Finite Group Databasebeta

← #14763279

Subgroups — #14763279

Order 2816.

1030 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic
2C2×#10622331C211yesmaximal, characteristic
3#13071011C211yesmaximal, characteristic
4#13069579C212yesmaximal, complemented
5#13069579C212yesmaximal, complemented
6#13069566C212yesmaximal, complemented
7#13069562C212yesmaximal, complemented
8#13068712C211yesmaximal, characteristic
9#13068711C211yesmaximal, characteristic
10#13068708C211yesmaximal, characteristic
11C11×#1825C211yesmaximal, characteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15#10623048—24no—
16#10623048C418yescomplemented
17C2×#66943C2211yescharacteristic
18C2×#66943C2211yescharacteristic
19C2×#66941C2211yescharacteristic
20C2×#66941C2211yescharacteristic
21C2×#66931—21no—
22C2×#66931—21no—
23C2×C4×Dic22—21no—
24C2×C4×Dic22—21no—
25C2×C11×C22⋊C8C2211yescharacteristic
26C11×#380C2211yescharacteristic
27#10622825C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×Dic11⋊C8C2212yes—
30C2×C8×Dic11C2212yes—
31#10622590C2212yes—
32C4⋊C4×Dic11C2212yes—
33#10622556—21no—
34C22⋊C4×Dic11—21no—
35#10622331—24no—
36#10622264—21no—
37#10622261—21no—
38C11×#340C2212yes—
39C11×#340C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11D411yescharacteristic
48C23×Dic11D411yescharacteristic
49C22×Dic22—21no—
50C22×Dic22—21no—
51C22×C8×C11C2312yes—
52C11×#117—22no—
53C11×#117C2×C414yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—21no—
59C2×C42×C11—21no—
60C2×C22⋊Dic11—21no—
61C2×C22⋊Dic11—21no—
62#66979—22no—
63#66979C2×C414yes—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—21no—
70C2×Dic11⋊C4—21no—
71C2×Dic11⋊C4—21no—
72C2×Dic11⋊C4—21no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11C2×C414yes—
76C2×C4×Dic11D411yescharacteristic
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11D414yes—
79C2×C4×Dic11C2311yescharacteristic
80C2×C4×Dic11C2311yescharacteristic
81C22×C11⋊C8C2312yes—
82#66943—22no—
83#66943—22no—
84#66943C2×C414yes—
85#66943C2×C414yes—
86#66941—22no—
87#66941—22no—
88#66941C2×C414yes—
89#66941C2×C414yes—
90#66931—28no—
91#66931—28no—
92C4×Dic22—28no—
93C4×Dic22—28no—
94C11×C22⋊C8—22no—
95C11×#95—21no—
96C11⋊#95—21no—
97C11⋊#95—22no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100C22⋊(C11⋊C8)—22no—
101Dic11⋊C8—24no—
102C8×Dic11—24no—
103#21837—111nomaximal, Sylow
104C24×C11C2×D411yescharacteristic
105C22×C4×C11—24no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11C22×C412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—24no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—22no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11C22⋊C414yes—
120C22×Dic11C22⋊C414yes—
121C22×Dic11C2×D411yescharacteristic
122C22×Dic11C2×D411yescharacteristic
123C22×Dic11C2×D411yescharacteristic
124C22×Dic11C2×D411yescharacteristic
125C2×Dic22—24no—
126C2×Dic22—24no—
127C2×Dic22—42no—
128C2×Dic22—42no—
129C2×Dic22—44no—
130C2×C8×C11—22no—
131C2×C8×C11—24no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4C22×C412yes—
136C11×C4⋊C4C22×C412yes—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—42no—
139C42×C11—24no—
140C22⋊Dic11—24no—
