Finite Group Databasebeta

← #15935602

Subgroups — #15935602

Order 3328.

792 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117850C211yesmaximal, characteristic
2#13116240C211yesmaximal, characteristic, complemented
3#13116207C211yesmaximal, characteristic, complemented
4#13116025C211yesmaximal, characteristic
5#13116025C211yesmaximal, characteristic
6#13115597C211yesmaximal, characteristic, complemented
7#13115561C211yesmaximal, characteristic, complemented
8#13115444C211yesmaximal, characteristic, complemented
9#13115418C211yesmaximal, characteristic, complemented
10#13115414C211yesmaximal, characteristic, complemented
11#13115096C211yesmaximal, characteristic, complemented
12#13115028C211yesmaximal, characteristic, complemented
13#13114920C211yesmaximal, characteristic, complemented
14C4×#88049C211yesmaximal, characteristic, complemented
15C13×#2497C211yesmaximal, characteristic, complemented
16C2×#88184C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C2×#88135—21no—
19C2×C4×D52C2211yescharacteristic
20C13×#400—21no—
21C13×#396—21no—
22C13×#389C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#388—21no—
25C13×#387—21no—
26C13×#384C2211yescharacteristic
27C13×#380C2211yescharacteristic
28C13×#380C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30C4×C13×C22⋊C4C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41#11718619—21no—
42#11718600C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44#11718589C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47#11718331—21no—
48#11718329—21no—
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C22×C22⋊D13—21no—
61C23×Dic13—21no—
62C22×D52C2311yescharacteristic
63C22×C4×D13—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C22⋊C4—21no—
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4D411yescharacteristic
75C2×C13×C22⋊C4D411yescharacteristic
76C2×C42×C13—21no—
77C2×C42×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79#88184—22no—
80#88184—22no—
81C2×#6103—21no—
82C2×#6103—21no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13—41no—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×#6101—21no—
92C2×C4×Dic13—21no—
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97#88135—44no—
98C4×D52—22no—
99C4×D52—41no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95D411yescharacteristic
106C13×#95D411yescharacteristic
107#88071—21no—
108#88071—21no—
109C22⋊#1055—22no—
110C22⋊#1055—41no—
111#88049—22no—
112#88049—22no—
113#88049—22no—
114#88049—41no—
115#88048—22no—
116#88048—22no—
117#88048—22no—
118#88048—41no—
119C4⋊#1055—22no—
120C4×#1055—41no—
121#27032—131nomaximal, Sylow
122C24×C13C2×D411yescharacteristic
123C23×D13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2411yescharacteristic
140C2×C22⋊D13—24no—
141C2×C22⋊D13—42no—
142C2×C22⋊D13—42no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—42no—
147C22×Dic13—42no—
148C22×Dic13—81no—
149C2×D52—21no—
150C2×D52—21no—
151C2×D52—21no—
152C2×D52—21no—
153C2×D52—21no—
154C2×D52#4112yes—
155C2×C4×D13—42no—
156C2×C4×D13—42no—
157C2×C4×D13—81no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—42no—
167C13×C4⋊C4—81no—
168C13×C4⋊C4—81no—
169C13×C4⋊C4—81no—
170C13×C22⋊C4—41no—
171C13×C22⋊C4—81no—
172C13×C22⋊C4—81no—
173C13×C22⋊C4SD1614yes—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13—81no—
179#6103—24no—
180#6103—42no—
181#6103—42no—
182#6103—81no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—42no—
188C4⋊Dic13#4112yes—
189C4⋊Dic13#4112yes—
190#6101—42no—
191C4×Dic13—42no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055#4112yes—
204#2497D1311yescharacteristic, complemented
205#2361—131no—
206#2071—131no—
207#2065—131no—
208#2034—131no—
209#2034—131no—
210#1948—131no—
211#1941—131no—
212#1923—131no—
213#1920—131no—
214#1919—131no—
