Finite Group Databasebeta

← #15867278

Subgroups — #15867278

Order 3328.

862 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718675C211yesmaximal, characteristic
2#13117480C211yesmaximal, characteristic, complemented
3#13115711C211yesmaximal, characteristic
4#13115701C211yesmaximal, characteristic
5#13115576C211yesmaximal, characteristic, complemented
6#13115561C211yesmaximal, characteristic, complemented
7#13115536C211yesmaximal, characteristic, complemented
8#13115532C211yesmaximal, characteristic, complemented
9#13115522C211yesmaximal, characteristic, complemented
10#13115518C211yesmaximal, characteristic, complemented
11#13114734C211yesmaximal, characteristic, complemented
12C4×#88049C211yesmaximal, characteristic, complemented
13C4×#88072C211yesmaximal, characteristic, complemented
14#13114523C211yesmaximal, characteristic, complemented
15C13×#2319C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17C22×#6104C2211yescharacteristic
18C2×C4×D52C2211yescharacteristic
19C13×#390C2211yescharacteristic
20C13×#390C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#388—21no—
24C13×#388—21no—
25C13×#381—21no—
26C13×#380—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C13×#376C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32#11718675C418yescomplemented
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39#11718600C2211yescharacteristic
40#11718600C2211yescharacteristic
41C4×C4⋊Dic13C2211yescharacteristic
42#11718589C2211yescharacteristic
43#11718589C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45C2×#88043C2211yescharacteristic
46C2×#88043C2211yescharacteristic
47C2×C4×#1055C2211yescharacteristic
48C2×C4×#1055C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50#11718330—21no—
51#11718330—21no—
52#11718328—21no—
53#11718325—21no—
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C22×D52C2311yescharacteristic
63C22×C4×D13—21no—
64C4×D4×C13—22no—
65C4×D4×C13C2×C414yes—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C22⋊C4—21no—
72C2×C13×C22⋊C4—21no—
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4—21no—
76C2×C42×C13—21no—
77C2×C42×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×#6104—22no—
81C2×#6104—22no—
82C2×#6104C2×C414yes—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×#6103—21no—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×#6101—21no—
92C2×#6101—21no—
93C2×C4×Dic13—21no—
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C4×D52—22no—
99C4×D52C2×C414yes—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95D411yescharacteristic
104C13×#95D411yescharacteristic
105C13×#95D411yescharacteristic
106C13×#95D411yescharacteristic
107#88072—22no—
108#88072—22no—
109#88072C2×C414yes—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88049—22no—
114#88049—22no—
115#88049C2×C414yes—
116#88048—22no—
117#88048C2×C414yes—
118#88047—22no—
119#88043—22no—
120#88043—22no—
121#88043C2×C414yes—
122C4×#1055—22no—
123C4×#1055—22no—
124C4×#1055—22no—
125#21290—131nomaximal, Sylow
126C24×C13—21no—
127C23×D13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13C22×C412yes—
134C22×C4×C13—21no—
135C22×C4×C13—24no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—81no—
139C22×C4×C13—81no—
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2411yescharacteristic
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C2×D52—21no—
151C2×D52—21no—
152C2×D52—21no—
153C2×D52—21no—
154C2×D52—21no—
155C2×D52C22×C412yes—
156C2×C4×D13—24no—
157C2×C4×D13—81no—
158C2×C4×D13—81no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—81no—
165C13×C4⋊C4—81no—
166C13×C4⋊C4C22×C412yes—
167C13×C22⋊C4—24no—
168C13×C22⋊C4—81no—
169C13×C22⋊C4—81no—
170C13×C22⋊C4—81no—
171C13×C22⋊C4—81no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—81no—
177C42×C13C22×C412yes—
178C42×C13#4112yes—
179#6104—28no—
180#6103—24no—
181#6103—81no—
182#6103—81no—
183#6103—81no—
184#6103—81no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13C22×C412yes—
191#6101—81no—
192#6101—81no—
193C4×Dic13—81no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055C22×C412yes—
201C2×#1055C22×C412yes—
202C2×#1055#4112yes—
203C2×#1055#4112yes—
