Finite Group Databasebeta

← #15925776

Subgroups — #15925776

Order 3328.

812 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718724C211yesmaximal, characteristic, complemented
2C2×#11718656C211yesmaximal, characteristic
3#13117839C211yesmaximal, characteristic
4#13116375C211yesmaximal, characteristic, complemented
5#13116327C211yesmaximal, characteristic, complemented
6#13116214C211yesmaximal, characteristic, complemented
7#13116171C211yesmaximal, characteristic, complemented
8#13115592C211yesmaximal, characteristic, complemented
9#13115411C211yesmaximal, characteristic, complemented
10#13115267C211yesmaximal, characteristic
11#13115148C211yesmaximal, characteristic
12#13115089C211yesmaximal, characteristic, complemented
13#13115023C211yesmaximal, characteristic
14#13115021C211yesmaximal, characteristic
15C13×#2441C211yesmaximal, characteristic
16C2×C13×#125C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C2×#88178C2211yescharacteristic
20C22×#6099C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C13×#399—21no—
23C13×#396—21no—
24C13×#389—21no—
25C13×#389C2211yescharacteristic
26C13×#389C2211yescharacteristic
27C13×#387—21no—
28C13×#384C2211yescharacteristic
29C13×#380C2211yescharacteristic
30C4×C13×C22⋊C4C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32#11718724—24no—
33#11718656—24no—
34C2×#88050C2211yescharacteristic
35C2×#88050C2211yescharacteristic
36C2×#88050C2211yescharacteristic
37C2×#88050C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718607—21no—
45C22⋊C4×Dic13—21no—
46C4×C4⋊Dic13C2211yescharacteristic
47#11718590C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51#11718316—21no—
52#11718308—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×Dic13—21no—
63C22×Dic26C2311yescharacteristic
64C13×#125—22no—
65C13×#125—41no—
66C13×#117—22no—
67C13×#117—41no—
68C2×C13×C4⋊C4—21no—
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⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4D411yescharacteristic
81C2×C13×C22⋊C4D411yescharacteristic
82C2×C42×C13—21no—
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C22⋊Dic13—21no—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—41no—
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92#88178—22no—
93#88178Q814yes—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C2×#6099—22no—
100C2×#6099—22no—
101C2×#6099—22no—
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C4×Dic26—22no—
107C4×Dic26—41no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95D411yescharacteristic
112C13×#95D411yescharacteristic
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117C22⋊#1055—22no—
118#88050—22no—
119#88050—22no—
120#88050—22no—
121#88050—41no—
122#88048—22no—
123#88048D414yes—
124#88047—22no—
125#88047—22no—
126#88047—22no—
127#88047—41no—
128C4⋊#1055—22no—
129C4⋊#1055—22no—
130#26362—131nomaximal, Sylow
131C24×C13C2×D411yescharacteristic
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×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×Q812yes—
146C22×C4×C13#4112yes—
147C22×C4×C13C2411yescharacteristic
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—42no—
153C22×Dic13—42no—
154C22×Dic13—81no—
155C2×Dic26—21no—
156C2×Dic26—21no—
157C2×Dic26—21no—
158C2×Dic26—21no—
159C2×Dic26—21no—
160C2×Dic26C2×Q812yes—
161C13×C4⋊C4—21no—
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—42no—
169C13×C4⋊C4—42no—
170C13×C4⋊C4—42no—
171C13×C4⋊C4—42no—
172C13×C4⋊C4—81no—
173C13×C4⋊C4—81no—
174C13×C4⋊C4C2×D412yes—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—41no—
177C13×C22⋊C4—42no—
178C13×C22⋊C4—81no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13—42no—
184C22⋊Dic13—24no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—42no—
190C4⋊Dic13C2×D412yes—
