Finite Group Databasebeta

← C2×#13131018 #16799372

Subgroups — C2×#13131018 #16799372

Order 3328.

1246 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D13⋊C8C211yesmaximal, characteristic
2C2×#11719060C211yesmaximal, characteristic
3#13131018C218yesmaximal, direct product factor
4C2×#11718246C214yesmaximal
5C2×D13×#125C211yesmaximal, characteristic
6C22×C4⋊#261C2212yes—
7C22×D13⋊C8C2212yes—
8C2×C13×#125C411yescharacteristic, complemented
9D13×#125—22no—
10D13×#125—22no—
11D13×#125C414yescomplemented
12D13×#125C2214yes—
13C2×C4⋊C4×D13—22no—
14C2×C4⋊C4×D13C2212yes—
15C2×#88144C412yescomplemented
16C2×#88143—22no—
17C2×C42×D13C2211yescharacteristic
18C2×#88124C411yescharacteristic, complemented
19C2×(C2×#261)⋊C4—22no—
20C2×C4×#1057—22no—
21#11719060—22no—
22#11719060C2214yes—
23C4×D13⋊C8—22no—
24C4×D13⋊C8C2214yes—
25#11718246C22116yes—
26C23×#261—22no—
27C22×C4×D13—22no—
28C22×C4×D13D412yes—
29C22×C4×D13C2311yescharacteristic
30C22×#1057—22no—
31C2×C4⋊#261—28no—
32C2×C4⋊#261—22no—
33C2×C4⋊#261C2314yes—
34C2×D13⋊C8—22no—
35C2×D13⋊C8—24no—
36C2×D13⋊C8Q818yes—
37C2×D13⋊C8C2314yes—
38C13×#125—22no—
39C13×#125C2×C414yescomplemented
40C2×C13×C4⋊C4—22no—
41C2×C13×C4⋊C4C2×C412yes—
42C2×C42×C13C2×C411yescharacteristic
43C2×C4⋊Dic13—22no—
44C2×C4⋊Dic13C2×C412yes—
45C2×#6101—22no—
46C2×#6101—22no—
47C2×#6101—22no—
48C2×C4×Dic13C2×C411yescharacteristic
49C2×C4×Dic13D412yes—
50C4⋊C4×D13—28no—
51C4⋊C4×D13—28no—
52C4⋊C4×D13—22no—
53C4⋊C4×D13—22no—
54C4⋊C4×D13C2×C414yes—
55C4⋊C4×D13C2314yes—
56#88144—24no—
57#88144C2×C418yescomplemented
58#88143—28no—
59#88143—28no—
60C42×D13C2×C412yes—
61C42×D13D412yes—
62C42×D13D412yes—
63C42×D13C2312yes—
64#88124—22no—
65#88124C2×C414yescomplemented
66(C2×#261)⋊C4—28no—
67C4×#1057—28no—
68C2×#1991—131nomaximal, Sylow
69C23×D13C2×D411yescharacteristic
70C22×#261—24no—
71C22×#261—44no—
72C22×#261—48no—
73C22×C4×C13—22no—
74C22×C4×C13C22⋊C412yes—
75C22×C4×C13C22×C411yescharacteristic
76C22×Dic13—22no—
77C22×Dic13C22⋊C412yes—
78C22×Dic13C2×D411yescharacteristic
79C2×C4×D13—28no—
80C2×C4×D13—24no—
81C2×C4×D13—24no—
82C2×C4×D13—48no—
83C2×C4×D13C22⋊C414yes—
84C2×C4×D13C22×C411yescharacteristic
85C2×C4×D13C2×D414yes—
86C2×C4×D13C2×D411yescharacteristic
87C2×C4×D13C2×D411yescharacteristic
88C2×C4×D13C2×Q814yes—
89C2×C4×D13#4114yes—
90C2×C4×D13C2411yescharacteristic
91C2×#1057—28no—
92C2×#1057—24no—
93C4⋊#261—28no—
94C4⋊#261—44no—
95D13⋊C8—28no—
96D13⋊C8—24no—
97D13⋊C8C2×Q818yes—
98C13×C4⋊C4—28no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4C22×C414yes—
101C42×C13C22⋊C412yes—
102C42×C13C22×C412yes—
103C4⋊Dic13—22no—
104C4⋊Dic13—28no—
105C4⋊Dic13C22×C414yes—
106#6101—28no—
107#6101—24no—
108#6101—28no—
109#6101—24no—
