Finite Group Databasebeta

← #14658748

Subgroups — #14658748

Order 2816.

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

normal subgroups only

This group has 372 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#13069413C211yesmaximal, characteristic
2#13068790C211yesmaximal, characteristic, complemented
3#13067390C211yesmaximal, characteristic, complemented
4#13067042C211yesmaximal, characteristic
5#13067040C211yesmaximal, characteristic
6#13066446C211yesmaximal, characteristic, complemented
7C11×#1571C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×#66886—22no—
13C2×(C2×D11)⋊C8—22no—
14#10622538C2211yescharacteristic
15#10622537C2211yescharacteristic
16C2×#66867C2211yescharacteristic
17C11×#335—22no—
18#10622121—22no—
19#10622117—22no—
20#10622097—22no—
21C22×D44Q811yescharacteristic
22C22×C4×D11—21no—
23C2×C11×M16—21no—
24C22×C8×C11—21no—
25C2×C42×C11C2311yescharacteristic
26C2×(C2×D11)⋊C4—21no—
27C2×C4⋊Dic11Q811yescharacteristic
28C2×#4318—21no—
29C22×C11⋊C8D412yes—
30C4×D44—21no—
31C4×D44—21no—
32C4×D44—21no—
33C4×D44—21no—
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C4⋊C8—21no—
37C11×C4⋊C8—21no—
38C11×C4⋊C8—21no—
39C11×C22⋊C8—21no—
40C4×C8×C11D412yes—
41C22⋊(C11⋊C8)—21no—
42#66886—44no—
43(C2×D11)⋊C8—44no—
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
51C23×D11—21no—
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11C2×Q811yescharacteristic
54C22×C4×C11#4111yescharacteristic
55C22×Dic11—21no—
56C2×D44—21no—
57C2×D44—21no—
58C2×D44—42no—
59C2×C4×D11—41no—
60C2×C4×D11—41no—
61C2×C4×D11—42no—
62C2×C4×D11—42no—
63C11×M16—42no—
64C2×C8×C11—22no—
65C2×C8×C11—41no—
66C2×C8×C11—41no—
67C2×C8×C11—42no—
68C42×C11C2×D411yescharacteristic
69C42×C11C2×D411yescharacteristic
70C42×C11#4111yescharacteristic
71C42×C11#4111yescharacteristic
72(C2×D11)⋊C4—41no—
73(C2×D11)⋊C4—41no—
74C4⋊Dic11—21no—
75C4⋊Dic11—21no—
76#4318—42no—
77C2×C11⋊C8—22no—
78C2×C11⋊C8—22no—
79C2×C11⋊C8—22no—
80C2×C11⋊C8—41no—
81C2×C11⋊C8D814yes—
82#1955—111no—
83#1849—111no—
84#1571—111no—
85#1571D1111yescharacteristic, complemented
86#1486—111no—
87#1486—111no—
88#1275—111no—
89C23×C11C22⋊Q811yescharacteristic
90C22×D11—22no—
91C22×D11—41no—
92C22×D11—42no—
93C22×D11—41no—
94C22×D11—42no—
95C2×C4×C11—41no—
96C2×C4×C11—41no—
97C2×C4×C11C22⋊Q811yescharacteristic
98C2×C4×C11C22⋊Q811yescharacteristic
99C2×C4×C11#12311yescharacteristic
100C2×C4×C11#12311yescharacteristic
101C2×C4×C11#12311yescharacteristic
102C2×C4×C11#12711yescharacteristic
103C2×C4×C11C2×D812yes—
104C2×C4×C11#13712yes—
105C2×Dic11—41no—
106C2×Dic11—42no—
107D44—22no—
108D44—22no—
109D44—41no—
110D44—41no—
111C4×D11—82no—
112C4×D11—81no—
113C4×D11—81no—
114C8×C11—42no—
115C8×C11—81no—
116C8×C11—81no—
117C11⋊C8—24no—
118C11⋊C8—42no—
119C11⋊C8—81no—
120C2×C4×D4—111no—
121#431—111no—
122#431C2×D1111yescharacteristic
123C2×#108—222no—
124#423—111no—
125#423C2×D1111yescharacteristic
126C2×C4⋊C8C2×D1111yescharacteristic
127C2×C22⋊C8—222no—
128C2×#97—111no—
129#335—22no—
130#335—222no—
131D4⋊C8—222no—
132D4⋊C8—222no—
