Finite Group Databasebeta

← C2×#13130387 #16794910

Subgroups — C2×#13130387 #16794910

Order 3328.

834 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719119C211yesmaximal, characteristic
2C22×C4⋊#1057C211yesmaximal, characteristic
3#13130387C218yesmaximal, direct product factor
4C2×#11718254C212yesmaximal, complemented
5C2×#11718253C212yesmaximal, complemented
6C2×M16×Dic13C211yesmaximal, characteristic
7C23×#1057—21no—
8C22×C13×M16C411yescharacteristic
9C22×C4×Dic13C2211yescharacteristic
10C22×#6099C411yescharacteristic
11C2×C22⋊#1057—21no—
12#11719119—22no—
13#11719119C2214yes—
14C2×C4⋊#1057—21no—
15C2×C4⋊#1057—22no—
16C2×C4⋊#1057C2211yescharacteristic
17C2×C4⋊#1057C2212yes—
18C2×C4⋊#1057C2211yescharacteristic
19C2×C4⋊#1057C2214yes—
20C2×C4×#1057—21no—
21M16×Dic13C414yes—
22M16×Dic13C2214yes—
23C2×#88055C412yes—
24C2×C8×Dic13C2212yes—
25#11718254C2218yescomplemented
26#11718253C2218yescomplemented
27C23×C4×C13C2×C411yescharacteristic
28C23×Dic13D411yescharacteristic
29C23×Dic13Q811yescharacteristic
30C22×#1057—21no—
31C22×#1057—21no—
32C22×#1057—24no—
33C22×#1057—22no—
34C22×#1057—44no—
35C2×C13×M16C818yescomplemented
36C2×C13×M16C2×C414yes—
37C22×C8×C13C2×C412yes—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13C2×C412yes—
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D412yes—
42C2×C4×Dic13Q811yescharacteristic
43C2×C4×Dic13Q812yes—
44C2×C4×Dic13C2311yescharacteristic
45C2×C4×Dic13C2312yes—
46C2×#6099—24no—
47C2×#6099C2×C414yes—
48C22×#1055C2×C412yes—
49C22⋊#1057—24no—
50C4⋊#1057—24no—
51C4⋊#1057—22no—
52C4⋊#1057—21no—
53C4⋊#1057—21no—
54C4⋊#1057C2312yes—
55C4⋊#1057C2314yes—
56C4⋊#1057C2312yes—
57C4×#1057—24no—
58#88055C2×C418yes—
59C8×Dic13C2×C414yes—
60C8×Dic13C2314yes—
61C2×#1565—131nomaximal, Sylow
62C24×C13C4⋊C411yescharacteristic
63C22×C4×C13C4⋊C412yes—
64C22×C4×C13C4⋊C411yescharacteristic
65C22×C4×C13C2×C814yes—
66C22×C4×C13M1614yes—
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C22×C412yes—
69C22×Dic13—22no—
70C22×Dic13—22no—
71C22×Dic13—42no—
72C22×Dic13C4⋊C411yescharacteristic
73C22×Dic13C4⋊C411yescharacteristic
74C22×Dic13C4⋊C412yes—
75C22×Dic13C4⋊C412yes—
76C22×Dic13C2×D412yes—
77C22×Dic13C2×D411yescharacteristic
78C22×Dic13C2×Q811yescharacteristic
79C22×Dic13C2×Q812yes—
80C2×#1057—22no—
81C2×#1057—22no—
82C2×#1057—24no—
83C2×#1057—48no—
84C2×#1057—42no—
85C2×#1057—44no—
86C2×#1057—42no—
87C13×M16C2×C8116yescomplemented
88C2×C8×C13C2×C818yescomplemented
89C2×C8×C13C22×C414yes—
90C4×Dic13C4⋊C412yes—
91C4×Dic13C4⋊C412yes—
92C4×Dic13C4⋊C412yes—
93C4×Dic13C22×C411yescharacteristic
94C4×Dic13C22×C412yes—
95C4×Dic13C2×D412yes—
96C4×Dic13C2×D411yescharacteristic
97C4×Dic13C2×Q812yes—
98C4×Dic13C2×Q811yescharacteristic
99C4×Dic13C2411yescharacteristic
100#6099—28no—
