yescharacteristic
424C8—114no—
425C8—1112no—
426C8C22×C4×D11112yes—
427C8C22×C4×D1114yes—
428C22—26no—
429C22—112no—
430C22—116no—
431C22—222no—
432C22—226no—
433C22—4412no—
434C22C2×C42×D1116yes—
435C22C23×C4×D1111yescharacteristic
436C4—22no—
437C4—26no—
438C4—112no—
439C4—116no—
440C4—114no—
441C4—226no—
442C4C2×C42×D1116yes—
443C4C23×C4×D1112yes—
444C2—26no—
445C2—222no—
446C2—226no—
447C2C22×C42×D1111yescharacteristic
448C2D11×#56812yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutatorC2×C11C23×C42
FittingC11×#2875C2
socleC22×C11C24×C4
prime radicalC2×#41×D11C22
cosocleC2×C4×C11C25
hypercenter#2875D11
hypocenterC11C4×#568
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2875

Complements

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

NH ≅ G/Ntype
3. #13077045C2semidirect
4. #13077044C2semidirect
5. #13077041C2semidirect
6. #13077038C2semidirect
7. #131×Dic11C2semidirect
8. #13077032C2semidirect
9. C2×#10622320C2semidirect
10. C4×M16×D11C2semidirect
11. C11×#2875C2semidirect
17. #10623281C4semidirect
30. C11×#405C22semidirect
31. C4×C11×M16C22semidirect
32. C2×C11×#97C22semidirect
33. #10622735C22semidirect
34. M16×Dic11C22semidirect
35. #10622714C22semidirect
36. C2×C8×Dic11C22semidirect
37. #10622610C22semidirect
38. C4×#4318C22semidirect
39. C2×#66867C22semidirect
40. #10622321C22semidirect
44. #10622320C22semidirect
45. #10622320C22semidirect
46. #10622320C22semidirect
47. D11×#97C22semidirect
48. #10622302C22semidirect
50. C4×C8×D11C22semidirect
60. C11×#131C2×C4semidirect
67. #67001C2×C4semidirect
76. #66960C2×C4semidirect
77. M16×D11C2×C4semidirect
78. #66954C2×C4semidirect
79. C2×#4313C2×C4semidirect
141. C11×M16C22×C4semidirect
142. C2×C8×C11C22×C4semidirect
161. #4318C22×C4semidirect
162. C2×C11⋊C8C22×C4semidirect
167. #4313C22×C4semidirect
168. #4313C22×C4semidirect
169. C8×D11C22×C4semidirect
175. #2875D11semidirect
238. #405C2×D11semidirect
248. C4×M16C2×D11semidirect
251. C2×#97C2×D11semidirect
269. Dic11#568semidirect
282. #131C4×D11semidirect
369. M16C2×C4×D11semidirect
374. C2×C8C2×C4×D11semidirect
393. C11C4×#568semidirect

Maximal subgroups

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

subgroupindex
C2×#106232812
C4×#41×D112
#130770452
#130770442
#130770412
#130770382
#131×Dic112
#130770322
C2×#106223202
C4×M16×D112
C11×#28752
C4×#56811