Finite Group Databasebeta

← #14738991

Subgroups — #14738991

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#13078413C211yesmaximal, characteristic
3C2×#10622632C211yesmaximal, characteristic
4#13068039C214yesmaximal, complemented
5#13067991C214yesmaximal, complemented
6#13067387C211yesmaximal, characteristic, complemented
7#13067287C211yesmaximal, characteristic, complemented
8#13067271C211yesmaximal, characteristic, complemented
9C11×#2972C211yesmaximal, characteristic
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4324—21no—
12#10623001C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C8×D4×C11—22no—
15C8×D4×C11C2214yes—
16C11×#431C2211yescharacteristic
17C11×#431C2211yescharacteristic
18C2×C11×C22⋊C8—22no—
19#10622828—21no—
20#10622632—22no—
21#10622632C2214yes—
22#10622622—22no—
23#10622621C2212yes—
24#10622620C2212yes—
25C2×#66874—21no—
26#10622577—21no—
27#10622537C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29#10622464—22no—
30#10622334—22no—
31#10622294C2212yescomplemented
32#10622293C2212yescomplemented
33#10622124C2214yescomplemented
34#10622120C2212yescomplemented
35#10622119C2212yescomplemented
36#10622095C2214yescomplemented
37C22×D4×C11D411yescharacteristic
38C23×C4×C11—21no—
39C22×Dic22—21no—
40C22×C8×C11—24no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11D412yes—
44C4×D4×C11C2312yes—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C22⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48C2×#4324—24no—
49C2×#4324—44no—
50#66979—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53#66977—21no—
54#66977—21no—
55C2×#4318—21no—
56C22×C11⋊C8—21no—
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⋊C8D412yes—
67C11×C4⋊C8C2312yes—
68C11×C22⋊C8—21no—
69C11×C22⋊C8—24no—
70C11×C22⋊C8D412yes—
71C4×C8×C11—21no—
72C4×C8×C11C2312yes—
73#66896—22no—
74#66896—22no—
75#66881—24no—
76#66880—24no—
77#66874—24no—
78#66872—22no—
79#66871—22no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)C2312yes—
83C4⋊(C11⋊C8)C2312yes—
84#19390—111nomaximal, Sylow
85C24×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—22no—
88C2×D4×C11SD1614yes—
89C2×D4×C11C2×D412yes—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—82no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C22×Dic11—41no—
98C2×Dic22—22no—
99C2×Dic22—21no—
100C2×Dic22—21no—
101C2×Dic22—41no—
102C2×Dic22—42no—
103C2×Dic22—42no—
104C2×C8×C11—22no—
105C2×C8×C11—84no—
106C2×C8×C11C2×D414yes—
107C11×C4⋊C4—21no—
108C11×C4⋊C4C2×D412yes—
109C11×C22⋊C4—22no—
110C11×C22⋊C4—22no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11#4111yescharacteristic
114C42×C11C2411yescharacteristic
115C22⋊Dic11—41no—
116#4324—48no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—22no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—22no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127C4×Dic11—41no—
128#4318—42no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—42no—
132#3229—111no—
133#3077—111no—
134C2×#461—111no—
135#2972D1111yescharacteristic
136#1679—114no—
137#1671—114no—
138#1570—111no—
139#1546—111no—
140#1542—111no—
141C23×C11—22no—
142C23×C11—24no—
143C23×C11—81no—
144C23×C11—81no—
145C23×C11#12111yescharacteristic
146D4×C11—22no—
147D4×C11—24no—
148D4×C11C2×SD1614yes—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—44no—
153C2×C4×C11—82no—
154C2×C4×C11—81no—
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11C2×SD1612yes—
159C2×C4×C11#13512yes—
160C2×C4×C11C22×D411yescharacteristic
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C11C2×#4111yescharacteristic
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—82no—
167Dic22—42no—
168Dic22—42no—
169Dic22—42no—
170Dic22—82no—
171Dic22—81no—
172C8×C11—24no—
173C8×C11—42no—
174C11⋊C8—42no—
175C11⋊C8—42no—
176C22×SD16—221no—
177#533—111no—
178C2×C4⋊Q8—111no—
179C2×C4×D4C2×D1111yescharacteristic
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—22no—
190C8×D4C2×D1114yes—
191#431C2×D1111yescharacteristic
192#431C2×D1111yescharacteristic
193#428—221no—
194#423—111no—
195C2×C4⋊C8—111no—
196#418—221no—
197C2×#103—221no—
198C2×C22⋊C8—22no—
199#334—114no—
200#333—112no—
201#332—112no—
