Finite Group Databasebeta

← #14680940

Subgroups — #14680940

Order 2816.

4390 conjugacy classes of subgroups; only the 467 normal subgroups are shown.

normal subgroups only

This group has 4390 conjugacy classes of subgroups — too many to draw. Only its 467 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
1C23×#4343C211yesmaximal, characteristic
2C2×#10622280C216yesmaximal, complemented
3#13066887C211yesmaximal, characteristic, complemented
4#13066856C216yesmaximal, complemented
5C11×#1446C211yesmaximal, characteristic, complemented
6C23×Q8×C11C2211yescharacteristic
7C22×#4343—224no—
8C22×#4343C418yescomplemented
9C23×D44C2213yes—
10C23×C4×D11C2213yes—
11C22×(C2×D11)⋊C4C22112yes—
12C22×Dic11⋊C4C2214yes—
13C2×C11×#95C2216yes—
14C2×C11⋊#95C2216yes—
15#10622280—224no—
16C24×D11C2313yes—
17C22×Q8×C11—212no—
18C22×Q8×C11C2×C414yes—
19C23×C4×C11C2314yes—
20C23×C4×C11C2313yes—
21C23×Dic11C2314yes—
22C23×Dic11C2311yescharacteristic
23C2×#4343—2128no—
24C2×#4343—296no—
25C22×D44—224no—
26C22×D44—212no—
27C22×D44C2×C4112yes—
28C22×C4×D11—224no—
29C22×C4×D11C2×C4112yes—
30C22×C4×D11D4124yes—
31C2×(C2×D11)⋊C4—224no—
32C2×(C2×D11)⋊C4—424no—
33C2×Dic11⋊C4—224no—
34C11×#95—212no—
35C11⋊#95—212no—
36#14337—111nomaximal, Sylow
37C24×C11C2411yescharacteristic
38C23×D11—212no—
39C23×D11—212no—
40C23×D11—212no—
41C23×D11C22×C416yes—
42C23×D11C2×D4112yes—
43C2×Q8×C11—232no—
44C2×Q8×C11—224no—
45C22×C4×C11—212no—
46C22×C4×C11—212no—
47C22×C4×C11—212no—
48C22×C4×C11—24no—
49C22×C4×C11C22×C416yes—
50C22×C4×C11C2×D4112yes—
51C22×Dic11—212no—
52C22×Dic11—212no—
53C22×Dic11—24no—
54C22×Dic11C22×C412yes—
55C22×Dic11C2×D4112yes—
56#4343—2256no—
57C2×D44—296no—
58C2×D44—248no—
59C2×D44—224no—
60C2×C4×D11—248no—
61C2×C4×D11—296no—
62C2×C4×D11C22⋊C4148yescomplemented
63(C2×D11)⋊C4—448no—
64Dic11⋊C4—416no—
65C23×#41—111no—
66C2×#380—116no—
67#1446—111no—
68#1446D1111yescharacteristic, complemented
69#1438—116no—
70C23×C11C23×C411yescharacteristic
71C23×C11C22×D416yes—
72C23×C11H(5,𝔽2)14yes—
73C23×C112−1+414yes—
74C22×D11—212no—
75C22×D11—224no—
76C22×D11—224no—
77C22×D11—212no—
78C22×D11—212no—
79C22×D11—224no—
80C22×D11—412no—
81C22×D11—412no—
82C22×D11—424no—
83C22×D11C2×C22⋊C4112yes—
84Q8×C11—232no—
85C2×C4×C11—212no—
86C2×C4×C11—224no—
87C2×C4×C11—44no—
88C2×C4×C11—412no—
89C2×C4×C11—412no—
90C2×C4×C11C2×C22⋊C4112yes—
91C2×Dic11—44no—
92C2×Dic11—412no—
93C2×Dic11—412no—
94C2×Dic11C2×C22⋊C4112yes—
95C2×Dic11#120116yes—
96D44—296no—
97C4×D11—296no—
98C22×#41—118no—
99C22×#41—2224no—
100C23×Q8C2×D1111yescharacteristic
101C23×D4—113no—
102C24×C4—113no—
103C22×C4⋊C4—114no—
104C22×C22⋊C4—1112no—
105#380—2224no—
106C2×#95—116no—
107C2×#95C2×D1116yes—
108C22×C11C22×C22⋊C413yes—
