Finite Group Databasebeta

← #15920075

Subgroups — #15920075

Order 3328.

946 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718460C211yesmaximal, characteristic, complemented
2#13118554C211yesmaximal, characteristic
3Q8×C22⋊Dic13C211yesmaximal, characteristic
4#13116386C211yesmaximal, characteristic, complemented
5#13116227C211yesmaximal, characteristic, complemented
6#13116215C211yesmaximal, characteristic, complemented
7#13115985C211yesmaximal, characteristic, complemented
8#13115106C211yesmaximal, characteristic, complemented
9#13115088C211yesmaximal, characteristic, complemented
10#13115024C211yesmaximal, characteristic
11#13115014C211yesmaximal, characteristic
12#13114861C211yesmaximal, characteristic
13#13114849C211yesmaximal, characteristic, complemented
14#13114771C211yesmaximal, characteristic
15C22×C13×#103C211yesmaximal, characteristic
16C23×Q8×C13C2211yescharacteristic
17C23×C8×C13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×Q8×Dic13C2211yescharacteristic
20C2×Q8×Dic13C2211yescharacteristic
21C2×#88144C2211yescharacteristic
22C2×C13×#103—24no—
23C2×C13×#103C2211yescharacteristic
24C2×C13×#103C2211yescharacteristic
25C2×C13×#103C2211yescharacteristic
26C2×C13×#103C2211yescharacteristic
27#11718891—21no—
28#11718891—21no—
29#11718891C2211yescharacteristic
30#11718891C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35#11718873—21no—
36#11718873—21no—
37#11718873C2211yescharacteristic
38#11718873C2211yescharacteristic
39#11718871—21no—
40C4×C22⋊Dic13—21no—
41C4×C22⋊Dic13C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43C2×#88057C2211yescharacteristic
44C2×#88057C2211yescharacteristic
45C2×#88054C2211yescharacteristic
46C2×#88054C2211yescharacteristic
47#11718647—21no—
48#11718646C2211yescharacteristic
49#11718645—21no—
50#11718638C2211yescharacteristic
51#11718634C2211yescharacteristic
52C2×#88047C2211yescharacteristic
53C2×#88047C2211yescharacteristic
54#11718460—24no—
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C22×Q8×C13—21no—
62C22×Q8×C13—22no—
63C22×Q8×C13—22no—
64C22×Q8×C13—22no—
65C22×Q8×C13—41no—
66C22×Q8×C13—41no—
67C22×Q8×C13Q814yes—
68C22×Q8×C13C2311yescharacteristic
69C22×Q8×C13C2311yescharacteristic
70C23×C4×C13—21no—
71C23×C4×C13—21no—
72C23×C4×C13C2311yescharacteristic
73C22×C8×C13—22no—
74C22×C8×C13—22no—
75C22×C8×C13—41no—
76C22×C8×C13C2311yescharacteristic
77C22×C8×C13C2311yescharacteristic
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—41no—
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C22⋊Dic13—21no—
84C2×C22⋊Dic13—21no—
85C2×C22⋊Dic13D411yescharacteristic
86C2×C22⋊Dic13D411yescharacteristic
87Q8×Dic13—22no—
88Q8×Dic13—22no—
89Q8×Dic13—41no—
90Q8×Dic13—41no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C2×#6101—21no—
100C2×#6101—21no—
101C2×C4×Dic13—21no—
102C2×C4×Dic13—21no—
103C2×C4×Dic13C2311yescharacteristic
104C2×C4×Dic13C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107#88144—22no—
108#88144—41no—
109C13×#103—22no—
110C13×#103—22no—
111C13×#103—22no—
112C13×#103D414yes—
113#88075—22no—
114#88075—22no—
115#88075—41no—
116#88075—41no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126#88071—21no—
127#88071D411yescharacteristic
128#88071D411yescharacteristic
129C22⋊#1055—22no—
130#88057—22no—
131#88057—41no—
132#88054—22no—
133#88054—41no—
134#88047—22no—
135#88047—41no—
136#25957—131nomaximal, Sylow
