Finite Group Databasebeta

← #14810450

Subgroups — #14810450

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623219C211yesmaximal, characteristic, complemented
2C2×#10622684C211yesmaximal, characteristic, complemented
3#13076958C211yesmaximal, characteristic
4#13069750C214yesmaximal, complemented
5#13069586C211yesmaximal, characteristic, complemented
6#13069585C211yesmaximal, characteristic, complemented
7#13068935C214yesmaximal, complemented
8#13068379C211yesmaximal, characteristic, complemented
9C2×C11×#490C211yesmaximal, characteristic, complemented
10C2×C11×#127C2211yescharacteristic
11C2×C11×#125C2211yescharacteristic
12C2×#66991—22no—
13C2×#66991C2212yes—
14#10623219—24no—
15#10623219—24no—
16C2×#66949—22no—
17C2×#66945C2212yes—
18C2×#66941C2212yes—
19C2×#66940—22no—
20C2×C42×D11C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C11×#490—24no—
23C2×C11×#102C2214yes—
24C2×C11×#97C2211yescharacteristic
25#10622834—22no—
26#10622834C2212yes—
27C2×#66896C2214yes—
28C2×(C2×D11)⋊C8C2212yes—
29#10622684—24no—
30#10622548C2211yescharacteristic
31C2×#66867C2211yescharacteristic
32#10622189C2214yes—
33#10622188C2212yes—
34#10622167C2214yes—
35C22×D4×C11—22no—
36C22×D4×C11C2312yes—
37C22×C22⋊D11—22no—
38C22×C4×D11D412yes—
39C22×C4×D11C2311yescharacteristic
40C22×Dic22—22no—
41C22×C8×C11C2312yes—
42C11×#127—22no—
43C11×#127—22no—
44C11×#125—22no—
45C11×#125D414yescomplemented
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4C2312yes—
48C2×C42×C11C2311yescharacteristic
49C2×C22⋊Dic11—24no—
50C2×C22⋊Dic11—22no—
51#66991—28no—
52#66991—48no—
53C2×(C2×D11)⋊C4—22no—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11C2312yes—
56C2×C4⋊Dic11C2312yes—
57C2×Dic11⋊C4—22no—
58C2×Dic11⋊C4—22no—
59C2×C4×Dic11—22no—
60C2×C4×Dic11D412yes—
61C2×C4×Dic11C2311yescharacteristic
62C22×C11⋊C8C2312yes—
63#66949—216no—
64#66945—24no—
65#66945—24no—
66#66941—24no—
67#66941—24no—
68#66940—216no—
69C42×D11—22no—
70C42×D11—22no—
71#66923—22no—
72#66923D414yescomplemented
73C11×#102—28no—
74C11×#97—22no—
75#66896—28no—
76(C2×D11)⋊C8—24no—
77#66867—22no—
78#25911—111nomaximal, Sylow
79C24×C11—22no—
80C23×D11C2×D411yescharacteristic
81C2×D4×C11—22no—
82C2×D4×C11—22no—
83C2×D4×C11—24no—
84C2×D4×C11—24no—
85C2×D4×C11—44no—
86C2×D4×C11—44no—
87C2×D4×C11—44no—
88C22×C4×C11—22no—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2411yescharacteristic
91C2×C22⋊D11—48no—
92C2×C22⋊D11—44no—
93C22×Dic11—22no—
94C22×Dic11—22no—
95C22×Dic11C2×D411yescharacteristic
96C22×Dic11C2×D412yes—
97C2×C4×D11—24no—
98C2×C4×D11—24no—
99C2×C4×D11—21no—
100C2×C4×D11—21no—
101C2×C4×D11—22no—
102C2×C4×D11—42no—
103C2×C4×D11#4114yes—
104C2×Dic22—28no—
105C2×Dic22—44no—
106C2×Dic22—44no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C11×C4⋊C4—28no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4C2×D414yes—
113C42×C11C2×D412yes—
114C42×C11C2×D412yes—
115C22⋊Dic11—44no—
116C22⋊Dic11—48no—
117(C2×D11)⋊C4—28no—
118C4⋊Dic11—22no—
119C4⋊Dic11—24no—
120C4⋊Dic11—44no—
121C4⋊Dic11C2×D414yes—