141C22⋊Dic11—42no—
142C4⋊Dic11—24no—
143C4⋊Dic11—24no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—24no—
147C4⋊Dic11C22×C412yes—
148C4⋊Dic11C22×C412yes—
149Dic11⋊C4—24no—
150Dic11⋊C4—24no—
151Dic11⋊C4—24no—
152Dic11⋊C4—24no—
153C4×Dic11—24no—
154C4×Dic11—44no—
155C4×Dic11C22⋊C414yes—
156C4×Dic11C22⋊C414yes—
157C4×Dic11C22×C412yes—
158C4×Dic11C22×C412yes—
159C4×Dic11C2×D412yes—
160C4×Dic11C2×D412yes—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—24no—
163C2×#533—111no—
164C2×#431—111no—
165#2283—111no—
166#1991—112no—
167#1991—112no—
168#1988—112no—
169#1987—112no—
170#1825—111no—
171#1825—111no—
172#1825—111no—
173#1825D1111yescharacteristic
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—21no—
177C23×C11—21no—
178C23×C11C2×C22⋊C412yes—
179C23×C11C22×D411yescharacteristic
180C2×C4×C11—22no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11C2×C22⋊C412yes—
192C2×C4×C11C23×C411yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C112−1+414yes—
195C2×Dic11—22no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—28no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—44no—
204C2×Dic11—42no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11C2×C22⋊C412yes—
211C2×Dic11C2×C22⋊C412yes—
212C2×Dic11C2×C22⋊C412yes—
213C2×Dic11C2×C22⋊C412yes—
214C2×Dic11#13514yes—
215Dic22—48no—
216Dic22—48no—
217C8×C11—42no—
218C11⋊C8—42no—
219#533—118no—
220#533—224no—
221C2×C4⋊Q8—111no—
222C2×C4⋊Q8—111no—
223C2×#125—111no—
224C2×#125—111no—
225C2×C22⋊Q8—221no—
226C2×C22⋊Q8—221no—
227C2×C4×Q8—221no—
228C2×C4×Q8—221no—
229C2×#117—111no—
230C2×#117C2×D1111yescharacteristic
231C22×C42—111no—
232#431—224no—
233C2×C4⋊C8—112no—
234C2×C22⋊C8—111no—
235C2×C22⋊C8C2×D1111yescharacteristic
236C2×C4×C8—112no—
237#383—221no—
238#382—112no—
239#381—221no—
240#380—111no—
241#380C2×D1111yescharacteristic
242C4×C4⋊C4—112no—
243C4×C22⋊C4—221no—
244#376—221no—
245#340—112no—
246#340—112no—
247#340—112no—
248#340—112no—
249#340—112no—
250#340—112no—
251#340C2×D1112yes—
252#340C2×D1112yes—
253C22×C11—22no—
254C22×C11—22no—
255C22×C11—22no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11C22×C22⋊C411yescharacteristic
259C22×C11#53612yes—
260C22×C11C2×#13512yes—
261C22×C11#57511yescharacteristic
262C22×C11#57511yescharacteristic
263C4×C11—22no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—82no—
267C4×C11#51912yes—
268C4×C11#53612yes—
269Dic11—22no—
270Dic11—22no—
271Dic11—22no—
272Dic11—42no—
273Dic11—42no—
274Dic11—82no—
275Dic11#41614yes—
276C22×Q8—221no—
277C22×Q8—221no—
278C23×C4—111no—
279C23×C4—111no—
280C23×C4C22×D1111yescharacteristic
281C22×C8—112no—
282C22×C8C22×D1112yes—
283C4⋊Q8—114no—
284C4⋊Q8—114no—
285C4⋊Q8—222no—
286C4⋊Q8—222no—
287#125—114no—
288#125—114no—
289#125—222no—
290#125—222no—
291C22⋊Q8—228no—
292C22⋊Q8—228no—
293C4×Q8—228no—
294C4×Q8—228no—
295#117—22no—
296#117—114no—
297#117—222no—
298#117C4×D1114yes—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4C22×D1112yes—
309C2×C4⋊C4C22×D1111yescharacteristic
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—221no—
314C2×C22⋊C4—221no—
315C2×C42—21no—
316C2×C42—114no—
317C2×C42—111no—
318C2×C42—111no—
319C2×C42—114no—
