Finite Group Databasebeta

← #14738992

Subgroups — #14738992

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079762C211yesmaximal, characteristic, complemented
2#13078415C211yesmaximal, characteristic
3C2×#10622454C211yesmaximal, characteristic
4#13077639C211yesmaximal, characteristic
5#13068040C214yesmaximal, complemented
6#13067992C214yesmaximal, complemented
7#13067289C211yesmaximal, characteristic, complemented
8#13067274C211yesmaximal, characteristic, complemented
9C11×#1570C211yesmaximal, characteristic, complemented
10C22×#4314—21no—
11C2×C4×D44C2211yescharacteristic
12#10623001C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17#10622744—21no—
18#10622734—21no—
19C2×#66880—21no—
20#10622538C2211yescharacteristic
21#10622464—22no—
22#10622460—22no—
23#10622459C2212yes—
24#10622455C2212yes—
25#10622454—22no—
26#10622454C2214yes—
27#10622447—22no—
28D11×C22⋊C8—22no—
29#10622334—22no—
30C8×D44C2214yes—
31#10622294C2212yescomplemented
32#10622293C2212yescomplemented
33C11×#334C2214yescomplemented
34#10622124C2212yescomplemented
35#10622120C2214yescomplemented
36#10622119C2212yescomplemented
37C22×D44D411yescharacteristic
38C22×C4×D11—21no—
39C22×Dic22—21no—
40C2×C11×M16—21no—
41C22×C8×C11—21no—
42C2×C42×C11C2311yescharacteristic
43C2×(C2×D11)⋊C4—21no—
44#66979—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11D411yescharacteristic
48#66977—21no—
49#66977—21no—
50C2×#4314—24no—
51C2×#4314—44no—
52C2×C8×D11—24no—
53C4×D44—21no—
54C4×D44—21no—
55C4×D44D412yes—
56C4×D44C2312yes—
57#66923—21no—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61#66922C2312yes—
62#66922C2311yescharacteristic
63#66922C2311yescharacteristic
64C4×Dic22—21no—
65C4×Dic22—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8D412yes—
69C11×C4⋊C8C2312yes—
70C11×C4⋊C8C2312yes—
71C11×C22⋊C8D412yes—
72C4×C8×C11C2312yes—
73C22⋊(C11⋊C8)—21no—
74#66885—22no—
75#66885—22no—
76(C2×D11)⋊C8—24no—
77#66882—22no—
78#66881—24no—
79#66881—22no—
80#66880—24no—
81#66880—24no—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8—21no—
84#19390—111nomaximal, Sylow
85C23×D11—21no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×Dic11—21no—
90C22×Dic11—41no—
91C2×D44—21no—
92C2×D44—22no—
93C2×D44SD1614yes—
94C2×D44C2×D412yes—
95C2×C4×D11—22no—
96C2×C4×D11—22no—
97C2×C4×D11—82no—
98C2×Dic22—21no—
99C2×Dic22—22no—
100C2×Dic22—21no—
101C2×Dic22—41no—
102C2×Dic22—42no—
103C2×Dic22—42no—
104C11×M16—42no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—42no—
108C2×C8×C11C2×D414yes—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112C42×C11C2411yescharacteristic
113C22⋊Dic11—41no—
114(C2×D11)⋊C4—22no—
115(C2×D11)⋊C4—22no—
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—22no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125C4⋊Dic11C2×D412yes—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128C4×Dic11—41no—
129C2×C11⋊C8—22no—
130#4314—48no—
131C8×D11—84no—
132#3229—111no—
133#3077—111no—
134C2×#461—111no—
135#2972—111no—
136#1679—114no—
137#1671—114no—
138#1570D1111yescharacteristic, complemented
139#1546—111no—
140#1542—111no—
141C23×C11#12111yescharacteristic
142C22×D11—22no—
143C22×D11—24no—
144C22×D11—81no—
145C22×D11—81no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11C2×SD1612yes—
152C2×C4×C11#13512yes—
153C2×C4×C11C22×D411yescharacteristic
154C2×C4×C11C22×D411yescharacteristic
155C2×C4×C11C2×#4111yescharacteristic
156C2×Dic11—22no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—42no—
160C2×Dic11—81no—
161C2×Dic11—82no—
162D44—22no—
163D44—24no—
164D44C2×SD1614yes—
165C4×D11—44no—
166C4×D11—82no—
167Dic22—42no—
168Dic22—42no—
169Dic22—42no—
170Dic22—82no—
171Dic22—81no—
172C8×C11—24no—
173C8×C11—42no—
174C8×C11—42no—
175C11⋊C8—42no—
176C22×SD16—221no—
177#533—111no—
178C2×C4⋊Q8—111no—
179C2×C4×D4—111no—
180#498—112no—
181#487—112no—
182#483—222no—
183#478—222no—
184#476—112no—
185#475—222no—
186#474—112no—
187#461—114no—
188#461—222no—
189C8×D4—114no—
190C8×D4—222no—
191#431—111no—
192#431C2×D1111yescharacteristic
193#428—221no—
194#423C2×D1111yescharacteristic
195C2×C4⋊C8C2×D1111yescharacteristic
196#418—221no—
197C2×#103—221no—
198C2×C22⋊C8—222no—
199#334C2×D1114yescomplemented
200#333—112no—
201#332—112no—
