Finite Group Databasebeta

← #15904271

Subgroups — #15904271

Order 3328.

794 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718670C211yesmaximal, characteristic, complemented
2C2×#11718661C211yesmaximal, characteristic, complemented
3#13120666C211yesmaximal, characteristic, complemented
4#13116272C211yesmaximal, characteristic, complemented
5#13116267C211yesmaximal, characteristic, complemented
6#13116015C211yesmaximal, characteristic
7#13116015C211yesmaximal, characteristic
8#13115793C211yesmaximal, characteristic, complemented
9#13115594C211yesmaximal, characteristic, complemented
10#13115571C211yesmaximal, characteristic, complemented
11#13115566C211yesmaximal, characteristic, complemented
12#13115536C211yesmaximal, characteristic, complemented
13#13115522C211yesmaximal, characteristic, complemented
14#13114836C211yesmaximal, characteristic, complemented
15C13×#2324C211yesmaximal, characteristic
16C2×C13×#121C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C2×#88124C2211yescharacteristic
20C13×#390—21no—
21C13×#390C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#388—21no—
24C13×#386—21no—
25C13×#385—21no—
26C13×#380C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C2×#88072C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32#11718873C2211yescharacteristic
33#11718873C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36#11718670—24no—
37#11718661—24no—
38#11718645—21no—
39#11718645—21no—
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718609—21no—
45#11718609—21no—
46#11718596C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51C2×#88043C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C22×D4×C13—21no—
62C22×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C23×C4×C13C2311yescharacteristic
65C13×#121—22no—
66C13×#121—22no—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C13×#117—22no—
70C13×#117—22no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4D411yescharacteristic
73C2×C13×C4⋊C4D411yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
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×C13C2311yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13—21no—
88C2×C22⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103#88124—22no—
104#88124—22no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108#88072—22no—
109#88072—22no—
110#88072—22no—
111#88072—22no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116C22⋊#1055—22no—
117C22⋊#1055—22no—
118#88048—22no—
119#88047—22no—
120#88047—22no—
121#88047—22no—
122C4⋊#1055—22no—
123C4⋊#1055D414yescomplemented
124#88043—22no—
125C4×#1055—22no—
126#24713—131nomaximal, Sylow
127C24×C13—21no—
128C24×C13C2×D411yescharacteristic
129C2×D4×C13—24no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13—81no—
136C2×D4×C13—81no—
137C2×D4×C13#4112yes—
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—42no—
148C22×C4×C13—81no—
149C22×C4×C13—81no—
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2411yescharacteristic
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—81no—
168C13×C4⋊C4#4112yes—
169C13×C22⋊C4—24no—
170C13×C22⋊C4—22no—
171C13×C22⋊C4—22no—
172C13×C22⋊C4—42no—
173C13×C22⋊C4—81no—
174C13×C22⋊C4—81no—
175C13×C22⋊C4—81no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13—81no—
179C42×C13C2×D412yes—
180C42×C13#4112yes—
181C22⋊Dic13—81no—
182C22⋊Dic13—81no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—81no—
192C4⋊Dic13—81no—
193#6101—42no—
194#6101—42no—
195#6101—81no—
196#6101—81no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055C2×D412yes—
208C2×#1055C2×D412yes—
209C2×#478—131no—
210C2×#433—131no—
211#2629—131no—
212#2324D1311yescharacteristic
213#2077—131no—
214#2076—131no—
215#2033—131no—
216#2033—131no—
217#1989—131no—
218#1947—131no—
219#1943—131no—
