Finite Group Databasebeta

← #15904273

Subgroups — #15904273

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×#11718727C211yesmaximal, characteristic, complemented
2C2×#11718661C211yesmaximal, characteristic, complemented
3#13117529C211yesmaximal, characteristic
4#13116273C211yesmaximal, characteristic, complemented
5#13116267C211yesmaximal, characteristic, complemented
6#13116018C211yesmaximal, characteristic
7#13116018C211yesmaximal, characteristic
8#13115794C211yesmaximal, characteristic, complemented
9#13115592C211yesmaximal, characteristic, complemented
10#13115571C211yesmaximal, characteristic, complemented
11#13115566C211yesmaximal, characteristic, complemented
12#13115532C211yesmaximal, characteristic, complemented
13#13115518C211yesmaximal, characteristic, complemented
14#13114833C211yesmaximal, characteristic, complemented
15C13×#2629C211yesmaximal, characteristic, complemented
16C2×C13×#125C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C2×#88184C2211yescharacteristic
19C2×C4×D52C2211yescharacteristic
20C13×#398—21no—
21C13×#398—21no—
22C13×#396—21no—
23C13×#396—21no—
24C13×#389C2211yescharacteristic
25C13×#389C2211yescharacteristic
26C13×#384C2211yescharacteristic
27C13×#380C2211yescharacteristic
28C13×#380C2211yescharacteristic
29#11718873C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32#11718727—24no—
33#11718661—24no—
34#11718651—21no—
35#11718650—21no—
36C2×#88049C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88049C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718618—21no—
45#11718617—21no—
46#11718600C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
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
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13—21no—
63C22×D52C2311yescharacteristic
64C22×C4×D13—21no—
65C13×#125—22no—
66C13×#125—22no—
67C13×#117—22no—
68C13×#117—22no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4D411yescharacteristic
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
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×C13C2311yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13—21no—
88#88184—22no—
89#88184—22no—
90C2×#6103—21no—
91C2×#6103—21no—
92C2×#6103—21no—
93C2×#6103—21no—
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×#6101—21no—
98C2×C4×Dic13—21no—
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—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112C22⋊#1055—22no—
113C22⋊#1055—22no—
114#88049—22no—
115#88049—22no—
116#88049—22no—
117#88049—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×C13C2×D411yescharacteristic
128C23×D13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
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×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2411yescharacteristic
145C2×C22⋊D13—24no—
146C2×C22⋊D13—81no—
147C2×C22⋊D13—81no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C2×D52—21no—
152C2×D52—21no—
153C2×D52—21no—
154C2×D52—21no—
155C2×D52—21no—
156C2×D52#4112yes—
157C2×C4×D13—42no—
158C2×C4×D13—81no—
159C2×C4×D13—81no—
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—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—42no—
171C13×C4⋊C4—42no—
172C13×C4⋊C4—81no—
173C13×C4⋊C4—81no—
174C13×C4⋊C4—81no—
175C13×C4⋊C4—81no—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—22no—
178C13×C22⋊C4—81no—
179C13×C22⋊C4—81no—
180C42×C13—21no—
181C42×C13—21no—
182C42×C13C2×D412yes—
183C42×C13#4112yes—
184C22⋊Dic13—81no—
185#6103—24no—
186#6103—42no—
187#6103—81no—
188#6103—81no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13#4112yes—
195#6101—81no—
196C4×Dic13—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#2629D1311yescharacteristic, complemented
212#2324—131no—
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—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13C22×D411yescharacteristic
232C22×D13—22no—
233C22×D13—41no—
234C22×D13—41no—
235C22×D13—41no—
236C22×D13—41no—
237C22×D13—41no—
238C22×D13—41no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
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—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
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#12112yes—
269C2×C4×C13#12112yes—
270C2×C4×C13C22×D411yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×C4×C132−1+411yescharacteristic
275C2×C4×C132−1+411yescharacteristic
276C22⋊D13—84no—
277C2×Dic13—22no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286D52—22no—
287D52—22no—
288D52—41no—
289D52—41no—
290C4×D13—84no—
291#1055—22no—
292#1055—22no—
293#1055—41no—
294#1055—41no—
295C2×#125C2×D1311yescharacteristic
296C2×#121—131no—
297C2×C4×D4—131no—
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—21no—
316#398—21no—
317#396—21no—
318#396—21no—
319#390—131no—
320#390—261no—
321#389—131no—
322#389C2×D1311yescharacteristic
323#389C2×D1311yescharacteristic
324#388—261no—
325#386—261no—
326#385—261no—
327#384C2×D1311yescharacteristic
328#380—131no—
329#380C2×D1311yescharacteristic
330#380C2×D1311yescharacteristic
331C4×C4⋊C4—131no—
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—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13—41no—
346C22×C13—41no—
347C22×C13C2×#12111yescharacteristic
348C22×C13#52511yescharacteristic
