Finite Group Databasebeta

← #14763728

Subgroups — #14763728

Order 2816.

1130 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
1C2×#10623259C211yesmaximal, characteristic
2C2×#10622450C211yesmaximal, characteristic
3#13071020C211yesmaximal, characteristic
4#13069569C211yesmaximal, characteristic, complemented
5#13069539C211yesmaximal, characteristic, complemented
6#13069538C211yesmaximal, characteristic, complemented
7#13069048C214yesmaximal
8#13068620C214yesmaximal, complemented
9C11×#1988C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999—21no—
12C2×Q8×Dic11—21no—
13C22×#4313C2212yes—
14#10623259—24no—
15#10623259C418yescomplemented
16C2×#66950C2212yes—
17C2×#66945—21no—
18C2×#66943—21no—
19C2×#66940C2212yes—
20C2×#66925—21no—
21C2×C42×D11C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66880C2214yes—
26C2×Dic11⋊C8C2212yes—
27#10622600C2212yes—
28#10622589C2212yes—
29C2×#66874C2214yes—
30C4×C4⋊Dic11C2211yescharacteristic
31C4×Dic11⋊C4—21no—
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33#10622450—24no—
34#10622280—21no—
35#10622263—21no—
36C11×#340C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C22×C4×D11D411yescharacteristic
40C22×C4×D11D411yescharacteristic
41C22×C4×D11C2311yescharacteristic
42C22×Dic22C2312yes—
43C22×C8×C11C2312yes—
44C11×C4⋊Q8—22no—
45C11×C4⋊Q8C2×C414yes—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51#66999—28no—
52Q8×Dic11—28no—
53C2×(C2×D11)⋊C4—22no—
54C2×(C2×D11)⋊C4—22no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11C2312yes—
59C2×Dic11⋊C4—22no—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11—21no—
64C2×C4×Dic11D411yescharacteristic
65C2×C4×Dic11D411yescharacteristic
66C2×C4×Dic11C2311yescharacteristic
67C22×C11⋊C8C2312yes—
68C2×#4313—24no—
69C2×#4313—44no—
70#66950—24no—
71#66950C2×C418yes—
72#66945—28no—
73#66943—28no—
74#66940—24no—
75#66940C2×C418yes—
76#66925—44no—
77C42×D11C2×C414yes—
78C42×D11D414yes—
79#66922—22no—
80#66922C2×C414yes—
81C11×C4⋊C8—22no—
82C11×#95—21no—
83C11⋊#95—21no—
84C11⋊#95—22no—
85#66880—44no—
86Dic11⋊C8—24no—
87#66874—44no—
88C4⋊(C11⋊C8)—22no—
89#21894—111nomaximal, Sylow
90C23×D11C2×D411yescharacteristic
91C2×Q8×C11—24no—
92C2×Q8×C11—42no—
93C2×Q8×C11—42no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2411yescharacteristic
99C22×Dic11—22no—
100C22×Dic11—22no—
101C22×Dic11C2×D411yescharacteristic
102C22×Dic11C2×D411yescharacteristic
103C22×Dic11C2×D411yescharacteristic
104C2×C4×D11—24no—
105C2×C4×D11—22no—
106C2×C4×D11—22no—
107C2×C4×D11—22no—
108C2×C4×D11—22no—
109C2×C4×D11C22⋊C414yes—
110C2×C4×D11C22⋊C414yes—
111C2×C4×D11C22×C412yes—
112C2×C4×D11C2×D412yes—
113C2×Dic22—22no—
114C2×Dic22—24no—
115C2×Dic22—24no—
116C2×Dic22C22×C414yes—
117C2×C8×C11—22no—
118C2×C8×C11—24no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4C22×C414yes—
124C42×C11—42no—
125C42×C11C22×C412yes—
126C42×C11C2×D412yes—
127(C2×D11)⋊C4—28no—
128(C2×D11)⋊C4—44no—
129C4⋊Dic11—28no—
130C4⋊Dic11—24no—
131C4⋊Dic11—24no—
132C4⋊Dic11—22no—
133C4⋊Dic11—22no—
134Dic11⋊C4—28no—
135Dic11⋊C4—44no—
136Dic11⋊C4—44no—
137C4×Dic11—28no—
138C4×Dic11—42no—
