Finite Group Databasebeta

← C2×#13129724 #16779946

Subgroups — C2×#13129724 #16779946

Order 3328.

786 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719130C211yesmaximal, characteristic
2C2×C4×#6122C211yesmaximal, characteristic
3#13129724C214yesmaximal, direct product factor
4C2×#11718309C211yesmaximal, characteristic
5C22×#6122—21no—
6C22×C4×Dic13—21no—
7C22×C4×Dic13C2211yescharacteristic
8C2×C22⋊#1057—21no—
9#11719130—21no—
10#11719130—21no—
11#11719130C412yescomplemented
12#11719130C2212yes—
13C4×#6122—21no—
14C4×#6122—21no—
15C4×#6122C412yescomplemented
16C4×#6122C2212yes—
17C2×#88110—21no—
18C2×#88110C412yescomplemented
19C2×C4⋊#1057C412yescomplemented
20C2×C4×#1057—21no—
21C2×C13×#95C411yescharacteristic
22C2×#88071—21no—
23C2×#88071C411yescharacteristic
24#11718309—21no—
25#11718309—21no—
26#11718309C412yes—
27#11718309C2212yes—
28C23×C4×C13—21no—
29C23×C4×C13C2×C411yescharacteristic
30C23×Dic13—21no—
31C23×Dic13D411yescharacteristic
32C23×Dic13D411yescharacteristic
33C2×#6122—24no—
34C2×#6122—24no—
35C2×#6122—22no—
36C2×#6122—22no—
37C22×#1057—22no—
38C22×#1057—22no—
39C2×C4×Dic13—28no—
40C2×C4×Dic13—22no—
41C2×C4×Dic13—22no—
42C2×C4×Dic13C2×C411yescharacteristic
43C2×C4×Dic13C2×C411yescharacteristic
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13C2×C411yescharacteristic
46C2×C4×Dic13C2×C411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×C4×Dic13D411yescharacteristic
49C2×C4×Dic13D411yescharacteristic
50C2×C4×Dic13D411yescharacteristic
51C2×C4×Dic13Q811yescharacteristic
52C2×C4×Dic13Q811yescharacteristic
53C2×C4×Dic13C2311yescharacteristic
54C22⋊#1057—22no—
55C22⋊#1057—22no—
56#88110—22no—
57#88110—22no—
58#88110—22no—
59#88110C2×C414yescomplemented
60C4⋊#1057—22no—
61C4⋊#1057C2×C414yescomplemented
62C4×#1057—22no—
63C4×#1057—22no—
64C13×#95—21no—
65C13×#95C2×C412yes—
66#88071—21no—
67#88071—22no—
68#88071—22no—
69#88071C2×C412yes—
70C2×#1300—131nomaximal, Sylow
71C24×C13C22⋊C411yescharacteristic
72C22×C4×C13—24no—
73C22×C4×C13—22no—
74C22×C4×C13—42no—
75C22×C4×C13—42no—
76C22×C4×C13—42no—
77C22×C4×C13C4211yescharacteristic
78C22×C4×C13C4211yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C4⋊C411yescharacteristic
81C22×C4×C13C4⋊C411yescharacteristic
82C22×C4×C13C22×C411yescharacteristic
83C22×Dic13—22no—
84C22×Dic13—22no—
85C22×Dic13—24no—
86C22×Dic13—24no—
87C22×Dic13—22no—
88C22×Dic13—42no—
89C22×Dic13—42no—
90C22×Dic13C22⋊C411yescharacteristic
91C22×Dic13C22⋊C411yescharacteristic
92C22×Dic13C22⋊C411yescharacteristic
93C22×Dic13C22⋊C411yescharacteristic
94C22×Dic13C22⋊C411yescharacteristic
95C22×Dic13C22⋊C411yescharacteristic
96C22×Dic13C4⋊C411yescharacteristic
97C22×Dic13C4⋊C411yescharacteristic
98C22×Dic13C4⋊C411yescharacteristic
99C22×Dic13C4⋊C411yescharacteristic
100C22×Dic13C2×D411yescharacteristic
101C22×Dic13C2×D411yescharacteristic
102#6122—28no—
103#6122—24no—
104#6122—24no—
105C2×#1057—28no—
106C2×#1057—24no—
107C2×#1057—24no—
108C2×#1057—44no—
109C4×Dic13—28no—
110C4×Dic13—28no—
111C4×Dic13C4211yescharacteristic
112C4×Dic13C4211yescharacteristic
113C4×Dic13C22⋊C411yescharacteristic
114C4×Dic13C22⋊C411yescharacteristic
115C4×Dic13C22⋊C411yescharacteristic
116C4×Dic13C22⋊C411yescharacteristic
117C4×Dic13C4⋊C411yescharacteristic
