Finite Group Databasebeta

← #15925714

Subgroups — #15925714

Order 3328.

820 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
1C2×#11718682C211yesmaximal, characteristic, complemented
2C2×#11718625C211yesmaximal, characteristic
3#13118527C211yesmaximal, characteristic
4#13116384C211yesmaximal, characteristic, complemented
5#13116338C211yesmaximal, characteristic, complemented
6#13116231C211yesmaximal, characteristic, complemented
7#13116164C211yesmaximal, characteristic, complemented
8#13115604C211yesmaximal, characteristic, complemented
9#13115407C211yesmaximal, characteristic, complemented
10#13115270C211yesmaximal, characteristic
11#13115149C211yesmaximal, characteristic
12#13115104C211yesmaximal, characteristic, complemented
13#13115024C211yesmaximal, characteristic
14#13115021C211yesmaximal, characteristic
15C13×#2360C211yesmaximal, characteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C22×#6099C2211yescharacteristic
21C2×#88123C2211yescharacteristic
22C13×#391C2211yescharacteristic
23C13×#389—21no—
24C13×#389C2211yescharacteristic
25C13×#387—21no—
26C13×#385—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C22⋊C4—21no—
29C4×C13×C22⋊C4C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34#11718873C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36#11718682—24no—
37#11718625—24no—
38C2×#88048C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718609—21no—
45#11718608—21no—
46#11718597C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51#11718316—21no—
52#11718307—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C23×C4×C13C2311yescharacteristic
64C22×Dic26—21no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8Q814yescomplemented
67C4×Q8×C13—22no—
68C4×Q8×C13—41no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—41no—
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4D411yescharacteristic
80C2×C13×C22⋊C4D411yescharacteristic
81C2×C42×C13—21no—
82C2×C42×C13—21no—
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C22⋊Dic13—21no—
86C2×C22⋊Dic13—21no—
87#88180—22no—
88#88180—41no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×#6101—21no—
95C2×#6101—21no—
96C2×C4×Dic13—21no—
97C2×#6099—22no—
98C2×#6099—22no—
99C2×#6099—22no—
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104#88123—22no—
105#88123—41no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95D411yescharacteristic
111C13×#95D411yescharacteristic
112#88075—22no—
113#88075—22no—
114#88075—22no—
115#88075—41no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121C22⋊#1055—22no—
122#88048—22no—
123#88048—22no—
124#88047—22no—
125#88047—22no—
126#88047—41no—
127#88047D414yes—
128C4⋊#1055—22no—
129C4⋊#1055—22no—
130#26358—131nomaximal, Sylow
131C24×C13C2×D411yescharacteristic
132C2×Q8×C13—21no—
133C2×Q8×C13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13C2×Q812yes—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—42no—
147C22×C4×C13—42no—
148C22×C4×C13—81no—
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×Q812yes—
155C22×C4×C13#4112yes—
156C22×C4×C13C2411yescharacteristic
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C2×Dic26—42no—
162C2×Dic26—42no—
163C2×Dic26—81no—
164C13×C4⋊C4—24no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—42no—
170C13×C4⋊C4—42no—
171C13×C4⋊C4—81no—
172C13×C4⋊C4C2×D412yes—
173C13×C4⋊C4C2×Q812yes—
174C13×C22⋊C4—24no—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—41no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—42no—
182C42×C13—81no—
183C22⋊Dic13—42no—
184C22⋊Dic13—81no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—42no—
193C4⋊Dic13C2×D412yes—
194#6101—42no—
195#6101—81no—
196C4×Dic13—42no—
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×#477—131no—
