Finite Group Databasebeta

← #14658570

Subgroups — #14658570

Order 2816.

310 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 87 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#13069435C211yesmaximal, characteristic
2#13068790C211yesmaximal, characteristic
3#13067289C211yesmaximal, characteristic
4#13067287C211yesmaximal, characteristic
5#13066474C211yesmaximal, characteristic
6#13066460C211yesmaximal, characteristic
7C11×#1286C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#382C2211yescharacteristic
12C2×#66886—21no—
13C2×#66886—21no—
14C2×#66874—21no—
15C2×#66874—21no—
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18C2×#66867C2211yescharacteristic
19#10622124—22no—
20#10622120—22no—
21C22×Dic22—21no—
22C2×C11×M16—21no—
23C2×C11×C4⋊C4—21no—
24C2×C42×C11C2311yescharacteristic
25C2×C4⋊Dic11—21no—
26C2×C4⋊Dic11—21no—
27C2×#4318—21no—
28C22×C11⋊C8D411yescharacteristic
29C22×C11⋊C8D411yescharacteristic
30#66922—21no—
31#66922—21no—
32#66922—21no—
33#66922D412yes—
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C4⋊C8—21no—
37C11×C22⋊C8—21no—
38C4×C8×C11—21no—
39C11×#95—21no—
40C11×#95—21no—
41C22⋊(C11⋊C8)—21no—
42#66886—42no—
43#66886—42no—
44#66874—42no—
45#66874—42no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49#66867—21no—
50#66867—21no—
51C4×C11⋊C8—21no—
52#10632—111nomaximal, Sylow
53C22×C4×C11—41no—
54C22×C4×C11C2×D411yescharacteristic
55C22×C4×C11#4111yescharacteristic
56C22×C4×C11#4111yescharacteristic
57C22×Dic11—41no—
58C2×Dic22—22no—
59C2×Dic22—41no—
60C2×Dic22—41no—
61C2×Dic22—41no—
62C2×Dic22—41no—
63C2×Dic22—41no—
64C11×M16—41no—
65C11×M16—41no—
66C2×C8×C11—41no—
67C2×C8×C11—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C42×C11C2×D411yescharacteristic
71C42×C11#4111yescharacteristic
72C42×C11#4111yescharacteristic
73C42×C11#4111yescharacteristic
74C4⋊Dic11—22no—
75C4⋊Dic11—22no—
76C4⋊Dic11—41no—
77C4⋊Dic11—41no—
78#4318—41no—
79#4318—41no—
80C2×C11⋊C8—21no—
81C2×C11⋊C8—21no—
82C2×C11⋊C8—21no—
83C2×C11⋊C8—21no—
84C2×C11⋊C8—41no—
85C2×C11⋊C8—41no—
86C2×C11⋊C8D812yes—
87C2×C11⋊C8SD1612yes—
88#1960—111no—
89#1849—111no—
90#1546—111no—
91#1546—111no—
92#1286—111no—
93#1286D1111yescharacteristic
94#1281—111no—
95C23×C11#12411yescharacteristic
96C2×C4×C11—41no—
97C2×C4×C11—41no—
98C2×C4×C11—81no—
99C2×C4×C11—81no—
100C2×C4×C11—81no—
101C2×C4×C11#12111yescharacteristic
102C2×C4×C11#12311yescharacteristic
103C2×C4×C11#12311yescharacteristic
104C2×C4×C11#12311yescharacteristic
105C2×C4×C11#12611yescharacteristic
106C2×C4×C11#12611yescharacteristic
107C2×C4×C11C2×D811yescharacteristic
108C2×C4×C11C2×SD1611yescharacteristic
109C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
110C2×C4×C11#13711yescharacteristic
111C2×Dic11—42no—
112C2×Dic11—81no—
113C2×Dic11—81no—
114Dic22—42no—
115Dic22—42no—
116Dic22—81no—
117Dic22—81no—
118C8×C11—81no—
119C8×C11—81no—
120C11⋊C8—22no—
121C11⋊C8—22no—
122C11⋊C8—81no—
123C11⋊C8—81no—
124C2×C4⋊Q8—111no—
125#431—111no—
126#431C2×D1111yescharacteristic
127C2×#108—221no—
128C2×#108—221no—
129#423—111no—
130#423C2×D1111yescharacteristic
131C2×#103—221no—
132C2×#103—221no—
133C2×#97—111no—
134#382C2×D1111yescharacteristic
135#332—222no—
136#332—222no—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11#39711yescharacteristic
