Finite Group Databasebeta

← #15913093

Subgroups — #15913093

Order 3328.

850 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718683C211yesmaximal, characteristic, complemented
2C2×D4×#1055C211yesmaximal, characteristic
3#13120002C211yesmaximal, characteristic
4#13116272C211yesmaximal, characteristic, complemented
5#13116262C211yesmaximal, characteristic, complemented
6#13116036C211yesmaximal, characteristic, complemented
7#13116029C211yesmaximal, characteristic, complemented
8#13115800C211yesmaximal, characteristic, complemented
9#13115602C211yesmaximal, characteristic, complemented
10#13115260C211yesmaximal, characteristic, complemented
11#13115260C211yesmaximal, characteristic, complemented
12#13114863C211yesmaximal, characteristic, complemented
13#13114859C211yesmaximal, characteristic, complemented
14C4×#88075C211yesmaximal, characteristic, complemented
15C13×#2536C211yesmaximal, characteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C2×C4×D4×C13C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C23×#1055C2211yescharacteristic
22C2×#88124C2211yescharacteristic
23C13×#398—21no—
24C13×#394—21no—
25C13×#388—21no—
26C13×#388—21no—
27C13×#382C2211yescharacteristic
28C13×#380C2211yescharacteristic
29C13×#380C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34#11718883—21no—
35#11718873C2211yescharacteristic
36#11718873C2211yescharacteristic
37#11718873C2211yescharacteristic
38#11718873C2211yescharacteristic
39C2×C22⋊#1055C2211yescharacteristic
40C2×C22⋊#1055C2211yescharacteristic
41#11718683—24no—
42D4×#1055—24no—
43#11718643—21no—
44C2×#88048C2211yescharacteristic
45C2×#88048C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47C2×#88047C2211yescharacteristic
48#11718606—21no—
49#11718606—21no—
50C4×C4⋊Dic13C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C22×Q8×C13C2311yescharacteristic
62C22×D4×C13D411yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—22no—
67C13×C22⋊Q8—41no—
68C13×C22⋊Q8—41no—
69C4×Q8×C13—22no—
70C4×Q8×C13—22no—
71C4×D4×C13—22no—
72C4×D4×C13—22no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C22⋊C4—21no—
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×C13—21no—
87C2×C42×C13C2311yescharacteristic
88C2×C22⋊Dic13—21no—
89C2×C22⋊Dic13—21no—
90C2×C22⋊Dic13—21no—
91C2×C22⋊Dic13—21no—
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×#6101—21no—
97C2×#6101—21no—
98C2×C4×Dic13—21no—
99C22×#1055—22no—
100C22×#1055—22no—
101C22×#1055—22no—
102C22×#1055—22no—
103C22×#1055—41no—
104C22×#1055—41no—
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109#88124—22no—
110#88124—22no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95—21no—
115#88075—22no—
116#88075—22no—
117#88075—22no—
118#88075—22no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88071—21no—
123#88071—21no—
124C22⋊#1055—22no—
125C22⋊#1055—22no—
126#88048—22no—
127#88048—41no—
128#88047—22no—
129#88047—41no—
130C4⋊#1055D414yes—
131C4×#1055—22no—
132#25343—131nomaximal, Sylow
133C24×C13C2×D411yescharacteristic
134C24×C13C2×D411yescharacteristic
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13—21no—
140C2×Q8×C13#4112yes—
141C2×D4×C13—22no—
142C2×D4×C13—22no—
143C2×D4×C13—22no—
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—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13C2411yescharacteristic
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—21no—
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—21no—
176C13×C4⋊C4—42no—
177C13×C4⋊C4—42no—
178C13×C4⋊C4—42no—
179C13×C22⋊C4—22no—
180C13×C22⋊C4—22no—
181C13×C22⋊C4—42no—
182C13×C22⋊C4—42no—
183C13×C22⋊C4—42no—
184C13×C22⋊C4—42no—
185C42×C13—42no—
186C42×C13C2×D412yes—
187C42×C13#4112yes—
188C22⋊Dic13—42no—
189C22⋊Dic13—42no—
190C22⋊Dic13—81no—
191C22⋊Dic13—81no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200#6101—42no—
201#6101—42no—
202C4×Dic13—81no—
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—44no—
213C2×#1055—44no—
214C2×#1055C2×D412yes—
215C2×#1055C2×D412yes—
