Finite Group Databasebeta

← #15931051

Subgroups — #15931051

Order 3328.

790 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117839C211yesmaximal, characteristic, complemented
2#13116153C211yesmaximal, characteristic, complemented
3#13116039C211yesmaximal, characteristic, complemented
4#13115984C211yesmaximal, characteristic, complemented
5#13115839C211yesmaximal, characteristic
6#13115794C211yesmaximal, characteristic, complemented
7#13115522C211yesmaximal, characteristic, complemented
8#13115453C211yesmaximal, characteristic, complemented
9#13115444C211yesmaximal, characteristic, complemented
10#13115428C211yesmaximal, characteristic, complemented
11#13115194C211yesmaximal, characteristic, complemented
12#13115154C211yesmaximal, characteristic
13#13114920C211yesmaximal, characteristic, complemented
14C4×#88050C211yesmaximal, characteristic, complemented
15C13×#2490C211yesmaximal, characteristic
16C2×C13×#125C2211yescharacteristic
17C2×C13×#121C2211yescharacteristic
18C22×#6105C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C2×#88178C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C13×#397—21no—
23C13×#394—21no—
24C13×#390—21no—
25C13×#390C2211yescharacteristic
26C13×#390C2211yescharacteristic
27C13×#388—21no—
28C13×#380C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30C4×C13×C22⋊C4C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
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×D4×C13—21no—
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×Dic13—21no—
63C22×Dic26C2311yescharacteristic
64C13×#125—22no—
65C13×#125—41no—
66C13×#121—22no—
67C13×#121—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⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4D411yescharacteristic
80C2×C13×C22⋊C4D411yescharacteristic
81C2×C42×C13—21no—
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×C22⋊Dic13—21no—
85C2×#6105—22no—
86C2×#6105—41no—
87C2×#6105—41no—
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—41no—
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94#88178—22no—
95#88178—22no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13—21no—
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C4×Dic26—22no—
106C4×Dic26—41no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95D411yescharacteristic
110C13×#95D411yescharacteristic
111#88072—22no—
112#88072—22no—
113#88072—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#26727—131nomaximal, Sylow
127C24×C13—21no—
128C24×C13C2×D411yescharacteristic
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13—42no—
136C2×D4×C13—42no—
137C2×D4×C13—81no—
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—22no—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—42no—
177C13×C22⋊C4—42no—
178C13×C22⋊C4—81no—
179C13×C22⋊C4—81no—
180C13×C22⋊C4—81no—
181C13×C22⋊C4—81no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—21no—
186C42×C13—81no—
187C22⋊Dic13—24no—
188#6105—44no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—42no—
194C4⋊Dic13#4112yes—
195C4⋊Dic13#4112yes—
196#6101—24no—
197#6101—42no—
198#6101—81no—
199C4×Dic13—42no—
200C4×Dic13—81no—
201C2×#1055—21no—
202C2×#1055—21no—
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—21no—
213#2490D1311yescharacteristic
214#2360—131no—
215#2055—131no—
216#2036—131no—
217#2026—131no—
218#2000—131no—
219#1989—131no—
220#1934—131no—
221#1925—131no—
222#1923—131no—
223#1921—131no—
224#1880—131no—
225#1874—131no—
226#1823—131no—
227C4×#103—131no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—41no—
235C23×C13—41no—
236C23×C13—41no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13#13512yes—
242C23×C13C22×D411yescharacteristic
243D4×C13—41no—
244D4×C13—41no—
245D4×C13—41no—
246D4×C13—41no—
247D4×C13—84no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
