Finite Group Databasebeta

← #15869441

Subgroups — #15869441

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718709C211yesmaximal, characteristic
2C2×C4×#6106C211yesmaximal, characteristic, complemented
3C2×#11718658C211yesmaximal, characteristic, complemented
4#13117529C211yesmaximal, characteristic
5#13115693C211yesmaximal, characteristic, complemented
6#13115561C211yesmaximal, characteristic, complemented
7#13115532C211yesmaximal, characteristic, complemented
8#13115529C211yesmaximal, characteristic, complemented
9#13115272C211yesmaximal, characteristic
10#13115270C211yesmaximal, characteristic, complemented
11#13114859C211yesmaximal, characteristic, complemented
12C4×#88048C211yesmaximal, characteristic, complemented
13#13114666C211yesmaximal, characteristic, complemented
14#13114664C211yesmaximal, characteristic, complemented
15C13×#2323C211yesmaximal, characteristic, complemented
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C22×#6106C2211yescharacteristic
20C2×#88184C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22C23×#1055C2211yescharacteristic
23C2×C4×D52C2211yescharacteristic
24C13×#391C2211yescharacteristic
25C13×#389—21no—
26C13×#389C2211yescharacteristic
27C13×#388—21no—
28C13×#388—21no—
29C13×#387—21no—
30C13×#380C2211yescharacteristic
31C4×C13×C4⋊C4C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35#11718873C2211yescharacteristic
36#11718709C418yescomplemented
37C4×#6106—24no—
38#11718658—24no—
39#11718651—21no—
40#11718650—21no—
41C2×#88049C2211yescharacteristic
42C2×#88049C2211yescharacteristic
43C2×#88049C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88048C2211yescharacteristic
46C2×#88048C2211yescharacteristic
47#11718618—21no—
48#11718617—21no—
49#11718600C2211yescharacteristic
50C4×C4⋊Dic13C2211yescharacteristic
51#11718589C2211yescharacteristic
52C2×#88043C2211yescharacteristic
53C2×#88043C2211yescharacteristic
54C2×C4×#1055C2211yescharacteristic
55C2×C4×#1055C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×Q8×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C22×C22⋊D13—21no—
65C22×D52C2311yescharacteristic
66C22×C4×D13—21no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8C2×C414yescomplemented
69C4×Q8×C13—22no—
70C4×Q8×C13—22no—
71C13×#117—22no—
72C13×#117—22no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4D411yescharacteristic
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C42×C13—21no—
86C2×C42×C13—21no—
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C2×C22⋊Dic13—21no—
90C2×#6106—22no—
91C2×#6106—22no—
92C2×#6106C2×C414yes—
93#88184—22no—
94#88184C2×C414yes—
95C2×#6103—21no—
96C2×#6103—21no—
97C2×#6103—21no—
98C2×#6103—21no—
99C2×C4⋊Dic13C2311yescharacteristic
100C2×C4⋊Dic13C2311yescharacteristic
101C2×C4⋊Dic13C2311yescharacteristic
102C2×#6101—21no—
103C2×C4×Dic13—21no—
104C2×#6099—22no—
105C2×#6099—22no—
106C2×#6099—22no—
107C22×#1055—22no—
108C22×#1055—22no—
109C22×#1055C2×C414yescomplemented
110C22×#1055C2311yescharacteristic
111C22×#1055C2311yescharacteristic
112C22×#1055C2311yescharacteristic
113C22×#1055C2311yescharacteristic
114C4×D52—22no—
115C4×D52—22no—
116C13×#95—21no—
117C13×#95—21no—
118C13×#95—21no—
119C13×#95—21no—
120C13×#95—21no—
121#88075—22no—
122#88075—22no—
123#88075C2×C414yescomplemented
124#88071—21no—
125#88071—21no—
126#88071—21no—
127#88049—22no—
128#88049—22no—
129#88049C2×C414yes—
130#88048—22no—
131#88048—22no—
132#88048C2×C414yescomplemented
133#88043—22no—
134#88043—22no—
135C4×#1055—22no—
136C4×#1055D414yescomplemented