216C2×#1055#4112yes—
217C2×#479—131no—
218C2×C8×D4—131no—
219#2562—131no—
220#2536D1311yescharacteristic
221#2077—131no—
222#2075—131no—
223#2036—131no—
224#2035—131no—
225#1991—131no—
226#1949—131no—
227#1892—131no—
228#1892—131no—
229#1808—131no—
230#1807—131no—
231C4×#103—131no—
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—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13#13512yes—
245C23×C13#13512yes—
246C23×C13C22×D411yescharacteristic
247Q8×C13—22no—
248Q8×C13—22no—
249Q8×C13—41no—
250Q8×C13—41no—
251D4×C13—28no—
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—22no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
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—41no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13#12112yes—
283C2×C4×C13#12112yes—
284C2×C4×C13C22×D411yescharacteristic
285C2×C4×C13C2×#4111yescharacteristic
286C2×C4×C13C2×#4111yescharacteristic
287C2×C4×C13C2×#4111yescharacteristic
288C2×C4×C13H(5,𝔽2)11yescharacteristic
289C2×C4×C132−1+411yescharacteristic
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—41no—
301C2×Dic13—41no—
302#1055—22no—
303#1055—22no—
304#1055—22no—
305#1055—41no—
306C23×C8—131no—
307C23×C8—131no—
308C2×#125—131no—
309C2×C22⋊Q8C2×D1311yescharacteristic
310C2×C22⋊Q8C2×D1311yescharacteristic
311C2×C4×Q8C2×D1311yescharacteristic
312C2×C4×D4C2×D1311yescharacteristic
313#479—264no—
314C8×D4—264no—
315C2×#107—131no—
316C2×#107—131no—
317C2×#106—131no—
318C2×#106—131no—
319C2×C4⋊C8—131no—
320C2×#103—131no—
321C2×#103—131no—
322C2×#103—131no—
323C2×#103—131no—
324C2×C22⋊C8—131no—
325C2×C22⋊C8—131no—
326C2×C4×C8—131no—
327#400—261no—
328#398—21no—
329#394—21no—
330#394—261no—
331#388—21no—
332#388—21no—
333#388—261no—
334#388—261no—
335#382C2×D1311yescharacteristic
336#380—131no—
337#380—131no—
338#380—131no—
339#380—131no—
340#380C2×D1311yescharacteristic
341#380C2×D1311yescharacteristic
342C4×C4⋊C4—131no—
343#340—131no—
344#340—131no—
345#340—131no—
346#340—131no—
347#340—131no—
348#340—131no—
349#340—131no—
350#340—131no—
351C22×C13—22no—
352C22×C13—22no—
353C22×C13—22no—
354C22×C13—22no—
355C22×C13—22no—
356C22×C13—22no—
357C22×C13—41no—
358C22×C13—41no—
359C22×C13—41no—
360C22×C13—41no—
361C22×C13—41no—
362C22×C13—41no—
363C22×C13—41no—
364C22×C13—41no—
365C22×C13C2×#12111yescharacteristic
366C22×C13#54611yescharacteristic
367C22×C13#54711yescharacteristic
368C22×C13C2×#13511yescharacteristic
369C22×C13C2×#13511yescharacteristic
370C22×C13#57711yescharacteristic
371C22×C13#57811yescharacteristic
372C4×C13—22no—
373C4×C13—22no—
374C4×C13—41no—
375C4×C13—41no—
376C4×C13—42no—
377C4×C13—81no—
378C4×C13—81no—
379C4×C13—81no—
380C4×C13#52911yescharacteristic
381C4×C13#54211yescharacteristic
382C4×C13#54611yescharacteristic
383C4×C13#54811yescharacteristic
384Dic13—81no—
385Dic13—81no—
386Dic13—81no—
387Dic13—81no—
388C22×Q8C22×D1311yescharacteristic
389C22×D4C22⋊D1311yescharacteristic
390C23×C4C22×D1311yescharacteristic
391C23×C4C22×D1311yescharacteristic
392C22×C8—131no—
393C22×C8—131no—
394C22×C8—131no—
395C22×C8—131no—
396C22×C8—262no—
397C22×C8—262no—
398C22×C8—262no—
399C22×C8—262no—
400C22×C8—521no—
401C22×C8—521no—
402#125—262no—
403#125—262no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—41no—
407C22⋊Q8—41no—
408C4×Q8—22no—
409C4×Q8—22no—
410C4×D4—22no—
411C4×D4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—131no—
416C2×C4⋊C4—131no—
417C2×C4⋊C4—131no—
418C2×C4⋊C4—131no—
419C2×C4⋊C4—261no—
420C2×C4⋊C4—261no—
421C2×C4⋊C4C22⋊D1311yescharacteristic
422C2×C4⋊C4C22×D1311yescharacteristic
423C2×C4⋊C4C22×D1311yescharacteristic
424C2×C4⋊C4C22×D1311yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—261no—
430C2×C22⋊C4—261no—
431C2×C22⋊C4—261no—
432C2×C22⋊C4—261no—
433C2×C22⋊C4C22⋊D1311yescharacteristic
434C2×C22⋊C4C22⋊D1311yescharacteristic
435C2×C42—21no—
436C2×C42—261no—
437C2×C42C22×D1311yescharacteristic
438#107—262no—
439#107—521no—
440#106—262no—
441#106—521no—
