Finite Group Databasebeta

← #14753782

Subgroups — #14753782

Order 2816.

1370 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66940C211yesmaximal, characteristic
2C2×#10622331C211yesmaximal, characteristic
3#13071018C211yesmaximal, characteristic
4#13068706C211yesmaximal, characteristic
5#13068620C214yesmaximal, complemented
6#13068552C211yesmaximal, characteristic
7#13068550C211yesmaximal, characteristic
8#13068435C214yesmaximal, complemented
9C11×#1824C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×Dic11⋊C4—21no—
13C22×C4×Dic11—21no—
14C22×C4×Dic11C2211yescharacteristic
15C2×#66940—21no—
16C2×#66940—21no—
17C2×#66940—24no—
18C2×#66940C418yescomplemented
19C2×#66940C2212yes—
20C2×#66940C2212yes—
21C2×#66930—21no—
22C2×C11×C22⋊C8C2211yescharacteristic
23C11×#380C2211yescharacteristic
24#10622825C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×#66880C2214yes—
27C2×Dic11⋊C8C2212yes—
28C2×C8×Dic11C2212yes—
29#10622589C2212yes—
30C4⋊C4×Dic11C2212yes—
31C2×#66874C2214yes—
32#10622555—21no—
33#10622331—24no—
34#10622263—21no—
35#10622262—21no—
36C11×#340C2214yes—
37#10622167C2214yes—
38C23×C4×C11—21no—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11—21no—
41C23×Dic11D411yescharacteristic
42C23×Dic11D411yescharacteristic
43C22×Dic22—21no—
44C22×Dic22—22no—
45C22×Dic22—28no—
46C22×Dic22C2×C414yes—
47C22×Dic22C2312yes—
48C22×C8×C11C2312yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4C2×C414yes—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—21no—
55C2×C22⋊Dic11—21no—
56C2×C4⋊Dic11C2312yes—
57C2×Dic11⋊C4—28no—
58C2×Dic11⋊C4—22no—
59C2×Dic11⋊C4—22no—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×C4×Dic11—28no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11C2×C414yes—
67C2×C4×Dic11D411yescharacteristic
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11D414yes—
70C2×C4×Dic11C2311yescharacteristic
71C2×C4×Dic11C2311yescharacteristic
72C22×C11⋊C8C2312yes—
73#66940—28no—
74#66940—28no—
75#66940—24no—
76#66940—24no—
77#66940C2×C418yes—
78#66940C2×C418yes—
79#66930—44no—
80C11×C22⋊C8—22no—
81C11×#95—21no—
82C11⋊#95—21no—
83C11⋊#95—22no—
84C22⋊(C11⋊C8)—22no—
85#66880—28no—
86Dic11⋊C8—24no—
87C8×Dic11—24no—
88#66874—28no—
89#20734—111nomaximal, Sylow
90C24×C11C2×D411yescharacteristic
91C22×C4×C11—24no—
92C22×C4×C11—24no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—44no—
96C22×C4×C11C22×C412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—28no—
101C22×Dic11—24no—
102C22×Dic11—22no—
103C22×Dic11—22no—
104C22×Dic11—42no—
105C22×Dic11C22⋊C414yes—
106C22×Dic11C22⋊C414yes—
107C22×Dic11SD1614yes—
108C22×Dic11Q1614yes—
109C22×Dic11C2×D411yescharacteristic
110C22×Dic11C2×D411yescharacteristic
111C22×Dic11C2×D411yescharacteristic
112C22×Dic11C2×D411yescharacteristic
113C2×Dic22—28no—
114C2×Dic22—216no—
115C2×Dic22—216no—
116C2×Dic22—24no—
117C2×Dic22—22no—
118C2×Dic22—24no—
119C2×Dic22C22×C414yes—
120C2×Dic22#4118yes—
121C2×C8×C11—22no—
122C2×C8×C11—24no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4C22×C414yes—
127C11×C22⋊C4—42no—
128C22⋊Dic11—42no—
129C4⋊Dic11—24no—
130Dic11⋊C4—28no—
131Dic11⋊C4—28no—
132Dic11⋊C4—44no—
133Dic11⋊C4—44no—
