Finite Group Databasebeta

← #15931036

Subgroups — #15931036

Order 3328.

764 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117839C211yesmaximal, characteristic
2#13116158C211yesmaximal, characteristic, complemented
3#13116039C211yesmaximal, characteristic
4#13115974C211yesmaximal, characteristic, complemented
5#13115844C211yesmaximal, characteristic
6#13115785C211yesmaximal, characteristic, complemented
7#13115515C211yesmaximal, characteristic, complemented
8#13115474C211yesmaximal, characteristic, complemented
9#13115444C211yesmaximal, characteristic
10#13115428C211yesmaximal, characteristic, complemented
11#13115180C211yesmaximal, characteristic, complemented
12#13115144C211yesmaximal, characteristic
13#13114924C211yesmaximal, characteristic
14C4×#88050C211yesmaximal, characteristic, complemented
15C13×#2492C211yesmaximal, characteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8C2211yescharacteristic
18C22×#6107C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C2×#88178C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C13×#400—21no—
23C13×#393—21no—
24C13×#391—21no—
25C13×#391C2211yescharacteristic
26C13×#391C2211yescharacteristic
27C13×#388—21no—
28C13×#380C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30C4×C13×C22⋊C4C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36C2×#88050C2211yescharacteristic
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40#11718607—21no—
41C22⋊C4×Dic13—21no—
42C4×C4⋊Dic13C2211yescharacteristic
43#11718590C2211yescharacteristic
44#11718589C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47#11718316—21no—
48#11718308—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
62C23×Dic13—21no—
63C22×Dic26C2311yescharacteristic
64C13×C4⋊Q8—22no—
65C13×C4⋊Q8—41no—
66C13×C22⋊Q8—22no—
67C13×C22⋊Q8—41no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4D411yescharacteristic
76C2×C13×C22⋊C4D411yescharacteristic
77C2×C42×C13—21no—
78C2×C42×C13C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×C22⋊Dic13—21no—
81C2×#6107—22no—
82C2×#6107—41no—
83C2×#6107—41no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—41no—
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90#88178—22no—
91#88178—22no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C4×Dic26—22no—
102C4×Dic26—41no—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95D411yescharacteristic
110C13×#95D411yescharacteristic
111#88075—22no—
112#88075—22no—
113#88075—41no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118C22⋊#1055—41no—
119C22⋊#1055—41no—
120#88050—22no—
121#88050—22no—
122#88050—41no—
123#88047—22no—
124C4⋊#1055—41no—
125C4×#1055—41no—
126#26726—131nomaximal, Sylow
127C24×C13C2×D411yescharacteristic
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13—21no—
132C2×Q8×C13—21no—
133C2×Q8×C13—21no—
134C2×Q8×C13—42no—
135C2×Q8×C13—42no—
136C2×Q8×C13—81no—
137C22×C4×C13—21no—
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×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2411yescharacteristic
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—42no—
158C22×Dic13—42no—
159C22×Dic13—81no—
160C2×Dic26—21no—
161C2×Dic26—21no—
162C2×Dic26—21no—
163C2×Dic26—21no—
164C2×Dic26—21no—
165C2×Dic26#4112yes—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—42no—
172C13×C4⋊C4—42no—
173C13×C4⋊C4#4112yes—
174C13×C22⋊C4—41no—
175C13×C22⋊C4—42no—
176C13×C22⋊C4—81no—
177C13×C22⋊C4Q1614yescomplemented
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—21no—
182C42×C13—81no—
183C22⋊Dic13—24no—
184#6107—44no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—42no—
190C4⋊Dic13#4112yes—
191C4⋊Dic13#4112yes—
192#6101—24no—
193#6101—42no—
194#6101—81no—
