Finite Group Databasebeta

← #14657272

Subgroups — #14657272

Order 2816.

402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 91 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#13076684C211yesmaximal, characteristic
2#13069584C212yesmaximal
3C2×#10622103C212yesmaximal
4#13066497C211yesmaximal, characteristic
5C11×#1847C211yesmaximal, characteristic
6C2×#66923C2212yes—
7C2×C11×#107—21no—
8C2×C11×#106—21no—
9C2×C11×#97C2211yescharacteristic
10C11×#384C2211yescharacteristic
11C11×#382C2211yescharacteristic
12#10622596—21no—
13#10622596—21no—
14C2×#66867C2212yes—
15#10622274—22no—
16#10622272—22no—
17#10622167—22no—
18#10622167—22no—
19#10622103—24no—
20C22×C8×C11—21no—
21C2×C11×C4⋊C4—21no—
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4D411yescharacteristic
24C2×C11×C4⋊C4D411yescharacteristic
25C2×C42×C11C2311yescharacteristic
26C2×C4⋊Dic11—21no—
27C2×C4⋊Dic11—21no—
28C2×C4⋊Dic11D412yes—
29C2×C4⋊Dic11D412yes—
30C2×Dic11⋊C4—22no—
31C2×Dic11⋊C4—22no—
32C22×C11⋊C8—22no—
33#66923—22no—
34#66923—22no—
35#66923—22no—
36#66923—22no—
37C11×#107—42no—
38C11×#106—42no—
39C11×#97—21no—
40C11×#97D412yes—
41C11×#95—22no—
42C11⋊#95—21no—
43C11⋊#95—21no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46#66867—22no—
47#66867—22no—
48#10429—111nomaximal, Sylow
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11—41no—
52C22×C4×C11C2×D412yes—
53C22×C4×C11C2×D411yescharacteristic
54C22×Dic11—22no—
55C22×Dic11—22no—
56C2×C8×C11—22no—
57C2×C8×C11—22no—
58C2×C8×C11—22no—
59C11×C4⋊C4—41no—
60C11×C4⋊C4—41no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—44no—
64C42×C11C2×D411yescharacteristic
65C42×C11#4111yescharacteristic
66C42×C11#4112yes—
67C4⋊Dic11—22no—
68C4⋊Dic11—22no—
69C4⋊Dic11—22no—
70C4⋊Dic11—22no—
71C4⋊Dic11—81no—
72C4⋊Dic11—81no—
73Dic11⋊C4—42no—
74Dic11⋊C4—42no—
75Dic11⋊C4—42no—
76Dic11⋊C4—42no—
77C2×C11⋊C8—24no—
78C2×C11⋊C8—42no—
79C2×C11⋊C8—42no—
80#2822—111no—
81#1992—112no—
82#1847D1111yescharacteristic
83C2×#330—112no—
84#1295—111no—
85C23×C11#12011yescharacteristic
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—21no—
90C2×C4×C11—41no—
91C2×C4×C11—41no—
92C2×C4×C11—42no—
93C2×C4×C11—42no—
94C2×C4×C11—81no—
95C2×C4×C11—82no—
96C2×C4×C11#12112yes—
97C2×C4×C11#12111yescharacteristic
98C2×C4×C11#12312yes—
99C2×C4×C11#12411yescharacteristic
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—42no—
105C2×Dic11—42no—
106C8×C11—24no—
107C11⋊C8—44no—
108C2×#125—112no—
109C2×#107—21no—
110C2×#106—21no—
111C2×#97—112no—
112C2×#97C2×D1111yescharacteristic
113#400—222no—
114#398—222no—
115#398—221no—
116#398—221no—
117#384C2×D1111yescharacteristic
118#382C2×D1111yescharacteristic
119#340—222no—
120#340—222no—
121#330—224no—
122C22×C11#39411yescharacteristic
123C22×C11#45311yescharacteristic
124C22×C11#45412yes—
125C22×C11#45612yes—
126C22×C11#45611yescharacteristic
127C4×C11—22no—
128C4×C11—22no—
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—81no—
132C4×C11—81no—
133C4×C11—161no—
134Dic11—82no—
135Dic11—82no—
136C22×C8—21no—
137C22×C8—222no—
138#125—222no—
139#125—222no—
140#125—222no—
141#125—222no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—112no—
145C2×C4⋊C4—112no—
146C2×C4⋊C4—222no—
147C2×C4⋊C4—222no—
148C2×C4⋊C4—221no—
149C2×C4⋊C4—221no—
150C2×C4⋊C4C22⋊D1111yescharacteristic
151C2×C4⋊C4C22⋊D1111yescharacteristic
152C2×C42C22×D1111yescharacteristic
153#107—42no—
154#106—42no—
155#97—21no—
156#97—222no—
157#97—222no—
158#97D4412yes—
159#95—22no—
160#95—222no—
161#95—222no—
162#95—221no—
163#95—221no—
164C2×C11#165711yescharacteristic
165C2×C11#166011yescharacteristic
166C2×C11#166312yes—
167C2×C11#203812yes—
168C2×C11#203911yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—41no—
172C22×C4—222no—
173C22×C4—222no—
174C22×C4D4×D1112yes—
175C22×C4C2×C22⋊D1111yescharacteristic
176C2×C8—22no—
177C2×C8—22no—
178C2×C8—22no—
179C2×C8—224no—
180C2×C8—442no—
181C2×C8—442no—
182C4⋊C4—41no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—44no—
187C4⋊C4—222no—
188C4⋊C4—222no—
189C4⋊C4—222no—
190C4⋊C4—222no—
191C4⋊C4—442no—
192C4⋊C4—442no—
193C4⋊C4—442no—
194C4⋊C4—442no—
195C4⋊C4—881no—
196C4⋊C4—881no—
197C42C2×D4411yescharacteristic
198C42#433911yescharacteristic
199C42#434312yes—
200C11#1042911yescharacteristic, complemented, Sylow
201C23#6699011yescharacteristic
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—82no—
211C2×C4—81no—
212C2×C4—442no—
213C2×C4—442no—
214C2×C4—442no—
215C2×C4—442no—
216C2×C4—442no—
217C2×C4—442no—
218C2×C4#6694712yes—
219C2×C4#6694812yes—
220C2×C4#6698311yescharacteristic
221C2×C4#6700011yescharacteristic
222C8—24no—
223C8—444no—
224C22#1062260411yescharacteristic
225C22#1062269011yescharacteristic
226C22#1062270811yescharacteristic
227C22#1062281412yes—
228C22#1062281812yes—
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—81no—
234C4—81no—
235C4—161no—
236C4—882no—
237C4—882no—
238C2#1306791211yescharacteristic
239C2#1306792511yescharacteristic
240C2#1306794312yes—
241C2#1306983512yes—
242C2#1306984011yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1847C2
socle, prime radicalC23×C11#120
hypercenter#1847D11
hypocenterC11#10429
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
200. C11#10429semidirect

Maximal subgroups

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

subgroupindex
#130766842
#130695842
C2×#106221032
#130664972
C11×#18472
#1042911