Finite Group Databasebeta

← #14657331

Subgroups — #14657331

Order 2816.

478 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 133 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#13068775C211yesmaximal, characteristic
2#13068621C212yesmaximal
3C2×Q8⋊(C11⋊C8)C212yesmaximal
4#13066499C211yesmaximal, characteristic
5C11×#2582C211yesmaximal, characteristic
6C2×C4×Q8×C11C2212yes—
7C11×#398—22no—
8C11×#391—22no—
9C11×#389—22no—
10C11×#384C2211yescharacteristic
11C2×#66899—22no—
12C2×#66871—22no—
13#10622548C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2212yes—
15C2×C4×C11⋊C8C2211yescharacteristic
16Q8⋊(C11⋊C8)—24no—
17#10622167—22no—
18C22×Q8×C11D412yes—
19C4×Q8×C11—22no—
20C4×Q8×C11—22no—
21C4×Q8×C11—22no—
22C4×Q8×C11—22no—
23C2×C11×C4⋊C4—22no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4D412yes—
27C2×C11×C4⋊C4D412yes—
28C2×C42×C11—22no—
29C2×C42×C11C2311yescharacteristic
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—22no—
32C22×C11⋊C8—21no—
33C22×C11⋊C8—22no—
34C11×#95—24no—
35C11×#95—22no—
36#66899—44no—
37#66871—44no—
38C4⋊(C11⋊C8)—22no—
39C4⋊(C11⋊C8)—22no—
40C4×C11⋊C8—21no—
41C4×C11⋊C8D412yes—
42#10439—111nomaximal, Sylow
43C2×Q8×C11—22no—
44C2×Q8×C11—22no—
45C2×Q8×C11—22no—
46C2×Q8×C11—22no—
47C2×Q8×C11—22no—
48C2×Q8×C11Q1614yes—
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11C2×D412yes—
54C22×Dic11—41no—
55C11×C4⋊C4—22no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4—42no—
58C11×C4⋊C4—42no—
59C11×C4⋊C4—42no—
60C11×C4⋊C4—42no—
61C11×C4⋊C4—42no—
62C11×C4⋊C4—82no—
63C42×C11—42no—
64C42×C11—42no—
65C42×C11C2×D411yescharacteristic
66C42×C11#4111yescharacteristic
67C42×C11#4112yes—
68C4⋊Dic11—42no—
69C4⋊Dic11—42no—
70C4⋊Dic11—42no—
71C2×C11⋊C8—22no—
72C2×C11⋊C8—22no—
73C2×C11⋊C8—22no—
74C2×C11⋊C8—42no—
75C2×C11⋊C8—42no—
76C2×C11⋊C8—42no—
77#2582D1111yescharacteristic
78#1845—111no—
79#1803—112no—
80C2×Q8⋊C8—112no—
81#1296—111no—
82C23×C11#12011yescharacteristic
83Q8×C11—24no—
84Q8×C11—24no—
85Q8×C11—42no—
86Q8×C11—42no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—24no—
90C2×C4×C11—42no—
91C2×C4×C11—42no—
92C2×C4×C11—42no—
93C2×C4×C11—44no—
94C2×C4×C11—42no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11#12111yescharacteristic
98C2×C4×C11#12112yes—
99C2×C4×C11#12312yes—
100C2×C4×C11#12411yescharacteristic
101C2×C4×C11C2×Q1612yes—
102C2×C4×C11#13512yes—
103C2×C4×C11AGL(1,ℤ/8)12yes—
104C2×C4×C11#13712yes—
105C2×Dic11—82no—
106C2×Dic11—81no—
107C11⋊C8—24no—
108C11⋊C8—82no—
109C2×C4×Q8C2×D1112yes—
110C2×#107—222no—
111C2×C4⋊C8—112no—
112C2×#103—222no—
113C2×C4×C8—111no—
114#398—22no—
115#391—22no—
116#389—22no—
117#384—111no—
118#384C2×D1111yescharacteristic
119#340—222no—
120Q8⋊C8—224no—
121C22×C11#39411yescharacteristic
122C22×C11#44912yes—
123C22×C11#45112yes—
124C22×C11#45311yescharacteristic
125C22×C11#45611yescharacteristic
126C4×C11—21no—
127C4×C11—21no—
128C4×C11—44no—
129C4×C11—82no—
130C4×C11—82no—
131C4×C11#46712yes—
132C4×C11#46812yes—
133C4×C11#48412yes—
134C4×C11#48512yes—
135Dic11—161no—
136C22×Q8C22⋊D1112yes—
137C22×C8—221no—
138C22×C8—222no—
139C4×Q8—22no—
140C4×Q8—22no—
141C4×Q8—22no—
142C4×Q8—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—222no—
147C2×C4⋊C4—221no—
148C2×C4⋊C4C22⋊D1112yes—
149C2×C4⋊C4C22⋊D1112yes—
150C2×C42—22no—
151C2×C42C22×D1111yescharacteristic
152#107—444no—
153C4⋊C8—222no—
154C4⋊C8—222no—
155#103—444no—
156C4×C8—112no—
157C4×C8—221no—
158#95—24no—
159#95—22no—
160C2×C11#162011yescharacteristic
161C2×C11#163311yescharacteristic
162C2×C11#164812yes—
163C2×C11#203612yes—
164C2×C11#203911yescharacteristic
165C2×Q8—22no—
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—22no—
170C2×Q8#432614yes—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—441no—
175C22×C4C2×C22⋊D1111yescharacteristic
176C22×C4C2×C22⋊D1112yes—
177C2×C8—222no—
178C2×C8—222no—
179C2×C8—222no—
180C2×C8—442no—
181C2×C8—442no—
182C2×C8—442no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—82no—
191C4⋊C4—442no—
192C4⋊C4—442no—
193C4⋊C4—442no—
194C42—42no—
195C42—42no—
196C42D4×D1111yescharacteristic
197C42#434111yescharacteristic
198C42#434112yes—
199C11#1043911yescharacteristic, complemented, Sylow
200C23#6700611yescharacteristic
201Q8—24no—
202Q8—24no—
203Q8—42no—
204Q8—42no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—24no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—44no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—882no—
216C2×C4—881no—
217C2×C4#6698812yes—
218C2×C4#6698911yescharacteristic
219C2×C4#6699111yescharacteristic
220C2×C4#6699212yes—
221C2×C4#6699512yes—
222C2×C4C2×#432612yes—
223C2×C4#6700212yes—
224C2×C4#6700312yes—
225C8—224no—
226C8—882no—
227C22#1062283511yescharacteristic
228C22#1062284112yes—
229C22#1062285112yes—
230C22#1062285411yescharacteristic
231C22#1062285911yescharacteristic
232C4—21no—
233C4—21no—
234C4—44no—
235C4—82no—
236C4—82no—
237C4—1761no—
238C4#1062265712yes—
239C4#1062265812yes—
240C4#1062266212yes—
241C4#1062266412yes—
242C2#1306767511yescharacteristic
243C2#1306775611yescharacteristic
244C2#1306785812yes—
245C2#1306981612yes—
246C2#1306983711yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2582C2
socle, prime radicalC23×C11#120
hypercenter#2582D11
hypocenterC11#10439
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2582

Complements

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

NH ≅ G/Ntype
199. C11#10439semidirect

Maximal subgroups

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

subgroupindex
#130687752
#130686212
C2×Q8⋊(C11⋊C8)2
#130664992
C11×#25822
#1043911