Finite Group Databasebeta

← #15907821

Subgroups — #15907821

Order 3328.

840 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119737C211yesmaximal, characteristic
2#13116272C211yesmaximal, characteristic, complemented
3#13116262C211yesmaximal, characteristic, complemented
4#13116025C211yesmaximal, characteristic, complemented
5#13116018C211yesmaximal, characteristic, complemented
6#13115631C211yesmaximal, characteristic, complemented
7#13115604C211yesmaximal, characteristic, complemented
8#13115158C211yesmaximal, characteristic, complemented
9#13115153C211yesmaximal, characteristic, complemented
10#13114966C211yesmaximal, characteristic, complemented
11#13114931C211yesmaximal, characteristic, complemented
12#13114926C211yesmaximal, characteristic, complemented
13#13114843C211yesmaximal, characteristic, complemented
14C4×#88049C211yesmaximal, characteristic, complemented
15C13×#2352C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88184C2211yescharacteristic
20C2×#88184C2211yescharacteristic
21C2×C4×D52C2211yescharacteristic
22C13×#388—21no—
23C13×#387—21no—
24C13×#386—21no—
25C13×#382C2211yescharacteristic
26C13×#380C2211yescharacteristic
27C13×#380C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4—21no—
30#11718884—21no—
31#11718873C2211yescharacteristic
32#11718873C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36C2×C22⋊#1055C2211yescharacteristic
37#11718654—21no—
38C2×#88049C2211yescharacteristic
39C2×#88049C2211yescharacteristic
40C2×#88049C2211yescharacteristic
41C2×#88049C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718617—21no—
45#11718617—21no—
46#11718597C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×C4×#1055C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59C22×D4×C13D411yescharacteristic
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C22×C22⋊D13—21no—
64C22×C22⋊D13—21no—
65C22×D52C2311yescharacteristic
66C22×C4×D13—21no—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C13×#117—22no—
70C13×#117—41no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—41no—
74C2×C13×C4⋊C4D411yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4D411yescharacteristic
83C2×C13×C22⋊C4D411yescharacteristic
84C2×C42×C13—21no—
85C2×C42×C13—21no—
86C2×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13—21no—
88C2×C22⋊Dic13—21no—
89#88184—22no—
90#88184—22no—
91#88184—41no—
92#88184—41no—
93C2×#6103—21no—
94C2×#6103—21no—
95C2×#6103—21no—
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C4×D52—22no—
104C4×D52—22no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114C22⋊#1055—41no—
115C22⋊#1055—41no—
116C22⋊#1055—41no—
117C22⋊#1055—41no—
118#88049—22no—
119#88049—22no—
120#88049—41no—
121#88049—41no—
122#88048—41no—
123#88047—41no—
124C4⋊#1055—22no—
125C4×#1055—22no—
126#24973—131nomaximal, Sylow
127C24×C13C2×D411yescharacteristic
128C24×C13C2×D411yescharacteristic
129C23×D13—21no—
130C2×D4×C13—22no—
131C2×D4×C13—22no—
132C2×D4×C13—41no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—42no—
150C22×C4×C13—42no—
151C22×C4×C13—81no—
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2411yescharacteristic
157C2×C22⋊D13—42no—
