Finite Group Databasebeta

← #14658743

Subgroups — #14658743

Order 2816.

356 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 93 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#13069414C211yesmaximal, characteristic
2#13068757C211yesmaximal, characteristic, complemented
3#13067391C211yesmaximal, characteristic, complemented
4#13067387C211yesmaximal, characteristic, complemented
5#13067042C211yesmaximal, characteristic
6#13067042C211yesmaximal, characteristic
7C11×#1275C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C2×C11×#97C2211yescharacteristic
12C2×(C2×D11)⋊C8—22no—
13#10622537C2211yescharacteristic
14#10622537C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16#10622190—22no—
17#10622097—22no—
18#10622097—22no—
19#10622096—22no—
20#10622095—22no—
21C22×D44Q811yescharacteristic
22C22×C4×D11—21no—
23C22×C8×C11D412yes—
24C2×C42×C11C2311yescharacteristic
25C2×(C2×D11)⋊C4—21no—
26C2×C4⋊Dic11Q811yescharacteristic
27C2×#4318—21no—
28C2×#4318—21no—
29C22×C11⋊C8—21no—
30C4×D44—21no—
31C4×D44—21no—
32C4×D44—21no—
33C4×D44—21no—
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C22⋊C8—21no—
37C11×C22⋊C8—21no—
38C11×#97—21no—
39C11×#97—21no—
40C4×C8×C11D412yes—
41C4×C8×C11D412yes—
42(C2×D11)⋊C8—44no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49#10659—111nomaximal, Sylow
50C23×D11—21no—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11C2×Q811yescharacteristic
53C22×C4×C11#4111yescharacteristic
54C22×Dic11—21no—
55C2×D44—21no—
56C2×D44—21no—
57C2×D44—42no—
58C2×C4×D11—41no—
59C2×C4×D11—41no—
60C2×C4×D11—42no—
61C2×C4×D11—42no—
62C2×C8×C11—22no—
63C2×C8×C11—22no—
64C2×C8×C11—22no—
65C2×C8×C11—22no—
66C2×C8×C11—22no—
67C42×C11C2×D411yescharacteristic
68C42×C11C2×D411yescharacteristic
69C42×C11#4111yescharacteristic
70C42×C11#4111yescharacteristic
71(C2×D11)⋊C4—41no—
72(C2×D11)⋊C4—41no—
73C4⋊Dic11—21no—
74C4⋊Dic11—21no—
75#4318—42no—
76#4318—42no—
77C2×C11⋊C8—41no—
78C2×C11⋊C8—41no—
79C2×C11⋊C8—41no—
80C2×C11⋊C8—42no—
81#1955—111no—
82#1838—111no—
83#1571—111no—
84#1570—111no—
85#1486—111no—
86#1486—111no—
87#1275D1111yescharacteristic, complemented
88C23×C11C22⋊Q811yescharacteristic
89C22×D11—22no—
90C22×D11—41no—
91C22×D11—42no—
92C22×D11—41no—
93C22×D11—42no—
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11C22⋊Q811yescharacteristic
97C2×C4×C11C22⋊Q811yescharacteristic
98C2×C4×C11#12311yescharacteristic
99C2×C4×C11#12311yescharacteristic
100C2×C4×C11#12311yescharacteristic
101C2×C4×C11#12711yescharacteristic
102C2×C4×C11#13512yes—
103C2×C4×C11AGL(1,ℤ/8)12yes—
104C2×Dic11—41no—
105C2×Dic11—42no—
106D44—22no—
107D44—22no—
108D44—41no—
109D44—41no—
110C4×D11—82no—
111C4×D11—81no—
112C4×D11—81no—
113C8×C11—42no—
114C8×C11—42no—
115C8×C11—42no—
116C11⋊C8—81no—
117C11⋊C8—81no—
118C11⋊C8—81no—
119C2×C4×D4—111no—
120#431C2×D1111yescharacteristic
121#431C2×D1111yescharacteristic
122#423—111no—
123#423—111no—
124C2×C4⋊C8—111no—
125C2×C22⋊C8—222no—
126C2×#97C2×D1111yescharacteristic
127#341—222no—
128#335—222no—
129#334—222no—
130D4⋊C8—222no—
131D4⋊C8—222no—
132C22×C11—21no—
133C22×C11—21no—
134C22×C11#39911yescharacteristic
