Finite Group Databasebeta

← D13×#2659 #16029462

Subgroups — D13×#2659 #16029462

Order 3328.

2982 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C22⋊Q8C212yesmaximal
2#13120953C214yesmaximal, complemented
3#13120952C212yesmaximal, complemented
4#13120951C214yesmaximal, complemented
5#13120950C211yesmaximal, characteristic, complemented
6#13120949C214yesmaximal, complemented
7D13×#398C214yesmaximal, complemented
8D13×#395C214yesmaximal, complemented
9D13×#380C214yesmaximal
10C2×D13×#95C211yesmaximal, characteristic
11C13×#2659C211yesmaximal, characteristic, complemented
12C22×Q8×D13C2212yes—
13C23×C4×D13C2211yescharacteristic
14C23×C4×D13C2212yes—
15C2×C13×C22⋊Q8C2212yes—
16C2×#88200C2212yes—
17C2×#88178C2212yes—
18D13×C22⋊Q8—216no—
19C2×#88151C2212yes—
20C2×#88150C2214yes—
21C2×C4⋊C4×D13C2214yes—
22C2×C4⋊C4×D13C2212yes—
23C2×C4⋊C4×D13C2214yes—
24C2×C4⋊C4×D13C2214yes—
25C2×C22⋊C4×D13C2214yes—
26C2×#88132C2214yes—
27C13×#398C2214yescomplemented
28C13×#395C2214yescomplemented
29C13×#380C2214yes—
30C2×C13×#95C2211yescharacteristic
31#11718890C2214yescomplemented
32#11718873C2214yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2212yes—
35#11718648C2214yes—
36#11718648C2214yes—
37#11718645C2218yescomplemented
38#11718644C2214yescomplemented
39#11718641C2214yescomplemented
40#11718640C2218yescomplemented
41#11718640C2214yescomplemented
42#11718603C2218yes—
43#11718328C2218yes—
44D13×#95C2218yes—
45D13×#95C2214yes—
46D13×#95C2214yes—
47#11718322C2214yescomplemented
48#11718318C2218yescomplemented
49#11718317C2214yescomplemented
50#11718317C2218yescomplemented
51C24×D13C2311yescharacteristic
52C22×Q8×C13C2312yes—
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2312yes—
55C23×Dic13C2311yescharacteristic
56C23×Dic13C2312yes—
57C2×Q8×D13—28no—
58C2×Q8×D13—48no—
59C22×C4×D13—44no—
60C22×C4×D13—44no—
61C22×C4×D13—44no—
62C22×C4×D13D418yes—
63C22×C4×D13Q8116yescomplemented
64C22×C4×D13C2314yes—
65C22×C4×D13C2314yes—
66C22×C4×D13C2312yes—
67C22×C4×D13C2314yes—
68C22×C4×D13C2312yes—
69C22×C4×D13C2314yes—
70C22×Dic26C2314yes—
71C22×Dic26C2312yes—
72C13×C22⋊Q8—28no—
73C2×C13×C4⋊C4C2314yes—
74C2×C13×C4⋊C4C2312yes—
75C2×C13×C4⋊C4C2314yes—
76C2×C13×C4⋊C4C2314yes—
77C2×C13×C22⋊C4C2314yes—
78C2×C22⋊Dic13C2314yes—
79#88200—28no—
80C2×#6103C2314yes—
81C2×#6103C2314yes—
82C2×C4⋊Dic13C2314yes—
83C2×C4⋊Dic13C2312yes—
84C2×C4⋊Dic13C2314yes—
85C2×C4⋊Dic13C2314yes—
86#88178—28no—
87C2×#6101C2314yes—
88C2×#6101C2314yes—
89C2×#6101C2314yes—
90C2×#6101C2318yes—
91C2×#6101C2318yes—
92#88151—28no—
93#88150—216no—
94C4⋊C4×D13—216no—
95C4⋊C4×D13—28no—
96C4⋊C4×D13—48no—
97C4⋊C4×D13—48no—
98C22⋊C4×D13—216no—
99#88132—216no—
100C13×#95C2318yes—
101C13×#95C2314yes—
102#88071C2318yes—
103#88071C2318yes—
104#88071C2318yes—
105#88071C2318yes—
106#88071C2314yes—
107C2×#2659—131nomaximal, Sylow
108C24×C13C2411yescharacteristic
109C23×D13—24no—
110C23×D13—22no—
111C23×D13—22no—
112C23×D13C2×D414yes—
113C23×D13C2×Q818yes—
114C23×D13C2411yescharacteristic
115C23×D13C2411yescharacteristic
116C2×Q8×C13—24no—
117C2×Q8×C13—44no—
118C22×C4×C13—42no—
119C22×C4×C13—42no—
120C22×C4×C13—42no—
121C22×C4×C13C2×D414yes—
122C22×C4×C13C2×Q818yescomplemented
123C22×C4×C13C2414yes—
124C22×C4×C13C2414yes—
125C22×C4×C13C2412yes—
126C22×C4×C13C2414yes—
127C22×Dic13—42no—
128C22×Dic13—42no—
129C22×Dic13—42no—
130C22×Dic13C2×D414yes—
131C22×Dic13C2×Q818yescomplemented
132C22×Dic13C2414yes—
133C22×Dic13C2414yes—
134C22×Dic13C2412yes—
135C22×Dic13C2414yes—
136Q8×D13—432no—
137C2×C4×D13—28no—
138C2×C4×D13—28no—
139C2×C4×D13—28no—
140C2×C4×D13—28no—
141C2×C4×D13—28no—
142C2×C4×D13—28no—
143C2×C4×D13—216no—
144C2×C4×D13—28no—