139C4×Dic11C22⋊C414yes—
140C4×Dic11C22⋊C414yes—
141C4×Dic11C22×C412yes—
142C4×Dic11C2×D412yes—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—24no—
145#4313—48no—
146C2×#533—111no—
147C2×#423—111no—
148#2285—111no—
149#1988—111no—
150#1988D1111yescharacteristic, complemented
151#1981—111no—
152#1981—111no—
153#1894—114no—
154#1803—114no—
155C23×C11C22×D411yescharacteristic
156C22×D11—22no—
157C22×D11—21no—
158C22×D11—21no—
159C22×D11—22no—
160C22×D11C2×C22⋊C412yes—
161Q8×C11—48no—
162C2×C4×C11—22no—
163C2×C4×C11—24no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11C2×C22⋊C412yes—
170C2×C4×C11C2×C22⋊C412yes—
171C2×C4×C11AGL(1,ℤ/8)12yes—
172C2×C4×C11#13712yes—
173C2×C4×C11C23×C411yescharacteristic
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11H(5,𝔽2)12yes—
176C2×C4×C112−1+412yes—
177C2×Dic11—22no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—24no—
181C2×Dic11—44no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11C2×C22⋊C412yes—
186C2×Dic11C2×C22⋊C412yes—
187C2×Dic11C2×C22⋊C412yes—
188C2×Dic11#13714yes—
189C4×D11—24no—
190C4×D11—22no—
191C4×D11—22no—
192C4×D11—28no—
193C4×D11—28no—
194Dic22—28no—
195Dic22—42no—
196Dic22—42no—
197C8×C11—42no—
198C11⋊C8—42no—
199C22×M16—112no—
200#533—118no—
201#533—224no—
202C2×C4⋊Q8—111no—
203C2×C4⋊Q8C2×D1111yescharacteristic
204C2×#125—221no—
205C2×C22⋊Q8—112no—
206C2×C22⋊Q8—221no—
207C2×C4×Q8—112no—
208C2×C4×Q8—221no—
209C2×#117—221no—
210C2×#117—221no—
211C22×C42—111no—
212#423—224no—
213C2×C4⋊C8—112no—
214C2×C4⋊C8—111no—
215C2×C4⋊C8C2×D1111yescharacteristic
216C2×#103—114no—
217C2×#103—114no—
218#384—112no—
219#382—221no—
220#380—112no—
221#380—221no—
222C4×C4⋊C4—111no—
223C4×C4⋊C4—221no—
224C4×C4⋊C4C2×D1111yescharacteristic
225#340—114no—
226#340C2×D1114yes—
227C22×C11C22×C22⋊C411yescharacteristic
228C22×C11#53712yes—
229C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
230C22×C11C2×#13711yescharacteristic
231C22×C11C2×#13712yes—
232C2×D11—22no—
233C2×D11—22no—
234C2×D11—22no—
235C2×D11—42no—
236C2×D11—42no—
237C4×C11—22no—
238C4×C11—44no—
239C4×C11—82no—
240C4×C11#41714yes—
241C4×C11#52012yes—
242C4×C11#53511yescharacteristic
243C4×C11#53611yescharacteristic
244Dic11—22no—
245Dic11—22no—
246Dic11—44no—
247Dic11—82no—
248Dic11#41914yes—
249C22×Q8—21no—
250C22×Q8—112no—
251C23×C4—111no—
252C23×C4—111no—
253C23×C4—111no—
254C2×M16—224no—
255C2×M16—444no—
256C22×C8—112no—
257C22×C8C22×D1112yes—
258C4⋊Q8—22no—
259C4⋊Q8—114no—
260C4⋊Q8—222no—
261C4⋊Q8C4×D1114yes—
262#125—228no—
263C22⋊Q8—118no—
264C22⋊Q8—224no—
265C22⋊Q8—228no—
266C4×Q8—118no—
267C4×Q8—224no—
268C4×Q8—228no—
269#117—228no—
270#117—444no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—112no—
273C2×C4⋊C4—222no—
274C2×C4⋊C4—222no—
275C2×C4⋊C4—221no—
276C2×C4⋊C4—221no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4—222no—
279C2×C4⋊C4C22×D1112yes—
280C2×C4⋊C4C22×D1112yes—
281C2×C22⋊C4—222no—
282C2×C22⋊C4—222no—
283C2×C42—21no—
284C2×C42—111no—
285C2×C42—111no—
286C2×C42—111no—
287C2×C42—114no—
288C2×C42—114no—
289C2×C42—222no—
290C2×C42—221no—
291C2×C42C22×D1111yescharacteristic
292C4⋊C8—22no—
293C4⋊C8—224no—
