Finite Group Databasebeta

← #15935690

Subgroups — #15935690

Order 3328.

734 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119247C211yesmaximal, characteristic, complemented
2#13116249C211yesmaximal, characteristic, complemented
3#13116224C211yesmaximal, characteristic, complemented
4#13116022C211yesmaximal, characteristic
5#13116015C211yesmaximal, characteristic
6#13115604C211yesmaximal, characteristic, complemented
7#13115566C211yesmaximal, characteristic, complemented
8#13115444C211yesmaximal, characteristic, complemented
9#13115421C211yesmaximal, characteristic, complemented
10#13115418C211yesmaximal, characteristic, complemented
11#13115097C211yesmaximal, characteristic, complemented
12#13115035C211yesmaximal, characteristic, complemented
13#13114931C211yesmaximal, characteristic, complemented
14C4×#88072C211yesmaximal, characteristic, complemented
15C13×#2363C211yesmaximal, characteristic
16C2×C13×#121C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C13×#390—21no—
20C13×#390C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#388—21no—
23C13×#386—21no—
24C4×C13×C4⋊C4C2211yescharacteristic
25C4×C13×C22⋊C4—21no—
26C4×C13×C22⋊C4C2211yescharacteristic
27C2×#88072C2211yescharacteristic
28C2×#88072C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31#11718873C2211yescharacteristic
32#11718873C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39#11718613—21no—
40#11718605—21no—
41#11718597C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43#11718589C2211yescharacteristic
44#11718589C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47#11718319—21no—
48#11718312—21no—
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D4×C13—21no—
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C23×C4×C13C2311yescharacteristic
63C13×#121—22no—
64C13×#121—22no—
65C4×D4×C13—22no—
66C4×D4×C13—41no—
67C13×#117—22no—
68C13×#117—41no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4D411yescharacteristic
79C2×C13×C22⋊C4D411yescharacteristic
80C2×C42×C13—21no—
81C2×C42×C13—21no—
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×C22⋊Dic13—21no—
85C2×C22⋊Dic13—21no—
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×#6101—21no—
91C2×#6101—21no—
92C2×C4×Dic13—21no—
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C13×#95—21no—
98C13×#95—21no—
99C13×#95D411yescharacteristic
100C13×#95D411yescharacteristic
101#88072—22no—
102#88072—22no—
103#88072—22no—
104#88072—41no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112C22⋊#1055—22no—
113C22⋊#1055—41no—
114#88048—22no—
115#88048—22no—
116#88047—22no—
117#88047—41no—
118C4⋊#1055—22no—
119C4×#1055—41no—
120#27038—131nomaximal, Sylow
121C24×C13—21no—
122C24×C13C2×D411yescharacteristic
123C2×D4×C13—24no—
124C2×D4×C13—21no—
125C2×D4×C13—21no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—81no—
130C2×D4×C13—81no—
131C2×D4×C13#4112yes—
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×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—42no—
142C22×C4×C13—42no—
143C22×C4×C13—81no—
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2411yescharacteristic
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—81no—
159C13×C4⋊C4#4112yes—
160C13×C4⋊C4#4112yes—
161C13×C22⋊C4—24no—
162C13×C22⋊C4—22no—
163C13×C22⋊C4—41no—
164C13×C22⋊C4—42no—
165C13×C22⋊C4—42no—
166C13×C22⋊C4—42no—
167C13×C22⋊C4—81no—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—42no—
173C42×C13—81no—
174C22⋊Dic13—42no—
175C22⋊Dic13—81no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184#6101—81no—
185#6101—81no—
186C4×Dic13—42no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055#4112yes—
199#2495—131no—