145C2×C4×D13—416no—
146C2×C4×D13—432no—
147C2×C4×D13—44no—
148C2×C4×D13—44no—
149C2×C4×D13—44no—
150C2×C4×D13C2×D418yes—
151C2×C4×D13C2×D418yes—
152C2×C4×D13C2×Q8116yes—
153C2×C4×D13C2×Q8116yescomplemented
154C2×Dic26—24no—
155C2×Dic26—28no—
156C2×Dic26—48no—
157C2×Dic26—44no—
158C13×C4⋊C4—28no—
159C13×C4⋊C4—24no—
160C13×C4⋊C4—44no—
161C13×C4⋊C4—44no—
162C13×C22⋊C4—28no—
163C22⋊Dic13—28no—
164#6103—28no—
165#6103—28no—
166C4⋊Dic13—24no—
167C4⋊Dic13—28no—
168C4⋊Dic13—44no—
169C4⋊Dic13—44no—
170#6101—28no—
171#6101—28no—
172#6101—28no—
173#6101—48no—
174#6101—48no—
175C22×C22⋊Q8—132no—
176#2659—134no—
177#2659—134no—
178#2659—134no—
179#2659—131no—
180#2659—132no—
181#2659D1311yescharacteristic, direct product factor
182C2×#398—134no—
183C2×#395—134no—
184C2×#380—134no—
185C22×#95—131no—
186C23×C13—22no—
187C23×C13—21no—
188C23×C13—21no—
189C23×C13C22×D412yes—
190C23×C13C22×Q814yes—
191C23×C13C2511yescharacteristic
192C22×D13—22no—
193C22×D13—21no—
194C22×D13—21no—
195C22×D13—28no—
196C22×D13—28no—
197C22×D13—216no—
198C22×D13—216no—
199C22×D13C4⋊Q8116yes—
200C22×D13C22×D412yes—
201C22×D13C22×D412yes—
202C22×D13C22×Q814yes—
203C22×D13C22×Q814yes—
204C22×D13H(5,𝔽2)14yes—
205C22×D13H(5,𝔽2)12yes—
206C22×D132−1+412yes—
207Q8×C13—48no—
208C2×C4×C13—24no—
209C2×C4×C13—24no—
210C2×C4×C13—24no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—28no—
215C2×C4×C13—24no—
216C2×C4×C13—44no—
217C2×C4×C13—48no—
218C2×C4×C13C22×D414yes—
219C2×C4×C13C22×Q818yes—
220C2×Dic13—24no—
221C2×Dic13—24no—
222C2×Dic13—24no—
223C2×Dic13—24no—
224C2×Dic13—24no—
225C2×Dic13—24no—
226C2×Dic13—28no—
227C2×Dic13—24no—
228C2×Dic13—44no—
229C2×Dic13—48no—
230C2×Dic13C22×D414yes—
231C2×Dic13C22×Q818yes—
232C4×D13—216no—
233C4×D13—232no—
234C4×D13—48no—
235C4×D13—416no—
236C4×D13—416no—
237C4×D13—416no—
238Dic26—416no—
239Dic26—48no—
240C23×Q8—132no—
241C24×C4—131no—
242C24×C4—132no—
243C2×C22⋊Q8—132no—
244C2×C22⋊Q8—132no—
245C2×C22⋊Q8—134no—
246C2×C22⋊Q8—132no—
247C2×C22⋊Q8—134no—
248C2×C22⋊Q8—2616no—
249C2×C22⋊Q8C2×D1312yes—
250C22×C4⋊C4—134no—
251C22×C4⋊C4—132no—
252C22×C4⋊C4—134no—
253C22×C4⋊C4—134no—
254C22×C22⋊C4—134no—
255#398—134no—
256#398—134no—
257#398—138no—
258#398—138no—
259#398—134no—
260#398C2×D1314yescomplemented
261#395—134no—
262#395—138no—
263#395—134no—
264#395—138no—
265#395—134no—
266#395C2×D1314yescomplemented
267#380—134no—
268#380—134no—
269#380—134no—
270#380—138no—
271#380—138no—
272#380C2×D1314yes—
273C2×#95—132no—
274C2×#95—131no—
275C2×#95—134no—
276C2×#95—138no—
277C2×#95—134no—
278C2×#95C2×D1311yescharacteristic
279C22×C13—22no—
280C22×C13—22no—
281C22×C13—24no—
282C22×C13—24no—
283C22×C13C2×C4⋊Q814yes—
284C22×C13C23×D411yescharacteristic
285C22×C13C23×Q812yes—
286C22×C13C2×H(5,𝔽2)12yes—
287C22×C13C2×H(5,𝔽2)11yescharacteristic
288C22×C13C2×2−1+411yescharacteristic
289C2×D13—22no—
290C2×D13—22no—
291C2×D13—24no—
292C2×D13—24no—
293C2×D13—232no—
294C2×D13C2×C4⋊Q814yes—
295C2×D13C2×C4⋊Q814yes—
296C2×D13#53414yes—
297C2×D13#53714yes—
298C2×D13#54318yes—
299C2×D13#54418yes—
300C4×C13—24no—
301C4×C13—28no—
302C4×C13—44no—
303C4×C13—44no—
304Dic13—24no—
305Dic13—28no—
306Dic13—44no—
307Dic13—44no—
308C25—131no—
309C22×Q8—134no—
310C22×Q8—132no—
311C22×Q8—268no—
312C22×Q8—528no—
313C22×Q8C22×D1312yes—
314C23×C4—131no—
315C23×C4—132no—
316C23×C4—132no—
317C23×C4—134no—
318C23×C4—138no—
319C23×C4—1316no—
320C23×C4—132no—
321C23×C4—134no—
322C23×C4—134no—
323C23×C4—134no—
324C23×C4—524no—
325C23×C4—524no—
326C23×C4—524no—
327C23×C4C22×D1311yescharacteristic
328C23×C4C22×D1312yes—
329C22⋊Q8—28no—
330C22⋊Q8—2616no—
331C22⋊Q8—2616no—
332C22⋊Q8—268no—
333C22⋊Q8—268no—
334C22⋊Q8—268no—
335C2×C4⋊C4—134no—