349C22×C13#53611yescharacteristic
350C22×C13#57611yescharacteristic
351C22×C13#57611yescharacteristic
352C22×C13#57711yescharacteristic
353C22×C13#57811yescharacteristic
354C2×D13—42no—
355C2×D13—42no—
356C2×D13—42no—
357C2×D13—81no—
358C2×D13—81no—
359C2×D13—81no—
360C2×D13—81no—
361C4×C13—22no—
362C4×C13—22no—
363C4×C13—41no—
364C4×C13—41no—
365C4×C13—41no—
366C4×C13—81no—
367C4×C13—81no—
368C4×C13—81no—
369C4×C13—81no—
370C4×C13#54711yescharacteristic
371C4×C13#54811yescharacteristic
372C4×C13#55211yescharacteristic
373C4×C13#55611yescharacteristic
374Dic13—42no—
375Dic13—81no—
376Dic13—81no—
377C22×D4—131no—
378C22×D4—261no—
379C23×C4—261no—
380C23×C4C22×D1311yescharacteristic
381C22×C8—131no—
382C22×C8—131no—
383C22×C8—131no—
384C22×C8—131no—
385#125—22no—
386#125—22no—
387#121—262no—
388#121—262no—
389C4×D4—262no—
390C4×D4—262no—
391#117—22no—
392#117—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—131no—
400C2×C4⋊C4—131no—
401C2×C4⋊C4—131no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4C22⋊D1311yescharacteristic
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—261no—
412C2×C22⋊C4—261no—
413C2×C22⋊C4—261no—
414C2×C22⋊C4—261no—
415C2×C22⋊C4—261no—
416C2×C22⋊C4C22⋊D1311yescharacteristic
417C2×C22⋊C4C22⋊D1311yescharacteristic
418C2×C42—261no—
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—21no—
439#95—261no—
440#95—261no—
441#95—261no—
442C2×C13—81no—
443C2×C13#241511yescharacteristic
444C2×C13#306111yescharacteristic
445C2×C13#306211yescharacteristic
446C2×C13#312011yescharacteristic
447C2×C13#312211yescharacteristic
448C2×C13#324111yescharacteristic
449C2×C13#324311yescharacteristic
450D13—82no—
451C24—261no—
452C24C2×C22⋊D1311yescharacteristic
453C2×D4—132no—
454C2×D4—264no—
455C2×D4—261no—
456C2×D4—261no—
457C2×D4—261no—
458C2×D4—261no—
459C2×D4—261no—
460C2×D4—1041no—
461C2×D4—1041no—
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—21no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—522no—
476C22×C4—1041no—
477C22×C4—1041no—
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—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—81no—
509C4⋊C4—81no—
510C4⋊C4—81no—
511C4⋊C4—81no—
512C4⋊C4—132no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—261no—
516C4⋊C4—261no—
517C4⋊C4—261no—
518C4⋊C4—1041no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—81no—
522C22⋊C4—81no—
523C22⋊C4—264no—
524C22⋊C4—522no—
525C22⋊C4—1041no—
526C22⋊C4—1041no—
527C22⋊C4—1041no—
528C42—21no—
529C42—21no—
530C42—1041no—
531C42D4×D1312yes—
532C42#612912yes—
533C13#2471311yescharacteristic, complemented, Sylow
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—262no—
542C23—521no—
543C23—521no—
544C23—521no—
545C23—521no—
546C23—521no—
547C23—521no—
548C23C22×C22⋊D1311yescharacteristic
549D4—262no—
550D4—262no—
551D4—521no—
552D4—521no—
553D4—1044no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
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—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—262no—
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—1044no—
593C2×C4#8819312yes—
594C2×C4#8819312yes—
595C2×C4C2×D4×D1311yescharacteristic
596C2×C4C2×#612911yescharacteristic
597C2×C4#8825411yescharacteristic
598C2×C4#8825411yescharacteristic
599C2×C4#41×D1311yescharacteristic
600C2×C4#41×D1311yescharacteristic
601C8—262no—
602C8—262no—
603C8—521no—
604C8—521no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—522no—
613C22—522no—
614C22—522no—
615C22—1041no—
616C22—1041no—
617C22—1041no—
618C22—1041no—
619C22C2×#8819311yescharacteristic
620C22#1171952111yescharacteristic
621C22#1171953311yescharacteristic
622C22#1171954011yescharacteristic
623C22#1171954011yescharacteristic
624C22#1171954211yescharacteristic
625C22#1171954311yescharacteristic
626C4—22no—
627C4—22no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—81no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—522no—
636C4—1041no—
637C4—1041no—
638C4#1171933611yescharacteristic
639C4#1171933811yescharacteristic
640C4#1171934411yescharacteristic
641C4#1171934611yescharacteristic
642C2—81no—
643C2—1042no—
644C2#1311826611yescharacteristic
645C2#1312450311yescharacteristic
646C2#1312451811yescharacteristic
647C2#1312504411yescharacteristic
648C2#1312507411yescharacteristic
649C2#1312608911yescharacteristic
650C2#1312611911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2629C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenter#2629D13
hypocenterC13#24713
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2629

Complements

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

NH ≅ G/Ntype
1. C2×#11718727C2semidirect
2. C2×#11718661C2semidirect
4. #13116273C2semidirect
5. #13116267C2semidirect
8. #13115794C2semidirect
9. #13115592C2semidirect
10. #13115571C2semidirect
11. #13115566C2semidirect
12. #13115532C2semidirect
13. #13115518C2semidirect
14. #13114833C2semidirect
15. C13×#2629C2semidirect
123. C4⋊#1055D4semidirect
211. #2629D13semidirect
533. C13#24713semidirect

Maximal subgroups

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

subgroupindex
C2×#117187272
C2×#117186612
#131175292
#131162732
#131162672
#131160182
#131157942
#131155922
#131155712
#131155662
#131155322
#131155182
#131148332
C13×#26292
#2471313