Finite Group Databasebeta

← #14808238

Subgroups — #14808238

Order 2816.

1072 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079169C211yesmaximal, characteristic, complemented
2#13078438C211yesmaximal, characteristic, complemented
3#13074561C211yesmaximal, characteristic, complemented
4#13069823C214yesmaximal, complemented
5#13069598C211yesmaximal, characteristic, complemented
6#13069457C211yesmaximal, characteristic, complemented
7#13068826C214yesmaximal, complemented
8#13068426C211yesmaximal, characteristic, complemented
9C11×#3508C211yesmaximal, characteristic
10C11×#559—22no—
11C11×#550—22no—
12C11×#546—24no—
13C11×#540—22no—
14C11×#535C2212yes—
15C11×#533C2211yescharacteristic
16C11×#532—22no—
17C2×C11×#127C2211yescharacteristic
18C11×#518C2212yes—
19C4×C11×#41C2211yescharacteristic
20C2×#66923C2211yescharacteristic
21C2×#66901C2212yes—
22#10622845C2212yes—
23#10622835—24no—
24#10622834C2214yes—
25C2×#66897C2214yes—
26#10622693—22no—
27#10622677—22no—
28#10622635—22no—
29#10622622—22no—
30#10622608C2212yes—
31#10622608C2214yes—
32#10622545C2211yescharacteristic
33#10622537C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35#10622170C2212yes—
36#10622170C2214yes—
37C2×C11×#41—24no—
38C2×C11×#41C2311yescharacteristic
39C22×D4×C11D414yes—
40C22×D4×C11C2312yes—
41C11×C4⋊Q8D412yes—
42C11×#127—22no—
43C11×#127—21no—
44C11×#127—21no—
45C11×#127—22no—
46C11×#125D412yes—
47C11×#124—24no—
48C11×#124—22no—
49C11×#123—28no—
50C11×C22⋊Q8—22no—
51C11×#121—24no—
52C11×#121—28no—
53C11×#121—24no—
54C11×#120—24no—
55C4×Q8×C11—22no—
56C4×Q8×C11D412yes—
57C4×D4×C11—24no—
58C4×D4×C11—22no—
59C4×D4×C11—24no—
60C4×D4×C11—24no—
61C4×D4×C11D412yes—
62C11×#117—21no—
63C11×#117C2311yescharacteristic
64C11×#117C2312yes—
65C2×C11×C22⋊C4—24no—
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11—28no—
69C2×C4⋊Dic11C2312yes—
70C2×Dic11⋊C4—22no—
71C2×C4×Dic11C2312yes—
72C2×#4318C2312yes—
73C2×#4318C2312yes—
74#66923—22no—
75#66923—21no—
76#66923—21no—
77#66901—24no—
78#66899—22no—
79#66897—28no—
80#66896—22no—
81C11⋊#95—22no—
82#66872—22no—
83#66872—24no—
84#66871—22no—
85#66871—24no—
86C4⋊(C11⋊C8)—22no—
87#66867—21no—
88C4×C11⋊C8—21no—
89#25690—111nomaximal, Sylow
90C24×C11C2×D414yes—
91C11×#41—22no—
92C11×#41—22no—
93C11×#41—88no—
94C2×Q8×C11—22no—
95C2×Q8×C11C2×D411yescharacteristic
96C2×D4×C11—21no—
97C2×D4×C11—28no—
98C2×D4×C11—24no—
99C2×D4×C11—24no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—24no—
103C2×D4×C11—24no—
104C2×D4×C11—84no—
105C2×D4×C11C2×D411yescharacteristic
106C22×C4×C11—28no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—22no—
112C22×Dic11—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4C2×D412yes—
117C11×C4⋊C4C2×D414yes—
118C11×C22⋊C4—28no—
119C11×C22⋊C4—28no—
120C11×C22⋊C4—21no—
121C11×C22⋊C4—22no—
122C11×C22⋊C4—22no—
123C42×C11—22no—
