Finite Group Databasebeta

← D13×#2099 #15892811

Subgroups — D13×#2099 #15892811

Order 3328.

998 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13×#389C211yesmaximal, characteristic
2D13×#384C211yesmaximal, characteristic
3#13116397C212yesmaximal, complemented
4#13116396C212yesmaximal, complemented
5#13116395C211yesmaximal, characteristic, complemented
6#13116394C211yesmaximal, characteristic, complemented
7#13116393C211yesmaximal, characteristic, complemented
8D13×#340C212yesmaximal
9D13×#340C212yesmaximal
10D13×#336C211yesmaximal, characteristic
11C13×#2099C211yesmaximal, characteristic, complemented
12C22×C8×D13C2212yes—
13C2×C4⋊C4×D13—21no—
14C2×C4⋊C4×D13—21no—
15C2×C4⋊C4×D13—21no—
16C2×C4⋊C4×D13C2212yes—
17C2×C4⋊C4×D13C2211yescharacteristic
18C2×C4⋊C4×D13C2211yescharacteristic
19C2×C42×D13C2211yescharacteristic
20C13×#389C2211yescharacteristic
21C13×#384C2211yescharacteristic
22#11718646C2211yescharacteristic
23#11718637—21no—
24#11718637—21no—
25#11718637C2212yes—
26#11718634C2211yescharacteristic
27#11718633—21no—
28#11718596C2211yescharacteristic
29#11718589C2211yescharacteristic
30D13×#95—21no—
31#11718308—21no—
32C13×#340C2212yes—
33C13×#340C2212yes—
34C13×#336C2211yescharacteristic
35#11718143C2212yes—
36#11718143C2212yes—
37#11718142C2212yes—
38#11718121C2212yes—
39#11718121C2212yes—
40#11718121C2212yes—
41#11718121C2212yes—
42#11718116C2211yescharacteristic
43C22×C4×D13—21no—
44C22×C4×D13—22no—
45C22×C4×D13—21no—
46C22×C4×D13D411yescharacteristic
47C22×C4×D13D411yescharacteristic
48C22×C4×D13C2311yescharacteristic
49C22×C8×C13C2312yes—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4C2312yes—
54C2×C13×C4⋊C4C2311yescharacteristic
55C2×C13×C4⋊C4C2311yescharacteristic
56C2×C42×C13C2311yescharacteristic
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13C2311yescharacteristic
61C2×C4⋊Dic13C2312yes—
62C2×C4⋊Dic13C2311yescharacteristic
63C2×#6101—21no—
64C2×#6101—21no—
65C2×#6101—21no—
66C2×#6101—22no—
67C2×#6101—22no—
68C2×#6101—21no—
69C2×#6101—22no—
70C2×C4×Dic13D411yescharacteristic
71C2×C4×Dic13D411yescharacteristic
72C2×C4×Dic13C2311yescharacteristic
73C22×#1055C2312yes—
74C2×C8×D13—24no—
75C2×C8×D13—24no—
76C2×C8×D13—24no—
77C4⋊C4×D13—22no—
78C4⋊C4×D13—24no—
79C4⋊C4×D13—28no—
80C4⋊C4×D13—44no—
81C4⋊C4×D13—44no—
82C4⋊C4×D13—44no—
83C4⋊C4×D13Q814yes—
84C42×D13—24no—
85C13×#95—21no—
86#88071—21no—
87#88071—21no—
88#88071—21no—
89C2×#2099—131nomaximal, Sylow
90C23×D13C2×D411yescharacteristic
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—22no—
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2411yescharacteristic
97C22×Dic13—21no—
98C22×Dic13—21no—
99C22×Dic13—22no—
100C22×Dic13C2×D411yescharacteristic
