Finite Group Databasebeta

← #14657036

Subgroups — #14657036

Order 2816.

526 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 75 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#13076880C211yesmaximal, characteristic
2#13068690C212yesmaximal
3C11⋊#1304C211yesmaximal, characteristic
4C11⋊#1304C212yesmaximal
5C11×#1819C211yesmaximal, characteristic
6C22×C11×C22⋊C4C2211yescharacteristic
7C11×#379C2211yescharacteristic
8C11×#379C2211yescharacteristic
9#10622860C2212yes—
10#10622860C2212yes—
11#10622562—22no—
12#10622561—24no—
13C11×#342—22no—
14#10622164—24no—
15C25×C11C2311yescharacteristic
16C23×C4×C11Q812yes—
17C2×C11×C22⋊C4—21no—
18C2×C11×C22⋊C4—22no—
19C2×C11×C22⋊C4—21no—
20C2×C11×C22⋊C4—22no—
21C2×C11×C22⋊C4—21no—
22C2×C11×C22⋊C4—22no—
23C2×C11×C22⋊C4—22no—
24C2×C11×C22⋊C4D412yes—
25C2×C22⋊Dic11—22no—
26C2×C22⋊Dic11—22no—
27C2×C22⋊Dic11—22no—
28C2×C22⋊Dic11—22no—
29C2×C22⋊Dic11—22no—
30C2×C22⋊Dic11D414yes—
31C2×C4⋊Dic11—22no—
32C2×Dic11⋊C4—24no—
33C11⋊#95—22no—
34#10393—111nomaximal, Sylow
35C24×C11—42no—
36C24×C11—82no—
37C24×C11C2×D412yes—
38C24×C11C2×D411yescharacteristic
39C24×C11C2×Q811yescharacteristic
40C24×C11#4111yescharacteristic
41C24×C11#4112yes—
42C22×C4×C11—22no—
43C22×C4×C11—22no—
44C22×C4×C11—22no—
45C22×C4×C11—22no—
46C22×C4×C11—41no—
47C22×C4×C11—82no—
48C22×Dic11—24no—
49C22×Dic11—42no—
50C11×C22⋊C4—41no—
51C11×C22⋊C4—42no—
52C11×C22⋊C4—41no—
53C11×C22⋊C4—42no—
54C11×C22⋊C4—42no—
55C11×C22⋊C4—82no—
56C11×C22⋊C4—82no—
57C22⋊Dic11—44no—
58C22⋊Dic11—44no—
59C22⋊Dic11—82no—
60C22⋊Dic11—82no—
61C22⋊Dic11—82no—
62C22⋊Dic11—82no—
63C4⋊Dic11—82no—
64Dic11⋊C4—84no—
65#2842—111no—
66#1819—112no—
67#1819D1111yescharacteristic
68#1304—112no—
69#1304—111no—
70C23×C11—24no—
71C23×C11—22no—
72C23×C11—42no—
73C23×C11—41no—
74C23×C11—42no—
75C23×C11—42no—
76C23×C11—42no—
77C23×C11—42no—
78C23×C11—42no—
79C23×C11—42no—
80C23×C11—41no—
81C23×C11—42no—
82C23×C11—88no—
83C23×C11#12011yescharacteristic
84C23×C11C22⋊Q812yes—
85C23×C11C22⋊Q811yescharacteristic
86C23×C11#12412yes—
87C23×C11#12411yescharacteristic
88C2×C4×C11—44no—
89C2×C4×C11—42no—
90C2×C4×C11—42no—
91C2×C4×C11—82no—
92C2×C4×C11—82no—
93C2×C4×C11—82no—
94C2×C4×C11—81no—
95C2×C4×C11—82no—
96C2×Dic11—44no—
97C2×Dic11—44no—
98C2×Dic11—44no—
99C2×Dic11—82no—
100C2×Dic11—82no—
101C2×Dic11—82no—
102C22×C22⋊C4C2×D1111yescharacteristic
103#399—222no—
104#396—224no—
105#379—112no—
106#379—112no—
107#379C2×D1111yescharacteristic
108#379C2×D1111yescharacteristic
109#342—22no—
110#342—224no—
111C22×C11—22no—
112C22×C11—21no—
113C22×C11—22no—
114C22×C11—21no—
115C22×C11—22no—
116C22×C11—22no—
117C22×C11—22no—
118C22×C11—22no—
119C22×C11—22no—
120C22×C11—22no—
