Finite Group Databasebeta

← #14658590

Subgroups — #14658590

Order 2816.

278 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 85 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#13069589C211yesmaximal, characteristic
2#13068757C211yesmaximal, characteristic
3#13067300C211yesmaximal, characteristic
4#13067296C211yesmaximal, characteristic
5#13066475C211yesmaximal, characteristic
6#13066475C211yesmaximal, characteristic
7C11×#1281C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C2×C11×#97C2211yescharacteristic
12#10622549C2211yescharacteristic
13#10622537C2211yescharacteristic
14#10622537C2211yescharacteristic
15#10622190—21no—
16#10622190—21no—
17#10622189—21no—
18#10622189—21no—
19#10622120—22no—
20#10622119—22no—
21C22×Dic22—21no—
22C22×C8×C11D411yescharacteristic
23C22×C8×C11D411yescharacteristic
24C2×C42×C11C2311yescharacteristic
25C2×C4⋊Dic11—21no—
26C2×C4⋊Dic11—21no—
27C2×C4⋊Dic11—21no—
28C2×#4318—21no—
29C2×#4318—21no—
30#66922—21no—
31#66922—21no—
32#66922—21no—
33#66922D412yes—
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C22⋊C8—21no—
37C11×C22⋊C8—21no—
38C11×#97—21no—
39C11×#97—21no—
40C4×C8×C11—21no—
41C4×C8×C11—21no—
42C11⋊#95—21no—
43C11⋊#95—21no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48#10636—111nomaximal, Sylow
49C22×C4×C11C2×D411yescharacteristic
50C22×C4×C11#4111yescharacteristic
51C22×C4×C11#4111yescharacteristic
52C22×Dic11—41no—
53C22×Dic11—41no—
54C2×Dic22—22no—
55C2×Dic22—41no—
56C2×Dic22—82no—
57C2×C8×C11—21no—
58C2×C8×C11—21no—
59C2×C8×C11—21no—
60C2×C8×C11—21no—
61C2×C8×C11—21no—
62C2×C8×C11—21no—
63C2×C8×C11—41no—
64C2×C8×C11—41no—
65C42×C11C2×D411yescharacteristic
66C42×C11#4111yescharacteristic
67C42×C11#4111yescharacteristic
68C42×C11#4111yescharacteristic
69C4⋊Dic11—22no—
70C4⋊Dic11—22no—
71C4⋊Dic11—41no—
72C4⋊Dic11—41no—
73C4⋊Dic11—41no—
74C4⋊Dic11—41no—
75#4318—41no—
76#4318—41no—
77#4318—41no—
78#4318—41no—
79C2×C11⋊C8—41no—
80C2×C11⋊C8—41no—
81#1993—111no—
82#1838—111no—
83#1549—111no—
84#1548—111no—
85#1286—111no—
86#1286—111no—
87#1281D1111yescharacteristic
88C23×C11#12411yescharacteristic
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11#12111yescharacteristic
92C2×C4×C11#12311yescharacteristic
93C2×C4×C11#12311yescharacteristic
94C2×C4×C11#12311yescharacteristic
95C2×C4×C11#12611yescharacteristic
96C2×C4×C11#12611yescharacteristic
97C2×C4×C11#13511yescharacteristic
98C2×C4×C11#13511yescharacteristic
99C2×C4×C11#13711yescharacteristic
100C2×C4×C11#13711yescharacteristic
101C2×Dic11—42no—
102C2×Dic11—82no—
103C2×Dic11—81no—
104C2×Dic11—81no—
105C2×Dic11—81no—
106Dic22—82no—
107Dic22—82no—
108C8×C11—41no—
109C8×C11—41no—
110C8×C11—81no—
111C8×C11—81no—
112C11⋊C8—81no—
113C11⋊C8—81no—
114C2×C4⋊Q8—111no—
115#431C2×D1111yescharacteristic
116#431C2×D1111yescharacteristic
117#423—111no—
118#423—111no—
119C2×#97C2×D1111yescharacteristic
120#382—111no—
121#341—221no—
122#341—221no—
123#340—221no—
124#340—221no—
125#333—222no—
126#332—222no—
127C22×C11—21no—
128C22×C11—21no—
129C22×C11#39711yescharacteristic
130C22×C11#48811yescharacteristic
131C22×C11#49111yescharacteristic
