Finite Group Databasebeta

← #15923627

Subgroups — #15923627

Order 3328.

780 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117785C211yesmaximal, characteristic
2#13116394C211yesmaximal, characteristic, complemented
3#13116267C211yesmaximal, characteristic, complemented
4#13116244C211yesmaximal, characteristic, complemented
5#13116029C211yesmaximal, characteristic, complemented
6#13115474C211yesmaximal, characteristic, complemented
7#13115411C211yesmaximal, characteristic, complemented
8#13115260C211yesmaximal, characteristic, complemented
9#13115149C211yesmaximal, characteristic, complemented
10#13115149C211yesmaximal, characteristic, complemented
11#13115129C211yesmaximal, characteristic
12#13115035C211yesmaximal, characteristic, complemented
13#13114928C211yesmaximal, characteristic, complemented
14#13114552C211yesmaximal, characteristic, complemented
15C13×#2415C211yesmaximal, characteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C2×C13×#117C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C2×#88180C2211yescharacteristic
22C23×#1055C2211yescharacteristic
23C13×#397—21no—
24C13×#394—21no—
25C13×#391C2211yescharacteristic
26C13×#389—21no—
27C13×#389C2211yescharacteristic
28C13×#388—21no—
29C13×#380C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34#11718882—21no—
35#11718873C2211yescharacteristic
36#11718873C2211yescharacteristic
37C2×C22⋊#1055C2211yescharacteristic
38C2×C22⋊#1055C2211yescharacteristic
39C2×C22⋊#1055C2211yescharacteristic
40C4⋊C4×Dic13—21no—
41C2×#88048C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43#11718612—21no—
44#11718612—21no—
45#11718596C2211yescharacteristic
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×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C13×C22⋊Q8—22no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—41no—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C13×#117—22no—
70C13×#117—41no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4D411yescharacteristic
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⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4D411yescharacteristic
83C2×C13×C22⋊C4D411yescharacteristic
84C2×C42×C13—21no—
85C2×C42×C13C2311yescharacteristic
86C2×C22⋊Dic13—21no—
87C2×C22⋊Dic13—21no—
88C2×C22⋊Dic13—21no—
89C2×C22⋊Dic13—21no—
90#88180—22no—
91#88180—22no—
92#88180—41no—
93#88180—41no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13—21no—
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C2×C4⋊Dic13C2311yescharacteristic
100C2×C4×Dic13—21no—
101C2×C4×Dic13—21no—
102C2×C4×Dic13—21no—
103C22×#1055—22no—
104C22×#1055—41no—
105C22×#1055—41no—
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110C13×#95—21no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95—21no—
114#88075—22no—
115#88075—41no—
116#88075—41no—
117#88075—41no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121C22⋊#1055—22no—
122C22⋊#1055—41no—
123C22⋊#1055—41no—
124#88048—22no—
125#88047—41no—
126#26207—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—41no—
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×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13#4112yes—
157C22×C4×C13#4112yes—
158C22×C4×C13C2411yescharacteristic
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—21no—
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—42no—
172C13×C4⋊C4#4112yes—
173C13×C22⋊C4—22no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—42no—
176C13×C22⋊C4—42no—
177C13×C22⋊C4—42no—
178C13×C22⋊C4—42no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—42no—
182C22⋊Dic13—42no—
183C22⋊Dic13—42no—
184C22⋊Dic13—81no—
185C22⋊Dic13—81no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—42no—
194C4⋊Dic13—81no—
195C4⋊Dic13#4112yes—
196C4×Dic13—42no—
197C4×Dic13—42no—
198C4×Dic13—42no—
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×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—44no—
