Finite Group Databasebeta

← #14653221

Subgroups — #14653221

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×#10622701C211yesmaximal, characteristic
2#13068753C211yesmaximal, characteristic, complemented
3#13067297C211yesmaximal, characteristic, complemented
4#13067285C211yesmaximal, characteristic
5#13067283C211yesmaximal, characteristic
6#13066900C211yesmaximal, characteristic, complemented
7C11×#1549C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66927C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12#10622701—21no—
13#10622701—21no—
14#10622701C414yes—
15C2×#66873—22no—
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19C11×#332—22no—
20#10622196—22no—
21#10622184—22no—
22#10622123—22no—
23#10622123—22no—
24#10622092—21no—
25C8×C11⋊C8—21no—
26C22×Q8×C11—21no—
27C22×D44—21no—
28C22×D44—21no—
29C22×D44—21no—
30C2×C11×M16—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8C2×C412yes—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38C2×#4318—21no—
39C22×C11⋊C8D412yes—
40#66927—21no—
41#66927—21no—
42#66927—21no—
43#66927C2×C412yes—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8D412yes—
47C11×C22⋊C8—21no—
48C4×C8×C11—21no—
49C22⋊(C11⋊C8)—21no—
50#66873—24no—
51#66873—24no—
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
60C23×D11—41no—
61C2×Q8×C11—22no—
62C2×Q8×C11—41no—
63C2×Q8×C11—82no—
64C22×C4×C11—41no—
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C2×D44—22no—
69C2×D44—22no—
70C2×D44—22no—
71C2×D44—41no—
72C2×D44—41no—
73C2×D44—41no—
74C2×D44—42no—
75C2×D44—42no—
76C2×D44—82no—
77C2×D44—82no—
78C11×M16—42no—
79C2×C8×C11—22no—
80C2×C8×C11—41no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C42×C11C22×C411yescharacteristic
86C42×C11C2×D411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
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#1549D1111yescharacteristic, complemented
99#1548—111no—
100#1545—111no—
101#1545—111no—
102#1450—111no—
103C23×C11#12411yescharacteristic
104C22×D11—42no—
105C22×D11—82no—
106C22×D11—82no—
107C22×D11—82no—
108Q8×C11—82no—
109Q8×C11—82no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—42no—
113C2×C4×C11—82no—
114C2×C4×C11C2×C22⋊C411yescharacteristic
115C2×C4×C11C4×D411yescharacteristic
116C2×C4×C11C4×D411yescharacteristic
117C2×C4×C11#12111yescharacteristic
118C2×C4×C11#12111yescharacteristic
119C2×C4×C11#12711yescharacteristic
120C2×C4×C11#13512yes—
121C2×C4×C11#13512yes—
122D44—44no—
123D44—82no—
124D44—82no—
125D44—82no—
126D44—82no—
127D44—81no—
128D44—81no—
129C8×C11—42no—
130C8×C11—81no—
131C11⋊C8—22no—
132C11⋊C8—22no—
133C11⋊C8—42no—
134C11⋊C8—81no—
135C2×C4⋊Q8C2×D1111yescharacteristic
136C2×#127—111no—
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—22no—
149#331—222no—
150#331—222no—
151#322—221no—
152C82—221no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11#39011yescharacteristic
156C22×C11#48812yes—
157C2×D11—82no—
158C2×D11—82no—
159C2×D11—82no—
160C2×D11—164no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—82no—
164C4×C11#41612yes—
165C4×C11#47112yes—
166C4×C11#47212yes—
167C4×C11#49511yescharacteristic
168C4×C11#49511yescharacteristic
169C22×Q8—21no—
170C22×D4—221no—
171C22×D4—221no—
172C22×D4—221no—
173C2×M16—21no—
174C2×M16—221no—
175C22×C8—112no—
176C4⋊Q8—21no—
177C4⋊Q8—21no—
178C4⋊Q8—21no—
179C4⋊Q8C4×D1112yes—
180#127—112no—
181#127—221no—
182#127—221no—
183#127—221no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
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#195811yescharacteristic
204C2×C11#197711yescharacteristic
205C2×C11#197811yescharacteristic
206D11—162no—
207C24—441no—
208C2×Q8—22no—
209C2×Q8—41no—
210C2×Q8—82no—
211C2×D4—222no—
212C2×D4—222no—
213C2×D4—222no—
214C2×D4—441no—
215C2×D4—442no—
216C2×D4—442no—
217C2×D4—441no—
218C2×D4—441no—
219C2×D4—882no—
220C2×D4—882no—
221C22×C4—41no—
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—22no—
236C4⋊C4—22no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C42C2×C4×D1111yescharacteristic
240C42D4×D1111yescharacteristic
241C42D4×D1111yescharacteristic
242C42C2×C22⋊D1111yescharacteristic
243C11#976911yescharacteristic, complemented, Sylow
244C23—442no—
245C23—882no—
246C23—882no—
247C23—882no—
248C23#6693811yescharacteristic
249Q8—82no—
250Q8—82no—
251D4—444no—
252D4—882no—
253D4—882no—
254D4—881no—
255D4—881no—
256D4—882no—
257D4—882no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—42no—
261C2×C4—82no—
262C2×C4C22⋊C4×D1111yescharacteristic
263C2×C4(C22⋊D11)⋊C411yescharacteristic
264C2×C4#6693711yescharacteristic
265C2×C4#6696912yes—
266C2×C4#6697212yes—
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—882no—
279C22—882no—
280C22—882no—
281C22—1764no—
282C22#1062241312yes—
283C22#1062257011yescharacteristic
284C4—21no—
285C4—21no—
286C4—82no—
287C4#1062236712yes—
288C4#1062241712yes—
289C4#1062278111yescharacteristic
290C4#1062280411yescharacteristic
291C4#1062281212yes—
292C2—22no—
293C2—1762no—
294C2#1306942411yescharacteristic
295C2#1306952011yescharacteristic
296C2#1306952511yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1549C2
socleC22×C11#390
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1549D11
hypocenterC11#9769
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
2. #13068753C2semidirect
3. #13067297C2semidirect
6. #13066900C2semidirect
7. C11×#1549C2semidirect
98. #1549D11semidirect
243. C11#9769semidirect

Maximal subgroups

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

subgroupindex
C2×#106227012
#130687532
#130672972
#130672852
#130672832
#130669002
C11×#15492
#976911