Finite Group Databasebeta

← C2×#13131016 #16799365

Subgroups — C2×#13131016 #16799365

Order 3328.

1294 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13⋊(C4⋊C8)C211yesmaximal, characteristic
2C2×C4×C4⋊#261C211yesmaximal, characteristic
3#13131016C218yesmaximal, direct product factor
4C2×#11718246C212yesmaximal
5C2×#11718246C212yesmaximal
6C2×D13×#125C211yesmaximal, characteristic
7C22×C4⋊#261C2212yes—
8C22×C4×#261—21no—
9C22×D13⋊C8C2212yes—
10C2×C13×#125C411yescharacteristic, complemented
11D13×#125—22no—
12D13×#125—22no—
13D13×#125C414yescomplemented
14D13×#125C2214yes—
15C2×C4⋊C4×D13—21no—
16C2×C4⋊C4×D13—21no—
17C2×C4⋊C4×D13C2211yescharacteristic
18C2×C4⋊C4×D13C2211yescharacteristic
19C2×#88144C411yescharacteristic, complemented
20C2×#88144C411yescharacteristic, complemented
21C2×#88143—21no—
22C2×#88143—21no—
23C2×C42×D13C2211yescharacteristic
24C2×#88124C411yescharacteristic, complemented
25C2×(C2×#261)⋊C4—21no—
26C2×#88112—21no—
27C2×C4⋊#1057—21no—
28C4×C4⋊#261—22no—
29C4×C4⋊#261C2214yes—
30D13⋊(C4⋊C8)—22no—
31D13⋊(C4⋊C8)C2214yes—
32#11718246C2218yes—
33#11718246C2218yes—
34C23×#261—22no—
35C22×C4×D13—21no—
36C22×C4×D13—21no—
37C22×C4×D13D411yescharacteristic
38C22×C4×D13D411yescharacteristic
39C22×C4×D13C2311yescharacteristic
40C22×#1057—22no—
41C2×C4⋊#261—22no—
42C2×C4⋊#261—24no—
43C2×C4⋊#261Q818yes—
44C2×C4⋊#261C2314yes—
45C2×C4×#261—24no—
46C2×C4×#261—44no—
47C2×D13⋊C8—28no—
48C2×D13⋊C8—22no—
49C2×D13⋊C8C2314yes—
50C13×#125—22no—
51C13×#125C2×C414yescomplemented
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4C2×C411yescharacteristic
55C2×C13×C4⋊C4C2×C411yescharacteristic
56C2×C42×C13C2×C411yescharacteristic
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13C2×C411yescharacteristic
60C2×C4⋊Dic13C2×C411yescharacteristic
61C2×#6101—21no—
62C2×#6101—21no—
63C2×#6101—21no—
64C2×#6101—21no—
65C2×#6101—21no—
66C2×#6101—21no—
67C2×C4×Dic13C2×C411yescharacteristic
68C2×C4×Dic13D411yescharacteristic
69C2×C4×Dic13D411yescharacteristic
70C4⋊C4×D13—24no—
71C4⋊C4×D13—24no—
72C4⋊C4×D13—24no—
73C4⋊C4×D13—24no—
74C4⋊C4×D13—21no—
75C4⋊C4×D13—21no—
76C4⋊C4×D13—21no—
77C4⋊C4×D13—21no—
78C4⋊C4×D13C2×C412yes—
79C4⋊C4×D13C2×C412yes—
80C4⋊C4×D13C2312yes—
81C4⋊C4×D13C2312yes—
82#88144—22no—
83#88144—22no—
84#88144C2×C414yescomplemented
85#88144C2×C414yescomplemented
86#88143—24no—
87#88143—24no—
88#88143—24no—
89#88143—24no—
90C42×D13C2×C412yes—
91C42×D13D412yes—
92C42×D13D412yes—
93C42×D13C2312yes—
94#88124—22no—
95#88124C2×C414yescomplemented
96(C2×#261)⋊C4—24no—
97#88112—24no—
98C4⋊#1057—24no—
99C2×#1989—131nomaximal, Sylow
100C23×D13C2×D411yescharacteristic
101C22×#261—28no—
102C22×#261—24no—
103C22×#261—44no—
104C22×#261—44no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13C22⋊C411yescharacteristic
108C22×C4×C13C22⋊C411yescharacteristic
109C22×C4×C13C22×C411yescharacteristic
