Finite Group Databasebeta

← #14650484

Subgroups — #14650484

Order 2816.

454 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 113 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#13079564C211yesmaximal, characteristic
2#13071365C211yesmaximal, characteristic
3#13069596C211yesmaximal, characteristic
4#13067181C211yesmaximal, characteristic
5#13066476C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic
7C11×#1548C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12#10622843—22no—
13#10622841—22no—
14#10622705C412yescomplemented
15#10622703—22no—
16#10622694C412yescomplemented
17#10622598—21no—
18#10622594—22no—
19C4⋊C4×Dic11—21no—
20#10622549C2211yescharacteristic
21#10622545C2211yescharacteristic
22#10622538C2211yescharacteristic
23C11×#333—22no—
24#10622193—21no—
25#10622193—21no—
26#10622105—22no—
27C22×Q8×C11D412yes—
28C2×C11×M16—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8C2×C412yes—
32C11×C4⋊Q8D412yes—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C42×C11C2311yescharacteristic
36C2×#4326—24no—
37#66979—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—22no—
40#66977—21no—
41#66977—21no—
42C2×C4×Dic11—22no—
43C2×C4×Dic11D411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45#66923—21no—
46#66922C2×C411yescharacteristic
47#66922C2×C411yescharacteristic
48C4×Dic22—21no—
49C4×Dic22—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C22⋊C8—21no—
54C4×C8×C11—21no—
55#66899—24no—
56C11⋊#95—22no—
57C11⋊#95—22no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95D412yes—
62C22⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4×C11⋊C8C2×C412yes—
65#9297—111nomaximal, Sylow
66C2×Q8×C11—22no—
67C2×Q8×C11—82no—
68C2×Q8×C11C22⋊C414yes—
69C22×C4×C11—22no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—22no—
76C2×Dic22—21no—
77C2×Dic22—21no—
78C11×M16—41no—
79C11×M16—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C42×C11C22×C411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11#4111yescharacteristic
89C42×C11#4111yescharacteristic
90C22⋊Dic11—41no—
91#4326—84no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—82no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—41no—
105C4×Dic11—82no—
106C4×Dic11Q1612yescomplemented
107C2×C11⋊C8—22no—
108#3209—111no—
109#2331—111no—
110#1995—111no—
111#1548D1111yescharacteristic
112#1518—111no—
113#1286—111no—
114#1274—111no—
115C23×C11#12011yescharacteristic
116Q8×C11—44no—
117Q8×C11—82no—
118C2×C4×C11—24no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11C2×C22⋊C411yescharacteristic
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11C4×D411yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12311yescharacteristic
129C2×C4×C11C2×Q1611yescharacteristic
130C2×C4×C11#13511yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×Dic11—22no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—42no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—42no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—42no—
144Dic22—42no—
145Dic22—81no—
146C8×C11—81no—
147C8×C11—81no—
148C11⋊C8—42no—
149#533—111no—
150C2×C4⋊Q8C2×D1111yescharacteristic
151#494—112no—
152#487—112no—
153#462—222no—
154#451—222no—
155#431—111no—
156#431C2×D1111yescharacteristic
157#423C2×D1111yescharacteristic
158#391—222no—
159#389—221no—
160#387—222no—
161#382—111no—
162C4×C4⋊C4—221no—
163#376—111no—
164#339—221no—
165#339—221no—
166#333—22no—
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—44no—
178C4×C11C4×Q1611yescharacteristic
179C4×C11#44111yescharacteristic
180C4×C11#46211yescharacteristic
181C4×C11#46411yescharacteristic
182Dic11—42no—
183Dic11—82no—
184Dic11—81no—
185Dic11—81no—
186Dic11—81no—
187C22×Q8D4412yes—
188C2×Q16—224no—
189C2×M16—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—111no—
193C4⋊Q8—111no—
194C4⋊Q8C4×D1112yes—
195C4⋊Q8C22⋊D1112yes—
196#125—221no—
197C22⋊Q8—221no—
198C22⋊Q8—221no—
199C4×Q8—221no—
200C4×Q8—221no—
201#117—221no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—222no—
206C2×C42—111no—
207C2×C42—111no—
208C2×C42—222no—
209C2×C42C22×D1111yescharacteristic
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—221no—
214#103—224no—
215C22⋊C8—21no—
216C22⋊C8—221no—
217C4×C8—21no—
218C4×C8—112no—
219#95—112no—
220#95—222no—
221#95—222no—
222#95—221no—
223#95—221no—
224#95—221no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11#187811yescharacteristic
228C2×C11#190511yescharacteristic
229C2×C11#191111yescharacteristic
230C2×Q8—22no—
231C2×Q8—82no—
232C2×Q8—221no—
233C2×Q8—221no—
234C2×Q8(C2×D11)⋊C414yes—
235C22×C4—22no—
236C22×C4—221no—
237C22×C4—222no—
238C22×C4—221no—
239C22×C4C2×D4411yescharacteristic
240C22×C4D4×D1111yescharacteristic
241C22×C4D4×D1111yescharacteristic
242Q16—884no—
243M16—41no—
244M16—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—222no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—882no—
261C22⋊C4—441no—
262C42—112no—
263C42—221no—
264C42—221no—
265C42—221no—
266C42—441no—
267C42—882no—
268C42C2×C4×D1111yescharacteristic
269C42#434111yescharacteristic
270C42#434111yescharacteristic
271C42C2×C22⋊D1111yescharacteristic
272C11#929711yescharacteristic, complemented, Sylow
273C23#6693511yescharacteristic
274Q8—44no—
275Q8—82no—
276Q8—442no—
277Q8—881no—
278C2×C4—24no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—222no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—442no—
287C2×C4—441no—
288C2×C4—442no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—442no—
294C2×C4(C22⋊D11)⋊C411yescharacteristic
295C2×C4(C22⋊D11)⋊C411yescharacteristic
296C2×C4#6693911yescharacteristic
297C2×C4#6696811yescharacteristic
298C2×C4#6696911yescharacteristic
299C2×C4Q16×D1111yescharacteristic
300C2×C4#6697111yescharacteristic
301C2×C4C2×(C2×D11)⋊C411yescharacteristic
302C2×C4#6699211yescharacteristic
303C2×C4#6699211yescharacteristic
304C8—81no—
305C8—81no—
306C8—442no—
307C22—21no—
308C22—21no—
309C22#1062242111yescharacteristic
310C22#1062242311yescharacteristic
311C22#1062257111yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—44no—
317C4—442no—
318C4—882no—
319C4—881no—
320C4—881no—
321C4—881no—
322C4#1062240211yescharacteristic
323C4#1062240311yescharacteristic
324C4#1062277911yescharacteristic
325C4#1062279511yescharacteristic
326C2—21no—
327C2—21no—
328C2#1306895511yescharacteristic
329C2#1306910811yescharacteristic
330C2#1306914611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1548C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#1548D11
hypocenterC11#9297
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
14. #10622705C4semidirect
16. #10622694C4semidirect
106. C4×Dic11Q16semidirect
272. C11#9297semidirect

Maximal subgroups

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

subgroupindex
#130795642
#130713652
#130695962
#130671812
#130664762
#130664442
C11×#15482
#929711