Finite Group Databasebeta

← #15759242

Subgroups — #15759242

Order 3328.

712 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123285C211yesmaximal, characteristic, complemented
2#13114780C211yesmaximal, characteristic, complemented
3#13113352C211yesmaximal, characteristic, complemented
4#13113196C211yesmaximal, characteristic, complemented
5#13112713C211yesmaximal, characteristic, complemented
6#13112683C211yesmaximal, characteristic, complemented
7C2×C13×#449C211yesmaximal, characteristic
8C22×C13×#41C2211yescharacteristic
9C22×C13×SD16C411yescharacteristic, complemented
10C22×C13×D8C411yescharacteristic, complemented
11C2×C13×#121C2211yescharacteristic
12C2×#88202—21no—
13C13×#449—21no—
14C13×#449—21no—
15C13×#449—21no—
16C13×#449—21no—
17C2×C13×#103C411yescharacteristic, complemented
18C2×C13×#102C411yescharacteristic, complemented
19C2×C13×C22⋊C8C2211yescharacteristic
20C2×#88077—21no—
21C2×#88077—21no—
22#11718895—21no—
23#11718895—22no—
24C4×C22⋊Dic13C2211yescharacteristic
25#11718868—21no—
26#11718868C2211yescharacteristic
27#11718868C2211yescharacteristic
28C2×C22⋊#1055—21no—
29C2×C22⋊#1055C2211yescharacteristic
30#11718129—22no—
31#11718117—21no—
32#11718117—21no—
33C2×C13×#41—21no—
34C2×C13×#41—21no—
35C2×C13×#41—42no—
36C2×C13×#41—42no—
37C2×C13×#41D411yescharacteristic
38C2×C13×#41D411yescharacteristic
39C2×C13×#41D411yescharacteristic
40C2×C13×#41D411yescharacteristic
41C22×Q8×C13C2×C411yescharacteristic
42C22×D4×C13—21no—
43C22×D4×C13—21no—
44C22×D4×C13C2×C411yescharacteristic
45C22×D4×C13C2×C411yescharacteristic
46C23×C4×C13—21no—
47C23×C4×C13C2311yescharacteristic
48C2×C13×SD16—21no—
49C2×C13×SD16—21no—
50C2×C13×SD16—42no—
51C2×C13×D8—21no—
52C2×C13×D8—21no—
53C2×C13×D8—42no—
54C22×C8×C13C2×C411yescharacteristic
55C22×C8×C13C2×C411yescharacteristic
56C13×#121—21no—
57C13×#121—21no—
58C13×#121—21no—
59C13×#121—21no—
60C2×C13×C4⋊C4C2×C411yescharacteristic
61C2×C13×C22⋊C4—21no—
62C2×C22⋊Dic13—21no—
63#88202—42no—
64#88202—42no—
65C2×C4×Dic13—21no—
66C2×#6099—22no—
67C2×#6099—21no—
68C2×#6099—21no—
69C22×#1055—22no—
70C22×#1055—21no—
71C13×#103—21no—
72C13×#103—21no—
73C13×#102—21no—
74C13×#102—21no—
75C13×C22⋊C8—21no—
76C13×C22⋊C8—21no—
77#88077—42no—
78#88077—42no—
79#88071—21no—
80C22⋊#1055—22no—
81C22⋊#1055—22no—
82C22⋊#1055—21no—
83C22⋊#1055—21no—
84C22⋊#1055—21no—
85C22⋊#1055—21no—
86C22⋊#1055D411yescharacteristic
87C22⋊#1055D411yescharacteristic
88C22⋊#1055D412yes—
89#9241—131nomaximal, Sylow
90C24×C13—21no—
91C24×C13—21no—
92C24×C13#4111yescharacteristic
93C13×#41—22no—
94C13×#41—22no—
95C13×#41—22no—
96C13×#41—22no—
97C13×#41—41no—
98C13×#41—41no—
99C13×#41—41no—
100C13×#41—41no—
101C13×#41—44no—
102C13×#41—44no—
103C2×Q8×C13—21no—
104C2×Q8×C13—22no—
105C2×Q8×C13—41no—
106C2×Q8×C13C22⋊C411yescharacteristic
107C2×Q8×C13C22⋊C411yescharacteristic
