Finite Group Databasebeta

← #14680931

Subgroups — #14680931

Order 2816.

6494 conjugacy classes of subgroups; only the 651 normal subgroups are shown.

normal subgroups only

This group has 6494 conjugacy classes of subgroups — too many to draw. Only its 651 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
1C2×#10622824C212yesmaximal, complemented
2C2×#10622860C214yesmaximal, complemented
3#13066857C218yesmaximal, complemented
4C24×D4×C11C211yesmaximal, characteristic
5C26×C11C2212yes—
6C23×D4×C11—216no—
7C23×D4×C11—28no—
8C23×D4×C11C418yescomplemented
9C23×D4×C11C2214yes—
10C24×C4×C11C2211yescharacteristic
11C22×C22⋊Dic11C2214yes—
12C22×C22⋊Dic11C22116yescomplemented
13#10622860—216no—
14#10622824—28no—
15C2×C11⋊#95C2218yescomplemented
16C25×C11—28no—
17C25×C11—28no—
18C25×C11—416no—
19C25×C11C2×C418yes—
20C25×C11D4116yes—
21C25×C11C2314yes—
22C25×C11C2311yescharacteristic
23C22×D4×C11—2128no—
24C22×D4×C11—264no—
25C22×D4×C11—232no—
26C22×D4×C11—232no—
27C22×D4×C11—216no—
28C22×D4×C11C2×C4116yes—
29C23×C4×C11—28no—
30C23×C4×C11C2×C414yes—
31C23×C4×C11D418yes—
32C23×C4×C11C2312yes—
33C23×Dic11C2318yes—
34C2×C22⋊Dic11—28no—
35C2×C22⋊Dic11—216no—
36C2×C22⋊Dic11—232no—
37C2×C22⋊Dic11—432no—
38C11⋊#95—216no—
39#14335—111nomaximal, Sylow
40C24×C11—28no—
41C24×C11—216no—
42C24×C11—216no—
43C24×C11—264no—
44C24×C11—28no—
45C24×C11—28no—
46C24×C11—232no—
47C24×C11—432no—
48C24×C11—464no—
49C24×C11—464no—
50C24×C11—464no—
51C24×C11C22⋊C4132yescomplemented
52C24×C11C22×C418yes—
53C24×C11C22×C412yes—
54C24×C11C2×D4116yes—
55C24×C11C2×D418yes—
56C24×C11C2×D414yes—
57C24×C11C2411yescharacteristic
58C2×D4×C11—2128no—
59C2×D4×C11—2256no—
60C2×D4×C11—264no—
61C2×D4×C11—232no—
62C22×C4×C11—216no—
63C22×C4×C11—232no—
64C22×C4×C11—28no—
65C22×C4×C11C22⋊C4116yescomplemented
66C22×C4×C11C22×C414yes—
67C22×C4×C11C2×D418yes—
68C22×Dic11—28no—
69C22×Dic11—216no—
70C22×Dic11—232no—
71C22⋊Dic11—464no—
72C22⋊Dic11—416no—
73C24×D4D1111yescharacteristic
74C2×#381—112no—
75C2×#379—114no—
76#1438—118no—
77C23×C11—28no—
78C23×C11—232no—
79C23×C11—216no—
80C23×C11—28no—
81C23×C11—28no—
82C23×C11—232no—
83C23×C11—232no—
84C23×C11—232no—
85C23×C11—232no—
86C23×C11—264no—
87C23×C11—464no—
88C23×C11—464no—
89C23×C11—464no—
90C23×C11—4256no—
91C23×C11—432no—
92C23×C11—432no—
93C23×C11C2×C22⋊C4116yes—
94C23×C11C2×C22⋊C418yes—
95C23×C11C2×C22⋊C414yes—
96C23×C11#120116yes—
97C23×C11C23×C411yescharacteristic
98C23×C11C22×D414yes—
99C23×C11C22×D412yes—
100C23×C11H(5,𝔽2)18yes—
101D4×C11—2128no—
102C2×C4×C11—28no—
103C2×C4×C11—216no—
104C2×C4×C11—232no—
105C2×C4×C11C2×C22⋊C418yes—
106C2×Dic11—48no—
107C2×Dic11—432no—
108C2×Dic11—416no—
109C26C2×D1112yes—
110C23×D4—216no—
111C23×D4—28no—
112C23×D4Dic1118yescomplemented
113C23×D4C2×D1114yes—
114C24×C4C2×D1111yescharacteristic
115C22×C22⋊C4—114no—
116C22×C22⋊C4—1116no—
117#381—228no—
118#379—2216no—
119C2×#95—118no—
120C22×C11—216no—
121C22×C11—28no—
122C22×C11—232no—
123C22×C11—232no—
124C22×C11—216no—
125C22×C11—4128no—
126C22×C11—416no—
127C22×C11—416no—
128C22×C11—464no—
129C22×C11#37918yes—
130C22×C11C22×C22⋊C412yes—
