Finite Group Databasebeta

← #15870281

Subgroups — #15870281

Order 3328.

844 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718657C211yesmaximal, characteristic
2#13117518C211yesmaximal, characteristic
3#13115470C211yesmaximal, characteristic, complemented
4#13115470C211yesmaximal, characteristic, complemented
5#13115428C211yesmaximal, characteristic, complemented
6#13115414C211yesmaximal, characteristic, complemented
7#13115143C211yesmaximal, characteristic
8#13115029C211yesmaximal, characteristic
9#13114931C211yesmaximal, characteristic
10#13114734C211yesmaximal, characteristic, complemented
11C4×#88048C211yesmaximal, characteristic, complemented
12#13114669C211yesmaximal, characteristic, complemented
13C4×#88050C211yesmaximal, characteristic, complemented
14#13114602C211yesmaximal, characteristic
15C13×#2274C211yesmaximal, characteristic
16C2×C13×#117C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88178C2211yescharacteristic
20C2×C4×Dic26C2211yescharacteristic
21C4×C13×C4⋊C4—21no—
22C4×C13×C4⋊C4—21no—
23C4×C13×C4⋊C4C2211yescharacteristic
24C4×C13×C4⋊C4C2211yescharacteristic
25C4×C13×C4⋊C4C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C22⋊C4—21no—
28C4×C13×C22⋊C4—21no—
29#11718873C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32#11718657C418yescomplemented
33#11718639—21no—
34#11718633—21no—
35C2×#88050C2211yescharacteristic
36C2×#88050C2211yescharacteristic
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43#11718606—21no—
44#11718605—21no—
45C4×C4⋊Dic13C2211yescharacteristic
46#11718590C2211yescharacteristic
47#11718589C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C22×Dic26C2311yescharacteristic
63C13×#117—22no—
64C13×#117—22no—
65C13×#117—22no—
66C13×#117C2×C414yes—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4D411yescharacteristic
71C2×C13×C4⋊C4D411yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4D411yescharacteristic
78C2×C13×C22⋊C4D411yescharacteristic
79C2×C42×C13—21no—
80C2×C42×C13—21no—
81C2×C42×C13—21no—
82C2×C42×C13—21no—
83C2×C42×C13—21no—
84C2×C42×C13C2311yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×C22⋊Dic13—21no—
87C2×C22⋊Dic13—21no—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91#88178—22no—
92#88178C2×C414yes—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×C4×Dic13—21no—
97C2×C4×Dic13—21no—
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C4×Dic26—22no—
103C4×Dic26—22no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113C22⋊#1055—22no—
114C22⋊#1055C2×C414yes—
115#88050—22no—
116#88050—22no—
117#88050C2×C414yescomplemented
118#88050C2×C414yescomplemented
119#88048—22no—
120#88048—22no—
121#88048C2×C414yescomplemented
122#88047C2×C414yescomplemented
123#88043—22no—
124C4×#1055—22no—
125#21591—131nomaximal, Sylow
126C24×C13C2×D411yescharacteristic
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—24no—
136C22×C4×C13—81no—
137C22×C4×C13—81no—
138C22×C4×C13C22×C412yes—
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13#4112yes—
145C22×C4×C13C2411yescharacteristic
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C2×Dic26—21no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26C22×C412yes—
156C13×C4⋊C4—24no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4C22×C412yes—
164C13×C4⋊C4C22×C412yes—
165C13×C4⋊C4#4112yes—
166C13×C4⋊C4#4112yes—
167C13×C22⋊C4—24no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—22no—
170C42×C13—24no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—81no—
174C42×C13—81no—
175C42×C13—81no—
176C42×C13—81no—
177C42×C13#4112yes—
178C42×C13#4112yes—
179C22⋊Dic13—24no—
180C22⋊Dic13—81no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13C22×C412yes—
187#6101—24no—
188#6101—42no—
