Finite Group Databasebeta

← #14739049

Subgroups — #14739049

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079559C211yesmaximal, characteristic
2#13078421C211yesmaximal, characteristic, complemented
3C2×#10622640C211yesmaximal, characteristic
4#13068032C214yesmaximal, complemented
5#13067964C214yesmaximal, complemented
6#13067387C211yesmaximal, characteristic, complemented
7#13067283C211yesmaximal, characteristic
8#13067271C211yesmaximal, characteristic, complemented
9C11×#2982C211yesmaximal, characteristic, complemented
10C2×C4×Q8×C11C2211yescharacteristic
11C22×#4325—21no—
12C2×#66927C2211yescharacteristic
13#10623001C2211yescharacteristic
14C8×Q8×C11—22no—
15C8×Q8×C11C2214yescomplemented
16C11×#431—22no—
17C11×#431C2211yescharacteristic
18C11×#431C2211yescharacteristic
19#10622838—21no—
20#10622640—22no—
21#10622640C2214yes—
22#10622635—22no—
23#10622634C2212yescomplemented
24#10622633C2212yescomplemented
25C2×#66873—21no—
26#10622577—21no—
27#10622537C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29#10622461—22no—
30#10622344—22no—
31#10622307C2212yes—
32#10622306C2212yes—
33#10622123C2214yes—
34#10622120C2212yescomplemented
35#10622119C2212yescomplemented
36#10622095C2214yescomplemented
37C22×Q8×C11D411yescharacteristic
38C22×D44—21no—
39C22×D44—21no—
40C22×D44—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11D412yes—
44C4×Q8×C11C2312yes—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C42×C11—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4325—24no—
50C2×#4325—44no—
51#66979—21no—
52#66977—21no—
53#66977—21no—
54C2×#4318—21no—
55C22×C11⋊C8—21no—
56C2×#4314—24no—
57#66927—21no—
58#66927—21no—
59#66927—21no—
60#66927C2312yes—
61#66923—21no—
62#66922C2311yescharacteristic
63#66922C2311yescharacteristic
64C4×Dic22—21no—
65C4×Dic22—21no—
66C11×C4⋊C8—24no—
67C11×C4⋊C8D412yes—
68C11×C4⋊C8C2312yes—
69C11×C22⋊C8—21no—
70C11×C22⋊C8D412yes—
71C4×C8×C11—24no—
72C4×C8×C11—21no—
73C4×C8×C11C2312yes—
74#66899—22no—
75#66899—22no—
76#66885—24no—
77#66873—24no—
78#66872—22no—
79#66871—22no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)C2312yes—
83C4⋊(C11⋊C8)C2312yes—
84#19396—111nomaximal, Sylow
85C23×D11—41no—
86C2×Q8×C11—21no—
87C2×Q8×C11—22no—
88C2×Q8×C11SD1614yescomplemented
89C2×Q8×C11C2×D412yes—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C2×D44—22no—
96C2×D44—22no—
97C2×D44—22no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44—42no—
102C2×D44—42no—
103C2×D44—82no—
104C2×D44—82no—
105C2×Dic22—21no—
106C2×Dic22—21no—
107C2×C8×C11—22no—
108C2×C8×C11C2×D414yes—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4C2×D412yes—
113C42×C11—22no—
114C42×C11—22no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118C42×C11C2411yescharacteristic
119C22⋊Dic11—41no—
120#4325—48no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
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#4314—84no—
133#3208—111no—
134#3078—111no—
135C2×#460—111no—
136#2982D1111yescharacteristic, complemented
137#1678—114no—
138#1666—114no—
139#1570—111no—
140#1545—111no—
141#1542—111no—
142C23×C11#12111yescharacteristic
143C22×D11—42no—
144C22×D11—82no—
145C22×D11—82no—
146C22×D11—82no—
147Q8×C11—22no—
148Q8×C11—24no—
149Q8×C11C2×SD1614yes—
150C2×C4×C11—22no—
151C2×C4×C11—24no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—41no—
155C2×C4×C11—81no—
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11C2×SD1612yes—
160C2×C4×C11#13512yes—
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C2×#4111yescharacteristic
164C2×Dic11—41no—
165C2×Dic11—41no—
166D44—42no—
167D44—42no—
168D44—44no—
169D44—82no—
170D44—82no—
171D44—82no—
172D44—82no—
173Dic22—42no—
174Dic22—81no—
175C8×C11—24no—
176C8×C11—42no—
177C11⋊C8—42no—
178C11⋊C8—42no—
179C22×SD16—221no—
180#533—111no—
181C2×#127—111no—
182C2×C4×Q8C2×D1111yescharacteristic
183#492—112no—
184#486—112no—
185#479—222no—
186#477—112no—
187#475—112no—
188#460—114no—
189#460—222no—
190#460—222no—
191#450—222no—
192C8×Q8—22no—
193C8×Q8C2×D1114yescomplemented
194#431—22no—
195#431C2×D1111yescharacteristic
196#431C2×D1111yescharacteristic
197#428—221no—
198#423—111no—
199C2×C4⋊C8—111no—
200#419—221no—
201C2×#102—221no—
202#334—114no—
203#333—112no—
204#332—112no—
205#331—114no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11#46512yes—