212#2415D1311yescharacteristic
213#2354—131no—
214#2099—131no—
215#2076—131no—
216#2072—131no—
217#2035—131no—
218#1928—131no—
219#1919—131no—
220#1892—131no—
221#1873—131no—
222#1873—131no—
223#1869—131no—
224#1854—131no—
225#1825—131no—
226#1735—131no—
227C23×C13—21no—
228C23×C13—21no—
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×C13C22×D411yescharacteristic
242Q8×C13—41no—
243Q8×C13—41no—
244Q8×C13—41no—
245Q8×C13—41no—
246D4×C13—44no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
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—22no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
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#12312yes—
278C2×C4×C13#13512yes—
279C2×C4×C13C2×#4111yescharacteristic
280C2×C4×C13C2×#4111yescharacteristic
281C2×C4×C13C2×#4111yescharacteristic
282C2×C4×C13C2×#4111yescharacteristic
283C2×C4×C13H(5,𝔽2)11yescharacteristic
284C2×C4×C13H(5,𝔽2)11yescharacteristic
285C2×Dic13—22no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297#1055—41no—
298#1055—41no—
299#1055—41no—
300#1055—41no—
301C23×C8—131no—
302C2×C22⋊Q8C2×D1311yescharacteristic
303C2×C22⋊Q8C2×D1311yescharacteristic
304C2×C4×D4C2×D1311yescharacteristic
305C2×#117—131no—
306C2×#117—131no—
307C2×#117C2×D1311yescharacteristic
308C2×#107—131no—
309C2×#106—131no—
310C2×#103—131no—
311C2×#103—131no—
312C2×#103—131no—
313C2×#103—131no—
314C2×C22⋊C8—131no—
315C2×C22⋊C8—131no—
316C2×C22⋊C8—131no—
317#397—21no—
318#394—21no—
319#391C2×D1311yescharacteristic
320#390—261no—
321#389—21no—
322#389C2×D1311yescharacteristic
323#388—21no—
324#388—261no—
325#388—261no—
326#384—131no—
327#380—131no—
328#380—131no—
329#380C2×D1311yescharacteristic
330C4×C4⋊C4—131no—
331C4×C4⋊C4—261no—
332#340—131no—
333#340—131no—
334#340—131no—
335#340—131no—
336#340—131no—
337#340—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#340—131no—
342#336—131no—
343#336—131no—
344C22×C13—22no—
345C22×C13—22no—
346C22×C13—22no—
347C22×C13—41no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13—41no—
351C22×C13—41no—
352C22×C13—41no—
353C22×C13—41no—
354C22×C13—41no—
355C22×C13—41no—
356C22×C13—41no—
357C22×C13—41no—
358C22×C13C2×#12311yescharacteristic
359C22×C13#54611yescharacteristic
360C22×C13#54611yescharacteristic
361C22×C13C2×#13511yescharacteristic
362C22×C13#57511yescharacteristic
363C22×C13#57711yescharacteristic
364C22×C13#57811yescharacteristic
365C4×C13—22no—
366C4×C13—22no—
367C4×C13—41no—
368C4×C13—41no—
369C4×C13—42no—
370C4×C13—81no—
371C4×C13—81no—
372C4×C13—81no—
373C4×C13#52911yescharacteristic
374C4×C13#53811yescharacteristic
375C4×C13#55311yescharacteristic
376C4×C13#55311yescharacteristic
377Dic13—42no—
378Dic13—81no—
379Dic13—81no—
380Dic13—81no—
381C22×Q8C22×D1311yescharacteristic
382C22×D4C22⋊D1311yescharacteristic
383C23×C4C22×D1311yescharacteristic
384C23×C4C22×D1311yescharacteristic
385C22×C8—131no—
386C22×C8—131no—
387C22×C8—131no—
388C22×C8—131no—
389C22×C8—262no—
390C22×C8—521no—
391C22×C8—521no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—41no—
396C4×D4—22no—
397C4×D4—22no—
398#117—22no—
399#117—41no—
400#117—262no—
401#117—262no—
402#117—521no—
403#117—521no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—131no—
408C2×C4⋊C4—131no—
409C2×C4⋊C4—131no—
410C2×C4⋊C4—131no—
411C2×C4⋊C4—261no—
412C2×C4⋊C4—261no—
413C2×C4⋊C4C22⋊D1311yescharacteristic
414C2×C4⋊C4C22×D1311yescharacteristic
415C2×C4⋊C4C22×D1311yescharacteristic
416C2×C4⋊C4C22×D1311yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—261no—
422C2×C22⋊C4—261no—
423C2×C22⋊C4—261no—
424C2×C22⋊C4—261no—
425C2×C22⋊C4C22⋊D1311yescharacteristic
426C2×C22⋊C4C22⋊D1311yescharacteristic
427C2×C42—21no—
428C2×C42—261no—
429C2×C42—261no—
430C2×C42—261no—
431C2×C42C22×D1311yescharacteristic
432#107—521no—
433#106—262no—
434#103—262no—
435#103—521no—
436#103—521no—
437#103—521no—