158C2×C22⋊D13—42no—
159C2×C22⋊D13—42no—
160C2×C22⋊D13—42no—
161C2×C22⋊D13—81no—
162C2×C22⋊D13—81no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C2×D52—21no—
167C2×D52—21no—
168C2×D52—21no—
169C2×D52—21no—
170C2×D52—21no—
171C2×D52#4112yes—
172C2×C4×D13—42no—
173C2×C4×D13—81no—
174C2×C4×D13—81no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—42no—
184C13×C4⋊C4#4112yes—
185C13×C22⋊C4—22no—
186C13×C22⋊C4—22no—
187C13×C22⋊C4—42no—
188C13×C22⋊C4—42no—
189C13×C22⋊C4—81no—
190C42×C13—42no—
191C42×C13—81no—
192C42×C13#4112yes—
193C42×C13#4112yes—
194C22⋊Dic13—81no—
195C22⋊Dic13—81no—
196#6103—42no—
197#6103—42no—
198#6103—42no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217#2535—131no—
218#2352D1311yescharacteristic, complemented
219#2077—131no—
220#2075—131no—
221#2034—131no—
222#2033—131no—
223#1954—131no—
224#1949—131no—
225#1875—131no—
226#1874—131no—
227#1835—131no—
228#1825—131no—
229#1824—131no—
230#1804—131no—
231C4×#102—131no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13#13512yes—
246C23×C13C22×D411yescharacteristic
247C22×D13—22no—
248C22×D13—41no—
249C22×D13—41no—
250C22×D13—41no—
251C22×D13—41no—
252C22×D13—41no—
253C22×D13—41no—
254D4×C13—44no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—22no—
265C2×C4×C13—21no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
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—41no—
277C2×C4×C13—41no—
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—84no—
286C2×C4×C13#12312yes—
287C2×C4×C13#12312yes—
288C2×C4×C13C2×#4111yescharacteristic
289C2×C4×C13C2×#4111yescharacteristic
290C2×C4×C13C2×#4111yescharacteristic
291C2×C4×C13C2×#4111yescharacteristic
292C2×C4×C13H(5,𝔽2)11yescharacteristic
293C2×C4×C13H(5,𝔽2)11yescharacteristic
294C22⋊D13—84no—
295C22⋊D13—84no—
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—
305D52—22no—
306D52—22no—
307D52—41no—
308D52—41no—
309C4×D13—84no—
310#1055—41no—
311#1055—41no—
312#1055—41no—
313#1055—41no—
314C2×#121—131no—
315C2×#121—131no—
316C2×C4×D4—131no—
317C2×C4×D4C2×D1311yescharacteristic
318C2×#117C2×D1311yescharacteristic
319C22×C4⋊C4C2×D1311yescharacteristic
320C2×#107—131no—
321C2×#106—131no—
322C2×C4⋊C8—131no—
323C2×#102—131no—
324C2×#102—131no—
325C2×#102—131no—
326C2×#102—131no—
327C2×C22⋊C8—131no—
328C2×C22⋊C8—131no—
329C2×C22⋊C8—131no—
330C2×C22⋊C8—131no—
331C2×C4×C8—131no—
332#397—261no—
333#392—261no—
334#388—21no—
335#387—21no—
336#386—21no—
337#386—261no—
338#386—261no—
339#382—131no—
340#382C2×D1311yescharacteristic
341#380—131no—
342#380—131no—
343#380C2×D1311yescharacteristic
344#380C2×D1311yescharacteristic
345C4×C4⋊C4C2×D1311yescharacteristic
346C4×C22⋊C4—21no—
347#340—131no—
348#340—131no—
349#340—131no—
350#340—131no—
351#340—131no—
352#340—131no—
353#340—131no—
354#340—131no—
355#340—131no—
356#340—131no—
357C22×C13—22no—
358C22×C13—22no—
359C22×C13—22no—
360C22×C13—41no—
361C22×C13—41no—
362C22×C13—41no—
363C22×C13—41no—
364C22×C13—41no—
365C22×C13—41no—
366C22×C13—41no—
367C22×C13—41no—
368C22×C13—41no—
369C22×C13—41no—
370C22×C13—41no—
371C22×C13C2×#12311yescharacteristic
372C22×C13#54611yescharacteristic
373C22×C13#54611yescharacteristic
