Finite Group Databasebeta

← #14758366

Subgroups — #14758366

Order 2816.

1382 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×#10622320C211yesmaximal, characteristic
3#13071022C211yesmaximal, characteristic
4#13069590C211yesmaximal, characteristic, complemented
5#13069589C211yesmaximal, characteristic, complemented
6#13069588C211yesmaximal, characteristic, complemented
7#13069575C214yesmaximal, complemented
8#13068334C214yesmaximal
9C11×#1993C211yesmaximal, characteristic, complemented
10C22×Q8×D11—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66997—21no—
13C22×#4313C2212yes—
14D11×C4⋊Q8—24no—
15D11×C4⋊Q8C418yescomplemented
16C2×#66945C2212yes—
17C2×C4⋊C4×D11—21no—
18C2×C4⋊C4×D11C2212yes—
19C2×#66941—21no—
20C2×#66941C2212yes—
21C2×C42×D11C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C11×#382C2211yescharacteristic
25C2×C8×Dic11C2212yes—
26#10622589C2212yes—
27#10622549C2211yescharacteristic
28C2×#66867C2211yescharacteristic
29#10622320—24no—
30#10622280—21no—
31#10622280—21no—
32#10622262—21no—
33#10622262—21no—
34C11×#340C2214yes—
35#10622189C2214yes—
36#10622167C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C2×Q8×D11—28no—
40C2×Q8×D11—48no—
41C22×C4×D11—22no—
42C22×C4×D11D411yescharacteristic
43C22×C4×D11D411yescharacteristic
44C22×C4×D11C2311yescharacteristic
45C22×Dic22—21no—
46C22×Dic22—22no—
47C22×C8×C11C2312yes—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8C2×C414yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2312yes—
53C2×C42×C11C2311yescharacteristic
54#66997—28no—
55C2×(C2×D11)⋊C4—22no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11C2312yes—
58C2×C4⋊Dic11C2312yes—
59C2×Dic11⋊C4—22no—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11D411yescharacteristic
65C2×C4×Dic11D411yescharacteristic
66C2×C4×Dic11C2311yescharacteristic
67C22×C11⋊C8C2312yes—
68C2×#4313—24no—
69C2×#4313—24no—
70C2×#4313Q818yescomplemented
71#66945—28no—
72C4⋊C4×D11—28no—
73C4⋊C4×D11—24no—
74C4⋊C4×D11C2×C418yes—
75#66941—28no—
76#66941—24no—
77#66941C2×C418yes—
78C42×D11C2×C414yes—
79C42×D11D414yes—
80#66922—22no—
81#66922C2×C414yes—
82C11×#97—22no—
83C11×#95—21no—
84C11×#95—21no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C8×Dic11—24no—
88#66867—22no—
89#21324—111nomaximal, Sylow
90C23×D11C2×D411yescharacteristic
91C2×Q8×C11—24no—
92C2×Q8×C11—44no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—22no—
99C22×Dic11—22no—
100C22×Dic11C2×D411yescharacteristic
101C22×Dic11C2×D411yescharacteristic
102C22×Dic11C2×D411yescharacteristic
103Q8×D11—432no—
104C2×C4×D11—24no—
105C2×C4×D11—24no—
106C2×C4×D11—28no—
107C2×C4×D11—48no—
108C2×C4×D11C22⋊C414yes—
109C2×C4×D11C22⋊C414yes—
110C2×C4×D11C22×C412yes—
111C2×C4×D11C2×D412yes—
112C2×C4×D11C2×Q814yes—
113C2×C4×D11#4114yes—
114C2×Dic22—28no—
115C2×Dic22—24no—
116C2×Dic22—44no—
117C2×Dic22—48no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11C2×Q814yescomplemented
121C11×C4⋊C4—24no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4C22×C414yes—
125C42×C11C22×C412yes—
126C42×C11C2×D412yes—
127(C2×D11)⋊C4—44no—
128C4⋊Dic11—24no—
129C4⋊Dic11—22no—
130C4⋊Dic11—24no—
131C4⋊Dic11C22×C414yes—
132Dic11⋊C4—28no—
133Dic11⋊C4—28no—
134Dic11⋊C4—44no—
