Finite Group Databasebeta

← #15930974

Subgroups — #15930974

Order 3328.

848 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119210C211yesmaximal, characteristic, complemented
2#13116153C211yesmaximal, characteristic, complemented
3#13116022C211yesmaximal, characteristic
4#13115972C211yesmaximal, characteristic, complemented
5#13115839C211yesmaximal, characteristic
6#13115784C211yesmaximal, characteristic, complemented
7#13115511C211yesmaximal, characteristic, complemented
8#13115470C211yesmaximal, characteristic, complemented
9#13115444C211yesmaximal, characteristic, complemented
10#13115411C211yesmaximal, characteristic, complemented
11#13115170C211yesmaximal, characteristic, complemented
12#13115143C211yesmaximal, characteristic, complemented
13#13114922C211yesmaximal, characteristic, complemented
14C4×#88072C211yesmaximal, characteristic, complemented
15C13×#2361C211yesmaximal, characteristic
16C2×C13×#121C2211yescharacteristic
17C2×C4×D4×C13—21no—
18C2×C4×D4×C13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×#6105C2211yescharacteristic
21C2×#88178C2211yescharacteristic
22C2×#88123C2211yescharacteristic
23C13×#390C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#388—21no—
26C13×#386—21no—
27C13×#385—21no—
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33#11718873C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36C2×#88050C2211yescharacteristic
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40#11718612—21no—
41#11718608—21no—
42C4×C4⋊Dic13C2211yescharacteristic
43#11718590C2211yescharacteristic
44#11718590C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47#11718321—21no—
48#11718307—21no—
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D4×C13—21no—
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C23×C4×C13—21no—
63C23×C4×C13C2311yescharacteristic
64C22×Dic26—21no—
65C22×Dic26C2311yescharacteristic
66C13×#121—22no—
67C13×#121—22no—
68C4×D4×C13—22no—
69C4×D4×C13—41no—
70C4×D4×C13—44no—
71C2×C13×C4⋊C4—22no—
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⋊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×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13—21no—
88C2×C22⋊Dic13—21no—
89C2×#6105—22no—
90C2×#6105—41no—
91C2×#6105—41no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96#88178—22no—
97#88178—41no—
98C2×#6101—21no—
99C2×C4×Dic13—21no—
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104#88123—22no—
105#88123—41no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95D411yescharacteristic
109C13×#95D411yescharacteristic
110#88072—22no—
111#88072—22no—
112#88072—41no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119C22⋊#1055—41no—
120C22⋊#1055—41no—
121#88050—22no—
122#88050—22no—
123#88050—41no—
124#88048—22no—
125C4⋊#1055—41no—
126C4×#1055—41no—
127#26722—131nomaximal, Sylow
128C24×C13—21no—
129C24×C13C2×D411yescharacteristic
130C2×D4×C13—24no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—42no—
137C2×D4×C13—42no—
138C2×D4×C13#4112yes—
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—42no—
149C22×C4×C13—42no—
150C22×C4×C13—42no—
151C22×C4×C13—42no—
152C22×C4×C13—81no—
153C22×C4×C13—81no—
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2411yescharacteristic
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C2×Dic26—21no—
165C2×Dic26—21no—
166C2×Dic26—21no—
167C2×Dic26—21no—
168C2×Dic26—21no—
169C2×Dic26—21no—
170C2×Dic26—42no—
171C2×Dic26—42no—
172C2×Dic26—81no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—42no—
178C13×C4⋊C4—42no—
179C13×C4⋊C4#4112yes—
180C13×C4⋊C4#4112yes—
181C13×C22⋊C4—24no—
182C13×C22⋊C4—41no—
183C13×C22⋊C4—42no—
184C13×C22⋊C4—42no—
185C13×C22⋊C4—81no—
186C13×C22⋊C4SD1614yescomplemented
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13—42no—
192C22⋊Dic13—42no—
193C22⋊Dic13—81no—
194#6105—44no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—42no—
201C4⋊Dic13#4112yes—
202#6101—42no—
203C4×Dic13—81no—
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—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216#2492—131no—
217#2361D1311yescharacteristic
