Finite Group Databasebeta

← C2×#11719401 #13128201

Subgroups — C2×#11719401 #13128201

Order 1664.

1004 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#125C211yesmaximal, characteristic, complemented
2#11719401C2116yesmaximal, direct product factor
3C2×#88152C211yesmaximal, characteristic
4C2×#88152C211yesmaximal, characteristic
5C2×#88152C211yesmaximal, characteristic
6C2×#88150C211yesmaximal, characteristic
7C2×#88150C211yesmaximal, characteristic
8C2×#88146C211yesmaximal, characteristic
9C2×#88144C211yesmaximal, characteristic, complemented
10C2×#88143C211yesmaximal, characteristic, complemented
11C2×#88143C211yesmaximal, characteristic, complemented
12C2×#88143C211yesmaximal, characteristic, complemented
13C2×#88142C211yesmaximal, characteristic, complemented
14C2×#88141C211yesmaximal, characteristic, complemented
15C2×#88130C211yesmaximal, characteristic
16C2×C4×Dic26C211yesmaximal, characteristic, complemented
17C22×C4×D13C2211yescharacteristic
18C22×Dic26C2211yescharacteristic
19C22×Dic26C2211yescharacteristic
20C13×#125C2218yescomplemented
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×C13×C4⋊C4C2211yescharacteristic
23C2×C13×C4⋊C4C2211yescharacteristic
24C2×C13×C4⋊C4C2211yescharacteristic
25C2×C13×C4⋊C4C2211yescharacteristic
26C2×C13×C4⋊C4C2211yescharacteristic
27C2×C42×C13C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×C4⋊Dic13C2211yescharacteristic
35C2×C4⋊Dic13C2211yescharacteristic
36C2×C4⋊Dic13C2211yescharacteristic
37C2×C4⋊Dic13C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×#6101C2211yescharacteristic
40C2×#6101C2211yescharacteristic
41C2×#6101C2211yescharacteristic
42C2×#6101C2211yescharacteristic
43C2×#6101C2211yescharacteristic
44C2×#6101C2211yescharacteristic
45C2×#6101C2211yescharacteristic
46C2×#6101C2211yescharacteristic
47C2×#6101C2211yescharacteristic
48C2×C4×Dic13C2211yescharacteristic
49C2×C4×Dic13C2211yescharacteristic
50C2×C4×Dic13C2211yescharacteristic
51C2×C4×Dic13C2211yescharacteristic
52C2×C4×Dic13C2211yescharacteristic
53#88152C2218yes—
54#88152C2218yes—
55#88152C2218yes—
56#88150C2218yes—
57#88150C2218yes—
58#88146C2218yes—
59#88144C2218yescomplemented
60#88143C2218yescomplemented
61#88143C2218yescomplemented
62#88143C2218yescomplemented
63#88142C2218yescomplemented
64#88141C2218yescomplemented
65#88130C2218yes—
66C4×Dic26C2218yescomplemented
67C23×D13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C22×C4×C13C2311yescharacteristic
70C22×C4×C13C2311yescharacteristic
71C22×C4×C13C2311yescharacteristic
72C22×C4×C13C2311yescharacteristic
73C22×C4×C13C2311yescharacteristic
74C22×C4×C13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2311yescharacteristic
79C22×Dic13C2311yescharacteristic
80C22×Dic13C2311yescharacteristic
81C22×Dic13C2311yescharacteristic
82C2×C4×D13—24no—
83C2×C4×D13C2314yes—
84C2×Dic26—24no—
85C2×Dic26—24no—
86C2×Dic26C2314yes—
87C2×Dic26C2314yes—
88C13×C4⋊C4C2314yes—
89C13×C4⋊C4C2314yes—
90C13×C4⋊C4C2314yes—
91C13×C4⋊C4C2314yes—
92C13×C4⋊C4C2314yes—
93C13×C4⋊C4C2314yes—
94C42×C13C2314yes—
95#6103C2314yes—