202#332—114no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11#46512yes—
206C22×C11C2×#12111yescharacteristic
207C2×D11—24no—
208C2×D11—42no—
209C2×D11—42no—
210C2×D11—84no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11#46512yes—
215C4×C11C22×SD1611yescharacteristic
216C4×C11C2×#13511yescharacteristic
217C4×C11#57712yes—
218Dic11—42no—
219Dic11—81no—
220Dic11—82no—
221Dic11—81no—
222C22×Q8—221no—
223C22×D4—111no—
224C23×C4—221no—
225C2×SD16—224no—
226C2×SD16—444no—
227C2×M16—21no—
228C22×C8—21no—
229C22×C8—224no—
230C4⋊Q8—112no—
231C4⋊Q8—111no—
232C4⋊Q8—111no—
233C4⋊Q8—221no—
234C4⋊Q8—221no—
235C4⋊Q8—221no—
236#125—221no—
237C22⋊Q8—221no—
238C22⋊Q8—221no—
239C4×Q8—221no—
240C4×Q8—221no—
241C4×D4—112no—
242C4×D4—112no—
243C4×D4—221no—
244C4×D4—221no—
245#117—221no—
246C2×C4⋊C4—111no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C22⋊C4—221no—
250C2×C42C22×D1111yescharacteristic
251#107—222no—
252#106—222no—
253#106—224no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—112no—
257C4⋊C8D4412yes—
258C4⋊C8C22×D1112yes—
259C4⋊C8C22×D1112yes—
260#103—224no—
261#103—224no—
262#102—222no—
263#102—222no—
264C22⋊C8—221no—
265C22⋊C8—224no—
266C22⋊C8D4412yes—
267C4×C8—221no—
268C4×C8C22×D1112yes—
269C2×C11—22no—
270C2×C11#304211yescharacteristic
271C2×C11C2×#46511yescharacteristic
272C2×C11#306911yescharacteristic
273D11—44no—
274C24—221no—
275C2×Q8—221no—
276C2×Q8—222no—
277C2×Q8—221no—
278C2×Q8—441no—
279C2×Q8—442no—
280C2×Q8—442no—
281C2×D4—114no—
282C2×D4—112no—
283C2×D4—221no—
284C2×D4—222no—
285C22×C4—221no—
286C22×C4—222no—
287C22×C4—222no—
288C22×C4—441no—
289C22×C4—882no—
290C22×C4C2×D4411yescharacteristic
291C22×C4D4×D1111yescharacteristic
292C22×C4#434311yescharacteristic
293SD16—448no—
294M16—42no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—42no—
298C2×C8—222no—
299C2×C8—884no—
300C2×C8C2×D4414yes—
301C4⋊C4—112no—
302C4⋊C4—221no—
303C4⋊C4—222no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—221no—
307C4⋊C4—222no—
308C4⋊C4—221no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C4⋊C4—441no—
313C22⋊C4—222no—
314C22⋊C4—222no—
315C22⋊C4—441no—
316C42—441no—
317C42C2×D4411yescharacteristic
318C42D4×D1111yescharacteristic
319C42#434311yescharacteristic
320C42C23×D1111yescharacteristic
321C11#1939011yescharacteristic, complemented, Sylow
322C23—222no—
323C23—224no—
324C23—881no—
325C23—881no—
326C23#6694811yescharacteristic
327Q8—442no—
328Q8—442no—
329Q8—442no—
330Q8—881no—
331Q8—882no—
332D4—114no—
333D4—224no—
334D4—222no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—222no—
338C2×C4—444no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—442no—
342C2×C4—882no—
343C2×C4—881no—
344C2×C4—882no—
345C2×C4#6694811yescharacteristic
346C2×C4#6694811yescharacteristic
347C2×C4#6694811yescharacteristic
348C2×C4SD16×D1112yes—
349C2×C4#6696912yes—
350C2×C4C22×D4411yescharacteristic
351C2×C4C2×D4×D1111yescharacteristic
352C2×C4C2×#434311yescharacteristic
353C8—24no—
354C8—42no—
355C8—42no—
356C8—442no—
357C22—21no—
358C22—21no—
359C22—224no—
360C22—442no—
361C22—442no—
362C22—884no—
363C22#1062247712yes—
364C22C2×#6694811yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—442no—
369C4—881no—
370C4—881no—
371C4—882no—
372C4#1062247712yes—
373C4#1062328212yes—
374C4C2×SD16×D1111yescharacteristic
375C4C2×#6696911yescharacteristic
376C2—22no—
377C2—444no—
378C2#1307812911yescharacteristic
379C2C2×#1062247711yescharacteristic
380C2#1307835411yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1570C2
socleC22×C11C2×#121
prime radicalC22×D44D4
hypercenter#1570D11
hypocenterC11#19390
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
1. #13079762C2semidirect
5. #13068040C2semidirect
6. #13067992C2semidirect
7. #13067289C2semidirect
8. #13067274C2semidirect
9. C11×#1570C2semidirect
31. #10622294C22semidirect
32. #10622293C22semidirect
33. C11×#334C22semidirect
34. #10622124C22semidirect
35. #10622120C22semidirect
36. #10622119C22semidirect
138. #1570D11semidirect
199. #334C2×D11semidirect
321. C11#19390semidirect

Maximal subgroups

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

subgroupindex
#130797622
#130784152
C2×#106224542
#130776392
#130680402
#130679922
#130672892
#130672742
C11×#15702
#1939011