137#21523—131nomaximal, Sylow
138C24×C13C2×D411yescharacteristic
139C23×D13—21no—
140C2×Q8×C13—21no—
141C2×Q8×C13—21no—
142C2×Q8×C13—21no—
143C2×Q8×C13—21no—
144C2×Q8×C13—21no—
145C2×Q8×C13C22×C412yes—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13C22×C412yes—
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13#4112yes—
161C22×C4×C13C2411yescharacteristic
162C2×C22⋊D13—24no—
163C2×C22⋊D13—81no—
164C2×C22⋊D13—81no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C2×D52—21no—
169C2×D52—21no—
170C2×D52—21no—
171C2×D52—21no—
172C2×D52—21no—
173C2×D52C22×C412yes—
174C2×C4×D13—42no—
175C2×C4×D13—81no—
176C2×C4×D13—81no—
177C13×C4⋊C4—24no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—42no—
186C13×C4⋊C4—81no—
187C13×C4⋊C4C22×C412yes—
188C13×C22⋊C4—24no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—81no—
192C42×C13—21no—
193C42×C13—21no—
194C42×C13—42no—
195C42×C13—81no—
196C42×C13C2×D412yes—
197C42×C13#4112yes—
198C22⋊Dic13—81no—
199#6106—28no—
200#6103—24no—
201#6103—42no—
202#6103—81no—
203#6103—81no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13—21no—
207C4⋊Dic13—21no—
208C4⋊Dic13—21no—
209C4⋊Dic13C22×C412yes—
210#6101—81no—
211C4×Dic13—81no—
212#6099—28no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—28no—
220C2×#1055C22×C412yes—
221C2×#1055C22×C412yes—
222C2×#1055C2×D412yes—
223C2×#1055C2×D412yes—
224C2×#1055#4112yes—
225C2×#1055#4112yes—
226C2×#465—131no—
227C2×C4×SD16—131no—
228C2×#405—131no—
229#2324—131no—
230#2323D1311yescharacteristic, complemented
231#1968—131no—
232#1941—131no—
233#1936—131no—
234#1935—131no—
235#1895—131no—
236#1894—131no—
237#1807—131no—
238C4×#106—131no—
239#1763—131no—
240#1762—131no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—21no—
247C23×C13C4×D412yes—
248C23×C13C22×D411yescharacteristic
249C22×D13—22no—
250C22×D13—41no—
251C22×D13—41no—
252C22×D13—41no—
253C22×D13—41no—
254C22×D13—41no—
255C22×D13—41no—
256Q8×C13—22no—
257Q8×C13—22no—
258Q8×C13—41no—
259Q8×C13—41no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—22no—
267C2×C4×C13—22no—
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—22no—
271C2×C4×C13—22no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—21no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13C4×D412yes—
289C2×C4×C13#12112yes—
290C2×C4×C13#12112yes—
291C2×C4×C13C23×C411yescharacteristic
292C2×C4×C13C22×D411yescharacteristic
293C2×C4×C13C2×#4111yescharacteristic
294C2×C4×C13C2×#4111yescharacteristic
295C2×C4×C13C2×#4111yescharacteristic
296C2×C4×C13C2×#4111yescharacteristic
297C22⋊D13—84no—
298C2×Dic13—22no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—41no—
302C2×Dic13—41no—
303C2×Dic13—41no—
304C2×Dic13—41no—
305C2×Dic13—41no—
306C2×Dic13—41no—
307D52—22no—
308D52—22no—
309D52—41no—
310D52—41no—
311C4×D13—84no—
312#1055—22no—
313#1055—22no—
314#1055—22no—
315#1055C4×D414yes—
316C22×SD16—131no—
317C22×M16—131no—
318C23×C8—131no—
319C2×C22⋊Q8C2×D1311yescharacteristic
320C2×#121—131no—
321C2×C4×Q8C2×D1311yescharacteristic
322C2×C4×D4—131no—
323C2×#117C2×D1311yescharacteristic
324#465—138no—
325C4×SD16—264no—
326C2×#106—131no—
327C2×#106—131no—
328C2×#106—131no—
329C2×#103—131no—
330C2×#103—131no—
331C2×#103—131no—
332C2×#102—131no—
333C2×#102—131no—
334C2×#102—131no—
335#405—264no—
336C2×#97—131no—
337C2×#97—131no—
338C2×C4×C8—131no—
339C2×C4×C8—131no—
340#391C2×D1311yescharacteristic
341#390—131no—
342#390—261no—
343#389—21no—
344#389—131no—
345#389C2×D1311yescharacteristic
346#388—21no—
347#388—21no—
348#388—261no—
349#387—21no—
