Finite Group Databasebeta

← C2×C22⋊C4×#1055 #15860489

Subgroups — C2×C22⋊C4×#1055 #15860489

Order 3328.

2046 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×#1055C211yesmaximal, characteristic
2C22×C22⋊#1055C211yesmaximal, characteristic
3C22×C4×#1055C212yesmaximal, complemented
4C22⋊C4×#1055C218yesmaximal, direct product factor
5C2×#11718116C212yesmaximal, complemented
6C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
7C24×C4×C13C2211yescharacteristic
8C22×C13×C22⋊C4C412yes—
9C22×C42×C13C2212yes—
10C23×#1055—28no—
11C23×#1055C418yescomplemented
12C23×#1055C2211yescharacteristic
13C23×#1055C2212yes—
14C23×#1055C2214yes—
15C23×#1055C2211yescharacteristic
16C4×C13×C22⋊C4C414yes—
17C4×C13×C22⋊C4C2214yes—
18C2×C13×#95C412yes—
19C2×C22⋊#1055C418yescomplemented
20C2×C22⋊#1055C2214yes—
21C2×C4×#1055—28no—
22C2×C4×#1055C2218yescomplemented
23#11718116C2218yescomplemented
24C25×C13C2×C411yescharacteristic
25C23×C4×C13—24no—
26C23×C4×C13—24no—
27C23×C4×C13C2×C414yes—
28C23×C4×C13C2×C414yes—
29C23×C4×C13C2×C412yes—
30C23×C4×C13C2×C411yescharacteristic
31C23×C4×C13C2×C414yes—
32C23×C4×C13C2312yes—
33C23×C4×C13C2311yescharacteristic
34C2×C13×C22⋊C4C8116yescomplemented
35C2×C13×C22⋊C4C2×C418yes—
36C2×C42×C13—24no—
37C2×C42×C13—24no—
38C2×C42×C13C2×C414yes—
39C2×C42×C13C2314yes—
40C22×#1055—24no—
41C22×#1055—24no—
42C22×#1055—24no—
43C22×#1055—232no—
44C22×#1055—216no—
45C22×#1055C2×C414yes—
46C22×#1055C2×C418yes—
47C22×#1055C2×C414yes—
48C22×#1055C2×C4116yescomplemented
49C22×#1055D418yes—
50C22×#1055C2312yes—
51C22×#1055C2314yes—
52C22×#1055C2312yes—
53C13×#95C2×C418yes—
54C22⋊#1055C2×C4116yescomplemented
55C4×#1055—216no—
56C2×C8×C22⋊C4—131nomaximal, Sylow
57C24×C13—24no—
58C24×C13—24no—
59C24×C13C4214yes—
60C24×C13C2×C818yes—
61C24×C13C22×C412yes—
62C24×C13C22×C411yescharacteristic
63C22×C4×C13—28no—
64C22×C4×C13—24no—
65C22×C4×C13—28no—
66C22×C4×C13—28no—
67C22×C4×C13—28no—
68C22×C4×C13—216no—
69C22×C4×C13—28no—
70C22×C4×C13—24no—
71C22×C4×C13—24no—
72C22×C4×C13C4214yes—
73C22×C4×C13C4218yes—
74C22×C4×C13C2×C8116yescomplemented
75C22×C4×C13C22×C414yes—
76C22×C4×C13C22×C414yes—
77C22×C4×C13C22×C412yes—
78C22×C4×C13C22×C412yes—
79C22×C4×C13C22×C412yes—
80C22×C4×C13C22×C418yes—
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C2×D414yes—
83C22×C4×C13#4114yes—
84C22×C4×C13C2411yescharacteristic
85C13×C22⋊C4C2×C8132yescomplemented
86C42×C13—28no—
87C42×C13—24no—
88C42×C13—24no—
89C2×#1055—28no—
90C2×#1055—216no—
91C2×#1055—24no—
92C2×#1055—24no—
93C2×#1055—24no—
94C2×#1055—232no—
95C2×#1055C22⋊C4116yesdirect product factor
96C2×#1055C22×C418yes—
97C2×#1055C22×C414yes—
98C2×#1055C22×C414yes—
99C2×#1055C2×D418yes—
100C24×C8—131no—
101C22×C22⋊C8—131no—
102C22×C4×C8—132no—
103C2×C4×C22⋊C4D1311yescharacteristic
104C8×C22⋊C4—138no—
105C2×#336—132no—
106C23×C13—24no—
107C23×C13—24no—
108C23×C13—28no—
109C23×C13—28no—
110C23×C13—232no—
111C23×C13C4×C8116yescomplemented
112C23×C13C2×C4214yes—
113C23×C13C2×C4212yes—