110C22×Dic13—21no—
111C22×Dic13—21no—
112C22×Dic13C22⋊C411yescharacteristic
113C22×Dic13C22⋊C411yescharacteristic
114C22×Dic13C2×D411yescharacteristic
115C2×C4×D13—24no—
116C2×C4×D13—22no—
117C2×C4×D13—22no—
118C2×C4×D13—22no—
119C2×C4×D13—22no—
120C2×C4×D13—22no—
121C2×C4×D13—22no—
122C2×C4×D13—44no—
123C2×C4×D13—42no—
124C2×C4×D13—42no—
125C2×C4×D13C22⋊C412yes—
126C2×C4×D13C22⋊C412yes—
127C2×C4×D13C22×C411yescharacteristic
128C2×C4×D13C2×D412yes—
129C2×C4×D13C2×D412yes—
130C2×C4×D13C2×D411yescharacteristic
131C2×C4×D13C2×D411yescharacteristic
132C2×C4×D13C2×Q814yes—
133C2×C4×D13#4114yes—
134C2×C4×D13C2411yescharacteristic
135C2×#1057—24no—
136C2×#1057—44no—
137C4⋊#261—28no—
138C4⋊#261—24no—
139C4⋊#261C2×Q818yes—
140C4×#261—48no—
141D13⋊C8—28no—
142D13⋊C8—44no—
143C13×C4⋊C4—24no—
144C13×C4⋊C4—24no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4C22×C412yes—
148C13×C4⋊C4C22×C412yes—
149C42×C13C22⋊C412yes—
150C42×C13C22×C412yes—
151C4⋊Dic13—21no—
152C4⋊Dic13—21no—
153C4⋊Dic13—24no—
154C4⋊Dic13—24no—
155C4⋊Dic13C22×C412yes—
156C4⋊Dic13C22×C412yes—
157#6101—24no—
158#6101—24no—
159#6101—22no—
160#6101—22no—
161#6101—24no—
162#6101—24no—
163#6101—22no—
164#6101—22no—
165C4×Dic13C22⋊C412yes—
166C4×Dic13C22⋊C412yes—
167C4×Dic13C22⋊C412yes—
168C4×Dic13C22×C412yes—
169C4×Dic13C2×D412yes—
170C4×Dic13C2×D412yes—
171C22×#125—131no—
172C22×C4⋊C8—131no—
173C2×C4×C4⋊C4—131no—
174#1989—138no—
175C2×#340—132no—
176C2×#340—132no—
177C23×C13C2×C22⋊C411yescharacteristic
178C22×D13C2×C22⋊C411yescharacteristic
179C22×D13C22⋊Q814yes—
180C22×D13#13514yes—
181C22×D13AGL(1,ℤ/8)12yes—
182C22×D13#13712yes—
183C22×D13C22×D411yescharacteristic
184C2×#261—28no—
185C2×#261—44no—
186C2×#261—44no—
187C2×#261—416no—
188C2×C4×C13—22no—
189C2×C4×C13—22no—
190C2×C4×C13—22no—
191C2×C4×C13—22no—
192C2×C4×C13—42no—
193C2×C4×C13—42no—
194C2×C4×C13C2×C22⋊C412yes—
195C2×C4×C13C2×C22⋊C412yes—
196C2×C4×C13C2×C22⋊C411yescharacteristic
197C2×C4×C13C4×Q814yes—
198C2×C4×C13C23×C411yescharacteristic
199C2×Dic13—22no—
200C2×Dic13—22no—
201C2×Dic13—22no—
202C2×Dic13—22no—
203C2×Dic13—42no—
204C2×Dic13—42no—
205C2×Dic13C2×C22⋊C412yes—
206C2×Dic13C2×C22⋊C412yes—
207C2×Dic13C2×C22⋊C411yescharacteristic
208C2×Dic13#12412yes—
209C2×Dic13C4⋊Q812yes—
210C2×Dic13C22×D411yescharacteristic
211C4×D13—24no—
212C4×D13—22no—
213C4×D13—22no—
214C4×D13—24no—
215C4×D13—24no—
216C4×D13—44no—
217C4×D13—42no—
218C4×D13—42no—
219C4×D13—44no—
220C4×D13—44no—
221C4×D13C4×Q814yes—
222C4×D13C22⋊Q814yes—
223C4×D13#12412yes—
224C4×D13C4⋊Q812yes—
225C4×D13C22×Q812yes—
226C4×D13C2×#4112yes—
227#1057—44no—
228C23×C8—132no—
229C2×#125—134no—
230C2×#125—134no—
231C2×#125—131no—
232C2×#125—131no—
233C2×#125—131no—
234C2×#125—261no—
235C2×#125—261no—
236C2×#125—262no—
237C2×#125—262no—
238C2×#125#26111yescharacteristic, complemented
239C22×C4⋊C4—132no—
240C22×C4⋊C4—131no—
241C22×C4⋊C4—131no—
