Finite Group Databasebeta

← C2×#13131382 #16807809

Subgroups — C2×#13131382 #16807809

Order 3328.

2198 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131382C2116yesmaximal, direct product factor
2C2×#11719083C214yesmaximal
3C2×#11719082C214yesmaximal
4C2×#11719082C214yesmaximal
5C2×#11719060C212yesmaximal
6C2×D13×#125C211yesmaximal, characteristic
7C22×C4⋊#261C2212yes—
8C22×C4⋊#261C2212yes—
9C22×C4⋊#261C2214yes—
10C22×C4×#261C2214yes—
11C2×C13×#125C411yescharacteristic, complemented
12D13×#125C418yescomplemented
13D13×#125C2218yes—
14C2×C4⋊C4×D13C2212yes—
15C2×C4⋊C4×D13C2214yes—
16C2×#88144C412yescomplemented
17C2×#88143C414yescomplemented
18C2×C42×D13C2211yescharacteristic
19C2×#88124C411yescharacteristic, complemented
20C2×(C2×#261)⋊C4C2214yes—
21C2×(C2×#261)⋊C4C2214yes—
22C2×(C2×#261)⋊C4C2214yes—
23C2×(C2×#261)⋊C4C2214yes—
24#11719083C22132yes—
25#11719082C22132yes—
26#11719082C22132yes—
27#11719060C22116yes—
28C23×#261C2314yes—
29C23×#261C2314yes—
30C22×C4×D13C2312yes—
31C22×C4×D13C2311yescharacteristic
32C22×C4×D13C2314yes—
33C2×C4⋊#261—48no—
34C2×C4⋊#261—44no—
35C2×C4⋊#261—44no—
36C2×C4⋊#261C2318yes—
37C2×C4⋊#261C2318yes—
38C2×C4⋊#261C23116yes—
39C2×C4×#261—48no—
40C2×C4×#261C23116yes—
41C13×#125C2×C418yescomplemented
42C2×C13×C4⋊C4C2×C414yes—
43C2×C13×C4⋊C4C2×C412yes—
44C2×C42×C13C2×C411yescharacteristic
45C2×C4⋊Dic13C2×C412yes—
46C2×C4⋊Dic13C2×C414yes—
47C2×#6101C2×C414yes—
48C2×#6101C2×C414yes—
49C2×#6101C2×C414yes—
50C2×C4×Dic13C2×C412yes—
51C2×C4×Dic13C2×C411yescharacteristic
52C4⋊C4×D13C2×C4116yes—
53C4⋊C4×D13C2×C418yes—
54C4⋊C4×D13C2318yes—
55C4⋊C4×D13C23116yes—
56#88144C2×C4116yescomplemented
57#88143C2×C4132yescomplemented
58C42×D13C2×C414yes—
59C42×D13C2314yes—
60#88124C2×C418yescomplemented
61(C2×#261)⋊C4C23116yes—
62(C2×#261)⋊C4C23116yes—
63(C2×#261)⋊C4C23116yes—
64(C2×#261)⋊C4C23116yes—
65C2×#2382—131nomaximal, Sylow
66C23×D13C2411yescharacteristic
67C22×#261—28no—
68C22×#261—28no—
69C22×#261—28no—
70C22×#261—28no—
71C22×#261—28no—
72C22×#261—28no—
73C22×#261C2418yes—
74C22×#261C2418yes—
75C22×C4×C13C22×C412yes—
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C22×C414yes—
78C22×Dic13C22×C411yescharacteristic
79C22×Dic13C22×C412yes—
80C22×Dic13C22×C414yes—
81C2×C4×D13—28no—
82C2×C4×D13—24no—
83C2×C4×D13—22no—
84C2×C4×D13—22no—
85C2×C4×D13—24no—
86C2×C4×D13—28no—
87C2×C4×D13C22×C412yes—
88C2×C4×D13C22×C414yes—
89C2×C4×D13C22×C418yes—
90C2×C4×D13C2412yes—
91C2×C4×D13C2414yes—
92C2×C4×D13C2418yes—
93C4⋊#261—416no—
94C4⋊#261—48no—
95C4⋊#261—48no—
96C4×#261—416no—
97C13×C4⋊C4C22×C4116yes—
98C13×C4⋊C4C22×C418yes—
99C42×C13C22×C414yes—
100C4⋊Dic13C22×C418yes—
101C4⋊Dic13C22×C4116yes—
102#6101C22×C4116yes—