200#2363D1311yescharacteristic
201#2073—131no—
202#2067—131no—
203#2034—131no—
204#2033—131no—
205#1949—131no—
206#1942—131no—
207#1923—131no—
208#1920—131no—
209#1920—131no—
210#1864—131no—
211#1854—131no—
212#1825—131no—
213C4×#102—131no—
214C23×C13—22no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13—21no—
218C23×C13—21no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—41no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13—41no—
228C23×C13C22×D411yescharacteristic
229D4×C13—22no—
230D4×C13—22no—
231D4×C13—41no—
232D4×C13—41no—
233D4×C13—84no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—22no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—22no—
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—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—84no—
262C2×C4×C13#13512yes—
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13C2×#4111yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13H(5,𝔽2)11yescharacteristic
268C2×C4×C132−1+411yescharacteristic
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281#1055—22no—
282#1055—41no—
283#1055—41no—
284#1055—41no—
285C2×#121C2×D1311yescharacteristic
286C2×C4×D4C2×D1311yescharacteristic
287C2×#117C2×D1311yescharacteristic
288C2×#107—131no—
289C2×#107—131no—
290C2×#106—131no—
291C2×#106—131no—
292C2×C4⋊C8—131no—
293C2×#102—131no—
294C2×#102—131no—
295C2×#102—131no—
296C2×#102—131no—
297C2×C22⋊C8—131no—
298C2×C22⋊C8—131no—
299C2×C4×C8—131no—
300#400—261no—
301#397—261no—
302#390—21no—
303#390C2×D1311yescharacteristic
304#389—131no—
305#389—131no—
306#389C2×D1311yescharacteristic
307#388—21no—
308#388—261no—
309#386—21no—
310#383—261no—
311#382—131no—
312#380—131no—
313#380—131no—
314C4×C4⋊C4—131no—
315C4×C4⋊C4C2×D1311yescharacteristic
316C4×C22⋊C4—21no—
317C4×C22⋊C4C2×D1311yescharacteristic
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#336—131no—
327#336—131no—
328C22×C13—41no—
329C22×C13—41no—
330C22×C13—41no—
331C22×C13—42no—
332C22×C13—41no—
333C22×C13—42no—
334C22×C13—41no—
335C22×C13—42no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—81no—
339C22×C13—81no—
340C22×C13—81no—
341C22×C13—81no—
342C22×C13#52511yescharacteristic
343C22×C13#54611yescharacteristic
344C22×C13#54711yescharacteristic
345C22×C13C2×#13511yescharacteristic
346C22×C13#57511yescharacteristic
347C22×C13#57611yescharacteristic
348C22×C13#57711yescharacteristic
349C4×C13—22no—
350C4×C13—41no—
351C4×C13—41no—
352C4×C13—42no—
353C4×C13—41no—
354C4×C13—42no—
355C4×C13—41no—
356C4×C13—81no—
357C4×C13#52911yescharacteristic
358C4×C13#53911yescharacteristic
359C4×C13#55311yescharacteristic
360C4×C13#55611yescharacteristic
361Dic13—81no—
362Dic13—81no—
363Dic13—81no—
364Dic13—81no—
365C22×D4—21no—
366C22×D4C22×D1311yescharacteristic
367C23×C4—21no—
368C23×C4C22×D1311yescharacteristic
369C22×C8—131no—
370C22×C8—131no—
371C22×C8—131no—
372C22×C8—131no—
373#121—22no—
374#121—22no—
375C4×D4—22no—
376C4×D4—41no—
377#117—22no—
378#117—41no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4C22×D1311yescharacteristic
387C2×C4⋊C4C22×D1311yescharacteristic
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—261no—
395C2×C22⋊C4—261no—
396C2×C22⋊C4C22⋊D1311yescharacteristic
397C2×C22⋊C4C22⋊D1311yescharacteristic
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—261no—
401C2×C42C22×D1311yescharacteristic
402C2×C42C22×D1311yescharacteristic
403#107—262no—
404#107—521no—
405#106—262no—
406#106—262no—
407C4⋊C8—262no—
408#102—262no—
409#102—262no—
410#102—262no—
411#102—521no—
412C22⋊C8—262no—
413C22⋊C8—521no—
414C4×C8—521no—
415#95—21no—
416#95—21no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95—261no—