137C24×C13C2×D411yescharacteristic
138C2×Q8×C13—24no—
139C2×Q8×C13—21no—
140C2×Q8×C13—21no—
141C2×Q8×C13—21no—
142C2×Q8×C13—21no—
143C2×Q8×C13—28no—
144C2×Q8×C13—21no—
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13—42no—
149C2×Q8×C13—42no—
150C2×Q8×C13—44no—
151C2×Q8×C13—44no—
152C2×Q8×C13—44no—
153C2×Q8×C13C2×D412yes—
154C2×Q8×C13C2×Q812yes—
155C2×Q8×C13C2×Q812yes—
156C2×Q8×C13#4112yes—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—24no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—42no—
167C22×C4×C13—42no—
168C22×C4×C13—42no—
169C22×C4×C13—42no—
170C22×C4×C13—81no—
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×Q812yes—
173C22×C4×C13#4112yes—
174C22×C4×C13C2411yescharacteristic
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13C2×D411yescharacteristic
180C22×Dic13C2×D411yescharacteristic
181C22×Dic13C2×D411yescharacteristic
182C22×Dic13C2×D411yescharacteristic
183C2×C8×C13—21no—
184C2×C8×C13—21no—
185C2×C8×C13—21no—
186C2×C8×C13—21no—
187C2×C8×C13—21no—
188C2×C8×C13—44no—
189C2×C8×C13C2×D412yes—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—42no—
194C13×C4⋊C4C2×D412yes—
195C22⋊Dic13—22no—
196C22⋊Dic13—22no—
197C22⋊Dic13—42no—
198C22⋊Dic13—42no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13—21no—
207C4⋊Dic13—42no—
208C4⋊Dic13—42no—
209C4⋊Dic13—42no—
210C4⋊Dic13—81no—
211#6101—42no—
212#6101—81no—
213C4×Dic13—21no—
214C4×Dic13—21no—
215C4×Dic13—21no—
216C4×Dic13—21no—
217C4×Dic13—42no—
218C4×Dic13—42no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×#479—131no—
226C22×#103D1311yescharacteristic
227#2442—131no—
228Q8×C22⋊C4—131no—
229#2097—131no—
230#2068—131no—
231#2066—131no—
232#2026—131no—
233#1865—131no—
234#1863—131no—
235#1852—131no—
236#1850—131no—
237#1807—131no—
238#1805—131no—
239#1787—131no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13C22⋊Q812yes—
245C23×C13#13512yes—
246C23×C13#13712yes—
247C23×C13C22×D411yescharacteristic
248Q8×C13—22no—
249Q8×C13—22no—
250Q8×C13—22no—
251Q8×C13—22no—
252Q8×C13—22no—
253Q8×C13—48no—
254Q8×C13—41no—
255Q8×C13—41no—
256Q8×C13C22⋊Q814yes—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—21no—
260C2×C4×C13—22no—
261C2×C4×C13—21no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—22no—
267C2×C4×C13—22no—
268C2×C4×C13—48no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—84no—
277C2×C4×C13C22⋊Q812yes—
278C2×C4×C13C22×D411yescharacteristic
279C2×C4×C13C22×Q811yescharacteristic
280C2×C4×C13C2×#4111yescharacteristic
281C2×C4×C13C2×#4111yescharacteristic
282C2×C4×C13H(5,𝔽2)11yescharacteristic
283C2×C4×C13H(5,𝔽2)11yescharacteristic
284C2×Dic13—21no—
285C2×Dic13—21no—
286C2×Dic13—21no—
287C2×Dic13—21no—
288C2×Dic13—21no—
289C2×Dic13—21no—
290C2×Dic13—21no—
291C2×Dic13—21no—
292C2×Dic13—21no—
293C2×Dic13—21no—
294C2×Dic13—21no—
295C2×Dic13—21no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—41no—
302C2×Dic13—41no—
303C2×Dic13—41no—
304C2×Dic13—41no—
305C2×Dic13—41no—
306C2×Dic13—41no—
307C2×Dic13—41no—
308C8×C13—22no—
309C8×C13—41no—
310#1055—41no—
311#1055—41no—
312C23×Q8C2×D1311yescharacteristic
313C23×C8C2×D1311yescharacteristic
314C2×#125—131no—
315C2×C4×Q8—131no—
316C2×C4×Q8—131no—
317C22×C4⋊C4C2×D1311yescharacteristic
318#479—264no—
319C2×#107—131no—
320C2×#107—131no—
321C2×#106—131no—
322C2×#106—131no—
323C2×C4⋊C8—131no—
324C2×C4⋊C8—131no—
325C2×#103—24no—
326C2×#103—131no—
327C2×#103—131no—