189#6101—81no—
190C4×Dic13—42no—
191C4×Dic13—81no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055C22×C412yes—
203C2×#1055C22×C412yes—
204C2×#485—131no—
205#2323—131no—
206#2274D1311yescharacteristic
207#1927—131no—
208#1927—131no—
209#1921—131no—
210#1919—131no—
211#1872—131no—
212#1853—131no—
213#1825—131no—
214#1776—131no—
215C4×#106—131no—
216#1763—131no—
217C4×#103—131no—
218#1750—131no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13C4×D412yes—
226C23×C13C22×D411yescharacteristic
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—84no—
256C2×C4×C13C4×D412yes—
257C2×C4×C13#12312yes—
258C2×C4×C13#12312yes—
259C2×C4×C13C23×C411yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13C2×#4111yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×Dic13—22no—
266C2×Dic13—22no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277Dic26—22no—
278Dic26—22no—
279Dic26—41no—
280Dic26—41no—
281#1055—22no—
282#1055—22no—
283#1055—41no—
284#1055—41no—
285C2×C22⋊Q8—131no—
286C2×C4×Q8—131no—
287C2×#117C2×D1311yescharacteristic
288C2×#117C2×D1311yescharacteristic
289C22×C4⋊C4C2×D1311yescharacteristic
290#485—138no—
291C2×#107—131no—
292C2×#106—131no—
293C2×#106—131no—
294C2×#106—131no—
295C2×#103—131no—
296C2×#103—131no—
297C2×#103—131no—
298C2×#103—131no—
299C2×C22⋊C8—131no—
300C2×C22⋊C8—131no—
301C2×#97—131no—
302C2×C4×C8—131no—
303#391—131no—
304#389—131no—
305#389—261no—
306#388—261no—
307#388—261no—
308#387—261no—
309#380—131no—
310C4×C4⋊C4—21no—
311C4×C4⋊C4—21no—
312C4×C4⋊C4—131no—
313C4×C4⋊C4C2×D1311yescharacteristic
314C4×C4⋊C4C2×D1311yescharacteristic
315C4×C4⋊C4C2×D1311yescharacteristic
316C4×C4⋊C4C2×D1311yescharacteristic
317C4×C22⋊C4—21no—
318C4×C22⋊C4—21no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#336—131no—
328#336—131no—
329C22×C13—22no—
330C22×C13—22no—
331C22×C13—22no—
332C22×C13—41no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13C2×C4×D411yescharacteristic
337C22×C13C2×#12311yescharacteristic
338C22×C13#52511yescharacteristic
339C22×C13#57711yescharacteristic
340C22×C13#57711yescharacteristic
341C22×C13#57711yescharacteristic
342C22×C13#57811yescharacteristic
343C4×C13—22no—
344C4×C13—22no—
345C4×C13—22no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13—42no—
349C4×C13—42no—
350C4×C13—42no—
351C4×C13—42no—
352C4×C13C4×#4111yescharacteristic
353C4×C13C4×#4111yescharacteristic
354C4×C13#52911yescharacteristic
355C4×C13#52911yescharacteristic
356Dic13—42no—
357Dic13—42no—
358Dic13—81no—
359Dic13—81no—
360C22×Q8—131no—
361C23×C4—21no—
362C23×C4C22×D1311yescharacteristic
363C22×C8—131no—
364C22×C8—131no—
365C22×C8—131no—
366C22×C8—131no—
367C22⋊Q8—134no—
368C22⋊Q8—262no—
369C4×Q8—262no—
370C4×Q8—262no—
371#117—22no—
372#117—22no—
373#117—22no—
374#117C4×D1314yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4C22⋊D1311yescharacteristic
385C2×C4⋊C4C22⋊D1311yescharacteristic
386C2×C4⋊C4C22×D1311yescharacteristic
387C2×C4⋊C4C22×D1311yescharacteristic
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C4⋊C4C22×D1311yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—261no—
392C2×C22⋊C4—261no—
393C2×C22⋊C4C22⋊D1311yescharacteristic
394C2×C22⋊C4C22⋊D1311yescharacteristic
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—261no—
401C2×C42—261no—
402C2×C42C22×D1311yescharacteristic
403C2×C42C22×D1311yescharacteristic
404#107—134no—
405#106—134no—
406#106—262no—
407#106—262no—
408#103—134no—
409#103—134no—
410#103—262no—
411#103—262no—
412C22⋊C8—134no—
413C22⋊C8—262no—
414#97—262no—
415C4×C8—262no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95—261no—
424#95—261no—
425C2×C13—42no—
426C2×C13C4×#12311yescharacteristic
427C2×C13#294711yescharacteristic
428C2×C13#295211yescharacteristic