424#95C22⋊D1311yescharacteristic
425#95C22⋊D1311yescharacteristic
426C2×C13—81no—
427C2×C13—82no—
428C2×C13#246611yescharacteristic
429C2×C13#310211yescharacteristic
430C2×C13#311811yescharacteristic
431C2×C13#329611yescharacteristic
432C2×C13#330911yescharacteristic
433C2×C13#334111yescharacteristic
434C2×C13#335111yescharacteristic
435C24—21no—
436C24C2×C22⋊D1311yescharacteristic
437C2×D4—24no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—81no—
444C2×D4—81no—
445C2×D4#612712yes—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—81no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4C2×C22⋊D1311yescharacteristic
463C22×C4C2×C22⋊D1311yescharacteristic
464C22×C4C2×C22⋊D1311yescharacteristic
465C22×C4C2×C22⋊D1311yescharacteristic
466C22×C4C2×C22⋊D1311yescharacteristic
467C22×C4C23×D1311yescharacteristic
468C2×C8—132no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—81no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—1041no—
494C4⋊C4—1041no—
495C4⋊C4#612712yes—
496C4⋊C4#612912yes—
497C22⋊C4—24no—
498C22⋊C4—22no—
499C22⋊C4—41no—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C22⋊C4—42no—
503C22⋊C4—81no—
504C22⋊C4—522no—
505C22⋊C4—1041no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—42no—
511C42—81no—
512C42—522no—
513C13#2703811yescharacteristic, complemented, Sylow
514C23—22no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23C22×C22⋊D1311yescharacteristic
529D4—22no—
530D4—22no—
531D4—41no—
532D4—41no—
533D4—84no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—84no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4#8820412yes—
575C2×C4C2×#612711yescharacteristic
576C2×C4C2×#612711yescharacteristic
577C2×C4C2×#612911yescharacteristic
578C2×C4#8825111yescharacteristic
579C2×C4#41×D1311yescharacteristic
580C2×C4#8825711yescharacteristic
581C8—262no—
582C8—521no—
583C8—521no—
584C8—521no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—42no—
589C22—41no—
590C22—42no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—42no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22#1171949611yescharacteristic
600C22#1171951111yescharacteristic
601C22C2×#8820411yescharacteristic
602C22#1171952711yescharacteristic
603C22#1171952911yescharacteristic
604C22#1171954011yescharacteristic
605C22#1171954111yescharacteristic
606C4—22no—
607C4—42no—
608C4—41no—
609C4—41no—
610C4—42no—
611C4—41no—
612C4—41no—
613C4—81no—
614C4—1041no—
615C4—1041no—
616C4—1041no—
617C4—1041no—
618C4#1171924311yescharacteristic
619C4#1171924711yescharacteristic
620C4#1171926311yescharacteristic
621C4#1171926911yescharacteristic
622C2—81no—
623C2—82no—
624C2#1311886611yescharacteristic
625C2#1312485411yescharacteristic
626C2#1312502011yescharacteristic
627C2#1312667111yescharacteristic
628C2#1312684211yescharacteristic
629C2#1312725411yescharacteristic
630C2#1312739011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2363C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenter#2363D13
hypocenterC13#27038
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
1. #13119247C2semidirect
2. #13116249C2semidirect
3. #13116224C2semidirect
6. #13115604C2semidirect
7. #13115566C2semidirect
8. #13115444C2semidirect
9. #13115421C2semidirect
10. #13115418C2semidirect
11. #13115097C2semidirect
12. #13115035C2semidirect
13. #13114931C2semidirect
14. C4×#88072C2semidirect
513. C13#27038semidirect

Maximal subgroups

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

subgroupindex
#131192472
#131162492
#131162242
#131160222
#131160152
#131156042
#131155662
#131154442
#131154212
#131154182
#131150972
#131150352
#131149312
C4×#880722
C13×#23632
#2703813