101C2×#1055—24no—
102C2×#1055C22×C414yes—
103C2×#431—131no—
104C22×C4⋊C8—131no—
105C2×C4×M16—131no—
106#1565—138no—
107C2×#335—132no—
108C2×#334—132no—
109C23×C13—22no—
110C23×C13—22no—
111C23×C13C4⋊C814yes—
112C23×C13C2×C4⋊C412yes—
113C23×C13C2×C4⋊C411yescharacteristic
114C2×C4×C13C4⋊C818yes—
115C2×C4×C13C4⋊C814yes—
116C2×C4×C13C2×C4⋊C412yes—
117C2×C4×C13C2×C4⋊C411yescharacteristic
118C2×C4×C13C22×C812yes—
119C2×C4×C13C22×C814yes—
120C2×C4×C13C2×M1612yes—
121C2×C4×C13C2×M1614yes—
122C2×C4×C13C23×C411yescharacteristic
123C2×Dic13—22no—
124C2×Dic13—22no—
125C2×Dic13—22no—
126C2×Dic13—22no—
127C2×Dic13—22no—
128C2×Dic13—24no—
129C2×Dic13—42no—
130C2×Dic13—42no—
131C2×Dic13C2×C4⋊C411yescharacteristic
132C2×Dic13C2×C4⋊C412yes—
133C2×Dic13C2×C4⋊C412yes—
134C2×Dic13C2×C4⋊C411yescharacteristic
135C2×Dic13AGL(1,ℤ/8)12yes—
136C2×Dic13#13712yes—
137C2×Dic13C22×D411yescharacteristic
138C2×Dic13C22×Q811yescharacteristic
139#1057—42no—
140#1057—44no—
141#1057—42no—
142C8×C13C22×C818yescomplemented
143#1055—24no—
144C22×M16—131no—
145C22×M16#26111yescharacteristic
146C23×C8—261no—
147C22×C42—131no—
148#431—134no—
149#431—262no—
150C2×C4⋊C8—131no—
151C2×C4⋊C8—132no—
152C2×C4⋊C8—131no—
153C2×C4⋊C8—134no—
154C2×C4⋊C8—261no—
155C2×C4⋊C8—262no—
156C2×C22⋊C8—261no—
157C4×M16—134no—
158C4×M16—134no—
159C2×#97—132no—
160C2×C4×C8—132no—
161C2×C4×C8—261no—
162#335—138no—
163#334—138no—
164C22×C13—28no—
165C22×C13—22no—
166C22×C13—22no—
167C22×C13C2×C4⋊C814yes—
168C22×C13C2×C4⋊C812yes—
169C22×C13#42812yes—
170C22×C13#43012yes—
171C22×C13C22×C4⋊C411yescharacteristic
172C4×C13C2×C4⋊C812yes—
173C4×C13C2×C4⋊C814yes—
174C4×C13C23×C811yescharacteristic
175C4×C13C22×M1611yescharacteristic
176Dic13—22no—
177Dic13—22no—
178Dic13—21no—
179Dic13—21no—
180Dic13#42812yes—
181Dic13C2×AGL(1,ℤ/8)11yescharacteristic
182Dic13C2×#13711yescharacteristic
183C23×C4—131no—
184C23×C4—131no—
185C23×C4C2×#26111yescharacteristic
186C2×M16—134no—
187C2×M16—264no—
188C2×M16#105718yescomplemented
189C2×M16C2×#26114yes—
190C22×C8—132no—
191C22×C8—262no—
192C22×C8—264no—
193C22×C8—261no—
194C22×C8—261no—
195C22×C8—524no—
196C22×C8C2×#26112yes—
197C2×C42—131no—
198C2×C42—132no—
199C2×C42—132no—
200C2×C42—131no—
201C2×C42—131no—
202C2×C42—132no—
203C2×C42—131no—
204C2×C42—132no—
205C4⋊C8—132no—
206C4⋊C8—134no—
207C4⋊C8—132no—
208C4⋊C8—264no—
209C4⋊C8—262no—
210C4⋊C8—261no—
211C4⋊C8—261no—
212C22⋊C8—264no—
213#97—138no—
214C4×C8—134no—
215C4×C8—134no—
216C4×C8—264no—
217C2×C13—24no—
218C2×C13#156514yescomplemented
219C2×C13C22×C4⋊C811yescharacteristic
220C2×C13C2×#42811yescharacteristic
221C2×C13C2×#43011yescharacteristic
222C24C4⋊#26111yescharacteristic
223C22×C4—131no—
224C22×C4—132no—
225C22×C4—132no—
226C22×C4—131no—
227C22×C4—131no—
228C22×C4—131no—
