Finite Group Databasebeta

← #15930976

Subgroups — #15930976

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#13117850C211yesmaximal, characteristic
2#13116151C211yesmaximal, characteristic, complemented
3#13116025C211yesmaximal, characteristic
4#13115969C211yesmaximal, characteristic, complemented
5#13115837C211yesmaximal, characteristic
6#13115785C211yesmaximal, characteristic, complemented
7#13115515C211yesmaximal, characteristic, complemented
8#13115467C211yesmaximal, characteristic, complemented
9#13115444C211yesmaximal, characteristic, complemented
10#13115414C211yesmaximal, characteristic, complemented
11#13115173C211yesmaximal, characteristic, complemented
12#13115144C211yesmaximal, characteristic, complemented
13#13114920C211yesmaximal, characteristic, complemented
14C4×#88049C211yesmaximal, characteristic, complemented
15C13×#2492C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8C2211yescharacteristic
18C22×#6106C2211yescharacteristic
19C2×#88184C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C2×#88135—21no—
22C2×C4×D52C2211yescharacteristic
23C13×#400—21no—
24C13×#393—21no—
25C13×#391—21no—
26C13×#391C2211yescharacteristic
27C13×#391C2211yescharacteristic
28C13×#388—21no—
29C13×#380C2211yescharacteristic
30C4×C13×C4⋊C4C2211yescharacteristic
31C4×C13×C22⋊C4C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36C2×C22⋊#1055C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88049C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41#11718619—21no—
42#11718600C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44#11718589C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47#11718331—21no—
48#11718329—21no—
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13—21no—
60C22×Q8×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13—21no—
63C23×Dic13—21no—
64C22×D52C2311yescharacteristic
65C22×C4×D13—21no—
66C13×C4⋊Q8—22no—
67C13×C4⋊Q8—41no—
68C13×C22⋊Q8—22no—
69C13×C22⋊Q8—41no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4D411yescharacteristic
78C2×C13×C22⋊C4D411yescharacteristic
79C2×C42×C13—21no—
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×#6106—22no—
83C2×#6106—41no—
84C2×#6106—41no—
85#88184—22no—
86#88184—22no—
87C2×#6103—21no—
88C2×#6103—21no—
89C2×#6103—21no—
90C2×#6103—21no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—41no—
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×#6101—21no—
98C2×C4×Dic13—21no—
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103#88135—44no—
104C4×D52—22no—
105C4×D52—41no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95—21no—
112C13×#95D411yescharacteristic
113C13×#95D411yescharacteristic
114#88075—22no—
115#88075—22no—
116#88075—41no—
117#88071—21no—
118#88071—21no—
119C22⋊#1055—41no—
120C22⋊#1055—41no—
121#88049—22no—
122#88049—22no—
123#88049—41no—
124#88048—22no—
125C4⋊#1055—41no—
126C4×#1055—41no—
127#26722—131nomaximal, Sylow
128C24×C13C2×D411yescharacteristic
129C23×D13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13—21no—
132C2×Q8×C13—21no—
133C2×Q8×C13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—42no—
137C2×Q8×C13—42no—
138C2×Q8×C13—81no—
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×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2411yescharacteristic
155C2×C22⋊D13—24no—
156C2×C22⋊D13—42no—
157C2×C22⋊D13—42no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—42no—
162C22×Dic13—42no—
163C22×Dic13—81no—
164C2×D52—21no—
165C2×D52—21no—
166C2×D52—21no—
167C2×D52—21no—
168C2×D52—21no—
169C2×D52#4112yes—
170C2×C4×D13—42no—
171C2×C4×D13—42no—
172C2×C4×D13—81no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—42no—
179C13×C4⋊C4—42no—