131C22×C11C22×C22⋊C411yescharacteristic
132C22×C11#51814yes—
133C22×C11C2×#12014yes—
134C22×C11#534116yes—
135C22×C11#53518yes—
136C4×C11—28no—
137Dic11—88no—
138C25—28no—
139C25—28no—
140C25—416no—
141C25C2×Dic1118yes—
142C25C22⋊D11116yes—
143C25C22×D1114yes—
144C25C22×D1111yescharacteristic
145C22×D4—2128no—
146C22×D4—264no—
147C22×D4—232no—
148C22×D4—232no—
149C22×D4—216no—
150C22×D4C2×Dic11116yes—
151C23×C4—28no—
152C23×C4—118no—
153C23×C4C2×Dic1114yes—
154C23×C4C22⋊D1118yes—
155C23×C4C22×D1112yes—
156C2×C22⋊C4—2232no—
157C2×C22⋊C4—2216no—
158C2×C22⋊C4—228no—
159C2×C22⋊C4—4432no—
160#95—2216no—
161C2×C11—28no—
162C2×C11—416no—
163C2×C11C2×#37911yescharacteristic
164C2×C11#230814yes—
165C2×C11#230912yes—
166C2×C11#261318yes—
167C24—28no—
168C24—216no—
169C24—216no—
170C24—264no—
171C24—232no—
172C24—28no—
173C24—28no—
174C24—432no—
175C24—464no—
176C24—464no—
177C24—464no—
178C24C22⋊Dic11132yescomplemented
179C24C22×Dic1118yes—
180C24C22×Dic1112yes—
181C24C2×C22⋊D11116yes—
182C24C2×C22⋊D1118yes—
183C24C2×C22⋊D1114yes—
184C24C23×D1111yescharacteristic
185C2×D4—2128no—
186C2×D4—2256no—
187C2×D4—264no—
188C2×D4—232no—
189C22×C4—216no—
190C22×C4—232no—
191C22×C4—28no—
192C22×C4—2232no—
193C22×C4—228no—
194C22×C4—2216no—
195C22×C4C22⋊Dic11116yescomplemented
196C22×C4C22×Dic1114yes—
197C22×C4C2×C22⋊D1118yes—
198C22⋊C4—4464no—
199C22⋊C4—4416no—
200C11#1433511yescharacteristic, complemented, Sylow
201C23—28no—
202C23—232no—
203C23—216no—
204C23—232no—
205C23—232no—
206C23—232no—
207C23—28no—
208C23—28no—
209C23—232no—
210C23—264no—
211C23—464no—
212C23—464no—
213C23—464no—
214C23—4256no—
215C23—432no—
216C23—432no—
217C23C2×C22⋊Dic11116yes—
218C23C2×C22⋊Dic1118yes—
219C23C2×C22⋊Dic1114yes—
220C23#67006116yes—
221C23#6703718yes—
222C23C23×Dic1111yescharacteristic
223C23C22×C22⋊D1114yes—
224C23C22×C22⋊D1112yes—
225D4—2128no—
226C2×C4—28no—
227C2×C4—216no—
228C2×C4—232no—
229C2×C4—4432no—
230C2×C4—4416no—
231C2×C4—448no—
232C2×C4C2×C22⋊Dic1118yes—
233C22—216no—
234C22—28no—
235C22—232no—
236C22—232no—
237C22—216no—
238C22—4128no—
239C22—416no—
240C22—416no—
241C22—464no—
242C22#1062286018yes—
243C22#1062332914yes—
244C22#10623335116yes—
245C22#1062333618yes—
246C22C22×C22⋊Dic1112yes—
247C22C22×C22⋊Dic1111yescharacteristic
248C22C2×#6700614yes—
249C4—28no—
250C4—888no—
251C2—28no—
252C2—416no—
253C2C2×#1062286011yescharacteristic
254C2#1307119414yes—
255C2#1307119812yes—
256C2#1307432818yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
Fitting, prime radicalC24×D4×C11C2
socle, cosocleC24×C11C24
hypercenterC24×D4D11
hypocenterC11#14335
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10622824C2semidirect
2. C2×#10622860C2semidirect
3. #13066857C2semidirect
8. C23×D4×C11C4semidirect
12. C22×C22⋊Dic11C22semidirect
15. C2×C11⋊#95C22semidirect
51. C24×C11C22⋊C4semidirect
65. C22×C4×C11C22⋊C4semidirect
112. C23×D4Dic11semidirect
178. C24C22⋊Dic11semidirect
195. C22×C4C22⋊Dic11semidirect
200. C11#14335semidirect

Maximal subgroups

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

subgroupindex
C2×#106228242
C2×#106228602
#130668572
C24×D4×C112
#1433511