122Dic11⋊C4—28no—
123Dic11⋊C4—28no—
124C4×Dic11—28no—
125C4×Dic11—24no—
126C4×Dic11—21no—
127C4×Dic11—21no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×#533—111no—
132C2×#490—111no—
133C2×#490D1111yescharacteristic, complemented
134#2856—111no—
135#2023—114no—
136#1992—111no—
137#1992—111no—
138#1875—114no—
139#1749—111no—
140C23×C11—42no—
141C23×C11—42no—
142C23×C11—42no—
143C23×C11—44no—
144C23×C11—44no—
145C23×C11C22×D411yescharacteristic
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—22no—
149C22×D11—22no—
150C22×D11#12412yes—
151D4×C11—44no—
152D4×C11—44no—
153D4×C11—88no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—24no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11#12014yes—
160C2×C4×C11C22×D411yescharacteristic
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C11C2×#4112yes—
163C2×C4×C112−1+412yes—
164C22⋊D11—88no—
165C2×Dic11—21no—
166C2×Dic11—22no—
167C2×Dic11—21no—
168C2×Dic11—22no—
169C2×Dic11—24no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—44no—
174C2×Dic11#12412yes—
175C2×Dic11AGL(1,ℤ/8)14yes—
176C4×D11—24no—
177C4×D11—24no—
178C4×D11—48no—
179Dic22—416no—
180C8×C11—42no—
181C11⋊C8—42no—
182#533—224no—
183#533—224no—
184C2×C4⋊Q8—112no—
185C2×#127C2×D1111yescharacteristic
186C2×#125—111no—
187C2×#125C2×D1111yescharacteristic
188C2×C22⋊Q8—222no—
189C2×#121—112no—
190C2×#121—222no—
191C2×C4×Q8—222no—
192C2×#117—112no—
193C22×C42—111no—
194#490—24no—
195#490—224no—
196C2×#102—114no—
197C2×#102C2×D1114yes—
198C2×C22⋊C8—112no—
199C2×#97—111no—
200C2×#97C2×D1111yescharacteristic
201#390—112no—
202#390—222no—
203#384—111no—
204#340—114no—
205#340—114no—
206#336—112no—
207C22×C11—82no—
208C22×C11—82no—
209C22×C11—82no—
210C22×C11—84no—
211C22×C11—84no—
212C22×C11C2×#12011yescharacteristic
213C22×C11C2×#12411yescharacteristic
214C22×C11#53611yescharacteristic
215C22×C11C2×AGL(1,ℤ/8)12yes—
216C22×C11#57512yes—
217C2×D11—22no—
218C2×D11—22no—
219C2×D11—22no—
220C2×D11—42no—
221C2×D11—42no—
222C4×C11—24no—
223C4×C11—44no—
224C4×C11#54812yes—
225C4×C11#54812yes—
226Dic11—22no—
227Dic11—24no—
228Dic11—44no—
229Dic11—82no—
230C22×Q8—222no—
231C22×D4—22no—
232C22×D4—222no—
233C22×D4C22×D1112yes—
234C23×C4—111no—
235C23×C4—112no—
236C22×C8—112no—
237C22×C8C22×D1112yes—
238C4⋊Q8—224no—
239C4⋊Q8—224no—
240#127—22no—
241#127—22no—
242#125—22no—
243#125—114no—
244#125—222no—
245#125C22⋊D1114yescomplemented
246C22⋊Q8—2216no—
247#121—228no—
248#121—448no—
249C4×Q8—2216no—
250#117—224no—
251#117—224no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—112no—
254C2×C4⋊C4—112no—
255C2×C4⋊C4—222no—
256C2×C4⋊C4—222no—
257C2×C4⋊C4—222no—
258C2×C4⋊C4C22×D1112yes—
259C2×C22⋊C4—222no—
260C2×C22⋊C4—222no—
261C2×C22⋊C4—224no—
262C2×C42—112no—
263C2×C42—111no—
264C2×C42—222no—
265C2×C42—222no—
266C2×C42—222no—
267C2×C42C22×D1111yescharacteristic
268#102—28no—
269#102—228no—
270C22⋊C8—224no—
271#97—22no—
272#97—222no—
273C2×C11—162no—
274C2×C11#243611yescharacteristic
275C2×C11#300612yes—
276C2×C11#313511yescharacteristic