195C4×Dic13—42no—
196C4×Dic13—81no—
197C2×#1055—21no—
198C2×#1055—21no—
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—
209#2492D1311yescharacteristic
210#2360—131no—
211#2056—131no—
212#2036—131no—
213#2024—131no—
214#2001—131no—
215#1987—131no—
216#1933—131no—
217#1928—131no—
218#1923—131no—
219#1921—131no—
220#1878—131no—
221#1872—131no—
222#1824—131no—
223C4×#103—131no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13C2×Q1612yes—
231C23×C13C22×D411yescharacteristic
232Q8×C13—41no—
233Q8×C13—41no—
234Q8×C13—41no—
235Q8×C13—41no—
236Q8×C13—84no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—22no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13C2×Q1612yes—
267C2×C4×C13C2×Q1612yes—
268C2×C4×C13C2×#4111yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13H(5,𝔽2)11yescharacteristic
273C2×C4×C13H(5,𝔽2)11yescharacteristic
274C2×Dic13—22no—
275C2×Dic13—22no—
276C2×Dic13—22no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—84no—
287Dic26—22no—
288Dic26—22no—
289Dic26—41no—
290Dic26—41no—
291#1055—41no—
292#1055—41no—
293#1055—41no—
294#1055—41no—
295C22×Q16—131no—
296C2×C4⋊Q8C2×D1311yescharacteristic
297C2×C22⋊Q8—131no—
298C2×C22⋊Q8C2×D1311yescharacteristic
299C2×C4×Q8—131no—
300C22×C4⋊C4—131no—
301C2×#107—131no—
302C2×C4⋊C8—131no—
303C2×#103—131no—
304C2×#103—131no—
305C2×#103—131no—
306C2×#103—131no—
307C2×#103—131no—
308C2×#103—131no—
309C2×C22⋊C8—131no—
310C2×C22⋊C8—131no—
311C2×C4×C8—131no—
312#400—21no—
313#393—21no—
314#391—21no—
315#391—131no—
316#391C2×D1311yescharacteristic
317#391C2×D1311yescharacteristic
318#389—131no—
319#389—261no—
320#388—21no—
321#387—261no—
322#385—261no—
323#380C2×D1311yescharacteristic
324C4×C4⋊C4—131no—
325C4×C4⋊C4C2×D1311yescharacteristic
326C4×C22⋊C4—261no—
327C4×C22⋊C4C2×D1311yescharacteristic
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#340—131no—
334#340—131no—
335#340—131no—
336#336—131no—
337#336—131no—
338C22×C13—22no—
339C22×C13—22no—
340C22×C13—22no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13#52511yescharacteristic
346C22×C13#54611yescharacteristic
347C22×C13#54611yescharacteristic
348C22×C13C22×Q1611yescharacteristic
349C22×C13#57511yescharacteristic
350C22×C13#57711yescharacteristic
351C22×C13#57711yescharacteristic
352C4×C13—22no—
353C4×C13—22no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13—41no—
357C4×C13—42no—
358C4×C13—81no—
359C4×C13—81no—
360C4×C13—81no—
361C4×C13#52911yescharacteristic
362C4×C13#53811yescharacteristic
363C4×C13#55511yescharacteristic
364C4×C13#55911yescharacteristic
365Dic13—42no—
366Dic13—42no—
367Dic13—42no—
368Dic13—81no—
369C22×Q8—21no—
370C22×Q8—131no—
371C22×Q8C22×D1311yescharacteristic
372C23×C4—261no—
373C23×C4C22×D1311yescharacteristic
374C2×Q16—262no—
375C2×Q16—521no—
376C2×Q16—521no—
377C22×C8—131no—
378C22×C8—131no—
379C22×C8—131no—
380C22×C8—131no—
381C4⋊Q8—22no—
382C4⋊Q8—41no—
383C22⋊Q8—22no—
384C22⋊Q8—41no—
385C22⋊Q8—262no—
386C22⋊Q8—262no—
387C4×Q8—262no—
388C4×Q8—521no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4—262no—
395C2×C4⋊C4—261no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—521no—
400C2×C4⋊C4C22×D1311yescharacteristic
401C2×C4⋊C4C22×D1311yescharacteristic
402C2×C4⋊C4C22×D1311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—261no—
406C2×C22⋊C4C22⋊D1311yescharacteristic
407C2×C22⋊C4C22⋊D1311yescharacteristic
408C2×C42—21no—
409C2×C42—261no—
410C2×C42—261no—
411C2×C42C22×D1311yescharacteristic
412C2×C42C22×D1311yescharacteristic
413#107—262no—
414C4⋊C8—521no—
415#103—262no—
416#103—262no—
417#103—262no—
418#103—262no—
419#103—521no—
420#103—521no—
421C22⋊C8—521no—
422C22⋊C8—521no—
423C4×C8—521no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—261no—
