Finite Group Databasebeta

← #14736974

Subgroups — #14736974

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079760C211yesmaximal, characteristic, complemented
2#13079559C211yesmaximal, characteristic
3C2×#10622698C211yesmaximal, characteristic
4#13077546C211yesmaximal, characteristic, complemented
5#13068091C214yesmaximal, complemented
6#13067967C214yesmaximal, complemented
7#13067362C211yesmaximal, characteristic, complemented
8#13067285C211yesmaximal, characteristic
9C11×#1546C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C22×#4325—21no—
12C22×#4325—21no—
13C2×#66927C2211yescharacteristic
14#10623001C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C11×#423C2211yescharacteristic
17#10622735—21no—
18#10622732—21no—
19#10622707C2214yescomplemented
20#10622706—21no—
21#10622698—21no—
22#10622698—21no—
23#10622698C2212yes—
24#10622698C2212yes—
25#10622692—21no—
26#10622584—22no—
27#10622538C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29#10622461C2214yes—
30#10622444—21no—
31#10622444C2212yescomplemented
32#10622443—21no—
33#10622443C2212yescomplemented
34#10622344—22no—
35#10622307—21no—
36#10622306—21no—
37C11×#332C2214yescomplemented
38#10622123C2214yes—
39#10622118C2212yescomplemented
40#10622117C2212yescomplemented
41C22×Q8×C11—21no—
42C22×D44—21no—
43C22×D44—21no—
44C22×D44—21no—
45C2×C11×M16—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8C2312yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4325—22no—
54C2×#4325—22no—
55C2×#4325—22no—
56C2×#4325—22no—
57C2×#4325—44no—
58C2×#4325—44no—
59#66979—21no—
60#66977—21no—
61#66977D412yes—
62C22×C11⋊C8D411yescharacteristic
63C22×C11⋊C8D411yescharacteristic
64C2×#4314—24no—
65#66927—21no—
66#66927—21no—
67#66927—21no—
68#66927C2312yes—
69#66923—21no—
70#66922D411yescharacteristic
71#66922D411yescharacteristic
72C4×Dic22—21no—
73C4×Dic22C2312yes—
74C11×C4⋊C8—21no—
75C11×C4⋊C8C2312yes—
76C11×C4⋊C8C2312yes—
77C11×C22⋊C8—21no—
78C4×C8×C11—21no—
79C22⋊(C11⋊C8)—21no—
80#66885—24no—
81#66879—22no—
82Dic11⋊C8—22no—
83Dic11⋊C8—22no—
84C8×Dic11—22no—
85#66874—24no—
86#66872—24no—
87C4⋊(C11⋊C8)C2312yes—
88C4×C11⋊C8—21no—
89C4×C11⋊C8D411yescharacteristic
90C4×C11⋊C8D411yescharacteristic
91C4×C11⋊C8C2311yescharacteristic
92C4×C11⋊C8C2311yescharacteristic
93#19202—111nomaximal, Sylow
94C23×D11—41no—
95C2×Q8×C11—22no—
96C2×Q8×C11—41no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C22×C4×C11—41no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C2×D44—22no—
104C2×D44—22no—
105C2×D44—22no—
106C2×D44—41no—
107C2×D44—41no—
108C2×D44—41no—
109C2×D44—42no—
110C2×D44—42no—
111C2×D44—82no—
112C2×D44—82no—
113C2×Dic22—21no—
114C2×Dic22C2×D412yes—
115C11×M16—42no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11#4111yescharacteristic
125C42×C11C2411yescharacteristic
126C22⋊Dic11—22no—
127#4325—44no—
128#4325—44no—
129#4325—44no—
130#4325—44no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11C2×D412yes—
135Dic11⋊C4—22no—
136Dic11⋊C4—22no—