277C2×C11#313811yescharacteristic
278C2×C11#323512yes—
279D11—42no—
280C24—22no—
281C24—111no—
282C2×Q8—228no—
283C2×Q8—444no—
284C2×Q8—444no—
285C2×D4—22no—
286C2×D4—24no—
287C2×D4—24no—
288C2×D4—22no—
289C2×D4—44no—
290C2×D4—44no—
291C2×D4—44no—
292C2×D4—444no—
293C2×D4—448no—
294C22×C4—22no—
295C22×C4—111no—
296C22×C4—112no—
297C22×C4—114no—
298C22×C4—224no—
299C22×C4—221no—
300C22×C4—222no—
301C22×C4—221no—
302C22×C4—222no—
303C22×C4—224no—
304C22×C4—222no—
305C22×C4—442no—
306C22×C4D4×D1112yes—
307C22×C4C23×D1111yescharacteristic
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—222no—
312C2×C8—222no—
313C2×C8—222no—
314C4⋊C4—28no—
315C4⋊C4—22no—
316C4⋊C4—114no—
317C4⋊C4—228no—
318C4⋊C4—228no—
319C4⋊C4—222no—
320C4⋊C4—224no—
321C4⋊C4—444no—
322C4⋊C4C2×C22⋊D1114yes—
323C22⋊C4—228no—
324C22⋊C4—444no—
325C22⋊C4—448no—
326C42—228no—
327C42—224no—
328C42—221no—
329C42—221no—
330C42D4×D1112yes—
331C42C2×C22⋊D1112yes—
332C11#2591111yescharacteristic, complemented, Sylow
333C23—44no—
334C23—44no—
335C23—42no—
336C23—42no—
337C23—42no—
338C23—112no—
339C23—222no—
340C23—222no—
341C23—221no—
342C23—221no—
343C23C2×D4×D1111yescharacteristic
344Q8—4416no—
345D4—44no—
346D4—44no—
347D4—88no—
348D4—888no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—24no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—114no—
355C2×C4—112no—
356C2×C4—222no—
357C2×C4—221no—
358C2×C4—222no—
359C2×C4—221no—
360C2×C4—224no—
361C2×C4—224no—
362C2×C4—224no—
363C2×C4—448no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—444no—
367C2×C4—442no—
368C2×C4#6699014yes—
369C2×C4C2×D4×D1111yescharacteristic
370C2×C4#41×D1112yes—
371C2×C4#6704312yes—
372C2×C4C22×C22⋊D1111yescharacteristic
373C8—42no—
374C8—442no—
375C22—84no—
376C22—84no—
377C22—82no—
378C22—82no—
379C22—82no—
380C22—222no—
381C22—222no—
382C22—222no—
383C22—442no—
384C22—442no—
385C22D11×#12411yescharacteristic
386C22#1062320611yescharacteristic
387C22D11×AGL(1,ℤ/8)12yes—
388C22#1062330412yes—
389C22C2×#6699011yescharacteristic
390C4—24no—
391C4—44no—
392C4—224no—
393C4—222no—
394C4—444no—
395C4—882no—
396C4#1062320812yes—
397C4#1062336212yes—
398C2—162no—
399C2—442no—
400C2#1307227111yescharacteristic
401C2#1307786412yes—
402C2#1307896011yescharacteristic
403C2#1307898911yescharacteristic
404C2#1307980912yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#490C2
socleC23×C11C22×D4
prime radical#13076958C2
hypercenterC2×#490D11
hypocenterC11#25911
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#10623219C2semidirect
2. C2×#10622684C2semidirect
4. #13069750C2semidirect
5. #13069586C2semidirect
6. #13069585C2semidirect
7. #13068935C2semidirect
8. #13068379C2semidirect
9. C2×C11×#490C2semidirect
45. C11×#125D4semidirect
72. #66923D4semidirect
133. C2×#490D11semidirect
245. #125C22⋊D11semidirect
332. C11#25911semidirect

Maximal subgroups

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

subgroupindex
C2×#106232192
C2×#106226842
#130769582
#130697502
#130695862
#130695852
#130689352
#130683792
C2×C11×#4902
#2591111