103#6101C22×C4116yes—
104#6101C22×C4116yes—
105C4×Dic13C22×C418yes—
106C4×Dic13C22×C414yes—
107C22×#125—131no—
108#2382—1316no—
109C2×#389—134no—
110C2×#387—134no—
111C2×#387—134no—
112C2×#382—132no—
113C23×C13C23×C411yescharacteristic
114C22×D13C23×C411yescharacteristic
115C22×D13H(5,𝔽2)14yes—
116C22×D132−1+412yes—
117C22×D132−1+412yes—
118C22×D132−1+414yes—
119C22×D13C2511yescharacteristic
120C2×#261—28no—
121C2×#261—28no—
122C2×#261—28no—
123C2×#261—28no—
124C2×#261—28no—
125C2×#261—28no—
126C2×#261—416no—
127C2×#261—416no—
128C2×C4×C13—22no—
129C2×C4×C13—28no—
130C2×C4×C13—24no—
131C2×C4×C13C23×C414yes—
132C2×C4×C13C23×C412yes—
133C2×C4×C13C23×C418yes—
134C2×Dic13—22no—
135C2×Dic13—28no—
136C2×Dic13—24no—
137C2×Dic13C23×C412yes—
138C2×Dic13C23×C414yes—
139C2×Dic13C23×C418yes—
140C4×D13—24no—
141C4×D13—216no—
142C4×D13—28no—
143C4×D13—28no—
144C4×D13—24no—
145C4×D13—22no—
146C4×D13—22no—
147C4×D13—24no—
148C4×D13—28no—
149C2×#125—138no—
150C2×#125—138no—
151C2×#125—134no—
152C2×#125—132no—
153C2×#125—131no—
154C2×#125#26111yescharacteristic, complemented
155C22×C4⋊C4—132no—
156C22×C4⋊C4—134no—
157C22×C4⋊C4—132no—
158C22×C4⋊C4—132no—
159C22×C4⋊C4—134no—
160C22×C42—131no—
161C22×C42—134no—
162#389—1332no—
163#387—1332no—
164#387—1332no—
165#382—1316no—
166C2×#95—134no—
167C2×#95—134no—
168C2×#95—134no—
169C2×#95—134no—
170C22×C13#51912yes—
171C22×C13#52014yes—
172C22×C13C24×C411yescharacteristic
173C2×D13#51912yes—
174C2×D13#52014yes—
175C2×D13#56214yes—
176C2×D13#56318yes—
177C2×D13#56414yes—
178C2×D13C2×H(5,𝔽2)12yes—
179C2×D13C2×2−1+411yescharacteristic
180C2×D13C2×2−1+411yescharacteristic
181C2×D13C2×2−1+412yes—
182#261—48no—
183#261—48no—
184C4×C13—22no—
185C4×C13—28no—
186C4×C13—24no—
187Dic13—22no—
188Dic13—28no—
189Dic13—24no—
190C23×C4—132no—
191C23×C4—134no—
192C23×C4—131no—
193C23×C4—134no—
194C23×C4—134no—
195#125—1332no—
196#125—1316no—
197#125—138no—
198#125C2×#26118yescomplemented
199C2×C4⋊C4—134no—
200C2×C4⋊C4—134no—
201C2×C4⋊C4—134no—
202C2×C4⋊C4—134no—
203C2×C4⋊C4—132no—
204C2×C4⋊C4—138no—
205C2×C4⋊C4—1316no—
206C2×C4⋊C4—138no—
207C2×C4⋊C4—1316no—
208C2×C4⋊C4—138no—
209C2×C4⋊C4—138no—
210C2×C4⋊C4—1316no—
211C2×C4⋊C4—528no—
212C2×C4⋊C4—524no—
213C2×C4⋊C4—524no—
214C2×C4⋊C4C2×#26112yes—
215C2×C4⋊C4C2×#26114yes—
216C2×C42—132no—
217C2×C42—131no—
218C2×C42—134no—
219C2×C42—134no—
220C2×C42—1316no—
221C2×C42—528no—
222C2×C42C2×#26111yescharacteristic
223#95—1316no—
224#95—1316no—
225#95—1316no—
226#95—1316no—
227C2×C13#238214yescomplemented
228C2×C13C2×#51911yescharacteristic
229C2×C13C2×#52012yes—
230D13#238214yescomplemented
231D13C2×#56211yescharacteristic
232D13C2×#56312yes—
233D13C2×#56411yescharacteristic