110C4×Dic13C22⋊C414yes—
111C4×Dic13C22⋊C412yes—
112C4×Dic13C22×C412yes—
113C4×Dic13C2×D414yes—
114C22×#125—131no—
115C22×C4×C8—131no—
116C2×#382—131no—
117#1991—138no—
118C2×#340—134no—
119C23×C13C2×C22⋊C411yescharacteristic
120C22×D13C2×C22⋊C411yescharacteristic
121C22×D13#12412yes—
122C22×D13C4⋊Q812yes—
123C22×D13#13518yes—
124C22×D13C22×D411yescharacteristic
125C2×#261—44no—
126C2×#261—48no—
127C2×#261—88no—
128C2×C4×C13—24no—
129C2×C4×C13—24no—
130C2×C4×C13—44no—
131C2×C4×C13C2×C22⋊C414yes—
132C2×C4×C13C2×C22⋊C411yescharacteristic
133C2×C4×C13C4×Q814yes—
134C2×C4×C13C23×C411yescharacteristic
135C2×Dic13—24no—
136C2×Dic13—24no—
137C2×Dic13—44no—
138C2×Dic13C2×C22⋊C414yes—
139C2×Dic13C2×C22⋊C411yescharacteristic
140C2×Dic13C22⋊Q814yes—
141C2×Dic13C22×D411yescharacteristic
142C4×D13—28no—
143C4×D13—28no—
144C4×D13—48no—
145C4×D13—48no—
146C4×D13C4×Q814yes—
147C4×D13C22⋊Q814yes—
148C4×D13#12412yes—
149C4×D13C4⋊Q812yes—
150C4×D13C22×Q812yes—
151C4×D13C2×#4112yes—
152#1057—28no—
153C23×C8—132no—
154C2×#125—134no—
155C2×#125—134no—
156C2×#125—132no—
157C2×#125—131no—
158C2×#125—262no—
159C2×#125—262no—
160C2×#125—262no—
161C2×#125#26111yescharacteristic, complemented
162C22×C4⋊C4—132no—
163C22×C4⋊C4—132no—
164C22×C4⋊C4—262no—
165C22×C42—131no—
166C2×C4×C8—134no—
167C2×C4×C8—262no—
168C2×C4×C8—262no—
169#382—134no—
170#382—262no—
171C2×#95—262no—
172#340—1316no—
173C22×C13#39112yes—
174C22×C13#41614yes—
175C22×C13C22×C22⋊C411yescharacteristic
176C2×D13#39112yes—
177C2×D13#41614yes—
178C2×D13#48818yes—
179C2×D13#49918yes—
180C2×D13C2×#12411yescharacteristic
181C2×D13C2×C4⋊Q811yescharacteristic
182C2×D13C2×#13514yes—
183#261—84no—
184C4×C13—24no—
185C4×C13—44no—
186C4×C13#39112yes—
187C4×C13C2×C4×Q812yes—
188Dic13—24no—
189Dic13—44no—
190Dic13#39112yes—
191Dic13C2×C22⋊Q812yes—
192C23×C4—131no—
193C23×C4—132no—
194C23×C4—262no—
195C23×C4—262no—
196C22×C8—134no—
197C22×C8—138no—
198C22×C8—262no—
199C22×C8—262no—
200C22×C8—264no—
201#125—22no—
202#125—138no—
203#125—134no—
204#125—268no—
205#125—268no—
206#125—264no—
207#125—262no—
208#125C2×#26114yescomplemented
209C2×C4⋊C4—22no—
210C2×C4⋊C4—132no—
211C2×C4⋊C4—134no—
212C2×C4⋊C4—134no—
213C2×C4⋊C4—134no—
214C2×C4⋊C4—262no—
215C2×C4⋊C4—262no—
216C2×C4⋊C4—268no—
217C2×C4⋊C4—268no—
218C2×C4⋊C4—262no—
219C2×C4⋊C4—262no—
220C2×C4⋊C4—262no—
221C2×C4⋊C4—262no—
222C2×C4⋊C4—268no—
223C2×C4⋊C4—262no—
224C2×C4⋊C4C2×#26112yes—
225C2×C42—132no—
226C2×C42—131no—
227C2×C42—132no—
228C2×C42—132no—
229C2×C42—132no—
230C2×C42—132no—
231C2×C42C2×#26111yescharacteristic
232C4×C8—268no—
233#95—268no—
234C2×C13#199114yescomplemented
235C2×C13C2×#39111yescharacteristic
236C2×C13C2×#41612yes—
237D13#199114yescomplemented