135Dic11⋊C4—44no—
136C4×Dic11—44no—
137C4×Dic11C22⋊C414yes—
138C4×Dic11C22⋊C414yes—
139C4×Dic11C22×C412yes—
140C4×Dic11C2×D412yes—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8C2×Q814yescomplemented
144#4313—216no—
145C22×C4⋊Q8—111no—
146C2×C4×M16—111no—
147#2285—111no—
148#1993—111no—
149#1993—111no—
150#1993—111no—
151#1993D1111yescharacteristic, complemented
152#1990—114no—
153#1736—114no—
154C23×C11C22×D411yescharacteristic
155C22×D11—22no—
156C22×D11—22no—
157C22×D11C2×C22⋊C412yes—
158C22×D11#12412yes—
159C22×D11C4⋊Q812yes—
160Q8×C11—48no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—24no—
164C2×C4×C11—44no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11C2×C22⋊C412yes—
169C2×C4×C11C2×C22⋊C412yes—
170C2×C4×C11C23×C411yescharacteristic
171C2×C4×C11C22×D411yescharacteristic
172C2×C4×C11C22×Q812yes—
173C2×C4×C11C2×#4112yes—
174C2×Dic11—24no—
175C2×Dic11—44no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11C2×C22⋊C412yes—
180C2×Dic11C2×C22⋊C412yes—
181C2×Dic11C2×C22⋊C412yes—
182C2×Dic11#12412yes—
183C2×Dic11C4⋊Q812yes—
184C2×Dic11AGL(1,ℤ/8)14yes—
185C2×Dic11#13714yes—
186C4×D11—28no—
187C4×D11—28no—
188C4×D11—416no—
189C4×D11C4×Q818yes—
190C4×D11C22⋊Q818yes—
191Dic22—48no—
192Dic22—416no—
193C8×C11—24no—
194C11⋊C8—24no—
195C23×Q8—221no—
196C22×M16—112no—
197C2×C4⋊Q8—118no—
198C2×C4⋊Q8—112no—
199C2×C4⋊Q8—111no—
200C2×C4⋊Q8—221no—
201C2×C4⋊Q8—224no—
202C2×C4⋊Q8—221no—
203C2×C4⋊Q8C2×D1111yescharacteristic
204C2×#117—112no—
205C22×C4⋊C4—112no—
206C22×C4⋊C4—221no—
207C22×C42—111no—
208C4×M16—224no—
209C2×#97—111no—
210C2×#97C2×D1111yescharacteristic
211C2×C4×C8—112no—
212#384—112no—
213#382—111no—
214#382C2×D1111yescharacteristic
215#380—221no—
216#380—221no—
217C4×C4⋊C4—221no—
218C4×C4⋊C4—221no—
219#340—114no—
220#340—114no—
221#340—114no—
222#340C2×D1114yes—
223C22×C11C22×C22⋊C411yescharacteristic
224C22×C11C2×#12411yescharacteristic
225C22×C11C2×C4⋊Q811yescharacteristic
226C22×C11C2×AGL(1,ℤ/8)12yes—
227C22×C11C2×#13712yes—
228C2×D11—24no—
229C2×D11—22no—
230C2×D11—22no—
231C2×D11—24no—
232C2×D11#39114yes—
233C4×C11—22no—
234C4×C11—22no—
235C4×C11—44no—
236C4×C11—82no—
237C4×C11C2×C4×Q812yes—
238C4×C11C2×C22⋊Q812yes—
239Dic11—44no—
240Dic11—82no—
241Dic11#39114yes—
242Dic11#41814yes—
243Dic11#41914yes—
244C22×Q8—21no—
245C22×Q8—222no—
246C22×Q8—228no—
247C22×Q8—221no—
248C22×Q8—448no—
249C23×C4—111no—
250C23×C4—111no—
251C23×C4—111no—
252C23×C4—222no—
253C2×M16—118no—
254C2×M16—224no—
255C2×M16—224no—
256C22×C8—112no—
257C22×C8C22×D1112yes—
258C4⋊Q8—22no—
259C4⋊Q8—118no—
260C4⋊Q8—114no—
261C4⋊Q8—228no—
262C4⋊Q8—224no—
263C4⋊Q8—228no—
264C4⋊Q8—222no—
265C4⋊Q8C4×D1114yes—
266#117—228no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—112no—
269C2×C4⋊C4—118no—
270C2×C4⋊C4—112no—
271C2×C4⋊C4—224no—
272C2×C4⋊C4—228no—
273C2×C4⋊C4—222no—
274C2×C4⋊C4—222no—
275C2×C4⋊C4—221no—
276C2×C4⋊C4—222no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4C22×D1112yes—
279C2×C4⋊C4C22×D1112yes—
280C2×C22⋊C4—222no—
281C2×C42—111no—
282C2×C42—111no—
283C2×C42—111no—
284C2×C42—114no—
285C2×C42—114no—
286C2×C42—222no—
287C2×C42C22×D1111yescharacteristic
288#97—22no—
289#97—222no—
290C4×C8—224no—
291#95—21no—
292#95—21no—
293#95—221no—