108C2×D4×C13—21no—
109C2×D4×C13—22no—
110C2×D4×C13—21no—
111C2×D4×C13—21no—
112C2×D4×C13—21no—
113C2×D4×C13—21no—
114C2×D4×C13—21no—
115C2×D4×C13—21no—
116C2×D4×C13—41no—
117C2×D4×C13—41no—
118C2×D4×C13—41no—
119C2×D4×C13—44no—
120C2×D4×C13—41no—
121C2×D4×C13—41no—
122C2×D4×C13—82no—
123C2×D4×C13C22⋊C411yescharacteristic
124C2×D4×C13C22⋊C411yescharacteristic
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—41no—
132C22×C4×C13—41no—
133C22×C4×C13—44no—
134C22×C4×C13C22×C411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13#4111yescharacteristic
140C22×Dic13—41no—
141C13×SD16—42no—
142C13×SD16—42no—
143C13×D8—42no—
144C13×D8—42no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—41no—
148C2×C8×C13—41no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C22⋊C4—41no—
152C13×C22⋊C4—41no—
153C22⋊Dic13—22no—
154C22⋊Dic13—41no—
155C4×Dic13—41no—
156C4×Dic13—41no—
157#6099—44no—
158#6099—41no—
159#6099—41no—
160#6099—41no—
161#6099—41no—
162C2×#1055—21no—
163C2×#1055—22no—
164C2×#1055—21no—
165C2×#1055—44no—
166C2×#1055—41no—
167C2×#1055—41no—
168C2×#1055—41no—
169C2×#449D1311yescharacteristic
170#2880—131no—
171#1789—131no—
172#1507—131no—
173#1471—131no—
174#1293—131no—
175#1282—131no—
176C23×C13—21no—
177C23×C13—21no—
178C23×C13—21no—
179C23×C13—21no—
180C23×C13—41no—
181C23×C13—41no—
182C23×C13—42no—
183C23×C13—41no—
184C23×C13—41no—
185C23×C13—41no—
186C23×C13—41no—
187C23×C13—41no—
188C23×C13—81no—
189C23×C13—81no—
190C23×C13—81no—
191C23×C13C4×D411yescharacteristic
192C23×C13#12111yescharacteristic
193C23×C13#12311yescharacteristic
194Q8×C13—21no—
195Q8×C13—21no—
196Q8×C13—21no—
197Q8×C13—42no—
198Q8×C13#9912yes—
199D4×C13—24no—
200D4×C13—21no—
201D4×C13—21no—
202D4×C13—21no—
203D4×C13—42no—
204D4×C13—42no—
205D4×C13—42no—
206D4×C13—42no—
207D4×C13—41no—
208D4×C13—41no—
209D4×C13—81no—
210D4×C13—82no—
211D4×C13—82no—
212D4×C13#9912yes—
213C2×C4×C13—24no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—41no—
230C2×C4×C13—81no—
231C2×C4×C13C2×C22⋊C411yescharacteristic
232C2×C4×C13C4×D411yescharacteristic
233C2×C4×C13#12011yescharacteristic
234C2×C4×C13#12111yescharacteristic
235C2×Dic13—42no—
236C2×Dic13—81no—
237C2×Dic13—81no—
238C8×C13—41no—
239C8×C13—41no—
240#1055—41no—
241#1055—42no—
242#1055—41no—
243#1055—81no—
244C22×#41C2×D1311yescharacteristic
245C22×SD16Dic1311yescharacteristic, complemented
246C22×D8Dic1311yescharacteristic, complemented
247C2×#131—261no—
248C2×#121C2×D1311yescharacteristic
249#449—21no—
250#449—21no—
251#449—21no—
252#449—21no—
253C2×#104—261no—
254C2×#104—261no—
255C2×#103Dic1311yescharacteristic, complemented
256C2×#102Dic1311yescharacteristic, complemented
257#408—262no—
258#408—261no—
259#407—131no—
260#407—131no—
261#407—261no—
262C2×C22⋊C8—131no—
263C2×C22⋊C8—261no—
264C2×C22⋊C8C2×D1311yescharacteristic
265C4×C22⋊C4—131no—