328C2×#103—131no—
329C2×#103—131no—
330C2×#103C2×D1311yescharacteristic
331C2×#103C2×D1311yescharacteristic
332C2×#103C2×D1311yescharacteristic
333C2×#103C2×D1311yescharacteristic
334C2×C22⋊C8—131no—
335#400—261no—
336#398—261no—
337#391—131no—
338#391—131no—
339#391—261no—
340#391—261no—
341#389—131no—
342#389—131no—
343#385—261no—
344#382—131no—
345#380—131no—
346#380—131no—
347#380—261no—
348#380—261no—
349C4×C22⋊C4—131no—
350C4×C22⋊C4—261no—
351#340—131no—
352#340—131no—
353#340—131no—
354#340—131no—
355#336—131no—
356#336—131no—
357C22×C13—22no—
358C22×C13—22no—
359C22×C13—22no—
360C22×C13—22no—
361C22×C13—22no—
362C22×C13—22no—
363C22×C13#47914yescomplemented
364C22×C13C2×C22⋊Q811yescharacteristic
365C22×C13D4211yescharacteristic
366C22×C13#54611yescharacteristic
367C22×C13C2×#13511yescharacteristic
368C22×C13C2×#13711yescharacteristic
369C22×C13#57711yescharacteristic
370C22×C13#57811yescharacteristic
371C4×C13—22no—
372C4×C13—24no—
373C4×C13—42no—
374C4×C13—42no—
375C4×C13—81no—
376C4×C13C2×C22⋊Q811yescharacteristic
377C4×C13#54311yescharacteristic
378C4×C13#54611yescharacteristic
379C4×C13#55111yescharacteristic
380Dic13—41no—
381Dic13—41no—
382Dic13—41no—
383Dic13—41no—
384Dic13—81no—
385Dic13—81no—
386Dic13—81no—
387Dic13—81no—
388C22×Q8—21no—
389C22×Q8—22no—
390C22×Q8—22no—
391C22×Q8—22no—
392C22×Q8—41no—
393C22×Q8—41no—
394C22×Q8Dic2614yes—
395C22×Q8C22×D1311yescharacteristic
396C22×Q8C22×D1311yescharacteristic
397C23×C4—21no—
398C23×C4—21no—
399C23×C4C22×D1311yescharacteristic
400C22×C8—22no—
401C22×C8—22no—
402C22×C8—41no—
403C22×C8—131no—
404C22×C8—131no—
405C22×C8C22×D1311yescharacteristic
406C22×C8C22×D1311yescharacteristic
407#125—262no—
408#125—521no—
409C4×Q8—262no—
410C4×Q8—262no—
411C4×Q8—521no—
412C4×Q8—521no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4—131no—
417C2×C4⋊C4—131no—
418C2×C4⋊C4—131no—
419C2×C4⋊C4—131no—
420C2×C4⋊C4—261no—
421C2×C4⋊C4—261no—
422C2×C4⋊C4—261no—
423C2×C4⋊C4—261no—
424C2×C4⋊C4—261no—
425C2×C4⋊C4—261no—
426C2×C4⋊C4C22×D1311yescharacteristic
427C2×C4⋊C4C22×D1311yescharacteristic
428C2×C22⋊C4—131no—
429C2×C22⋊C4—131no—
430C2×C22⋊C4—261no—
431C2×C22⋊C4—261no—
432C2×C42—131no—
433C2×C42—131no—
434C2×C42—261no—
435C2×C42—261no—
436#107—262no—
437#107—521no—
438#106—262no—
439#106—521no—
440C4⋊C8—262no—
441C4⋊C8—521no—
442#103—22no—
443#103—22no—
444#103—22no—
445#103—262no—
446#103—262no—
447#103—521no—
448#103—521no—
449#103C22⋊D1314yes—
450C22⋊C8—262no—
451#95—131no—
452#95—131no—
453#95—261no—
454#95—261no—
455#95—261no—
456#95—261no—
457#95—261no—
458#95—261no—
459#95—261no—
460#95—261no—
461#95—261no—
462#95—261no—
463C2×C13—24no—
464C2×C13#243711yescharacteristic
465C2×C13C2×#47911yescharacteristic
466C2×C13#308211yescharacteristic
467C2×C13#327011yescharacteristic
468C2×C13#328211yescharacteristic
469C2×C13#330011yescharacteristic
470C2×C13#332011yescharacteristic
471C24D4×D1311yescharacteristic
472C2×Q8—24no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—28no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8C2×Dic2612yes—
488C2×Q8C2×Dic2612yes—
489C2×Q8#612712yes—
490C2×Q8C2×C22⋊D1312yes—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4—131no—
506C22×C4—131no—
507C22×C4—131no—
508C22×C4—131no—
509C22×C4—261no—
510C22×C4—261no—
511C22×C4—261no—
512C22×C4—261no—
513C22×C4C2×Dic2612yes—
514C22×C4D4×D1311yescharacteristic
515C22×C4#612912yes—
