Finite Group Databasebeta

← #14648240

Subgroups — #14648240

Order 2816.

476 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 155 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#13071706C211yesmaximal, characteristic
2#13069419C211yesmaximal, characteristic
3#13069380C212yesmaximal
4#13066455C212yesmaximal
5C2×C11×#333C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C11×C4⋊C8C2212yes—
8#10622843—22no—
9C2×#66899—22no—
10C2×#66881—22no—
11#10622598—22no—
12C4⋊C4×Dic11—22no—
13#10622548C2211yescharacteristic
14C4×C4⋊Dic11C2212yes—
15C2×C4×C11⋊C8C2211yescharacteristic
16C11×#333C414yescomplemented
17#10622189—22no—
18C22×Q8×C11D412yes—
19C22×C8×C11—22no—
20C11×C4⋊Q8—22no—
21C11×C4⋊Q8C2×C412yes—
22C11×C4⋊Q8Q812yes—
23C2×C11×C4⋊C4—22no—
24C2×C42×C11C2311yescharacteristic
25C2×C4⋊Dic11—21no—
26C2×C4⋊Dic11—22no—
27C2×C4⋊Dic11—22no—
28C2×C4⋊Dic11D412yes—
29C2×C4⋊Dic11D412yes—
30C2×C4×Dic11—22no—
31C2×C4×Dic11—22no—
32C22×C11⋊C8—21no—
33C11×C4⋊C8—22no—
34C11×C4⋊C8C2×C414yes—
35#66899—44no—
36C11⋊#95—24no—
37C11⋊#95—22no—
38#66881—44no—
39C4×C11⋊C8—22no—
40#8928—111nomaximal, Sylow
41C2×Q8×C11—22no—
42C2×Q8×C11—42no—
43C2×Q8×C11—42no—
44C2×Q8×C11C4⋊C414yes—
45C22×C4×C11—22no—
46C22×C4×C11C2×D411yescharacteristic
47C22×C4×C11C2×D412yes—
48C22×Dic11—22no—
49C22×Dic11—22no—
50C22×Dic11—41no—
51C2×C8×C11—24no—
52C2×C8×C11—42no—
53C2×C8×C11—42no—
54C11×C4⋊C4—24no—
55C11×C4⋊C4—24no—
56C42×C11C22×C411yescharacteristic
57C42×C11C2×Q811yescharacteristic
58C42×C11#4112yes—
59C4⋊Dic11—22no—
60C4⋊Dic11—22no—
61C4⋊Dic11—22no—
62C4⋊Dic11—42no—
63C4⋊Dic11—42no—
64C4⋊Dic11—42no—
65C4⋊Dic11—82no—
66C4⋊Dic11SD1614yes—
67C4×Dic11—42no—
68C4×Dic11—42no—
69C4×Dic11—82no—
70C2×C11⋊C8—22no—
71C2×C11⋊C8—41no—
72C2×C11⋊C8—41no—
73#2369—111no—
74#1956—111no—
75#1948—112no—
76C2×#333D1111yescharacteristic
77#1279—112no—
78C23×C11#12011yescharacteristic
79Q8×C11—44no—
80Q8×C11—82no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—24no—
84C2×C4×C11—42no—
85C2×C4×C11—42no—
86C2×C4×C11C2×C4⋊C411yescharacteristic
87C2×C4×C11C4×D412yes—
88C2×C4×C11C22⋊Q812yes—
89C2×C4×C11#12311yescharacteristic
90C2×C4×C11C2×SD1612yes—
91C2×C4×C11#13512yes—
92C2×C4×C11#13712yes—
93C2×C4×C11#13712yes—
94C2×Dic11—24no—
95C2×Dic11—42no—
96C2×Dic11—42no—
97C2×Dic11—42no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11—82no—
101C2×Dic11—81no—
102C8×C11—44no—
103C11⋊C8—42no—
104C2×C4⋊Q8C2×D1111yescharacteristic
105C2×#106—222no—
106C2×C4⋊C8C2×D1112yes—
107C2×#103—222no—
108C2×C4×C8—111no—
109#391—222no—
110#389—222no—
111#384—111no—
112C4×C4⋊C4—112no—
113C4×C4⋊C4—222no—
114#340—222no—
115#333Dic1114yescomplemented
116C22×C11#38511yescharacteristic
117C22×C11#44812yes—
118C22×C11#45212yes—
119C22×C11#45311yescharacteristic
120C22×C11#45511yescharacteristic
121C4×C11—21no—