215#1864—131no—
216#1853—131no—
217#1823—131no—
218C4×#102—131no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13C2×SD1612yes—
226C23×C13C22×D411yescharacteristic
227C22×D13—22no—
228C22×D13—41no—
229C22×D13—41no—
230C22×D13—41no—
231C22×D13—41no—
232C22×D13—41no—
233C22×D13—41no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
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—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
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×C13C2×SD1612yes—
264C2×C4×C13C2×SD1612yes—
265C2×C4×C13C2×#4111yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×C4×C13C2×#4111yescharacteristic
269C2×C4×C13H(5,𝔽2)11yescharacteristic
270C2×C4×C132−1+411yescharacteristic
271C22⋊D13—48no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—84no—
282D52—22no—
283D52—22no—
284D52—41no—
285D52—41no—
286C4×D13—84no—
287#1055—22no—
288#1055—41no—
289#1055—41no—
290#1055—41no—
291C2×#121—131no—
292C2×C4×D4—131no—
293C2×C4×D4—261no—
294C22×C4⋊C4—131no—
295C2×#106—131no—
296C2×#106—131no—
297C2×#106—131no—
298C2×#106—131no—
299C2×C4⋊C8—131no—
300C2×#102—131no—
301C2×#102—131no—
302C2×#102—131no—
303C2×#102—131no—
304C2×C22⋊C8—131no—
305C2×C22⋊C8—131no—
306C2×C4×C8—131no—
307#400—21no—
308#396—21no—
309#390—131no—
310#389—131no—
311#389C2×D1311yescharacteristic
312#389C2×D1311yescharacteristic
313#388—21no—
314#388—261no—
315#387—21no—
316#386—261no—
317#385—261no—
318#384C2×D1311yescharacteristic
319#380C2×D1311yescharacteristic
320#380C2×D1311yescharacteristic
321C4×C4⋊C4—131no—
322C4×C4⋊C4C2×D1311yescharacteristic
323C4×C22⋊C4C2×D1311yescharacteristic
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332#336—131no—
333#336—131no—
334C22×C13—22no—
335C22×C13—22no—
336C22×C13—22no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13#52511yescharacteristic
342C22×C13#54611yescharacteristic
343C22×C13#54711yescharacteristic
344C22×C13C22×SD1611yescharacteristic
345C22×C13#57511yescharacteristic
346C22×C13#57611yescharacteristic
347C22×C13#57711yescharacteristic
348C2×D13—42no—
349C2×D13—42no—
350C2×D13—42no—
351C2×D13—81no—
352C2×D13—81no—
353C2×D13—81no—
354C2×D13—81no—
355C4×C13—22no—
356C4×C13—22no—
357C4×C13—41no—
358C4×C13—41no—
359C4×C13—41no—
360C4×C13—81no—
361C4×C13—81no—
362C4×C13—81no—
363C4×C13—81no—
364C4×C13#52911yescharacteristic
365C4×C13#53911yescharacteristic
366C4×C13#55311yescharacteristic
367C4×C13#55611yescharacteristic
368Dic13—42no—
369Dic13—42no—
370Dic13—81no—
371C22×D4—131no—
372C22×D4—261no—
373C23×C4—261no—
374C23×C4—261no—
375C23×C4C22×D1311yescharacteristic
376C22×C8—131no—
377C22×C8—131no—
378C22×C8—131no—
379C22×C8—131no—
380#121—262no—
381#121—262no—
382C4×D4—262no—
383C4×D4—521no—
384C4×D4—524no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—131no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—262no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4—521no—
396C2×C4⋊C4C22×D1311yescharacteristic
397C2×C4⋊C4C22×D1311yescharacteristic
398C2×C4⋊C4C22×D1311yescharacteristic
399C2×C4⋊C4C22×D1311yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—261no—
403C2×C22⋊C4—261no—
404C2×C22⋊C4—261no—
405C2×C22⋊C4—261no—
406C2×C22⋊C4C22⋊D1311yescharacteristic
407C2×C22⋊C4C22⋊D1311yescharacteristic
408C2×C42—21no—
409C2×C42—261no—
410C2×C42C22×D1311yescharacteristic
411C2×C42C22×D1311yescharacteristic
412#106—262no—
413#106—262no—
414#106—262no—
415#106—521no—
416C4⋊C8—262no—
417#102—262no—
418#102—262no—
419#102—262no—
420#102—521no—
421C22⋊C8—262no—
422C22⋊C8—521no—
423C4×C8—521no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—261no—
430#95—261no—
431#95C22⋊D1311yescharacteristic
432#95C22⋊D1311yescharacteristic
433C2×C13—42no—
434C2×C13#246611yescharacteristic
435C2×C13#310111yescharacteristic
436C2×C13#311911yescharacteristic