96#6103C2314yes—
97#6103C2314yes—
98#6103C2314yes—
99#6103C2314yes—
100#6103C2314yes—
101C4⋊Dic13C2314yes—
102C4⋊Dic13C2314yes—
103C4⋊Dic13C2314yes—
104C4⋊Dic13C2314yes—
105#6101C2314yes—
106#6101C2314yes—
107#6101C2314yes—
108#6101C2314yes—
109#6101C2314yes—
110#6101C2314yes—
111#6101C2314yes—
112#6101C2314yes—
113#6101C2314yes—
114#6101C2314yes—
115C4×Dic13C2314yes—
116C4×Dic13C2314yes—
117C4×Dic13C2314yes—
118C4×Dic13C2314yes—
119C4×Dic13C2314yes—
120C2×#541—131nomaximal, Sylow
121C23×C13C2411yescharacteristic
122C22×D13—22no—
123C22×D13—22no—
124C22×D13—22no—
125C22×D13C2412yes—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13C2412yes—
134C2×C4×C13C2412yes—
135C2×C4×C13C2412yes—
136C2×C4×C13C2412yes—
137C2×C4×C13C2412yes—
138C2×C4×C13C2412yes—
139C2×C4×C13C2412yes—
140C2×Dic13—22no—
141C2×Dic13—22no—
142C2×Dic13—22no—
143C2×Dic13—22no—
144C2×Dic13—22no—
145C2×Dic13—22no—
146C2×Dic13#4114yes—
147C2×Dic13C2412yes—
148C2×Dic13C2412yes—
149C2×Dic13C2412yes—
150C2×Dic13C2412yes—
151C2×Dic13C2412yes—
152C2×Dic13C2412yes—
153C2×Dic13C2412yes—
154C4×D13—28no—
155Dic26—28no—
156Dic26—28no—
157#541—1316no—
158C2×C4⋊Q8—131no—
159C2×#126—131no—
160C2×#126—131no—
161C2×#126—131no—
162C2×#126—131no—
163C2×#125—131no—
164C2×#125—131no—
165C2×#125—131no—
166C2×#125—131no—
167C2×#125D1311yescharacteristic, complemented
168C2×C22⋊Q8—131no—
169C2×C22⋊Q8—131no—
170C2×C4×Q8—131no—
171C2×C4×Q8—131no—
172C2×#117—131no—
173C22×C13C2×#4112yes—
174C22×C132−1+412yes—
175C22×C132−1+412yes—
176C22×C13C2511yescharacteristic
177C2×D13—22no—
178C2×D13—22no—
179C2×D13—22no—
180C2×D13—44no—
181C4×C13—22no—
182C4×C13—22no—
183C4×C13—22no—
184C4×C13—22no—
185C4×C13—22no—
186C4×C13—22no—
187C4×C13—22no—
188Dic13—22no—
189Dic13—22no—
190Dic13—22no—
191Dic13—22no—
192Dic13—22no—
193Dic13—22no—
194Dic13C2×#4114yes—
195C22×Q8—131no—
196C22×Q8—131no—
197C23×C4—131no—
198C4⋊Q8—138no—
199#126—138no—
200#126—138no—
201#126—138no—
202#126—138no—
203#125—138no—
204#125—138no—
205#125—138no—
206#125—138no—
207#125C2×D1318yescomplemented
208C22⋊Q8—138no—
209C22⋊Q8—138no—
210C4×Q8—138no—
211C4×Q8—138no—
212#117—138no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—131no—
215C2×C4⋊C4—131no—
216C2×C4⋊C4—131no—
217C2×C4⋊C4—131no—
218C2×C4⋊C4—131no—
219C2×C4⋊C4—131no—
220C2×C4⋊C4—131no—
221C2×C4⋊C4—131no—
222C2×C4⋊C4—131no—
223C2×C4⋊C4—131no—
224C2×C4⋊C4—131no—
225C2×C4⋊C4—131no—
226C2×C4⋊C4—131no—
227C2×C4⋊C4C2×D1311yescharacteristic
228C2×C4⋊C4C2×D1311yescharacteristic
229C2×C4⋊C4C2×D1311yescharacteristic
230C2×C4⋊C4C2×D1311yescharacteristic
231C2×C4⋊C4C2×D1311yescharacteristic
232C2×C4⋊C4C2×D1311yescharacteristic
233C2×C22⋊C4—131no—
234C2×C22⋊C4—131no—
235C2×C22⋊C4—131no—
236C2×C22⋊C4—131no—
237C2×C22⋊C4—131no—
238C2×C22⋊C4—131no—
239C2×C42—131no—
240C2×C42—131no—
241C2×C42—131no—
242C2×C42—131no—
243C2×C42—131no—
244C2×C42C2×D1311yescharacteristic
245C2×C13#54114yescomplemented
246C2×C13C22×#4111yescharacteristic
247C2×C13C2×2−1+411yescharacteristic
248C2×C13C2×2−1+411yescharacteristic
249D13—42no—
250C24—131no—
251C2×Q8—134no—
