Finite Group Databasebeta

← #14656871

Subgroups — #14656871

Order 2816.

438 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 99 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#13076979C211yesmaximal, characteristic, complemented
2#13067176C212yesmaximal
3#13066476C212yesmaximal, complemented
4#13066449C211yesmaximal, characteristic, complemented
5C11×#1962C211yesmaximal, characteristic
6C11×#532C2211yescharacteristic
7C2×#66923—21no—
8C11×#423C2211yescharacteristic
9C2×C11×#104—21no—
10C2×C11×#104—21no—
11C43×C11C2211yescharacteristic
12#10622549C2212yes—
13#10622548—21no—
14#10622541—24no—
15#10622538C2212yes—
16#10622175—24no—
17C2×C11×#41—21no—
18C2×C11×M16—21no—
19C11×C4⋊Q8Q811yescharacteristic
20C11×#127Q811yescharacteristic
21C11×#124—21no—
22C11×#121—22no—
23C4×D4×C11—22no—
24C2×C42×C11—22no—
25C2×C42×C11D411yescharacteristic
26C2×C42×C11D411yescharacteristic
27C2×C42×C11C2311yescharacteristic
28C2×C4⋊Dic11—24no—
29C2×C4⋊Dic11—22no—
30C2×Dic11⋊C4—24no—
31#66923—42no—
32#66923—42no—
33C11×C4⋊C8—22no—
34C11×#104—42no—
35C11×#104—42no—
36C11⋊#95—22no—
37C11⋊#95D414yes—
38C22⋊(C11⋊C8)—22no—
39C4⋊(C11⋊C8)—22no—
40C4×C11⋊C8—22no—
41#10364—111nomaximal, Sylow
42C11×#41—41no—
43C11×#41—41no—
44C11×#41—41no—
45C11×#41—41no—
46C2×Q8×C11—21no—
47C2×D4×C11—21no—
48C2×D4×C11—22no—
49C2×D4×C11—41no—
50C22×C4×C11—21no—
51C22×C4×C11—21no—
52C22×C4×C11—41no—
53C22×C4×C11C2×D412yes—
54C22×C4×C11C2×D411yescharacteristic
55C22×Dic11—24no—
56C11×M16—41no—
57C11×M16—41no—
58C2×C8×C11—41no—
59C11×C4⋊C4—22no—
60C11×C22⋊C4—42no—
61C42×C11—21no—
62C42×C11—21no—
63C42×C11—44no—
64C42×C11D812yes—
65C42×C11SD1612yes—
66C42×C11C2×Q811yescharacteristic
67C42×C11#4111yescharacteristic
68C42×C11#4112yes—
69C4⋊Dic11—48no—
70C4⋊Dic11—42no—
71C4⋊Dic11—42no—
72Dic11⋊C4—48no—
73C2×C11⋊C8—42no—
74#2859—111no—
75#1962D1111yescharacteristic
76#1517—112no—
77#1286—112no—
78#1276—111no—
79C23×C11—41no—
80C23×C11#12011yescharacteristic
81Q8×C11—41no—
82Q8×C11—41no—
83D4×C11—41no—
84D4×C11—41no—
85D4×C11—82no—
86D4×C11—81no—
87D4×C11—81no—
88C2×C4×C11—24no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—42no—
92C2×C4×C11—42no—
93C2×C4×C11—41no—
94C2×C4×C11—81no—
95C2×C4×C11—81no—
96C2×C4×C11C22⋊Q812yes—
97C2×C4×C11C22⋊Q811yescharacteristic
98C2×C4×C11#12412yes—
99C2×C4×C11#12411yescharacteristic
100C2×C4×C11C2×D811yescharacteristic
101C2×C4×C11C2×SD1611yescharacteristic
102C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
103C2×C4×C11#13711yescharacteristic
104C2×Dic11—48no—
105C2×Dic11—44no—
106C8×C11—81no—
107C11⋊C8—82no—
108#532C2×D1111yescharacteristic
109C2×#125—221no—
110#431—112no—
111#423C2×D1111yescharacteristic
112C2×#104—21no—
113C2×#104—21no—
114#389—224no—
115#384—221no—
116#382—112no—
117C43C2×D1111yescharacteristic
118#327—224no—
119C22×C11—22no—
120C22×C11—81no—
121C22×C11—82no—
122C22×C11#39311yescharacteristic
123C22×C11#44711yescharacteristic
124C22×C11#44811yescharacteristic