140C22×C11#48611yescharacteristic
141C22×C11#48911yescharacteristic
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—21no—
145C4×C11—21no—
146C4×C11—161no—
147C4×C11#45911yescharacteristic
148C4×C11#46111yescharacteristic
149C4×C11#48011yescharacteristic
150C4×C11#48111yescharacteristic
151Dic11—82no—
152C22×Q8—221no—
153C2×M16—21no—
154C2×M16—221no—
155C22×C8—111no—
156C22×C8—111no—
157C4⋊Q8—112no—
158C4⋊Q8—221no—
159C4⋊Q8—221no—
160C4⋊Q8—221no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—221no—
163C2×C4⋊C4—221no—
164C2×C42C22×D1111yescharacteristic
165#108—442no—
166#108—442no—
167C4⋊C8—21no—
168C4⋊C8—21no—
169C4⋊C8—21no—
170C4⋊C8—221no—
171C4⋊C8—221no—
172C4⋊C8—221no—
173#103—442no—
174#103—442no—
175C22⋊C8—21no—
176C22⋊C8—221no—
177#97—221no—
178#97—221no—
179C4×C8—21no—
180C4×C8—221no—
181#95—21no—
182#95—21no—
183C2×C11—21no—
184C2×C11—21no—
185C2×C11#207111yescharacteristic
186C2×C11#208211yescharacteristic
187C2×C11#208211yescharacteristic
188C2×Q8—222no—
189C2×Q8—441no—
190C2×Q8—441no—
191C2×Q8—441no—
192C2×Q8—441no—
193C2×Q8—441no—
194C22×C4—41no—
195C22×C4—441no—
196C22×C4#433911yescharacteristic
197C22×C4D4×D1111yescharacteristic
198C22×C4#434111yescharacteristic
199M16—41no—
200M16—41no—
201M16—441no—
202M16—441no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—112no—
206C2×C8—112no—
207C2×C8—221no—
208C2×C8—221no—
209C2×C8—221no—
210C2×C8—221no—
211C2×C8—441no—
212C2×C8—441no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—222no—
216C4⋊C4—222no—
217C4⋊C4—441no—
218C4⋊C4—441no—
219C42#433911yescharacteristic
220C42#433911yescharacteristic
221C42D4×D1111yescharacteristic
222C42#434311yescharacteristic
223C11#1063211yescharacteristic, complemented, Sylow
224C23#6693811yescharacteristic
225Q8—442no—
226Q8—442no—
227Q8—881no—
228Q8—881no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4—442no—
235C2×C4—881no—
236C2×C4—881no—
237C2×C4#6692911yescharacteristic
238C2×C4#6693611yescharacteristic
239C2×C4#6693711yescharacteristic
240C2×C4#6694711yescharacteristic
241C2×C4#6694711yescharacteristic
242C2×C4#6695111yescharacteristic
243C2×C4D8×D1111yescharacteristic
244C2×C4SD16×D1111yescharacteristic
245C2×C4#6696711yescharacteristic
246C2×C4#6697111yescharacteristic
247C8—81no—
248C8—81no—
249C8—222no—
250C8—222no—
251C8—881no—
252C8—881no—
253C22—21no—
254C22—21no—
255C22#1062228811yescharacteristic
256C22#1062237311yescharacteristic
257C22#1062240811yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—21no—
262C4—161no—
263C4—882no—
264C4#1062239911yescharacteristic
265C4#1062243111yescharacteristic
266C4#1062247611yescharacteristic
267C4#1062249511yescharacteristic
268C2—21no—
269C2—21no—
270C2#1307002311yescharacteristic
271C2#1307008511yescharacteristic
272C2#1307008611yescharacteristic
subgroupG/H
centerC22#10622288
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#397
prime radicalC23×C11#124
hypercenter#1286D11
hypocenterC11#10632
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
223. C11#10632semidirect

Maximal subgroups

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

subgroupindex
#130694352
#130687902
#130672892
#130672872
#130664742
#130664602
C11×#12862
#1063211