Finite Group Databasebeta

← #14658573

Subgroups — #14658573

Order 2816.

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

normal subgroups only

This group has 294 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#13069589C211yesmaximal, characteristic
2#13068791C211yesmaximal, 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
12C2×#66883—21no—
13C2×#66883—21no—
14#10622549C2211yescharacteristic
15#10622537C2211yescharacteristic
16#10622537C2211yescharacteristic
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—
44#66883—42no—
45#66883—42no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49C4⋊(C11⋊C8)—21no—
50#10633—111nomaximal, Sylow
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11#4111yescharacteristic
53C22×C4×C11#4111yescharacteristic
54C22×Dic11—41no—
55C22×Dic11—41no—
56C2×Dic22—22no—
57C2×Dic22—41no—
58C2×Dic22—82no—
59C2×C8×C11—21no—
60C2×C8×C11—21no—
61C2×C8×C11—21no—
62C2×C8×C11—21no—
63C2×C8×C11—41no—
64C2×C8×C11—41no—
65C2×C8×C11SD1612yes—
66C2×C8×C11Q1612yes—
67C42×C11C2×D411yescharacteristic
68C42×C11#4111yescharacteristic
69C42×C11#4111yescharacteristic
70C42×C11#4111yescharacteristic
71C4⋊Dic11—22no—
72C4⋊Dic11—22no—
73C4⋊Dic11—41no—
74C4⋊Dic11—41no—
75C4⋊Dic11—41no—
76C4⋊Dic11—41no—
77#4318—41no—
78#4318—41no—
79#4318—41no—
80#4318—41no—
81C2×C11⋊C8—41no—
82C2×C11⋊C8—41no—
83#1993—111no—
84#1849—111no—
85#1549—111no—
86#1548—111no—
87#1286—111no—
88#1286—111no—
89#1281D1111yescharacteristic
90C23×C11#12411yescharacteristic
91C2×C4×C11—41no—
92C2×C4×C11—41no—
93C2×C4×C11#12111yescharacteristic
94C2×C4×C11#12311yescharacteristic
95C2×C4×C11#12311yescharacteristic
96C2×C4×C11#12311yescharacteristic
97C2×C4×C11#12611yescharacteristic
98C2×C4×C11#12611yescharacteristic
99C2×C4×C11C2×SD1611yescharacteristic
100C2×C4×C11C2×Q1611yescharacteristic
101C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
102C2×C4×C11#13711yescharacteristic
103C2×Dic11—42no—
104C2×Dic11—82no—
105C2×Dic11—81no—
106C2×Dic11—81no—
107C2×Dic11—81no—
108Dic22—82no—
109Dic22—82no—
110C8×C11—22no—
111C8×C11—22no—
112C8×C11—81no—
113C8×C11—81no—
114C11⋊C8—81no—
115C11⋊C8—81no—
116C2×C4⋊Q8—111no—
117#431C2×D1111yescharacteristic
118#431C2×D1111yescharacteristic
119C2×#108—221no—
120C2×#108—221no—
121#423—111no—
122#423—111no—
123C2×#97C2×D1111yescharacteristic
124#382—111no—
125#340—221no—
126#340—221no—
127#333—222no—
128#332—222no—
129C22×C11—21no—
130C22×C11—21no—
131C22×C11#39711yescharacteristic
132C22×C11#48711yescharacteristic
133C22×C11#48911yescharacteristic
134C4×C11—21no—
135C4×C11—21no—
136C4×C11—21no—
137C4×C11—21no—
138C4×C11#46011yescharacteristic
139C4×C11#46211yescharacteristic
140C4×C11#48311yescharacteristic
141C4×C11#48411yescharacteristic
142Dic11—82no—
143Dic11—161no—
144C22×Q8—221no—
145C2×M16—221no—
146C2×M16—221no—
147C22×C8D4411yescharacteristic
148C22×C8D4411yescharacteristic
149C4⋊Q8—112no—
150C4⋊Q8—221no—
151C4⋊Q8—221no—
152C4⋊Q8—221no—
153C2×C4⋊C4—221no—
154C2×C4⋊C4—221no—
155C2×C4⋊C4—221no—
156C2×C42C22×D1111yescharacteristic
157#108—442no—
158#108—442no—
159C4⋊C8—21no—
160C4⋊C8—21no—
161C4⋊C8—221no—
162C4⋊C8—221no—
163C4⋊C8—221no—
164C4⋊C8—221no—
165C22⋊C8—21no—
166C22⋊C8—21no—
167#97—21no—
168#97—21no—
169C4×C8—21no—
170C4×C8—21no—
171#95—221no—
172#95—221no—
173C2×C11—21no—
174C2×C11—21no—
175C2×C11#207211yescharacteristic
176C2×C11#208111yescharacteristic
177C2×C11#208211yescharacteristic
178C2×Q8—222no—
179C2×Q8—441no—
180C2×Q8—882no—
181C22×C4—441no—
182C22×C4—441no—
183C22×C4C2×D4411yescharacteristic
184C22×C4#433911yescharacteristic
185C22×C4#433911yescharacteristic
186M16—441no—
187M16—441no—
188M16—441no—
189M16—441no—
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—441no—
197C2×C8—441no—
198C2×C8#431412yes—
199C2×C8Dic4412yes—
200C4⋊C4—222no—
201C4⋊C4—222no—
202C4⋊C4—441no—
203C4⋊C4—441no—
204C4⋊C4—441no—
205C4⋊C4—441no—
206C42D4×D1111yescharacteristic
207C42#434111yescharacteristic
208C42#434111yescharacteristic
209C42#434311yescharacteristic
210C11#1063311yescharacteristic, complemented, Sylow
211C23#6692811yescharacteristic
212Q8—882no—
213Q8—882no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—442no—
217C2×C4—882no—
218C2×C4—881no—
219C2×C4—881no—
220C2×C4—881no—
221C2×C4#6693611yescharacteristic
222C2×C4#6693611yescharacteristic
223C2×C4#6693911yescharacteristic
224C2×C4#6694811yescharacteristic
225C2×C4#6695111yescharacteristic
226C2×C4#6695111yescharacteristic
227C2×C4C2×#431411yescharacteristic
228C2×C4C2×Dic4411yescharacteristic
229C2×C4#6696111yescharacteristic
230C2×C4#6696211yescharacteristic
231C8—22no—
232C8—22no—
233C8—81no—
234C8—81no—
235C8—881no—
236C8—881no—
237C22—21no—
238C22—21no—
239C22#1062228711yescharacteristic
240C22#1062229411yescharacteristic
241C22#1062232711yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—882no—
247C4—1761no—
248C4#1062233411yescharacteristic
249C4#1062233511yescharacteristic
250C4#1062246111yescharacteristic
251C4#1062246211yescharacteristic
252C2—21no—
253C2—21no—
254C2#1307002611yescharacteristic
255C2#1307007511yescharacteristic
256C2#1307008211yescharacteristic
subgroupG/H
centerC22#10622287
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1281C2
socleC22×C11#397
prime radicalC23×C11#124
hypercenter#1281D11
hypocenterC11#10633
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
210. C11#10633semidirect

Maximal subgroups

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

subgroupindex
#130695892
#130687912
#130673002
#130672962
#130664752
C11×#12812
#1063311