101C22×Dic13C2×D411yescharacteristic
102C22×Dic13C2×D411yescharacteristic
103C2×C4×D13—22no—
104C2×C4×D13—22no—
105C2×C4×D13—22no—
106C2×C4×D13—22no—
107C2×C4×D13—24no—
108C2×C4×D13—42no—
109C2×C4×D13—42no—
110C2×C4×D13—42no—
111C2×C4×D13—44no—
112C2×C4×D13—42no—
113C2×C4×D13—44no—
114C2×C4×D13—44no—
115C2×C4×D13—42no—
116C2×C4×D13D814yes—
117C2×C4×D13SD1614yes—
118C2×C4×D13C2×Q812yes—
119C2×C4×D13#4114yes—
120C2×C4×D13#4114yes—
121C2×C4×D13#4112yes—
122C2×C8×C13—22no—
123C2×C8×C13—22no—
124C2×C8×C13—22no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4—22no—
127C13×C4⋊C4—24no—
128C13×C4⋊C4—42no—
129C13×C4⋊C4—42no—
130C13×C4⋊C4—42no—
131C13×C4⋊C4C2×Q812yes—
132C42×C13—22no—
133C4⋊Dic13—21no—
134C4⋊Dic13—22no—
135C4⋊Dic13—24no—
136C4⋊Dic13—42no—
137C4⋊Dic13—42no—
138C4⋊Dic13—42no—
139C4⋊Dic13C2×Q812yes—
140#6101—24no—
141#6101—42no—
142#6101—42no—
143#6101—44no—
144#6101—42no—
145#6101—44no—
146#6101—44no—
147C4×Dic13—22no—
148C4×Dic13—22no—
149C4×Dic13—22no—
150C2×#1055—22no—
151C2×#1055—22no—
152C2×#1055—22no—
153C8×D13—48no—
154C2×#389—131no—
155C2×#384—131no—
156#2099—131no—
157#2099—131no—
158#2099—132no—
159#2099—132no—
160#2099—131no—
161#2099D1311yescharacteristic, direct product factor
162C2×#340—132no—
163C2×#340—132no—
164C2×#336—131no—
165C23×C13C22×D411yescharacteristic
166C22×D13C22⋊Q812yes—
167C22×D13#12312yes—
168C22×D13#12412yes—
169C22×D13C2×D812yes—
170C22×D13C2×SD1612yes—
171C22×D13#13712yes—
172C22×D13#13712yes—
173C2×C4×C13—21no—
174C2×C4×C13—21no—
175C2×C4×C13—21no—
176C2×C4×C13—21no—
177C2×C4×C13—22no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—42no—
182C2×C4×C13—41no—
183C2×C4×C13—42no—
184C2×C4×C13—42no—
185C2×C4×C13—41no—
186C2×C4×C13C2×D812yes—
187C2×C4×C13C2×SD1612yes—
188C2×C4×C13C22×Q811yescharacteristic
189C2×C4×C13C2×#4112yes—
190C2×C4×C13C2×#4112yes—
191C2×C4×C13C2×#4111yescharacteristic
192C2×Dic13—21no—
193C2×Dic13—21no—
194C2×Dic13—21no—
195C2×Dic13—21no—
196C2×Dic13—22no—
197C2×Dic13—41no—
198C2×Dic13—41no—
199C2×Dic13—41no—
200C2×Dic13—42no—
201C2×Dic13—41no—
202C2×Dic13—42no—
203C2×Dic13—42no—
204C2×Dic13—41no—
205C2×Dic13C22⋊Q812yes—
206C2×Dic13#12312yes—
207C2×Dic13#12412yes—
208C2×Dic13C2×D812yes—
209C2×Dic13C2×SD1612yes—
210C4×D13—28no—
211C4×D13—28no—
212C4×D13—48no—
213C4×D13—84no—
214C4×D13—88no—
215C4×D13#12518yes—
216C4×D13#12618yes—
217C8×C13—42no—
218#1055—42no—
219C23×C8—132no—
220C22×C4⋊C4—131no—
221C22×C4⋊C4—132no—
222C22×C4⋊C4—131no—
223C22×C4⋊C4—261no—
224C22×C4⋊C4—261no—
225C22×C4⋊C4—261no—
226C22×C42—131no—
227#389—131no—
228#389—131no—
229#389—131no—
230#389—261no—
231#389—261no—
232#389C2×D1311yescharacteristic
233#384—132no—
234#384—131no—
235#384—261no—
236#384—261no—
237#384C2×D1311yescharacteristic