114C23×C13C4×D414yes—
115C23×C13C22×C818yes—
116C23×C13C22×C814yes—
117C23×C13#13114yes—
118C23×C13C23×C411yescharacteristic
119C2×C4×C13—28no—
120C2×C4×C13—24no—
121C2×C4×C13—28no—
122C2×C4×C13—28no—
123C2×C4×C13—232no—
124C2×C4×C13—24no—
125C2×C4×C13—24no—
126C2×C4×C13—28no—
127C2×C4×C13—216no—
128C2×C4×C13C2×C4214yes—
129C2×C4×C13C2×C4212yes—
130C2×C4×C13C2×C22⋊C414yes—
131C2×C4×C13#11714yes—
132C2×C4×C13C4×D418yes—
133C2×C4×C13C4×D414yes—
134C2×C4×C13C22×C8116yescomplemented
135C2×C4×C13C23×C411yescharacteristic
136C2×C4×C13C23×C411yescharacteristic
137C2×C4×C13C22×D412yes—
138C2×C4×C13C2×#4112yes—
139#1055—24no—
140#1055—28no—
141#1055C2×C22⋊C418yesdirect product factor
142C24×C4C2×D1311yescharacteristic
143C23×C8—131no—
144C23×C8—138no—
145C23×C8—134no—
146C23×C8—132no—
147C23×C8—131no—
148C23×C8—268no—
149C22×C22⋊C4Dic1312yes—
150C22×C42C2×D1312yes—
151C2×C22⋊C8—138no—
152C2×C22⋊C8—134no—
153C2×C4×C8—138no—
154C2×C4×C8—268no—
155C4×C22⋊C4Dic1314yes—
156C4×C22⋊C4C2×D1314yes—
157C2×#95Dic1312yes—
158#336—138no—
159C22×C13—24no—
160C22×C13—216no—
161C22×C13—232no—
162C22×C13—24no—
163C22×C13C4×C22⋊C414yes—
164C22×C13C2×C4×C814yes—
165C22×C13C2×C4×C818yescomplemented
166C22×C13#40514yes—
167C22×C13C8×D4116yes—
168C22×C13C22×C4211yescharacteristic
169C22×C13C2×C4×D412yes—
170C22×C13C23×C812yes—
171C22×C13C2×#13112yes—
172C4×C13—216no—
173C4×C13—24no—
174C4×C13C4×C22⋊C414yes—
175C4×C13C22×C22⋊C411yescharacteristic
176C4×C13C2×#11711yescharacteristic
177C4×C13C2×C4×D412yes—
178C25C2×Dic1311yescharacteristic
179C23×C4—24no—
180C23×C4—24no—
181C23×C4C4×D1314yes—
182C23×C4C4×D1314yes—
183C23×C4C2×Dic1314yes—
184C23×C4C2×Dic1311yescharacteristic
185C23×C4C2×Dic1312yes—
186C23×C4C22×D1312yes—
187C23×C4C22×D1311yescharacteristic
188C22×C8—134no—
189C22×C8—138no—
190C22×C8—132no—
191C22×C8—134no—
192C22×C8—1316no—
193C22×C8—138no—
194C22×C8—132no—
195C22×C8—134no—
196C22×C8—2632no—
197C22×C8—2616no—
198C22×C8—264no—
199C22×C8—264no—
200C22×C8—264no—
201C2×C22⋊C4#1055116yesdirect product factor
202C2×C22⋊C4C2×Dic1318yes—
203C2×C42—24no—
204C2×C42—24no—
205C2×C42C2×Dic1314yes—
206C2×C42C22×D1314yes—
207C22⋊C8—1316no—
208C4×C8—2616no—
209#95C2×Dic1318yes—
210C2×C13—28no—
211C2×C13C8×C22⋊C418yescomplemented
212C2×C13C2×C4×C22⋊C411yescharacteristic
213C2×C13C22×C4×C811yescharacteristic
214C2×C13C2×#40511yescharacteristic
215C2×C13C2×C8×D414yes—
216C24—24no—
217C24—24no—
218C24C2×#105518yes—
219C24C4×Dic1314yes—
220C24C22×Dic1312yes—
221C24C22×Dic1311yescharacteristic
222C22×C4—28no—
223C22×C4—24no—
224C22×C4—28no—
225C22×C4—28no—
226C22×C4—28no—
227C22×C4—216no—
228C22×C4—28no—
229C22×C4—24no—
230C22×C4—24no—
231C22×C4C2×#1055116yescomplemented
232C22×C4C4×Dic1314yes—
233C22×C4C4×Dic1318yes—
234C22×C4C2×C4×D1314yes—
235C22×C4C2×C4×D1314yes—
236C22×C4C2×C4×D1312yes—
237C22×C4C2×C4×D1312yes—
238C22×C4D4×D1314yes—
239C22×C4#612914yes—
240C22×C4C22×Dic1318yes—
241C22×C4C22×Dic1312yes—
242C22×C4C22×Dic1311yescharacteristic