132C4×C11—21no—
133C4×C11—21no—
134C4×C11—21no—
135C4×C11—21no—
136C4×C11#46411yescharacteristic
137C4×C11#46411yescharacteristic
138C4×C11#48511yescharacteristic
139C4×C11#48511yescharacteristic
140Dic11—82no—
141Dic11—161no—
142C22×Q8—221no—
143C2×M16—221no—
144C2×M16—221no—
145C22×C8D4411yescharacteristic
146C22×C8D4411yescharacteristic
147C4⋊Q8—112no—
148C4⋊Q8—221no—
149C4⋊Q8—221no—
150C4⋊Q8—221no—
151C2×C4⋊C4—221no—
152C2×C4⋊C4—221no—
153C2×C4⋊C4—221no—
154C2×C42C22×D1111yescharacteristic
155C4⋊C8—21no—
156C4⋊C8—21no—
157C4⋊C8—221no—
158C4⋊C8—221no—
159C4⋊C8—221no—
160C4⋊C8—221no—
161C22⋊C8—21no—
162C22⋊C8—21no—
163#97—21no—
164#97—21no—
165C4×C8—21no—
166C4×C8—21no—
167#95—221no—
168#95—221no—
169C2×C11—21no—
170C2×C11—21no—
171C2×C11#207411yescharacteristic
172C2×C11#208111yescharacteristic
173C2×C11#208211yescharacteristic
174C2×Q8—222no—
175C2×Q8—441no—
176C2×Q8—882no—
177C22×C4—441no—
178C22×C4—441no—
179C22×C4C2×D4411yescharacteristic
180C22×C4#433911yescharacteristic
181C22×C4#433911yescharacteristic
182M16—441no—
183M16—441no—
184M16—441no—
185M16—441no—
186C2×C8—21no—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—21no—
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—441no—
195C2×C8—441no—
196C4⋊C4—222no—
197C4⋊C4—222no—
198C4⋊C4—441no—
199C4⋊C4—441no—
200C4⋊C4—441no—
201C4⋊C4—441no—
202C42D4×D1111yescharacteristic
203C42#434111yescharacteristic
204C42#434111yescharacteristic
205C42#434311yescharacteristic
206C11#1063611yescharacteristic, complemented, Sylow
207C23#6692811yescharacteristic
208Q8—882no—
209Q8—882no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—442no—
213C2×C4—882no—
214C2×C4—881no—
215C2×C4—881no—
216C2×C4—881no—
217C2×C4#6693611yescharacteristic
218C2×C4#6693611yescharacteristic
219C2×C4#6693911yescharacteristic
220C2×C4#6694811yescharacteristic
221C2×C4#6695111yescharacteristic
222C2×C4#6695111yescharacteristic
223C2×C4#6695711yescharacteristic
224C2×C4#6695711yescharacteristic
225C2×C4#6696211yescharacteristic
226C2×C4#6696211yescharacteristic
227C8—41no—
228C8—41no—
229C8—81no—
230C8—81no—
231C8—881no—
232C8—881no—
233C22—21no—
234C22—21no—
235C22#1062228711yescharacteristic
236C22#1062231011yescharacteristic
237C22#1062231611yescharacteristic
238C4—21no—
239C4—21no—
240C4—21no—
241C4—21no—
242C4—882no—
243C4—1761no—
244C4#1062233611yescharacteristic
245C4#1062233611yescharacteristic
246C4#1062245811yescharacteristic
247C4#1062245811yescharacteristic
248C2—21no—
249C2—21no—
250C2#1307003611yescharacteristic
251C2#1307007511yescharacteristic
252C2#1307008211yescharacteristic
subgroupG/H
centerC22#10622287
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1281C2
socleC22×C11#397
prime radicalC23×C11#124
hypercenter#1281D11
hypocenterC11#10636
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1281

Complements

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

NH ≅ G/Ntype
206. C11#10636semidirect

Maximal subgroups

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

subgroupindex
#130695892
#130687572
#130673002
#130672962
#130664752
C11×#12812
#1063611