204C2×#1055#4112yes—
205C2×#1055#4112yes—
206C2×#442—131no—
207#2319—131no—
208#2319D1311yescharacteristic, complemented
209#1972—131no—
210#1970—131no—
211#1944—131no—
212#1941—131no—
213#1936—131no—
214#1936—131no—
215#1934—131no—
216#1934—131no—
217#1776—131no—
218C4×#102—131no—
219C4×#102—131no—
220#1726—131no—
221C23×C13—22no—
222C23×C13—41no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13—41no—
228C23×C13C22×D411yescharacteristic
229C22×D13—22no—
230C22×D13—41no—
231C22×D13—41no—
232C22×D13—41no—
233C22×D13—41no—
234C22×D13—41no—
235C22×D13—41no—
236D4×C13—22no—
237D4×C13—22no—
238D4×C13—41no—
239D4×C13—41no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—22no—
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—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
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—84no—
266C2×C4×C13C4×D412yes—
267C2×C4×C13C4×D412yes—
268C2×C4×C13C23×C411yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×Dic13—22no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283D52—22no—
284D52—22no—
285D52—41no—
286D52—41no—
287C4×D13—84no—
288#1055—22no—
289#1055—22no—
290#1055—22no—
291#1055#11714yes—
292C22×D8—131no—
293C2×C4×D4—131no—
294C2×C4×D4C2×D1311yescharacteristic
295#442—138no—
296C2×#107—131no—
297C2×#106—131no—
298C2×#106—131no—
299C2×#102—131no—
300C2×#102—131no—
301C2×#102—131no—
302C2×#102—131no—
303C2×#102—131no—
304C2×#102—131no—
305C2×#97—131no—
306C2×#97—131no—
307C2×#97—131no—
308C2×C4×C8—131no—
309C2×C4×C8—131no—
310C2×C4×C8—131no—
311#390—131no—
312#390—131no—
313#390C2×D1311yescharacteristic
314#390C2×D1311yescharacteristic
315#389—131no—
316#389—131no—
317#389C2×D1311yescharacteristic
318#389C2×D1311yescharacteristic
319#388—21no—
320#388—21no—
321#388—261no—
322#388—261no—
323#381—21no—
324#381—261no—
325#380—21no—
326#380—261no—
327C4×C4⋊C4—131no—
328C4×C4⋊C4C2×D1311yescharacteristic
329#376C2×D1311yescharacteristic
330#340—131no—
331#340—131no—
332#340—131no—
333#340—131no—
334#340—131no—
335#340—131no—
336C22×C13—42no—
337C22×C13—42no—
338C22×C13—42no—
339C22×C13—81no—
340C22×C13—81no—
341C22×C13—81no—
342C22×C13—81no—
343C22×C13C2×C4×D411yescharacteristic
344C22×C13#53211yescharacteristic
345C22×C13#53211yescharacteristic
346C22×C13#57611yescharacteristic
347C22×C13#57611yescharacteristic
348C22×C13#57711yescharacteristic
349C22×C13#57711yescharacteristic
350C2×D13—42no—
351C2×D13—42no—
352C2×D13—42no—
353C2×D13—81no—
354C2×D13—81no—
355C2×D13—81no—
356C2×D13—81no—
357C4×C13—22no—
358C4×C13—22no—
359C4×C13—41no—
360C4×C13—41no—
361C4×C13—41no—
362C4×C13—41no—
363C4×C13—42no—
364C4×C13—81no—
365C4×C13—81no—
366C4×C13C2×#11711yescharacteristic
367C4×C13C4×#4111yescharacteristic
368C4×C13#52911yescharacteristic
369C4×C13#52911yescharacteristic
370Dic13—42no—
371Dic13—81no—
372Dic13—81no—
373C22×D4—131no—
374C22×D4C22×D1311yescharacteristic
375C23×C4—21no—
376C23×C4—261no—
377C2×D8—134no—
378C2×D8—262no—
379C2×D8—262no—
380C22×C8—131no—
381C22×C8—131no—
382C22×C8—131no—
383C22×C8—131no—
384C4×D4—22no—
385C4×D4—134no—
386C4×D4—262no—
387C4×D4C4×D1314yes—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—131no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4C22×D1311yescharacteristic
396C2×C4⋊C4C22×D1311yescharacteristic
397C2×C4⋊C4C22×D1311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—261no—
404C2×C22⋊C4—261no—
405C2×C22⋊C4—261no—
406C2×C22⋊C4—261no—
407C2×C22⋊C4—261no—
408C2×C42—21no—
409C2×C42—261no—
410C2×C42C22×D1311yescharacteristic
411C2×C42C22×D1311yescharacteristic
412C2×C42C22×D1311yescharacteristic
413#107—262no—
414#106—134no—
415#106—262no—
416#102—134no—
417#102—134no—
418#102—262no—
419#102—262no—
420#102—262no—
421#102—262no—
422#97—134no—
423#97—262no—
424#97—262no—
425C4×C8—262no—
426C4×C8—262no—
427C4×C8—262no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—261no—
432#95—261no—
433#95—261no—
434#95C22⋊D1311yescharacteristic
435#95C22⋊D1311yescharacteristic
436#95C22⋊D1311yescharacteristic
437#95C22⋊D1311yescharacteristic
438C2×C13—82no—
439C2×C13#229311yescharacteristic
440C2×C13#294611yescharacteristic
441C2×C13#294611yescharacteristic