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—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#13712yes—
276C2×C4×C13C2×#4111yescharacteristic
277C2×C4×C13C2×#4111yescharacteristic
278C2×C4×C13C2×#4111yescharacteristic
279C2×C4×C13C2×#4111yescharacteristic
280C2×C4×C13H(5,𝔽2)11yescharacteristic
281C2×C4×C13H(5,𝔽2)11yescharacteristic
282C2×Dic13—22no—
283C2×Dic13—22no—
284C2×Dic13—22no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—84no—
295Dic26—22no—
296Dic26—22no—
297Dic26—41no—
298Dic26—41no—
299#1055—41no—
300#1055—41no—
301#1055—41no—
302#1055—41no—
303C22×SD16—131no—
304C2×#125C2×D1311yescharacteristic
305C2×C22⋊Q8—131no—
306C2×#121C2×D1311yescharacteristic
307C2×C4×Q8—131no—
308C22×C4⋊C4—131no—
309C2×#107—131no—
310C2×C4⋊C8—131no—
311C2×#103—131no—
312C2×#103—131no—
313C2×#103—131no—
314C2×#102—131no—
315C2×#102—131no—
316C2×#102—131no—
317C2×C22⋊C8—131no—
318C2×C22⋊C8—131no—
319C2×C4×C8—131no—
320#397—21no—
321#394—21no—
322#391—131no—
323#390—21no—
324#390C2×D1311yescharacteristic
325#390C2×D1311yescharacteristic
326#389—131no—
327#389—261no—
328#388—21no—
329#387—261no—
330#385—261no—
331#380C2×D1311yescharacteristic
332C4×C4⋊C4—131no—
333C4×C4⋊C4C2×D1311yescharacteristic
334C4×C22⋊C4—261no—
335C4×C22⋊C4C2×D1311yescharacteristic
336#340—131no—
337#340—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#340—131no—
342#340—131no—
343#340—131no—
344#336—131no—
345#336—131no—
346C22×C13—22no—
347C22×C13—22no—
348C22×C13—22no—
349C22×C13—41no—
350C22×C13—41no—
351C22×C13—41no—
352C22×C13—41no—
353C22×C13—81no—
354C22×C13—81no—
355C22×C13—81no—
356C22×C13—81no—
357C22×C13—81no—
358C22×C13—81no—
359C22×C13—81no—
360C22×C13#52511yescharacteristic
361C22×C13#54611yescharacteristic
362C22×C13#54611yescharacteristic
363C22×C13C2×#13511yescharacteristic
364C22×C13C2×#13711yescharacteristic
365C22×C13#57611yescharacteristic
366C22×C13#57711yescharacteristic
367C4×C13—22no—
368C4×C13—41no—
369C4×C13—41no—
370C4×C13—41no—
371C4×C13—42no—
372C4×C13—41no—
373C4×C13—81no—
374C4×C13—81no—
375C4×C13#52911yescharacteristic
376C4×C13#53811yescharacteristic
377C4×C13#55511yescharacteristic
378C4×C13#55911yescharacteristic
379Dic13—42no—
380Dic13—42no—
381Dic13—42no—
382Dic13—81no—
383C22×Q8—131no—
384C22×D4—21no—
385C22×D4C22×D1311yescharacteristic
386C23×C4—261no—
387C23×C4C22×D1311yescharacteristic
388C2×SD16—262no—
389C2×SD16—521no—
390C2×SD16—521no—
391C22×C8—131no—
392C22×C8—131no—
393C22×C8—131no—
394C22×C8—131no—
395#125—22no—
396#125—41no—
397C22⋊Q8—262no—
398C22⋊Q8—262no—
399#121—22no—
400#121—41no—
401C4×Q8—262no—
402C4×Q8—521no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—131no—
406C2×C4⋊C4—131no—
407C2×C4⋊C4—131no—
408C2×C4⋊C4—262no—
409C2×C4⋊C4—261no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4—261no—
412C2×C4⋊C4—261no—
413C2×C4⋊C4—521no—
414C2×C4⋊C4C22×D1311yescharacteristic
415C2×C4⋊C4C22×D1311yescharacteristic
416C2×C4⋊C4C22×D1311yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—261no—
424C2×C22⋊C4C22⋊D1311yescharacteristic
425C2×C22⋊C4C22⋊D1311yescharacteristic
426C2×C42—21no—
427C2×C42—261no—
428C2×C42—261no—
429C2×C42C22×D1311yescharacteristic
430C2×C42C22×D1311yescharacteristic
431#107—262no—
432C4⋊C8—521no—
433#103—262no—
434#103—262no—
435#103—521no—
436#102—262no—
437#102—262no—
438#102—521no—
439C22⋊C8—521no—
440C22⋊C8—521no—
441C4×C8—521no—
442#95—21no—
443#95—21no—
444#95—261no—
445#95—261no—
446#95—261no—
447#95—261no—
448#95C22⋊D1311yescharacteristic
449#95C22⋊D1311yescharacteristic
450C2×C13—42no—
451C2×C13—161no—
452C2×C13#245911yescharacteristic
453C2×C13#310811yescharacteristic
454C2×C13#311911yescharacteristic
455C2×C13#329611yescharacteristic
456C2×C13#329711yescharacteristic
457C2×C13#332011yescharacteristic