294C4⋊C8—222no—
295#103—444no—
296#103—444no—
297#95—21no—
298#95—222no—
299#95—221no—
300C2×C11#231111yescharacteristic
301C2×C11C2×#41911yescharacteristic
302C2×C11C2×#41711yescharacteristic
303C2×C11#325412yes—
304C2×C11#325512yes—
305D11—42no—
306C24—111no—
307C2×Q8—24no—
308C2×Q8—42no—
309C2×Q8—42no—
310C2×Q8—114no—
311C2×Q8—222no—
312C2×Q8—224no—
313C2×Q8—224no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—111no—
317C22×C4—111no—
318C22×C4—111no—
319C22×C4—114no—
320C22×C4—114no—
321C22×C4—112no—
322C22×C4—112no—
323C22×C4—224no—
324C22×C4—222no—
325C22×C4—222no—
326C22×C4—222no—
327C22×C4—222no—
328C22×C4—222no—
329C22×C4—222no—
330C22×C4D4×D1111yescharacteristic
331C22×C4D4×D1111yescharacteristic
332C22×C4C23×D1111yescharacteristic
333M16—448no—
334C2×C8—22no—
335C2×C8—24no—
336C2×C8—222no—
337C2×C8—224no—
338C4⋊C4—24no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—228no—
343C4⋊C4—228no—
344C4⋊C4—224no—
345C4⋊C4—224no—
346C4⋊C4—222no—
347C4⋊C4—222no—
348C4⋊C4—444no—
349C4⋊C4—444no—
350C4⋊C4C2×C4×D1114yes—
351C22⋊C4—228no—
352C22⋊C4—444no—
353C42—42no—
354C42—114no—
355C42—114no—
356C42—112no—
357C42—112no—
358C42—228no—
359C42—442no—
360C42C2×C4×D1112yes—
361C42D4×D1112yes—
362C11#2189411yescharacteristic, complemented, Sylow
363C23—112no—
364C23—221no—
365C23—221no—
366C23—222no—
367C23—222no—
368C23C2×D4×D1111yescharacteristic
369Q8—48no—
370Q8—228no—
371Q8—442no—
372Q8—442no—
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—112no—
381C2×C4—114no—
382C2×C4—112no—
383C2×C4—112no—
384C2×C4—228no—
385C2×C4—221no—
386C2×C4—221no—
387C2×C4—222no—
388C2×C4—222no—
389C2×C4—224no—
390C2×C4—228no—
391C2×C4—222no—
392C2×C4—224no—
393C2×C4—444no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4C22⋊C4×D1112yes—
398C2×C4C22⋊C4×D1112yes—
399C2×C4#6696412yes—
400C2×C4#6696812yes—
401C2×C4C22×C4×D1111yescharacteristic
402C2×C4C2×D4×D1111yescharacteristic
403C2×C4#6704012yes—
404C2×C4#6704212yes—
405C8—42no—
406C8—442no—
407C22—222no—
408C22—222no—
409C22—222no—
410C22—442no—
411C22—442no—
412C22C2×C22⋊C4×D1111yescharacteristic
413C22#1062316012yes—
414C22C2×#6696411yescharacteristic
415C22C2×#6696811yescharacteristic
416C22D11×#13712yes—
417C4—22no—
418C4—44no—
419C4—82no—
420C4—114no—
421C4—222no—
422C4—222no—
423C4—444no—
424C4—882no—
425C4#1062238414yes—
426C4#1062310512yes—
427C4#1062320511yescharacteristic
428C4#1062325511yescharacteristic
429C2—442no—
430C2#1307120711yescharacteristic
431C2D11×#41911yescharacteristic
432C2C2×#1062238411yescharacteristic
433C2#1308000512yes—
434C2#1308000912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1988C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1988D11
hypocenterC11#21894
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
4. #13069569C2semidirect
5. #13069539C2semidirect
6. #13069538C2semidirect
8. #13068620C2semidirect
9. C11×#1988C2semidirect
15. #10623259C4semidirect
150. #1988D11semidirect
362. C11#21894semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106224502
#130710202
#130695692
#130695392
#130695382
#130690482
#130686202
C11×#19882
#2189411