Finite Group Databasebeta

← #14658749

Subgroups — #14658749

Order 2816.

372 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 95 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#13069415C211yesmaximal, characteristic
2#13068790C211yesmaximal, characteristic, complemented
3#13067392C211yesmaximal, characteristic, complemented
4#13067391C211yesmaximal, characteristic, complemented
5#13067041C211yesmaximal, characteristic
6#13066446C211yesmaximal, characteristic, complemented
7C11×#1486C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×C22⋊(C11⋊C8)—22no—
12C2×#66886—22no—
13#10622538C2211yescharacteristic
14#10622537C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C2×#66867C2211yescharacteristic
17C11×D4⋊C8—22no—
18D4⋊(C11⋊C8)—22no—
19#10622117—22no—
20#10622096—22no—
21C22×D4×C11Q811yescharacteristic
22C23×C4×C11—21no—
23C2×C11×M16—21no—
24C4×D4×C11—21no—
25C4×D4×C11—21no—
26C4×D4×C11—21no—
27C4×D4×C11—21no—
28C2×C11×C4⋊C4Q811yescharacteristic
29C2×C11×C22⋊C4—21no—
30C2×C42×C11C2311yescharacteristic
31C2×#4318—21no—
32C22×C11⋊C8—21no—
33C22×C11⋊C8D412yes—
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C4⋊C8—21no—
37C11×C22⋊C8—21no—
38C4×C8×C11D412yes—
39C22⋊(C11⋊C8)—21no—
40C22⋊(C11⋊C8)—44no—
41#66886—44no—
42C4⋊(C11⋊C8)—21no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47#66867—21no—
48#66867—21no—
49C4×C11⋊C8D412yes—
50#10660—111nomaximal, Sylow
51C24×C11—21no—
52C2×D4×C11—21no—
53C2×D4×C11—21no—
54C2×D4×C11—42no—
55C22×C4×C11—21no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11—42no—
59C22×C4×C11—42no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×Q811yescharacteristic
62C22×C4×C11#4111yescharacteristic
63C11×M16—42no—
64C2×C8×C11—22no—
65C2×C8×C11—41no—
66C11×C4⋊C4—21no—
67C11×C4⋊C4—21no—
68C11×C22⋊C4—41no—
69C11×C22⋊C4—41no—
70C42×C11C2×D411yescharacteristic
71C42×C11C2×D411yescharacteristic
72C42×C11#4111yescharacteristic
73C42×C11#4111yescharacteristic
74#4318—42no—
75C2×C11⋊C8—22no—
76C2×C11⋊C8—22no—
77C2×C11⋊C8—22no—
78C2×C11⋊C8—41no—
79C2×C11⋊C8—41no—
80C2×C11⋊C8—42no—
81C2×C11⋊C8D814yes—
82#1955—111no—
83#1849—111no—
84#1571—111no—
85#1571—111no—
86#1486—111no—
87#1486D1111yescharacteristic
88#1275—111no—
89C23×C11—22no—
90C23×C11—41no—
91C23×C11—42no—
92C23×C11—41no—
93C23×C11—42no—
94C23×C11C22⋊Q811yescharacteristic
95D4×C11—22no—
96D4×C11—22no—
97D4×C11—41no—
98D4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11—42no—
103C2×C4×C11—82no—
104C2×C4×C11—81no—
105C2×C4×C11—81no—
106C2×C4×C11C22⋊Q811yescharacteristic
107C2×C4×C11C22⋊Q811yescharacteristic
108C2×C4×C11#12311yescharacteristic
109C2×C4×C11#12311yescharacteristic
110C2×C4×C11#12311yescharacteristic
111C2×C4×C11#12711yescharacteristic
112C2×C4×C11C2×D812yes—
113C2×C4×C11#13712yes—
114C8×C11—42no—
115C8×C11—81no—
116C11⋊C8—24no—
117C11⋊C8—42no—
118C11⋊C8—81no—
119C11⋊C8—81no—
120C2×C4×D4C2×D1111yescharacteristic
121#431—111no—
122#431C2×D1111yescharacteristic
123C2×#108—222no—
124#423—111no—
125#423C2×D1111yescharacteristic
126C2×C4⋊C8—111no—
127C2×C22⋊C8—222no—
128C2×#97—111no—
129#335—222no—
130#335—222no—
131D4⋊C8—22no—
132D4⋊C8—222no—