137C4×Dic11—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8SD1614yescomplemented
141C2×C11⋊C8C2×D411yescharacteristic
142C2×C11⋊C8C2×D411yescharacteristic
143C2×C11⋊C8C2×D411yescharacteristic
144C2×C11⋊C8C2×D411yescharacteristic
145#4314—84no—
146#3229—111no—
147#3208—111no—
148C2×#492—111no—
149#2960—111no—
150#1686—114no—
151#1666—114no—
152#1564—111no—
153#1546D1111yescharacteristic, complemented
154#1545—111no—
155C23×C11#12111yescharacteristic
156C22×D11—42no—
157C22×D11—82no—
158C22×D11—82no—
159C22×D11—82no—
160Q8×C11—42no—
161Q8×C11—42no—
162Q8×C11—82no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—42no—
166C2×C4×C11—82no—
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11C2×SD1612yes—
171C2×C4×C11AGL(1,ℤ/8)12yes—
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C2×#4111yescharacteristic
175C2×Dic11—22no—
176C2×Dic11—22no—
177D44—42no—
178D44—42no—
179D44—44no—
180D44—82no—
181D44—82no—
182D44—82no—
183D44—82no—
184Dic22—24no—
185Dic22—42no—
186C8×C11—42no—
187C8×C11—42no—
188C11⋊C8—21no—
189C11⋊C8—21no—
190C11⋊C8—42no—
191C11⋊C8C2×SD1612yes—
192C11⋊C8C2×SD1612yes—
193C22×SD16—221no—
194C22×SD16—221no—
195#533—111no—
196C2×C4⋊Q8C2×D1111yescharacteristic
197C2×#127—111no—
198#498—221no—
199#492—112no—
200#492—112no—
201#492—221no—
202#492—221no—
203#492—221no—
204#487—221no—
205#486—221no—
206#483—222no—
207#475—114no—
208#460—114no—
209#450—222no—
210#446—112no—
211#446—221no—
212C8×Q8—112no—
213C8×Q8—221no—
214#431—111no—
215#431C2×D1111yescharacteristic
216#424—221no—
217#423C2×D1111yescharacteristic
218#405—221no—
219C2×C4×C8—111no—
220#335—112no—
221#334—112no—
222#332C2×D1114yescomplemented
223#331—114no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11#46012yes—
227C22×C11C2×#12111yescharacteristic
228C2×D11—82no—
229C2×D11—82no—
230C2×D11—82no—
231C2×D11—164no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—82no—
235C4×C11#46012yes—
236C4×C11#47112yes—
237C4×C11C22×SD1611yescharacteristic
238C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
239C4×C11#57712yes—
240Dic11—42no—
241Dic11—42no—
242C22×Q8—21no—
243C22×D4—221no—
244C22×D4—221no—
245C22×D4—221no—
246C2×SD16—224no—
247C2×SD16—222no—
248C2×SD16—222no—
249C2×SD16—222no—
250C2×SD16—222no—
251C2×SD16—444no—
252C2×SD16—444no—
253C2×M16—21no—
254C22×C8—111no—
255C22×C8—111no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8—111no—
260C4⋊Q8—111no—
261C4⋊Q8C22×D1112yes—
262#127—112no—
263#127—221no—
264#127—221no—
265#127—221no—
266#125—221no—
267C22⋊Q8—112no—
268C22⋊Q8—221no—
269C4×Q8—112no—
270C4×Q8—221no—
271#117—221no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C42C22×D1111yescharacteristic
275#106—224no—
276C4⋊C8—21no—
277C4⋊C8—112no—
278C4⋊C8—222no—
279C4⋊C8—222no—
280C4⋊C8C22×D1112yes—
281C4⋊C8C22×D1112yes—
282#103—224no—
283#102—224no—
284C22⋊C8—21no—
285C22⋊C8—221no—
286#97—222no—
287C4×C8—21no—
288C4×C8—111no—
289C4×C8—111no—
290C4×C8—111no—
291C4×C8—111no—
292C4×C8—222no—
293C4×C8—221no—
294C2×C11—22no—
295C2×C11C2×#46011yescharacteristic
296C2×C11#305711yescharacteristic