320C2×C42—111no—
321C2×C42—111no—
322C2×C42—221no—
323C2×C42—222no—
324C4⋊C8—224no—
325C22⋊C8—22no—
326C22⋊C8—222no—
327C4×C8—224no—
328#95—21no—
329#95—222no—
330#95—222no—
331#95—222no—
332#95—221no—
333C2×C11—42no—
334C2×C11#231011yescharacteristic
335C2×C11C2×#41611yescharacteristic
336C2×C11#289611yescharacteristic
337C2×C11#323312yes—
338C2×C11#323312yes—
339C24D4×D1111yescharacteristic
340C2×Q8—224no—
341C2×Q8—224no—
342C2×Q8—444no—
343C2×Q8—442no—
344C2×Q8—442no—
345C22×C4—24no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—111no—
350C22×C4—114no—
351C22×C4—111no—
352C22×C4—111no—
353C22×C4—111no—
354C22×C4—114no—
355C22×C4—224no—
356C22×C4—221no—
357C22×C4—221no—
358C22×C4—222no—
359C22×C4—441no—
360C22×C4—441no—
361C22×C4C2×C4×D1112yes—
362C22×C4D4×D1111yescharacteristic
363C22×C4D4×D1112yes—
364C22×C4C23×D1111yescharacteristic
365C2×C8—22no—
366C2×C8—24no—
367C2×C8—222no—
368C2×C8—224no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—24no—
372C4⋊C4—112no—
373C4⋊C4—112no—
374C4⋊C4—224no—
375C4⋊C4—224no—
376C4⋊C4—224no—
377C4⋊C4—224no—
378C4⋊C4—224no—
379C4⋊C4—224no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—224no—
383C4⋊C4C2×C4×D1112yes—
384C4⋊C4C2×C4×D1112yes—
385C22⋊C4—24no—
386C22⋊C4—42no—
387C22⋊C4—224no—
388C22⋊C4—442no—
389C42—24no—
390C42—114no—
391C42—114no—
392C42—112no—
393C42—112no—
394C42—112no—
395C42—112no—
396C42—224no—
397C42—444no—
398C11#2183711yescharacteristic, complemented, Sylow
399C23—22no—
400C23—21no—
401C23—21no—
402C23—22no—
403C23C22⋊C4×D1112yes—
404C23C2×D4×D1111yescharacteristic
405Q8—448no—
406Q8—448no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—112no—
419C2×C4—114no—
420C2×C4—112no—
421C2×C4—112no—
422C2×C4—112no—
423C2×C4—228no—
424C2×C4—222no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—221no—
428C2×C4—221no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—444no—
432C2×C4—442no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4C22⋊C4×D1112yes—
439C2×C4C22×C4×D1111yescharacteristic
440C2×C4C2×D4×D1111yescharacteristic
441C2×C4#6704314yes—
442C8—42no—
443C8—442no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—42no—
448C22—42no—
449C22C2×C22⋊C4×D1111yescharacteristic
450C22#1062317912yes—
451C22D11×#13512yes—
452C22#1062330411yescharacteristic
453C22#1062330811yescharacteristic
454C4—22no—
455C4—42no—
456C4—42no—
457C4—82no—
458C4—114no—
459C4—222no—
460C4—222no—
461C4—222no—
462C4—442no—
463C4—442no—
464C4—882no—
465C4#1062304712yes—
466C4#1062317912yes—
467C2—42no—
468C2#1307120111yescharacteristic
469C2D11×#41611yescharacteristic
470C2#1307713211yescharacteristic
471C2#1307979212yes—
472C2#1307979812yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1825C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1825D11
hypocenterC11#21837
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
4. #13069579C2semidirect
5. #13069579C2semidirect
6. #13069566C2semidirect
7. #13069562C2semidirect
16. #10623048C4semidirect
398. C11#21837semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×#106223312
#130710112
#130695792
#130695662
#130695622
#130687122
#130687112
#130687082
C11×#18252
#2183711