218#2055—131no—
219#2034—131no—
220#2023—131no—
221#2000—131no—
222#1987—131no—
223#1933—131no—
224#1927—131no—
225#1923—131no—
226#1919—131no—
227#1877—131no—
228#1872—131no—
229#1823—131no—
230C4×#102—131no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—22no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13C2×SD1612yes—
245C23×C13C22×D411yescharacteristic
246D4×C13—22no—
247D4×C13—22no—
248D4×C13—48no—
249D4×C13—41no—
250D4×C13—41no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—22no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—22no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
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—84no—
278C2×C4×C13—84no—
279C2×C4×C13C2×SD1612yes—
280C2×C4×C13C2×SD1612yes—
281C2×C4×C13C2×#4111yescharacteristic
282C2×C4×C13C2×#4111yescharacteristic
283C2×C4×C13C2×#4111yescharacteristic
284C2×C4×C13C2×#4111yescharacteristic
285C2×C4×C13H(5,𝔽2)11yescharacteristic
286C2×C4×C13H(5,𝔽2)11yescharacteristic
287C2×Dic13—22no—
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—
297C2×Dic13—41no—
298C2×Dic13—41no—
299Dic26—41no—
300Dic26—41no—
301Dic26—41no—
302Dic26—41no—
303Dic26—84no—
304#1055—41no—
305#1055—41no—
306#1055—41no—
307#1055—41no—
308C22×SD16—131no—
309C2×C4⋊Q8—131no—
310C2×C22⋊Q8—131no—
311C2×#121C2×D1311yescharacteristic
312C2×C4×D4—21no—
313C2×C4×D4C2×D1311yescharacteristic
314C22×C4⋊C4C2×D1311yescharacteristic
315C2×#106—131no—
316C2×C4⋊C8—131no—
317C2×#103—131no—
318C2×#103—131no—
319C2×#103—131no—
320C2×#102—131no—
321C2×#102—131no—
322C2×#102—131no—
323C2×C22⋊C8—131no—
324C2×C22⋊C8—131no—
325C2×C4×C8—131no—
326#400—261no—
327#393—261no—
328#391—131no—
329#391—131no—
330#391—261no—
331#390C2×D1311yescharacteristic
332#389C2×D1311yescharacteristic
333#388—21no—
334#388—261no—
335#386—21no—
336#385—21no—
337#380—131no—
338C4×C4⋊C4—131no—
339C4×C4⋊C4C2×D1311yescharacteristic
340C4×C22⋊C4C2×D1311yescharacteristic
341#340—131no—
342#340—131no—
343#340—131no—
344#340—131no—
345#340—131no—
346#340—131no—
347#340—131no—
348#340—131no—
349#336—131no—
350#336—131no—
351C22×C13—22no—
352C22×C13—22no—
353C22×C13—22no—
354C22×C13—41no—
355C22×C13—41no—
356C22×C13—41no—
357C22×C13—41no—
358C22×C13—42no—
359C22×C13—42no—
360C22×C13—42no—
361C22×C13—81no—
362C22×C13—81no—
363C22×C13—81no—
364C22×C13—81no—
365C22×C13#52511yescharacteristic
366C22×C13#54611yescharacteristic
367C22×C13#54611yescharacteristic
368C22×C13C22×SD1611yescharacteristic
369C22×C13#57511yescharacteristic
370C22×C13#57611yescharacteristic
371C22×C13#57811yescharacteristic
372C4×C13—22no—
373C4×C13—22no—
374C4×C13—42no—
375C4×C13—41no—
376C4×C13—42no—
377C4×C13—41no—
378C4×C13—41no—
379C4×C13—81no—
380C4×C13#52911yescharacteristic
381C4×C13#53811yescharacteristic
382C4×C13#55511yescharacteristic
383C4×C13#55911yescharacteristic
384Dic13—42no—
385Dic13—81no—
386Dic13—81no—
387Dic13—81no—
388C22×Q8—131no—
389C22×Q8—261no—
390C22×D4—21no—
391C22×D4C22×D1311yescharacteristic
392C23×C4—21no—
393C23×C4—21no—
394C23×C4C22×D1311yescharacteristic
395C2×SD16—262no—
396C2×SD16—521no—
397C2×SD16—521no—
398C22×C8—131no—
399C22×C8—131no—
400C22×C8—131no—
401C22×C8—131no—
402C4⋊Q8—262no—
403C4⋊Q8—521no—
404C22⋊Q8—262no—
405C22⋊Q8—521no—
406#121—22no—
407#121—22no—
408C4×D4—22no—
409C4×D4—41no—
410C4×D4—44no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—41no—
415C2×C4⋊C4—131no—
416C2×C4⋊C4—131no—
417C2×C4⋊C4—131no—
418C2×C4⋊C4—261no—
419C2×C4⋊C4—261no—
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—21no—
427C2×C22⋊C4—261no—
428C2×C22⋊C4—261no—
429C2×C22⋊C4C22⋊D1311yescharacteristic
430C2×C22⋊C4C22⋊D1311yescharacteristic
431C2×C42—21no—
432C2×C42—261no—
433C2×C42C22×D1311yescharacteristic
434C2×C42C22×D1311yescharacteristic
435#106—262no—
436C4⋊C8—521no—
437#103—262no—
438#103—262no—
439#103—521no—
440#102—262no—
441#102—262no—
442#102—521no—
443C22⋊C8—521no—
444C22⋊C8—521no—
445C4×C8—521no—
446#95—21no—
447#95—21no—
448#95—261no—
449#95—261no—
450#95—261no—
451#95—261no—
452#95—261no—
453#95—261no—
454#95C22⋊D1311yescharacteristic
455#95C22⋊D1311yescharacteristic