297C2×C11C2×#47111yescharacteristic
298D11—162no—
299C24—441no—
300C2×Q8—22no—
301C2×Q8—41no—
302C2×Q8—42no—
303C2×Q8—42no—
304C2×Q8—112no—
305C2×Q8—221no—
306C2×D4—222no—
307C2×D4—222no—
308C2×D4—222no—
309C2×D4—441no—
310C2×D4—441no—
311C2×D4—441no—
312C2×D4—442no—
313C2×D4—442no—
314C2×D4—882no—
315C2×D4—882no—
316C22×C4—41no—
317C22×C4#433911yescharacteristic
318C22×C4D4×D1111yescharacteristic
319C22×C4D4×D1111yescharacteristic
320SD16—444no—
321SD16—444no—
322SD16—444no—
323SD16—444no—
324SD16—884no—
325M16—42no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—114no—
329C2×C8—111no—
330C2×C8—111no—
331C2×C8—111no—
332C2×C8—111no—
333C2×C8—222no—
334C2×C8—222no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—112no—
340C4⋊C4—221no—
341C4⋊C4—221no—
342C4⋊C4—222no—
343C4⋊C4—221no—
344C4⋊C4—222no—
345C22⋊C4—222no—
346C42—222no—
347C42#433911yescharacteristic
348C42D4×D1111yescharacteristic
349C42D4×D1111yescharacteristic
350C42C23×D1111yescharacteristic
351C11#1920211yescharacteristic, complemented, Sylow
352C23—442no—
353C23—882no—
354C23—882no—
355C23—882no—
356C23#6693711yescharacteristic
357Q8—42no—
358Q8—42no—
359Q8—82no—
360Q8—224no—
361Q8—442no—
362D4—442no—
363D4—442no—
364D4—444no—
365D4—882no—
366D4—882no—
367D4—882no—
368D4—882no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—42no—
372C2×C4—82no—
373C2×C4—222no—
374C2×C4—222no—
375C2×C4#6693711yescharacteristic
376C2×C4#6693711yescharacteristic
377C2×C4#6693711yescharacteristic
378C2×C4#6696412yes—
379C2×C4SD16×D1112yes—
380C2×C4C2×#433911yescharacteristic
381C2×C4C2×D4×D1111yescharacteristic
382C2×C4C2×D4×D1111yescharacteristic
383C8—42no—
384C8—42no—
385C8—112no—
386C8—112no—
387C8—221no—
388C8—221no—
389C8—442no—
390C22—21no—
391C22—21no—
392C22—882no—
393C22—882no—
394C22—882no—
395C22—1764no—
396C22#1062237512yes—
397C22C2×#6693711yescharacteristic
398C4—21no—
399C4—21no—
400C4—82no—
401C4—442no—
402C4—442no—
403C4#1062236712yes—
404C4#1062237512yes—
405C4C2×#6696411yescharacteristic
406C4C2×SD16×D1111yescharacteristic
407C4#1062330912yes—
408C2—22no—
409C2—1762no—
410C2C2×#1062237511yescharacteristic
411C2#1307825811yescharacteristic
412C2C2×#1062236711yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1546C2
socleC22×C11C2×#121
prime radicalC2×#66927C22
hypercenter#1546D11
hypocenterC11#19202
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
1. #13079760C2semidirect
4. #13077546C2semidirect
5. #13068091C2semidirect
6. #13067967C2semidirect
7. #13067362C2semidirect
9. C11×#1546C2semidirect
19. #10622707C22semidirect
31. #10622444C22semidirect
33. #10622443C22semidirect
37. C11×#332C22semidirect
39. #10622118C22semidirect
40. #10622117C22semidirect
140. C2×C11⋊C8SD16semidirect
153. #1546D11semidirect
222. #332C2×D11semidirect
351. C11#19202semidirect

Maximal subgroups

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

subgroupindex
#130797602
#130795592
C2×#106226982
#130775462
#130680912
#130679672
#130673622
#130672852
C11×#15462
#1920211