Finite Group Databasebeta

← #14758298

Subgroups — #14758298

Order 2816.

1390 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×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×#10622450C211yesmaximal, characteristic
3C4×#66945C211yesmaximal, characteristic
4#13069566C214yesmaximal, complemented
5#13069565C211yesmaximal, characteristic, complemented
6#13069564C211yesmaximal, characteristic, complemented
7#13069563C211yesmaximal, characteristic, complemented
8#13068334C214yesmaximal
9C11×#1987C211yesmaximal, 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×C4⋊C8C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×Dic11⋊C8C2212yes—
26C4⋊C4×Dic11C2212yes—
27C4×(C2×D11)⋊C4—21no—
28C4×C4⋊Dic11C2211yescharacteristic
29C42×Dic11—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31#10622450—24no—
32#10622279—21no—
33#10622261—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×C11—21no—
54C2×C42×C11C2311yescharacteristic
55#66997—28no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11C2312yes—
59C2×C4⋊Dic11C2312yes—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11—21no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11D411yescharacteristic
66C2×C4×Dic11D411yescharacteristic
67C2×C4×Dic11C2311yescharacteristic
68C22×C11⋊C8C2312yes—
69C2×#4313—24no—
70C2×#4313—28no—
71#66945—24no—
72#66945Q818yescomplemented
73C4⋊C4×D11—28no—
74C4⋊C4×D11—24no—
75C4⋊C4×D11C2×C418yes—
76#66941—28no—
77#66941—24no—
78#66941C2×C418yes—
79C42×D11C2×C414yes—
80C42×D11D414yes—
81#66922—22no—
82#66922C2×C414yes—
83C11×C4⋊C8—22no—
84C11×#95—21no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87Dic11⋊C8—24no—
88C4⋊(C11⋊C8)—22no—
89#21313—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—28no—
106C2×C4×D11—22no—
107C2×C4×D11—22no—
108C2×C4×D11—48no—
109C2×C4×D11C22⋊C414yes—
110C2×C4×D11C22⋊C414yes—
111C2×C4×D11C22×C412yes—
112C2×C4×D11C2×D412yes—
113C2×C4×D11C2×Q814yes—
114C2×C4×D11#4114yes—
115C2×Dic22—28no—
116C2×Dic22—24no—
117C2×Dic22—44no—
118C2×Dic22—48no—
119C2×C8×C11—22no—
120C2×C8×C11—24no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4C22×C414yes—
125C11×C4⋊C4C2×Q814yescomplemented
126C42×C11—42no—
127C42×C11C22×C412yes—
128C42×C11C2×D412yes—
129(C2×D11)⋊C4—28no—
130C4⋊Dic11—24no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11C22×C414yes—
134C4⋊Dic11C2×Q814yescomplemented
135Dic11⋊C4—28no—
136Dic11⋊C4—28no—
137C4×Dic11—28no—
138C4×Dic11—44no—
139C4×Dic11—42no—
140C4×Dic11C22⋊C414yes—
141C4×Dic11C22⋊C414yes—
142C4×Dic11C22×C412yes—
143C4×Dic11C2×D412yes—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—24no—
146#4313—48no—
147C22×C4⋊Q8—111no—
148C2×#423—111no—
149C4×#117—111no—
150#1988—114no—
151#1987—111no—
152#1987—111no—
153#1987—111no—
154#1987D1111yescharacteristic, complemented
155#1736—114no—
156C23×C11C22×D411yescharacteristic
157C22×D11—22no—
158C22×D11—21no—
159C22×D11—21no—
160C22×D11C2×C22⋊C412yes—
161C22×D11C22⋊Q814yes—
162Q8×C11—48no—
163C2×C4×C11—22no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—42no—
