Finite Group Databasebeta

← #14726259

Subgroups — #14726259

Order 2816.

1210 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1210 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623041C211yesmaximal, characteristic
2#13078556C212yesmaximal, complemented
3#13067652C214yesmaximal, complemented
4#13067618C214yesmaximal, complemented
5#13067144C212yesmaximal, complemented
6#13066946C211yesmaximal, characteristic, complemented
7C11×#2484C211yesmaximal, characteristic, complemented
8C22×#4339—21no—
9C2×C11×#117C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C2×#66983—21no—
12C2×#66983C2212yes—
13#10623041—22no—
14#10623041—24no—
15#10623041C2214yes—
16C2×#66950—22no—
17C2×#66948—22no—
18C11×#400C2212yescomplemented
19C11×#398C2212yescomplemented
20C11×#387—22no—
21C11×#385—21no—
22C11×#381—21no—
23C11×#381C2211yescharacteristic
24#10622820C2212yes—
25#10622616—24no—
26#10622614—22no—
27#10622608—22no—
28#10622581C2214yescomplemented
29#10622580C2214yescomplemented
30#10622166C2214yescomplemented
31#10622089C2218yescomplemented
32C23×C4×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C22×C22⋊D11—22no—
36C2×#4339—24no—
37C2×#4339—24no—
38C2×#4339—48no—
39C22×D44—21no—
40C22×D44—21no—
41C22×D44D412yes—
42C22×C4×D11—22no—
43C22×Dic22—21no—
44C11×#117—22no—
45C11×#117—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4D412yes—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C22⋊C4—21no—
54C2×C11×C22⋊C4—21no—
55C2×C42×C11—21no—
56#66983—24no—
57#66983—22no—
58#66983—22no—
59#66983—24no—
60#66983D414yes—
61#66983C2314yes—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11D412yes—
66C2×#4318—22no—
67#66950—28no—
68#66950—28no—
69#66948—28no—
70#66948—28no—
71C11×#95—22no—
72C11×#95—22no—
73C11×#95—21no—
74C11×#95—22no—
75C11×#95C2312yes—
76C22⋊(C11⋊C8)—22no—
77C22⋊(C11⋊C8)C2314yes—
78#66873—24no—
79#66873—24no—
80#66872—24no—
81#66871—24no—
82#18147—111nomaximal, Sylow
83C24×C11C2×D411yescharacteristic
84C23×D11—22no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—24no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2411yescharacteristic
101C2×C22⋊D11—24no—
102C2×C22⋊D11—24no—
103C2×C22⋊D11—48no—
104C22×Dic11—22no—
105#4339—416no—
106#4339—48no—
107#4339—48no—
108C2×D44—24no—
109C2×D44—24no—
110C2×D44—22no—
111C2×D44—44no—
112C2×D44—44no—
113C2×D44—82no—
114C2×D44C2×D414yes—
115C2×C4×D11—28no—
116C2×C4×D11—48no—
117C2×Dic22—24no—
118C2×Dic22—44no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—44no—
124C11×C22⋊C4—42no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C42×C11—42no—
128(C2×D11)⋊C4—28no—
129(C2×D11)⋊C4—24no—
130(C2×D11)⋊C4—24no—
131C4⋊Dic11—24no—
132C4⋊Dic11—22no—
133C4⋊Dic11C2×D414yes—
134#4318—44no—
135C2×C11⋊C8—24no—
136C2×#537—111no—
137#3094—112no—
138#2484D1111yescharacteristic, complemented
139#1616—114no—
140#1610—114no—
141#1510—112no—
142#1463—111no—
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—41no—
146C23×C11#12011yescharacteristic
147C23×C11#12011yescharacteristic
148C23×C11C22×D411yescharacteristic
149C22×D11—24no—
150C22×D11—44no—
151C22×D11—44no—
152C22×D11—44no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—24no—
158C2×C4×C11—22no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—81no—
172C2×C4×C11#12012yes—
173C2×C4×C11AGL(1,ℤ/8)14yes—
174C2×C4×C11C22×D412yes—
175C22⋊D11—48no—
176C22⋊D11—48no—
177C2×Dic11—24no—
178C2×Dic11—44no—
179D44—44no—
180D44—48no—
181D44—82no—
182D44—84no—
183C4×D11—416no—
184Dic22—48no—
185C11⋊C8—44no—
186C22×#41—221no—
187#537—114no—
188#537—224no—
189#537—222no—
190C2×C22⋊Q8—222no—
191C2×#121—112no—
192C2×#121—222no—
193C2×#121—221no—
194C2×#117C2×D1111yescharacteristic
195C22×C4⋊C4C2×D1111yescharacteristic
196#482—224no—
197#481—114no—
198#480—114no—
199#428—222no—
200#418—222no—
201#407—112no—
202#400C2×D1112yescomplemented
203#398C2×D1112yescomplemented
204#387—22no—
205#385—21no—
206#381—21no—
207#381C2×D1111yescharacteristic
208#327—118no—
209#324—114no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—44no—
218C22×C11#45812yes—
219C22×C11C2×#12011yescharacteristic
