Finite Group Databasebeta

← #15923612

Subgroups — #15923612

Order 3328.

816 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117765C211yesmaximal, characteristic
2#13116404C211yesmaximal, characteristic, complemented
3#13116272C211yesmaximal, characteristic, complemented
4#13116254C211yesmaximal, characteristic, complemented
5#13116029C211yesmaximal, characteristic, complemented
6#13115467C211yesmaximal, characteristic, complemented
7#13115411C211yesmaximal, characteristic, complemented
8#13115260C211yesmaximal, characteristic, complemented
9#13115149C211yesmaximal, characteristic, complemented
10#13115144C211yesmaximal, characteristic, complemented
11#13115129C211yesmaximal, characteristic
12#13115029C211yesmaximal, characteristic, complemented
13#13114928C211yesmaximal, characteristic, complemented
14C2×#11718121C211yesmaximal, characteristic, complemented
15C13×#2417C211yesmaximal, characteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C23×#1055C2211yescharacteristic
23C13×#398—21no—
24C13×#396—21no—
25C13×#391C2211yescharacteristic
26C13×#389C2211yescharacteristic
27C13×#386—21no—
28C13×#380—21no—
29C13×#380C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34#11718881—21no—
35#11718873C2211yescharacteristic
36#11718873C2211yescharacteristic
37C2×C22⋊#1055C2211yescharacteristic
38C2×C22⋊#1055C2211yescharacteristic
39C2×C22⋊#1055C2211yescharacteristic
40#11718642—21no—
41C2×#88048C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43#11718612—21no—
44C22⋊C4×Dic13—21no—
45#11718597C2211yescharacteristic
46C4×C4⋊Dic13C2211yescharacteristic
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C22×D4×C13D411yescharacteristic
61C23×C4×C13—21no—
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×Dic13—21no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—22no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8—41no—
69C4×D4×C13—22no—
70C4×D4×C13—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—41no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13—21no—
88C2×C22⋊Dic13—21no—
89C2×C22⋊Dic13—21no—
90#88180—22no—
91#88180—41no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13—41no—
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C2×C4×Dic13—21no—
100C2×C4×Dic13—21no—
101C22×#1055—22no—
102C22×#1055—41no—
103C22×#1055—41no—
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C13×#95—21no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95—21no—
112#88075—22no—
113#88075—41no—
114#88075—41no—
115#88075—41no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121C22⋊#1055—22no—
122C22⋊#1055—41no—
123C22⋊#1055—41no—
124#88048—22no—
125#88048—41no—
126#26206—131nomaximal, Sylow
127C24×C13C2×D411yescharacteristic
128C24×C13C2×D411yescharacteristic
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13—21no—
132C2×Q8×C13—21no—
133C2×Q8×C13—21no—
134C2×Q8×C13—21no—
135C2×D4×C13—22no—
136C2×D4×C13—22no—
137C2×D4×C13—22no—
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—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—42no—
153C22×C4×C13—42no—
154C22×C4×C13—81no—
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13#4112yes—
160C22×C4×C13#4112yes—
161C22×C4×C13C2411yescharacteristic
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—42no—
167C22×Dic13—42no—
168C22×Dic13—81no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—42no—
176C13×C4⋊C4—42no—
177C13×C4⋊C4—42no—
178C13×C4⋊C4—81no—
179C13×C4⋊C4#4112yes—
180C13×C22⋊C4—22no—
181C13×C22⋊C4—22no—
182C13×C22⋊C4—42no—
183C13×C22⋊C4—42no—
184C13×C22⋊C4—81no—
185C42×C13—21no—
186C42×C13—21no—
187C22⋊Dic13—42no—
188C22⋊Dic13—42no—
189C22⋊Dic13—81no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—42no—
198C4⋊Dic13#4112yes—
199C4×Dic13—42no—
200C4×Dic13—81no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—44no—
214#2417D1311yescharacteristic