167C2×C4×C11—44no—
168C2×C4×C11—42no—
169C2×C4×C11C2×C22⋊C412yes—
170C2×C4×C11C2×C22⋊C412yes—
171C2×C4×C11#13712yes—
172C2×C4×C11#13712yes—
173C2×C4×C11C23×C411yescharacteristic
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C22×Q812yes—
176C2×C4×C11C2×#4112yes—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—24no—
180C2×Dic11—24no—
181C2×Dic11—42no—
182C2×Dic11—44no—
183C2×Dic11—42no—
184C2×Dic11C2×C22⋊C412yes—
185C2×Dic11C2×C22⋊C412yes—
186C2×Dic11C2×C22⋊C412yes—
187C2×Dic11C22⋊Q814yes—
188C2×Dic11AGL(1,ℤ/8)14yes—
189C4×D11—28no—
190C4×D11—28no—
191C4×D11—416no—
192C4×D11C4×Q818yes—
193C4×D11#12414yes—
194C4×D11C4⋊Q814yes—
195Dic22—48no—
196Dic22—416no—
197C8×C11—42no—
198C11⋊C8—42no—
199C23×Q8—221no—
200C22×M16—112no—
201C2×C4⋊Q8—118no—
202C2×C4⋊Q8—112no—
203C2×C4⋊Q8—111no—
204C2×C4⋊Q8—221no—
205C2×C4⋊Q8—224no—
206C2×C4⋊Q8—221no—
207C2×C4⋊Q8C2×D1111yescharacteristic
208C2×#117—112no—
209C22×C4⋊C4—112no—
210C22×C4⋊C4—221no—
211C22×C42—111no—
212#423—224no—
213C2×C4⋊C8—112no—
214C2×C4⋊C8—111no—
215C2×C4⋊C8C2×D1111yescharacteristic
216C4×C4⋊C4—112no—
217C4×C4⋊C4—111no—
218C4×C4⋊C4C2×D1111yescharacteristic
219C4×C22⋊C4—221no—
220C4×C22⋊C4—221no—
221#376—221no—
222C43—221no—
223#340—114no—
224#340—114no—
225#340—114no—
226#340C2×D1114yes—
227C22×C11C22×C22⋊C411yescharacteristic
228C22×C11C2×C22⋊Q812yes—
229C22×C11C2×AGL(1,ℤ/8)12yes—
230C22×C11C2×#13711yescharacteristic
231C22×C11C2×#13711yescharacteristic
232C2×D11—24no—
233C2×D11—24no—
234C2×D11—22no—
235C2×D11—22no—
236C2×D11#39114yes—
237C4×C11—22no—
238C4×C11—44no—
239C4×C11—44no—
240C4×C11#41914yes—
241C4×C11C2×C4×Q812yes—
242C4×C11C2×#12411yescharacteristic
243C4×C11C2×C4⋊Q811yescharacteristic
244Dic11—22no—
245Dic11—44no—
246Dic11—44no—
247Dic11#39114yes—
248Dic11#41814yes—
249C22×Q8—21no—
250C22×Q8—222no—
251C22×Q8—228no—
252C22×Q8—221no—
253C22×Q8—448no—
254C23×C4—111no—
255C23×C4—111no—
256C23×C4—111no—
257C23×C4—222no—
258C2×M16—228no—
259C2×M16—224no—
260C22×C8—112no—
261C22×C8C22×D1112yes—
262C4⋊Q8—22no—
263C4⋊Q8—118no—
264C4⋊Q8—114no—
265C4⋊Q8—228no—
266C4⋊Q8—224no—
267C4⋊Q8—228no—
268C4⋊Q8—222no—
269C4⋊Q8C4×D1114yes—
270#117—118no—
271#117—224no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—112no—
274C2×C4⋊C4—112no—
275C2×C4⋊C4—118no—
276C2×C4⋊C4—224no—
277C2×C4⋊C4—228no—
278C2×C4⋊C4—222no—
279C2×C4⋊C4—222no—
280C2×C4⋊C4—221no—
281C2×C4⋊C4C22×D1112yes—
282C2×C4⋊C4C22×D1112yes—
283C2×C22⋊C4—222no—
284C2×C42—21no—
285C2×C42—111no—
286C2×C42—111no—
287C2×C42—111no—
288C2×C42—114no—
289C2×C42—114no—
290C2×C42—222no—
291C2×C42—222no—
292C2×C42—221no—
293C2×C42C22×D1111yescharacteristic
294C4⋊C8—22no—
295C4⋊C8—224no—
296C4⋊C8—222no—
297#95—21no—
298#95—222no—
299#95—221no—
300C2×C11C2×#39111yescharacteristic
301C2×C11C2×#41811yescharacteristic
302C2×C11C2×#41911yescharacteristic
303C2×C11#307912yes—
304C2×C11#307912yes—
305D11—24no—
306C24—111no—
307C2×Q8—24no—
308C2×Q8—44no—
309C2×Q8—228no—
310C2×Q8—224no—