211C2×#428—131no—
212#2439—131no—
213#2360D1311yescharacteristic
214#2097—131no—
215#2088—131no—
216#2068—131no—
217#2057—131no—
218#1949—131no—
219#1918—131no—
220#1894—131no—
221#1873—131no—
222#1865—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
233Q8×C13—22no—
234Q8×C13—22no—
235Q8×C13—41no—
236Q8×C13—41no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—21no—
248C2×C4×C13—22no—
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—41no—
266C2×C4×C13—84no—
267C2×C4×C13C22⋊Q812yes—
268C2×C4×C13#13712yes—
269C2×C4×C13C22×D411yescharacteristic
270C2×C4×C13C22×Q811yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13H(5,𝔽2)11yescharacteristic
274C2×C4×C132−1+411yescharacteristic
275C2×Dic13—22no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287Dic26—84no—
288#1055—22no—
289#1055—22no—
290#1055—41no—
291#1055—41no—
292C22×M16—131no—
293C2×C4⋊Q8—131no—
294C2×C22⋊Q8C2×D1311yescharacteristic
295C2×C4×Q8C2×D1311yescharacteristic
296C2×#117—131no—
297C22×C4⋊C4C2×D1311yescharacteristic
298#477—264no—
299#428—264no—
300C2×#107—131no—
301C2×#107—131no—
302C2×#107—131no—
303C2×#107—131no—
304C2×#106—131no—
305C2×#106—131no—
306C2×C4⋊C8—131no—
307C2×C4⋊C8—131no—
308C2×#103—131no—
309C2×#103—131no—
310C2×#103—131no—
311C2×#103—131no—
312C2×C22⋊C8—131no—
313#396—261no—
314#393—261no—
315#391—261no—
316#391C2×D1311yescharacteristic
317#389—21no—
318#389—131no—
319#389—131no—
320#389C2×D1311yescharacteristic
321#387—21no—
322#387—261no—
323#385—21no—
324#382—131no—
325#380—131no—
326C4×C4⋊C4C2×D1311yescharacteristic
327C4×C22⋊C4—21no—
328C4×C22⋊C4C2×D1311yescharacteristic
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#340—131no—
334#340—131no—
335#336—131no—
336#336—131no—
337C22×C13—22no—
338C22×C13—22no—
339C22×C13—22no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13C2×C22⋊Q811yescharacteristic
345C22×C13D4211yescharacteristic
346C22×C13#54711yescharacteristic
347C22×C13C2×#13711yescharacteristic
348C22×C13#57511yescharacteristic
349C22×C13#57611yescharacteristic
350C22×C13#57811yescharacteristic
351C4×C13—22no—
352C4×C13—22no—
353C4×C13—42no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13—42no—
357C4×C13—41no—
358C4×C13—42no—
359C4×C13—81no—
360C4×C13#52511yescharacteristic
361C4×C13#53911yescharacteristic
362C4×C13D4×Q811yescharacteristic
363C4×C13#55411yescharacteristic
364Dic13—42no—
365Dic13—81no—
366Dic13—81no—
367Dic13—81no—
368C22×Q8—261no—
369C22×Q8C22×D1311yescharacteristic
370C23×C4—21no—
371C23×C4C22×D1311yescharacteristic
372C2×M16—262no—
373C2×M16—262no—
374C2×M16—262no—
375C22×C8—131no—
376C22×C8—131no—
377C22×C8—131no—
378C22×C8—131no—
379C4⋊Q8—262no—
380C4⋊Q8—521no—
381C22⋊Q8—22no—
382C22⋊Q8Dic2614yescomplemented
383C4×Q8—22no—
384C4×Q8—41no—
385#117—262no—
386#117—521no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—41no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4—131no—
396C2×C4⋊C4—131no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4C22×D1311yescharacteristic
401C2×C4⋊C4C22×D1311yescharacteristic
402C2×C4⋊C4C22×D1311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—261no—
405C2×C22⋊C4—261no—
406C2×C22⋊C4C22⋊D1311yescharacteristic
407C2×C22⋊C4C22⋊D1311yescharacteristic
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—261no—
411C2×C42C22×D1311yescharacteristic
412C2×C42C22×D1311yescharacteristic
413#107—134no—
414#107—262no—
415#107—262no—
416#107—521no—
417#106—262no—
418#106—262no—
419C4⋊C8—262no—
420C4⋊C8—262no—
421#103—262no—
422#103—262no—
423#103—262no—
424#103—521no—
425C22⋊C8—262no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—261no—
431#95—261no—
432#95—261no—
433#95—261no—
434#95—261no—
435#95C22⋊D1311yescharacteristic
