Finite Group Databasebeta

← #14658776

Subgroups — #14658776

Order 2816.

334 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 91 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#13069449C211yesmaximal, characteristic
2#13068735C211yesmaximal, characteristic, complemented
3#13067391C211yesmaximal, characteristic, complemented
4#13067386C211yesmaximal, characteristic, complemented
5#13067015C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic, complemented
7C11×#1480C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×#66901—22no—
12#10622545C2211yescharacteristic
13#10622538C2211yescharacteristic
14#10622537C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C11×D4⋊C8—22no—
17#10622188—22no—
18D4⋊(C11⋊C8)—22no—
19#10622118—22no—
20#10622096—22no—
21C2×C11×#41—21no—
22C22×C8×C11—21no—
23C11×C4⋊Q8Q811yescharacteristic
24C11×#127Q811yescharacteristic
25C11×#124—21no—
26C11×#121—21no—
27C11×#121—21no—
28C4×D4×C11—21no—
29C4×D4×C11—21no—
30C2×C42×C11C2311yescharacteristic
31C2×C4×Dic11D412yes—
32C2×#4318—21no—
33C22×C11⋊C8—21no—
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C4⋊C8—21no—
37C11×C22⋊C8—21no—
38C4×C8×C11D412yes—
39#66901—44no—
40C11⋊#95—21no—
41C11⋊#95—21no—
42C22⋊(C11⋊C8)—21no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48C4×C11⋊C8D412yes—
49#10665—111nomaximal, Sylow
50C11×#41—42no—
51C11×#41—42no—
52C2×Q8×C11—21no—
53C2×D4×C11—21no—
54C2×D4×C11—21no—
55C2×D4×C11—21no—
56C2×D4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11#4111yescharacteristic
60C22×C4×C11#4111yescharacteristic
61C22×Dic11—22no—
62C2×C8×C11—22no—
63C2×C8×C11—41no—
64C2×C8×C11—42no—
65C11×C4⋊C4—21no—
66C11×C4⋊C4—21no—
67C11×C22⋊C4—41no—
68C11×C22⋊C4—41no—
69C42×C11C2×D411yescharacteristic
70C42×C11C2×D411yescharacteristic
71C42×C11C2×Q811yescharacteristic
72C42×C11#4111yescharacteristic
73C4×Dic11—22no—
74C4×Dic11—22no—
75#4318—42no—
76C2×C11⋊C8—22no—
77C2×C11⋊C8—41no—
78C2×C11⋊C8—41no—
79C2×C11⋊C8—42no—
80#1963—111no—
81#1832—111no—
82#1571—111no—
83#1570—111no—
84#1480—111no—
85#1480D1111yescharacteristic
86#1274—111no—
87C23×C11—41no—
88C23×C11#12311yescharacteristic
89Q8×C11—42no—
90D4×C11—42no—
91D4×C11—42no—
92D4×C11—42no—
93D4×C11—82no—
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11—41no—
97C2×C4×C11—81no—
98C2×C4×C11—81no—
99C2×C4×C11C22⋊Q811yescharacteristic
100C2×C4×C11C22⋊Q811yescharacteristic
101C2×C4×C11C22⋊Q811yescharacteristic
102C2×C4×C11#12311yescharacteristic
103C2×C4×C11#12311yescharacteristic
104C2×C4×C11#12711yescharacteristic
105C2×C4×C11#13512yes—
106C2×C4×C11AGL(1,ℤ/8)12yes—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110C8×C11—42no—
111C8×C11—81no—
112C11⋊C8—42no—
113C11⋊C8—81no—
114C11⋊C8—81no—
115#532C2×D1111yescharacteristic
116#431—111no—
117#431C2×D1111yescharacteristic
118#423—111no—
119C2×C4⋊C8—111no—
120C2×C4⋊C8C2×D1111yescharacteristic
121C2×#104—222no—
122#376—111no—
123#336—222no—
124#335—222no—
125#334—222no—
126D4⋊C8—22no—
127D4⋊C8—222no—
