Finite Group Databasebeta

← #14656855

Subgroups — #14656855

Order 2816.

392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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#13076891C211yesmaximal, characteristic
2#13069589C212yesmaximal
3#13069435C211yesmaximal, characteristic
4#13066498C212yesmaximal
5C11×#1295C211yesmaximal, characteristic
6C2×#66922C2211yescharacteristic
7C2×C11×#97C2212yes—
8C11×#382C2211yescharacteristic
9#10622597—22no—
10C2×#66874—22no—
11#10622549C2212yes—
12C2×#66867C2211yescharacteristic
13#10622274—22no—
14#10622270—22no—
15#10622189—22no—
16#10622189—22no—
17C22×Dic22—21no—
18C22×C8×C11—22no—
19C2×C11×C4⋊C4D412yes—
20C2×C42×C11C2311yescharacteristic
21C2×C4⋊Dic11—22no—
22C2×C4⋊Dic11—22no—
23C2×C4⋊Dic11D412yes—
24C2×C4⋊Dic11D412yes—
25C2×Dic11⋊C4—22no—
26C2×Dic11⋊C4—22no—
27C22×C11⋊C8—21no—
28#66922—22no—
29#66922—21no—
30#66922Q812yes—
31C11×#97—22no—
32C11×#97—22no—
33C11×#95—22no—
34C11⋊#95—22no—
35C11⋊#95—22no—
36C11⋊#95—22no—
37#66874—44no—
38#66867—22no—
39#10361—111nomaximal, Sylow
40C22×C4×C11—22no—
41C22×C4×C11C2×D411yescharacteristic
42C22×C4×C11C2×D412yes—
43C22×Dic11—22no—
44C22×Dic11—22no—
45C22×Dic11—41no—
46C2×Dic22—22no—
47C2×Dic22—42no—
48C2×Dic22—42no—
49C2×Dic22—41no—
50C2×C8×C11—24no—
51C2×C8×C11—42no—
52C2×C8×C11—42no—
53C11×C4⋊C4—42no—
54C42×C11C2×Q811yescharacteristic
55C42×C11#4112yes—
56C42×C11#4111yescharacteristic
57C4⋊Dic11—24no—
58C4⋊Dic11—42no—
59C4⋊Dic11—42no—
60C4⋊Dic11—42no—
61C4⋊Dic11—82no—
62Dic11⋊C4—82no—
63Dic11⋊C4—82no—
64C2×C11⋊C8—22no—
65C2×C11⋊C8—41no—
66C2×C11⋊C8—41no—
67#2845—111no—
68#1993—112no—
69#1960—111no—
70#1295—112no—
71#1295D1111yescharacteristic
72C23×C11#12011yescharacteristic
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—42no—
78C2×C4×C11—42no—
79C2×C4×C11—42no—
80C2×C4×C11C22⋊Q812yes—
81C2×C4×C11C22⋊Q811yescharacteristic
82C2×C4×C11#12411yescharacteristic
83C2×C4×C11#12412yes—
84C2×Dic11—42no—
85C2×Dic11—42no—
86C2×Dic11—42no—
87C2×Dic11—42no—
88C2×Dic11—42no—
89C2×Dic11—42no—
90C2×Dic11—42no—
91C2×Dic11—81no—
92C2×Dic11—81no—
93Dic22—44no—
94Dic22—82no—
95C8×C11—44no—
96C11⋊C8—42no—
97C2×C4⋊Q8—111no—
98C2×#103—222no—
99C2×#97—111no—
100C2×#97C2×D1112yes—
101#398—222no—
102#398—222no—
103#398—222no—
104#382—112no—
105#382C2×D1111yescharacteristic
106#340—222no—
107#340—222no—
108C22×C11#39311yescharacteristic
109C22×C11#45311yescharacteristic
110C22×C11#45411yescharacteristic
111C22×C11#45512yes—
112C22×C11#45612yes—
113C4×C11—21no—
114C4×C11—21no—
115C4×C11—22no—
116C4×C11—22no—
117C4×C11—82no—
118Dic11—82no—
119Dic11—82no—
120Dic11—82no—
121C22×Q8—221no—
122C22×C8—22no—
123C22×C8—221no—
124C4⋊Q8—112no—
125C4⋊Q8—222no—
126C4⋊Q8—221no—
127C2×C4⋊C4—112no—
128C2×C4⋊C4—112no—
129C2×C4⋊C4—222no—
130C2×C4⋊C4—222no—
131C2×C4⋊C4—222no—
132C2×C4⋊C4—222no—
133C2×C4⋊C4D4412yes—
134C2×C42C22×D1111yescharacteristic
135#103—444no—
136#97—22no—
137#97—22no—
138#97—222no—
139#95—22no—
140#95—222no—
141#95—222no—
142#95—222no—
143C2×C11#166112yes—
144C2×C11#166211yescharacteristic
145C2×C11#166311yescharacteristic
146C2×C11#202711yescharacteristic
147C2×C11#202812yes—
148C2×Q8—222no—
149C2×Q8—442no—
150C2×Q8—442no—
151C2×Q8—441no—
152C22×C4—22no—
153C22×C4—222no—
154C22×C4—222no—
155C22×C4—441no—
156C22×C4C2×D4411yescharacteristic
157C22×C4D4×D1112yes—
158C2×C8—24no—
159C2×C8—42no—
160C2×C8—42no—
161C2×C8—222no—
162C2×C8—441no—
163C2×C8—441no—
164C4⋊C4—42no—
165C4⋊C4—224no—
166C4⋊C4—442no—
167C4⋊C4—442no—
168C4⋊C4—442no—
169C4⋊C4—882no—
170C4⋊C4—882no—
171C4⋊C4—882no—
172C42#433912yes—
173C42#434111yescharacteristic
174C42Q8×D1111yescharacteristic
175C11#1036111yescharacteristic, complemented, Sylow
176C23#6693511yescharacteristic
177Q8—444no—
178Q8—882no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—442no—
187C2×C4—442no—
188C2×C4—442no—
189C2×C4—442no—
190C2×C4—442no—
191C2×C4—442no—
192C2×C4—442no—
193C2×C4—881no—
194C2×C4—881no—
195C2×C4#6692811yescharacteristic
196C2×C4#6693812yes—
197C2×C4#6694912yes—
198C2×C4#6695011yescharacteristic
199C8—44no—
200C8—442no—
201C22#1062228611yescharacteristic
202C22#1062236011yescharacteristic
203C22#1062236611yescharacteristic
204C22#1062243812yes—
205C22#1062243912yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—882no—
212C4—882no—
213C4—882no—
214C2#1306793412yes—
215C2#1306794011yescharacteristic
216C2#1306794511yescharacteristic
217C2#1306977311yescharacteristic
218C2#1306977612yes—
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socle, prime radicalC23×C11#120
hypercenter#1295D11
hypocenterC11#10361
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
175. C11#10361semidirect

Maximal subgroups

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

subgroupindex
#130768912
#130695892
#130694352
#130664982
C11×#12952
#1036111