350#386—261no—
351#385—261no—
352#380—131no—
353#380C2×D1311yescharacteristic
354C4×C4⋊C4—131no—
355C4×C4⋊C4C2×D1311yescharacteristic
356#340—131no—
357#340—131no—
358#340—131no—
359#340—131no—
360#340—131no—
361#340—131no—
362C22×C13—22no—
363C22×C13—22no—
364C22×C13—22no—
365C22×C13—41no—
366C22×C13—41no—
367C22×C13—41no—
368C22×C13—41no—
369C22×C13C2×C4×D411yescharacteristic
370C22×C13C2×#12111yescharacteristic
371C22×C13#53211yescharacteristic
372C22×C13#57711yescharacteristic
373C22×C13#57711yescharacteristic
374C22×C13#57711yescharacteristic
375C22×C13#57711yescharacteristic
376C2×D13—42no—
377C2×D13—42no—
378C2×D13—42no—
379C2×D13—81no—
380C2×D13—81no—
381C2×D13—81no—
382C2×D13—81no—
383C4×C13—22no—
384C4×C13—22no—
385C4×C13—22no—
386C4×C13—42no—
387C4×C13—41no—
388C4×C13—41no—
389C4×C13—42no—
390C4×C13—81no—
391C4×C13—81no—
392C4×C13C2×C4×D411yescharacteristic
393C4×C13C4×#4111yescharacteristic
394C4×C13#52511yescharacteristic
395C4×C13#52911yescharacteristic
396Dic13—42no—
397Dic13—81no—
398Dic13—81no—
399C22×Q8C22×D1311yescharacteristic
400C22×D4—131no—
401C22×D4—261no—
402C23×C4—261no—
403C23×C4C22×D1311yescharacteristic
404C2×SD16—134no—
405C2×SD16—262no—
406C2×SD16—262no—
407C2×M16—262no—
408C2×M16—262no—
409C2×M16—262no—
410C22×C8—131no—
411C22×C8—134no—
412C22×C8—131no—
413C22×C8—131no—
414C22×C8—131no—
415C22×C8—262no—
416C22×C8—262no—
417C22⋊Q8—22no—
418C22⋊Q8C4×D1314yescomplemented
419#121—134no—
420#121—262no—
421C4×Q8—22no—
422C4×Q8—22no—
423C4×D4—262no—
424C4×D4—262no—
425#117—22no—
426#117—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—131no—
431C2×C4⋊C4—131no—
432C2×C4⋊C4—131no—
433C2×C4⋊C4—261no—
434C2×C4⋊C4C22⋊D1311yescharacteristic
435C2×C4⋊C4C22⋊D1311yescharacteristic
436C2×C4⋊C4C22×D1311yescharacteristic
437C2×C4⋊C4C22×D1311yescharacteristic
438C2×C4⋊C4C22×D1311yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—261no—
442C2×C22⋊C4—261no—
443C2×C22⋊C4—261no—
444C2×C22⋊C4—261no—
445C2×C22⋊C4—261no—
446C2×C22⋊C4C22⋊D1311yescharacteristic
447C2×C22⋊C4C22⋊D1311yescharacteristic
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—261no—
451C2×C42C22×D1311yescharacteristic
452C2×C42C22×D1311yescharacteristic
453#106—134no—
454#106—262no—
455#106—262no—
456#103—134no—
457#103—262no—
458#103—262no—
459#102—134no—
460#102—262no—
461#102—262no—
462#97—262no—
463#97—262no—
464C4×C8—134no—
465C4×C8—262no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—261no—
472#95—261no—
473#95—261no—
474C2×C13—42no—
475C2×C13C4×#12111yescharacteristic
476C2×C13#294911yescharacteristic
477C2×C13#295211yescharacteristic
478C2×C13#305711yescharacteristic
479C2×C13#306011yescharacteristic
480C2×C13#317311yescharacteristic
481C2×C13#317411yescharacteristic
482D13—82no—
483C24—261no—
484C24C2×C22⋊D1311yescharacteristic
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8C2×C4×D1312yes—
491C2×D4—132no—
492C2×D4—264no—
493C2×D4—261no—
494C2×D4—261no—
495C2×D4—261no—
496C2×D4—261no—
497C2×D4—261no—
498C2×D4—1041no—
499C2×D4—1041no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—261no—
509C22×C4—261no—
510C22×C4—261no—
511C22×C4—522no—
512C22×C4—1041no—
513C22×C4—1041no—
514C22×C4C2×C4×D1312yes—
515C22×C4#612712yes—
516C22×C4C2×C22⋊D1311yescharacteristic
517C22×C4C2×C22⋊D1311yescharacteristic
518C22×C4C2×C22⋊D1311yescharacteristic
519C22×C4C2×C22⋊D1311yescharacteristic
520C22×C4C2×C22⋊D1311yescharacteristic
521C22×C4C23×D1311yescharacteristic
522SD16—268no—
523M16—268no—
524C2×C8—132no—
525C2×C8—132no—
526C2×C8—132no—
527C2×C8—132no—