202#332—114no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—24no—
206C22×C11—42no—
207C22×C11—42no—
208C22×C11—84no—
209C22×C11#46512yes—
210C22×C11C2×#12111yescharacteristic
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—42no—
215C4×C11#46512yes—
216C4×C11C22×SD1611yescharacteristic
217C4×C11C2×#13511yescharacteristic
218C4×C11#57712yes—
219Dic11—81no—
220Dic11—82no—
221Dic11—81no—
222C22×Q8—221no—
223C22×D4D4411yescharacteristic
224C23×C4—21no—
225C2×SD16—224no—
226C2×SD16—444no—
227C2×M16—221no—
228C22×C8—24no—
229C22×C8—221no—
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—21no—
242C4×D4—21no—
243C4×D4D4412yes—
244C4×D4C22×D1112yes—
245#117—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4D4411yescharacteristic
249C2×C22⋊C4—21no—
250C2×C42C22×D1111yescharacteristic
251#107—222no—
252#106—224no—
253#106—222no—
254C4⋊C8—112no—
255C4⋊C8—112no—
256C4⋊C8—221no—
257C4⋊C8—221no—
258C4⋊C8C22⋊D1112yes—
259C4⋊C8C22×D1112yes—
260#103—224no—
261#103—224no—
262#102—222no—
263#102—222no—
264C22⋊C8—21no—
265C22⋊C8—24no—
266C22⋊C8C22⋊D1112yes—
267C4×C8—21no—
268C4×C8C22×D1112yes—
269C2×C11—22no—
270C2×C11—44no—
271C2×C11#304211yescharacteristic
272C2×C11C2×#46511yescharacteristic
273C2×C11#306911yescharacteristic
274C24—21no—
275C2×Q8—222no—
276C2×Q8—221no—
277C2×Q8—221no—
278C2×Q8—441no—
279C2×Q8—442no—
280C2×Q8—442no—
281C2×D4—22no—
282C2×D4—21no—
283C2×D4#431414yes—
284C2×D4C2×D4412yes—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—82no—
289C22×C4—441no—
290C22×C4C2×D4411yescharacteristic
291C22×C4#433911yescharacteristic
292C22×C4C2×C22⋊D1111yescharacteristic
293SD16—448no—
294M16—442no—
295C2×C8—22no—
296C2×C8—84no—
297C2×C8—222no—
298C2×C8—222no—
299C2×C8—442no—
300C2×C8C2×C22⋊D1114yes—
301C4⋊C4—21no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—222no—
305C4⋊C4—221no—
306C4⋊C4—222no—
307C4⋊C4—221no—
308C4⋊C4—441no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C4⋊C4C2×D4412yes—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—441no—
316C42—441no—
317C42C2×D4411yescharacteristic
318C42#433911yescharacteristic
319C42C2×C22⋊D1111yescharacteristic
320C42C23×D1111yescharacteristic
321C11#1939011yescharacteristic, complemented, Sylow
322C23—22no—
323C23—24no—
324C23—81no—
325C23—81no—
326C23#6698311yescharacteristic
327Q8—442no—
328Q8—442no—
329Q8—442no—
330Q8—881no—
331Q8—882no—
332D4—24no—
333D4—22no—
334D4C2×#431414yes—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—44no—
339C2×C4—82no—
340C2×C4—81no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—442no—
344C2×C4—882no—
345C2×C4C2×#431412yes—
346C2×C4#6695712yes—
347C2×C4#6698311yescharacteristic
348C2×C4#6698311yescharacteristic
349C2×C4#6698311yescharacteristic
350C2×C4C22×D4411yescharacteristic
351C2×C4C2×#433911yescharacteristic
352C2×C4C22×C22⋊D1111yescharacteristic
353C8—24no—
354C8—42no—
355C8—442no—
356C8—442no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—42no—
361C22—42no—
362C22—84no—
363C22#1062272712yes—
364C22C2×#6698311yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—42no—
369C4—881no—
370C4—881no—
371C4—882no—
372C4#1062272712yes—
373C4C22×#431411yescharacteristic
374C4C2×#6695711yescharacteristic
375C4#1062336712yes—
376C2—22no—
377C2—44no—
378C2#1307812811yescharacteristic
379C2C2×#1062272711yescharacteristic
380C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2972C2
socleC22×C11C2×#121
prime radicalC22×D4×C11D4
hypercenter#2972D11
hypocenterC11#19390
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2972

Complements

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

NH ≅ G/Ntype
1. #13079762C2semidirect
4. #13068039C2semidirect
5. #13067991C2semidirect
6. #13067387C2semidirect
7. #13067287C2semidirect
8. #13067271C2semidirect
31. #10622294C22semidirect
32. #10622293C22semidirect
33. #10622124C22semidirect
34. #10622120C22semidirect
35. #10622119C22semidirect
36. #10622095C22semidirect
321. C11#19390semidirect

Maximal subgroups

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

subgroupindex
#130797622
#130784132
C2×#106226322
#130680392
#130679912
#130673872
#130672872
#130672712
C11×#29722
#1939011