134C4×Dic11—28no—
135C4×Dic11—28no—
136C4×Dic11—44no—
137C4×Dic11C22⋊C414yes—
138C4×Dic11C22⋊C414yes—
139C4×Dic11C22×C412yes—
140C4×Dic11C22×C412yes—
141C4×Dic11C2×D412yes—
142C4×Dic11C2×D412yes—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—24no—
145C22×C4×Q8—111no—
146C2×#431—111no—
147#2285—111no—
148#1824—111no—
149#1824D1111yescharacteristic
150#1803—114no—
151#1787—111no—
152#1787—111no—
153C4×#103—114no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11C2×C22⋊C412yes—
157C23×C11C2×SD1612yes—
158C23×C11C2×Q1612yes—
159C23×C11C22×D411yescharacteristic
160C2×C4×C11—22no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—48no—
165C2×C4×C11—44no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11C2×C22⋊C412yes—
170C2×C4×C11C23×C411yescharacteristic
171C2×C4×C11C22×D411yescharacteristic
172C2×C4×C11C2×#4114yes—
173C2×Dic11—216no—
174C2×Dic11—24no—
175C2×Dic11—28no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—44no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11#103116yescomplemented
183C2×Dic11C2×C22⋊C412yes—
184C2×Dic11C2×C22⋊C412yes—
185C2×Dic11C2×C22⋊C412yes—
186C2×Dic11C2×C22⋊C412yes—
187C2×Dic11C2×SD1612yes—
188C2×Dic11C2×SD1612yes—
189C2×Dic11C2×Q1612yes—
190C2×Dic11C2×Q1612yes—
191Dic22—216no—
192Dic22—24no—
193Dic22—28no—
194Dic22#11718yescomplemented
195C8×C11—42no—
196C11⋊C8—42no—
197C23×Q8—111no—
198C2×C4×Q8—112no—
199C2×C4×Q8—112no—
200C2×C4×Q8—118no—
201C2×C4×Q8—221no—
202C2×C4×Q8—221no—
203C2×C4×Q8—224no—
204C2×#117—221no—
205C22×C4⋊C4—221no—
206C22×C4⋊C4C2×D1111yescharacteristic
207C22×C42—111no—
208C22×C42—221no—
209#431—224no—
210C2×C4⋊C8—112no—
211C2×#103—114no—
212C2×#103—114no—
213C2×C22⋊C8—111no—
214C2×C22⋊C8C2×D1111yescharacteristic
215C2×C4×C8—112no—
216#384—112no—
217#382—221no—
218#380—111no—
219#380—221no—
220#380C2×D1111yescharacteristic
221C4×C4⋊C4—112no—
222C4×C4⋊C4—221no—
223#340—114no—
224#340C2×D1114yes—
225C22×C11—24no—
226C22×C11—24no—
227C22×C11—22no—
228C22×C11—22no—
229C22×C11C2×#10314yes—
230C22×C11C22×C22⋊C411yescharacteristic
231C22×C11#52512yes—
232C22×C11C22×SD1611yescharacteristic
233C22×C11C22×Q1611yescharacteristic
234C22×C11#57512yes—
235C4×C11—22no—
236C4×C11—44no—
237C4×C11—82no—
238C4×C11C2×#11712yes—
239C4×C11#52512yes—
240Dic11—22no—
241Dic11—22no—
242Dic11—28no—
243Dic11—82no—
244Dic11C2×#10314yes—
245Dic11C2×#10314yes—
246C22×Q8—114no—
247C22×Q8—112no—
248C22×Q8—228no—
249C22×Q8—222no—
250C22×Q8—221no—
251C23×C4—21no—
252C23×C4—111no—
253C23×C4—111no—
254C23×C4—221no—
255C23×C4C22×D1111yescharacteristic
256C22×C8—112no—
257C22×C8C22×D1112yes—
258C4×Q8—118no—
259C4×Q8—118no—
260C4×Q8—228no—
261C4×Q8—228no—
262C4×Q8—224no—
263C4×Q8—224no—
264#117—444no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—112no—
268C2×C4⋊C4—228no—
269C2×C4⋊C4—222no—
270C2×C4⋊C4—222no—
271C2×C4⋊C4—222no—
272C2×C4⋊C4—222no—
273C2×C4⋊C4C4×D1114yes—
274C2×C4⋊C4C22×D1112yes—
275C2×C4⋊C4C22×D1112yes—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—221no—
278C2×C42—114no—
279C2×C42—111no—
280C2×C42—111no—
281C2×C42—114no—
282C2×C42—111no—
283C2×C42—111no—
284C2×C42—228no—
285C2×C42—222no—
286C2×C42—222no—
287C2×C42—222no—