238D13C2×#48812yes—
239D13C2×#49912yes—
240C24—131no—
241C22×C4—22no—
242C22×C4—131no—
243C22×C4—134no—
244C22×C4—134no—
245C22×C4—131no—
246C22×C4—131no—
247C22×C4—131no—
248C22×C4—131no—
249C22×C4—132no—
250C22×C4—134no—
251C22×C4—134no—
252C22×C4—268no—
253C22×C4—264no—
254C22×C4—264no—
255C22×C4—262no—
256C22×C4—264no—
257C22×C4—528no—
258C22×C4—524no—
259C22×C4—528no—
260C22×C4C22⋊#26112yes—
261C22×C4C22×#26111yescharacteristic
262C2×C8—138no—
263C2×C8—264no—
264C2×C8—264no—
265C2×C8—268no—
266C2×C8—268no—
267C4⋊C4—28no—
268C4⋊C4—22no—
269C4⋊C4—134no—
270C4⋊C4—264no—
271C4⋊C4—264no—
272C4⋊C4—268no—
273C4⋊C4—268no—
274C4⋊C4—268no—
275C4⋊C4—262no—
276C4⋊C4—268no—
277C4⋊C4—524no—
278C4⋊C4C22×#26114yes—
279C42—134no—
280C42—134no—
281C42—132no—
282C42—132no—
283C42C22⋊#26112yes—
284C42C22×#26112yes—
285C13C2×#199111yescharacteristic, complemented, Sylow
286C23—131no—
287C23—131no—
288C23—132no—
289C23—132no—
290C23—138no—
291C23C2×C22⋊#26111yescharacteristic
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—44no—
295C2×C4—131no—
296C2×C4—131no—
297C2×C4—134no—
298C2×C4—132no—
299C2×C4—132no—
300C2×C4—134no—
301C2×C4—132no—
302C2×C4—134no—
303C2×C4—132no—
304C2×C4—134no—
305C2×C4—268no—
306C2×C4—268no—
307C2×C4—264no—
308C2×C4—264no—
309C2×C4—528no—
310C2×C4—528no—
311C2×C4—524no—
312C2×C4—524no—
313C2×C4—528no—
314C2×C4—1048no—
315C2×C4Q8×#26114yes—
316C2×C4C2×C22⋊#26114yes—
317C2×C4C2×C22⋊#26111yescharacteristic
318C2×C4C23×#26111yescharacteristic
319C8—268no—
320C22—138no—
321C22—138no—
322C22—131no—
323C22—131no—
324C22—132no—
325C22—134no—
326C22—134no—
327C22(C2×#261)⋊Q812yes—
328C22#1171916514yes—
329C22C22×C22⋊#26111yescharacteristic
330C4—24no—
331C4—44no—
332C4—132no—
333C4—132no—
334C4—264no—
335C4—524no—
336C4—1044no—
337C4(C2×#261)⋊Q812yes—
338C4C2×Q8×#26112yes—
339C2—132no—
340C2—132no—
341C2—134no—
342C2#1313101814yesdirect product factor
343C2C2×(C2×#261)⋊Q811yescharacteristic
344C2C2×#1171916512yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×#125C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C2×D4
cosocleC2×C4×D13C24
hypercenterC2×#125#261
hypocenterC13C2×#1991
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
3. #13131018C2direct (N × H)
8. C2×C13×#125C4semidirect
11. D13×#125C4semidirect
15. C2×#88144C4semidirect
18. C2×#88124C4semidirect
39. C13×#125C2×C4semidirect
57. #88144C2×C4semidirect
65. #88124C2×C4semidirect
161. C2×#125#261semidirect
208. #125C2×#261semidirect
234. C2×C13#1991semidirect
237. D13#1991semidirect
285. C13C2×#1991semidirect
342. C2#13131018direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D13⋊C82
C2×#117190602
#131310182
C2×#117182462
C2×D13×#1252
C2×#199113