429C2×C13#309711yescharacteristic
430C2×C13#309911yescharacteristic
431C2×C13#312111yescharacteristic
432C2×C13#312311yescharacteristic
433C24C2×C22⋊D1311yescharacteristic
434C2×Q8—132no—
435C2×Q8—261no—
436C2×Q8—261no—
437C2×Q8—261no—
438C2×Q8—261no—
439C2×Q8—261no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—24no—
449C22×C4—81no—
450C22×C4—81no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4C2×C4×D1312yes—
456C22×C4#612712yes—
457C22×C4C2×C22⋊D1311yescharacteristic
458C22×C4C2×C22⋊D1311yescharacteristic
459C22×C4C2×C22⋊D1311yescharacteristic
460C22×C4C2×C22⋊D1311yescharacteristic
461C22×C4C2×C22⋊D1311yescharacteristic
462C22×C4C23×D1311yescharacteristic
463C2×C8—132no—
464C2×C8—132no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C4⋊C4—24no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—132no—
483C4⋊C4—264no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—522no—
490C4⋊C4—1041no—
491C4⋊C4C2×C4×D1312yes—
492C4⋊C4C2×C4×D1312yes—
493C4⋊C4#612712yes—
494C4⋊C4#612712yes—
495C22⋊C4—24no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—264no—
499C22⋊C4—1041no—
500C42—24no—
501C42—21no—
502C42—21no—
503C42—81no—
504C42—81no—
505C42—81no—
506C42—81no—
507C42—522no—
508C42—1041no—
509C42#612712yes—
510C42#612712yes—
511C13#2159111yescharacteristic, complemented, Sylow
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23C4×C22⋊D1312yes—
519C23C22×C22⋊D1311yescharacteristic
520Q8—262no—
521Q8—262no—
522Q8—521no—
523Q8—521no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—84no—
553C2×C4—262no—
554C2×C4—262no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4C4×C22⋊D1312yes—
566C2×C4#8818312yes—
567C2×C4#8818312yes—
568C2×C4C22×C4×D1311yescharacteristic
569C2×C4C2×#612711yescharacteristic
570C2×C4C2×#612711yescharacteristic
571C2×C4C2×#612711yescharacteristic
572C2×C4C2×#612711yescharacteristic
573C2×C4C2×#612711yescharacteristic
574C8—262no—
575C8—262no—
576C8—521no—
577C8—521no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22C2×C4×C22⋊D1311yescharacteristic
586C22C2×#8818311yescharacteristic
587C22#1171949611yescharacteristic
588C22#1171954111yescharacteristic
589C22#1171954111yescharacteristic
590C22#1171954211yescharacteristic
591C22#1171954311yescharacteristic
592C4—22no—
593C4—22no—
594C4—22no—
595C4—42no—
596C4—42no—
597C4—41no—
598C4—41no—
599C4—42no—
600C4—42no—
601C4—522no—
602C4—522no—
603C4—1041no—
604C4—1041no—
605C4C4×#612711yescharacteristic
606C4C4×#612711yescharacteristic
607C4#1171918411yescharacteristic
608C4#1171918411yescharacteristic
609C2—42no—
610C2C4×#8818311yescharacteristic
611C2#1312367511yescharacteristic
612C2#1312371711yescharacteristic
613C2#1312480511yescharacteristic
614C2#1312482511yescharacteristic
615C2#1312506511yescharacteristic
616C2#1312508811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2274C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenter#2274D13
hypocenterC13#21591
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2274

Complements

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

NH ≅ G/Ntype
3. #13115470C2semidirect
4. #13115470C2semidirect
5. #13115428C2semidirect
6. #13115414C2semidirect
10. #13114734C2semidirect
11. C4×#88048C2semidirect
12. #13114669C2semidirect
13. C4×#88050C2semidirect
32. #11718657C4semidirect
117. #88050C2×C4semidirect
118. #88050C2×C4semidirect
121. #88048C2×C4semidirect
122. #88047C2×C4semidirect
511. C13#21591semidirect

Maximal subgroups

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

subgroupindex
C2×#117186572
#131175182
#131154702
#131154282
#131154142
#131151432
#131150292
#131149312
#131147342
C4×#880482
#131146692
C4×#880502
#131146022
C13×#22742
#2159113