Finite Group Databasebeta

← #14656804

Subgroups — #14656804

Order 2816.

416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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#13073858C211yesmaximal, characteristic
2#13069563C212yesmaximal
3#13069417C211yesmaximal, characteristic
4#13066455C212yesmaximal
5C11×#1296C211yesmaximal, characteristic
6C2×#66922C2211yescharacteristic
7C2×C11×C4⋊C8C2212yes—
8C11×#384C2211yescharacteristic
9#10622599—22no—
10#10622598—22no—
11#10622590—22no—
12C2×#66874—22no—
13C4×C4⋊Dic11C2212yes—
14C2×C4×C11⋊C8C2211yescharacteristic
15#10622189—22no—
16#10622189—22no—
17C22×Dic22—21no—
18C22×C8×C11—22no—
19C2×C11×C4⋊C4—22no—
20C2×C11×C4⋊C4D412yes—
21C2×C42×C11C2311yescharacteristic
22C2×C4⋊Dic11—22no—
23C2×C4⋊Dic11—22no—
24C2×C4⋊Dic11D412yes—
25C2×C4⋊Dic11D412yes—
26C2×C4×Dic11—22no—
27C22×C11⋊C8—21no—
28#66922—22no—
29#66922—21no—
30#66922Q812yes—
31C11×C4⋊C8—22no—
32C11×C4⋊C8—22no—
33C11⋊#95—22no—
34C11⋊#95—24no—
35C11⋊#95—22no—
36#66874—44no—
37C4×C11⋊C8—22no—
38#10352—111nomaximal, Sylow
39C22×C4×C11—22no—
40C22×C4×C11C2×D411yescharacteristic
41C22×C4×C11C2×D412yes—
42C22×Dic11—22no—
43C22×Dic11—22no—
44C22×Dic11—41no—
45C2×Dic22—22no—
46C2×Dic22—42no—
47C2×Dic22—42no—
48C2×Dic22—41no—
49C2×C8×C11—42no—
50C2×C8×C11—42no—
51C2×C8×C11—42no—
52C11×C4⋊C4—42no—
53C11×C4⋊C4—42no—
54C11×C4⋊C4—42no—
55C42×C11C2×Q811yescharacteristic
56C42×C11#4112yes—
57C42×C11#4111yescharacteristic
58C4⋊Dic11—24no—
59C4⋊Dic11—22no—
60C4⋊Dic11—22no—
61C4⋊Dic11—22no—
62C4⋊Dic11—22no—
63C4⋊Dic11—42no—
64C4⋊Dic11—82no—
65C4×Dic11—42no—
66C4×Dic11—42no—
67C2×C11⋊C8—22no—
68C2×C11⋊C8—41no—
69C2×C11⋊C8—41no—
70#2571—111no—
71#1987—112no—
72#1956—111no—
73#1296D1111yescharacteristic
74#1279—112no—
75C23×C11#12011yescharacteristic
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—44no—
79C2×C4×C11—42no—
80C2×C4×C11C22⋊Q812yes—
81C2×C4×C11C22⋊Q811yescharacteristic
82C2×C4×C11#12411yescharacteristic
83C2×C4×C11#12412yes—
84C2×C4×C11#13512yes—
85C2×C4×C11#13512yes—
86C2×C4×C11#13712yes—
87C2×C4×C11#13712yes—
88C2×Dic11—42no—
89C2×Dic11—42no—
90C2×Dic11—42no—
91C2×Dic11—42no—
92C2×Dic11—42no—
93C2×Dic11—42no—
94C2×Dic11—42no—
95C2×Dic11—81no—
96C2×Dic11—81no—
97Dic22—44no—
98Dic22—82no—
99C8×C11—82no—
100C11⋊C8—42no—
101C2×C4⋊Q8—111no—
102C2×C4⋊C8C2×D1112yes—
103C2×#103—222no—
104C2×C4×C8—111no—
105#400—222no—
106#389—222no—
107#384C2×D1111yescharacteristic
108#382—222no—
109C4×C4⋊C4—112no—
110#340—222no—
111#340—222no—
112C22×C11#39311yescharacteristic
113C22×C11#45212yes—
114C22×C11#45212yes—
115C22×C11#45311yescharacteristic
116C22×C11#45411yescharacteristic
