Finite Group Databasebeta

← #14653263

Subgroups — #14653263

Order 2816.

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

normal subgroups only

This group has 506 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
1C2×#10622689C211yesmaximal, characteristic
2#13068753C211yesmaximal, characteristic, complemented
3#13067289C211yesmaximal, characteristic, complemented
4#13067287C211yesmaximal, characteristic, complemented
5#13067284C211yesmaximal, characteristic
6#13066909C211yesmaximal, characteristic, complemented
7C11×#1545C211yesmaximal, characteristic
8C2×C11×#127C2211yescharacteristic
9C22×#4324—22no—
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622689—21no—
14#10622689—21no—
15#10622689C414yes—
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19C11×#331—22no—
20#10622196—22no—
21#10622182—22no—
22#10622124—22no—
23#10622120—22no—
24#10622093—21no—
25#10622092—21no—
26C22×D4×C11—21no—
27C22×D4×C11—21no—
28C22×D4×C11—21no—
29C22×Dic22—21no—
30C2×C11×M16—21no—
31C11×#127—21no—
32C11×#127—21no—
33C11×#127—21no—
34C11×#127C2×C412yes—
35C2×C42×C11C2311yescharacteristic
36C2×#4324—24no—
37C2×#4324—24no—
38C2×#4324—44no—
39C2×#4324—44no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×#4318—21no—
43C22×C11⋊C8D412yes—
44#66922—21no—
45#66922—21no—
46#66922—21no—
47#66922C2×C412yes—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8D412yes—
51C11×C22⋊C8—21no—
52C4×C8×C11—21no—
53C22⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)D412yes—
57C4×C11⋊C8—21no—
58C4×C11⋊C8C2×C412yes—
59C4×C11⋊C8D411yescharacteristic
60C4×C11⋊C8D411yescharacteristic
61#9777—111nomaximal, Sylow
62C24×C11—41no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—22no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—42no—
70C2×D4×C11—42no—
71C2×D4×C11—82no—
72C2×D4×C11—82no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C22×Dic11—41no—
77C2×Dic22—22no—
78C2×Dic22—41no—
79C2×Dic22—42no—
80C2×Dic22—42no—
81C11×M16—42no—
82C2×C8×C11—22no—
83C2×C8×C11—41no—
84C42×C11C22×C411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C42×C11C2×D411yescharacteristic
87C42×C11C2×D411yescharacteristic
88#4324—48no—
89#4324—48no—
90C4⋊Dic11—22no—
91C4⋊Dic11—22no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94#4318—42no—
95C2×C11⋊C8—22no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—22no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8C22⋊C412yes—
100C2×C11⋊C8C22⋊C412yes—
101C2×#492—111no—
102#1837—111no—
103#1546—111no—
104#1546—111no—
105#1545—111no—
106#1545D1111yescharacteristic
107#1452—111no—
108C23×C11—42no—
109C23×C11—82no—
110C23×C11—82no—
111C23×C11—82no—
112C23×C11#12411yescharacteristic
113D4×C11—44no—
114D4×C11—82no—
115D4×C11—82no—
116D4×C11—82no—
117D4×C11—82no—
118D4×C11—81no—
119D4×C11—81no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11C2×C22⋊C411yescharacteristic
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12711yescharacteristic
128C2×C4×C11AGL(1,ℤ/8)12yes—
129C2×C4×C11AGL(1,ℤ/8)12yes—
130C2×Dic11—42no—
131C2×Dic11—82no—
132Dic22—44no—
133Dic22—81no—
134Dic22—81no—
135C8×C11—42no—
136C8×C11—81no—
137C11⋊C8—22no—
138C11⋊C8—22no—
139C11⋊C8—42no—
140C11⋊C8—81no—
141C22×SD16—222no—
142C2×C4⋊Q8—111no—
143C2×#127C2×D1111yescharacteristic
144#492—114no—
145#492—221no—
146#492—221no—
147#431—111no—
148#431C2×D1111yescharacteristic
149#423—111no—
150#423C2×D1111yescharacteristic
151C2×C4×C8—111no—
152#341—222no—
153#332—222no—
154#332—222no—
155#331—22no—
156#331—222no—
157#322—221no—