191C4⋊Dic13C2×Q812yes—
192#6101—24no—
193#6101—42no—
194#6101—81no—
195C4×Dic13—42no—
196C4×Dic13—81no—
197#6099—28no—
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×#1055—21no—
208C2×#1055C2×D412yes—
209C2×#1055#4112yes—
210C2×#479—131no—
211C2×#428—131no—
212#2441D1311yescharacteristic
213#2360—131no—
214#2095—131no—
215#2086—131no—
216#2066—131no—
217#2059—131no—
218#1947—131no—
219#1919—131no—
220#1894—131no—
221#1873—131no—
222#1863—131no—
223#1852—131no—
224#1851—131no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13C22⋊Q812yes—
232C23×C13C22×D411yescharacteristic
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—22no—
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—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×C13C22⋊Q812yes—
263C2×C4×C13#13712yes—
264C2×C4×C13C22×D411yescharacteristic
265C2×C4×C13C22×Q811yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×C4×C13H(5,𝔽2)11yescharacteristic
269C2×C4×C132−1+411yescharacteristic
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—22no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—84no—
283Dic26—22no—
284Dic26—22no—
285Dic26—41no—
286Dic26—41no—
287#1055—22no—
288#1055—22no—
289#1055—41no—
290#1055—41no—
291C22×M16—131no—
292C2×#125C2×D1311yescharacteristic
293C2×C22⋊Q8—131no—
294C2×C4×Q8—131no—
295C2×#117C2×D1311yescharacteristic
296C22×C4⋊C4—131no—
297#479—264no—
298#428—264no—
299C2×#107—131no—
300C2×#107—131no—
301C2×#107—131no—
302C2×#107—131no—
303C2×#106—131no—
304C2×#106—131no—
305C2×C4⋊C8—131no—
306C2×C4⋊C8—131no—
307C2×#103—131no—
308C2×#103—131no—
309C2×#103—131no—
310C2×#103—131no—
311C2×C22⋊C8—131no—
312#399—21no—
313#396—21no—
314#391—131no—
315#389—21no—
316#389—131no—
317#389—261no—
318#389C2×D1311yescharacteristic
319#389C2×D1311yescharacteristic
320#387—21no—
321#387—261no—
322#385—261no—
323#384C2×D1311yescharacteristic
324#380C2×D1311yescharacteristic
325C4×C4⋊C4—131no—
326C4×C22⋊C4—261no—
327C4×C22⋊C4C2×D1311yescharacteristic
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#340—131no—
334#336—131no—
335#336—131no—
336C22×C13—22no—
337C22×C13—22no—
338C22×C13—22no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13C2×C22⋊Q811yescharacteristic
344C22×C13D4211yescharacteristic
345C22×C13#54711yescharacteristic
346C22×C13C2×#13711yescharacteristic
347C22×C13#57511yescharacteristic
348C22×C13#57611yescharacteristic
349C22×C13#57811yescharacteristic
350C4×C13—22no—
351C4×C13—22no—
352C4×C13—41no—
353C4×C13—41no—
354C4×C13—41no—
355C4×C13—42no—
356C4×C13—81no—
357C4×C13—81no—
358C4×C13—81no—
359C4×C13#52511yescharacteristic
360C4×C13#53911yescharacteristic
361C4×C13D4×Q811yescharacteristic
362C4×C13#55411yescharacteristic
363Dic13—42no—
364Dic13—42no—
365Dic13—42no—
366Dic13—81no—
367C22×Q8—131no—
368C23×C4—261no—
369C23×C4C22×D1311yescharacteristic
370C2×M16—262no—
371C2×M16—262no—
372C2×M16—262no—
373C22×C8—131no—
374C22×C8—131no—
375C22×C8—131no—
376C22×C8—131no—
377#125—22no—
378#125—41no—
379C22⋊Q8—134no—
380C22⋊Q8—262no—
381C4×Q8—262no—
382C4×Q8—521no—
383#117—22no—
384#117—41no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4—262no—
395C2×C4⋊C4—261no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—521no—
400C2×C4⋊C4C22×D1311yescharacteristic
401C2×C4⋊C4C22×D1311yescharacteristic
402C2×C4⋊C4C22×D1311yescharacteristic
403C2×C4⋊C4C22×D1311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—261no—
407C2×C22⋊C4C22⋊D1311yescharacteristic
408C2×C22⋊C4C22⋊D1311yescharacteristic
409C2×C42—21no—
410C2×C42—261no—
411C2×C42—261no—
412C2×C42C22×D1311yescharacteristic
413C2×C42C22×D1311yescharacteristic
414#107—262no—
415#107—262no—
416#107—262no—
417#107—521no—
418#106—134no—
419#106—262no—
420C4⋊C8—262no—
421C4⋊C8—262no—
422#103—262no—
423#103—262no—