220#1942—131no—
221#1936—131no—
222#1934—131no—
223#1802—131no—
224C23×C13—21no—
225C23×C13—22no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—41no—
233C23×C13—41no—
234C23×C13—41no—
235C23×C13—41no—
236C23×C13—41no—
237C23×C13—41no—
238C23×C13C22×D411yescharacteristic
239D4×C13—22no—
240D4×C13—22no—
241D4×C13—41no—
242D4×C13—41no—
243D4×C13—84no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—22no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—84no—
271C2×C4×C13#12112yes—
272C2×C4×C13#12112yes—
273C2×C4×C13C22×D411yescharacteristic
274C2×C4×C13C2×#4111yescharacteristic
275C2×C4×C13C2×#4111yescharacteristic
276C2×C4×C13C2×#4111yescharacteristic
277C2×C4×C132−1+411yescharacteristic
278C2×C4×C132−1+411yescharacteristic
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291#1055—22no—
292#1055—22no—
293#1055—41no—
294#1055—41no—
295C2×#125—131no—
296C2×#121C2×D1311yescharacteristic
297C2×C4×D4C2×D1311yescharacteristic
298C2×#117C2×D1311yescharacteristic
299#478—264no—
300#433—264no—
301C2×#107—131no—
302C2×#107—131no—
303C2×#107—131no—
304C2×#106—131no—
305C2×C4⋊C8—131no—
306C2×C4⋊C8—131no—
307C2×#102—131no—
308C2×#102—131no—
309C2×#102—131no—
310C2×#102—131no—
311C2×C22⋊C8—131no—
312C2×C22⋊C8—131no—
313C2×#97—131no—
314C2×C4×C8—131no—
315#398—261no—
316#398—261no—
317#396—261no—
318#396—261no—
319#390—21no—
320#390C2×D1311yescharacteristic
321#389—131no—
322#389—131no—
323#389C2×D1311yescharacteristic
324#388—21no—
325#386—21no—
326#385—21no—
327#384—131no—
328#380—131no—
329#380—131no—
330#380C2×D1311yescharacteristic
331C4×C4⋊C4C2×D1311yescharacteristic
332#340—131no—
333#340—131no—
334#340—131no—
335#340—131no—
336#340—131no—
337#340—131no—
338#340—131no—
339#340—131no—
340C22×C13—41no—
341C22×C13—42no—
342C22×C13—41no—
343C22×C13—42no—
344C22×C13—41no—
345C22×C13—42no—
346C22×C13—41no—
347C22×C13—41no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13—81no—
351C22×C13—81no—
352C22×C13—81no—
353C22×C13—81no—
354C22×C13C2×#12111yescharacteristic
355C22×C13#52511yescharacteristic
356C22×C13#53611yescharacteristic
357C22×C13#57611yescharacteristic
358C22×C13#57611yescharacteristic
359C22×C13#57711yescharacteristic
360C22×C13#57811yescharacteristic
361C4×C13—22no—
362C4×C13—22no—
363C4×C13—42no—
364C4×C13—41no—
365C4×C13—41no—
366C4×C13—41no—
367C4×C13—81no—
368C4×C13—81no—
369C4×C13#54711yescharacteristic
370C4×C13#54811yescharacteristic
371C4×C13#55211yescharacteristic
372C4×C13#55611yescharacteristic
373Dic13—81no—
374Dic13—81no—
375Dic13—81no—
376Dic13—81no—
377C22×D4—21no—
378C22×D4C22×D1311yescharacteristic
379C23×C4—21no—
380C23×C4C22×D1311yescharacteristic
381C22×C8—131no—
382C22×C8—131no—
383C22×C8—131no—
384C22×C8—131no—
385#125—262no—
386#125—262no—
387#121—22no—
388#121—22no—
389C4×D4—22no—
390C4×D4—22no—
391#117—22no—
392#117—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4—131no—
396C2×C4⋊C4—131no—
397C2×C4⋊C4—131no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4—261no—
401C2×C4⋊C4—261no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4C22⋊D1311yescharacteristic
405C2×C4⋊C4C22⋊D1311yescharacteristic
406C2×C4⋊C4C22×D1311yescharacteristic
407C2×C4⋊C4C22×D1311yescharacteristic
408C2×C4⋊C4C22×D1311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—261no—
415C2×C22⋊C4—261no—
416C2×C22⋊C4C22⋊D1311yescharacteristic
417C2×C22⋊C4C22⋊D1311yescharacteristic
418C2×C42—21no—
419C2×C42C22×D1311yescharacteristic
420C2×C42C22×D1311yescharacteristic
421#107—262no—
422#107—262no—
423#107—262no—
424#106—262no—
425C4⋊C8—134no—
426C4⋊C8—262no—
427#102—262no—
428#102—262no—
429#102—262no—
430#102—262no—
431C22⋊C8—262no—
432C22⋊C8—262no—
433#97—262no—
434C4×C8—262no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—261no—
439#95—261no—
440#95—261no—