234C24—131no—
235C22×C4—131no—
236C22×C4—132no—
237C22×C4—134no—
238C22×C4—132no—
239C22×C4—134no—
240C22×C4—138no—
241C22×C4—134no—
242C22×C4—132no—
243C22×C4—138no—
244C22×C4—138no—
245C22×C4—138no—
246C22×C4—268no—
247C22×C4—264no—
248C22×C4—262no—
249C22×C4—262no—
250C22×C4—268no—
251C22×C4—264no—
252C22×C4—268no—
253C22×C4—268no—
254C22×C4—268no—
255C22×C4—268no—
256C22×C4—268no—
257C22×C4—268no—
258C22×C4C22×#26111yescharacteristic
259C22×C4C22×#26112yes—
260C22×C4C22×#26114yes—
261C4⋊C4—1316no—
262C4⋊C4—1316no—
263C4⋊C4—1316no—
264C4⋊C4—1316no—
265C4⋊C4—138no—
266C4⋊C4—5216no—
267C4⋊C4—528no—
268C4⋊C4—528no—
269C4⋊C4C22×#26118yes—
270C4⋊C4C22×#261116yes—
271C42—138no—
272C42—134no—
273C42—5216no—
274C42C22×#26114yes—
275C13C2×#238211yescharacteristic, complemented, Sylow
276C23—132no—
277C23—132no—
278C23—134no—
279C23—134no—
280C23—131no—
281C23—131no—
282C23C23×#26111yescharacteristic
283C2×C4—22no—
284C2×C4—28no—
285C2×C4—24no—
286C2×C4—132no—
287C2×C4—134no—
288C2×C4—138no—
289C2×C4—268no—
290C2×C4—264no—
291C2×C4—264no—
292C2×C4—262no—
293C2×C4—262no—
294C2×C4—268no—
295C2×C4—2616no—
296C2×C4—268no—
297C2×C4—264no—
298C2×C4—262no—
299C2×C4—264no—
300C2×C4—268no—
301C2×C4—268no—
302C2×C4—268no—
303C2×C4—268no—
304C2×C4—268no—
305C2×C4—268no—
306C2×C4—268no—
307C2×C4—5216no—
308C2×C4—5216no—
309C2×C4C23×#26112yes—
310C2×C4C23×#26114yes—
311C2×C4C23×#26118yes—
312C22—132no—
313C22—131no—
314C22—131no—
315C22—134no—
316C22—132no—
317C22—132no—
318C22—134no—
319C22—138no—
320C22—134no—
321C22#1171962712yes—
322C22#1171963114yes—
323C22C24×#26111yescharacteristic
324C4—22no—
325C4—28no—
326C4—24no—
327C4—262no—
328C4—264no—
329C4—268no—
330C4—528no—
331C4—528no—
332C2—131no—
333C2—132no—
334C2—134no—
335C2—131no—
336C2#1313138214yesdirect product factor
337C2C2×#1171962711yescharacteristic
338C2C2×#1171963112yes—
subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C13×#125C4
socleC23×C13C23×C4
prime radicalC23×D13C24
cosocleC22×D13C25
hypercenterC2×#125#261
hypocenterC13C2×#2382
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #13131382C2direct (N × H)
11. C2×C13×#125C4semidirect
12. D13×#125C4semidirect
16. C2×#88144C4semidirect
17. C2×#88143C4semidirect
19. C2×#88124C4semidirect
41. C13×#125C2×C4semidirect
56. #88144C2×C4semidirect
57. #88143C2×C4semidirect
60. #88124C2×C4semidirect
154. C2×#125#261semidirect
198. #125C2×#261semidirect
227. C2×C13#2382semidirect
230. D13#2382semidirect
275. C13C2×#2382semidirect
336. C2#13131382direct (N × H)

Maximal subgroups

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

subgroupindex
#131313822
C2×#117190832
C2×#117190822
C2×#117190602
C2×D13×#1252
C2×#238213