109C22×C11#52014yes—
110C22×C11C2×#12014yes—
111C22×C11#53516yes—
112C22×C11#53616yes—
113C22×C11#537112yes—
114C2×D11—224no—
115C2×D11—212no—
116C2×D11—424no—
117C2×D11—424no—
118C2×D11—424no—
119C4×C11—212no—
120C4×C11—84no—
121Dic11—84no—
122Dic11#37918yes—
123C25—113no—
124C2×#41—2296no—
125C2×#41—22128no—
126C22×Q8—212no—
127C22×Q8C4×D1114yes—
128C22×D4—1112no—
129C22×D4—2224no—
130C22×D4—2212no—
131C23×C4—111no—
132C23×C4—1112no—
133C23×C4—1124no—
134C23×C4—114no—
135C23×C4—2224no—
136C23×C4C22×D1114yes—
137C23×C4C22×D1113yes—
138C2×C4⋊C4—2224no—
139C2×C22⋊C4—2224no—
140C2×C22⋊C4—4424no—
141#95—212no—
142#95—2212no—
143C2×C11C2×#37911yescharacteristic
144C2×C11#231116yes—
145C2×C11#261514yes—
146C2×C11#261614yes—
147D11—412no—
148C24—116no—
149C24—1112no—
150C24—2212no—
151C24—2212no—
152C24—2212no—
153C24C23×D1111yescharacteristic
154#41—22256no—
155C2×Q8—232no—
156C2×Q8—224no—
157C2×D4—2248no—
158C2×D4—2296no—
159C2×D4—2224no—
160C22×C4—212no—
161C22×C4—212no—
162C22×C4—24no—
163C22×C4—212no—
164C22×C4—112no—
165C22×C4—1112no—
166C22×C4—1148no—
167C22×C4—2248no—
168C22×C4—2296no—
169C22×C4—2212no—
170C22×C4—224no—
171C22×C4—2212no—
172C22×C4C2×C4×D1116yes—
173C22×C4D4×D11112yes—
174C4⋊C4—4416no—
175C22⋊C4—4448no—
176C11#1433711yescharacteristic, complemented, Sylow
177C23—1112no—
178C23—2212no—
179C23—2212no—
180C23—2224no—
181C23—2224no—
182C23—2224no—
183C23—2212no—
184C23—4412no—
185C23—4424no—
186C23—4412no—
187C23C22×C4×D1111yescharacteristic
188C23C2×D4×D1116yes—
189C23#6704014yes—
190C23#6704214yes—
191Q8—232no—
192D4—2296no—
193C2×C4—212no—
194C2×C4—224no—
195C2×C4—44no—
196C2×C4—412no—
197C2×C4—412no—
198C2×C4—1112no—
199C2×C4—1116no—
200C2×C4—2296no—
201C2×C4—444no—
202C2×C4—4412no—
203C2×C4—4412no—
204C2×C4C22⋊C4×D11112yes—
205C22—2224no—
206C22—2212no—
207C22—4424no—
208C22—4424no—
209C22—4424no—
210C22C2×C22⋊C4×D1113yes—
211C22#1062310514yes—
212C22D11×#12014yes—
213C22#10623160112yes—
214C22#1062320516yes—
215C22#1062325516yes—
216C4—212no—
217C4—84no—
218C4—118no—
219C4—884no—
220C2—4412no—
221C2D11×#37911yescharacteristic
222C2#1307120716yes—
223C2#1307434314yes—
224C2#1307434814yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1446C2
socle, cosocleC24×C11C24
prime radicalC23×#4343C2
hypercenter#1446D11
hypocenterC11#14337
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
2. C2×#10622280C2semidirect
3. #13066887C2semidirect
4. #13066856C2semidirect
5. C11×#1446C2semidirect
8. C22×#4343C4semidirect
62. C2×C4×D11C22⋊C4semidirect
68. #1446D11semidirect
176. C11#14337semidirect

Maximal subgroups

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

subgroupindex
C23×#43432
C2×#106222802
#130668872
#130668562
C11×#14462
#1433711