Finite Group Databasebeta

← C2×#13125369 #16732546

Subgroups — C2×#13125369 #16732546

Order 3328.

1854 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719434C212yesmaximal
2#13125369C2116yesmaximal, direct product factor
3C2×#11718537C212yesmaximal, complemented
4C2×#11718741C212yesmaximal, complemented
5C2×#11718535C211yesmaximal, characteristic, complemented
6C2×#11718344C211yesmaximal, characteristic, complemented
7C2×#11718539C211yesmaximal, characteristic, complemented
8C2×#11718542C212yesmaximal
9C2×#11718541C211yesmaximal, characteristic
10C2×D13×#107C211yesmaximal, characteristic
11C2×#11718350C211yesmaximal, characteristic
12C2×C13×#500C211yesmaximal, characteristic, complemented
13C2×C13×C4⋊Q8C2212yes—
14C2×#88200—22no—
15C2×#88198—22no—
16C22×#6094C2211yescharacteristic
17C22×C8×D13C2211yescharacteristic
18#11719434—28no—
19#11719434C22116yes—
20C2×#88150—22no—
21C2×#88146C2212yes—
22C2×C4⋊C4×D13C2212yes—
23C2×#88144C2212yes—
24C2×#88143—22no—
25C2×#88142C2212yes—
26C2×#88126C2211yescharacteristic
27C2×#88124C2212yes—
28C13×#500C2218yescomplemented
29C2×C13×#107C2211yescharacteristic
30C2×C13×#107C2211yescharacteristic
31C2×C13×#107C2212yes—
32C2×C4×C8×C13C2211yescharacteristic
33C2×#88058C2211yescharacteristic
34C2×#88058C2211yescharacteristic
35C2×#88057C2212yes—
36C2×#88055C2211yescharacteristic
37C2×C8×Dic13C2211yescharacteristic
38#11718741C22116yescomplemented
39C2×#88048C2212yes—
40C2×#88048C2212yes—
41C2×#88047C2212yes—
42C2×#88047C2212yes—
43C2×#88043C2211yescharacteristic
44#11718542C22116yes—
45#11718541C2218yes—
46D13×#107C2218yes—
47#11718539C2218yescomplemented
48#11718537C22116yescomplemented
49#11718535C2218yescomplemented
50#11718350C2218yes—
51#11718344C2218yescomplemented
52C22×Q8×C13—22no—
53C22×C4×D13—22no—
54C22×C4×D13C2311yescharacteristic
55C22×Dic26—22no—
56C22×C8×C13C2311yescharacteristic
57C22×C8×C13C2311yescharacteristic
58C13×C4⋊Q8—24no—
59C13×C4⋊Q8C2318yes—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4C2312yes—
62C2×C13×C4⋊C4C2312yes—
63C2×C42×C13C2311yescharacteristic
64#88200—216no—
65#88198—216no—
66C2×#6103—22no—
67C2×#6103D411yescharacteristic
68C2×#6103D411yescharacteristic
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13C2312yes—
71C2×C4⋊Dic13C2312yes—
72C2×#6101—22no—
73C2×#6101—22no—
74C2×#6101—22no—
75C2×#6101—22no—
76C2×#6101—22no—
77C2×#6101D411yescharacteristic
78C2×#6101D411yescharacteristic
79C2×C4×Dic13—22no—
80C2×C4×Dic13C2311yescharacteristic
81C22×#1055C2311yescharacteristic
82C22×#1055C2311yescharacteristic
83C2×#6094Q818yescomplemented
84C2×#6094C2314yes—
85C2×C8×D13Q818yescomplemented
86C2×C8×D13C2314yes—
87#88150—216no—
88#88146—24no—
89#88146C2318yes—
90C4⋊C4×D13—24no—
91C4⋊C4×D13C2318yes—
92#88144—24no—
93#88144C2318yes—
94#88143—216no—
95#88142—24no—