135C22×C11#47812yes—
136C2×D11—44no—
137C2×D11—42no—
138C2×D11—82no—
139C2×D11—81no—
140C2×D11—81no—
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—21no—
145C4×C11#48212yes—
146C4×C11#49511yescharacteristic
147C4×C11#49611yescharacteristic
148Dic11—81no—
149C22×D4—111no—
150C23×C4—221no—
151C2×M16—221no—
152C2×M16—221no—
153C22×C8—221no—
154C22×C8D4412yes—
155C4×D4—221no—
156C4×D4—221no—
157C4×D4—221no—
158C4×D4—221no—
159C2×C4⋊C4—111no—
160C2×C22⋊C4—221no—
161C2×C42C22×D1111yescharacteristic
162C4⋊C8—21no—
163C4⋊C8—21no—
164C4⋊C8—221no—
165C4⋊C8—221no—
166C4⋊C8—221no—
167C4⋊C8—221no—
168C4⋊C8—221no—
169C4⋊C8—221no—
170C22⋊C8—21no—
171C22⋊C8—21no—
172C22⋊C8—444no—
173#97—21no—
174#97—21no—
175C4×C8D4412yes—
176C4×C8D4412yes—
177C2×C11—22no—
178C2×C11#209111yescharacteristic
179C2×C11#209211yescharacteristic
180C2×C11#209811yescharacteristic
181D11—82no—
182C24—221no—
183C2×D4—221no—
184C2×D4—221no—
185C2×D4—442no—
186C22×C4—221no—
187C22×C4—441no—
188C22×C4—441no—
189C22×C4—442no—
190C22×C4—442no—
191C22×C4C2×D4411yescharacteristic
192C22×C4#434111yescharacteristic
193C22×C4Q8×D1111yescharacteristic
194M16—442no—
195M16—442no—
196C2×C8—22no—
197C2×C8—22no—
198C2×C8—22no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—441no—
202C2×C8—441no—
203C2×C8—441no—
204C2×C8—442no—
205C4⋊C4—221no—
206C4⋊C4—221no—
207C22⋊C4—441no—
208C22⋊C4—441no—
209C42C2×D4411yescharacteristic
210C42C2×D4411yescharacteristic
211C42#434111yescharacteristic
212C42#434111yescharacteristic
213C11#1065911yescharacteristic, complemented, Sylow
214C23—222no—
215C23—441no—
216C23—442no—
217C23—441no—
218C23—442no—
219C23#6695011yescharacteristic
220D4—222no—
221D4—222no—
222D4—441no—
223D4—441no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—441no—
227C2×C4—442no—
228C2×C4—881no—
229C2×C4—881no—
230C2×C4—882no—
231C2×C4#6692711yescharacteristic
232C2×C4#6693911yescharacteristic
233C2×C4#6693911yescharacteristic
234C2×C4#6693911yescharacteristic
235C2×C4#6695011yescharacteristic
236C2×C4#6695011yescharacteristic
237C2×C4#6695712yes—
238C2×C4#6696112yes—
239C8—42no—
240C8—42no—
241C8—42no—
242C8—881no—
243C8—881no—
244C8—881no—
245C22—21no—
246C22—21no—
247C22—444no—
248C22—442no—
249C22—882no—
250C22—881no—
251C22—881no—
252C22#1062229011yescharacteristic
253C22#1062246012yes—
254C4—21no—
255C4—21no—
256C4—21no—
257C4—21no—
258C4—881no—
259C4#1062230911yescharacteristic
260C4#1062232511yescharacteristic
261C4#1062235012yes—
262C2—22no—
263C2—882no—
264C2#1307013311yescharacteristic
265C2#1307013611yescharacteristic
266C2#1307017011yescharacteristic
subgroupG/H
centerC2×C4#66927
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1275C2
socleC22×C11#399
prime radicalC22×D44Q8
hypercenter#1275D11
hypocenterC11#10659
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
2. #13068757C2semidirect
3. #13067391C2semidirect
4. #13067387C2semidirect
7. C11×#1275C2semidirect
87. #1275D11semidirect
213. C11#10659semidirect

Maximal subgroups

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

subgroupindex
#130694142
#130687572
#130673912
#130673872
#130670422
C11×#12752
#1065911