436#95C22⋊D1311yescharacteristic
437C2×C13—42no—
438C2×C13#244911yescharacteristic
439C2×C13#307811yescharacteristic
440C2×C13#308311yescharacteristic
441C2×C13#327011yescharacteristic
442C2×C13#327311yescharacteristic
443C2×C13#334911yescharacteristic
444C2×C13#335711yescharacteristic
445C24C2×C22⋊D1311yescharacteristic
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—522no—
452C2×Q8—522no—
453C2×Q8—1041no—
454C2×Q8C2×Dic2612yes—
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—42no—
464C22×C4—42no—
465C22×C4—81no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4C2×Dic2612yes—
471C22×C4#612712yes—
472C22×C4C2×C22⋊D1311yescharacteristic
473C22×C4C2×C22⋊D1311yescharacteristic
474C22×C4C2×C22⋊D1311yescharacteristic
475C22×C4C2×C22⋊D1311yescharacteristic
476C22×C4C2×C22⋊D1311yescharacteristic
477C22×C4C23×D1311yescharacteristic
478M16—268no—
479C2×C8—132no—
480C2×C8—132no—
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—
490C2×C8—261no—
491C4⋊C4—24no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—81no—
499C4⋊C4—132no—
500C4⋊C4—261no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—522no—
508C4⋊C4—522no—
509C4⋊C4—1041no—
510C4⋊C4C2×Dic2612yes—
511C4⋊C4D4×D1312yes—
512C22⋊C4—24no—
513C22⋊C4—22no—
514C22⋊C4—41no—
515C22⋊C4—522no—
516C22⋊C4—1041no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—42no—
522C42—81no—
523C42—522no—
524C13#2635811yescharacteristic, complemented, Sylow
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23#8817812yes—
532C23C22×C22⋊D1311yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—41no—
536Q8—41no—
537Q8—1044no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—22no—
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—84no—
568C2×C4—262no—
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—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4#8817812yes—
581C2×C4#8819612yes—
582C2×C4C22×Dic2611yescharacteristic
583C2×C4C2×#612711yescharacteristic
584C2×C4C2×D4×D1311yescharacteristic
585C2×C4#8825111yescharacteristic
586C2×C4#41×D1311yescharacteristic
587C2×C4#8825711yescharacteristic
588C8—262no—
589C8—262no—
590C8—521no—
591C8—521no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22C2×#8817811yescharacteristic
600C22D4×C22⋊D1311yescharacteristic
601C22C2×#8819611yescharacteristic
602C22#1171952711yescharacteristic
603C22#1171952911yescharacteristic
604C22#1171954011yescharacteristic
605C22#1171954311yescharacteristic
606C4—22no—
607C4—22no—
608C4—41no—
609C4—41no—
610C4—42no—
611C4—42no—
612C4—42no—
613C4—41no—
614C4—81no—
615C4—522no—
616C4—1041no—
617C4—1041no—
618C4—1041no—
619C4D4×Dic2611yescharacteristic
620C4#1171924411yescharacteristic
621C4#1171925211yescharacteristic
622C4#1171926911yescharacteristic
623C2—42no—
624C2#1311863911yescharacteristic
625C2#1312464111yescharacteristic
626C2#1312468711yescharacteristic
627C2#1312640711yescharacteristic
628C2#1312644311yescharacteristic
629C2#1312736611yescharacteristic
630C2#1312746211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2360C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2360D13
hypocenterC13#26358
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
1. C2×#11718682C2semidirect
4. #13116384C2semidirect
5. #13116338C2semidirect
6. #13116231C2semidirect
7. #13116164C2semidirect
8. #13115604C2semidirect
9. #13115407C2semidirect
12. #13115104C2semidirect
66. C13×C22⋊Q8Q8semidirect
382. C22⋊Q8Dic26semidirect
524. C13#26358semidirect

Maximal subgroups

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

subgroupindex
C2×#117186822
C2×#117186252
#131185272
#131163842
#131163382
#131162312
#131161642
#131156042
#131154072
#131152702
#131151492
#131151042
#131150242
#131150212
C13×#23602
#2635813