431#95—261no—
432#95—261no—
433#95—261no—
434#95C22⋊D1311yescharacteristic
435#95C22⋊D1311yescharacteristic
436C2×C13—42no—
437C2×C13#245911yescharacteristic
438C2×C13#310411yescharacteristic
439C2×C13#312511yescharacteristic
440C2×C13#329911yescharacteristic
441C2×C13#329911yescharacteristic
442C2×C13#331111yescharacteristic
443C2×C13#332311yescharacteristic
444C24C2×C22⋊D1311yescharacteristic
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—42no—
452C2×Q8—42no—
453C2×Q8—81no—
454C2×Q8—132no—
455C2×Q8—261no—
456C2×Q8—261no—
457C2×Q8—261no—
458C2×Q8—261no—
459C2×Q8—261no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4—522no—
475C22×C4—522no—
476C22×C4—1041no—
477C22×C4C2×C22⋊D1311yescharacteristic
478C22×C4C2×C22⋊D1311yescharacteristic
479C22×C4C2×C22⋊D1311yescharacteristic
480C22×C4C2×C22⋊D1311yescharacteristic
481C22×C4C2×C22⋊D1311yescharacteristic
482C22×C4C23×D1311yescharacteristic
483Q16—524no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—132no—
504C4⋊C4—132no—
505C4⋊C4—264no—
506C4⋊C4—261no—
507C4⋊C4—261no—
508C4⋊C4—261no—
509C4⋊C4—261no—
510C4⋊C4—522no—
511C4⋊C4—522no—
512C4⋊C4—1041no—
513C4⋊C4#612912yes—
514C22⋊C4—41no—
515C22⋊C4—42no—
516C22⋊C4—81no—
517C22⋊C4—264no—
518C22⋊C4#610714yescomplemented
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—81no—
524C42—522no—
525C42—1041no—
526C13#2672611yescharacteristic, complemented, Sylow
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23C2×#610712yes—
534C23C22×C22⋊D1311yescharacteristic
535Q8—41no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—84no—
540Q8—262no—
541Q8—262no—
542Q8—521no—
543Q8—521no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—262no—
574C2×C4—262no—
575C2×C4—262no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—1044no—
586C2×C4C2×#610712yes—
587C2×C4C2×#610712yes—
588C2×C4C2×#612911yescharacteristic
589C2×C4#8825111yescharacteristic
590C2×C4#41×D1311yescharacteristic
591C2×C4#41×D1311yescharacteristic
592C2×C4#41×D1311yescharacteristic
593C2×C4#8825611yescharacteristic
594C8—521no—
595C8—521no—
596C8—521no—
597C8—521no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22#1171951111yescharacteristic
606C22C22×#610711yescharacteristic
607C22#1171952711yescharacteristic
608C22#1171953311yescharacteristic
609C22#1171953411yescharacteristic
610C22#1171954111yescharacteristic
611C22#1171954211yescharacteristic
612C4—22no—
613C4—22no—
614C4—41no—
615C4—41no—
616C4—42no—
617C4—41no—
618C4—81no—
619C4—81no—
620C4—81no—
621C4—522no—
622C4—522no—
623C4—522no—
624C4—1041no—
625C4#1171937511yescharacteristic
626C4#1171938311yescharacteristic
627C4#1171938511yescharacteristic
628C4#1171938611yescharacteristic
629C2—42no—
630C2#1311876911yescharacteristic
631C2#1312487111yescharacteristic
632C2#1312510711yescharacteristic
633C2#1312670611yescharacteristic
634C2#1312671211yescharacteristic
635C2#1312686611yescharacteristic
636C2#1312705211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2492C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2492D13
hypocenterC13#26726
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. #13116158C2semidirect
4. #13115974C2semidirect
6. #13115785C2semidirect
7. #13115515C2semidirect
8. #13115474C2semidirect
10. #13115428C2semidirect
11. #13115180C2semidirect
14. C4×#88050C2semidirect
177. C13×C22⋊C4Q16semidirect
518. C22⋊C4#6107semidirect
526. C13#26726semidirect

Maximal subgroups

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

subgroupindex
#131178392
#131161582
#131160392
#131159742
#131158442
#131157852
#131155152
#131154742
#131154442
#131154282
#131151802
#131151442
#131149242
C4×#880502
C13×#24922
#2672613