516C22×C4C23×D1311yescharacteristic
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—44no—
523C2×C8—261no—
524C2×C8—261no—
525C2×C8—261no—
526C2×C8—261no—
527C2×C8—261no—
528C2×C8—261no—
529C2×C8C2×C22⋊D1312yes—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—42no—
534C4⋊C4—261no—
535C4⋊C4—261no—
536C4⋊C4—261no—
537C4⋊C4—261no—
538C4⋊C4—261no—
539C4⋊C4—261no—
540C4⋊C4—261no—
541C4⋊C4—261no—
542C4⋊C4—522no—
543C4⋊C4—522no—
544C4⋊C4—522no—
545C4⋊C4—522no—
546C4⋊C4—1041no—
547C4⋊C4—1041no—
548C4⋊C4C2×C22⋊D1312yes—
549C22⋊C4—262no—
550C22⋊C4—262no—
551C22⋊C4—522no—
552C22⋊C4—522no—
553C42—261no—
554C42—261no—
555C42—261no—
556C42—261no—
557C42—522no—
558C42—522no—
559C13#2595711yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23#8813212yes—
565C23#8817012yes—
566C23#8817212yes—
567C23C2×D4×D1311yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—22no—
571Q8—22no—
572Q8—22no—
573Q8—48no—
574Q8—41no—
575Q8—41no—
576Q8#8817814yes—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—48no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—84no—
597C2×C4—261no—
598C2×C4—261no—
599C2×C4—261no—
600C2×C4—261no—
601C2×C4—261no—
602C2×C4—261no—
603C2×C4—261no—
604C2×C4—261no—
605C2×C4—261no—
606C2×C4—261no—
607C2×C4—261no—
608C2×C4—261no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4—521no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4—521no—
616C2×C4—521no—
617C2×C4—521no—
618C2×C4—521no—
619C2×C4—521no—
620C2×C4—521no—
621C2×C4#8813212yes—
622C2×C4C22×Dic2611yescharacteristic
623C2×C4C2×#612711yescharacteristic
624C2×C4C2×#612911yescharacteristic
625C2×C4#8825111yescharacteristic
626C2×C4#8825111yescharacteristic
627C2×C4C22×C22⋊D1311yescharacteristic
628C8—22no—
629C8—41no—
630C8—521no—
631C8—521no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22#1171846014yescomplemented
639C22C2×#8813211yescharacteristic
640C22#1171919511yescharacteristic
641C22C2×#8817011yescharacteristic
642C22#1171946711yescharacteristic
643C22C2×#8817211yescharacteristic
644C22#1171947111yescharacteristic
645C22D4×C22⋊D1311yescharacteristic
646C4—22no—
647C4—24no—
648C4—42no—
649C4—42no—
650C4—81no—
651C4—521no—
652C4—521no—
653C4—521no—
654C4—521no—
655C4—1041no—
656C4—1041no—
657C4—1041no—
658C4—1041no—
659C4#1171918811yescharacteristic
660C4#1171920011yescharacteristic
661C4C2×#8817811yescharacteristic
662C4#1171951111yescharacteristic
663C2—24no—
664C2#1311849711yescharacteristic
665C2C2×#1171846011yescharacteristic
666C2#1312467411yescharacteristic
667C2#1312640611yescharacteristic
668C2#1312654311yescharacteristic
669C2#1312671911yescharacteristic
670C2#1312700311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×#103C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC22×#103D13
hypocenterC13#25957
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C2×#11718460C2semidirect
4. #13116386C2semidirect
5. #13116227C2semidirect
6. #13116215C2semidirect
7. #13115985C2semidirect
8. #13115106C2semidirect
9. #13115088C2semidirect
13. #13114849C2semidirect
363. C22×C13#479semidirect
559. C13#25957semidirect
638. C22#11718460semidirect

Maximal subgroups

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

subgroupindex
C2×#117184602
#131185542
Q8×C22⋊Dic132
#131163862
#131162272
#131162152
#131159852
#131151062
#131150882
#131150242
#131150142
#131148612
#131148492
#131147712
C22×C13×#1032
#2595713