118C4×Dic13C4⋊C411yescharacteristic
119C4×Dic13C4⋊C411yescharacteristic
120C4×Dic13C4⋊C411yescharacteristic
121C4×Dic13C4⋊C411yescharacteristic
122C4×Dic13C4⋊C411yescharacteristic
123C4×Dic13C22×C411yescharacteristic
124C4×Dic13C22×C411yescharacteristic
125C4×Dic13C2×D411yescharacteristic
126C4×Dic13C2×Q811yescharacteristic
127C2×#432—131no—
128C2×C4×M16—131no—
129C2×#376—131no—
130#1300—134no—
131C23×C13—22no—
132C23×C13—22no—
133C23×C13#9511yescharacteristic
134C23×C13#9511yescharacteristic
135C23×C13#10412yes—
136C23×C13#10412yes—
137C23×C13C2×C22⋊C411yescharacteristic
138C2×C4×C13—22no—
139C2×C4×C13—22no—
140C2×C4×C13—24no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—48no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13#9511yescharacteristic
149C2×C4×C13#9511yescharacteristic
150C2×C4×C13C2×C4211yescharacteristic
151C2×C4×C13C2×C4⋊C411yescharacteristic
152C2×Dic13—22no—
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—22no—
156C2×Dic13—22no—
157C2×Dic13—21no—
158C2×Dic13—21no—
159C2×Dic13—21no—
160C2×Dic13—21no—
161C2×Dic13—22no—
162C2×Dic13—22no—
163C2×Dic13—22no—
164C2×Dic13—22no—
165C2×Dic13—24no—
166C2×Dic13—48no—
167C2×Dic13—42no—
168C2×Dic13—42no—
169C2×Dic13#9511yescharacteristic
170C2×Dic13#9511yescharacteristic
171C2×Dic13#9511yescharacteristic
172C2×Dic13#9511yescharacteristic
173C2×Dic13#10414yes—
174C2×Dic13C2×C22⋊C411yescharacteristic
175C2×Dic13C2×C22⋊C411yescharacteristic
176C2×Dic13C2×C4⋊C411yescharacteristic
177C2×Dic13C2×C4⋊C411yescharacteristic
178#1057—28no—
179#1057—44no—
180C22×M16—261no—
181C22×C42—131no—
182C22×C42—261no—
183#432—132no—
184#432—132no—
185#432—261no—
186#432—261no—
187C2×C4⋊C8—132no—
188C2×C22⋊C8—261no—
189C4×M16—132no—
190C4×M16—132no—
191C4×M16—261no—
192C4×M16—261no—
193C2×#97—132no—
194C2×#97—261no—
195C2×C4×C8—261no—
196#376—132no—
197#376—132no—
198#376—261no—
199#376—261no—
200C2×#95—131no—
201C2×#95—261no—
202C2×#95#26111yescharacteristic
203C22×C13—24no—
204C22×C13—24no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13#33912yes—
210C22×C13#33912yes—
211C22×C13#33912yes—
212C22×C13#34412yes—
213C22×C13C2×#9511yescharacteristic
214C22×C13C2×#10411yescharacteristic
215C22×C13C2×#10411yescharacteristic
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—44no—
221Dic13—21no—
222Dic13—21no—
223Dic13—21no—
224Dic13—21no—
225Dic13—21no—
226Dic13—21no—
227Dic13—44no—
228Dic13#33912yes—
229Dic13C2×#10412yes—
230C23×C4—21no—
231C23×C4—131no—
232C23×C4—131no—
233C23×C4—261no—
234C23×C4C2×#26111yescharacteristic
235C2×M16—262no—
236C2×M16—262no—
237C2×M16—264no—
238C2×M16—264no—
239C22×C8—262no—
240C22×C8—262no—
241C2×C42—131no—
242C2×C42—131no—
243C2×C42—131no—
244C2×C42—131no—
245C2×C42—131no—
246C2×C42—131no—
247C2×C42—131no—
248C2×C42—131no—
249C2×C42—131no—
250C2×C42—131no—
251C2×C42—131no—
252C2×C42—131no—
253C2×C42—262no—
254C2×C42—262no—
255C2×C42—268no—
256C4⋊C8—134no—
257C4⋊C8—262no—
258C22⋊C8—262no—
259C22⋊C8—262no—
260#97—134no—
261#97—262no—
262#97—262no—
263#97—262no—
264C4×C8—262no—
265C4×C8—262no—
266#95—21no—
267#95—132no—
268#95—262no—
269#95—262no—
270#95—261no—
271#95C2×#26112yes—
272C2×C13—21no—
273C2×C13—21no—
274C2×C13—22no—
275C2×C13#130014yescomplemented
276C2×C13C2×#33911yescharacteristic