238C2×#95—261no—
239#340—132no—
240#340—132no—
241#340—132no—
242#340—132no—
243#340—132no—
244#340—132no—
245#340C2×D1312yes—
246#340C2×D1312yes—
247#336—132no—
248#336—131no—
249#336C2×D1311yescharacteristic
250C22×C13C2×C22⋊Q811yescharacteristic
251C22×C13C2×#12311yescharacteristic
252C22×C13C2×#12411yescharacteristic
253C22×C13C22×D811yescharacteristic
254C22×C13C22×SD1611yescharacteristic
255C22×C13C2×#13711yescharacteristic
256C22×C13C2×#13711yescharacteristic
257C2×D13#40014yes—
258C2×D13#47414yes—
259C2×D13#47514yes—
260C2×D13#48014yes—
261C2×D13#48314yes—
262C2×D13#48614yes—
263C2×D13#49114yes—
264C4×C13—22no—
265C4×C13—22no—
266C4×C13—42no—
267C4×C13—81no—
268C4×C13—82no—
269C4×C13C2×#12512yes—
270C4×C13C2×#12612yes—
271Dic13—22no—
272Dic13—22no—
273Dic13—42no—
274Dic13—81no—
275Dic13—82no—
276Dic13#40014yes—
277C23×C4—131no—
278C23×C4—131no—
279C23×C4—131no—
280C23×C4—261no—
281C23×C4—262no—
282C23×C4—261no—
283C22×C8—132no—
284C22×C8—264no—
285C22×C8—264no—
286C22×C8—264no—
287C22×C8C22×D1312yes—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—131no—
292C2×C4⋊C4—134no—
293C2×C4⋊C4—132no—
294C2×C4⋊C4—131no—
295C2×C4⋊C4—262no—
296C2×C4⋊C4—264no—
297C2×C4⋊C4—268no—
298C2×C4⋊C4—261no—
299C2×C4⋊C4—262no—
300C2×C4⋊C4—261no—
301C2×C4⋊C4—262no—
302C2×C4⋊C4—262no—
303C2×C4⋊C4—261no—
304C2×C4⋊C4—261no—
305C2×C4⋊C4—261no—
306C2×C4⋊C4—261no—
307C2×C4⋊C4—261no—
308C2×C4⋊C4—524no—
309C2×C4⋊C4—524no—
310C2×C4⋊C4—524no—
311C2×C4⋊C4C22×D1312yes—
312C2×C4⋊C4C22×D1311yescharacteristic
313C2×C4⋊C4C22×D1311yescharacteristic
314C2×C42—131no—
315C2×C42—131no—
316C2×C42—131no—
317C2×C42—264no—
318C2×C42C22×D1311yescharacteristic
319#95—21no—
320#95—261no—
321#95—261no—
322#95—261no—
323C2×C13C2×#40011yescharacteristic
324C2×C13C2×#47411yescharacteristic
325C2×C13C2×#47511yescharacteristic
326C2×C13C2×#48011yescharacteristic
327C2×C13C2×#48311yescharacteristic
328C2×C13C2×#48611yescharacteristic
329C2×C13C2×#49111yescharacteristic
330D13#209918yesdirect product factor
331C24—131no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—131no—
336C22×C4—132no—
337C22×C4—134no—
338C22×C4—134no—
339C22×C4—132no—
340C22×C4—131no—
341C22×C4—131no—
342C22×C4—134no—
343C22×C4—134no—
344C22×C4—262no—
345C22×C4—262no—
346C22×C4—262no—
347C22×C4—262no—
348C22×C4—264no—
349C22×C4—261no—
350C22×C4—261no—
351C22×C4—262no—
352C22×C4—522no—
353C22×C4—522no—
354C22×C4—522no—
355C22×C4—524no—
356C22×C4—524no—
357C22×C4—522no—
358C22×C4—524no—
359C22×C4—522no—
360C22×C4D4×D1311yescharacteristic
361C22×C4D4×D1311yescharacteristic
362C22×C4C23×D1311yescharacteristic
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—262no—
367C2×C8—262no—
368C2×C8—262no—
