Finite Group Databasebeta

← #14643090

Subgroups — #14643090

Order 2816.

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

normal subgroups only

This group has 438 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#13076562C211yesmaximal, characteristic
2#13070155C212yesmaximal, complemented
3#13066441C212yesmaximal, complemented
4#13066437C211yesmaximal, characteristic
5C11×#2094C211yesmaximal, characteristic
6C2×C11×#106—21no—
7C2×C11×#102—21no—
8C11×#390C2211yescharacteristic
9C11×#384C2211yescharacteristic
10#10622833—21no—
11#10622599—21no—
12C2×#66874—22no—
13C2×#66871—22no—
14#10622563—22no—
15#10622560—22no—
16#10622542C2212yes—
17C11×#336C2211yescharacteristic
18#10622162C2212yes—
19C22×D4×C11D411yescharacteristic
20C23×Dic11—21no—
21C22×Dic22D412yes—
22C22×C8×C11—21no—
23C2×C11×C4⋊C4—22no—
24C2×C11×C4⋊C4—21no—
25C2×C11×C4⋊C4D411yescharacteristic
26C2×C11×C22⋊C4—22no—
27C2×C42×C11C2311yescharacteristic
28C2×C22⋊Dic11—21no—
29C2×C22⋊Dic11—22no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11D412yes—
32C22×C11⋊C8—22no—
33C11×#106—42no—
34C11×#102—42no—
35C11⋊#95—21no—
36C11⋊#95—22no—
37C11⋊#95—22no—
38C11⋊#95—22no—
39#66874—44no—
40#66871—44no—
41#7833—111nomaximal, Sylow
42C24×C11—21no—
43C2×D4×C11—21no—
44C2×D4×C11—41no—
45C2×D4×C11—41no—
46C2×D4×C11Q1612yes—
47C22×C4×C11—21no—
48C22×C4×C11—41no—
49C22×C4×C11C2×D411yescharacteristic
50C22×C4×C11C2×D412yes—
51C22×Dic11—22no—
52C22×Dic11—22no—
53C22×Dic11—82no—
54C22×Dic11—81no—
55C2×Dic22—22no—
56C2×Dic22—22no—
57C2×Dic22—42no—
58C2×Dic22—42no—
59C2×C8×C11—22no—
60C2×C8×C11—41no—
61C2×C8×C11—41no—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—42no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—41no—
67C11×C22⋊C4—42no—
68C11×C22⋊C4—42no—
69C42×C11—41no—
70C22⋊Dic11—82no—
71C22⋊Dic11—81no—
72C4⋊Dic11—42no—
73C4⋊Dic11—81no—
74C2×C11⋊C8—24no—
75C2×C11⋊C8—42no—
76C2×C11⋊C8—42no—
77#2804—111no—
78#2095—112no—
79#2094D1111yescharacteristic
80#1272—112no—
81#1270—111no—
82C23×C11—22no—
83C23×C11—42no—
84C23×C11—42no—
85C23×C11—41no—
86C23×C11—41no—
87C23×C11#12011yescharacteristic
88D4×C11—42no—
89D4×C11—81no—
90C2×C4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—21no—
94C2×C4×C11—42no—
95C2×C4×C11—41no—
96C2×C4×C11—82no—
97C2×C4×C11—81no—
98C2×C4×C11C2×Q1611yescharacteristic
99C2×C4×C11#13512yes—
100C2×C4×C11#13712yes—
101C2×C4×C11#13711yescharacteristic
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—84no—
109Dic22—44no—
110Dic22—82no—
111C8×C11—42no—
112C11⋊C8—44no—
113C2×#107—222no—
114C2×#106—21no—
115C2×#103—222no—
116C2×#102—21no—
117#400—221no—
118#393—222no—
119#391—112no—
120#390C2×D1111yescharacteristic
121#386—221no—
122#385—222no—
123#384C2×D1111yescharacteristic
124#336—112no—
125#336C2×D1111yescharacteristic
126C22×C11—42no—
127C22×C11—44no—
128C22×C11—82no—
129C22×C11—81no—
130C22×C11—81no—
131C22×C11#45111yescharacteristic