180C13×C4⋊C4#4112yes—
181C13×C22⋊C4—41no—
182C13×C22⋊C4—42no—
183C13×C22⋊C4—81no—
184C13×C22⋊C4SD1614yescomplemented
185C42×C13—21no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—81no—
190#6106—44no—
191#6103—24no—
192#6103—42no—
193#6103—42no—
194#6103—81no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—42no—
200C4⋊Dic13#4112yes—
201C4⋊Dic13#4112yes—
202#6101—42no—
203C4×Dic13—42no—
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#2492D1311yescharacteristic, complemented
217#2361—131no—
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×C13C2×SD1612yes—
238C23×C13C22×D411yescharacteristic
239C22×D13—22no—
240C22×D13—41no—
241C22×D13—41no—
242C22×D13—41no—
243C22×D13—41no—
244C22×D13—41no—
245C22×D13—41no—
246Q8×C13—41no—
247Q8×C13—41no—
248Q8×C13—41no—
249Q8×C13—41no—
250Q8×C13—84no—
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—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×C13C2×SD1612yes—
281C2×C4×C13C2×SD1612yes—
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
288C22⋊D13—48no—
289C2×Dic13—22no—
290C2×Dic13—22no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—84no—
299D52—22no—
300D52—22no—
301D52—41no—
302D52—41no—
303C4×D13—84no—
304#1055—41no—
305#1055—41no—
306#1055—41no—
307#1055—41no—
308C22×SD16—131no—
309C2×C4⋊Q8C2×D1311yescharacteristic
310C2×C22⋊Q8C2×D1311yescharacteristic
311C2×#121—131no—
312C2×C4×D4—131no—
313C2×C4×D4—261no—
314C22×C4⋊C4—131no—
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—21no—
327#393—21no—
328#391—21no—
329#391C2×D1311yescharacteristic
330#391C2×D1311yescharacteristic
331#390—131no—
332#389—131no—
333#388—21no—
334#388—261no—
335#386—261no—
336#385—261no—
337#380C2×D1311yescharacteristic
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#52511yescharacteristic
359C22×C13#54611yescharacteristic
360C22×C13#54611yescharacteristic
361C22×C13C22×SD1611yescharacteristic
362C22×C13#57511yescharacteristic
363C22×C13#57611yescharacteristic
364C22×C13#57811yescharacteristic
365C2×D13—42no—
366C2×D13—42no—
367C2×D13—42no—
368C2×D13—81no—
369C2×D13—81no—
370C2×D13—81no—
371C2×D13—81no—
372C4×C13—22no—
373C4×C13—22no—
374C4×C13—41no—
375C4×C13—41no—
376C4×C13—41no—
377C4×C13—42no—
378C4×C13—81no—
379C4×C13—81no—
380C4×C13—81no—
381C4×C13#52911yescharacteristic
382C4×C13#53811yescharacteristic
383C4×C13#55511yescharacteristic
384C4×C13#55911yescharacteristic
385Dic13—42no—
386Dic13—42no—
387Dic13—81no—
388C22×Q8—21no—
389C22×Q8C22×D1311yescharacteristic
390C22×D4—131no—
391C22×D4—261no—
392C23×C4—261no—
393C23×C4—261no—
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—22no—
403C4⋊Q8—41no—
404C22⋊Q8—22no—
405C22⋊Q8—41no—
406#121—262no—
407#121—262no—
408C4×D4—262no—
409C4×D4—521no—
410C4×D4—524no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—131no—
414C2×C4⋊C4—131no—
415C2×C4⋊C4—131no—
416C2×C4⋊C4—262no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4—261no—
419C2×C4⋊C4—521no—
420C2×C4⋊C4C22×D1311yescharacteristic
421C2×C4⋊C4C22×D1311yescharacteristic
422C2×C4⋊C4C22×D1311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—261no—
426C2×C22⋊C4—261no—
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—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—261no—
453#95—261no—
454#95C22⋊D1311yescharacteristic
455#95C22⋊D1311yescharacteristic
456C2×C13—42no—
457C2×C13#245911yescharacteristic
458C2×C13#310111yescharacteristic
459C2×C13#312411yescharacteristic
460C2×C13#329511yescharacteristic
461C2×C13#329811yescharacteristic
462C2×C13#331311yescharacteristic
463C2×C13#332211yescharacteristic
464D13—82no—
465C24—261no—
466C24C2×C22⋊D1311yescharacteristic
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8—81no—
