Finite Group Databasebeta

← #14657323

Subgroups — #14657323

Order 2816.

478 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 125 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#13073989C211yesmaximal, characteristic
2#13068772C211yesmaximal, characteristic
3#13068622C212yesmaximal
4C2×#10622122C212yesmaximal
5C11×#1296C211yesmaximal, characteristic
6C2×C4×Dic22C2212yes—
7C2×C11×C4⋊C8C2212yes—
8C11×#384C2211yescharacteristic
9C2×#66880—22no—
10#10622598—22no—
11#10622596—22no—
12#10622587—22no—
13C2×#66872—22no—
14#10622548C2211yescharacteristic
15C2×C4×C11⋊C8C2211yescharacteristic
16#10622189—22no—
17#10622122—24no—
18C22×Dic22D412yes—
19C22×C8×C11—22no—
20C2×C11×C4⋊C4—22no—
21C2×C11×C4⋊C4D412yes—
22C2×C42×C11C2311yescharacteristic
23C2×C4⋊Dic11—21no—
24C2×C4⋊Dic11—22no—
25C2×C4⋊Dic11—22no—
26C2×C4⋊Dic11D412yes—
27C2×Dic11⋊C4—22no—
28C2×C4×Dic11—22no—
29C22×C11⋊C8—21no—
30C4×Dic22—22no—
31C4×Dic22—22no—
32C4×Dic22—22no—
33C4×Dic22—22no—
34C11×C4⋊C8—22no—
35C11×C4⋊C8—22no—
36C11⋊#95—22no—
37C11⋊#95—24no—
38#66880—44no—
39#66872—44no—
40C4×C11⋊C8—21no—
41C4×C11⋊C8D412yes—
42#10437—111nomaximal, Sylow
43C22×C4×C11—22no—
44C22×C4×C11C2×D411yescharacteristic
45C22×C4×C11C2×D412yes—
46C22×Dic11—22no—
47C22×Dic11—22no—
48C22×Dic11—41no—
49C2×Dic22—22no—
50C2×Dic22—22no—
51C2×Dic22—22no—
52C2×Dic22—22no—
53C2×Dic22—22no—
54C2×Dic22SD1614yes—
55C2×C8×C11—42no—
56C2×C8×C11—42no—
57C2×C8×C11—42no—
58C11×C4⋊C4—42no—
59C11×C4⋊C4—42no—
60C11×C4⋊C4—42no—
61C42×C11C2×D411yescharacteristic
62C42×C11#4111yescharacteristic
63C42×C11#4112yes—
64C4⋊Dic11—22no—
65C4⋊Dic11—22no—
66C4⋊Dic11—42no—
67C4⋊Dic11—42no—
68C4⋊Dic11—42no—
69C4⋊Dic11—82no—
70Dic11⋊C4—42no—
71Dic11⋊C4—42no—
72C4×Dic11—42no—
73C4×Dic11—42no—
74C2×C11⋊C8—22no—
75C2×C11⋊C8—22no—
76C2×C11⋊C8—22no—
77#2582—111no—
78#1844—111no—
79#1803—112no—
80C2×Q8⋊C8—112no—
81#1296D1111yescharacteristic
82C23×C11#12011yescharacteristic
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—44no—
86C2×C4×C11—42no—
87C2×C4×C11#12112yes—
88C2×C4×C11#12111yescharacteristic
89C2×C4×C11#12312yes—
90C2×C4×C11#12411yescharacteristic
91C2×C4×C11C2×SD1612yes—
92C2×C4×C11#13512yes—
93C2×C4×C11#13712yes—
94C2×C4×C11#13712yes—
95C2×Dic11—24no—
96C2×Dic11—42no—
97C2×Dic11—42no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—82no—
102C2×Dic11—81no—
103Dic22—24no—
104Dic22—24no—
105Dic22—42no—
106Dic22—42no—
107C8×C11—82no—
108C11⋊C8—24no—
109C2×C4×Q8—112no—
110C2×#106—222no—
111C2×C4⋊C8C2×D1112yes—
112C2×#103—222no—
113C2×C4×C8—111no—
114#398—222no—
115#391—222no—
116#389—222no—
117#384—111no—
118#384C2×D1111yescharacteristic
119#340—222no—
120Q8⋊C8—224no—
121C22×C11#39411yescharacteristic
122C22×C11#44812yes—
123C22×C11#45212yes—
124C22×C11#45311yescharacteristic