215#2352—131no—
216#2101—131no—
217#2077—131no—
218#2074—131no—
219#2035—131no—
220#1927—131no—
221#1919—131no—
222#1892—131no—
223#1873—131no—
224#1872—131no—
225#1869—131no—
226#1853—131no—
227#1825—131no—
228C2×#340—131no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13#12312yes—
241C23×C13#13512yes—
242C23×C13#13712yes—
243C23×C13C22×D411yescharacteristic
244Q8×C13—41no—
245Q8×C13—41no—
246Q8×C13—41no—
247Q8×C13—41no—
248D4×C13—44no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—22no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13—84no—
281C2×C4×C13#12312yes—
282C2×C4×C13C2×#4111yescharacteristic
283C2×C4×C13C2×#4111yescharacteristic
284C2×C4×C13C2×#4111yescharacteristic
285C2×C4×C13C2×#4111yescharacteristic
286C2×C4×C13H(5,𝔽2)11yescharacteristic
287C2×C4×C13H(5,𝔽2)11yescharacteristic
288C2×Dic13—22no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—84no—
301#1055—41no—
302#1055—41no—
303#1055—41no—
304#1055—41no—
305C23×C8—131no—
306C2×C22⋊Q8C2×D1311yescharacteristic
307C2×C22⋊Q8C2×D1311yescharacteristic
308C2×C4×D4C2×D1311yescharacteristic
309C2×#117—131no—
310C22×C4⋊C4—131no—
311C22×C4⋊C4C2×D1311yescharacteristic
312C2×#106—131no—
313C2×#106—131no—
314C2×#103—131no—
315C2×#103—131no—
316C2×#103—131no—
317C2×#103—131no—
318C2×C22⋊C8—131no—
319C2×C22⋊C8—131no—
320C2×C22⋊C8—131no—
321#398—21no—
322#396—21no—
323#391C2×D1311yescharacteristic
324#389C2×D1311yescharacteristic
325#388—261no—
326#387—261no—
327#386—21no—
328#386—261no—
329#382—131no—
330#380—21no—
331#380—131no—
332#380—131no—
333#380C2×D1311yescharacteristic
334C4×C4⋊C4—131no—
335C4×C22⋊C4—261no—
336#340—131no—
337#340—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#340—131no—
342#340—131no—
343#340—131no—
344#340—131no—
345#340—131no—
346#336—131no—
347#336—131no—
348C22×C13—22no—
349C22×C13—22no—
350C22×C13—22no—
351C22×C13—22no—
352C22×C13—22no—
353C22×C13—22no—
354C22×C13—41no—
355C22×C13—41no—
356C22×C13—41no—
357C22×C13—41no—
358C22×C13—41no—
359C22×C13—41no—
360C22×C13—41no—
361C22×C13#48514yes—
362C22×C13C2×#12311yescharacteristic
363C22×C13#54611yescharacteristic
364C22×C13#54611yescharacteristic
365C22×C13C2×#13511yescharacteristic
366C22×C13C2×#13711yescharacteristic
367C22×C13#57711yescharacteristic
368C22×C13#57711yescharacteristic
369C4×C13—22no—
370C4×C13—41no—
371C4×C13—41no—
372C4×C13—41no—
373C4×C13—42no—
374C4×C13—81no—
375C4×C13—81no—
376C4×C13—81no—
377C4×C13#52911yescharacteristic
378C4×C13#53811yescharacteristic
379C4×C13#55311yescharacteristic
380C4×C13#55311yescharacteristic
381Dic13—42no—
382Dic13—81no—
383Dic13—81no—
384Dic13—81no—
385C22×Q8C22×D1311yescharacteristic
386C22×D4C22⋊D1311yescharacteristic
387C23×C4—21no—
388C23×C4—261no—
389C23×C4C22×D1311yescharacteristic
390C23×C4C22×D1311yescharacteristic
391C22×C8—131no—
392C22×C8—131no—
393C22×C8—131no—
394C22×C8—131no—
395C22×C8—262no—
396C22×C8—521no—
397C22×C8—521no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—41no—
402C4×D4—22no—
403C4×D4—22no—
404#117—262no—
405#117—521no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—41no—
412C2×C4⋊C4—131no—
413C2×C4⋊C4—131no—
414C2×C4⋊C4—131no—
415C2×C4⋊C4—131no—
416C2×C4⋊C4—262no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4—521no—
419C2×C4⋊C4C22⋊D1311yescharacteristic
420C2×C4⋊C4C22×D1311yescharacteristic
421C2×C4⋊C4C22×D1311yescharacteristic
422C2×C4⋊C4C22×D1311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—261no—
427C2×C22⋊C4—261no—
428C2×C22⋊C4—261no—
429C2×C22⋊C4C22⋊D1311yescharacteristic
430C2×C22⋊C4C22⋊D1311yescharacteristic
431C2×C42—261no—
432C2×C42—261no—
433C2×C42C22×D1311yescharacteristic
434#106—262no—
435#106—521no—
436#103—262no—
437#103—521no—
438#103—521no—
439#103—521no—
440C22⋊C8—262no—
441C22⋊C8—521no—
442C22⋊C8—521no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—261no—
