Finite Group Databasebeta

← #14653219

Subgroups — #14653219

Order 2816.

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

normal subgroups only

This group has 450 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×#10622683C211yesmaximal, characteristic
2#13068753C211yesmaximal, characteristic, complemented
3#13067302C211yesmaximal, characteristic, complemented
4#13067296C211yesmaximal, characteristic, complemented
5#13067284C211yesmaximal, characteristic
6#13066900C211yesmaximal, characteristic, complemented
7C11×#1545C211yesmaximal, characteristic
8C2×C11×#127C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×#66896—22no—
13#10622683—21no—
14#10622683—21no—
15#10622683C414yes—
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19C11×#331—22no—
20#10622196—22no—
21#10622182—22no—
22#10622124—22no—
23#10622119—22no—
24#10622092—21no—
25C8×C11⋊C8—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×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×#4318—21no—
39C22×C11⋊C8D412yes—
40#66922—21no—
41#66922—21no—
42#66922—21no—
43#66922C2×C412yes—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8D412yes—
47C11×C22⋊C8—21no—
48C4×C8×C11—21no—
49#66896—24no—
50#66896—24no—
51C22⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)D412yes—
55C4×C11⋊C8—21no—
56C4×C11⋊C8C2×C412yes—
57C4×C11⋊C8D411yescharacteristic
58C4×C11⋊C8D411yescharacteristic
59#9769—111nomaximal, Sylow
60C24×C11—41no—
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C2×D4×C11—42no—
68C2×D4×C11—42no—
69C2×D4×C11—82no—
70C2×D4×C11—82no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C22×Dic11—41no—
75C2×Dic22—22no—
76C2×Dic22—41no—
77C2×Dic22—82no—
78C11×M16—42no—
79C2×C8×C11—22no—
80C2×C8×C11—41no—
81C42×C11C22×C411yescharacteristic
82C42×C11C2×D411yescharacteristic
83C42×C11C2×D411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C4⋊Dic11—22no—
86C4⋊Dic11—22no—
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89#4318—42no—
90C2×C11⋊C8—22no—
91C2×C11⋊C8—22no—
92C2×C11⋊C8—22no—
93C2×C11⋊C8—41no—
94C2×C11⋊C8C22⋊C412yes—
95C2×C11⋊C8C22⋊C412yes—
96C2×#486—111no—
97#1837—111no—
98#1549—111no—
99#1548—111no—
100#1545—111no—
101#1545D1111yescharacteristic
102#1450—111no—
103C23×C11—42no—
104C23×C11—82no—
105C23×C11—82no—
106C23×C11—82no—
107C23×C11#12411yescharacteristic
108D4×C11—44no—
109D4×C11—82no—
110D4×C11—82no—
111D4×C11—82no—
112D4×C11—82no—
113D4×C11—81no—
114D4×C11—81no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11C2×C22⋊C411yescharacteristic
118C2×C4×C11C4×D411yescharacteristic
119C2×C4×C11C4×D411yescharacteristic
120C2×C4×C11#12111yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12711yescharacteristic
123C2×C4×C11#13512yes—
124C2×C4×C11#13512yes—
125C2×Dic11—42no—
126C2×Dic11—82no—
127Dic22—82no—
128Dic22—82no—
129C8×C11—42no—
130C8×C11—81no—
131C11⋊C8—22no—
132C11⋊C8—22no—
133C11⋊C8—42no—
134C11⋊C8—81no—
135C2×C4⋊Q8—111no—
136C2×#127C2×D1111yescharacteristic
137#486—114no—
138#486—221no—
139#486—221no—
140#431—111no—
141#431C2×D1111yescharacteristic
142#423—111no—
143#423C2×D1111yescharacteristic
144C2×#102—222no—
145C2×C4×C8—111no—
146#341—222no—
147#333—222no—
148#332—222no—
149#331—22no—
150#331—222no—
151#322—221no—