438C22⋊C8—262no—
439C22⋊C8—521no—
440C22⋊C8—521no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—261no—
446#95—261no—
447#95—261no—
448C2×C13—42no—
449C2×C13—81no—
450C2×C13#244411yescharacteristic
451C2×C13#309111yescharacteristic
452C2×C13#309711yescharacteristic
453C2×C13#330211yescharacteristic
454C2×C13#330411yescharacteristic
455C2×C13#331511yescharacteristic
456C2×C13#332111yescharacteristic
457C24C2×C22⋊D1311yescharacteristic
458C24C2×C22⋊D1311yescharacteristic
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—41no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
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—261no—
483C22×C4—261no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4#612912yes—
487C22×C4#612912yes—
488C22×C4C2×C22⋊D1311yescharacteristic
489C22×C4C2×C22⋊D1311yescharacteristic
490C22×C4C2×C22⋊D1311yescharacteristic
491C22×C4C2×C22⋊D1311yescharacteristic
492C22×C4C23×D1311yescharacteristic
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—261no—
503C2×C8—261no—
504C2×C8—261no—
505C2×C8—524no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4—42no—
515C4⋊C4—132no—
516C4⋊C4—261no—
517C4⋊C4—261no—
518C4⋊C4—261no—
519C4⋊C4—261no—
520C4⋊C4—261no—
521C4⋊C4—261no—
522C4⋊C4—261no—
523C4⋊C4—522no—
524C4⋊C4—1041no—
525C4⋊C4#612912yes—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—522no—
533C22⋊C4—522no—
534C22⋊C4—1041no—
535C22⋊C4—1041no—
536C42—21no—
537C42—21no—
538C42—42no—
539C42—522no—
540C42—522no—
541C42—522no—
542C13#2620711yescharacteristic, complemented, Sylow
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23#8818912yes—
557C23C22×C22⋊D1311yescharacteristic
558Q8—41no—
559Q8—41no—
560Q8—41no—
561Q8—41no—
562D4—44no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
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—262no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4#8818912yes—
606C2×C4#8820412yes—
607C2×C4C2×#612911yescharacteristic
608C2×C4C2×#612911yescharacteristic
609C2×C4C2×#612911yescharacteristic
610C2×C4#8825111yescharacteristic
611C2×C4#41×D1311yescharacteristic
612C2×C4#8825611yescharacteristic
613C8—521no—
614C8—521no—
615C8—521no—
616C8—521no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22C2×#8818911yescharacteristic
632C22#1171951111yescharacteristic
633C22C2×#8820411yescharacteristic
634C22#1171952711yescharacteristic
635C22#1171953411yescharacteristic
636C22#1171954211yescharacteristic
637C22#1171954311yescharacteristic
638C4—22no—
639C4—22no—
640C4—42no—
641C4—41no—
642C4—41no—
643C4—81no—
644C4—81no—
645C4—81no—
646C4—522no—
647C4—1041no—
648C4—1041no—
649C4—1041no—
650C4#1171930511yescharacteristic
651C4#1171930611yescharacteristic
652C4#1171932211yescharacteristic
653C4#1171932311yescharacteristic
654C2—42no—
655C2—81no—
656C2#1311858211yescharacteristic
657C2#1312474511yescharacteristic
658C2#1312479911yescharacteristic
659C2#1312675311yescharacteristic
660C2#1312676911yescharacteristic
661C2#1312692611yescharacteristic
662C2#1312702211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2415C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenter#2415D13
hypocenterC13#26207
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2415

Complements

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

NH ≅ G/Ntype
2. #13116394C2semidirect
3. #13116267C2semidirect
4. #13116244C2semidirect
5. #13116029C2semidirect
6. #13115474C2semidirect
7. #13115411C2semidirect
8. #13115260C2semidirect
9. #13115149C2semidirect
10. #13115149C2semidirect
12. #13115035C2semidirect
13. #13114928C2semidirect
14. #13114552C2semidirect
542. C13#26207semidirect

Maximal subgroups

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

subgroupindex
#131177852
#131163942
#131162672
#131162442
#131160292
#131154742
#131154112
#131152602
#131151492
#131151292
#131150352
#131149282
#131145522
C13×#24152
#2620713