374C22×C13C2×#13511yescharacteristic
375C22×C13#57511yescharacteristic
376C22×C13#57611yescharacteristic
377C22×C13#57711yescharacteristic
378C2×D13—42no—
379C2×D13—42no—
380C2×D13—42no—
381C2×D13—81no—
382C2×D13—81no—
383C2×D13—81no—
384C2×D13—81no—
385C4×C13—22no—
386C4×C13—22no—
387C4×C13—41no—
388C4×C13—41no—
389C4×C13—42no—
390C4×C13—81no—
391C4×C13—81no—
392C4×C13—81no—
393C4×C13#52911yescharacteristic
394C4×C13#54011yescharacteristic
395C4×C13#55311yescharacteristic
396C4×C13#55511yescharacteristic
397Dic13—81no—
398Dic13—81no—
399Dic13—81no—
400C22×D4—131no—
401C22×D4—261no—
402C22×D4—261no—
403C22×D4C22⋊D1311yescharacteristic
404C23×C4—21no—
405C23×C4—261no—
406C23×C4C22×D1311yescharacteristic
407C23×C4C22×D1311yescharacteristic
408C22×C8—131no—
409C22×C8—131no—
410C22×C8—131no—
411C22×C8—131no—
412#121—262no—
413#121—262no—
414#121—521no—
415#121—521no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—262no—
419C4×D4—262no—
420#117—22no—
421#117—41no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4—131no—
426C2×C4⋊C4—131no—
427C2×C4⋊C4—131no—
428C2×C4⋊C4C22⋊D1311yescharacteristic
429C2×C4⋊C4C22×D1311yescharacteristic
430C2×C4⋊C4C22×D1311yescharacteristic
431C2×C4⋊C4C22×D1311yescharacteristic
432C2×C4⋊C4C22×D1311yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—261no—
437C2×C22⋊C4—261no—
438C2×C22⋊C4—261no—
439C2×C22⋊C4—261no—
440C2×C22⋊C4—261no—
441C2×C22⋊C4C22⋊D1311yescharacteristic
442C2×C22⋊C4C22⋊D1311yescharacteristic
443C2×C42—21no—
444C2×C42—21no—
445C2×C42C22×D1311yescharacteristic
446#107—521no—
447#106—521no—
448C4⋊C8—262no—
449#102—262no—
450#102—262no—
451#102—521no—
452#102—521no—
453C22⋊C8—521no—
454C22⋊C8—521no—
455C22⋊C8—521no—
456C22⋊C8—521no—
457C4×C8—262no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—261no—
464#95—261no—
465#95—261no—
466#95—261no—
467C2×C13—42no—
468C2×C13—81no—
469C2×C13#242011yescharacteristic
470C2×C13#309111yescharacteristic
471C2×C13#309611yescharacteristic
472C2×C13#329711yescharacteristic
473C2×C13#330111yescharacteristic
474C2×C13#332211yescharacteristic
475C2×C13#332311yescharacteristic
476D13—82no—
477C24—261no—
478C24C2×C22⋊D1311yescharacteristic
479C24C2×C22⋊D1311yescharacteristic
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—41no—
483C2×D4—132no—
484C2×D4—261no—
485C2×D4—261no—
486C2×D4—261no—
487C2×D4—261no—
488C2×D4—261no—
489C2×D4—522no—
490C2×D4—522no—
491C2×D4—522no—
492C2×D4—522no—
493C2×D4—1041no—
494C2×D4—1041no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
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—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—81no—
514C22×C4—261no—
515C22×C4—261no—
516C22×C4—261no—
517C22×C4—522no—
518C22×C4—1041no—
519C22×C4—1041no—
520C22×C4C2×C22⋊D1311yescharacteristic
521C22×C4C2×C22⋊D1311yescharacteristic
522C22×C4C2×C22⋊D1311yescharacteristic
523C22×C4C2×C22⋊D1311yescharacteristic
524C22×C4C23×D1311yescharacteristic
525C2×C8—261no—
526C2×C8—261no—
527C2×C8—261no—
528C2×C8—261no—
529C2×C8—261no—
530C2×C8—261no—
531C2×C8—261no—
532C2×C8—261no—
533C2×C8—261no—
534C2×C8—261no—
535C2×C8—261no—
536C2×C8—261no—