209C22×C11C2×#12111yescharacteristic
210C2×D11—82no—
211C2×D11—82no—
212C2×D11—82no—
213C2×D11—164no—
214C4×C11—21no—
215C4×C11—24no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—42no—
219C4×C11#46512yes—
220C4×C11C22×SD1611yescharacteristic
221C4×C11C2×#13511yescharacteristic
222C4×C11#57712yes—
223Dic11—81no—
224Dic11—81no—
225C22×Q8D4411yescharacteristic
226C22×D4—221no—
227C22×D4—221no—
228C22×D4—221no—
229C2×SD16—224no—
230C2×SD16—224no—
231C2×SD16—444no—
232C2×M16—221no—
233C22×C8—221no—
234C4⋊Q8—111no—
235C4⋊Q8—111no—
236#127—112no—
237#127—221no—
238#127—221no—
239#127—221no—
240#125—221no—
241C22⋊Q8—221no—
242C22⋊Q8—221no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—221no—
246C4×Q8—221no—
247C4×Q8D4412yes—
248C4×Q8C22×D1112yes—
249#117—221no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4D4411yescharacteristic
252C2×C42—21no—
253C2×C42C22×D1111yescharacteristic
254#107—222no—
255#106—222no—
256C4⋊C8—24no—
257C4⋊C8—112no—
258C4⋊C8—112no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261C4⋊C8C22⋊D1112yes—
262C4⋊C8C22×D1112yes—
263#103—222no—
264#103—222no—
265#102—224no—
266#102—224no—
267C22⋊C8—21no—
268C22⋊C8C22⋊D1112yes—
269C4×C8—24no—
270C4×C8—21no—
271C4×C8C22×D1112yes—
272C2×C11—22no—
273C2×C11#304311yescharacteristic
274C2×C11C2×#46511yescharacteristic
275C2×C11#306811yescharacteristic
276D11—162no—
277C24—441no—
278C2×Q8—22no—
279C2×Q8—21no—
280C2×Q8—221no—
281C2×Q8—221no—
282C2×Q8#431414yescomplemented
283C2×Q8C2×D4412yes—
284C2×D4—222no—
285C2×D4—222no—
286C2×D4—222no—
287C2×D4—442no—
288C2×D4—442no—
289C2×D4—441no—
290C2×D4—441no—
291C2×D4—441no—
292C2×D4—882no—
293C2×D4—882no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4C2×D4411yescharacteristic
297C22×C4#433911yescharacteristic
298C22×C4C2×C22⋊D1111yescharacteristic
299SD16—448no—
300SD16—884no—
301M16—442no—
302C2×C8—22no—
303C2×C8—222no—
304C2×C8—222no—
305C2×C8—442no—
306C2×C8C2×C22⋊D1114yes—
307C4⋊C4—22no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—221no—
311C4⋊C4—221no—
312C4⋊C4—221no—
313C4⋊C4—221no—
314C4⋊C4—441no—
315C4⋊C4—441no—
316C4⋊C4C2×D4412yes—
317C22⋊C4—441no—
318C42—22no—
319C42—22no—
320C42—441no—
321C42C2×D4411yescharacteristic
322C42#433911yescharacteristic
323C42C2×C22⋊D1111yescharacteristic
324C42C23×D1111yescharacteristic
325C11#1939611yescharacteristic, complemented, Sylow
326C23—442no—
327C23—882no—
328C23—882no—
329C23—882no—
330C23#6698311yescharacteristic
331Q8—24no—
332Q8—22no—
333Q8—442no—
334Q8—881no—
335Q8C2×#431414yes—
336D4—442no—
337D4—442no—
338D4—444no—
339D4—882no—
340D4—882no—
341D4—882no—
342D4—882no—
343C2×C4—24no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4C2×#431412yes—
352C2×C4#6695712yes—
353C2×C4#6698311yescharacteristic
354C2×C4#6698311yescharacteristic
355C2×C4#6698311yescharacteristic
356C2×C4C22×D4411yescharacteristic
357C2×C4C2×#433911yescharacteristic
358C2×C4C22×C22⋊D1111yescharacteristic
359C8—24no—
360C8—42no—
361C8—442no—
362C8—442no—
363C22—21no—
364C22—21no—
365C22—882no—
366C22—882no—
367C22—882no—
368C22—1764no—
369C22#1062272712yes—
370C22C2×#6698311yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—24no—
375C4—42no—
376C4—881no—
377C4—881no—
378C4#1062272712yes—
379C4C22×#431411yescharacteristic
380C4C2×#6695711yescharacteristic
381C4#1062336812yes—
382C2—22no—
383C2—1762no—
384C2#1307813711yescharacteristic
385C2C2×#1062272711yescharacteristic
386C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2982C2
socleC22×C11C2×#121
prime radicalC2×#66927C22
hypercenter#2982D11
hypocenterC11#19396
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. #13078421C2semidirect
4. #13068032C2semidirect
5. #13067964C2semidirect
6. #13067387C2semidirect
8. #13067271C2semidirect
9. C11×#2982C2semidirect
15. C8×Q8×C11C22semidirect
23. #10622634C22semidirect
24. #10622633C22semidirect
34. #10622120C22semidirect
35. #10622119C22semidirect
36. #10622095C22semidirect
88. C2×Q8×C11SD16semidirect
136. #2982D11semidirect
193. C8×Q8C2×D11semidirect
282. C2×Q8#4314semidirect
325. C11#19396semidirect

Maximal subgroups

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

subgroupindex
#130795592
#130784212
C2×#106226402
#130680322
#130679642
#130673872
#130672832
#130672712
C11×#29822
#1939611