441#95—261no—
442C2×C13—81no—
443C2×C13—82no—
444C2×C13#241511yescharacteristic
445C2×C13#306111yescharacteristic
446C2×C13#306211yescharacteristic
447C2×C13#312011yescharacteristic
448C2×C13#312211yescharacteristic
449C2×C13#324111yescharacteristic
450C2×C13#324311yescharacteristic
451C24—21no—
452C24C2×C22⋊D1311yescharacteristic
453C2×D4—24no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—81no—
460C2×D4—81no—
461C2×D4#612712yes—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—42no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4C2×C22⋊D1311yescharacteristic
479C22×C4C2×C22⋊D1311yescharacteristic
480C22×C4C2×C22⋊D1311yescharacteristic
481C22×C4C2×C22⋊D1311yescharacteristic
482C22×C4C2×C22⋊D1311yescharacteristic
483C22×C4C23×D1311yescharacteristic
484C2×C8—132no—
485C2×C8—132no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—81no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—261no—
508C4⋊C4—261no—
509C4⋊C4—261no—
510C4⋊C4—261no—
511C4⋊C4—261no—
512C4⋊C4—522no—
513C4⋊C4—522no—
514C4⋊C4—1041no—
515C4⋊C4—1041no—
516C4⋊C4—1041no—
517C4⋊C4—1041no—
518C4⋊C4#612712yes—
519C22⋊C4—24no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—42no—
523C22⋊C4—81no—
524C22⋊C4—81no—
525C22⋊C4—81no—
526C22⋊C4—1041no—
527C22⋊C4—1041no—
528C42—21no—
529C42—21no—
530C42—81no—
531C42D4×D1312yes—
532C42#612912yes—
533C13#2471311yescharacteristic, complemented, Sylow
534C23—22no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23C22×C22⋊D1311yescharacteristic
549D4—22no—
550D4—22no—
551D4—41no—
552D4—41no—
553D4—84no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—84no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4#8819312yes—
594C2×C4#8819312yes—
595C2×C4C2×#612711yescharacteristic
596C2×C4C2×#612711yescharacteristic
597C2×C4C2×D4×D1311yescharacteristic
598C2×C4C2×#612911yescharacteristic
599C2×C4#8825711yescharacteristic
600C2×C4#8825711yescharacteristic
601C8—262no—
602C8—262no—
603C8—521no—
604C8—521no—
605C22—41no—
606C22—42no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—42no—
611C22—41no—
612C22—41no—
613C22—42no—
614C22—41no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22#1171949611yescharacteristic
620C22C2×#8819311yescharacteristic
621C22#1171953011yescharacteristic
622C22#1171954011yescharacteristic
623C22#1171954011yescharacteristic
624C22#1171954111yescharacteristic
625C22#1171954311yescharacteristic
626C4—22no—
627C4—22no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—42no—
632C4—81no—
633C4—81no—
634C4—1041no—
635C4—1041no—
636C4—1041no—
637C4—1041no—
638C4#1171924611yescharacteristic
639C4#1171924711yescharacteristic
640C4#1171925611yescharacteristic
641C4#1171925711yescharacteristic
642C2—81no—
643C2—82no—
644C2#1311826511yescharacteristic
645C2#1312450311yescharacteristic
646C2#1312451211yescharacteristic
647C2#1312505011yescharacteristic
648C2#1312507911yescharacteristic
649C2#1312608311yescharacteristic
650C2#1312611311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2324C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenter#2324D13
hypocenterC13#24713
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
1. C2×#11718670C2semidirect
2. C2×#11718661C2semidirect
3. #13120666C2semidirect
4. #13116272C2semidirect
5. #13116267C2semidirect
8. #13115793C2semidirect
9. #13115594C2semidirect
10. #13115571C2semidirect
11. #13115566C2semidirect
12. #13115536C2semidirect
13. #13115522C2semidirect
14. #13114836C2semidirect
123. C4⋊#1055D4semidirect
533. C13#24713semidirect

Maximal subgroups

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

subgroupindex
C2×#117186702
C2×#117186612
#131206662
#131162722
#131162672
#131160152
#131157932
#131155942
#131155712
#131155662
#131155362
#131155222
#131148362
C13×#23242
#2471313