Finite Group Databasebeta

← C22×#11718290 #16796743

Subgroups — C22×#11718290 #16796743

Order 3328.

3086 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×#1057C212yesmaximal
2C2×#11718290C2112yesmaximal, direct product factor
3C23×C4×Dic13C211yesmaximal, characteristic
4C24×C4×C13C411yescharacteristic
5C24×Dic13C411yescharacteristic
6C24×Dic13C2211yescharacteristic
7C23×#1057—28no—
8C23×#1057—28no—
9C23×#1057C4116yescomplemented
10C23×#1057C22112yes—
11C22×C4×Dic13—28no—
12C22×C4×Dic13C416yes—
13C22×C4×Dic13C2216yes—
14#11718290C22116yesdirect product factor
15C25×C13C2×C411yescharacteristic
16C23×C4×C13—24no—
17C23×C4×C13—24no—
18C23×C4×C13C818yescomplemented
19C23×C4×C13C2×C416yes—
20C23×Dic13—24no—
21C23×Dic13—24no—
22C23×Dic13C818yescomplemented
23C23×Dic13C2×C416yes—
24C23×Dic13C2×C413yes—
25C23×Dic13C2×C418yes—
26C23×Dic13D414yes—
27C23×Dic13D418yes—
28C23×Dic13Q814yes—
29C23×Dic13C2313yes—
30C22×#1057—264no—
31C22×#1057—224no—
32C22×#1057—224no—
33C22×#1057C2×C4148yescomplemented
34C22×#1057C2318yes—
35C2×C4×Dic13—224no—
36C2×C4×Dic13—224no—
37C2×C4×Dic13C2×C4112yes—
38C2×C4×Dic13C2314yes—
39C22×#336—131nomaximal, Sylow
40C24×C13C4214yes—
41C24×C13C22⋊C414yes—
42C24×C13C4⋊C414yes—
43C24×C13C2×C814yes—
44C24×C13C2×C814yes—
45C24×C13M1614yes—
46C24×C13M1614yes—
47C24×C13C22×C413yes—
48C22×C4×C13—232no—
49C22×C4×C13—212no—
50C22×C4×C13—212no—
51C22×C4×C13C2×C8124yescomplemented
52C22×C4×C13C22×C414yes—
53C22×Dic13—232no—
54C22×Dic13—212no—
55C22×Dic13—212no—
56C22×Dic13C42112yes—
57C22×Dic13C22⋊C4112yes—
58C22×Dic13C22⋊C4132yes—
59C22×Dic13C4⋊C4112yes—
60C22×Dic13C4⋊C4132yes—
61C22×Dic13C2×C8124yescomplemented
62C22×Dic13C22×C414yes—
63C22×Dic13C22×C413yes—
64C22×Dic13C22×C4112yes—
65C22×Dic13C2×D416yes—
66C22×Dic13C2×D4112yes—
67C22×Dic13C2×Q816yes—
68C22×Dic13C2411yescharacteristic
69C2×#1057—296no—
70C2×#1057—28no—
71C2×#1057—28no—
72C2×#1057C22×C4116yescomplemented
73C4×Dic13—224no—
74C4×Dic13—28no—
75C24×C8—132no—
76C23×C42—131no—
77C2×#336—1312no—
78C23×C13#95116yes—
79C23×C13C4×C8116yes—
80C23×C13#97116yes—
81C23×C13C22⋊C8116yes—
82C23×C13C22⋊C8116yes—
83C23×C13C4⋊C8116yes—
84C23×C13C4⋊C8116yes—
85C23×C13C2×C4216yes—
86C23×C13C2×C22⋊C416yes—
87C23×C13C2×C4⋊C416yes—
88C23×C13C22×C816yes—
89C23×C13C22×C816yes—
90C23×C13C2×M1616yes—
91C23×C13C2×M1616yes—
92C23×C13C23×C411yescharacteristic
93C2×C4×C13—24no—
94C2×C4×C13—24no—
95C2×C4×C13—248no—
96C2×C4×C13C22×C818yescomplemented
97C2×Dic13—24no—
98C2×Dic13—24no—
99C2×Dic13—248no—
100C2×Dic13#95148yes—