133C22×C11—21no—
134C22×C11—21no—
135C22×C11#39911yescharacteristic
136C22×C11#47412yes—
137C2×D11—44no—
138C2×D11—42no—
139C2×D11—82no—
140C2×D11—81no—
141C2×D11—81no—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—21no—
145C4×C11—21no—
146C4×C11#48012yes—
147C4×C11#49311yescharacteristic
148C4×C11#49711yescharacteristic
149Dic11—81no—
150C22×D4—111no—
151C23×C4—221no—
152C2×M16—21no—
153C2×M16—221no—
154C22×C8—21no—
155C22×C8—112no—
156C4×D4—221no—
157C4×D4—221no—
158C4×D4—221no—
159C4×D4—221no—
160C2×C4⋊C4—111no—
161C2×C22⋊C4—221no—
162C2×C42C22×D1111yescharacteristic
163#108—444no—
164C4⋊C8—21no—
165C4⋊C8—21no—
166C4⋊C8—21no—
167C4⋊C8—21no—
168C4⋊C8—21no—
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#209111yescharacteristic
181C2×C11#209311yescharacteristic
182C2×C11#209811yescharacteristic
183D11—82no—
184C24—221no—
185C2×D4—221no—
186C2×D4—221no—
187C2×D4—442no—
188C22×C4—221no—
189C22×C4—441no—
190C22×C4—442no—
191C22×C4—442no—
192C22×C4—441no—
193C22×C4#433911yescharacteristic
194C22×C4D4×D1111yescharacteristic
195C22×C4Q8×D1111yescharacteristic
196M16—42no—
197M16—442no—
198C2×C8—22no—
199C2×C8—42no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—114no—
203C2×C8—222no—
204C2×C8—222no—
205C2×C8—222no—
206C2×C8—441no—
207C4⋊C4—221no—
208C4⋊C4—221no—
209C22⋊C4—441no—
210C22⋊C4—441no—
211C42#433911yescharacteristic
212C42D4×D1111yescharacteristic
213C42#434311yescharacteristic
214C42C2×C22⋊D1111yescharacteristic
215C11#1066011yescharacteristic, complemented, Sylow
216C23—222no—
217C23—441no—
218C23—442no—
219C23—442no—
220C23—441no—
221C23#6694911yescharacteristic
222D4—222no—
223D4—222no—
224D4—441no—
225D4—441no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—442no—
229C2×C4—441no—
230C2×C4—882no—
231C2×C4—881no—
232C2×C4—881no—
233C2×C4#6694711yescharacteristic
234C2×C4#6694711yescharacteristic
235C2×C4#6694911yescharacteristic
236C2×C4D8×D1112yes—
237C2×C4#6697112yes—
238C2×C4#6698211yescharacteristic
239C2×C4#6699311yescharacteristic
240C2×C4#6699911yescharacteristic
241C8—42no—
242C8—81no—
243C8—81no—
244C8—224no—
245C8—442no—
246C8—881no—
247C22—21no—
248C22—21no—
249C22—444no—
250C22—442no—
251C22—882no—
252C22—881no—
253C22—881no—
254C22#1062250312yes—
255C22#1062260511yescharacteristic
256C4—21no—
257C4—21no—
258C4—21no—
259C4—21no—
260C4—881no—
261C4#1062249512yes—
262C4#1062276411yescharacteristic
263C4#1062280311yescharacteristic
264C2—22no—
265C2—882no—
266C2#1307013111yescharacteristic
267C2#1307014111yescharacteristic
268C2#1307017211yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1571C2
socleC22×C11#399
prime radicalC22×D44Q8
hypercenter#1571D11
hypocenterC11#10660
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
2. #13068790C2semidirect
3. #13067390C2semidirect
6. #13066446C2semidirect
7. C11×#1571C2semidirect
85. #1571D11semidirect
215. C11#10660semidirect

Maximal subgroups

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

subgroupindex
#130694132
#130687902
#130673902
#130670422
#130670402
#130664462
C11×#15712
#1066011