124C42×C11—21no—
125C42×C11—22no—
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D412yes—
129C22⋊Dic11—88no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132Dic11⋊C4—42no—
133Dic11⋊C4—42no—
134C4×Dic11—22no—
135C4×Dic11—22no—
136#4318—24no—
137#4318—22no—
138#4318#4114yescomplemented
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141#3508D1111yescharacteristic
142#3166—111no—
143#3080—111no—
144#2641—111no—
145#2037—114no—
146#1995—111no—
147#1965—111no—
148#1856—114no—
149#1759—111no—
150C23×C11—24no—
151C23×C11—21no—
152C23×C11—28no—
153C23×C11—48no—
154C23×C11C22×D411yescharacteristic
155Q8×C11—21no—
156Q8×C11—21no—
157Q8×C11—44no—
158D4×C11—21no—
159D4×C11—21no—
160D4×C11—48no—
161D4×C11—42no—
162D4×C11—42no—
163D4×C11—42no—
164D4×C11—44no—
165D4×C11—84no—
166D4×C11—88no—
167C2×C4×C11—21no—
168C2×C4×C11—22no—
169C2×C4×C11—24no—
170C2×C4×C11—42no—
171C2×C4×C11—44no—
172C2×C4×C11—42no—
173C2×C4×C11—88no—
174C2×C4×C11#12012yes—
175C2×C4×C11#12012yes—
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C2×#4112yes—
179C2×C4×C112−1+412yes—
180C2×Dic11—44no—
181C2×Dic11—44no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C11⋊C8—24no—
185C11⋊C8—42no—
186#559—22no—
187#550—22no—
188#546—24no—
189#540—22no—
190#535C2×D1112yes—
191#533C2×D1111yescharacteristic
192#532—22no—
193C2×#127C2×D1111yescharacteristic
194C2×#125—111no—
195#518C2×D1112yes—
196C4×#41C2×D1111yescharacteristic
197#501—222no—
198#499—222no—
199#479—222no—
200#478—222no—
201#428—112no—
202#428—114no—
203#423—111no—
204C2×#104—112no—
205#417—112no—
206C2×#100—114no—
207C4×M16—111no—
208#394—224no—
209#390—114no—
210#376—111no—
211#339—112no—
212#339—114no—
213C22×C11—22no—
214C22×C11—41no—
215C22×C11—44no—
216C22×C11—42no—
217C22×C11—48no—
218C22×C11—88no—
219C22×C11C2×#12011yescharacteristic
220C22×C11#54712yes—
221C4×C11—22no—
222C4×C11—22no—
223C4×C11—41no—
224C4×C11—42no—
225C4×C11—44no—
226C4×C11#53211yescharacteristic
227C4×C11#53611yescharacteristic
228C4×C11#54812yes—
229Dic11—82no—
230Dic11—82no—
231C2×#41—24no—
232C2×#41C22×D1111yescharacteristic
233C22×D4C22⋊D1114yes—
234C22×D4C22×D1112yes—
235C2×M16—112no—
236C2×M16—112no—
237C4⋊Q8C22⋊D1112yes—
238#127—22no—
239#127—21no—
240#127—21no—
241#127—22no—
242#125—222no—
243#125—221no—
244#125—221no—
245#125C22⋊D1112yes—
246#124—24no—
247#124—22no—
248#123—28no—
249C22⋊Q8—22no—
250#121—24no—
251#121—28no—
252#121—24no—
253#120—24no—
254C4×Q8—22no—
255C4×Q8C22⋊D1112yes—
256C4×D4—24no—
257C4×D4—22no—
258C4×D4—24no—
259C4×D4—24no—
260C4×D4C22⋊D1112yes—
261#117—21no—
262#117C22×D1111yescharacteristic
263#117C22×D1112yes—
264C2×C4⋊C4—112no—
265C2×C4⋊C4—222no—
266C2×C22⋊C4—24no—
267C2×C22⋊C4—228no—
268C2×C42—21no—
269C2×C42—112no—
270C2×C42C22×D1111yescharacteristic
271#107—222no—
272#107—224no—
273#106—222no—
274#106—224no—
275C4⋊C8—222no—