442C2×C13#317311yescharacteristic
443C2×C13#317611yescharacteristic
444C2×C13#317911yescharacteristic
445C2×C13#317911yescharacteristic
446D13—82no—
447C24—21no—
448C24—261no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—132no—
455C2×D4—261no—
456C2×D4—261no—
457C2×D4—261no—
458C2×D4—261no—
459C2×D4—261no—
460C2×D4C2×C4×D1312yes—
461C22×C4—21no—
462C22×C4—24no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—81no—
466C22×C4—81no—
467C22×C4—261no—
468C22×C4—264no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—1041no—
472C22×C4—1041no—
473C22×C4C2×C22⋊D1311yescharacteristic
474C22×C4C2×C22⋊D1311yescharacteristic
475C22×C4C2×C22⋊D1311yescharacteristic
476C22×C4C2×C22⋊D1311yescharacteristic
477C22×C4C2×C22⋊D1311yescharacteristic
478C22×C4C2×C22⋊D1311yescharacteristic
479C22×C4C23×D1311yescharacteristic
480D8—268no—
481C2×C8—132no—
482C2×C8—132no—
483C2×C8—132no—
484C2×C8—132no—
485C2×C8—132no—
486C2×C8—132no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—81no—
499C4⋊C4—81no—
500C4⋊C4—132no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—1041no—
507C4⋊C4—1041no—
508C4⋊C4C2×C4×D1312yes—
509C22⋊C4—24no—
510C22⋊C4—81no—
511C22⋊C4—81no—
512C22⋊C4—81no—
513C22⋊C4—81no—
514C22⋊C4—264no—
515C22⋊C4—1041no—
516C22⋊C4—1041no—
517C22⋊C4—1041no—
518C22⋊C4—1041no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—81no—
524C42—1041no—
525C42C2×C4×D1312yes—
526C42#612712yes—
527C13#2129011yescharacteristic, complemented, Sylow
528C23—22no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—262no—
536C23—521no—
537C23—521no—
538C23—521no—
539C23—521no—
540C23—521no—
541C23—521no—
542C23C22×C22⋊D1311yescharacteristic
543D4—22no—
544D4—22no—
545D4—41no—
546D4—41no—
547D4—262no—
548D4—262no—
549D4—521no—
550D4—521no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
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—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—84no—
577C2×C4—262no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—1044no—
587C2×C4C4×C22⋊D1312yes—
588C2×C4C4×C22⋊D1312yes—
589C2×C4C22×C4×D1311yescharacteristic
590C2×C4C2×#612711yescharacteristic
591C2×C4#41×D1311yescharacteristic
592C2×C4#41×D1311yescharacteristic
593C2×C4#41×D1311yescharacteristic
594C2×C4#41×D1311yescharacteristic
595C8—134no—
596C8—262no—
597C8—262no—
598C8—262no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—522no—
607C22—522no—
608C22—522no—
609C22—1041no—
610C22—1041no—
611C22—1041no—
612C22—1041no—
613C22C2×C4×C22⋊D1311yescharacteristic
614C22#1171953711yescharacteristic
615C22#1171953711yescharacteristic
616C22#1171954011yescharacteristic
617C22#1171954011yescharacteristic
618C22#1171954111yescharacteristic
619C22#1171954211yescharacteristic
620C4—22no—
621C4—22no—
622C4—41no—
623C4—42no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—81no—
628C4—81no—
629C4—522no—
630C4—1041no—
631C4—1041no—
632C4D13×#11711yescharacteristic
633C4#1171922711yescharacteristic
634C4#1171923311yescharacteristic
635C4#1171923311yescharacteristic
636C2—82no—
637C2—1042no—
638C2#1311729511yescharacteristic
639C2#1312366411yescharacteristic
640C2#1312366811yescharacteristic
641C2#1312544711yescharacteristic
642C2#1312548011yescharacteristic
643C2#1312551311yescharacteristic
644C2#1312552111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2319C2
socleC23×C13C22×D4
prime radicalC22×#6104C22
cosocleC22×C4×C13C24
hypercenter#2319D13
hypocenterC13#21290
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #13117480C2semidirect
5. #13115576C2semidirect
6. #13115561C2semidirect
7. #13115536C2semidirect
8. #13115532C2semidirect
9. #13115522C2semidirect
10. #13115518C2semidirect
11. #13114734C2semidirect
12. C4×#88049C2semidirect
13. C4×#88072C2semidirect
14. #13114523C2semidirect
15. C13×#2319C2semidirect
32. #11718675C4semidirect
208. #2319D13semidirect
527. C13#21290semidirect

Maximal subgroups

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

subgroupindex
C2×#117186752
#131174802
#131157112
#131157012
#131155762
#131155612
#131155362
#131155322
#131155222
#131155182
#131147342
C4×#880492
C4×#880722
#131145232
C13×#23192
#2129013