294#95—221no—
295C2×C11C2×#39111yescharacteristic
296C2×C11C2×#41811yescharacteristic
297C2×C11C2×#41911yescharacteristic
298C2×C11#314112yes—
299C2×C11#316512yes—
300D11—24no—
301C24—111no—
302C2×Q8—24no—
303C2×Q8—44no—
304C2×Q8—228no—
305C2×Q8—224no—
306C2×Q8—444no—
307C2×Q8—448no—
308C2×Q8—4432no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—111no—
312C22×C4—111no—
313C22×C4—111no—
314C22×C4—112no—
315C22×C4—112no—
316C22×C4—114no—
317C22×C4—114no—
318C22×C4—114no—
319C22×C4—114no—
320C22×C4—224no—
321C22×C4—224no—
322C22×C4—228no—
323C22×C4—222no—
324C22×C4—222no—
325C22×C4—448no—
326C22×C4D4×D1111yescharacteristic
327C22×C4D4×D1111yescharacteristic
328C22×C4C23×D1111yescharacteristic
329M16—2216no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—114no—
333C2×C8—222no—
334C2×C8—222no—
335C2×C8Q8×D1114yescomplemented
336C4⋊C4—24no—
337C4⋊C4—22no—
338C4⋊C4—24no—
339C4⋊C4—114no—
340C4⋊C4—228no—
341C4⋊C4—228no—
342C4⋊C4—224no—
343C4⋊C4—222no—
344C4⋊C4—224no—
345C4⋊C4—444no—
346C4⋊C4—444no—
347C4⋊C4C2×C4×D1114yes—
348C22⋊C4—444no—
349C42—114no—
350C42—114no—
351C42—112no—
352C42—112no—
353C42—444no—
354C42C2×C4×D1112yes—
355C42D4×D1112yes—
356C11#2132411yescharacteristic, complemented, Sylow
357C23—112no—
358C23—112no—
359C23—112no—
360C23—222no—
361C23—222no—
362C23C2×D4×D1111yescharacteristic
363Q8—48no—
364Q8—448no—
365Q8—4416no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—44no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—112no—
374C2×C4—112no—
375C2×C4—112no—
376C2×C4—112no—
377C2×C4—114no—
378C2×C4—114no—
379C2×C4—112no—
380C2×C4—118no—
381C2×C4—118no—
382C2×C4—228no—
383C2×C4—228no—
384C2×C4—224no—
385C2×C4—4416no—
386C2×C4—444no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4C22⋊C4×D1112yes—
391C2×C4C22⋊C4×D1112yes—
392C2×C4C22×C4×D1111yescharacteristic
393C2×C4C2×D4×D1111yescharacteristic
394C2×C4C2×Q8×D1112yes—
395C2×C4#41×D1112yes—
396C8—24no—
397C8—224no—
398C22—114no—
399C22—224no—
400C22—222no—
401C22—222no—
402C22—224no—
403C22C2×C22⋊C4×D1111yescharacteristic
404C22D11×#12411yescharacteristic
405C22D11×C4⋊Q811yescharacteristic
406C22D11×AGL(1,ℤ/8)12yes—
407C22D11×#13712yes—
408C4—22no—
409C4—22no—
410C4—44no—
411C4—82no—
412C4—114no—
413C4—114no—
414C4—114no—
415C4—444no—
416C4—882no—
417C4C4×Q8×D1112yes—
418C4D11×C22⋊Q812yes—
419C2—224no—
420C2D11×#39111yescharacteristic
421C2D11×#41811yescharacteristic
422C2D11×#41911yescharacteristic
423C2#1307900812yes—
424C2#1307916112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1993C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1993D11
hypocenterC11#21324
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1993

Complements

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

NH ≅ G/Ntype
4. #13069590C2semidirect
5. #13069589C2semidirect
6. #13069588C2semidirect
7. #13069575C2semidirect
9. C11×#1993C2semidirect
15. D11×C4⋊Q8C4semidirect
70. C2×#4313Q8semidirect
120. C2×C8×C11C2×Q8semidirect
143. C2×C11⋊C8C2×Q8semidirect
151. #1993D11semidirect
335. C2×C8Q8×D11semidirect
356. C11#21324semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×#106223202
#130710222
#130695902
#130695892
#130695882
#130695752
#130683342
C11×#19932
#2132411