266#327—262no—
267#323—261no—
268#323—261no—
269C22×C13—21no—
270C22×C13—21no—
271C22×C13—21no—
272C22×C13—21no—
273C22×C13—21no—
274C22×C13—21no—
275C22×C13—22no—
276C22×C13—21no—
277C22×C13—21no—
278C22×C13—41no—
279C22×C13—41no—
280C22×C13—41no—
281C22×C13—41no—
282C22×C13—41no—
283C22×C13—81no—
284C22×C13—81no—
285C22×C13—82no—
286C22×C13—82no—
287C22×C13—81no—
288C22×C13—81no—
289C22×C13—81no—
290C22×C13—161no—
291C22×C13—161no—
292C22×C13#38611yescharacteristic
293C22×C13#44311yescharacteristic
294C22×C13#44411yescharacteristic
295C4×C13—21no—
296C4×C13—21no—
297C4×C13—22no—
298C4×C13—21no—
299C4×C13—41no—
300C4×C13—81no—
301C4×C13C2×#9911yescharacteristic
302C4×C13C2×#9911yescharacteristic
303Dic13—82no—
304C2×#41—21no—
305C2×#41—21no—
306C2×#41—42no—
307C2×#41—42no—
308C2×#41C22⋊D1311yescharacteristic
309C2×#41C22⋊D1311yescharacteristic
310C2×#41C22⋊D1311yescharacteristic
311C2×#41C22⋊D1311yescharacteristic
312C22×Q8C2×Dic1311yescharacteristic
313C22×D4—21no—
314C22×D4—21no—
315C22×D4C2×Dic1311yescharacteristic
316C22×D4C2×Dic1311yescharacteristic
317C23×C4—21no—
318C23×C4C22×D1311yescharacteristic
319C2×SD16—21no—
320C2×SD16—21no—
321C2×SD16—42no—
322C2×D8—21no—
323C2×D8—21no—
324C2×D8—42no—
325#131—522no—
326#131—522no—
327C2×M16—262no—
328C2×M16—261no—
329C2×M16—261no—
330C22×C8—262no—
331C22×C8—261no—
332C22×C8C2×Dic1311yescharacteristic
333C22×C8C2×Dic1311yescharacteristic
334#121—21no—
335#121—21no—
336#121—21no—
337#121—21no—
338C2×C4⋊C4C2×Dic1311yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—261no—
341C2×C42—261no—
342#104—522no—
343#104—522no—
344#103—21no—
345#103—21no—
346#102—21no—
347#102—21no—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C22⋊C8—131no—
351C22⋊C8—131no—
352C22⋊C8—132no—
353C22⋊C8—262no—
354C22⋊C8—262no—
355C22⋊C8—261no—
356C22⋊C8—261no—
357C22⋊C8—261no—
358C22⋊C8—261no—
359#95—261no—
360C2×C13—21no—
361C2×C13—21no—
362C2×C13—41no—
363C2×C13—41no—
364C2×C13—42no—
365C2×C13—81no—
366C2×C13—161no—
367C2×C13#187611yescharacteristic
368C2×C13#189811yescharacteristic
369C2×C13#190311yescharacteristic
370C24—21no—
371C24—21no—
372C24#612911yescharacteristic
373#41—22no—
374#41—22no—
375#41—22no—
376#41—22no—
377#41—41no—
378#41—41no—
379#41—41no—
380#41—41no—
381#41—44no—
382#41—44no—
383C2×Q8—21no—
384C2×Q8—22no—
385C2×Q8—41no—
386C2×Q8C22⋊Dic1311yescharacteristic
387C2×Q8C22⋊Dic1311yescharacteristic
388C2×D4—21no—
389C2×D4—22no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—44no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—82no—
403C2×D4C22⋊Dic1311yescharacteristic
404C2×D4C22⋊Dic1311yescharacteristic
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—44no—
414C22×C4—521no—
415C22×C4D4×D1311yescharacteristic
416C22×C4D4×D1311yescharacteristic
417C22×C4#612911yescharacteristic
418C22×C4C22×Dic1311yescharacteristic
