Finite Group Databasebeta

← #15935692

Subgroups — #15935692

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#13117872C211yesmaximal, characteristic
2#13116250C211yesmaximal, characteristic, complemented
3#13116221C211yesmaximal, characteristic, complemented
4#13116025C211yesmaximal, characteristic
5#13116018C211yesmaximal, characteristic
6#13115602C211yesmaximal, characteristic, complemented
7#13115566C211yesmaximal, characteristic, complemented
8#13115444C211yesmaximal, characteristic, complemented
9#13115421C211yesmaximal, characteristic, complemented
10#13115418C211yesmaximal, characteristic, complemented
11#13115096C211yesmaximal, characteristic, complemented
12#13115033C211yesmaximal, characteristic, complemented
13#13114928C211yesmaximal, characteristic, complemented
14C4×#88049C211yesmaximal, characteristic, complemented
15C13×#2495C211yesmaximal, characteristic, complemented
16C2×#88184C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C2×C4×D52C2211yescharacteristic
19C13×#400—21no—
20C13×#397—21no—
21C13×#389C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#388—21no—
24C13×#383—21no—
25C13×#382C2211yescharacteristic
26C13×#380C2211yescharacteristic
27C13×#380C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×#88049C2211yescharacteristic
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40#11718618—21no—
41#11718617—21no—
42#11718600C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44#11718589C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47#11718330—21no—
48#11718327—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—
61C22×D52C2311yescharacteristic
62C22×C4×D13—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—21no—
71C2×C13×C22⋊C4D411yescharacteristic
72C2×C13×C22⋊C4D411yescharacteristic
73C2×C42×C13—21no—
74C2×C42×C13C2311yescharacteristic
75C2×C42×C13C2311yescharacteristic
76C2×C22⋊Dic13—21no—
77#88184—22no—
78#88184—22no—
79C2×#6103—21no—
80C2×#6103—21no—
81C2×#6103—21no—
82C2×#6103—21no—
83#88180—22no—
84#88180—41no—
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×#6101—21no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13—21no—
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C4×D52—22no—
96C4×D52—41no—
97C13×#95—21no—
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95D411yescharacteristic
105C13×#95D411yescharacteristic
106#88071—21no—
107#88071—21no—
108C22⋊#1055—22no—
109C22⋊#1055—41no—
110#88049—22no—
111#88049—22no—
112#88049—22no—
113#88049—41no—
114#88048—22no—
115#88048—22no—
116#88047—22no—
117#88047—41no—
118C4⋊#1055—22no—
119C4×#1055—41no—
120#27038—131nomaximal, Sylow
121C24×C13C2×D411yescharacteristic
122C23×D13—21no—
123C22×C4×C13—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×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2411yescharacteristic
139C2×C22⋊D13—24no—
140C2×C22⋊D13—81no—
141C2×C22⋊D13—81no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C2×D52—21no—
146C2×D52—21no—
147C2×D52—21no—
148C2×D52—21no—
149C2×D52—21no—
150C2×D52#4112yes—
151C2×C4×D13—42no—
152C2×C4×D13—42no—
153C2×C4×D13—81no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—81no—
163C13×C4⋊C4—81no—
164C13×C22⋊C4—22no—
165C13×C22⋊C4—41no—
166C13×C22⋊C4—42no—
167C13×C22⋊C4—81no—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—42no—
173C22⋊Dic13—42no—
174#6103—24no—
175#6103—42no—
176#6103—42no—
177#6103—81no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13#4112yes—
183C4⋊Dic13#4112yes—
184#6101—81no—
185C4×Dic13—42no—
186C4×Dic13—81no—
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#2495D1311yescharacteristic, complemented
200#2363—131no—
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—21no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13—21no—
218C23×C13—21no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13C22×D411yescharacteristic
222C22×D13—22no—
223C22×D13—41no—
224C22×D13—41no—
225C22×D13—41no—
226C22×D13—41no—
227C22×D13—41no—
228C22×D13—41no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
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—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
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#13512yes—
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13C2×#4111yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13H(5,𝔽2)11yescharacteristic
265C2×C4×C132−1+411yescharacteristic
266C22⋊D13—84no—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276D52—22no—
277D52—22no—
278D52—41no—
279D52—41no—
280C4×D13—84no—
281#1055—22no—
282#1055—41no—
283#1055—41no—
284#1055—41no—
285C2×#121—131no—
286C2×C4×D4—131no—
287C2×#117—131no—
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—21no—
301#397—21no—
302#390—131no—
303#390—261no—
304#389—131no—
305#389C2×D1311yescharacteristic
306#389C2×D1311yescharacteristic
307#388—21no—
308#388—261no—
309#386—261no—
310#383—21no—
311#382C2×D1311yescharacteristic
312#380C2×D1311yescharacteristic
313#380C2×D1311yescharacteristic
314C4×C4⋊C4—131no—
315C4×C4⋊C4C2×D1311yescharacteristic
316C4×C22⋊C4—261no—
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—41no—
332C22×C13—41no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13#52511yescharacteristic