456C2×C13—42no—
457C2×C13—82no—
458C2×C13#245911yescharacteristic
459C2×C13#310111yescharacteristic
460C2×C13#312411yescharacteristic
461C2×C13#329511yescharacteristic
462C2×C13#329811yescharacteristic
463C2×C13#331311yescharacteristic
464C2×C13#332211yescharacteristic
465C24—21no—
466C24C2×C22⋊D1311yescharacteristic
467C2×Q8—261no—
468C2×Q8—261no—
469C2×Q8—261no—
470C2×Q8—261no—
471C2×Q8—261no—
472C2×Q8—261no—
473C2×Q8—522no—
474C2×Q8—522no—
475C2×Q8—1041no—
476C2×D4—24no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4#612712yes—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—81no—
499C22×C4—81no—
500C22×C4—261no—
501C22×C4—261no—
502C22×C4—261no—
503C22×C4—261no—
504C22×C4C2×C22⋊D1311yescharacteristic
505C22×C4C2×C22⋊D1311yescharacteristic
506C22×C4C2×C22⋊D1311yescharacteristic
507C22×C4C2×C22⋊D1311yescharacteristic
508C22×C4C2×C22⋊D1311yescharacteristic
509C22×C4C23×D1311yescharacteristic
510SD16—524no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C2×C8—261no—
522C2×C8—261no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—42no—
528C4⋊C4—42no—
529C4⋊C4—132no—
530C4⋊C4—261no—
531C4⋊C4—261no—
532C4⋊C4—261no—
533C4⋊C4—261no—
534C4⋊C4—261no—
535C4⋊C4—522no—
536C4⋊C4—522no—
537C4⋊C4#612712yes—
538C4⋊C4#612912yes—
539C22⋊C4—24no—
540C22⋊C4—41no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—81no—
544C22⋊C4—522no—
545C22⋊C4—1041no—
546C22⋊C4#610514yescomplemented
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—42no—
552C42—1041no—
553C13#2672211yescharacteristic, complemented, Sylow
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—22no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23C2×#610512yes—
568C23C22×C22⋊D1311yescharacteristic
569Q8—521no—
570Q8—521no—
571Q8—521no—
572Q8—521no—
573Q8—1044no—
574D4—22no—
575D4—22no—
576D4—48no—
577D4—41no—
578D4—41no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—84no—
606C2×C4—84no—
607C2×C4—262no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4—521no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4—521no—
616C2×C4—521no—
617C2×C4—521no—
618C2×C4—521no—
619C2×C4C2×#610512yes—
620C2×C4C2×#610512yes—
621C2×C4C2×#612711yescharacteristic
622C2×C4C2×#612711yescharacteristic
623C2×C4C2×#612911yescharacteristic
624C2×C4#8825111yescharacteristic
625C2×C4#41×D1311yescharacteristic
626C2×C4#8825611yescharacteristic
627C8—521no—
628C8—521no—
629C8—521no—
630C8—521no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22#1171949611yescharacteristic
646C22C22×#610511yescharacteristic
647C22#1171951111yescharacteristic
648C22#1171952711yescharacteristic
649C22#1171953411yescharacteristic
650C22#1171954011yescharacteristic
651C22#1171954311yescharacteristic
652C4—22no—
653C4—22no—
654C4—42no—
655C4—41no—
656C4—41no—
657C4—42no—
658C4—41no—
659C4—81no—
660C4—522no—
661C4—1041no—
662C4—1041no—
663C4—1041no—
664C4#1171924311yescharacteristic
665C4#1171926411yescharacteristic
666C4#1171926511yescharacteristic
667C4#1171926811yescharacteristic
668C2—42no—
669C2—82no—
670C2#1311876711yescharacteristic
671C2#1312484411yescharacteristic
672C2#1312509811yescharacteristic
673C2#1312666011yescharacteristic
674C2#1312669511yescharacteristic
675C2#1312690211yescharacteristic
676C2#1312703111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2361C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenter#2361D13
hypocenterC13#26722
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
1. #13119210C2semidirect
2. #13116153C2semidirect
4. #13115972C2semidirect
6. #13115784C2semidirect
7. #13115511C2semidirect
8. #13115470C2semidirect
9. #13115444C2semidirect
10. #13115411C2semidirect
11. #13115170C2semidirect
12. #13115143C2semidirect
13. #13114922C2semidirect
14. C4×#88072C2semidirect
186. C13×C22⋊C4SD16semidirect
546. C22⋊C4#6105semidirect
553. C13#26722semidirect

Maximal subgroups

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

subgroupindex
#131192102
#131161532
#131160222
#131159722
#131158392
#131157842
#131155112
#131154702
#131154442
#131154112
#131151702
#131151432
#131149222
C4×#880722
C13×#23612
#2672213