Finite Group Databasebeta

← C22×#10622738 #15617466

Subgroups — C22×#10622738 #15617466

Order 2816.

2718 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4318C212yesmaximal
2C2×#10622738C2124yesmaximal, direct product factor
3C22×#66883C214yesmaximal, complemented
4C23×C11×M16C211yesmaximal, characteristic
5C24×C4×C11C2211yescharacteristic
6C22×C11×M16C414yes—
7C22×C11×M16C4112yes—
8C22×C11×M16C22112yes—
9C23×C8×C11C2212yes—
10C22×#4318—22no—
11C22×#4318—212no—
12C22×#4318C2214yes—
13C22×#4318C22124yes—
14C23×C11⋊C8—22no—
15#10622738C22164yesdirect product factor
16C2×#66883C22148yescomplemented
17C25×C11Q811yescharacteristic
18C23×C4×C11C2×C412yes—
19C23×C4×C11C2×C416yes—
20C23×C4×C11D412yes—
21C23×C4×C11D416yes—
22C23×C4×C11Q811yescharacteristic
23C23×C4×C11Q816yes—
24C23×C4×C11C2311yescharacteristic
25C23×C4×C11C2316yes—
26C2×C11×M16C2×C4148yes—
27C2×C11×M16C2×C4148yes—
28C2×C11×M16C23116yes—
29C22×C8×C11C2×C4112yes—
30C22×C8×C11C2×C414yes—
31C22×C8×C11C23112yes—
32C2×#4318—224no—
33C2×#4318—212no—
34C2×#4318—248no—
35C2×#4318C23124yes—
36C2×#4318C23132yes—
37C22×C11⋊C8—224no—
38C22×C11⋊C8—24no—
39#66883C23164yescomplemented
40C22×#430—111nomaximal, Sylow
41C24×C11—44no—
42C24×C11C4⋊C412yes—
43C24×C11C4⋊C416yes—
44C24×C11C2×Q811yescharacteristic
45C24×C11C2×Q816yes—
46C22×C4×C11C4⋊C4112yes—
47C22×C4×C11C4⋊C4112yes—
48C22×C4×C11C4⋊C416yes—
49C22×C4×C11C4⋊C4124yes—
50C22×C4×C11C4⋊C412yes—
51C22×C4×C11C22×C413yes—
52C22×C4×C11C22×C411yescharacteristic
53C22×C4×C11C22×C4112yes—
54C22×C4×C11C22×C4112yes—
55C22×C4×C11C2×D4112yes—
56C22×C4×C11C2×D413yes—
57C22×C4×C11C2×D4112yes—
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×Q813yes—
60C22×C4×C11C2×Q816yes—
61C22×C4×C11C2×Q8112yes—
62C22×C4×C11C2413yes—
63C22×C4×C11C2414yes—
64C11×M16C22×C4164yes—
65C2×C8×C11C22×C4124yes—
66C2×C8×C11C22×C4124yes—
67C2×C8×C11C2418yes—
68#4318—232no—
69#4318—224no—
70#4318C24116yes—
71C2×C11⋊C8—224no—
72C2×C11⋊C8—232no—
73C23×M16—112no—
74C23×M16D1111yescharacteristic
75C2×#430—1124no—
76C22×#108—114no—
77C23×C11—28no—
78C23×C11—24no—
79C23×C11—412no—
80C23×C11—412no—
81C23×C11C2×C4⋊C413yes—
82C23×C11C2×C4⋊C4112yes—
83C23×C11C2×C4⋊C4112yes—
84C23×C11C2×C4⋊C411yescharacteristic
85C23×C11C22×Q813yes—
86C23×C11C22×Q814yes—
87C2×C4×C11C2×C4⋊C416yes—
88C2×C4×C11C2×C4⋊C4124yes—
89C2×C4×C11C2×C4⋊C4124yes—
90C2×C4×C11C2×C4⋊C4112yes—
91C2×C4×C11C2×C4⋊C413yes—
92C2×C4×C11C2×C4⋊C4112yes—
93C2×C4×C11C2×C4⋊C413yes—
94C2×C4×C11C23×C413yes—
95C2×C4×C11C23×C413yes—
96C2×C4×C11C23×C418yes—
97C2×C4×C11C22×D413yes—
98C2×C4×C11C22×D418yes—
99C2×C4×C11C22×D413yes—
100C2×C4×C11C22×Q813yes—
101C2×C4×C11C22×Q814yes—
102C2×C4×C11C2511yescharacteristic
103C8×C11C23×C4116yes—
104C11⋊C8—216no—
105C24×C4C2×D1111yescharacteristic
106C22×M16—114no—
107C22×M16—1124no—
108C22×M16—2212no—
109C22×M16—222no—
110C22×M16Dic1114yes—
111C22×M16Dic11112yes—
112C22×M16C2×D11112yes—
113C23×C8—222no—
114C23×C8C2×D1112yes—
115#430—1164no—
116C2×#108—1148no—
117C22×C11—224no—
118C22×C11—26no—
119C22×C11—26no—
120C22×C11—412no—
121C22×C11—44no—
122C22×C11#43014yescomplemented
123C22×C11C22×C4⋊C413yes—
124C22×C11C22×C4⋊C418yes—
125C22×C11C22×C4⋊C413yes—
126C22×C11C23×Q811yescharacteristic
127C4×C11C22×C4⋊C413yes—
128C4×C11C22×C4⋊C413yes—
129C4×C11C22×C4⋊C418yes—
130C4×C11C24×C411yescharacteristic