476C2×D4—132no—
477C2×D4—264no—
478C2×D4—261no—
479C2×D4—261no—
480C2×D4—261no—
481C2×D4—261no—
482C2×D4—261no—
483C2×D4—522no—
484C2×D4—522no—
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—21no—
495C22×C4—261no—
496C22×C4—261no—
497C22×C4—261no—
498C22×C4—522no—
499C22×C4—522no—
500C22×C4—522no—
501C22×C4—522no—
502C22×C4—1041no—
503C22×C4—1041no—
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—21no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—132no—
531C4⋊C4—132no—
532C4⋊C4—261no—
533C4⋊C4—261no—
534C4⋊C4—261no—
535C4⋊C4—261no—
536C4⋊C4—522no—
537C4⋊C4—522no—
538C4⋊C4#612912yes—
539C22⋊C4—41no—
540C22⋊C4—42no—
541C22⋊C4—81no—
542C22⋊C4—264no—
543C22⋊C4—522no—
544C22⋊C4—522no—
545C22⋊C4—1041no—
546C22⋊C4#610614yescomplemented
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—81no—
552C42—522no—
553C13#2672211yescharacteristic, complemented, Sylow
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—262no—
561C23—521no—
562C23—521no—
563C23—521no—
564C23—521no—
565C23—521no—
566C23—521no—
567C23C2×#610612yes—
568C23C22×C22⋊D1311yescharacteristic
569Q8—41no—
570Q8—41no—
571Q8—41no—
572Q8—41no—
573Q8—84no—
574D4—262no—
575D4—262no—
576D4—528no—
577D4—521no—
578D4—521no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
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—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—262no—
609C2×C4—262no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4—521no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4—521no—
616C2×C4—521no—
617C2×C4—1044no—
618C2×C4—1044no—
619C2×C4C2×#610612yes—
620C2×C4C2×#610612yes—
621C2×C4C2×#612911yescharacteristic
622C2×C4#8825111yescharacteristic
623C2×C4#41×D1311yescharacteristic
624C2×C4#41×D1311yescharacteristic
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—522no—
639C22—522no—
640C22—522no—
641C22—1041no—
642C22—1041no—
643C22—1041no—
644C22—1041no—
645C22#1171951111yescharacteristic
646C22C22×#610611yescharacteristic
647C22#1171952711yescharacteristic
648C22#1171953311yescharacteristic
649C22#1171953411yescharacteristic
650C22#1171954011yescharacteristic
651C22#1171954311yescharacteristic
652C4—22no—
653C4—22no—
654C4—41no—
655C4—41no—
656C4—42no—
657C4—41no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—522no—
662C4—522no—
663C4—1041no—
664C4#1171937511yescharacteristic
665C4#1171938311yescharacteristic
666C4#1171938511yescharacteristic
667C4#1171938611yescharacteristic
668C2—42no—
669C2—1042no—
670C2#1311876911yescharacteristic
671C2#1312484011yescharacteristic
672C2#1312509211yescharacteristic
673C2#1312665411yescharacteristic
674C2#1312670111yescharacteristic
675C2#1312689611yescharacteristic
676C2#1312703711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2492C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenter#2492D13
hypocenterC13#26722
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2492

Complements

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

NH ≅ G/Ntype
2. #13116151C2semidirect
4. #13115969C2semidirect
6. #13115785C2semidirect
7. #13115515C2semidirect
8. #13115467C2semidirect
9. #13115444C2semidirect
10. #13115414C2semidirect
11. #13115173C2semidirect
12. #13115144C2semidirect
13. #13114920C2semidirect
14. C4×#88049C2semidirect
15. C13×#2492C2semidirect
184. C13×C22⋊C4SD16semidirect
216. #2492D13semidirect
546. C22⋊C4#6106semidirect
553. C13#26722semidirect

Maximal subgroups

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

subgroupindex
#131178502
#131161512
#131160252
#131159692
#131158372
#131157852
#131155152
#131154672
#131154442
#131154142
#131151732
#131151442
#131149202
C4×#880492
C13×#24922
#2672213