448#95—261no—
449#95—261no—
450#95—261no—
451#95—261no—
452C2×C13—24no—
453C2×C13—81no—
454C2×C13#244411yescharacteristic
455C2×C13C2×#48511yescharacteristic
456C2×C13#309911yescharacteristic
457C2×C13#329611yescharacteristic
458C2×C13#329611yescharacteristic
459C2×C13#331611yescharacteristic
460C2×C13#332011yescharacteristic
461C24C2×C22⋊D1311yescharacteristic
462C24C2×C22⋊D1311yescharacteristic
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—81no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4—522no—
494C22×C4—522no—
495C22×C4—1041no—
496C22×C4#612912yes—
497C22×C4#612912yes—
498C22×C4C2×C22⋊D1311yescharacteristic
499C22×C4C2×C22⋊D1311yescharacteristic
500C22×C4C2×C22⋊D1311yescharacteristic
501C22×C4C2×C22⋊D1311yescharacteristic
502C22×C4C23×D1311yescharacteristic
503C2×C8—261no—
504C2×C8—261no—
505C2×C8—261no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—261no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—524no—
516C4⋊C4—22no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—42no—
525C4⋊C4—81no—
526C4⋊C4—132no—
527C4⋊C4—261no—
528C4⋊C4—261no—
529C4⋊C4—261no—
530C4⋊C4—261no—
531C4⋊C4—261no—
532C4⋊C4—261no—
533C4⋊C4—261no—
534C4⋊C4—522no—
535C4⋊C4#612912yes—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—81no—
541C22⋊C4—522no—
542C22⋊C4—522no—
543C22⋊C4—1041no—
544C42—21no—
545C42—21no—
546C42—522no—
547C42—1041no—
548C13#2620611yescharacteristic, complemented, Sylow
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23#8818912yes—
561C23#8819612yes—
562C23#8820412yes—
563C23C22×C22⋊D1311yescharacteristic
564Q8—41no—
565Q8—41no—
566Q8—41no—
567Q8—41no—
568D4—44no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—84no—
601C2×C4—262no—
602C2×C4—521no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4—521no—
613C2×C4—1044no—
614C2×C4#8818912yes—
615C2×C4C2×#612911yescharacteristic
616C2×C4C2×#612911yescharacteristic
617C2×C4C2×#612911yescharacteristic
618C2×C4#8825111yescharacteristic
619C2×C4#41×D1311yescharacteristic
620C2×C4#8825611yescharacteristic
621C8—521no—
622C8—521no—
623C8—521no—
624C8—521no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22#1171870614yes—
639C22C2×#8818911yescharacteristic
640C22#1171951111yescharacteristic
641C22C2×#8819611yescharacteristic
642C22C2×#8820411yescharacteristic
643C22#1171953411yescharacteristic
644C22#1171954111yescharacteristic
645C22#1171954211yescharacteristic
646C4—22no—
647C4—42no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—81no—
652C4—81no—
653C4—81no—
654C4—522no—
655C4—1041no—
656C4—1041no—
657C4—1041no—
658C4#1171930511yescharacteristic
659C4#1171930611yescharacteristic
660C4#1171932211yescharacteristic
661C4#1171932311yescharacteristic
662C2—24no—
663C2—81no—
664C2#1311858211yescharacteristic
665C2C2×#1171870611yescharacteristic
666C2#1312482111yescharacteristic
667C2#1312666511yescharacteristic
668C2#1312667111yescharacteristic
669C2#1312694111yescharacteristic
670C2#1312700711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2417C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenter#2417D13
hypocenterC13#26206
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2417

Complements

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

NH ≅ G/Ntype
2. #13116404C2semidirect
3. #13116272C2semidirect
4. #13116254C2semidirect
5. #13116029C2semidirect
6. #13115467C2semidirect
7. #13115411C2semidirect
8. #13115260C2semidirect
9. #13115149C2semidirect
10. #13115144C2semidirect
12. #13115029C2semidirect
13. #13114928C2semidirect
14. C2×#11718121C2semidirect
548. C13#26206semidirect

Maximal subgroups

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

subgroupindex
#131177652
#131164042
#131162722
#131162542
#131160292
#131154672
#131154112
#131152602
#131151492
#131151442
#131151292
#131150292
#131149282
C2×#117181212
C13×#24172
#2620613