Finite Group Databasebeta

← #14650494

Subgroups — #14650494

Order 2816.

442 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 107 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
1#13079769C211yesmaximal, characteristic
2#13071362C211yesmaximal, characteristic
3#13069596C211yesmaximal, characteristic
4#13067302C211yesmaximal, characteristic
5#13067179C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic
7C11×#1286C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#382C2211yescharacteristic
13C4⋊C4×Dic11—21no—
14#10622586—21no—
15#10622545C2211yescharacteristic
16#10622538C2211yescharacteristic
17#10622463—22no—
18#10622335—22no—
19#10622295C412yescomplemented
20#10622294C412yescomplemented
21#10622266—22no—
22#10622259—22no—
23#10622193—21no—
24#10622193—21no—
25#10622124—22no—
26#10622090—22no—
27C22×Dic22—21no—
28C2×C11×M16—21no—
29C2×C11×C4⋊C4—21no—
30C2×C42×C11C2311yescharacteristic
31#66979—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11D412yes—
34#66977—21no—
35#66977—21no—
36C2×Dic11⋊C4—22no—
37C2×C4×Dic11—22no—
38C2×C4×Dic11D411yescharacteristic
39C2×C4×Dic11D411yescharacteristic
40#66923—21no—
41#66922—21no—
42#66922—21no—
43#66922C2×C411yescharacteristic
44#66922C2×C411yescharacteristic
45#66922C2×C412yes—
46#66922D412yes—
47C4×Dic22—21no—
48C4×Dic22—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C22⋊C8—21no—
53C4×C8×C11C2×C412yes—
54C11×#95—21no—
55C11×#95D412yes—
56C11⋊#95—22no—
57C11⋊#95—22no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C22⋊(C11⋊C8)—21no—
61#66882—24no—
62#66880—24no—
63C4⋊(C11⋊C8)—21no—
64C4×C11⋊C8—21no—
65#9298—111nomaximal, Sylow
66C22×C4×C11—22no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—22no—
72C22×Dic11—21no—
73C2×Dic22—21no—
74C2×Dic22—22no—
75C2×Dic22—21no—
76C2×Dic22—22no—
77C2×Dic22—82no—
78C11×M16—41no—
79C11×M16—41no—
80C2×C8×C11—22no—
81C2×C8×C11—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C42×C11C22×C411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C42×C11#4111yescharacteristic
87C42×C11#4111yescharacteristic
88C22⋊Dic11—41no—
89C4⋊Dic11—21no—
90C4⋊Dic11—22no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—22no—
95C4⋊Dic11—22no—
96C4⋊Dic11C22⋊C414yes—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99Dic11⋊C4—82no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—41no—
104C4×Dic11—82no—
105C4×Dic11Q1612yes—
106C2×C11⋊C8—41no—
107#3230—111no—
108#2331—111no—
109#1995—111no—
110#1549—111no—
111#1518—111no—
112#1286D1111yescharacteristic
113#1274—111no—
114C23×C11#12011yescharacteristic
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11C2×C22⋊C411yescharacteristic
121C2×C4×C11C4×D411yescharacteristic
122C2×C4×C11C4×D411yescharacteristic
123C2×C4×C11#12111yescharacteristic
124C2×C4×C11#12111yescharacteristic
125C2×C4×C11#12311yescharacteristic
126C2×C4×C11C2×Q1611yescharacteristic
127C2×C4×C11#13511yescharacteristic
128C2×C4×C11#13711yescharacteristic
129C2×C4×C11#13711yescharacteristic
130C2×Dic11—24no—
131C2×Dic11—22no—
132C2×Dic11—41no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141Dic22—42no—
142Dic22—82no—
143Dic22—82no—
144Dic22—81no—
145C8×C11—42no—
146C8×C11—81no—
147C11⋊C8—81no—
148#533—111no—
149C2×C4⋊Q8—111no—
150#500—112no—
151#487—112no—
152#484—222no—
153#477—222no—
154#431—111no—
155#431C2×D1111yescharacteristic
156#423C2×D1111yescharacteristic
157#391—222no—
158#389—221no—
159#387—222no—
160#382C2×D1111yescharacteristic
161C4×C4⋊C4—221no—
162#376—111no—
163#339—221no—
164#339—221no—
165#332—222no—