125C22×C11#45611yescharacteristic
126C4×C11—21no—
127C4×C11—21no—
128C4×C11—82no—
129C4×C11#46512yes—
130C4×C11#47012yes—
131C4×C11#48312yes—
132C4×C11#48512yes—
133Dic11—44no—
134Dic11—82no—
135Dic11—161no—
136C22×Q8—112no—
137C22×C8—22no—
138C22×C8—221no—
139C4×Q8—222no—
140C4×Q8—222no—
141C4×Q8—222no—
142C4×Q8—222no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—112no—
145C2×C4⋊C4—222no—
146C2×C4⋊C4—221no—
147C2×C4⋊C4—222no—
148C2×C4⋊C4—222no—
149C2×C4⋊C4D4412yes—
150C2×C42—222no—
151C2×C42C22×D1111yescharacteristic
152#106—444no—
153C4⋊C8—22no—
154C4⋊C8—22no—
155#103—444no—
156C4×C8—112no—
157C4×C8—221no—
158#95—224no—
159#95—222no—
160C2×C11#162311yescharacteristic
161C2×C11#163011yescharacteristic
162C2×C11#165312yes—
163C2×C11#203512yes—
164C2×C11#203911yescharacteristic
165C2×Q8—114no—
166C2×Q8—222no—
167C2×Q8—222no—
168C2×Q8—222no—
169C2×Q8—222no—
170C2×Q8—222no—
171C22×C4—22no—
172C22×C4—222no—
173C22×C4—222no—
174C22×C4—441no—
175C22×C4C2×D4411yescharacteristic
176C22×C4D4×D1112yes—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—222no—
181C2×C8—222no—
182C2×C8—222no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—222no—
187C4⋊C4—222no—
188C4⋊C4—442no—
189C4⋊C4—442no—
190C4⋊C4—442no—
191C4⋊C4—442no—
192C4⋊C4—442no—
193C4⋊C4—882no—
194C42—442no—
195C42—442no—
196C42#433912yes—
197C42D4×D1111yescharacteristic
198C42#434311yescharacteristic
199C11#1043711yescharacteristic, complemented, Sylow
200C23#6693511yescharacteristic
201Q8—224no—
202Q8—224no—
203Q8—442no—
204Q8—442no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—44no—
209C2×C4—224no—
210C2×C4—442no—
211C2×C4—442no—
212C2×C4—442no—
213C2×C4—442no—
214C2×C4—442no—
215C2×C4—881no—
216C2×C4—882no—
217C2×C4#6692811yescharacteristic
218C2×C4#6693712yes—
219C2×C4#6694712yes—
220C2×C4#6694811yescharacteristic
221C2×C4#6696512yes—
222C2×C4SD16×D1112yes—
223C2×C4#6696812yes—
224C2×C4#6697112yes—
225C8—82no—
226C8—224no—
227C22#1062228511yescharacteristic
228C22#1062236011yescharacteristic
229C22#1062236511yescharacteristic
230C22#1062239612yes—
231C22#1062241912yes—
232C4—21no—
233C4—21no—
234C4—82no—
235C4—444no—
236C4—882no—
237C4—1761no—
238C4#1062239112yes—
239C4#1062242912yes—
240C4#1062247512yes—
241C4#1062250112yes—
242C2#1306769511yescharacteristic
243C2#1306773811yescharacteristic
244C2#1306789412yes—
245C2#1306981512yes—
246C2#1306984111yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socle, prime radicalC23×C11#120
hypercenter#1296D11
hypocenterC11#10437
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
199. C11#10437semidirect

Maximal subgroups

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

subgroupindex
#130739892
#130687722
#130686222
C2×#106221222
C11×#12962
#1043711