158#322—221no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—82no—
162C22×C11—82no—
163C22×C11—82no—
164C22×C11—164no—
165C22×C11#39011yescharacteristic
166C22×C11#49012yes—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11#41812yes—
170C4×C11#47112yes—
171C4×C11#47112yes—
172C4×C11#49611yescharacteristic
173C4×C11#49611yescharacteristic
174Dic11—82no—
175C22×Q8—221no—
176C22×D4—21no—
177C22×D4—21no—
178C22×D4—21no—
179C2×SD16—224no—
180C2×SD16—224no—
181C2×SD16—444no—
182C2×SD16—444no—
183C2×M16—21no—
184C2×M16—221no—
185C22×C8—112no—
186C4⋊Q8—112no—
187C4⋊Q8—221no—
188C4⋊Q8—221no—
189C4⋊Q8—221no—
190#127—21no—
191#127—21no—
192#127—21no—
193#127C4×D1112yes—
194C2×C4⋊C4—221no—
195C2×C4⋊C4—221no—
196C2×C42C22×D1111yescharacteristic
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—112no—
200C4⋊C8—221no—
201C4⋊C8—221no—
202C4⋊C8C22⋊D1112yes—
203C22⋊C8—21no—
204C22⋊C8—221no—
205C4×C8—21no—
206C4×C8—112no—
207C4×C8—111no—
208C4×C8—111no—
209C4×C8—221no—
210C2×C11—22no—
211C2×C11—162no—
212C2×C11#196111yescharacteristic
213C2×C11#197711yescharacteristic
214C2×C11#197711yescharacteristic
215C24—41no—
216C2×Q8—222no—
217C2×Q8—441no—
218C2×Q8—442no—
219C2×Q8—442no—
220C2×D4—22no—
221C2×D4—22no—
222C2×D4—22no—
223C2×D4—41no—
224C2×D4—42no—
225C2×D4—42no—
226C2×D4—41no—
227C2×D4—41no—
228C2×D4—82no—
229C2×D4—82no—
230C22×C4—441no—
231C22×C4#433911yescharacteristic
232C22×C4D4×D1111yescharacteristic
233C22×C4#434111yescharacteristic
234SD16—448no—
235SD16—448no—
236M16—42no—
237M16—442no—
238C2×C8—22no—
239C2×C8—41no—
240C2×C8—112no—
241C2×C8—112no—
242C2×C8—222no—
243C2×C8—222no—
244C2×C8—222no—
245C2×C8—441no—
246C4⋊C4—222no—
247C4⋊C4—222no—
248C4⋊C4—441no—
249C4⋊C4—441no—
250C42C2×C4×D1111yescharacteristic
251C42D4×D1111yescharacteristic
252C42D4×D1111yescharacteristic
253C42C2×C22⋊D1111yescharacteristic
254C11#977711yescharacteristic, complemented, Sylow
255C23—42no—
256C23—82no—
257C23—82no—
258C23—82no—
259C23#6693811yescharacteristic
260Q8—444no—
261Q8—881no—
262Q8—881no—
263D4—44no—
264D4—82no—
265D4—82no—
266D4—81no—
267D4—81no—
268D4—82no—
269D4—82no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—442no—
273C2×C4—882no—
274C2×C4C22⋊C4×D1111yescharacteristic
275C2×C4(C22⋊D11)⋊C411yescharacteristic
276C2×C4#6693711yescharacteristic
277C2×C4#6696412yes—
278C2×C4#6696712yes—
279C2×C4C4×C22⋊D1111yescharacteristic
280C2×C4#6699211yescharacteristic
281C2×C4#6699311yescharacteristic
282C8—42no—
283C8—81no—
284C8—222no—
285C8—222no—
286C8—442no—
287C8—881no—
288C22—21no—
289C22—21no—
290C22—82no—
291C22—82no—
292C22—82no—
293C22—164no—
294C22#1062237712yes—
295C22#1062257011yescharacteristic
296C4—21no—
297C4—21no—
298C4—882no—
299C4#1062236112yes—
300C4#1062238312yes—
301C4#1062276711yescharacteristic
302C4#1062278911yescharacteristic
303C4#1062281312yes—
304C2—22no—
305C2—162no—
306C2#1306943811yescharacteristic
307C2#1306951611yescharacteristic
308C2#1306952211yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1545C2
socleC22×C11#390
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenter#1545D11
hypocenterC11#9777
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1545

Complements

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

NH ≅ G/Ntype
2. #13068753C2semidirect
3. #13067289C2semidirect
4. #13067287C2semidirect
6. #13066909C2semidirect
254. C11#9777semidirect

Maximal subgroups

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

subgroupindex
C2×#106226892
#130687532
#130672892
#130672872
#130672842
#130669092
C11×#15452
#977711