458C2×C13#333311yescharacteristic
459C24—21no—
460C24C2×C22⋊D1311yescharacteristic
461C2×Q8—132no—
462C2×Q8—261no—
463C2×Q8—261no—
464C2×Q8—261no—
465C2×Q8—261no—
466C2×Q8—261no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—81no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—261no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—522no—
490C22×C4—522no—
491C22×C4—1041no—
492C22×C4C2×C22⋊D1311yescharacteristic
493C22×C4C2×C22⋊D1311yescharacteristic
494C22×C4C2×C22⋊D1311yescharacteristic
495C22×C4C2×C22⋊D1311yescharacteristic
496C22×C4C2×C22⋊D1311yescharacteristic
497C22×C4C23×D1311yescharacteristic
498SD16—524no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—261no—
503C2×C8—261no—
504C2×C8—261no—
505C2×C8—261no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—261no—
509C2×C8—261no—
510C2×C8—261no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—42no—
517C4⋊C4—42no—
518C4⋊C4—132no—
519C4⋊C4—132no—
520C4⋊C4—264no—
521C4⋊C4—261no—
522C4⋊C4—261no—
523C4⋊C4—261no—
524C4⋊C4—261no—
525C4⋊C4—522no—
526C4⋊C4—522no—
527C4⋊C4—1041no—
528C4⋊C4#612912yes—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—42no—
532C22⋊C4—42no—
533C22⋊C4—81no—
534C22⋊C4—81no—
535C22⋊C4—81no—
536C22⋊C4—81no—
537C22⋊C4—264no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—81no—
543C42—522no—
544C42—1041no—
545C13#2672711yescharacteristic, complemented, Sylow
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23#8820412yes—
560C23C22×C22⋊D1311yescharacteristic
561Q8—262no—
562Q8—262no—
563Q8—521no—
564Q8—521no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—84no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
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—262no—
598C2×C4—262no—
599C2×C4—262no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—1044no—
610C2×C4#8820512yes—
611C2×C4C2×#612911yescharacteristic
612C2×C4#8825111yescharacteristic
613C2×C4#41×D1311yescharacteristic
614C2×C4#41×D1311yescharacteristic
615C2×C4#41×D1311yescharacteristic
616C2×C4#8825611yescharacteristic
617C8—521no—
618C8—521no—
619C8—521no—
620C8—521no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22#1171951111yescharacteristic
636C22C2×#8820411yescharacteristic
637C22C2×#8820511yescharacteristic
638C22#1171953311yescharacteristic
639C22#1171953411yescharacteristic
640C22#1171954011yescharacteristic
641C22#1171954111yescharacteristic
642C4—22no—
643C4—41no—
644C4—41no—
645C4—42no—
646C4—41no—
647C4—41no—
648C4—81no—
649C4—81no—
650C4—522no—
651C4—522no—
652C4—522no—
653C4—1041no—
654C4#1171937511yescharacteristic
655C4#1171938311yescharacteristic
656C4#1171938511yescharacteristic
657C4#1171938611yescharacteristic
658C2—42no—
659C2—161no—
660C2#1311876911yescharacteristic
661C2#1312491211yescharacteristic
662C2#1312502911yescharacteristic
663C2#1312667111yescharacteristic
664C2#1312668011yescharacteristic
665C2#1312700111yescharacteristic
666C2#1312717411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2490C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenter#2490D13
hypocenterC13#26727
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2490

Complements

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

NH ≅ G/Ntype
1. #13117839C2semidirect
2. #13116153C2semidirect
3. #13116039C2semidirect
4. #13115984C2semidirect
6. #13115794C2semidirect
7. #13115522C2semidirect
8. #13115453C2semidirect
9. #13115444C2semidirect
10. #13115428C2semidirect
11. #13115194C2semidirect
13. #13114920C2semidirect
14. C4×#88050C2semidirect
545. C13#26727semidirect

Maximal subgroups

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

subgroupindex
#131178392
#131161532
#131160392
#131159842
#131158392
#131157942
#131155222
#131154532
#131154442
#131154282
#131151942
#131151542
#131149202
C4×#880502
C13×#24902
#2672713