96#88142C2318yes—
97#88126D414yes—
98#88126C2314yes—
99#88124—24no—
100#88124C2318yes—
101C13×#107C2314yes—
102C13×#107C2318yes—
103C13×#107C2314yes—
104C4×C8×C13C2314yes—
105#88058C2314yes—
106#88058C2314yes—
107#88057C2318yes—
108#88055C2314yes—
109C8×Dic13C2314yes—
110#88048C2318yes—
111#88048C2318yes—
112#88047C2318yes—
113#88047C2318yes—
114#88043C2314yes—
115C2×#3164—131nomaximal, Sylow
116C23×D13C2×D411yescharacteristic
117C2×Q8×C13—28no—
118C2×Q8×C13—84no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2411yescharacteristic
124C22×Dic13—22no—
125C22×Dic13—22no—
126C22×Dic13C2×D411yescharacteristic
127C22×Dic13C2×D411yescharacteristic
128C22×Dic13C2×D411yescharacteristic
129C2×C4×D13—28no—
130C2×C4×D13—84no—
131C2×C4×D13C2×D412yes—
132C2×C4×D13C2×Q814yes—
133C2×C4×D13C2×Q814yes—
134C2×C4×D13C2412yes—
135C2×Dic26—28no—
136C2×Dic26—84no—
137C2×C8×C13C2×Q814yes—
138C2×C8×C13C2×Q814yes—
139C2×C8×C13C2412yes—
140C2×C8×C13C2412yes—
141C13×C4⋊C4—22no—
142C13×C4⋊C4—28no—
143C13×C4⋊C4—22no—
144C13×C4⋊C4C2414yes—
145C13×C4⋊C4C2414yes—
146C42×C13C2×D412yes—
147C42×C13C2412yes—
148#6103—28no—
149#6103C2×D414yes—
150#6103C2×D414yes—
151C4⋊Dic13—22no—
152C4⋊Dic13—22no—
153C4⋊Dic13—28no—
154C4⋊Dic13C2414yes—
155C4⋊Dic13C2414yes—
156#6101—28no—
157#6101—28no—
158#6101—28no—
159#6101—28no—
160#6101—28no—
161#6101C2×D414yes—
162#6101C2×D414yes—
163C4×Dic13—28no—
164C4×Dic13C2×D412yes—
165C4×Dic13C2412yes—
166C2×#1055C2×Q814yes—
167C2×#1055C2×Q814yes—
168C2×#1055C2412yes—
169C2×#1055C2412yes—
170#6094C2×Q8116yescomplemented
171C8×D13C2×Q8116yescomplemented
172C2×#544—132no—
173#3164—1316no—
174C2×#501—132no—
175C2×#501—132no—
176C2×#500—131no—
177C2×#500D1311yescharacteristic, complemented
178C2×#499—131no—
179C2×#499—131no—
180C2×#428—132no—
181C2×#427—131no—
182C22×#107—131no—
183C2×#405—131no—
184C23×C13C22×D411yescharacteristic
185C22×D13—22no—
186C22×D13—22no—
187C22×D13C4⋊Q814yes—
188C22×D13C22×D412yes—
189Q8×C13—88no—
190C2×C4×C13—22no—
191C2×C4×C13—22no—
192C2×C4×C13—24no—
193C2×C4×C13—24no—
194C2×C4×C13—44no—
195C2×C4×C13—44no—
196C2×C4×C13C22×D412yes—
197C2×C4×C13C22×D412yes—
198C2×C4×C13C22×D411yescharacteristic
199C2×C4×C13C22×Q812yes—
200C2×C4×C13C22×Q812yes—
201C2×C4×C13C2511yescharacteristic
202C2×Dic13—22no—
203C2×Dic13—22no—
204C2×Dic13—24no—
205C2×Dic13—24no—
206C2×Dic13—44no—
207C2×Dic13—44no—
208C2×Dic13C4⋊Q814yes—
209C2×Dic13C22×D412yes—
210C2×Dic13C22×D412yes—
211C2×Dic13C22×D412yes—
212C4×D13—88no—
213C4×D13C4⋊Q818yes—
214C4×D13C22×Q814yes—
215C4×D13C22×Q814yes—
216Dic26—88no—
217C8×C13C22×Q814yes—
218C8×C13C22×Q814yes—
219#1055C22×Q814yes—
220#1055C22×Q814yes—
221C22×M16—131no—
222C23×C8—131no—
223#544—1316no—
224#544—268no—
225C2×C4⋊Q8—132no—
226C2×C4⋊Q8—262no—
227C2×C4⋊Q8C2×D1312yes—
228C2×#125—132no—
229C2×#125—132no—
