Finite Group Databasebeta

← #14650489

Subgroups — #14650489

Order 2816.

454 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079561C211yesmaximal, characteristic
2#13071364C211yesmaximal, characteristic
3#13067298C211yesmaximal, characteristic
4#13067180C211yesmaximal, characteristic
5#13066476C211yesmaximal, characteristic
6#13066445C211yesmaximal, characteristic
7C11×#1995C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#376C2211yescharacteristic
12#10622706C412yescomplemented
13#10622705C412yescomplemented
14#10622663—22no—
15#10622644—22no—
16#10622549C2211yescharacteristic
17C4×C4⋊Dic11—21no—
18#10622541—21no—
19#10622538C2211yescharacteristic
20#10622538C2211yescharacteristic
21#10622267—22no—
22#10622259—22no—
23C11×#339—21no—
24C11×#339—21no—
25#10622176—22no—
26#10622119—22no—
27C22×Dic22D412yes—
28C2×C11×M16—21no—
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×#125—21no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C11×#117—21no—
37C2×C42×C11D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11C2311yescharacteristic
40C2×#4326—24no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×Dic11⋊C4—22no—
45C2×C4×Dic11—22no—
46#66922—21no—
47#66922—21no—
48#66922C2×C412yes—
49#66922D412yes—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11⋊#95—22no—
55C11⋊#95—22no—
56C11⋊#95—21no—
57C11⋊#95D412yes—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66874—24no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4×C11⋊C8—21no—
64C4×C11⋊C8C2×C412yes—
65#9297—111nomaximal, Sylow
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—22no—
74C22×Dic11—22no—
75C2×Dic22—22no—
76C2×Dic22—82no—
77C2×Dic22C22⋊C414yes—
78C11×M16—41no—
79C11×M16—41no—
80C2×C8×C11—41no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C22⋊C4—41no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—41no—
92C42×C11Q1612yescomplemented
93C42×C11C22×C411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11#4111yescharacteristic
96C42×C11#4111yescharacteristic
97#4326—84no—
98C4⋊Dic11—22no—
99C4⋊Dic11—22no—
100C4⋊Dic11—22no—
101C4⋊Dic11—22no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104Dic11⋊C4—82no—
105C4×Dic11—82no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—41no—
108#3209—111no—
109#2331—111no—
110#1995D1111yescharacteristic
111#1548—111no—
112#1518—111no—
113#1286—111no—
114#1274—111no—
115C23×C11#12011yescharacteristic
116Q8×C11—42no—
117Q8×C11—81no—
118C2×C4×C11—22no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11C2×C22⋊C411yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12311yescharacteristic
134C2×C4×C11C2×Q1611yescharacteristic
135C2×C4×C11#13511yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C2×Dic11—24no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144Dic22—44no—
145Dic22—82no—
146C8×C11—81no—
147C11⋊C8—42no—
148C11⋊C8—81no—
149#533C2×D1111yescharacteristic
150C2×C4⋊Q8—111no—
151#494—112no—
152#487—112no—
153#462—222no—
154#451—222no—
155#431—111no—
156#431—111no—
157#423C2×D1111yescharacteristic
158#391—222no—
159#389—221no—
160#387—222no—
161#382—111no—
162C4×C4⋊C4—221no—
163#376C2×D1111yescharacteristic
164#339—21no—
165#339—21no—
166#333—222no—
167#328—222no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11#38611yescharacteristic
171C22×C11#45111yescharacteristic
172C22×C11#45211yescharacteristic
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—42no—
178C4×C11—81no—
179C4×C11—81no—
180C4×C11—81no—
181C4×C11C4×Q1611yescharacteristic
182C4×C11#44111yescharacteristic
183C4×C11#46211yescharacteristic
184C4×C11#46411yescharacteristic
185Dic11—44no—
186Dic11—82no—
187C22×Q8—112no—
188C2×Q16—224no—
189C2×M16—21no—
190C4⋊Q8—112no—
191C4⋊Q8—112no—
192C4⋊Q8—221no—
193C4⋊Q8—221no—
194C4⋊Q8C4×D1111yescharacteristic
195C4⋊Q8C4×D1111yescharacteristic
196#125—21no—
197C22⋊Q8—21no—
198C22⋊Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201#117—21no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—222no—
206C2×C42—222no—
207C2×C42C22⋊D1111yescharacteristic
208C2×C42C22⋊D1111yescharacteristic
209C2×C42C22×D1111yescharacteristic
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—221no—
213C4⋊C8—221no—
214#103—224no—
215C22⋊C8—221no—
216C22⋊C8—221no—
217C4×C8—112no—
218C4×C8—221no—
219#95—21no—
220#95—21no—
221#95—112no—
222#95—222no—
223#95—222no—
224#95—221no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11#187811yescharacteristic
228C2×C11#190511yescharacteristic
229C2×C11#191111yescharacteristic
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—114no—
233C2×Q8—222no—
234C2×Q8—882no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—222no—
238C22×C4—222no—
239C22×C4D4×D1111yescharacteristic
240C22×C4D4×D1111yescharacteristic
241C22×C4C2×C22⋊D1111yescharacteristic
242Q16—884no—
243M16—41no—
244M16—41no—
245C2×C8—41no—
246C2×C8—222no—
247C2×C8—441no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—222no—
255C4⋊C4—222no—
256C4⋊C4—222no—
257C4⋊C4—222no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—882no—
261C22⋊C4—41no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—41no—
266C42—882no—
267C42#432612yescomplemented
268C42C2×C4×D1111yescharacteristic
269C42#433911yescharacteristic
270C42D4×D1111yescharacteristic
271C42#434111yescharacteristic
272C11#929711yescharacteristic, complemented, Sylow
273C23#6699011yescharacteristic
274Q8—42no—
275Q8—81no—
276Q8—444no—
277Q8—882no—
278C2×C4—22no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—224no—
289C2×C4—442no—
290C2×C4—442no—
291C2×C4—442no—
292C2×C4—442no—
293C2×C4—442no—
294C2×C4C22⋊C4×D1111yescharacteristic
295C2×C4(C22⋊D11)⋊C411yescharacteristic
296C2×C4#6693611yescharacteristic
297C2×C4#6693711yescharacteristic
298C2×C4C4×C22⋊D1111yescharacteristic
299C2×C4#6699111yescharacteristic
300C2×C4#6699511yescharacteristic
301C2×C4C2×#432611yescharacteristic
302C2×C4#6700311yescharacteristic
303C2×C4#6700411yescharacteristic
304C8—81no—
305C8—442no—
306C8—881no—
307C22—21no—
308C22—21no—
309C22#1062256911yescharacteristic
310C22#1062266011yescharacteristic
311C22#1062266311yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—42no—
317C4—81no—
318C4—81no—
319C4—81no—
320C4—444no—
321C4—882no—
322C4C4×#432611yescharacteristic
323C4#1062264311yescharacteristic
324C4#1062266711yescharacteristic
325C4#1062270311yescharacteristic
326C2—21no—
327C2—21no—
328C2#1306896011yescharacteristic
329C2#1306910711yescharacteristic
330C2#1306914511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1995C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#1995D11
hypocenterC11#9297
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
12. #10622706C4semidirect
13. #10622705C4semidirect
92. C42×C11Q16semidirect
267. C42#4326semidirect
272. C11#9297semidirect

Maximal subgroups

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

subgroupindex
#130795612
#130713642
#130672982
#130671802
#130664762
#130664452
C11×#19952
#929711