528C2×C8—132no—
529C2×C8—132no—
530C2×C8—268no—
531C2×C8—261no—
532C2×C8—261no—
533C2×C8—261no—
534C2×C8—261no—
535C2×C8—261no—
536C2×C8—261no—
537C4⋊C4—24no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—42no—
546C4⋊C4—81no—
547C4⋊C4—132no—
548C4⋊C4—261no—
549C4⋊C4—261no—
550C4⋊C4—261no—
551C4⋊C4—261no—
552C4⋊C4—261no—
553C4⋊C4—1041no—
554C4⋊C4C2×C4×D1312yes—
555C22⋊C4—24no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—81no—
559C22⋊C4—264no—
560C22⋊C4—522no—
561C22⋊C4—1041no—
562C22⋊C4—1041no—
563C22⋊C4—1041no—
564C42—21no—
565C42—21no—
566C42—42no—
567C42—81no—
568C42—1041no—
569C42D4×D1312yes—
570C42#612912yes—
571C13#2152311yescharacteristic, complemented, Sylow
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—262no—
579C23—521no—
580C23—521no—
581C23—521no—
582C23—521no—
583C23—521no—
584C23—521no—
585C23C4×C22⋊D1312yes—
586C23C22×C22⋊D1311yescharacteristic
587Q8—22no—
588Q8—22no—
589Q8—41no—
590Q8—41no—
591D4—262no—
592D4—262no—
593D4—521no—
594D4—521no—
595D4—1044no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—262no—
625C2×C4—521no—
626C2×C4—521no—
627C2×C4—521no—
628C2×C4—521no—
629C2×C4—521no—
630C2×C4—521no—
631C2×C4—521no—
632C2×C4—521no—
633C2×C4—1044no—
634C2×C4C4×C22⋊D1312yes—
635C2×C4#8819312yes—
636C2×C4#8819312yes—
637C2×C4C22×C4×D1311yescharacteristic
638C2×C4C2×#612711yescharacteristic
639C2×C4C2×D4×D1311yescharacteristic
640C2×C4C2×#612911yescharacteristic
641C2×C4#41×D1311yescharacteristic
642C2×C4#41×D1311yescharacteristic
643C8—134no—
644C8—262no—
645C8—262no—
646C8—262no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—522no—
655C22—522no—
656C22—522no—
657C22—1041no—
658C22—1041no—
659C22—1041no—
660C22—1041no—
661C22C2×C4×C22⋊D1311yescharacteristic
662C22C2×#8819311yescharacteristic
663C22#1171953711yescharacteristic
664C22#1171954111yescharacteristic
665C22#1171954211yescharacteristic
666C22#1171954211yescharacteristic
667C22#1171954211yescharacteristic
668C4—22no—
669C4—22no—
670C4—22no—
671C4—41no—
672C4—42no—
673C4—41no—
674C4—42no—
675C4—81no—
676C4—81no—
677C4—522no—
678C4—1041no—
679C4—1041no—
680C4C4×#612911yescharacteristic
681C4#1171924311yescharacteristic
682C4C4×D4×D1311yescharacteristic
683C4#1171925211yescharacteristic
684C2—42no—
685C2—1042no—
686C2C4×#8819311yescharacteristic
687C2#1312369511yescharacteristic
688C2#1312371711yescharacteristic
689C2#1312447711yescharacteristic
690C2#1312449511yescharacteristic
691C2#1312544711yescharacteristic
692C2#1312546511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2323C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
cosocleC22×C4×C13C24
hypercenter#2323D13
hypocenterC13#21523
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6106C2semidirect
3. C2×#11718658C2semidirect
5. #13115693C2semidirect
6. #13115561C2semidirect
7. #13115532C2semidirect
8. #13115529C2semidirect
10. #13115270C2semidirect
11. #13114859C2semidirect
12. C4×#88048C2semidirect
13. #13114666C2semidirect
14. #13114664C2semidirect
15. C13×#2323C2semidirect
36. #11718709C4semidirect
68. C13×C22⋊Q8C2×C4semidirect
109. C22×#1055C2×C4semidirect
123. #88075C2×C4semidirect
132. #88048C2×C4semidirect
136. C4×#1055D4semidirect
230. #2323D13semidirect
418. C22⋊Q8C4×D13semidirect
571. C13#21523semidirect

Maximal subgroups

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

subgroupindex
C2×#117187092
C2×C4×#61062
C2×#117186582
#131175292
#131156932
#131155612
#131155322
#131155292
#131152722
#131152702
#131148592
C4×#880482
#131146662
#131146642
C13×#23232
#2152313