Finite Group Databasebeta

← #14658587

Subgroups — #14658587

Order 2816.

294 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 83 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#13068756C211yesmaximal, 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×#66874—21no—
13C2×#66874—21no—
14#10622538C2211yescharacteristic
15#10622537C2211yescharacteristic
16C2×#66867C2211yescharacteristic
17#10622196—21no—
18#10622196—21no—
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#66874—42no—
43#66874—42no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47#66867—21no—
48#66867—21no—
49C4×C11⋊C8—21no—
50#10635—111nomaximal, Sylow
51C22×C4×C11—41no—
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11#4111yescharacteristic
54C22×C4×C11#4111yescharacteristic
55C22×Dic11—41no—
56C2×Dic22—22no—
57C2×Dic22—41no—
58C2×Dic22—41no—
59C2×Dic22—41no—
60C2×Dic22—41no—
61C2×Dic22—41no—
62C11×M16—41no—
63C11×M16—41no—
64C2×C8×C11—41no—
65C2×C8×C11—41no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C42×C11C2×D411yescharacteristic
69C42×C11#4111yescharacteristic
70C42×C11#4111yescharacteristic
71C42×C11#4111yescharacteristic
72C4⋊Dic11—22no—
73C4⋊Dic11—22no—
74C4⋊Dic11—41no—
75C4⋊Dic11—41no—
76#4318—41no—
77#4318—41no—
78C2×C11⋊C8—21no—
79C2×C11⋊C8—21no—
80C2×C11⋊C8—21no—
81C2×C11⋊C8—21no—
82C2×C11⋊C8—21no—
83C2×C11⋊C8—21no—
84C2×C11⋊C8—41no—
85C2×C11⋊C8—41no—
86#1960—111no—
87#1838—111no—
88#1546—111no—
89#1546—111no—
90#1286—111no—
91#1286D1111yescharacteristic
92#1281—111no—
93C23×C11#12411yescharacteristic
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11—81no—
97C2×C4×C11—81no—
98C2×C4×C11—81no—
99C2×C4×C11#12111yescharacteristic
100C2×C4×C11#12311yescharacteristic
101C2×C4×C11#12311yescharacteristic
102C2×C4×C11#12311yescharacteristic
103C2×C4×C11#12611yescharacteristic
104C2×C4×C11#12611yescharacteristic
105C2×C4×C11#13511yescharacteristic
106C2×C4×C11#13511yescharacteristic
107C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
108C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
109C2×Dic11—42no—
110C2×Dic11—81no—
111C2×Dic11—81no—
112Dic22—42no—
113Dic22—42no—
114Dic22—81no—
115Dic22—81no—
116C8×C11—81no—
117C8×C11—81no—
118C11⋊C8—41no—
119C11⋊C8—41no—
120C11⋊C8—81no—
121C11⋊C8—81no—
122C2×C4⋊Q8—111no—
123#431—111no—
124#431C2×D1111yescharacteristic
125#423—111no—
126#423C2×D1111yescharacteristic
127C2×#103—221no—
128C2×#103—221no—
129C2×#97—111no—
130#382C2×D1111yescharacteristic
131#341—221no—
132#341—221no—
133#332—222no—
134#332—222no—
135C22×C11—21no—
136C22×C11—21no—
137C22×C11#39711yescharacteristic
138C22×C11#48811yescharacteristic
139C22×C11#49011yescharacteristic
140C4×C11—21no—
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—161no—
145C4×C11#46311yescharacteristic
146C4×C11#46311yescharacteristic
147C4×C11#48211yescharacteristic
148C4×C11#48211yescharacteristic
149Dic11—82no—
150C22×Q8—221no—
151C2×M16—21no—
152C2×M16—221no—
153C22×C8—111no—
154C22×C8—111no—
155C4⋊Q8—112no—
156C4⋊Q8—221no—
157C4⋊Q8—221no—
158C4⋊Q8—221no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—221no—
161C2×C4⋊C4—221no—
162C2×C42C22×D1111yescharacteristic
163C4⋊C8—21no—
164C4⋊C8—21no—
165C4⋊C8—21no—
166C4⋊C8—221no—
167C4⋊C8—221no—
168C4⋊C8—221no—
169#103—442no—
170#103—442no—
171C22⋊C8—21no—
172C22⋊C8—221no—
173#97—221no—
174#97—221no—
175C4×C8—21no—
176C4×C8—221no—
177#95—21no—
178#95—21no—
179C2×C11—21no—
180C2×C11—21no—
181C2×C11#207311yescharacteristic
182C2×C11#208211yescharacteristic
183C2×C11#208211yescharacteristic
184C2×Q8—222no—
185C2×Q8—441no—
186C2×Q8—441no—
187C2×Q8—441no—
188C2×Q8—441no—
189C2×Q8—441no—
190C22×C4—41no—
191C22×C4—441no—
192C22×C4#433911yescharacteristic
193C22×C4D4×D1111yescharacteristic
194C22×C4#434111yescharacteristic
195M16—41no—
196M16—41no—
197M16—441no—
198M16—441no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—221no—
202C2×C8—221no—
203C2×C8—221no—
204C2×C8—221no—
205C2×C8—221no—
206C2×C8—221no—
207C2×C8—441no—
208C2×C8—441no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—222no—
212C4⋊C4—222no—
213C4⋊C4—441no—
214C4⋊C4—441no—
215C42#433911yescharacteristic
216C42#433911yescharacteristic
217C42D4×D1111yescharacteristic
218C42#434311yescharacteristic
219C11#1063511yescharacteristic, complemented, Sylow
220C23#6693811yescharacteristic
221Q8—442no—
222Q8—442no—
223Q8—881no—
224Q8—881no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—81no—
228C2×C4—81no—
229C2×C4—81no—
230C2×C4—442no—
231C2×C4—881no—
232C2×C4—881no—
233C2×C4#6692911yescharacteristic
234C2×C4#6693611yescharacteristic
235C2×C4#6693711yescharacteristic
236C2×C4#6694711yescharacteristic
237C2×C4#6694711yescharacteristic
238C2×C4#6695111yescharacteristic
239C2×C4#6696411yescharacteristic
240C2×C4#6696711yescharacteristic
241C2×C4#6696911yescharacteristic
242C2×C4#6697211yescharacteristic
243C8—81no—
244C8—81no—
245C8—441no—
246C8—441no—
247C8—881no—
248C8—881no—
249C22—21no—
250C22—21no—
251C22#1062228811yescharacteristic
252C22#1062237711yescharacteristic
253C22#1062241311yescharacteristic
254C4—21no—
255C4—21no—
256C4—21no—
257C4—21no—
258C4—161no—
259C4—882no—
260C4#1062240011yescharacteristic
261C4#1062243211yescharacteristic
262C4#1062247911yescharacteristic
263C4#1062249811yescharacteristic
264C2—21no—
265C2—21no—
266C2#1307003311yescharacteristic
267C2#1307008511yescharacteristic
268C2#1307008611yescharacteristic
subgroupG/H
centerC22#10622288
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#397
prime radicalC23×C11#124
hypercenter#1286D11
hypocenterC11#10635
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
219. C11#10635semidirect

Maximal subgroups

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

subgroupindex
#130694352
#130687562
#130672892
#130672872
#130664742
#130664602
C11×#12862
#1063511