101C2×Dic13C2×C4216yes—
102C2×Dic13C2×C22⋊C4124yes—
103C2×Dic13C2×C22⋊C416yes—
104C2×Dic13C2×C4⋊C4124yes—
105C2×Dic13C2×C4⋊C416yes—
106C2×Dic13C22×C818yescomplemented
107C2×Dic13C23×C412yes—
108C2×Dic13C22×D411yescharacteristic
109C2×Dic13C22×D412yes—
110C2×Dic13C22×Q811yescharacteristic
111#1057—216no—
112C24×C4—131no—
113C24×C4—131no—
114C24×C4#26111yescharacteristic
115C23×C8—1312no—
116C23×C8—1316no—
117C23×C8—268no—
118C23×C8—268no—
119C22×C42—136no—
120C22×C42—136no—
121C22×C42—268no—
122#336—1316no—
123C22×C13#336164yescomplemented
124C22×C13C2×#95112yes—
125C22×C13C2×C4×C8112yes—
126C22×C13C2×#97112yes—
127C22×C13C2×C22⋊C8112yes—
128C22×C13C2×C22⋊C8112yes—
129C22×C13C2×C4⋊C8112yes—
130C22×C13C2×C4⋊C8112yes—
131C22×C13C22×C4211yescharacteristic
132C22×C13C22×C22⋊C411yescharacteristic
133C22×C13C22×C4⋊C411yescharacteristic
134C22×C13C23×C811yescharacteristic
135C22×C13C23×C811yescharacteristic
136C22×C13C22×M1611yescharacteristic
137C22×C13C22×M1611yescharacteristic
138C4×C13—28no—
139Dic13—28no—
140Dic13C2×#95112yes—
141Dic13C22×C22⋊C412yes—
142Dic13C22×C4⋊C412yes—
143C25C2×#26111yescharacteristic
144C23×C4—24no—
145C23×C4—24no—
146C23×C4—138no—
147C23×C4—134no—
148C23×C4—134no—
149C23×C4—138no—
150C23×C4—133no—
151C23×C4—133no—
152C23×C4—138no—
153C23×C4—136no—
154C23×C4—264no—
155C23×C4—264no—
156C23×C4#105718yescomplemented
157C23×C4C2×#26116yes—
158C22×C8—138no—
159C22×C8—1348no—
160C22×C8—2664no—
161C22×C8—2624no—
162C22×C8—2624no—
163C2×C42—134no—
164C2×C42—1312no—
165C2×C42—2624no—
166C2×C42—2624no—
167C2×C13C2×#336124yescomplemented
168C2×C13C22×#9511yescharacteristic
169C2×C13C22×C4×C811yescharacteristic
170C2×C13C22×#9711yescharacteristic
171C2×C13C22×C22⋊C811yescharacteristic
172C2×C13C22×C22⋊C811yescharacteristic
173C2×C13C22×C4⋊C811yescharacteristic
174C2×C13C22×C4⋊C811yescharacteristic
175C24D13⋊C814yes—
176C24#611814yes—
177C24C4×#26114yes—
178C24C4⋊#26114yes—
179C24C2×#105714yes—
180C24#612214yes—
181C24C22⋊#26114yes—
182C24C22×#26113yes—
183C22×C4—232no—
184C22×C4—212no—
185C22×C4—212no—
186C22×C4—1332no—
187C22×C4—1332no—
188C22×C4—1312no—
189C22×C4—1312no—
190C22×C4—136no—
191C22×C4—1312no—
192C22×C4—136no—
193C22×C4—1312no—
194C22×C4—1312no—
195C22×C4—131no—
196C22×C4—133no—
197C22×C4—1324no—
198C22×C4—134no—
199C22×C4—2632no—
200C22×C4—2612no—
201C22×C4—2612no—
202C22×C4C2×#1057124yescomplemented
203C22×C4C22×#26114yes—
204C2×C8—1316no—
205C2×C8—268no—
206C2×C8—268no—
207C2×C8—2696no—
208C42—268no—
209C42—2624no—
210C13C22×#33611yescharacteristic, complemented, Sylow