336C2×C4⋊C4—134no—
337C2×C4⋊C4—134no—
338C2×C4⋊C4—134no—
339C2×C4⋊C4—132no—
340C2×C4⋊C4—138no—
341C2×C4⋊C4—138no—
342C2×C4⋊C4—134no—
343C2×C4⋊C4—134no—
344C2×C4⋊C4—268no—
345C2×C4⋊C4—2616no—
346C2×C4⋊C4—528no—
347C2×C4⋊C4—528no—
348C2×C4⋊C4C22×D1314yes—
349C2×C4⋊C4C22×D1312yes—
350C2×C4⋊C4C22×D1314yes—
351C2×C4⋊C4C22×D1314yes—
352C2×C22⋊C4—134no—
353C2×C22⋊C4—134no—
354C2×C22⋊C4—134no—
355C2×C22⋊C4—2616no—
356C2×C22⋊C4C22×D1314yes—
357#95—134no—
358#95—138no—
359#95—138no—
360#95—138no—
361#95—138no—
362#95C22×D1314yes—
363#95C22×D1318yes—
364C2×C13—24no—
365C2×C13C22×C4⋊Q811yescharacteristic
366C2×C13C2×#53411yescharacteristic
367C2×C13C2×#53711yescharacteristic
368C2×C13C2×#54312yes—
369C2×C13C2×#54412yes—
370D13—24no—
371D13#265918yesdirect product factor
372C24—131no—
373C24—134no—
374C24—138no—
375C24—131no—
376C24—262no—
377C24—264no—
378C24—262no—
379C24C23×D1311yescharacteristic
380C2×Q8—24no—
381C2×Q8—44no—
382C2×Q8—268no—
383C2×Q8—264no—
384C2×Q8—524no—
385C2×Q8—528no—
386C2×Q8—5232no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—134no—
391C22×C4—132no—
392C22×C4—134no—
393C22×C4—138no—
394C22×C4—138no—
395C22×C4—1316no—
396C22×C4—138no—
397C22×C4—1316no—
398C22×C4—134no—
399C22×C4—134no—
400C22×C4—268no—
401C22×C4—268no—
402C22×C4—268no—
403C22×C4—268no—
404C22×C4—268no—
405C22×C4—268no—
406C22×C4—2616no—
407C22×C4—268no—
408C22×C4—524no—
409C22×C4—524no—
410C22×C4—524no—
411C22×C4—5216no—
412C22×C4—5232no—
413C22×C4—522no—
414C22×C4—522no—
415C22×C4—522no—
416C22×C4D4×D1314yes—
417C22×C4Q8×D1318yescomplemented
418C22×C4C23×D1314yes—
419C22×C4C23×D1314yes—
420C22×C4C23×D1312yes—
421C22×C4C23×D1314yes—
422C4⋊C4—24no—
423C4⋊C4—28no—
424C4⋊C4—44no—
425C4⋊C4—44no—
426C4⋊C4—268no—
427C4⋊C4—268no—
428C4⋊C4—268no—
429C4⋊C4—268no—
430C4⋊C4—264no—
431C4⋊C4—528no—
432C4⋊C4—528no—
433C4⋊C4—524no—
434C4⋊C4—524no—
435C22⋊C4—28no—
436C22⋊C4—268no—
437C22⋊C4—268no—
438C22⋊C4—268no—
439C13C2×#265911yescharacteristic, complemented, Sylow
440C23—21no—
441C23—22no—
442C23—21no—
443C23—132no—
444C23—134no—
445C23—132no—
446C23—134no—
447C23—132no—
448C23—1316no—
449C23—132no—
450C23—134no—
451C23—2616no—
452C23—268no—
453C23—2616no—
454C23—268no—
455C23—261no—
456C23—262no—
457C23—261no—
458C23C2×D4×D1312yes—
459C23C2×Q8×D1314yes—
460C23C24×D1311yescharacteristic
461Q8—48no—
462Q8—528no—
463Q8—5216no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—28no—
471C2×C4—24no—
472C2×C4—44no—
473C2×C4—48no—
474C2×C4—134no—
475C2×C4—138no—
476C2×C4—2632no—
477C2×C4—2616no—
478C2×C4—264no—
479C2×C4—264no—
480C2×C4—264no—
481C2×C4—264no—
482C2×C4—264no—
483C2×C4—264no—
484C2×C4—268no—
485C2×C4—264no—
486C2×C4—5216no—
487C2×C4—528no—
488C2×C4—5216no—
489C2×C4—5216no—
490C2×C4—528no—
491C2×C4—524no—
492C2×C4C2×D4×D1314yes—
493C2×C4C2×Q8×D1318yes—
494C22—24no—
495C22—24no—
496C22—22no—
497C22—22no—
498C22—138no—
499C22—138no—
500C22—134no—
501C22—134no—
502C22—134no—
503C22—134no—
504C22—2632no—
505C22—264no—
506C22—264no—
507C22—262no—
508C22—262no—
509C22D13×C4⋊Q814yes—
510C22C22×D4×D1311yescharacteristic
511C22C22×Q8×D1312yes—
512C22D13×H(5,𝔽2)11yescharacteristic
513C22D13×H(5,𝔽2)12yes—
514C22D13×2−1+411yescharacteristic
515C4—28no—
516C4—24no—
517C4—44no—
518C4—44no—
519C4—268no—
520C4—264no—
521C4—524no—
522C4—524no—
523C2—24no—
524C2—138no—
525C2—264no—
526C2C2×D13×C4⋊Q811yescharacteristic
527C2D13×#53411yescharacteristic
528C2D13×#53711yescharacteristic
529C2D13×#54312yes—
530C2D13×#54412yes—
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC13×#2659C2
prime radicalC24×D13C23
hypercenter#2659D13
hypocenterC13C2×#2659
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2659