230C2×#125—262no—
231C2×C22⋊Q8—262no—
232C2×C22⋊Q8—262no—
233C2×#117—131no—
234C2×#117—132no—
235C22×C4⋊C4—132no—
236#501—1316no—
237#501—1316no—
238#500—138no—
239#500C2×D1318yescomplemented
240#499—138no—
241#499—138no—
242#428—1316no—
243#427—138no—
244C2×#107—131no—
245C2×#107—131no—
246C2×#107—132no—
247C2×#107—132no—
248C2×#107—138no—
249C2×#107C2×D1311yescharacteristic
250C2×#107C2×D1311yescharacteristic
251C2×#107C2×D1312yes—
252C2×#106—132no—
253C2×#106—132no—
254C2×#106—132no—
255#405—138no—
256C2×#97—131no—
257C2×#97—131no—
258C2×C4×C8—131no—
259C2×C4×C8C2×D1311yescharacteristic
260C22×C13C2×C4⋊Q812yes—
261C22×C13#57612yes—
262C22×C13#57812yes—
263C22×C13C23×D411yescharacteristic
264C2×D13—28no—
265C2×D13—22no—
266C2×D13—22no—
267C2×D13C2×C4⋊Q814yes—
268C4×C13—22no—
269C4×C13—22no—
270C4×C13—44no—
271C4×C13—44no—
272C4×C13C2×C4⋊Q812yes—
273C4×C13C23×Q811yescharacteristic
274C4×C13C23×Q811yescharacteristic
275Dic13—22no—
276Dic13—22no—
277Dic13—44no—
278Dic13—44no—
279Dic13C2×C4⋊Q814yes—
280C22×Q8—22no—
281C22×Q8—262no—
282C23×C4—131no—
283C23×C4—262no—
284C2×M16—138no—
285C2×M16—134no—
286C22×C8—131no—
287C22×C8—131no—
288C22×C8—138no—
289C22×C8—134no—
290C22×C8C22×D1311yescharacteristic
291C22×C8C22×D1311yescharacteristic
292C4⋊Q8—24no—
293C4⋊Q8—138no—
294C4⋊Q8—264no—
295C4⋊Q8—2616no—
296C4⋊Q8C22×D1318yes—
297#125—138no—
298#125—138no—
299#125—264no—
300#125—2616no—
301#125—264no—
302C22⋊Q8—2616no—
303C22⋊Q8—2616no—
304#117—134no—
305#117—134no—
306#117—138no—
307#117—264no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—131no—
310C2×C4⋊C4—131no—
311C2×C4⋊C4—132no—
312C2×C4⋊C4—132no—
313C2×C4⋊C4—138no—
314C2×C4⋊C4—264no—
315C2×C4⋊C4—262no—
316C2×C4⋊C4—262no—
317C2×C4⋊C4—262no—
318C2×C4⋊C4—262no—
319C2×C4⋊C4—262no—
320C2×C4⋊C4—262no—
321C2×C4⋊C4C22×D1312yes—
322C2×C4⋊C4C22×D1312yes—
323C2×C22⋊C4—131no—
324C2×C22⋊C4—131no—
325C2×C22⋊C4—262no—
326C2×C42—131no—
327C2×C42—262no—
328C2×C42C22×D1311yescharacteristic
329#107—134no—
330#107—134no—
331#107—138no—
332#107—138no—
333#107C22×D1314yes—
334#107C22×D1314yes—
335#107C22×D1318yes—
336#106—138no—
337#106—138no—
338#106—138no—
339#97—134no—
340#97—134no—
341C4×C8—134no—
342C4×C8C22×D1314yes—
343C2×C13#316414yescomplemented
344C2×C13C22×C4⋊Q811yescharacteristic
345C2×C13C2×#57611yescharacteristic
346C2×C13C2×#57811yescharacteristic
347D13—24no—
348C24—131no—
349C2×Q8—28no—
350C2×Q8—84no—
351C2×Q8—268no—
352C2×Q8—1044no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—131no—
356C22×C4—132no—
357C22×C4—134no—
358C22×C4—134no—
359C22×C4—132no—
360C22×C4—131no—
361C22×C4—131no—
362C22×C4—268no—
363C22×C4—262no—
364C22×C4—262no—
365C22×C4—1044no—
366C22×C4D4×D1311yescharacteristic
367C22×C4D4×D1311yescharacteristic
368C22×C4C23×D1311yescharacteristic
369M16—1316no—