166#328—222no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11#38611yescharacteristic
170C22×C11#45111yescharacteristic
171C22×C11#45211yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—82no—
177C4×C11C4×Q1611yescharacteristic
178C4×C11#44111yescharacteristic
179C4×C11#46211yescharacteristic
180C4×C11#46411yescharacteristic
181Dic11—42no—
182Dic11—44no—
183Dic11—81no—
184Dic11—81no—
185Dic11—81no—
186C22×Q8—221no—
187C2×M16—21no—
188C4⋊Q8—112no—
189C4⋊Q8—111no—
190C4⋊Q8—111no—
191C4⋊Q8—112no—
192C4⋊Q8—221no—
193C4⋊Q8—221no—
194#125—221no—
195C22⋊Q8—221no—
196C22⋊Q8—221no—
197C4×Q8—221no—
198C4×Q8—221no—
199#117—221no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—112no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—222no—
204C2×C42—111no—
205C2×C42—111no—
206C2×C42—222no—
207C2×C42C22×D1111yescharacteristic
208#107—224no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—221no—
213#103—224no—
214C22⋊C8—21no—
215C22⋊C8—221no—
216C4×C8—221no—
217C4×C8C4×D1112yes—
218#95—21no—
219#95—222no—
220#95—222no—
221#95—221no—
222#95—221no—
223#95D4412yes—
224C2×C11—21no—
225C2×C11—21no—
226C2×C11#187811yescharacteristic
227C2×C11#190411yescharacteristic
228C2×C11#191211yescharacteristic
229C2×Q8—222no—
230C2×Q8—222no—
231C2×Q8—221no—
232C2×Q8—221no—
233C2×Q8—882no—
234C22×C4—22no—
235C22×C4—221no—
236C22×C4—222no—
237C22×C4—221no—
238C22×C4C2×D4411yescharacteristic
239C22×C4D4×D1111yescharacteristic
240C22×C4D4×D1111yescharacteristic
241M16—41no—
242M16—41no—
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—441no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—114no—
249C4⋊C4—222no—
250C4⋊C4—222no—
251C4⋊C4—222no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—882no—
259C22⋊C4—441no—
260C42—112no—
261C42—221no—
262C42—221no—
263C42—221no—
264C42—441no—
265C42—882no—
266C42C2×C4×D1111yescharacteristic
267C42#433911yescharacteristic
268C42D4×D1111yescharacteristic
269C42#434311yescharacteristic
270C11#929811yescharacteristic, complemented, Sylow
271C23#6693511yescharacteristic
272Q8—442no—
273Q8—882no—
274Q8—882no—
275Q8—881no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—224no—
282C2×C4—222no—
283C2×C4—441no—
284C2×C4—442no—
285C2×C4—442no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4C4×D4411yescharacteristic
293C2×C4C22⋊C4×D1111yescharacteristic
294C2×C4#6693711yescharacteristic
295C2×C4#6694611yescharacteristic
296C2×C4#6694711yescharacteristic
297C2×C4#6694811yescharacteristic
298C2×C4#6696511yescharacteristic
299C2×C4#6696811yescharacteristic
300C2×C4#6696811yescharacteristic
301C2×C4Q16×D1111yescharacteristic
302C8—42no—
303C8—81no—
304C8—881no—
305C22—21no—
306C22—21no—
307C22#1062227811yescharacteristic
308C22#1062239611yescharacteristic
309C22#1062242111yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—82no—
315C4—442no—
316C4—444no—
317C4—881no—
318C4—881no—
319C4—881no—
320C4#1062238011yescharacteristic
321C4#1062240611yescharacteristic
322C4#1062246611yescharacteristic
323C4#1062248611yescharacteristic
324C2—21no—
325C2—21no—
326C2#1306895811yescharacteristic
327C2#1306910211yescharacteristic
328C2#1306915211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#1286D11
hypocenterC11#9298
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
19. #10622295C4semidirect
20. #10622294C4semidirect
270. C11#9298semidirect

Maximal subgroups

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

subgroupindex
#130797692
#130713622
#130695962
#130673022
#130671792
#130664442
C11×#12862
#929811