220C22×C11C2×AGL(1,ℤ/8)12yes—
221C2×D11—44no—
222C2×D11—44no—
223C2×D11—44no—
224C2×D11—88no—
225C4×C11—24no—
226C4×C11—22no—
227C4×C11—22no—
228C4×C11—42no—
229C4×C11—82no—
230C4×C11—81no—
231C4×C11—81no—
232Dic11—44no—
233C2×#41—224no—
234C2×#41—224no—
235C2×#41—448no—
236C22×Q8—221no—
237C22×D4—112no—
238C22×D4—221no—
239C22×D4—221no—
240C22×D4—222no—
241C23×C4—222no—
242C23×C4C22⋊D1111yescharacteristic
243C23×C4C22⋊D1111yescharacteristic
244C23×C4C22×D1111yescharacteristic
245C2×M16—222no—
246C22⋊Q8—228no—
247C22⋊Q8—228no—
248#121—114no—
249#121—114no—
250#121—228no—
251#121—228no—
252#121—224no—
253#121—222no—
254#121—222no—
255#121—224no—
256#117—22no—
257#117—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—112no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4C22⋊D1112yes—
264C2×C4⋊C4C22×D1111yescharacteristic
265C2×C4⋊C4C22×D1111yescharacteristic
266C2×C4⋊C4C22×D1112yes—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—222no—
270C2×C22⋊C4—222no—
271C2×C42—21no—
272#107—224no—
273#106—224no—
274#102—224no—
275#102—224no—
276C22⋊C8—114no—
277C22⋊C8—222no—
278#95—22no—
279#95—22no—
280#95—21no—
281#95—22no—
282#95C22×D1112yes—
283C2×C11—22no—
284C2×C11—22no—
285C2×C11—41no—
286C2×C11#300311yescharacteristic
287C2×C11#302011yescharacteristic
288C2×C11C2×#45811yescharacteristic
289D11—84no—
290C24—222no—
291C24C2×C22⋊D1111yescharacteristic
292#41—4416no—
293#41—448no—
294#41—448no—
295C2×Q8—224no—
296C2×Q8—444no—
297C2×D4—114no—
298C2×D4—224no—
299C2×D4—224no—
300C2×D4—224no—
301C2×D4—224no—
302C2×D4—222no—
303C2×D4—444no—
304C2×D4—444no—
305C2×D4—448no—
306C2×D4—882no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—24no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—228no—
318C22×C4—222no—
319C22×C4—448no—
320C22×C4D4×D1112yes—
321C22×C4D4×D1112yes—
322C22×C4C2×C22⋊D1112yes—
323C22×C4C2×C22⋊D1112yes—
324C22×C4C2×C22⋊D1111yescharacteristic
325C22×C4C23×D1111yescharacteristic
326M16—444no—
327C2×C8—224no—
328C4⋊C4—24no—
329C4⋊C4—24no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—44no—
333C4⋊C4—114no—
334C4⋊C4—224no—
335C4⋊C4—222no—
336C22⋊C4—42no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—228no—
340C22⋊C4—224no—
341C22⋊C4—224no—
342C42—42no—
343C11#1814711yescharacteristic, complemented, Sylow
344C23—22no—
345C23—22no—
346C23—41no—
347C23—224no—
348C23—444no—
349C23—444no—
350C23—444no—
351C23#6699011yescharacteristic
352C23#6699011yescharacteristic
353C23C22×C22⋊D1111yescharacteristic
354Q8—448no—
355D4—444no—
356D4—448no—
357D4—448no—
358D4—448no—
359D4—882no—
360D4—884no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—24no—
366C2×C4—22no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—81no—
380C2×C4—224no—
381C2×C4—4416no—
382C2×C4—444no—
383C2×C4#6699012yes—
384C2×C4#6700214yes—
385C2×C4C2×D4×D1112yes—
386C8—444no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—44no—
395C22—444no—
396C22—444no—
397C22—444no—
398C22—888no—
399C22#1062266612yes—
400C22C2×#6699011yescharacteristic
401C22C2×#6700212yes—
402C4—24no—
403C4—22no—
404C4—22no—
405C4—42no—
406C4—82no—
407C4—81no—
408C4—81no—
409C4—444no—
410C2—22no—
411C2—22no—
412C2—41no—
413C2—884no—
414C2#1307784211yescharacteristic
415C2#1307797911yescharacteristic
416C2C2×#1062266611yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2484C2
socleC22×C11C2×#120
prime radicalC2×#10623041C2
hypercenter#2484D11
hypocenterC11#18147
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
2. #13078556C2semidirect
3. #13067652C2semidirect
4. #13067618C2semidirect
5. #13067144C2semidirect
6. #13066946C2semidirect
7. C11×#2484C2semidirect
18. C11×#400C22semidirect
19. C11×#398C22semidirect
28. #10622581C22semidirect
29. #10622580C22semidirect
30. #10622166C22semidirect
31. #10622089C22semidirect
138. #2484D11semidirect
202. #400C2×D11semidirect
203. #398C2×D11semidirect
343. C11#18147semidirect

Maximal subgroups

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

subgroupindex
C2×#106230412
#130785562
#130676522
#130676182
#130671442
#130669462
C11×#24842
#1814711