131C4×C11C23×D411yescharacteristic
132C25Dic2211yescharacteristic
133C23×C4Dic2211yescharacteristic
134C23×C4Dic2216yes—
135C23×C4D4416yes—
136C23×C4D4412yes—
137C23×C4C2×Dic1112yes—
138C23×C4C2×Dic1116yes—
139C23×C4C22×D1116yes—
140C23×C4C22×D1111yescharacteristic
141C2×M16—1124no—
142C2×M16—1132no—
143C2×M16—2224no—
144C2×M16—2212no—
145C2×M16—2248no—
146C2×M16C2×Dic11148yes—
147C2×M16C2×Dic11148yes—
148C2×M16C22×D11116yes—
149C22×C8—2224no—
150C22×C8—224no—
151C22×C8C2×Dic1114yes—
152C22×C8C2×Dic11112yes—
153C22×C8C22×D11112yes—
154#108—1164no—
155C2×C11—28no—
156C2×C11—23no—
157C2×C11—21no—
158C2×C11C2×#43016yescomplemented
159C2×C11C23×C4⋊C411yescharacteristic
160C24—44no—
161C24C4⋊Dic1112yes—
162C24C4⋊Dic1116yes—
163C24C2×Dic2211yescharacteristic
164C24C2×Dic2216yes—
165C22×C4C4⋊Dic1116yes—
166C22×C4C4⋊Dic11112yes—
167C22×C4C4⋊Dic11124yes—
168C22×C4C4⋊Dic1112yes—
169C22×C4C4⋊Dic11112yes—
170C22×C4C2×Dic2216yes—
171C22×C4C2×Dic22112yes—
172C22×C4C2×Dic2213yes—
173C22×C4C2×D44112yes—
174C22×C4C2×D4413yes—
175C22×C4C2×D44112yes—
176C22×C4C2×D4411yescharacteristic
177C22×C4C22×Dic1111yescharacteristic
178C22×C4C22×Dic1113yes—
179C22×C4C22×Dic11112yes—
180C22×C4C22×Dic11112yes—
181C22×C4C23×D1113yes—
182C22×C4C23×D1114yes—
183M16—1116no—
184M16—2232no—
185M16—2224no—
186M16C22×Dic11164yes—
187C2×C8—2224no—
188C2×C8—2232no—
189C2×C8C22×Dic11124yes—
190C2×C8C22×Dic11124yes—
191C2×C8C23×D1118yes—
192C11C22×#43011yescharacteristic, complemented, Sylow
193C23—28no—
194C23—24no—
195C23—412no—
196C23—412no—
197C23C2×C4⋊Dic11112yes—
198C23C2×C4⋊Dic1113yes—
199C23C2×C4⋊Dic11112yes—
200C23C2×C4⋊Dic1111yescharacteristic
201C23C22×Dic2213yes—
202C23C22×Dic2214yes—
203C2×C4C2×C4⋊Dic11124yes—
204C2×C4C2×C4⋊Dic1116yes—
205C2×C4C2×C4⋊Dic11112yes—
206C2×C4C2×C4⋊Dic11124yes—
207C2×C4C2×C4⋊Dic11112yes—
208C2×C4C2×C4⋊Dic1113yes—
209C2×C4C2×C4⋊Dic1113yes—
210C2×C4C22×Dic2213yes—
211C2×C4C22×Dic2214yes—
212C2×C4C22×D4413yes—
213C2×C4C22×D4418yes—
214C2×C4C22×D4413yes—
215C2×C4C23×Dic1113yes—
216C2×C4C23×Dic1113yes—
217C2×C4C23×Dic1118yes—
218C2×C4C24×D1111yescharacteristic
219C8—2216no—
220C8C23×Dic11116yes—
221C22—224no—
222C22—26no—
223C22—26no—
224C22—412no—
225C22—44no—
226C22#1062273814yesdirect product factor
227C22C22×C4⋊Dic1118yes—
228C22C22×C4⋊Dic1113yes—
229C22C22×C4⋊Dic1113yes—
230C22C23×Dic2211yescharacteristic
231C4C22×C4⋊Dic1118yes—
232C4C22×C4⋊Dic1113yes—
233C4C22×C4⋊Dic1113yes—
234C4C23×D4411yescharacteristic
235C4C24×Dic1111yescharacteristic
236C2—28no—
237C2—23no—
238C2—21no—
239C2C2×#1062273816yesdirect product factor
240C2C23×C4⋊Dic1111yescharacteristic
subgroupG/H
centerC22×C4C2×D44
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC23×C11×M16C2
socleC23×C11C2×C4⋊C4
prime radicalC25×C11Q8
cosocleC2×C4×C11C25
hypercenterC23×M16D11
hypocenterC11C22×#430
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C23×M16

Complements

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

NH ≅ G/Ntype
2. C2×#10622738C2direct (N × H)
3. C22×#66883C2semidirect
15. #10622738C22direct (N × H)
16. C2×#66883C22semidirect
39. #66883C23semidirect
122. C22×C11#430semidirect
158. C2×C11C2×#430semidirect
192. C11C22×#430semidirect
226. C22#10622738direct (N × H)
239. C2C2×#10622738direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43182
C2×#106227382
C22×#668832
C23×C11×M162
C22×#43011