229C22×C4—132no—
230C22×C4—132no—
231C22×C4—262no—
232C22×C4—262no—
233C22×C4—522no—
234C22×C4#611814yes—
235C22×C4C4⋊#26112yes—
236C22×C4C4⋊#26111yescharacteristic
237C22×C4C2×#105714yes—
238C22×C4C22×#26112yes—
239C22×C4C22×#26111yescharacteristic
240M16—268no—
241M16C2×#1057116yescomplemented
242C2×C8—134no—
243C2×C8—264no—
244C2×C8—262no—
245C2×C8—262no—
246C2×C8—264no—
247C2×C8—524no—
248C2×C8—522no—
249C2×C8—522no—
250C2×C8—528no—
251C2×C8C2×#105718yescomplemented
252C2×C8C22×#26114yes—
253C42—132no—
254C42—131no—
255C42—132no—
256C42—132no—
257C42—132no—
258C42—131no—
259C42—132no—
260C42—131no—
261C42—131no—
262C42—132no—
263C13C2×#156511yescharacteristic, complemented, Sylow
264C23—22no—
265C23—22no—
266C23C4⋊#105714yes—
267C23C2×C4⋊#26112yes—
268C23C2×C4⋊#26111yescharacteristic
269C2×C4—132no—
270C2×C4—132no—
271C2×C4—131no—
272C2×C4—131no—
273C2×C4—132no—
274C2×C4—132no—
275C2×C4—131no—
276C2×C4—131no—
277C2×C4—262no—
278C2×C4—262no—
279C2×C4—264no—
280C2×C4—262no—
281C2×C4—262no—
282C2×C4—262no—
283C2×C4—522no—
284C2×C4—522no—
285C2×C4C4⋊#105718yes—
286C2×C4C4⋊#105714yes—
287C2×C4C2×#611812yes—
288C2×C4C2×#611814yes—
289C2×C4C2×C4⋊#26112yes—
290C2×C4C2×C4⋊#26111yescharacteristic
291C2×C4C22×#105712yes—
292C2×C4C22×#105714yes—
293C2×C4C23×#26111yescharacteristic
294C8—264no—
295C8—524no—
296C8—522no—
297C8—522no—
298C8C22×#105718yescomplemented
299C22—28no—
300C22—22no—
301C22—22no—
302C22#1171909812yes—
303C22#1171910012yes—
304C22C2×C4⋊#105714yes—
305C22C2×C4⋊#105712yes—
306C22C22×C4⋊#26111yescharacteristic
307C4—131no—
308C4—131no—
309C4—132no—
310C4—262no—
311C4—262no—
312C4—261no—
313C4—261no—
314C4C2×C4⋊#105712yes—
315C4C2×C4⋊#105714yes—
316C4C22×#611811yescharacteristic
317C4C23×#105711yescharacteristic
318C2—24no—
319C2#1313038714yesdirect product factor
320C2C22×C4⋊#105711yescharacteristic
321C2C2×#1171909811yescharacteristic
322C2C2×#1171910011yescharacteristic
subgroupG/H
centerC23C2×C4⋊#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
FittingC22×C13×M16C4
socleC23×C13C2×C4⋊C4
prime radicalC24×C13C4⋊C4
cosocleC4×Dic13C24
hypercenterC22×M16#261
hypocenterC13C2×#1565
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
3. #13130387C2direct (N × H)
4. C2×#11718254C2semidirect
5. C2×#11718253C2semidirect
25. #11718254C22semidirect
26. #11718253C22semidirect
35. C2×C13×M16C8semidirect
87. C13×M16C2×C8semidirect
88. C2×C8×C13C2×C8semidirect
142. C8×C13C22×C8semidirect
188. C2×M16#1057semidirect
218. C2×C13#1565semidirect
241. M16C2×#1057semidirect
251. C2×C8C2×#1057semidirect
263. C13C2×#1565semidirect
298. C8C22×#1057semidirect
319. C2#13130387direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191192
C22×C4⋊#10572
#131303872
C2×#117182542
C2×#117182532
C2×M16×Dic132
C2×#156513