276#104—224no—
277#103—222no—
278#102—222no—
279#100—228no—
280#97—221no—
281C4×C8—221no—
282#95—222no—
283C2×C11—22no—
284C2×C11—81no—
285C2×C11—84no—
286C2×C11#243211yescharacteristic
287C2×C11#301912yes—
288C24C2×C22⋊D1114yes—
289#41—22no—
290#41—22no—
291#41—88no—
292C2×Q8—22no—
293C2×Q8C2×C22⋊D1111yescharacteristic
294C2×D4—21no—
295C2×D4—28no—
296C2×D4—24no—
297C2×D4—24no—
298C2×D4—24no—
299C2×D4—24no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—84no—
303C2×D4C2×C22⋊D1111yescharacteristic
304C22×C4—28no—
305C22×C4—22no—
306C22×C4—21no—
307C22×C4—222no—
308C22×C4—222no—
309C22×C4C2×C22⋊D1112yes—
310C22×C4C23×D1111yescharacteristic
311M16—114no—
312M16—222no—
313M16—224no—
314C2×C8—222no—
315C2×C8—222no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—24no—
319C4⋊C4—222no—
320C4⋊C4—222no—
321C4⋊C4—442no—
322C4⋊C4—442no—
323C4⋊C4C2×C22⋊D1112yes—
324C4⋊C4C2×C22⋊D1114yes—
325C22⋊C4—28no—
326C22⋊C4—28no—
327C22⋊C4—21no—
328C22⋊C4—22no—
329C22⋊C4—22no—
330C22⋊C4—888no—
331C42—22no—
332C42—21no—
333C42—22no—
334C42—222no—
335C42—222no—
336C42C2×C22⋊D1111yescharacteristic
337C42C2×C22⋊D1111yescharacteristic
338C42C2×C22⋊D1112yes—
339C11#2569011yescharacteristic, complemented, Sylow
340C23—24no—
341C23—21no—
342C23—28no—
343C23—48no—
344C23C22×C22⋊D1111yescharacteristic
345Q8—21no—
346Q8—21no—
347Q8—44no—
348D4—21no—
349D4—21no—
350D4—48no—
351D4—42no—
352D4—42no—
353D4—44no—
354D4—42no—
355D4—84no—
356D4—88no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—24no—
360C2×C4—42no—
361C2×C4—44no—
362C2×C4—42no—
363C2×C4—88no—
364C2×C4—444no—
365C2×C4—444no—
366C2×C4—442no—
367C2×C4—442no—
368C2×C4#6700612yes—
369C2×C4#6700612yes—
370C2×C4#41×D1112yes—
371C2×C4#6704312yes—
372C2×C4C22×C22⋊D1111yescharacteristic
373C2×C4C22×C22⋊D1111yescharacteristic
374C8—224no—
375C8—442no—
376C22—22no—
377C22—41no—
378C22—44no—
379C22—42no—
380C22—48no—
381C22—88no—
382C22#1062335512yes—
383C22C2×#6700611yescharacteristic
384C4—22no—
385C4—22no—
386C4—41no—
387C4—42no—
388C4—44no—
389C4—882no—
390C4—882no—
391C4#1062335611yescharacteristic
392C4#1062336212yes—
393C4#1062336311yescharacteristic
394C2—22no—
395C2—84no—
396C2—81no—
397C2#1307224011yescharacteristic
398C2#1307797312yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3508C2
socleC22×C11C2×#120
hypercenter#3508D11
hypocenterC11#25690
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #13079169C2semidirect
2. #13078438C2semidirect
3. #13074561C2semidirect
4. #13069823C2semidirect
5. #13069598C2semidirect
6. #13069457C2semidirect
7. #13068826C2semidirect
8. #13068426C2semidirect
138. #4318#41semidirect
339. C11#25690semidirect

Maximal subgroups

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

subgroupindex
#130791692
#130784382
#130745612
#130698232
#130695982
#130694572
#130688262
#130684262
C11×#35082
#2569011