Finite Group Databasebeta

← #14651144

Subgroups — #14651144

Order 2816.

506 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 139 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#13077697C211yesmaximal, characteristic
2#13068612C211yesmaximal, characteristic
3#13067288C212yesmaximal
4#13066519C212yesmaximal
5C11×#2546C211yesmaximal, characteristic
6C2×C11×C4⋊Q8—21no—
7C2×C11×C4⋊Q8C2211yescharacteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C11×#398C414yes—
10C11×#391—21no—
11C11×#389—22no—
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×#66900—21no—
14Q8×C11⋊C8—24no—
15#10622538—22no—
16#10622538C2212yes—
17#10622537C2212yes—
18#10622185—24no—
19#10622168—21no—
20C22×Q8×C11—21no—
21C22×Q8×C11D411yescharacteristic
22C11×C4⋊Q8—22no—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8—42no—
25C11×C4⋊Q8—42no—
26C4×Q8×C11—22no—
27C4×Q8×C11—22no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—24no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4C2×C412yes—
32C2×C11×C4⋊C4C2×C412yes—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11—21no—
35C2×C42×C11D412yes—
36C2×C42×C11C2311yescharacteristic
37C2×#4318—22no—
38C11×#95—24no—
39C11×#95C2×C412yes—
40#66900—42no—
41C22⋊(C11⋊C8)—22no—
42C4⋊(C11⋊C8)—24no—
43C4⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)D414yes—
46C4×C11⋊C8—24no—
47C4×C11⋊C8—22no—
48#9394—111nomaximal, Sylow
49C2×Q8×C11—22no—
50C2×Q8×C11—22no—
51C2×Q8×C11—42no—
52C2×Q8×C11—41no—
53C2×Q8×C11—41no—
54C2×Q8×C11—42no—
55C2×Q8×C11D812yes—
56C2×Q8×C11SD1612yes—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11C22⋊C412yes—
60C22×C4×C11C22⋊C412yes—
61C22×C4×C11C22×C411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C11×C4⋊C4—24no—
65C11×C4⋊C4—24no—
66C11×C4⋊C4—22no—
67C11×C4⋊C4—24no—
68C11×C4⋊C4—48no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—41no—
71C42×C11—22no—
72C42×C11—22no—
73C42×C11—41no—
74C42×C11—41no—
75C42×C11C2×D412yes—
76C42×C11#4112yes—
77#4318—42no—
78#4318—42no—
79C2×C11⋊C8—24no—
80C2×C11⋊C8—42no—
81#2982—111no—
82#2546D1111yescharacteristic
83#1801—111no—
84#1546—112no—
85#1303—112no—
86C23×C11C2×C22⋊C411yescharacteristic
87Q8×C11—24no—
88Q8×C11—24no—
89Q8×C11—82no—
90Q8×C11—82no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—24no—
95C2×C4×C11—22no—
96C2×C4×C11—41no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11#10214yes—
104C2×C4×C11C4×D412yes—
105C2×C4×C11#12011yescharacteristic
106C2×C4×C11#12112yes—
107C2×C4×C11#12311yescharacteristic
108C2×C4×C11C2×D811yescharacteristic
109C2×C4×C11C2×SD1611yescharacteristic
110C2×C4×C11#13512yes—
111C11⋊C8—44no—
112C11⋊C8—82no—
113C2×C4⋊Q8—21no—
114C2×C4⋊Q8C2×D1111yescharacteristic
115C2×C4×Q8C2×D1111yescharacteristic
116C8×Q8—224no—
117#431—112no—
118#431—222no—
119#423—112no—
120C2×#101—221no—
121#398Dic1114yes—
122#391—21no—
123#389—22no—
124C4×C4⋊C4C2×D1111yescharacteristic
125#343—221no—
126#332—224no—
127C22×C11—21no—
128C22×C11—21no—
129C22×C11#38611yescharacteristic
130C22×C11C2×#10211yescharacteristic
131C22×C11#41611yescharacteristic
132C4×C11—21no—
133C4×C11—24no—
134C4×C11—22no—
135C4×C11—44no—
136C4×C11—42no—
137C4×C11—82no—
138C4×C11#45612yes—
139C4×C11#46512yes—
140C4×C11#46612yes—
141C22×Q8—21no—
142C22×Q8C22⋊D1111yescharacteristic
143C2×M16—222no—
144C4⋊Q8—22no—
145C4⋊Q8—22no—
146C4⋊Q8—42no—
147C4⋊Q8—42no—
148C4×Q8—22no—
149C4×Q8—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—24no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4C2×Dic1112yes—
154C2×C4⋊C4C2×Dic1112yes—
155C2×C4⋊C4C22⋊D1111yescharacteristic
156C2×C42—21no—
157C2×C42C22⋊D1112yes—
158C2×C42C22×D1111yescharacteristic
159C4⋊C8—114no—
160C4⋊C8—224no—
161C4⋊C8—222no—
162C4⋊C8—222no—
163#101—442no—
164C22⋊C8—222no—
165C4×C8—224no—
166C4×C8—222no—
167#95—24no—
168#95C2×Dic1112yes—
169C2×C11—21no—
170C2×C11—21no—
171C2×C11#188611yescharacteristic
172C2×C11#189311yescharacteristic
173C2×C11#191511yescharacteristic
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—42no—
179C2×Q8—42no—
180C2×Q8#432312yes—
181C2×Q8#432412yes—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4C22⋊Dic1112yes—
185C22×C4C22⋊Dic1112yes—
186C22×C4C22×Dic1111yescharacteristic
187C22×C4C2×C22⋊D1111yescharacteristic
188C22×C4C2×C22⋊D1111yescharacteristic
189M16—442no—
190M16—442no—
191C2×C8—224no—
192C2×C8—442no—
193C4⋊C4—24no—
194C4⋊C4—24no—
195C4⋊C4—22no—
196C4⋊C4—24no—
197C4⋊C4—48no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C42—22no—
201C42—22no—
202C42—41no—
203C42—41no—
204C42D4×D1112yes—
205C42#434112yes—
206C11#939411yescharacteristic, complemented, Sylow
207C23C2×C22⋊Dic1111yescharacteristic
208Q8—24no—
209Q8—24no—
210Q8—82no—
211Q8—82no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4#6689614yes—
225C2×C4C2×#432311yescharacteristic
226C2×C4C2×#432411yescharacteristic
227C2×C4D4×Dic1112yes—
228C2×C4#6698811yescharacteristic
229C2×C4#6699011yescharacteristic
230C2×C4#6699212yes—
231C2×C4#6700312yes—
232C8—444no—
233C8—882no—
234C22—21no—
235C22—21no—
236C22C2×#6689611yescharacteristic
237C22#1062283311yescharacteristic
238C22#1062284611yescharacteristic
239C4—22no—
240C4—21no—
241C4—24no—
242C4—44no—
243C4—42no—
244C4—82no—
245C4#1062265112yes—
246C4#1062265412yes—
247C4#1062270812yes—
248C2—21no—
249C2—21no—
250C2#1306901011yescharacteristic
251C2#1306904511yescharacteristic
252C2#1306916911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2546C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2546D11
hypocenterC11#9394
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2546

Complements

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

NH ≅ G/Ntype
206. C11#9394semidirect

Maximal subgroups

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

subgroupindex
#130776972
#130686122
#130672882
#130665192
C11×#25462
#939411