243C22×C4C23×D1311yescharacteristic
244C2×C8—1316no—
245C2×C8—134no—
246C2×C8—138no—
247C2×C8—138no—
248C2×C8—134no—
249C2×C8—2632no—
250C2×C8—268no—
251C2×C8—2616no—
252C2×C8—264no—
253C2×C8—264no—
254C2×C8—264no—
255C22⋊C4C2×#1055132yesdirect product factor
256C42—28no—
257C42—24no—
258C42—24no—
259C13C2×C8×C22⋊C411yescharacteristic, complemented, Sylow
260C23—28no—
261C23—232no—
262C23—24no—
263C23—24no—
264C23—28no—
265C23C4×#1055116yescomplemented
266C23C22×#105518yes—
267C23C22×#105514yes—
268C23C2×C4×Dic1314yes—
269C23C2×C4×Dic1312yes—
270C23D4×Dic1314yes—
271C23#8820214yes—
272C23C23×Dic1311yescharacteristic
273C2×C4—232no—
274C2×C4—28no—
275C2×C4—24no—
276C2×C4—28no—
277C2×C4—28no—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—28no—
281C2×C4—216no—
282C2×C4#8813114yes—
283C2×C4C22⋊C4×D1314yes—
284C2×C4#8813518yes—
285C2×C4C22×#1055116yescomplemented
286C2×C4C2×C4×Dic1314yes—
287C2×C4C2×C4×Dic1312yes—
288C2×C4D4×Dic1314yes—
289C2×C4C22×C4×D1311yescharacteristic
290C2×C4C22×C4×D1311yescharacteristic
291C2×C4C2×D4×D1312yes—
292C2×C4C2×#612912yes—
293C8—138no—
294C8—264no—
295C8—268no—
296C22—24no—
297C22—216no—
298C22—24no—
299C22—232no—
300C22C2×C4×#105514yes—
301C22C2×C4×#105518yescomplemented
302C22C22⋊C4×Dic1314yes—
303C22#1171865814yes—
304C22D4×#1055116yes—
305C22C23×#105512yes—
306C22C22×C4×Dic1311yescharacteristic
307C22C2×D4×Dic1312yes—
308C22C2×#8820212yes—
309C4—216no—
310C4—24no—
311C4C22⋊C4×Dic1314yes—
312C4C2×#8813111yescharacteristic
313C4C2×C22⋊C4×D1311yescharacteristic
314C4C2×#8813512yes—
315C2—28no—
316C2C22⋊C4×#105518yesdirect product factor
317C2C2×C22⋊C4×Dic1311yescharacteristic
318C2C22×C4×#105511yescharacteristic
319C2C2×#1171865811yescharacteristic
320C2C2×D4×#105514yes—
subgroupG/H
centerC23×C4C22×D13
commutatorC2×C13C22×C4×C8
FrattiniC22×C4C23×D13
FittingC2×C4×C13×C22⋊C4C2
socleC24×C13C22×C4
prime radicalC25×C13C2×C4
cosocleC22×C4×C13C24
hypercenterC2×C4×C22⋊C4D13
hypocenterC13C2×C8×C22⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C4×#1055C2semidirect
4. C22⋊C4×#1055C2direct (N × H)
5. C2×#11718116C2semidirect
11. C23×#1055C4semidirect
19. C2×C22⋊#1055C4semidirect
22. C2×C4×#1055C22semidirect
23. #11718116C22semidirect
34. C2×C13×C22⋊C4C8semidirect
48. C22×#1055C2×C4semidirect
54. C22⋊#1055C2×C4semidirect
74. C22×C4×C13C2×C8semidirect
85. C13×C22⋊C4C2×C8semidirect
95. C2×#1055C22⋊C4direct (N × H)
111. C23×C13C4×C8semidirect
134. C2×C4×C13C22×C8semidirect
141. #1055C2×C22⋊C4direct (N × H)
165. C22×C13C2×C4×C8semidirect
201. C2×C22⋊C4#1055direct (N × H)
211. C2×C13C8×C22⋊C4semidirect
231. C22×C4C2×#1055semidirect
255. C22⋊C4C2×#1055direct (N × H)
259. C13C2×C8×C22⋊C4semidirect
265. C23C4×#1055semidirect
285. C2×C4C22×#1055semidirect
301. C22C2×C4×#1055semidirect
316. C2C22⋊C4×#1055direct (N × H)

Maximal subgroups

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

subgroupindex
C24×#10552
C22×C22⋊#10552
C22×C4×#10552
C22⋊C4×#10552
C2×#117181162
C2×C4×C13×C22⋊C42
C2×C8×C22⋊C413