277C2×C13C2×#33911yescharacteristic
278C2×C13C2×#34411yescharacteristic
279C24C22⋊#26111yescharacteristic
280C22×C4—24no—
281C22×C4—22no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—131no—
288C22×C4—131no—
289C22×C4—131no—
290C22×C4—131no—
291C22×C4—131no—
292C22×C4—131no—
293C22×C4—131no—
294C22×C4—131no—
295C22×C4—131no—
296C22×C4—131no—
297C22×C4—264no—
298C22×C4—262no—
299C22×C4—262no—
300C22×C4—264no—
301C22×C4—262no—
302C22×C4—522no—
303C22×C4—522no—
304C22×C4C4×#26111yescharacteristic
305C22×C4C4×#26111yescharacteristic
306C22×C4C4⋊#26111yescharacteristic
307C22×C4C4⋊#26111yescharacteristic
308C22×C4C22⋊#26111yescharacteristic
309C22×C4C22×#26111yescharacteristic
310M16—268no—
311M16—264no—
312M16—264no—
313C2×C8—264no—
314C2×C8—268no—
315C2×C8—264no—
316C2×C8—524no—
317C42—131no—
318C42—131no—
319C42—131no—
320C42—131no—
321C42—131no—
322C42—131no—
323C42—131no—
324C42—131no—
325C42—131no—
326C42—131no—
327C42—131no—
328C42—131no—
329C42—131no—
330C42—131no—
331C42—131no—
332C42—131no—
333C42—268no—
334C42—268no—
335C13C2×#130011yescharacteristic, complemented, Sylow
336C23—22no—
337C23—22no—
338C23(C2×#261)⋊C411yescharacteristic
339C23(C2×#261)⋊C411yescharacteristic
340C23#8811612yes—
341C23#8811812yes—
342C23C2×C22⋊#26111yescharacteristic
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—24no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—48no—
352C2×C4—42no—
353C2×C4—134no—
354C2×C4—131no—
355C2×C4—131no—
356C2×C4—131no—
357C2×C4—131no—
358C2×C4—131no—
359C2×C4—131no—
360C2×C4—131no—
361C2×C4—131no—
362C2×C4—262no—
363C2×C4—262no—
364C2×C4—262no—
365C2×C4—262no—
366C2×C4—262no—
367C2×C4—262no—
368C2×C4—262no—
369C2×C4—262no—
370C2×C4—262no—
371C2×C4—261no—
372C2×C4—261no—
373C2×C4—261no—
374C2×C4—261no—
375C2×C4—264no—
376C2×C4—522no—
377C2×C4—528no—
378C2×C4—522no—
379C2×C4(C2×#261)⋊C411yescharacteristic
380C2×C4(C2×#261)⋊C411yescharacteristic
381C2×C4C2×C4×#26111yescharacteristic
382C2×C4C2×C4⋊#26111yescharacteristic
383C8—268no—
384C8—524no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—24no—
390C22—24no—
391C22#1171823412yes—
392C22#1171823912yes—
393C22#1171824712yes—
394C22#1171824712yes—
395C22C2×(C2×#261)⋊C411yescharacteristic
396C22C2×#8811611yescharacteristic
397C22C2×#8811811yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—44no—
403C4—132no—
404C4—132no—
405C4—261no—
406C4—261no—
407C4—261no—
408C4—261no—
409C4—261no—
410C4—261no—
411C4—524no—
412C2—21no—
413C2—21no—
414C2—22no—
415C2#1312972414yesdirect product factor
416C2C2×#1171824711yescharacteristic
417C2C2×#1171823411yescharacteristic
418C2C2×#1171823911yescharacteristic
subgroupG/H
centerC23(C2×#261)⋊C4
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC2×C13×#95C4
socleC23×C13#95
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#95#261
hypocenterC13C2×#1300
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. #13129724C2direct (N × H)
11. #11719130C4semidirect
15. C4×#6122C4semidirect
18. C2×#88110C4semidirect
19. C2×C4⋊#1057C4semidirect
59. #88110C2×C4semidirect
61. C4⋊#1057C2×C4semidirect
275. C2×C13#1300semidirect
335. C13C2×#1300semidirect
415. C2#13129724direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191302
C2×C4×#61222
#131297242
C2×#117183092
C2×#130013