133C22×C11—21no—
134C22×C11—21no—
135C22×C11—44no—
136C22×C11—42no—
137C22×C11—82no—
138C22×C11—81no—
139C22×C11—81no—
140C22×C11#39911yescharacteristic
141C22×C11#47412yes—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—21no—
145C4×C11—21no—
146C4×C11—81no—
147C4×C11#48012yes—
148C4×C11#49311yescharacteristic
149C4×C11#49711yescharacteristic
150C22×D4Dic2211yescharacteristic
151C23×C4—21no—
152C2×M16—21no—
153C2×M16—221no—
154C22×C8—112no—
155C22×C8—221no—
156C4×D4—21no—
157C4×D4—21no—
158C4×D4—21no—
159C4×D4—21no—
160C2×C4⋊C4Dic2211yescharacteristic
161C2×C22⋊C4—21no—
162C2×C42C22×D1111yescharacteristic
163#108—444no—
164C4⋊C8—21no—
165C4⋊C8—21no—
166C4⋊C8—21no—
167C4⋊C8—221no—
168C4⋊C8—221no—
169C4⋊C8—221no—
170C4⋊C8—221no—
171C4⋊C8—221no—
172C22⋊C8—21no—
173C22⋊C8—221no—
174C22⋊C8—444no—
175#97—221no—
176#97—221no—
177C4×C8—112no—
178C4×C8C22⋊D1112yes—
179C2×C11—22no—
180C2×C11—82no—
181C2×C11#209111yescharacteristic
182C2×C11#209311yescharacteristic
183C2×C11#209811yescharacteristic
184C24—21no—
185C2×D4—21no—
186C2×D4—21no—
187C2×D4—42no—
188C22×C4—21no—
189C22×C4—41no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4—41no—
193C22×C4C2×Dic2211yescharacteristic
194C22×C4D4×D1111yescharacteristic
195C22×C4#434111yescharacteristic
196M16—42no—
197M16—442no—
198C2×C8—22no—
199C2×C8—41no—
200C2×C8—114no—
201C2×C8—222no—
202C2×C8—222no—
203C2×C8—222no—
204C2×C8—442no—
205C2×C8—441no—
206C2×C8—441no—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C22⋊C4—41no—
210C22⋊C4—41no—
211C42#433911yescharacteristic
212C42D4×D1111yescharacteristic
213C42#434111yescharacteristic
214C42C2×C22⋊D1111yescharacteristic
215C11#1066011yescharacteristic, complemented, Sylow
216C23—22no—
217C23—41no—
218C23—42no—
219C23—41no—
220C23—42no—
221C23#6693111yescharacteristic
222D4—22no—
223D4—22no—
224D4—41no—
225D4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—82no—
233C2×C4#6693111yescharacteristic
234C2×C4#6693611yescharacteristic
235C2×C4#6693611yescharacteristic
236C2×C4D8×D1112yes—
237C2×C4#6696812yes—
238C2×C4#6697711yescharacteristic
239C2×C4#6698811yescharacteristic
240C2×C4#6699311yescharacteristic
241C8—42no—
242C8—81no—
243C8—224no—
244C8—442no—
245C8—881no—
246C8—881no—
247C22—21no—
248C22—21no—
249C22—44no—
250C22—42no—
251C22—82no—
252C22—81no—
253C22—81no—
254C22#1062237212yes—
255C22#1062256211yescharacteristic
256C4—21no—
257C4—21no—
258C4—21no—
259C4—21no—
260C4—81no—
261C4#1062238712yes—
262C4#1062276411yescharacteristic
263C4#1062278011yescharacteristic
264C2—22no—
265C2—82no—
266C2#1307013211yescharacteristic
267C2#1307014211yescharacteristic
268C2#1307017111yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1486C2
socleC22×C11#399
prime radicalC22×D4×C11Q8
hypercenter#1486D11
hypocenterC11#10660
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #13068790C2semidirect
3. #13067392C2semidirect
4. #13067391C2semidirect
6. #13066446C2semidirect
215. C11#10660semidirect

Maximal subgroups

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

subgroupindex
#130694152
#130687902
#130673922
#130673912
#130670412
#130664462
C11×#14862
#1066011