252C2×Q8—134no—
253C2×Q8—264no—
254C2×Q8—264no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—131no—
258C22×C4—131no—
259C22×C4—131no—
260C22×C4—131no—
261C22×C4—131no—
262C22×C4—134no—
263C22×C4—264no—
264C22×C4C22×D1311yescharacteristic
265C22×C4C22×D1311yescharacteristic
266C22×C4C22×D1311yescharacteristic
267C22×C4C22×D1311yescharacteristic
268C22×C4C22×D1311yescharacteristic
269C22×C4C22×D1311yescharacteristic
270C22×C4C22×D1311yescharacteristic
271C4⋊C4—134no—
272C4⋊C4—134no—
273C4⋊C4—134no—
274C4⋊C4—134no—
275C4⋊C4—134no—
276C4⋊C4—134no—
277C4⋊C4—134no—
278C4⋊C4—134no—
279C4⋊C4—134no—
280C4⋊C4—134no—
281C4⋊C4—134no—
282C4⋊C4—134no—
283C4⋊C4—134no—
284C4⋊C4—134no—
285C4⋊C4C22×D1314yes—
286C4⋊C4C22×D1314yes—
287C4⋊C4C22×D1314yes—
288C4⋊C4C22×D1314yes—
289C4⋊C4C22×D1314yes—
290C4⋊C4C22×D1314yes—
291C22⋊C4—134no—
292C22⋊C4—134no—
293C22⋊C4—134no—
294C22⋊C4—134no—
295C22⋊C4—134no—
296C22⋊C4—134no—
297C42—134no—
298C42—134no—
299C42—134no—
300C42—134no—
301C42—134no—
302C42C22×D1314yes—
303C13C2×#54111yescharacteristic, complemented, Sylow
304C23—132no—
305C23—262no—
306C23—262no—
307C23—262no—
308C23C23×D1311yescharacteristic
309Q8—268no—
310Q8—268no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—134no—
319C2×C4—132no—
320C2×C4—132no—
321C2×C4—132no—
322C2×C4—132no—
323C2×C4—132no—
324C2×C4—132no—
325C2×C4—132no—
326C2×C4—268no—
327C2×C4—262no—
328C2×C4—262no—
329C2×C4—262no—
330C2×C4—262no—
331C2×C4—262no—
332C2×C4—262no—
333C2×C4C23×D1312yes—
334C2×C4C23×D1312yes—
335C2×C4C23×D1312yes—
336C2×C4C23×D1312yes—
337C2×C4C23×D1312yes—
338C2×C4C23×D1312yes—
339C2×C4C23×D1312yes—
340C22—262no—
341C22—262no—
342C22—262no—
343C22—524no—
344C22#8825412yes—
345C22#41×D1312yes—
346C22#8825712yes—
347C22C24×D1311yescharacteristic
348C4—22no—
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—134no—
356C4—262no—
357C4—262no—
358C4—262no—
359C4—262no—
360C4—262no—
361C4—262no—
362C2—522no—
363C2#1171940114yesdirect product factor
364C2C2×#8825411yescharacteristic
365C2C2×#41×D1311yescharacteristic
366C2C2×#8825711yescharacteristic
subgroupG/H
centerC23C23×D13
commutator, cosocleC22×C13C25
FrattiniC22C24×D13
FittingC2×C13×#125C2
socleC23×C13C24
prime radicalC23×D13C23
hypercenterC2×#125D13
hypocenterC13C2×#541
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C13×#125C2semidirect
2. #11719401C2direct (N × H)
9. C2×#88144C2semidirect
10. C2×#88143C2semidirect
11. C2×#88143C2semidirect
12. C2×#88143C2semidirect
13. C2×#88142C2semidirect
14. C2×#88141C2semidirect
16. C2×C4×Dic26C2semidirect
20. C13×#125C22semidirect
59. #88144C22semidirect
60. #88143C22semidirect
61. #88143C22semidirect
62. #88143C22semidirect
63. #88142C22semidirect
64. #88141C22semidirect
66. C4×Dic26C22semidirect
167. C2×#125D13semidirect
207. #125C2×D13semidirect
245. C2×C13#541semidirect
303. C13C2×#541semidirect
363. C2#11719401direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#1252
#117194012
C2×#881522
C2×#881502
C2×#881462
C2×#881442
C2×#881432
C2×#881422
C2×#881412
C2×#881302
C2×C4×Dic262
C2×#54113