311C2×Q8—444no—
312C2×Q8—448no—
313C2×Q8—4432no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—111no—
317C22×C4—111no—
318C22×C4—112no—
319C22×C4—112no—
320C22×C4—114no—
321C22×C4—114no—
322C22×C4—111no—
323C22×C4—114no—
324C22×C4—114no—
325C22×C4—224no—
326C22×C4—228no—
327C22×C4—222no—
328C22×C4—222no—
329C22×C4—222no—
330C22×C4—222no—
331C22×C4—448no—
332C22×C4D4×D1111yescharacteristic
333C22×C4D4×D1111yescharacteristic
334C22×C4C23×D1111yescharacteristic
335M16—448no—
336C2×C8—22no—
337C2×C8—24no—
338C2×C8—222no—
339C2×C8—224no—
340C4⋊C4—24no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—114no—
344C4⋊C4—114no—
345C4⋊C4—228no—
346C4⋊C4—228no—
347C4⋊C4—224no—
348C4⋊C4—222no—
349C4⋊C4—222no—
350C4⋊C4C2×C4×D1114yes—
351C4⋊C4Q8×D1114yescomplemented
352C22⋊C4—228no—
353C42—42no—
354C42—114no—
355C42—114no—
356C42—112no—
357C42—112no—
358C42—228no—
359C42—444no—
360C42—442no—
361C42C2×C4×D1112yes—
362C42D4×D1112yes—
363C11#2131311yescharacteristic, complemented, Sylow
364C23—112no—
365C23—114no—
366C23—221no—
367C23—221no—
368C23—222no—
369C23C2×D4×D1111yescharacteristic
370Q8—48no—
371Q8—448no—
372Q8—4416no—
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—44no—
379C2×C4—112no—
380C2×C4—112no—
381C2×C4—114no—
382C2×C4—114no—
383C2×C4—114no—
384C2×C4—118no—
385C2×C4—114no—
386C2×C4—112no—
387C2×C4—228no—
388C2×C4—221no—
389C2×C4—221no—
390C2×C4—228no—
391C2×C4—224no—
392C2×C4—224no—
393C2×C4—4416no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—444no—
397C2×C4C22⋊C4×D1112yes—
398C2×C4C22⋊C4×D1112yes—
399C2×C4#6696812yes—
400C2×C4#6697112yes—
401C2×C4C22×C4×D1111yescharacteristic
402C2×C4C2×D4×D1111yescharacteristic
403C2×C4C2×Q8×D1112yes—
404C2×C4#41×D1112yes—
405C8—42no—
406C8—442no—
407C22—114no—
408C22—222no—
409C22—222no—
410C22—224no—
411C22—224no—
412C22C2×C22⋊C4×D1111yescharacteristic
413C22D11×C22⋊Q812yes—
414C22C2×#6696811yescharacteristic
415C22C2×#6697111yescharacteristic
416C22D11×AGL(1,ℤ/8)12yes—
417C4—22no—
418C4—44no—
419C4—44no—
420C4—114no—
421C4—114no—
422C4—222no—
423C4—444no—
424C4—444no—
425C4#1062241514yes—
426C4C4×Q8×D1112yes—
427C4D11×#12411yescharacteristic
428C4D11×C4⋊Q811yescharacteristic
429C2—224no—
430C2D11×#39111yescharacteristic
431C2D11×#41811yescharacteristic
432C2C2×#1062241511yescharacteristic
433C2#1307842812yes—
434C2#1307843012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1987C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1987D11
hypocenterC11#21313
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
4. #13069566C2semidirect
5. #13069565C2semidirect
6. #13069564C2semidirect
7. #13069563C2semidirect
9. C11×#1987C2semidirect
15. D11×C4⋊Q8C4semidirect
72. #66945Q8semidirect
125. C11×C4⋊C4C2×Q8semidirect
134. C4⋊Dic11C2×Q8semidirect
154. #1987D11semidirect
351. C4⋊C4Q8×D11semidirect
363. C11#21313semidirect

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×#106224502
C4×#669452
#130695662
#130695652
#130695642
#130695632
#130683342
C11×#19872
#2131311