336C22×C13#54611yescharacteristic
337C22×C13#54711yescharacteristic
338C22×C13C2×#13511yescharacteristic
339C22×C13#57511yescharacteristic
340C22×C13#57611yescharacteristic
341C22×C13#57711yescharacteristic
342C2×D13—42no—
343C2×D13—42no—
344C2×D13—42no—
345C2×D13—81no—
346C2×D13—81no—
347C2×D13—81no—
348C2×D13—81no—
349C4×C13—22no—
350C4×C13—41no—
351C4×C13—41no—
352C4×C13—41no—
353C4×C13—41no—
354C4×C13—81no—
355C4×C13—81no—
356C4×C13—81no—
357C4×C13—81no—
358C4×C13#52911yescharacteristic
359C4×C13#53911yescharacteristic
360C4×C13#55311yescharacteristic
361C4×C13#55611yescharacteristic
362Dic13—42no—
363Dic13—42no—
364Dic13—81no—
365C22×D4—131no—
366C22×D4—261no—
367C23×C4—261no—
368C23×C4C22×D1311yescharacteristic
369C22×C8—131no—
370C22×C8—131no—
371C22×C8—131no—
372C22×C8—131no—
373#121—262no—
374#121—262no—
375C4×D4—262no—
376C4×D4—521no—
377#117—262no—
378#117—521no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4C22×D1311yescharacteristic
386C2×C4⋊C4C22×D1311yescharacteristic
387C2×C4⋊C4C22×D1311yescharacteristic
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—261no—
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C22⋊C4—261no—
395C2×C22⋊C4—261no—
396C2×C22⋊C4C22⋊D1311yescharacteristic
397C2×C22⋊C4C22⋊D1311yescharacteristic
398C2×C42—21no—
399C2×C42—261no—
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—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—261no—
423#95—261no—
424#95C22⋊D1311yescharacteristic
425#95C22⋊D1311yescharacteristic
426C2×C13—81no—
427C2×C13#246611yescharacteristic
428C2×C13#310211yescharacteristic
429C2×C13#311811yescharacteristic
430C2×C13#329611yescharacteristic
431C2×C13#330911yescharacteristic
432C2×C13#334111yescharacteristic
433C2×C13#335111yescharacteristic
434D13—82no—
435C24—261no—
436C24C2×C22⋊D1311yescharacteristic
437C2×D4—132no—
438C2×D4—264no—
439C2×D4—261no—
440C2×D4—261no—
441C2×D4—261no—
442C2×D4—261no—
443C2×D4—261no—
444C2×D4—1041no—
445C2×D4—1041no—
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—21no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—522no—
460C22×C4—522no—
461C22×C4—1041no—
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—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—81no—
489C4⋊C4—81no—
490C4⋊C4—132no—
491C4⋊C4—132no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—1041no—
497C22⋊C4—22no—
498C22⋊C4—41no—
499C22⋊C4—42no—
500C22⋊C4—81no—
501C22⋊C4—264no—
502C22⋊C4—522no—
503C22⋊C4—522no—
504C22⋊C4—522no—
505C22⋊C4—1041no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—42no—
511C42—522no—
512C42—1041no—
513C13#2703811yescharacteristic, complemented, Sylow
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—262no—
522C23—521no—
523C23—521no—
524C23—521no—
525C23—521no—
526C23—521no—
527C23—521no—
528C23C22×C22⋊D1311yescharacteristic
529D4—262no—
530D4—262no—
531D4—521no—
532D4—521no—
533D4—1044no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
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—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—262no—
565C2×C4—262no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—1044no—
574C2×C4#8820412yes—
575C2×C4#41×D1311yescharacteristic
576C2×C4#41×D1311yescharacteristic
577C2×C4#41×D1311yescharacteristic
578C2×C4#41×D1311yescharacteristic
579C2×C4#8825611yescharacteristic
580C2×C4#8825711yescharacteristic
581C8—262no—
582C8—521no—
583C8—521no—
584C8—521no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—522no—
593C22—522no—
594C22—522no—
595C22—1041no—
596C22—1041no—
597C22—1041no—
598C22—1041no—
599C22C2×#8820411yescharacteristic
600C22#1171952711yescharacteristic
601C22#1171952911yescharacteristic
602C22#1171953311yescharacteristic
603C22#1171953411yescharacteristic
604C22#1171954011yescharacteristic
605C22#1171954211yescharacteristic
606C4—22no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4—522no—
616C4—522no—
617C4—1041no—
618C4#1171940711yescharacteristic
619C4#1171941111yescharacteristic
620C4#1171941211yescharacteristic
621C4#1171941411yescharacteristic
622C2—81no—
623C2—1042no—
624C2#1311886811yescharacteristic
625C2#1312484811yescharacteristic
626C2#1312501411yescharacteristic
627C2#1312666511yescharacteristic
628C2#1312683611yescharacteristic
629C2#1312725411yescharacteristic
630C2#1312739611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2495C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenter#2495D13
hypocenterC13#27038
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2495

Complements

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

NH ≅ G/Ntype
2. #13116250C2semidirect
3. #13116221C2semidirect
6. #13115602C2semidirect
7. #13115566C2semidirect
8. #13115444C2semidirect
9. #13115421C2semidirect
10. #13115418C2semidirect
11. #13115096C2semidirect
12. #13115033C2semidirect
13. #13114928C2semidirect
14. C4×#88049C2semidirect
15. C13×#2495C2semidirect
199. #2495D13semidirect
513. C13#27038semidirect

Maximal subgroups

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

subgroupindex
#131178722
#131162502
#131162212
#131160252
#131160182
#131156022
#131155662
#131154442
#131154212
#131154182
#131150962
#131150332
#131149282
C4×#880492
C13×#24952
#2703813