442C4⋊C8—134no—
443#103—262no—
444#103—262no—
445#103—262no—
446#103—262no—
447C22⋊C8—262no—
448C22⋊C8—262no—
449C4×C8—262no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—261no—
455#95—261no—
456#95—261no—
457#95—261no—
458#95—261no—
459C2×C13—42no—
460C2×C13—42no—
461C2×C13#242711yescharacteristic
462C2×C13#305011yescharacteristic
463C2×C13#306311yescharacteristic
464C2×C13#330011yescharacteristic
465C2×C13#330111yescharacteristic
466C2×C13#333611yescharacteristic
467C2×C13#333711yescharacteristic
468C24C2×C22⋊D1311yescharacteristic
469C24C2×C22⋊D1311yescharacteristic
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8#612912yes—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
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—261no—
499C22×C4C2×C22⋊D1311yescharacteristic
500C22×C4C2×C22⋊D1311yescharacteristic
501C22×C4C2×C22⋊D1311yescharacteristic
502C22×C4C2×C22⋊D1311yescharacteristic
503C22×C4C23×D1311yescharacteristic
504C2×C8—132no—
505C2×C8—132no—
506C2×C8—132no—
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—261no—
516C2×C8—524no—
517C2×C8—524no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—261no—
529C4⋊C4—261no—
530C4⋊C4—261no—
531C4⋊C4—261no—
532C4⋊C4—261no—
533C4⋊C4—261no—
534C4⋊C4—261no—
535C4⋊C4—261no—
536C4⋊C4—522no—
537C4⋊C4—522no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—522no—
545C22⋊C4—522no—
546C22⋊C4—1041no—
547C22⋊C4—1041no—
548C42—42no—
549C42—1041no—
550C42D4×D1312yes—
551C42#612912yes—
552C13#2534311yescharacteristic, complemented, Sylow
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23#8820412yes—
566C23#8820412yes—
567C23C22×C22⋊D1311yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572D4—28no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
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—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—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—521no—
614C2×C4—521no—
615C2×C4#8819312yes—
616C2×C4#8819312yes—
617C2×C4C2×D4×D1311yescharacteristic
618C2×C4C2×#612911yescharacteristic
619C2×C4C2×#612911yescharacteristic
620C2×C4#8825111yescharacteristic
621C2×C4#41×D1311yescharacteristic
622C2×C4#8825711yescharacteristic
623C8—262no—
624C8—262no—
625C8—262no—
626C8—521no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22C2×#8819311yescharacteristic
642C22#1171951111yescharacteristic
643C22C2×#8820411yescharacteristic
644C22C2×#8820411yescharacteristic
645C22#1171952911yescharacteristic
646C22#1171954211yescharacteristic
647C22#1171954311yescharacteristic
648C4—22no—
649C4—22no—
650C4—41no—
651C4—41no—
652C4—42no—
653C4—81no—
654C4—81no—
655C4—81no—
656C4—1041no—
657C4—1041no—
658C4—1041no—
659C4—1041no—
660C4#1171930311yescharacteristic
661C4#1171930511yescharacteristic
662C4#1171930811yescharacteristic
663C4#1171931711yescharacteristic
664C2—42no—
665C2—42no—
666C2#1311841511yescharacteristic
667C2#1312441411yescharacteristic
668C2#1312452311yescharacteristic
669C2#1312672311yescharacteristic
670C2#1312673811yescharacteristic
671C2#1312719811yescharacteristic
672C2#1312721511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2536C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenter#2536D13
hypocenterC13#25343
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2536

Complements

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

NH ≅ G/Ntype
1. C2×#11718683C2semidirect
4. #13116272C2semidirect
5. #13116262C2semidirect
6. #13116036C2semidirect
7. #13116029C2semidirect
8. #13115800C2semidirect
9. #13115602C2semidirect
10. #13115260C2semidirect
11. #13115260C2semidirect
12. #13114863C2semidirect
13. #13114859C2semidirect
14. C4×#88075C2semidirect
552. C13#25343semidirect

Maximal subgroups

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

subgroupindex
C2×#117186832
C2×D4×#10552
#131200022
#131162722
#131162622
#131160362
#131160292
#131158002
#131156022
#131152602
#131148632
#131148592
C4×#880752
C13×#25362
#2534313