242C22×C4⋊C4—261no—
243C22×C4⋊C4—261no—
244C22×C42—131no—
245C22×C42—261no—
246C2×C4⋊C8—134no—
247C2×C4⋊C8—262no—
248C2×C4⋊C8—261no—
249C2×C4⋊C8—261no—
250C4×C4⋊C4—134no—
251C4×C4⋊C4—262no—
252C2×#95—261no—
253#340—138no—
254#340—138no—
255C22×C13#39112yes—
256C22×C13#41612yes—
257C22×C13#41712yes—
258C22×C13C22×C22⋊C411yescharacteristic
259C2×D13#39112yes—
260C2×D13#41612yes—
261C2×D13#41712yes—
262C2×D13#47818yes—
263C2×D13#47918yes—
264C2×D13C2×C22⋊Q812yes—
265C2×D13C2×#13512yes—
266C2×D13C2×AGL(1,ℤ/8)11yescharacteristic
267C2×D13C2×#13711yescharacteristic
268#261—48no—
269C4×C13—22no—
270C4×C13—22no—
271C4×C13—42no—
272C4×C13—42no—
273C4×C13#39112yes—
274C4×C13C2×C4×Q812yes—
275Dic13—22no—
276Dic13—22no—
277Dic13—42no—
278Dic13—42no—
279Dic13#39112yes—
280Dic13C2×#12411yescharacteristic
281Dic13C2×C4⋊Q811yescharacteristic
282C23×C4—131no—
283C23×C4—131no—
284C23×C4—131no—
285C23×C4—261no—
286C23×C4—261no—
287C23×C4—262no—
288C22×C8—134no—
289C22×C8—262no—
290C22×C8—262no—
291C22×C8—268no—
292#125—22no—
293#125—134no—
294#125—134no—
295#125—134no—
296#125—264no—
297#125—264no—
298#125—264no—
299#125—264no—
300#125—262no—
301#125—262no—
302#125—262no—
303#125C2×#26114yescomplemented
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—134no—
307C2×C4⋊C4—138no—
308C2×C4⋊C4—131no—
309C2×C4⋊C4—131no—
310C2×C4⋊C4—132no—
311C2×C4⋊C4—132no—
312C2×C4⋊C4—132no—
313C2×C4⋊C4—132no—
314C2×C4⋊C4—261no—
315C2×C4⋊C4—261no—
316C2×C4⋊C4—261no—
317C2×C4⋊C4—261no—
318C2×C4⋊C4—264no—
319C2×C4⋊C4—264no—
320C2×C4⋊C4—264no—
321C2×C4⋊C4—264no—
322C2×C4⋊C4—261no—
323C2×C4⋊C4—261no—
324C2×C4⋊C4—261no—
325C2×C4⋊C4—261no—
326C2×C4⋊C4—261no—
327C2×C4⋊C4—261no—
328C2×C4⋊C4—262no—
329C2×C4⋊C4—264no—
330C2×C4⋊C4—261no—
331C2×C4⋊C4—261no—
332C2×C4⋊C4C2×#26111yescharacteristic
333C2×C4⋊C4C2×#26111yescharacteristic
334C2×C42—131no—
335C2×C42—131no—
336C2×C42—131no—
337C2×C42—132no—
338C2×C42—132no—
339C2×C42—132no—
340C2×C42—132no—
341C2×C42—264no—
342C2×C42—524no—
343C2×C42C2×#26111yescharacteristic
344C4⋊C8—264no—
345C4⋊C8—264no—
346#95—264no—
347C2×C13#198914yescomplemented
348C2×C13C2×#39111yescharacteristic
349C2×C13C2×#41611yescharacteristic
350C2×C13C2×#41711yescharacteristic
351D13#198914yescomplemented
352D13C2×#47812yes—
353D13C2×#47912yes—
354C24—131no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—131no—
358C22×C4—134no—
359C22×C4—134no—
360C22×C4—131no—
361C22×C4—131no—
362C22×C4—131no—
363C22×C4—131no—
364C22×C4—131no—
365C22×C4—131no—
366C22×C4—132no—
367C22×C4—132no—
368C22×C4—132no—
369C22×C4—132no—
370C22×C4—262no—
371C22×C4—262no—
372C22×C4—264no—
373C22×C4—262no—
374C22×C4—262no—
375C22×C4—262no—
376C22×C4—262no—
377C22×C4—264no—
378C22×C4—268no—
379C22×C4—261no—
380C22×C4—261no—
381C22×C4—522no—
382C22×C4—522no—
383C22×C4—524no—
384C22×C4—524no—
385C22×C4—524no—
386C22×C4C22⋊#26111yescharacteristic