288C4⋊C8—224no—
289#103—228no—
290#103—228no—
291C22⋊C8—22no—
292C22⋊C8—222no—
293C4×C8—224no—
294#95—21no—
295#95—222no—
296#95—221no—
297C2×C11—24no—
298C2×C11#228011yescharacteristic
299C2×C11C22×#10311yescharacteristic
300C2×C11#289611yescharacteristic
301C2×C11#310312yes—
302C2×C11#310412yes—
303C24D4×D1111yescharacteristic
304C2×Q8—114no—
305C2×Q8—118no—
306C2×Q8—2216no—
307C2×Q8—228no—
308C2×Q8—2216no—
309C2×Q8—224no—
310C2×Q8—222no—
311C2×Q8—224no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—44no—
317C22×C4—114no—
318C22×C4—114no—
319C22×C4—114no—
320C22×C4—111no—
321C22×C4—111no—
322C22×C4—111no—
323C22×C4—111no—
324C22×C4—114no—
325C22×C4—228no—
326C22×C4—224no—
327C22×C4—222no—
328C22×C4—222no—
329C22×C4—442no—
330C22×C4C2×C4×D1112yes—
331C22×C4D4×D1111yescharacteristic
332C22×C4D4×D1112yes—
333C22×C4C23×D1111yescharacteristic
334C2×C8—22no—
335C2×C8—24no—
336C2×C8—222no—
337C2×C8—224no—
338C4⋊C4—24no—
339C4⋊C4—22no—
340C4⋊C4—24no—
341C4⋊C4—228no—
342C4⋊C4—228no—
343C4⋊C4—224no—
344C4⋊C4—444no—
345C4⋊C4—444no—
346C4⋊C4C2×C4×D1114yes—
347C22⋊C4—42no—
348C22⋊C4—442no—
349C42—114no—
350C42—114no—
351C42—112no—
352C42—112no—
353C42—112no—
354C42—112no—
355C42—228no—
356C42—228no—
357C42—444no—
358C11#2073411yescharacteristic, complemented, Sylow
359C23—22no—
360C23—22no—
361C23C22⋊C4×D1112yes—
362C23SD16×D1112yes—
363C23Q16×D1112yes—
364C23C2×D4×D1111yescharacteristic
365Q8—118no—
366Q8—2216no—
367Q8—224no—
368Q8—228no—
369C2×C4—22no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—48no—
374C2×C4—44no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—112no—
379C2×C4—112no—
380C2×C4—112no—
381C2×C4—112no—
382C2×C4—112no—
383C2×C4—112no—
384C2×C4—1116no—
385C2×C4—112no—
386C2×C4—112no—
387C2×C4—2216no—
388C2×C4—224no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—228no—
392C2×C4—444no—
393C2×C4—442no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4C22⋊C4×D1112yes—
397C2×C4C22×C4×D1111yescharacteristic
398C2×C4C2×D4×D1111yescharacteristic
399C2×C4#41×D1114yes—
400C8—42no—
401C8—442no—
402C22—24no—
403C22—24no—
404C22—22no—
405C22—22no—
406C22D11×#10314yes—
407C22C2×C22⋊C4×D1111yescharacteristic
408C22#1062318712yes—
409C22C2×SD16×D1111yescharacteristic
410C22C2×Q16×D1111yescharacteristic
411C22#1062330412yes—
412C4—22no—
413C4—44no—
414C4—82no—
415C4—114no—
416C4—114no—
417C4—222no—
418C4—222no—
419C4—228no—
420C4—882no—
421C4D11×#11712yes—
422C4#1062318712yes—
423C2—24no—
424C2#1307099611yescharacteristic
425C2C2×D11×#10311yescharacteristic
426C2#1307713011yescharacteristic
427C2#1307864412yes—
428C2#1307865212yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1824C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1824D11
hypocenterC11#20734
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
5. #13068620C2semidirect
8. #13068435C2semidirect
18. C2×#66940C4semidirect
182. C2×Dic11#103semidirect
194. Dic22#117semidirect
358. C11#20734semidirect

Maximal subgroups

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

subgroupindex
C22×#669402
C2×#106223312
#130710182
#130687062
#130686202
#130685522
#130685502
#130684352
C11×#18242
#2073411