125C4×C11—24no—
126C4×C11—22no—
127C4×C11—22no—
128C4×C11—42no—
129C4×C11—81no—
130C4×C11#47411yescharacteristic
131C4×C11#47611yescharacteristic
132C4×C11#48611yescharacteristic
133C4×C11#48911yescharacteristic
134Dic11—84no—
135C2×#41—21no—
136C2×M16—21no—
137C4⋊Q8Dic2211yescharacteristic
138#127Dic2211yescharacteristic
139#125—442no—
140#125—442no—
141#124—21no—
142#121—22no—
143C4×D4—22no—
144C2×C4⋊C4—224no—
145C2×C4⋊C4—224no—
146C2×C4⋊C4—222no—
147C2×C42—22no—
148C2×C42C22⋊D1111yescharacteristic
149C2×C42C22⋊D1111yescharacteristic
150C2×C42C22×D1111yescharacteristic
151C4⋊C8—22no—
152C4⋊C8—222no—
153#104—42no—
154#104—42no—
155C22⋊C8—222no—
156C4×C8—222no—
157#95—114no—
158#95—222no—
159C2×C11—21no—
160C2×C11—21no—
161C2×C11—161no—
162C2×C11#202311yescharacteristic
163C2×C11#203112yes—
164#41—41no—
165#41—41no—
166#41—41no—
167#41—41no—
168C2×Q8—21no—
169C2×D4—22no—
170C2×D4—21no—
171C2×D4—41no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—41no—
175C22×C4—224no—
176C22×C4D4×D1112yes—
177C22×C4C2×C22⋊D1111yescharacteristic
178M16—41no—
179M16—41no—
180C2×C8—41no—
181C2×C8—442no—
182C4⋊C4—22no—
183C4⋊C4—448no—
184C4⋊C4—448no—
185C4⋊C4—442no—
186C4⋊C4—442no—
187C22⋊C4—42no—
188C42—21no—
189C42—21no—
190C42—44no—
191C42#432312yes—
192C42#432412yes—
193C42C2×Dic2211yescharacteristic
194C42#433911yescharacteristic
195C42#434112yes—
196C11#1036411yescharacteristic, complemented, Sylow
197C23—41no—
198C23#6699011yescharacteristic
199Q8—41no—
200Q8—41no—
201D4—41no—
202D4—41no—
203D4—82no—
204D4—81no—
205D4—81no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—81no—
213C2×C4—81no—
214C2×C4—448no—
215C2×C4—444no—
216C2×C4#6693112yes—
217C2×C4#6693812yes—
218C2×C4#6697711yescharacteristic
219C2×C4C2×#432311yescharacteristic
220C2×C4C2×#432411yescharacteristic
221C2×C4#6698911yescharacteristic
222C2×C4#6700211yescharacteristic
223C2×C4#6700411yescharacteristic
224C8—81no—
225C8—882no—
226C22—22no—
227C22—81no—
228C22—82no—
229C22#1062256011yescharacteristic
230C22#1062264911yescharacteristic
231C22#1062265311yescharacteristic
232C4—24no—
233C4—22no—
234C4—22no—
235C4—42no—
236C4—81no—
237C4—884no—
238C4#1062262011yescharacteristic
239C4#1062262111yescharacteristic
240C4#1062266811yescharacteristic
241C4#1062268311yescharacteristic
242C2—21no—
243C2—21no—
244C2—161no—
245C2#1306975211yescharacteristic
246C2#1306978812yes—
subgroupG/H
centerC22#10622560
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1962C2
socleC22×C11#393
prime radicalC11×#532C22
hypercenter#1962D11
hypocenterC11#10364
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1962

Complements

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

NH ≅ G/Ntype
1. #13076979C2semidirect
3. #13066476C2semidirect
4. #13066449C2semidirect
196. C11#10364semidirect

Maximal subgroups

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

subgroupindex
#130769792
#130671762
#130664762
#130664492
C11×#19622
#1036411