537C4⋊C4—22no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—42no—
546C4⋊C4—261no—
547C4⋊C4—261no—
548C4⋊C4—261no—
549C4⋊C4—261no—
550C4⋊C4—261no—
551C4⋊C4—261no—
552C4⋊C4#612912yes—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—81no—
558C22⋊C4—522no—
559C22⋊C4—522no—
560C22⋊C4—522no—
561C22⋊C4—1041no—
562C22⋊C4—1041no—
563C42—42no—
564C42—81no—
565C42#612712yes—
566C42#612712yes—
567C13#2497311yescharacteristic, complemented, Sylow
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—262no—
582C23—521no—
583C23—521no—
584C23—521no—
585C23—521no—
586C23—521no—
587C23—521no—
588C23#8820412yes—
589C23C22×C22⋊D1311yescharacteristic
590D4—44no—
591D4—262no—
592D4—262no—
593D4—521no—
594D4—521no—
595D4—1044no—
596D4—1044no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
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—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—84no—
628C2×C4—521no—
629C2×C4—521no—
630C2×C4—521no—
631C2×C4—521no—
632C2×C4—521no—
633C2×C4—521no—
634C2×C4—521no—
635C2×C4—521no—
636C2×C4—521no—
637C2×C4—1044no—
638C2×C4#8818312yes—
639C2×C4#8818312yes—
640C2×C4C2×#612711yescharacteristic
641C2×C4C2×#612711yescharacteristic
642C2×C4C2×#612911yescharacteristic
643C2×C4#8825111yescharacteristic
644C2×C4#41×D1311yescharacteristic
645C2×C4#8825611yescharacteristic
646C8—521no—
647C8—521no—
648C8—521no—
649C8—521no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—522no—
665C22—522no—
666C22—522no—
667C22—1041no—
668C22—1041no—
669C22—1041no—
670C22—1041no—
671C22C2×#8818311yescharacteristic
672C22#1171951111yescharacteristic
673C22C2×#8820411yescharacteristic
674C22#1171952711yescharacteristic
675C22#1171953411yescharacteristic
676C22#1171954011yescharacteristic
677C22#1171954211yescharacteristic
678C4—22no—
679C4—22no—
680C4—41no—
681C4—41no—
682C4—42no—
683C4—81no—
684C4—81no—
685C4—81no—
686C4—1041no—
687C4—1041no—
688C4—1041no—
689C4#1171926211yescharacteristic
690C4#1171926311yescharacteristic
691C4#1171926711yescharacteristic
692C4#1171926811yescharacteristic
693C2—42no—
694C2—81no—
695C2—1042no—
696C2#1311832211yescharacteristic
697C2#1312474911yescharacteristic
698C2#1312479411yescharacteristic
699C2#1312668011yescharacteristic
700C2#1312673811yescharacteristic
701C2#1312703711yescharacteristic
702C2#1312704611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2352C2
socleC23×C13C22×D4
prime radical#13119737C2
hypercenter#2352D13
hypocenterC13#24973
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. #13116272C2semidirect
3. #13116262C2semidirect
4. #13116025C2semidirect
5. #13116018C2semidirect
6. #13115631C2semidirect
7. #13115604C2semidirect
8. #13115158C2semidirect
9. #13115153C2semidirect
10. #13114966C2semidirect
11. #13114931C2semidirect
12. #13114926C2semidirect
13. #13114843C2semidirect
14. C4×#88049C2semidirect
15. C13×#2352C2semidirect
218. #2352D13semidirect
567. C13#24973semidirect

Maximal subgroups

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

subgroupindex
#131197372
#131162722
#131162622
#131160252
#131160182
#131156312
#131156042
#131151582
#131151532
#131149662
#131149312
#131149262
#131148432
C4×#880492
C13×#23522
#2497313