117C4×C11—21no—
118C4×C11—21no—
119C4×C11—82no—
120C4×C11#47912yes—
121C4×C11#47912yes—
122C4×C11#48812yes—
123C4×C11#49112yes—
124Dic11—82no—
125Dic11—82no—
126Dic11—82no—
127C22×Q8—221no—
128C22×C8—22no—
129C22×C8—221no—
130C4⋊Q8—112no—
131C4⋊Q8—222no—
132C4⋊Q8—221no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—112no—
135C2×C4⋊C4—112no—
136C2×C4⋊C4—222no—
137C2×C4⋊C4—222no—
138C2×C4⋊C4D4412yes—
139C2×C42—222no—
140C2×C42C22×D1111yescharacteristic
141C4⋊C8—22no—
142C4⋊C8—22no—
143#103—444no—
144C4×C8—222no—
145#95—222no—
146#95—224no—
147#95—222no—
148C2×C11#163011yescharacteristic
149C2×C11#163411yescharacteristic
150C2×C11#163812yes—
151C2×C11#202612yes—
152C2×C11#202711yescharacteristic
153C2×Q8—222no—
154C2×Q8—442no—
155C2×Q8—442no—
156C2×Q8—441no—
157C22×C4—22no—
158C22×C4—222no—
159C22×C4—222no—
160C22×C4—441no—
161C22×C4C2×D4411yescharacteristic
162C22×C4D4×D1112yes—
163C2×C8—42no—
164C2×C8—42no—
165C2×C8—42no—
166C2×C8—222no—
167C2×C8—441no—
168C2×C8—441no—
169C4⋊C4—42no—
170C4⋊C4—42no—
171C4⋊C4—42no—
172C4⋊C4—224no—
173C4⋊C4—222no—
174C4⋊C4—222no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4—442no—
178C4⋊C4—882no—
179C42—442no—
180C42—442no—
181C42#433912yes—
182C42#434111yescharacteristic
183C42Q8×D1111yescharacteristic
184C11#1035211yescharacteristic, complemented, Sylow
185C23#6693511yescharacteristic
186Q8—444no—
187Q8—882no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—42no—
191C2×C4—44no—
192C2×C4—442no—
193C2×C4—442no—
194C2×C4—442no—
195C2×C4—442no—
196C2×C4—442no—
197C2×C4—442no—
198C2×C4—442no—
199C2×C4—881no—
200C2×C4—881no—
201C2×C4#6692811yescharacteristic
202C2×C4#6693812yes—
203C2×C4#6694912yes—
204C2×C4#6695011yescharacteristic
205C2×C4#6696512yes—
206C2×C4#6696812yes—
207C2×C4#6696912yes—
208C2×C4#6697112yes—
209C8—82no—
210C8—442no—
211C22#1062228611yescharacteristic
212C22#1062236011yescharacteristic
213C22#1062236611yescharacteristic
214C22#1062239612yes—
215C22#1062242312yes—
216C4—21no—
217C4—21no—
218C4—82no—
219C4—882no—
220C4—882no—
221C4—882no—
222C4#1062238112yes—
223C4#1062241012yes—
224C4#1062247012yes—
225C4#1062249012yes—
226C2#1306773811yescharacteristic
227C2#1306776211yescharacteristic
228C2#1306778912yes—
229C2#1306976612yes—
230C2#1306977311yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socle, prime radicalC23×C11#120
hypercenter#1296D11
hypocenterC11#10352
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
184. C11#10352semidirect

Maximal subgroups

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

subgroupindex
#130738582
#130695632
#130694172
#130664552
C11×#12962
#1035211