Complements

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

NH ≅ G/Ntype
2. #13120953C2semidirect
3. #13120952C2semidirect
4. #13120951C2semidirect
5. #13120950C2semidirect
6. #13120949C2semidirect
7. D13×#398C2semidirect
8. D13×#395C2semidirect
11. C13×#2659C2semidirect
27. C13×#398C22semidirect
28. C13×#395C22semidirect
31. #11718890C22semidirect
37. #11718645C22semidirect
38. #11718644C22semidirect
39. #11718641C22semidirect
40. #11718640C22semidirect
41. #11718640C22semidirect
47. #11718322C22semidirect
48. #11718318C22semidirect
49. #11718317C22semidirect
50. #11718317C22semidirect
63. C22×C4×D13Q8semidirect
122. C22×C4×C13C2×Q8semidirect
131. C22×Dic13C2×Q8semidirect
153. C2×C4×D13C2×Q8semidirect
181. #2659D13direct (N × H)
260. #398C2×D13semidirect
266. #395C2×D13semidirect
371. D13#2659direct (N × H)
417. C22×C4Q8×D13semidirect
439. C13C2×#2659semidirect

Maximal subgroups

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

subgroupindex
C2×D13×C22⋊Q82
#131209532
#131209522
#131209512
#131209502
#131209492
D13×#3982
D13×#3952
D13×#3802
C2×D13×#952
C13×#26592
C2×#265913