152C82—221no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—82no—
156C22×C11—82no—
157C22×C11—82no—
158C22×C11—164no—
159C22×C11#39011yescharacteristic
160C22×C11#48812yes—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11#41612yes—
164C4×C11#47112yes—
165C4×C11#47212yes—
166C4×C11#49511yescharacteristic
167C4×C11#49511yescharacteristic
168Dic11—82no—
169C22×Q8—221no—
170C22×D4—21no—
171C22×D4—21no—
172C22×D4—21no—
173C2×M16—21no—
174C2×M16—221no—
175C22×C8—112no—
176C4⋊Q8—112no—
177C4⋊Q8—221no—
178C4⋊Q8—221no—
179C4⋊Q8—221no—
180#127—21no—
181#127—21no—
182#127—21no—
183#127C4×D1112yes—
184C2×C4⋊C4—221no—
185C2×C4⋊C4—221no—
186C2×C42C22×D1111yescharacteristic
187C4⋊C8—21no—
188C4⋊C8—21no—
189C4⋊C8—112no—
190C4⋊C8—221no—
191C4⋊C8—221no—
192C4⋊C8C22⋊D1112yes—
193#102—224no—
194#102—224no—
195C22⋊C8—21no—
196C22⋊C8—221no—
197C4×C8—21no—
198C4×C8—112no—
199C4×C8—111no—
200C4×C8—111no—
201C4×C8—221no—
202C2×C11—22no—
203C2×C11—162no—
204C2×C11#195811yescharacteristic
205C2×C11#197711yescharacteristic
206C2×C11#197811yescharacteristic
207C24—41no—
208C2×Q8—222no—
209C2×Q8—441no—
210C2×Q8—882no—
211C2×D4—22no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—41no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—41no—
218C2×D4—41no—
219C2×D4—82no—
220C2×D4—82no—
221C22×C4—441no—
222C22×C4#433911yescharacteristic
223C22×C4D4×D1111yescharacteristic
224C22×C4#434111yescharacteristic
225M16—42no—
226M16—442no—
227C2×C8—22no—
228C2×C8—41no—
229C2×C8—112no—
230C2×C8—112no—
231C2×C8—222no—
232C2×C8—222no—
233C2×C8—222no—
234C2×C8—441no—
235C4⋊C4—222no—
236C4⋊C4—222no—
237C4⋊C4—441no—
238C4⋊C4—441no—
239C42C2×C4×D1111yescharacteristic
240C42D4×D1111yescharacteristic
241C42D4×D1111yescharacteristic
242C42C2×C22⋊D1111yescharacteristic
243C11#976911yescharacteristic, complemented, Sylow
244C23—42no—
245C23—82no—
246C23—82no—
247C23—82no—
248C23#6693811yescharacteristic
249Q8—882no—
250Q8—882no—
251D4—44no—
252D4—82no—
253D4—82no—
254D4—81no—
255D4—81no—
256D4—82no—
257D4—82no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—442no—
261C2×C4—882no—
262C2×C4C22⋊C4×D1111yescharacteristic
263C2×C4(C22⋊D11)⋊C411yescharacteristic
264C2×C4#6693711yescharacteristic
265C2×C4#6696512yes—
266C2×C4#6696912yes—
267C2×C4C4×C22⋊D1111yescharacteristic
268C2×C4#6699211yescharacteristic
269C2×C4#6699311yescharacteristic
270C8—42no—
271C8—81no—
272C8—222no—
273C8—222no—
274C8—442no—
275C8—881no—
276C22—21no—
277C22—21no—
278C22—82no—
279C22—82no—
280C22—82no—
281C22—164no—
282C22#1062238112yes—
283C22#1062257011yescharacteristic
284C4—21no—
285C4—21no—
286C4—882no—
287C4#1062236212yes—
288C4#1062238512yes—
289C4#1062276811yescharacteristic
290C4#1062278111yescharacteristic
291C4#1062281312yes—
292C2—22no—
293C2—162no—
294C2#1306942611yescharacteristic
295C2#1306952211yescharacteristic
296C2#1306952311yescharacteristic
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#9769
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. #13067302C2semidirect
4. #13067296C2semidirect
6. #13066900C2semidirect
243. C11#9769semidirect

Maximal subgroups

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

subgroupindex
C2×#106226832
#130687532
#130673022
#130672962
#130672842
#130669002
C11×#15452
#976911