419C22×C4C2×C22⋊D1311yescharacteristic
420C22×C4C2×C22⋊D1311yescharacteristic
421SD16—42no—
422SD16—42no—
423D8—42no—
424D8—42no—
425M16—524no—
426M16—521no—
427M16—521no—
428M16—521no—
429M16—521no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—41no—
433C2×C8—41no—
434C2×C8—261no—
435C2×C8—261no—
436C2×C8—262no—
437C2×C8—524no—
438C2×C8—521no—
439C2×C8—521no—
440C2×C8—521no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C22⋊C4—41no—
444C22⋊C4—41no—
445C22⋊C4—262no—
446C22⋊C4—521no—
447C42—521no—
448C42—521no—
449C13#924111yescharacteristic, complemented, Sylow
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—81no—
463C23—81no—
464C23—81no—
465C23D4×Dic1311yescharacteristic
466C23#8818911yescharacteristic
467C23#8819311yescharacteristic
468Q8—21no—
469Q8—21no—
470Q8—21no—
471Q8—42no—
472Q8#8807412yes—
473D4—24no—
474D4—21no—
475D4—21no—
476D4—21no—
477D4—42no—
478D4—42no—
479D4—42no—
480D4—42no—
481D4—41no—
482D4—41no—
483D4—81no—
484D4—82no—
485D4—82no—
486D4#8807412yes—
487C2×C4—24no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—81no—
505C2×C4—522no—
506C2×C4—1041no—
507C2×C4—1041no—
508C2×C4D4×Dic1311yescharacteristic
509C2×C4#8819111yescharacteristic
510C2×C4#8819311yescharacteristic
511C2×C4C2×C22⋊Dic1311yescharacteristic
512C8—41no—
513C8—41no—
514C8—521no—
515C8—521no—
516C8—522no—
517C8—1041no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—22no—
525C22—21no—
526C22—21no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—81no—
534C22—82no—
535C22—82no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—161no—
540C22—161no—
541C22#1171885711yescharacteristic
542C22#1171885811yescharacteristic
543C22#1171888111yescharacteristic
544C4—21no—
545C4—21no—
546C4—22no—
547C4—21no—
548C4—41no—
549C4—81no—
550C4—1042no—
551C4C2×#8807411yescharacteristic
552C4C2×#8807411yescharacteristic
553C2—21no—
554C2—21no—
555C2—41no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—161no—
560C2#1311516511yescharacteristic
561C2#1311529011yescharacteristic
562C2#1311531811yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
Fitting, prime radicalC2×C13×#449C2
socleC22×C13#386
cosocleC23×C4×C13C23
hypercenterC2×#449D13
hypocenterC13#9241
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. #13123285C2semidirect
2. #13114780C2semidirect
3. #13113352C2semidirect
4. #13113196C2semidirect
5. #13112713C2semidirect
6. #13112683C2semidirect
9. C22×C13×SD16C4semidirect
10. C22×C13×D8C4semidirect
17. C2×C13×#103C4semidirect
18. C2×C13×#102C4semidirect
245. C22×SD16Dic13semidirect
246. C22×D8Dic13semidirect
255. C2×#103Dic13semidirect
256. C2×#102Dic13semidirect
449. C13#9241semidirect

Maximal subgroups

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

subgroupindex
#131232852
#131147802
#131133522
#131131962
#131127132
#131126832
C2×C13×#4492
#924113