437C2×C13#329511yescharacteristic
438C2×C13#332111yescharacteristic
439C2×C13#333511yescharacteristic
440C2×C13#335511yescharacteristic
441D13—82no—
442C24—261no—
443C24C2×C22⋊D1311yescharacteristic
444C2×D4—132no—
445C2×D4—264no—
446C2×D4—261no—
447C2×D4—261no—
448C2×D4—261no—
449C2×D4—261no—
450C2×D4—261no—
451C2×D4—522no—
452C2×D4—522no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—522no—
467C22×C4—522no—
468C22×C4—522no—
469C22×C4—522no—
470C22×C4—1041no—
471C22×C4—1041no—
472C22×C4C2×C22⋊D1311yescharacteristic
473C22×C4C2×C22⋊D1311yescharacteristic
474C22×C4C2×C22⋊D1311yescharacteristic
475C22×C4C2×C22⋊D1311yescharacteristic
476C22×C4C2×C22⋊D1311yescharacteristic
477C22×C4C23×D1311yescharacteristic
478C2×C8—132no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—42no—
499C4⋊C4—81no—
500C4⋊C4—81no—
501C4⋊C4—81no—
502C4⋊C4—132no—
503C4⋊C4—132no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—261no—
508C4⋊C4—522no—
509C4⋊C4—522no—
510C22⋊C4—41no—
511C22⋊C4—81no—
512C22⋊C4—81no—
513C22⋊C4—264no—
514C22⋊C4—522no—
515C22⋊C4—522no—
516C22⋊C4—1041no—
517C22⋊C4#610614yes—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—81no—
523C42—522no—
524C13#2703211yescharacteristic, complemented, Sylow
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—262no—
532C23—521no—
533C23—521no—
534C23—521no—
535C23—521no—
536C23—521no—
537C23—521no—
538C23C2×#610612yes—
539C23C22×C22⋊D1311yescharacteristic
540D4—262no—
541D4—262no—
542D4—528no—
543D4—521no—
544D4—521no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—262no—
575C2×C4—262no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—1044no—
584C2×C4—1044no—
585C2×C4C2×#610612yes—
586C2×C4C2×#610612yes—
587C2×C4#41×D1311yescharacteristic
588C2×C4#41×D1311yescharacteristic
589C2×C4#41×D1311yescharacteristic
590C2×C4#41×D1311yescharacteristic
591C2×C4#8825611yescharacteristic
592C2×C4#8825711yescharacteristic
593C8—262no—
594C8—521no—
595C8—521no—
596C8—521no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—522no—
605C22—522no—
606C22—522no—
607C22—1041no—
608C22—1041no—
609C22—1041no—
610C22—1041no—
611C22C22×#610611yescharacteristic
612C22#1171952711yescharacteristic
613C22#1171952911yescharacteristic
614C22#1171953311yescharacteristic
615C22#1171953411yescharacteristic
616C22#1171954011yescharacteristic
617C22#1171954111yescharacteristic
618C4—22no—
619C4—22no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—81no—
625C4—81no—
626C4—81no—
627C4—522no—
628C4—522no—
629C4—1041no—
630C4#1171940711yescharacteristic
631C4#1171941111yescharacteristic
632C4#1171941211yescharacteristic
633C4#1171941411yescharacteristic
634C2—42no—
635C2—1042no—
636C2#1311886811yescharacteristic
637C2#1312484011yescharacteristic
638C2#1312502911yescharacteristic
639C2#1312665411yescharacteristic
640C2#1312701611yescharacteristic
641C2#1312718711yescharacteristic
642C2#1312743611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2497C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenter#2497D13
hypocenterC13#27032
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2497

Complements

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

NH ≅ G/Ntype
2. #13116240C2semidirect
3. #13116207C2semidirect
6. #13115597C2semidirect
7. #13115561C2semidirect
8. #13115444C2semidirect
9. #13115418C2semidirect
10. #13115414C2semidirect
11. #13115096C2semidirect
12. #13115028C2semidirect
13. #13114920C2semidirect
14. C4×#88049C2semidirect
15. C13×#2497C2semidirect
204. #2497D13semidirect
524. C13#27032semidirect

Maximal subgroups

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

subgroupindex
#131178502
#131162402
#131162072
#131160252
#131155972
#131155612
#131154442
#131154182
#131154142
#131150962
#131150282
#131149202
C4×#880492
C13×#24972
#2703213