Finite Group Databasebeta

← #15907259

Subgroups — #15907259

Order 3328.

854 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119138C211yesmaximal, characteristic
2C4⋊C4×C22⋊D13C211yesmaximal, characteristic
3#13116396C211yesmaximal, characteristic, complemented
4#13116311C211yesmaximal, characteristic, complemented
5#13116263C211yesmaximal, characteristic, complemented
6#13116261C211yesmaximal, characteristic, complemented
7#13115406C211yesmaximal, characteristic, complemented
8#13115405C211yesmaximal, characteristic, complemented
9#13115128C211yesmaximal, characteristic
10#13115025C211yesmaximal, characteristic, complemented
11#13115024C211yesmaximal, characteristic, complemented
12#13114922C211yesmaximal, characteristic, complemented
13#13114921C211yesmaximal, characteristic, complemented
14#13114865C211yesmaximal, characteristic, complemented
15C2×C13×#340C211yesmaximal, characteristic, complemented
16C23×C8×C13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88183—21no—
20C2×C4×C22⋊D13—21no—
21C2×C4×C22⋊D13C2211yescharacteristic
22C2×C4⋊C4×D13C2211yescharacteristic
23#11718873C2211yescharacteristic
24#11718873C2211yescharacteristic
25#11718872—21no—
26#11718871—21no—
27C2×C22⋊#1055C2211yescharacteristic
28C2×#88060C2211yescharacteristic
29C2×#88060C2211yescharacteristic
30C2×#88058C2211yescharacteristic
31C2×#88058C2211yescharacteristic
32#11718654—21no—
33#11718650—21no—
34#11718648C2211yescharacteristic
35#11718648C2211yescharacteristic
36#11718648C2211yescharacteristic
37#11718641—21no—
38#11718637C2211yescharacteristic
39C4⋊C4×Dic13C2211yescharacteristic
40#11718634C2211yescharacteristic
41#11718634C2211yescharacteristic
42#11718633—21no—
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45C13×#340C2211yescharacteristic
46C13×#340C2211yescharacteristic
47C13×#340C2211yescharacteristic
48C13×#340C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59C23×C4×C13—21no—
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13D411yescharacteristic
63C22×C4×D13—21no—
64C22×C4×D13C2311yescharacteristic
65C22×C8×C13—22no—
66C22×C8×C13—22no—
67C22×C8×C13—41no—
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—41no—
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13—21no—
82C2×C22⋊Dic13D411yescharacteristic
83#88183—44no—
84C4×C22⋊D13—22no—
85C4×C22⋊D13—22no—
86C4×C22⋊D13—44no—
87C2×#6103—21no—
88C2×#6103—21no—
89C2×#6103—21no—
90C2×#6103D411yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×#6101D411yescharacteristic
101C2×C4×Dic13—21no—
102C2×C4×Dic13C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C4⋊C4×D13—22no—
106C4⋊C4×D13—41no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115C22⋊#1055—22no—
116#88060—22no—
117#88060—41no—
118#88058—22no—
119#88058—41no—
120#88047—22no—
121#88047—41no—
122#24933—131nomaximal, Sylow
123C24×C13C2×D411yescharacteristic
124C23×D13C2×D411yescharacteristic
125C22×C4×C13—21no—
126C22×C4×C13—21no—
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—42no—
134C22×C4×C13—42no—
135C22×C4×C13—42no—
136C22×C4×C13—42no—
137C22×C4×C13—42no—
138C22×C4×C13—81no—
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13#4112yes—
141C22×C4×C13#4112yes—
142C22×C4×C13C2411yescharacteristic
143C2×C22⋊D13—22no—
144C2×C22⋊D13—22no—
145C2×C22⋊D13D814yes—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13C2×D411yescharacteristic
151C22×Dic13C2×D411yescharacteristic
152C22×Dic13C2×D411yescharacteristic
153C2×C4×D13—21no—
154C2×C4×D13—21no—
155C2×C4×D13—21no—
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×C4×D13—42no—
160C2×C4×D13—42no—
161C2×C4×D13—81no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—44no—
168C2×C8×C13#4112yes—
169C13×C4⋊C4—21no—
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#4112yes—
179C22⋊Dic13—22no—
180C22⋊Dic13—42no—
181C22⋊Dic13—42no—
182#6103—22no—
183#6103—42no—
184#6103—42no—
185#6103—42no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194#6101—22no—
195#6101—42no—
196#6101—42no—
197#6101—42no—
198#6101—42no—