369C2×C8—528no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—24no—
373C4⋊C4—42no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—132no—
377C4⋊C4—264no—
378C4⋊C4—261no—
379C4⋊C4—262no—
380C4⋊C4—264no—
381C4⋊C4—522no—
382C4⋊C4—524no—
383C4⋊C4—522no—
384C4⋊C4—524no—
385C4⋊C4—524no—
386C4⋊C4—522no—
387C4⋊C4—522no—
388C4⋊C4—522no—
389C4⋊C4—522no—
390C4⋊C4Q8×D1312yes—
391C42—22no—
392C42—262no—
393C42—262no—
394C42—262no—
395C13C2×#209911yescharacteristic, complemented, Sylow
396C23—132no—
397C23—132no—
398C23—132no—
399C23—132no—
400C23—132no—
401C23—132no—
402C23—132no—
403C23C2×D4×D1311yescharacteristic
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—132no—
418C2×C4—132no—
419C2×C4—132no—
420C2×C4—138no—
421C2×C4—138no—
422C2×C4—132no—
423C2×C4—132no—
424C2×C4—268no—
425C2×C4—268no—
426C2×C4—261no—
427C2×C4—261no—
428C2×C4—261no—
429C2×C4—261no—
430C2×C4—262no—
431C2×C4—528no—
432C2×C4—521no—
433C2×C4—521no—
434C2×C4—522no—
435C2×C4—521no—
436C2×C4—522no—
437C2×C4—521no—
438C2×C4—521no—
439C2×C4—522no—
440C2×C4—1048no—
441C2×C4—1044no—
442C2×C4D8×D1312yes—
443C2×C4SD16×D1312yes—
444C2×C4C2×Q8×D1311yescharacteristic
445C2×C4#41×D1312yes—
446C2×C4#41×D1312yes—
447C2×C4#41×D1311yescharacteristic
448C8—42no—
449C8—522no—
450C22—134no—
451C22—134no—
452C22—134no—
453C22—134no—
454C22—134no—
455C22—134no—
456C22—134no—
457C22D13×C22⋊Q811yescharacteristic
458C22D13×#12311yescharacteristic
459C22D13×#12411yescharacteristic
460C22C2×D8×D1311yescharacteristic
461C22C2×SD16×D1311yescharacteristic
462C22D13×#13711yescharacteristic
463C22D13×#13711yescharacteristic
464C4—22no—
465C4—22no—
466C4—42no—
467C4—82no—
468C4—81no—
469C4—134no—
470C4—262no—
471C4—262no—
472C4—522no—
473C4—1042no—
474C4—1041no—
475C4D13×#12512yes—
476C4D13×#12612yes—
477C2—138no—
478C2D13×#40011yescharacteristic
479C2D13×#47411yescharacteristic
480C2D13×#47511yescharacteristic
481C2D13×#48011yescharacteristic
482C2D13×#48311yescharacteristic
483C2D13×#48611yescharacteristic
484C2D13×#49111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2099C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenter#2099D13
hypocenterC13C2×#2099
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2099

Complements

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

NH ≅ G/Ntype
3. #13116397C2semidirect
4. #13116396C2semidirect
5. #13116395C2semidirect
6. #13116394C2semidirect
7. #13116393C2semidirect
11. C13×#2099C2semidirect
161. #2099D13direct (N × H)
330. D13#2099direct (N × H)
395. C13C2×#2099semidirect

Maximal subgroups

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

subgroupindex
D13×#3892
D13×#3842
#131163972
#131163962
#131163952
#131163942
#131163932
D13×#3402
D13×#3362
C13×#20992
C2×#209913