Finite Group Databasebeta

← #14658593

Subgroups — #14658593

Order 2816.

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

normal subgroups only

This group has 278 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#13069588C211yesmaximal, characteristic
2#13068756C211yesmaximal, characteristic
3#13067300C211yesmaximal, characteristic
4#13067298C211yesmaximal, characteristic
5#13066474C211yesmaximal, characteristic
6#13066460C211yesmaximal, characteristic
7C11×#1286C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#382C2211yescharacteristic
12#10622538C2211yescharacteristic
13#10622537C2211yescharacteristic
14C2×#66867C2211yescharacteristic
15#10622196—21no—
16#10622196—21no—
17#10622167—21no—
18#10622167—21no—
19#10622120—22no—
20#10622119—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—
42C4⋊(C11⋊C8)—21no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45#66867—21no—
46#66867—21no—
47C4×C11⋊C8—21no—
48#10636—111nomaximal, Sylow
49C22×C4×C11—41no—
50C22×C4×C11C2×D411yescharacteristic
51C22×C4×C11#4111yescharacteristic
52C22×C4×C11#4111yescharacteristic
53C22×Dic11—41no—
54C2×Dic22—22no—
55C2×Dic22—41no—
56C2×Dic22—82no—
57C11×M16—41no—
58C11×M16—41no—
59C2×C8×C11—41no—
60C2×C8×C11—41no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—41no—
63C42×C11C2×D411yescharacteristic
64C42×C11#4111yescharacteristic
65C42×C11#4111yescharacteristic
66C42×C11#4111yescharacteristic
67C4⋊Dic11—22no—
68C4⋊Dic11—22no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71#4318—41no—
72#4318—41no—
73C2×C11⋊C8—21no—
74C2×C11⋊C8—21no—
75C2×C11⋊C8—21no—
76C2×C11⋊C8—21no—
77C2×C11⋊C8—21no—
78C2×C11⋊C8—21no—
79C2×C11⋊C8—41no—
80C2×C11⋊C8—41no—
81#1993—111no—
82#1838—111no—
83#1549—111no—
84#1548—111no—
85#1286—111no—
86#1286D1111yescharacteristic
87#1281—111no—
88C23×C11#12411yescharacteristic
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11—81no—
92C2×C4×C11—81no—
93C2×C4×C11—81no—
94C2×C4×C11#12111yescharacteristic
95C2×C4×C11#12311yescharacteristic
96C2×C4×C11#12311yescharacteristic
97C2×C4×C11#12311yescharacteristic
98C2×C4×C11#12611yescharacteristic
99C2×C4×C11#12611yescharacteristic
100C2×C4×C11#13511yescharacteristic
101C2×C4×C11#13511yescharacteristic
102C2×C4×C11#13711yescharacteristic
103C2×C4×C11#13711yescharacteristic
104C2×Dic11—42no—
105C2×Dic11—82no—
106Dic22—82no—
107Dic22—82no—
108C8×C11—81no—
109C8×C11—81no—
110C11⋊C8—41no—
111C11⋊C8—41no—
112C11⋊C8—81no—
113C11⋊C8—81no—
114C2×C4⋊Q8—111no—
115#431—111no—
116#431C2×D1111yescharacteristic
117#423—111no—
118#423C2×D1111yescharacteristic
119C2×#97—111no—
120#382C2×D1111yescharacteristic
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—161no—
137C4×C11#46411yescharacteristic
138C4×C11#46411yescharacteristic
139C4×C11#48511yescharacteristic
140C4×C11#48511yescharacteristic
141Dic11—82no—
142C22×Q8—221no—
143C2×M16—21no—
144C2×M16—221no—
145C22×C8—111no—
146C22×C8—111no—
147C4⋊Q8—112no—
148C4⋊Q8—221no—
149C4⋊Q8—221no—
150C4⋊Q8—221no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—221no—
153C2×C4⋊C4—221no—
154C2×C42C22×D1111yescharacteristic
155C4⋊C8—21no—
156C4⋊C8—21no—
157C4⋊C8—21no—
158C4⋊C8—221no—
159C4⋊C8—221no—
160C4⋊C8—221no—
161C22⋊C8—21no—
162C22⋊C8—221no—
163#97—221no—
164#97—221no—
165C4×C8—21no—
166C4×C8—221no—
167#95—21no—
168#95—21no—
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—41no—
178C22×C4—441no—
179C22×C4#433911yescharacteristic
180C22×C4D4×D1111yescharacteristic
181C22×C4#434111yescharacteristic
182M16—41no—
183M16—41no—
184M16—441no—
185M16—441no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—221no—
189C2×C8—221no—
190C2×C8—221no—
191C2×C8—221no—
192C2×C8—221no—
193C2×C8—221no—
194C2×C8—441no—
195C2×C8—441no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—222no—
199C4⋊C4—222no—
200C4⋊C4—441no—
201C4⋊C4—441no—
202C42#433911yescharacteristic
203C42#433911yescharacteristic
204C42D4×D1111yescharacteristic
205C42#434311yescharacteristic
206C11#1063611yescharacteristic, complemented, Sylow
207C23#6693811yescharacteristic
208Q8—882no—
209Q8—882no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—81no—
213C2×C4—81no—
214C2×C4—81no—
215C2×C4—442no—
216C2×C4—882no—
217C2×C4#6692911yescharacteristic
218C2×C4#6693611yescharacteristic
219C2×C4#6693711yescharacteristic
220C2×C4#6694711yescharacteristic
221C2×C4#6694711yescharacteristic
222C2×C4#6695111yescharacteristic
223C2×C4#6696511yescharacteristic
224C2×C4#6696811yescharacteristic
225C2×C4#6696911yescharacteristic
226C2×C4#6697111yescharacteristic
227C8—81no—
228C8—81no—
229C8—441no—
230C8—441no—
231C8—881no—
232C8—881no—
233C22—21no—
234C22—21no—
235C22#1062228811yescharacteristic
236C22#1062238111yescharacteristic
237C22#1062241011yescharacteristic
238C4—21no—
239C4—21no—
240C4—21no—
241C4—21no—
242C4—161no—
243C4—882no—
244C4#1062238011yescharacteristic
245C4#1062241111yescharacteristic
246C4#1062248011yescharacteristic
247C4#1062250111yescharacteristic
248C2—21no—
249C2—21no—
250C2#1307003811yescharacteristic
251C2#1307007811yescharacteristic
252C2#1307008611yescharacteristic
subgroupG/H
centerC22#10622288
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#397
prime radicalC23×C11#124
hypercenter#1286D11
hypocenterC11#10636
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
206. C11#10636semidirect

Maximal subgroups

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

subgroupindex
#130695882
#130687562
#130673002
#130672982
#130664742
#130664602
C11×#12862
#1063611