199#6101—81no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C4×Dic13—42no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209#2486—131no—
210D4×C4⋊C4—131no—
211#2099—131no—
212#2083—131no—
213#2075—131no—
214#2075—131no—
215#1918—131no—
216#1918—131no—
217#1869—131no—
218#1852—131no—
219#1852—131no—
220#1823—131no—
221#1823—131no—
222#1808—131no—
223C2×#340D1311yescharacteristic, complemented
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13#12312yes—
229C23×C13C2×D812yes—
230C23×C13#13712yes—
231C23×C13C22×D411yescharacteristic
232C22×D13—21no—
233C22×D13—21no—
234C22×D13—21no—
235C22×D13—21no—
236C22×D13—21no—
237C22×D13—21no—
238C22×D13C2×D812yes—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—41no—
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—41no—
256C2×C4×C13—41no—
257C2×C4×C13—84no—
258C2×C4×C13—84no—
259C2×C4×C13#12312yes—
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13C2×#4111yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13H(5,𝔽2)11yescharacteristic
265C2×C4×C132−1+411yescharacteristic
266C22⋊D13—28no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—41no—
276C2×Dic13—41no—
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—41no—
287C2×Dic13C2×D812yes—
288C4×D13—41no—
289C4×D13—41no—
290C4×D13—41no—
291C4×D13—41no—
292C4×D13—84no—
293C8×C13—22no—
294C8×C13—41no—
295#1055—41no—
296#1055—41no—
297C23×C8C2×D1311yescharacteristic
298C2×#123—261no—
299C2×C4×D4—131no—
300C2×C4×D4—261no—
301C22×C4⋊C4—131no—
302C22×C4⋊C4C2×D1311yescharacteristic
303C22×C4⋊C4C2×D1311yescharacteristic
304C2×#107—131no—
305C2×#107—131no—
306C2×#107—131no—
307C2×#107—131no—
308C2×C22⋊C8—131no—
309C2×C22⋊C8—131no—
310C2×C22⋊C8—131no—
311#398—261no—
312#397—261no—
313#389—131no—
314#389—131no—
315#389—261no—
316#385—261no—
317#385—261no—
318#384—131no—
319#381—261no—
320#380—131no—
321#380—131no—
322#380—131no—
323#380—131no—
324#380—131no—
325C4×C4⋊C4—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#340—131no—
334#340C2×D1311yescharacteristic
335#340C2×D1311yescharacteristic
336#340C2×D1311yescharacteristic
337#340C2×D1311yescharacteristic
338#336—131no—
339#336—131no—
340C22×C13—22no—
341C22×C13—22no—
342C22×C13—22no—
343C22×C13—22no—
344C22×C13—22no—
345C22×C13—22no—
346C22×C13#48014yes—
347C22×C13C2×#12311yescharacteristic
348C22×C13#54611yescharacteristic
349C22×C13#54711yescharacteristic
350C22×C13C22×D811yescharacteristic
351C22×C13C2×#13711yescharacteristic
352C22×C13#57711yescharacteristic
353C22×C13#57811yescharacteristic
354C2×D13—22no—
355C2×D13—22no—
356C2×D13—22no—
357C2×D13—41no—
358C2×D13—41no—
359C2×D13—41no—
360C2×D13—41no—
361C4×C13—22no—
362C4×C13—42no—
363C4×C13—81no—
364C4×C13—81no—
365C4×C13—81no—
366C4×C13#52911yescharacteristic
367C4×C13#53911yescharacteristic
368C4×C13#55111yescharacteristic
369C4×C13#55211yescharacteristic
370Dic13—22no—
371Dic13—41no—
372Dic13—41no—
373Dic13—81no—
374Dic13—81no—
375Dic13—81no—
376Dic13—81no—
377C22×D4—131no—
378C23×C4—21no—
379C23×C4—21no—
380C23×C4—131no—
381C23×C4—261no—
382C23×C4C22×D1311yescharacteristic
383C22×C8—22no—
384C22×C8—22no—
385C22×C8—41no—
386C22×C8—131no—
387C22×C8—131no—
388C22×C8C22×D1311yescharacteristic
389C22×C8C22×D1311yescharacteristic
390#123—524no—
391C4×D4—262no—
392C4×D4—262no—
393C4×D4—524no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—41no—
400C2×C4⋊C4—131no—
401C2×C4⋊C4—131no—
402C2×C4⋊C4—131no—
403C2×C4⋊C4—131no—
404C2×C4⋊C4—131no—
405C2×C4⋊C4—262no—
406C2×C4⋊C4—261no—
407C2×C4⋊C4—261no—
408C2×C4⋊C4—261no—
409C2×C4⋊C4—261no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4—521no—
412C2×C4⋊C4C22×D1311yescharacteristic
413C2×C4⋊C4C22×D1311yescharacteristic
414C2×C4⋊C4C22×D1311yescharacteristic
415C2×C4⋊C4C22×D1311yescharacteristic
416C2×C22⋊C4—131no—
417C2×C22⋊C4—131no—
418C2×C22⋊C4—261no—
419C2×C22⋊C4—261no—
420C2×C22⋊C4—261no—
421C2×C22⋊C4—261no—
422C2×C22⋊C4—261no—
423C2×C42—131no—
424C2×C42—261no—
425#107—262no—
426#107—262no—
427#107—521no—
428#107—521no—
429C22⋊C8—262no—
430C22⋊C8—262no—
431C22⋊C8—521no—
432#95—261no—
433#95—261no—
434#95—261no—
435#95—261no—
436#95—261no—
437#95—261no—