370C2×C8—134no—
371C2×C8—134no—
372C2×C8—132no—
373C2×C8—132no—
374C2×C8—1316no—
375C2×C8Q8×D1314yes—
376C2×C8Q8×D1314yes—
377C2×C8C23×D1312yes—
378C2×C8C23×D1312yes—
379C4⋊C4—28no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—134no—
383C4⋊C4—134no—
384C4⋊C4—134no—
385C4⋊C4—134no—
386C4⋊C4—268no—
387C4⋊C4—268no—
388C4⋊C4—268no—
389C4⋊C4—268no—
390C4⋊C4—262no—
391C4⋊C4—262no—
392C4⋊C4—268no—
393C4⋊C4—268no—
394C4⋊C4C23×D1314yes—
395C4⋊C4C23×D1314yes—
396C22⋊C4—134no—
397C22⋊C4—134no—
398C22⋊C4—268no—
399C42—132no—
400C42—132no—
401C42—268no—
402C42D4×D1312yes—
403C42C23×D1312yes—
404C13C2×#316411yescharacteristic, complemented, Sylow
405C23—134no—
406C23—132no—
407C23—262no—
408C23—262no—
409C23C2×D4×D1311yescharacteristic
410Q8—88no—
411Q8—1048no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—134no—
419C2×C4—132no—
420C2×C4—138no—
421C2×C4—134no—
422C2×C4—134no—
423C2×C4—132no—
424C2×C4—132no—
425C2×C4—262no—
426C2×C4—262no—
427C2×C4—264no—
428C2×C4—264no—
429C2×C4—524no—
430C2×C4—524no—
431C2×C4—1048no—
432C2×C4C2×D4×D1312yes—
433C2×C4C2×D4×D1312yes—
434C2×C4C2×D4×D1311yescharacteristic
435C2×C4C2×Q8×D1312yes—
436C2×C4C2×Q8×D1312yes—
437C2×C4C24×D1311yescharacteristic
438C8—134no—
439C8—134no—
440C8C2×Q8×D1314yes—
441C8C2×Q8×D1314yes—
442C22—134no—
443C22—262no—
444C22—262no—
445C22—268no—
446C22D13×C4⋊Q812yes—
447C22#1171946212yes—
448C22#1171947112yes—
449C22C22×D4×D1311yescharacteristic
450C4—22no—
451C4—22no—
452C4—44no—
453C4—44no—
454C4—134no—
455C4—262no—
456C4—262no—
457C4—524no—
458C4—524no—
459C4D13×C4⋊Q812yes—
460C4C22×Q8×D1311yescharacteristic
461C4C22×Q8×D1311yescharacteristic
462C2—264no—
463C2#1312536914yesdirect product factor
464C2C2×D13×C4⋊Q811yescharacteristic
465C2C2×#1171946211yescharacteristic
466C2C2×#1171947111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#500C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenterC2×#500D13
hypocenterC13C2×#3164
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
2. #13125369C2direct (N × H)
3. C2×#11718537C2semidirect
4. C2×#11718741C2semidirect
5. C2×#11718535C2semidirect
6. C2×#11718344C2semidirect
7. C2×#11718539C2semidirect
12. C2×C13×#500C2semidirect
28. C13×#500C22semidirect
38. #11718741C22semidirect
47. #11718539C22semidirect
48. #11718537C22semidirect
49. #11718535C22semidirect
51. #11718344C22semidirect
83. C2×#6094Q8semidirect
85. C2×C8×D13Q8semidirect
170. #6094C2×Q8semidirect
171. C8×D13C2×Q8semidirect
177. C2×#500D13semidirect
239. #500C2×D13semidirect
343. C2×C13#3164semidirect
404. C13C2×#3164semidirect
463. C2#13125369direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117194342
#131253692
C2×#117185372
C2×#117187412
C2×#117185352
C2×#117183442
C2×#117185392
C2×#117185422
C2×#117185412
C2×D13×#1072
C2×#117183502
C2×C13×#5002
C2×#316413