122C4×C11—21no—
123C4×C11—44no—
124C4×C11C4×SD1612yes—
125C4×C11#44112yes—
126C4×C11#47512yes—
127C4×C11#47912yes—
128Dic11—44no—
129Dic11—82no—
130Dic11—161no—
131C22×Q8D4412yes—
132C22×C8—22no—
133C22×C8—221no—
134C4⋊Q8—22no—
135C4⋊Q8Dic2212yes—
136C4⋊Q8C2×Dic1112yes—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—112no—
139C2×C4⋊C4—112no—
140C2×C4⋊C4—221no—
141C2×C4⋊C4—222no—
142C2×C4⋊C4—222no—
143C2×C42—222no—
144C2×C42—222no—
145C2×C42C22×D1111yescharacteristic
146#106—444no—
147C4⋊C8—22no—
148C4⋊C8C2×Dic1114yes—
149#103—444no—
150C4×C8—222no—
151#95—224no—
152#95—222no—
153C2×C11#162311yescharacteristic
154C2×C11#163411yescharacteristic
155C2×C11#164312yes—
156C2×C11#185611yescharacteristic
157C2×C11#186512yes—
158C2×Q8—22no—
159C2×Q8—42no—
160C2×Q8—42no—
161C2×Q8C4⋊Dic1114yes—
162C22×C4—22no—
163C22×C4—222no—
164C22×C4—222no—
165C22×C4—441no—
166C22×C4C2×D4411yescharacteristic
167C22×C4D4×D1112yes—
168C2×C8—24no—
169C2×C8—42no—
170C2×C8—42no—
171C2×C8—222no—
172C2×C8—441no—
173C2×C8—441no—
174C4⋊C4—24no—
175C4⋊C4—24no—
176C4⋊C4—114no—
177C4⋊C4—222no—
178C4⋊C4—222no—
179C4⋊C4—222no—
180C4⋊C4—442no—
181C4⋊C4—442no—
182C4⋊C4—442no—
183C4⋊C4—882no—
184C42—442no—
185C42—442no—
186C42—882no—
187C42C2×Dic2211yescharacteristic
188C42#434112yes—
189C42C22×Dic1111yescharacteristic
190C11#892811yescharacteristic, complemented, Sylow
191C23#6693511yescharacteristic
192Q8—44no—
193Q8—82no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—24no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—224no—
200C2×C4—442no—
201C2×C4—442no—
202C2×C4—442no—
203C2×C4—442no—
204C2×C4—442no—
205C2×C4—881no—
206C2×C4—882no—
207C2×C4#6693112yes—
208C2×C4#6693911yescharacteristic
209C2×C4SD16×D1112yes—
210C2×C4#6696912yes—
211C2×C4#6697112yes—
212C2×C4#6697112yes—
213C2×C4C2×C4⋊Dic1111yescharacteristic
214C2×C4D4×Dic1112yes—
215C8—44no—
216C8—442no—
217C22#1062235911yescharacteristic
218C22#1062236011yescharacteristic
219C22#1062241912yes—
220C22#1062242312yes—
221C22#1062256311yescharacteristic
222C4—21no—
223C4—21no—
224C4—44no—
225C4—444no—
226C4—882no—
227C4—1761no—
228C4#1062240412yes—
229C4#1062241212yes—
230C4SD16×Dic1112yes—
231C4#1062279712yes—
232C2#1306769511yescharacteristic
233C2#1306776211yescharacteristic
234C2#1306782412yes—
235C2#1306882811yescharacteristic
236C2#1306888612yes—
subgroupG/H
centerC23#66935
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#333C2
socle, prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenterC2×#333D11
hypocenterC11#8928
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
16. C11×#333C4semidirect
115. #333Dic11semidirect
190. C11#8928semidirect

Maximal subgroups

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

subgroupindex
#130717062
#130694192
#130693802
#130664552
C2×C11×#3332
#892811