121C22×C11—22no—
122C22×C11—44no—
123C22×C11—84no—
124C22×C11—82no—
125C22×C11—82no—
126C22×C11—84no—
127C22×C11#39311yescharacteristic
128C22×C11#45812yes—
129C4×C11—82no—
130C4×C11—82no—
131C4×C11—161no—
132Dic11—84no—
133Dic11—162no—
134C25C22×D1111yescharacteristic
135C23×C4Dic2212yes—
136C2×C4⋊C4—224no—
137C2×C4⋊C4—222no—
138C2×C22⋊C4—21no—
139C2×C22⋊C4—22no—
140C2×C22⋊C4—22no—
141C2×C22⋊C4—21no—
142C2×C22⋊C4—21no—
143C2×C22⋊C4—22no—
144C2×C22⋊C4—22no—
145C2×C22⋊C4—114no—
146C2×C22⋊C4—222no—
147C2×C22⋊C4—222no—
148C2×C22⋊C4—222no—
149C2×C22⋊C4—222no—
150C2×C22⋊C4—222no—
151C2×C22⋊C4C22⋊D1112yes—
152#95—222no—
153C2×C11—22no—
154C2×C11—42no—
155C2×C11—41no—
156C2×C11—42no—
157C2×C11—41no—
158C2×C11#203011yescharacteristic
159C2×C11#203212yes—
160C24—42no—
161C24—82no—
162C24C2×Dic2211yescharacteristic
163C24#433911yescharacteristic
164C24D4×D1112yes—
165C24#434112yes—
166C24C2×C22⋊D1111yescharacteristic
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—41no—
172C22×C4—82no—
173C22×C4—224no—
174C22×C4—442no—
175C4⋊C4—884no—
176C4⋊C4—882no—
177C22⋊C4—42no—
178C22⋊C4—41no—
179C22⋊C4—41no—
180C22⋊C4—42no—
181C22⋊C4—42no—
182C22⋊C4—82no—
183C22⋊C4—82no—
184C22⋊C4—444no—
185C22⋊C4—444no—
186C22⋊C4—882no—
187C22⋊C4—882no—
188C22⋊C4—882no—
189C22⋊C4—882no—
190C11#1039311yescharacteristic, complemented, Sylow
191C23—22no—
192C23—24no—
193C23—42no—
194C23—41no—
195C23—42no—
196C23—42no—
197C23—42no—
198C23—42no—
199C23—42no—
200C23—42no—
201C23—41no—
202C23—42no—
203C23—88no—
204C23#6693112yes—
205C23#6693812yes—
206C23#6697711yescharacteristic
207C23#6698911yescharacteristic
208C23#6699011yescharacteristic
209C2×C4—44no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—82no—
213C2×C4—82no—
214C2×C4—82no—
215C2×C4—81no—
216C2×C4—82no—
217C2×C4—444no—
218C2×C4—444no—
219C2×C4—444no—
220C2×C4—882no—
221C2×C4—882no—
222C2×C4—882no—
223C22—22no—
224C22—21no—
225C22—22no—
226C22—22no—
227C22—21no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—44no—
235C22—82no—
236C22—84no—
237C22—84no—
238C22—82no—
239C22#1062256011yescharacteristic
240C22#1062266612yes—
241C4—82no—
242C4—82no—
243C4—161no—
244C4—884no—
245C4—1762no—
246C2—22no—
247C2—41no—
248C2—42no—
249C2—42no—
250C2—41no—
251C2#1306978311yescharacteristic
252C2#1306979312yes—
subgroupG/H
centerC22#10622560
commutator, prime radical, cosocleC25×C11C23
FrattiniC25C22×D11
FittingC11×#1819C2
socleC22×C11#393
hypercenter#1819D11
hypocenterC11#10393
LCSG ▷ C25×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
190. C11#10393semidirect

Maximal subgroups

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

subgroupindex
#130768802
#130686902
C11⋊#13042
C11×#18192
#1039311