211C23C4×#1057116yes—
212C23C4⋊#1057116yes—
213C23#88110116yes—
214C23#88111116yes—
215C23#88112116yes—
216C23(C2×#261)⋊C4116yes—
217C23C22⋊#1057116yes—
218C23C2×D13⋊C816yes—
219C23C2×#611816yes—
220C23C2×C4×#26116yes—
221C23C2×C4⋊#26116yes—
222C23C22×#105716yes—
223C23C2×#612216yes—
224C23C2×C22⋊#26116yes—
225C23C23×#26111yescharacteristic
226C2×C4—248no—
227C2×C4—24no—
228C2×C4—24no—
229C2×C4—132no—
230C2×C4—136no—
231C2×C4—131no—
232C2×C4—136no—
233C2×C4—131no—
234C2×C4—132no—
235C2×C4—136no—
236C2×C4—1324no—
237C2×C4—1348no—
238C2×C4—1324no—
239C2×C4—138no—
240C2×C4—264no—
241C2×C4—2648no—
242C2×C4—264no—
243C2×C4C22×#105718yescomplemented
244C8—2616no—
245C22#11718290164yesdirect product factor
246C22C2×C4×#1057112yes—
247C22C2×C4⋊#1057112yes—
248C22C2×#88110112yes—
249C22C2×#88111112yes—
250C22C2×#88112112yes—
251C22C2×(C2×#261)⋊C4112yes—
252C22C2×C22⋊#1057112yes—
253C22C22×D13⋊C811yescharacteristic
254C22C22×#611811yescharacteristic
255C22C22×C4×#26111yescharacteristic
256C22C22×C4⋊#26111yescharacteristic
257C22C23×#105711yescharacteristic
258C22C22×#612211yescharacteristic
259C22C22×C22⋊#26111yescharacteristic
260C4—28no—
261C4—132no—
262C4—132no—
263C4—1312no—
264C4—268no—
265C2C2×#11718290124yesdirect product factor
266C2C22×(C2×#261)⋊C411yescharacteristic
267C2C22×C4×#105711yescharacteristic
268C2C22×#8811011yescharacteristic
269C2C22×C22⋊#105711yescharacteristic
270C2C22×#8811111yescharacteristic
271C2C22×C4⋊#105711yescharacteristic
272C2C22×#8811211yescharacteristic
subgroupG/H
centerC25C2×#261
commutatorC2×C13C22×C4×C8
FrattiniC23C23×#261
FittingC24×C4×C13C4
socle, prime radicalC25×C13C2×C4
cosocleC22×Dic13C24
hypercenterC24×C4#261
hypocenterC13C22×#336
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C25 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
2. C2×#11718290C2direct (N × H)
9. C23×#1057C4semidirect
14. #11718290C22direct (N × H)
18. C23×C4×C13C8semidirect
22. C23×Dic13C8semidirect
33. C22×#1057C2×C4semidirect
51. C22×C4×C13C2×C8semidirect
61. C22×Dic13C2×C8semidirect
72. C2×#1057C22×C4semidirect
96. C2×C4×C13C22×C8semidirect
106. C2×Dic13C22×C8semidirect
123. C22×C13#336semidirect
156. C23×C4#1057semidirect
167. C2×C13C2×#336semidirect
202. C22×C4C2×#1057semidirect
210. C13C22×#336semidirect
243. C2×C4C22×#1057semidirect
245. C22#11718290direct (N × H)
265. C2C2×#11718290direct (N × H)

Maximal subgroups

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

subgroupindex
C24×#10572
C2×#117182902
C23×C4×Dic132
C22×#33613