387C22×C4C22⋊#26111yescharacteristic
388C22×C4C22×#26111yescharacteristic
389C2×C8—264no—
390C2×C8—268no—
391C2×C8—524no—
392C2×C8—524no—
393C4⋊C4—24no—
394C4⋊C4—24no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—138no—
398C4⋊C4—132no—
399C4⋊C4—132no—
400C4⋊C4—262no—
401C4⋊C4—262no—
402C4⋊C4—262no—
403C4⋊C4—262no—
404C4⋊C4—264no—
405C4⋊C4—264no—
406C4⋊C4—264no—
407C4⋊C4—264no—
408C4⋊C4—264no—
409C4⋊C4—268no—
410C4⋊C4—261no—
411C4⋊C4—261no—
412C4⋊C4—264no—
413C4⋊C4—264no—
414C4⋊C4C22×#26112yes—
415C4⋊C4C22×#26112yes—
416C42—132no—
417C42—132no—
418C42—132no—
419C42—132no—
420C42—132no—
421C42—132no—
422C42—528no—
423C42C22⋊#26112yes—
424C42C22×#26112yes—
425C13C2×#198911yescharacteristic, complemented, Sylow
426C23—131no—
427C23—131no—
428C23—134no—
429C23—132no—
430C23—132no—
431C23—134no—
432C23C2×C22⋊#26111yescharacteristic
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—131no—
440C2×C4—131no—
441C2×C4—132no—
442C2×C4—132no—
443C2×C4—132no—
444C2×C4—132no—
445C2×C4—134no—
446C2×C4—134no—
447C2×C4—132no—
448C2×C4—132no—
449C2×C4—132no—
450C2×C4—132no—
451C2×C4—262no—
452C2×C4—264no—
453C2×C4—264no—
454C2×C4—262no—
455C2×C4—264no—
456C2×C4—262no—
457C2×C4—262no—
458C2×C4—268no—
459C2×C4—262no—
460C2×C4—262no—
461C2×C4—524no—
462C2×C4—524no—
463C2×C4—522no—
464C2×C4—522no—
465C2×C4—524no—
466C2×C4—524no—
467C2×C4—5216no—
468C2×C4—524no—
469C2×C4—522no—
470C2×C4—522no—
471C2×C4Q8×#26114yes—
472C2×C4C2×C22⋊#26112yes—
473C2×C4C2×C22⋊#26112yes—
474C2×C4C2×C22⋊#26111yescharacteristic
475C2×C4C23×#26111yescharacteristic
476C8—524no—
477C22—138no—
478C22—138no—
479C22—132no—
480C22—132no—
481C22—132no—
482C22—132no—
483C22—131no—
484C22—131no—
485C22—132no—
486C22(C2×#261)⋊Q812yes—
487C22#1171916412yes—
488C22#1171916512yes—
489C22C22×C22⋊#26111yescharacteristic
490C4—22no—
491C4—22no—
492C4—42no—
493C4—42no—
494C4—131no—
495C4—131no—
496C4—132no—
497C4—262no—
498C4—262no—
499C4—528no—
500C4—522no—
501C4—522no—
502C4(C2×#261)⋊Q812yes—
503C4C2×Q8×#26112yes—
504C2—132no—
505C2—132no—
506C2—134no—
507C2#1313101614yesdirect product factor
508C2C2×(C2×#261)⋊Q811yescharacteristic
509C2C2×#1171916511yescharacteristic
510C2C2×#1171916411yescharacteristic
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×#1989
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. #13131016C2direct (N × H)
10. C2×C13×#125C4semidirect
13. D13×#125C4semidirect
19. C2×#88144C4semidirect
20. C2×#88144C4semidirect
24. C2×#88124C4semidirect
51. C13×#125C2×C4semidirect
84. #88144C2×C4semidirect
85. #88144C2×C4semidirect
95. #88124C2×C4semidirect
238. C2×#125#261semidirect
303. #125C2×#261semidirect
347. C2×C13#1989semidirect
351. D13#1989semidirect
425. C13C2×#1989semidirect
507. C2#13131016direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D13⋊(C4⋊C8)2
C2×C4×C4⋊#2612
#131310162
C2×#117182462
C2×D13×#1252
C2×#198913