438#95—261no—
439#95—261no—
440C2×C13—24no—
441C2×C13#241911yescharacteristic
442C2×C13C2×#48011yescharacteristic
443C2×C13#309711yescharacteristic
444C2×C13#329411yescharacteristic
445C2×C13#331211yescharacteristic
446C2×C13#333411yescharacteristic
447C2×C13#334411yescharacteristic
448D13—42no—
449C24—131no—
450C24D4×D1311yescharacteristic
451C2×D4—134no—
452C2×D4—262no—
453C2×D4—262no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—81no—
468C22×C4—131no—
469C22×C4—131no—
470C22×C4—131no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4—522no—
482C22×C4—522no—
483C22×C4—1041no—
484C22×C4#612712yes—
485C22×C4D4×D1311yescharacteristic
486C22×C4#612912yes—
487C22×C4C23×D1311yescharacteristic
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—44no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8#612712yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—262no—
511C4⋊C4—261no—
512C4⋊C4—261no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—261no—
516C4⋊C4—261no—
517C4⋊C4—261no—
518C4⋊C4—261no—
519C4⋊C4—522no—
520C4⋊C4—522no—
521C4⋊C4—522no—
522C4⋊C4—522no—
523C4⋊C4—1041no—
524C4⋊C4#612712yes—
525C22⋊C4—262no—
526C22⋊C4—262no—
527C22⋊C4—522no—
528C22⋊C4—522no—
529C22⋊C4—522no—
530C22⋊C4—522no—
531C22⋊C4—522no—
532C42—261no—
533C42—261no—
534C42—522no—
535C13#2493311yescharacteristic, complemented, Sylow
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—132no—
541C23—261no—
542C23—261no—
543C23—261no—
544C23—261no—
545C23—261no—
546C23—261no—
547C23#8813712yes—
548C23D8×D1312yes—
549C23#8816912yes—
550C23C2×D4×D1311yescharacteristic
551D4—268no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
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—84no—
571C2×C4—84no—
572C2×C4—132no—
573C2×C4—261no—
574C2×C4—261no—
575C2×C4—261no—
576C2×C4—261no—
577C2×C4—261no—
578C2×C4—261no—
579C2×C4—261no—
580C2×C4—261no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4—521no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—1044no—
598C2×C4#8813712yes—
599C2×C4C2×#612711yescharacteristic
600C2×C4C2×#612711yescharacteristic
601C2×C4C2×#612711yescharacteristic
602C2×C4C2×#612911yescharacteristic
603C2×C4#8825111yescharacteristic
604C2×C4#8825411yescharacteristic
605C8—22no—
606C8—41no—
607C8—521no—
608C8—521no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—262no—
616C22—262no—
617C22—262no—
618C22—521no—
619C22—521no—
620C22—521no—
621C22—521no—
622C22#1171843514yes—
623C22C2×#8813711yescharacteristic
624C22#1171919511yescharacteristic
625C22#1171921211yescharacteristic
626C22C2×D8×D1311yescharacteristic
627C22C2×#8816911yescharacteristic
628C22#1171946711yescharacteristic
629C22#1171947111yescharacteristic
630C4—22no—
631C4—42no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—262no—
636C4—521no—
637C4—521no—
638C4—1041no—
639C4—1041no—
640C4—1041no—
641C4—1041no—
642C4#1171918411yescharacteristic
643C4#1171920011yescharacteristic
644C4#1171921811yescharacteristic
645C4#1171922011yescharacteristic
646C2—24no—
647C2—522no—
648C2#1311831311yescharacteristic
649C2C2×#1171843511yescharacteristic
650C2#1312480111yescharacteristic
651C2#1312664511yescharacteristic
652C2#1312688311yescharacteristic
653C2#1312718111yescharacteristic
654C2#1312728711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#340C2
socleC23×C13C22×D4
prime radicalC22×C22⋊D13D4
hypercenterC2×#340D13
hypocenterC13#24933
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
3. #13116396C2semidirect
4. #13116311C2semidirect
5. #13116263C2semidirect
6. #13116261C2semidirect
7. #13115406C2semidirect
8. #13115405C2semidirect
10. #13115025C2semidirect
11. #13115024C2semidirect
12. #13114922C2semidirect
13. #13114921C2semidirect
14. #13114865C2semidirect
15. C2×C13×#340C2semidirect
223. C2×#340D13semidirect
535. C13#24933semidirect

Maximal subgroups

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

subgroupindex
#131191382
C4⋊C4×C22⋊D132
#131163962
#131163112
#131162632
#131162612
#131154062
#131154052
#131151282
#131150252
#131150242
#131149222
#131149212
#131148652
C2×C13×#3402
#2493313