128C22×C11—21no—
129C22×C11—21no—
130C22×C11—81no—
131C22×C11—81no—
132C22×C11—81no—
133C22×C11#39911yescharacteristic
134C22×C11#48212yes—
135C4×C11—21no—
136C4×C11—21no—
137C4×C11—21no—
138C4×C11—21no—
139C4×C11—81no—
140C4×C11#47812yes—
141C4×C11#49511yescharacteristic
142C4×C11#49611yescharacteristic
143Dic11—82no—
144C2×#41—21no—
145C2×M16—221no—
146C22×C8—21no—
147C22×C8—221no—
148C4⋊Q8Dic2211yescharacteristic
149#127Dic2211yescharacteristic
150#124—21no—
151#121—21no—
152#121—21no—
153C4×D4—21no—
154C4×D4—21no—
155C2×C42—112no—
156C2×C42C22×D1111yescharacteristic
157C4⋊C8—21no—
158C4⋊C8—21no—
159C4⋊C8—21no—
160C4⋊C8—221no—
161C4⋊C8—221no—
162C4⋊C8—221no—
163C4⋊C8—221no—
164C4⋊C8—221no—
165#104—444no—
166C22⋊C8—21no—
167C22⋊C8—221no—
168C4×C8—112no—
169C4×C8C22⋊D1112yes—
170#95—221no—
171#95—221no—
172C2×C11—22no—
173C2×C11—161no—
174C2×C11#209211yescharacteristic
175C2×C11#209811yescharacteristic
176C2×C11#209811yescharacteristic
177#41—42no—
178#41—42no—
179C2×Q8—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—41no—
184C22×C4—41no—
185C22×C4—222no—
186C22×C4#433911yescharacteristic
187C22×C4D4×D1111yescharacteristic
188C22×C4#434111yescharacteristic
189M16—442no—
190C2×C8—22no—
191C2×C8—42no—
192C2×C8—41no—
193C2×C8—222no—
194C2×C8—442no—
195C2×C8—441no—
196C2×C8—441no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C22⋊C4—41no—
200C22⋊C4—41no—
201C42—222no—
202C42—222no—
203C42C2×Dic2211yescharacteristic
204C42D4×D1111yescharacteristic
205C42#434111yescharacteristic
206C42C2×C22⋊D1111yescharacteristic
207C11#1066511yescharacteristic, complemented, Sylow
208C23—41no—
209C23#6693611yescharacteristic
210Q8—42no—
211D4—42no—
212D4—42no—
213D4—42no—
214D4—82no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—442no—
221C2×C4—442no—
222C2×C4—442no—
223C2×C4#6693111yescharacteristic
224C2×C4#6693111yescharacteristic
225C2×C4#6693611yescharacteristic
226C2×C4#6696512yes—
227C2×C4#6696712yes—
228C2×C4#6697711yescharacteristic
229C2×C4#6698811yescharacteristic
230C2×C4#6699311yescharacteristic
231C8—42no—
232C8—81no—
233C8—442no—
234C8—881no—
235C8—881no—
236C22—21no—
237C22—21no—
238C22—81no—
239C22—81no—
240C22—81no—
241C22#1062239712yes—
242C22#1062256211yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—81no—
248C4—882no—
249C4#1062237912yes—
250C4#1062276811yescharacteristic
251C4#1062278911yescharacteristic
252C2—22no—
253C2—161no—
254C2#1307013511yescharacteristic
255C2#1307016911yescharacteristic
256C2#1307017111yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1480C2
socleC22×C11#399
prime radicalC11×#532C22
hypercenter#1480D11
hypocenterC11#10665
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
2. #13068735C2semidirect
3. #13067391C2semidirect
4. #13067386C2semidirect
6. #13066444C2semidirect
207. C11#10665semidirect

Maximal subgroups

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

subgroupindex
#130694492
#130687352
#130673912
#130673862
#130670152
#130664442
C11×#14802
#1066511