424#103—262no—
425#103—521no—
426C22⋊C8—262no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—261no—
431#95—261no—
432#95—261no—
433#95—261no—
434#95C22⋊D1311yescharacteristic
435#95C22⋊D1311yescharacteristic
436C2×C13—42no—
437C2×C13#244911yescharacteristic
438C2×C13#307811yescharacteristic
439C2×C13#308311yescharacteristic
440C2×C13#326811yescharacteristic
441C2×C13#327611yescharacteristic
442C2×C13#334611yescharacteristic
443C2×C13#335211yescharacteristic
444C24C2×C22⋊D1311yescharacteristic
445C2×Q8—132no—
446C2×Q8—261no—
447C2×Q8—261no—
448C2×Q8—261no—
449C2×Q8—261no—
450C2×Q8—261no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4—522no—
464C22×C4—522no—
465C22×C4—1041no—
466C22×C4Q8×D1312yes—
467C22×C4#613112yes—
468C22×C4C2×C22⋊D1311yescharacteristic
469C22×C4C2×C22⋊D1311yescharacteristic
470C22×C4C2×C22⋊D1311yescharacteristic
471C22×C4C2×C22⋊D1311yescharacteristic
472C22×C4C2×C22⋊D1311yescharacteristic
473C22×C4C23×D1311yescharacteristic
474M16—268no—
475C2×C8—132no—
476C2×C8—132no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—81no—
499C4⋊C4—81no—
500C4⋊C4—132no—
501C4⋊C4—132no—
502C4⋊C4—264no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—522no—
508C4⋊C4—522no—
509C4⋊C4—1041no—
510C4⋊C4D4×D1312yes—
511C22⋊C4—22no—
512C22⋊C4—41no—
513C22⋊C4—42no—
514C22⋊C4—81no—
515C22⋊C4—264no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—42no—
521C42—522no—
522C42—1041no—
523C13#2636211yescharacteristic, complemented, Sylow
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23#8820012yes—
531C23C22×C22⋊D1311yescharacteristic
532Q8—262no—
533Q8—262no—
534Q8—521no—
535Q8—521no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
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—41no—
565C2×C4—262no—
566C2×C4—262no—
567C2×C4—262no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—1044no—
578C2×C4#8820012yes—
579C2×C4#8820512yes—
580C2×C4C2×D4×D1311yescharacteristic
581C2×C4#8825111yescharacteristic
582C2×C4C2×Q8×D1311yescharacteristic
583C2×C4C2×#613111yescharacteristic
584C2×C4#41×D1311yescharacteristic
585C2×C4#8825711yescharacteristic
586C8—262no—
587C8—262no—
588C8—521no—
589C8—521no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22D4×C22⋊D1311yescharacteristic
598C22C2×#8820011yescharacteristic
599C22#1171952711yescharacteristic
600C22C2×#8820511yescharacteristic
601C22#1171952911yescharacteristic
602C22#1171954011yescharacteristic
603C22#1171954311yescharacteristic
604C4—22no—
605C4—22no—
606C4—41no—
607C4—42no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4—522no—
614C4—522no—
615C4—522no—
616C4—1041no—
617C4#1171933211yescharacteristic
618C4#1171933711yescharacteristic
619C4#1171934111yescharacteristic
620C4#1171935011yescharacteristic
621C2—42no—
622C2#1311864111yescharacteristic
623C2#1312463711yescharacteristic
624C2#1312468311yescharacteristic
625C2#1312637711yescharacteristic
626C2#1312647811yescharacteristic
627C2#1312732111yescharacteristic
628C2#1312740511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2441C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2441D13
hypocenterC13#26362
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2441

Complements

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

NH ≅ G/Ntype
1. C2×#11718724C2semidirect
4. #13116375C2semidirect
5. #13116327C2semidirect
6. #13116214C2semidirect
7. #13116171C2semidirect
8. #13115592C2semidirect
9. #13115411C2semidirect
12. #13115089C2semidirect
523. C13#26362semidirect

Maximal subgroups

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

subgroupindex
C2×#117187242
C2×#117186562
#131178392
#131163752
#131163272
#131162142
#131161712
#131155922
#131154112
#131152672
#131151482
#131150892
#131150232
#131150212
C13×#24412
#2636213