132C22×C11#45212yes—
133C22×C11#45312yes—
134C22×C11#45311yescharacteristic
135C22×C11#45811yescharacteristic
136C4×C11—21no—
137C4×C11—21no—
138C4×C11—22no—
139C4×C11—22no—
140C4×C11—81no—
141C4×C11—161no—
142Dic11—82no—
143Dic11—82no—
144C22×Q8—112no—
145C22×D4C22⋊D1111yescharacteristic
146C23×C4—221no—
147C22×C8—21no—
148C22×C8—222no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—112no—
152C2×C4⋊C4—221no—
153C2×C4⋊C4C22⋊D1111yescharacteristic
154C2×C22⋊C4—22no—
155C2×C22⋊C4—222no—
156C2×C22⋊C4—221no—
157C2×C42C22×D1111yescharacteristic
158#107—444no—
159#106—42no—
160#103—444no—
161#102—42no—
162#95—222no—
163#95—221no—
164#95—222no—
165#95—222no—
166C2×C11—82no—
167C2×C11#161411yescharacteristic
168C2×C11#161812yes—
169C2×C11#163011yescharacteristic
170C2×C11#163212yes—
171C2×C11#165511yescharacteristic
172C24—21no—
173C2×Q8—222no—
174C2×Q8—222no—
175C2×Q8—442no—
176C2×Q8—442no—
177C2×D4—21no—
178C2×D4—41no—
179C2×D4—41no—
180C2×D4#432612yes—
181C22×C4—21no—
182C22×C4—41no—
183C22×C4—222no—
184C22×C4—222no—
185C22×C4—882no—
186C22×C4—881no—
187C22×C4D4×D1112yes—
188C22×C4C2×C22⋊D1111yescharacteristic
189C2×C8—22no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—224no—
193C2×C8—442no—
194C2×C8—442no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—442no—
201C4⋊C4—881no—
202C22⋊C4—42no—
203C22⋊C4—42no—
204C22⋊C4—882no—
205C22⋊C4—881no—
206C42—41no—
207C11#783311yescharacteristic, complemented, Sylow
208C23—22no—
209C23—42no—
210C23—42no—
211C23—41no—
212C23—41no—
213C23#6699011yescharacteristic
214Q8—444no—
215Q8—882no—
216D4—42no—
217D4—81no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—82no—
225C2×C4—81no—
226C2×C4—442no—
227C2×C4—442no—
228C2×C4—442no—
229C2×C4—442no—
230C2×C4—442no—
231C2×C4—442no—
232C2×C4—884no—
233C2×C4#6696812yes—
234C2×C4#6696912yes—
235C2×C4C2×#432611yescharacteristic
236C2×C4#6700411yescharacteristic
237C8—42no—
238C8—444no—
239C22—42no—
240C22—44no—
241C22—81no—
242C22—82no—
243C22—81no—
244C22#1062266311yescharacteristic
245C22#1062266611yescharacteristic
246C22#1062269011yescharacteristic
247C22#1062278612yes—
248C22#1062281112yes—
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—81no—
254C4—161no—
255C4—882no—
256C4—882no—
257C2—82no—
258C2#1306764011yescharacteristic
259C2#1306766112yes—
260C2#1306773511yescharacteristic
261C2#1306774812yes—
262C2#1306790411yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2094C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenter#2094D11
hypocenterC11#7833
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2094

Complements

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

NH ≅ G/Ntype
2. #13070155C2semidirect
3. #13066441C2semidirect
207. C11#7833semidirect

Maximal subgroups

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

subgroupindex
#130765622
#130701552
#130664412
#130664372
C11×#20942
#783311