Finite Group Databasebeta

← #15907630

Subgroups — #15907630

Order 3328.

770 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117785C211yesmaximal, characteristic
2#13116399C211yesmaximal, characteristic, complemented
3#13116312C211yesmaximal, characteristic, complemented
4#13116273C211yesmaximal, characteristic, complemented
5#13116267C211yesmaximal, characteristic, complemented
6#13115404C211yesmaximal, characteristic, complemented
7#13115404C211yesmaximal, characteristic, complemented
8#13115134C211yesmaximal, characteristic
9#13115033C211yesmaximal, characteristic, complemented
10#13115033C211yesmaximal, characteristic, complemented
11#13114928C211yesmaximal, characteristic, complemented
12#13114926C211yesmaximal, characteristic, complemented
13#13114867C211yesmaximal, characteristic, complemented
14#13114555C211yesmaximal, characteristic, complemented
15C13×#2486C211yesmaximal, characteristic
16C2×C13×#123—21no—
17C2×C4×D4×C13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22C13×#398—21no—
23C13×#397—21no—
24C13×#389C2211yescharacteristic
25C13×#389C2211yescharacteristic
26C13×#381—21no—
27C13×#380C2211yescharacteristic
28C13×#380C2211yescharacteristic
29C13×#380C2211yescharacteristic
30#11718882—21no—
31#11718873C2211yescharacteristic
32#11718873C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36C4⋊C4×Dic13—21no—
37C2×#88048C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41#11718612—21no—
42#11718612—21no—
43#11718596C2211yescharacteristic
44C4×C4⋊Dic13C2211yescharacteristic
45#11718121C2211yescharacteristic
46#11718121C2211yescharacteristic
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D4×C13D411yescharacteristic
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C13×#123—44no—
64C4×D4×C13—22no—
65C4×D4×C13—22no—
66C2×C13×C4⋊C4—22no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
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⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4D411yescharacteristic
80C2×C13×C22⋊C4D411yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×C22⋊Dic13—21no—
83C2×C22⋊Dic13—21no—
84C2×C22⋊Dic13—21no—
85C2×C22⋊Dic13—21no—
86#88180—22no—
87#88180—22no—
88#88180—41no—
89#88180—41no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4×Dic13—21no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C2×#6099—22no—
100C2×#6099—22no—
101C2×#6099—41no—
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114C22⋊#1055—22no—
115C22⋊#1055—22no—
116C22⋊#1055—41no—
117#88048—41no—
118#88048—41no—
119#88047—22no—
120#88047—22no—
121#24958—131nomaximal, Sylow
122C24×C13C2×D411yescharacteristic
123C24×C13C2×D411yescharacteristic
124C2×D4×C13—22no—
125C2×D4×C13—22no—
126C2×D4×C13—41no—
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—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—42no—
142C22×C4×C13—42no—
143C22×C4×C13—42no—
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13#4112yes—
149C22×C4×C13#4112yes—
150C22×C4×C13C2411yescharacteristic
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—42no—
165C13×C4⋊C4—42no—
166C13×C4⋊C4—42no—
167C13×C22⋊C4—22no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—42no—
170C13×C22⋊C4—42no—
171C13×C22⋊C4—42no—
172C42×C13—21no—
173C42×C13—21no—
174C22⋊Dic13—42no—
175C22⋊Dic13—42no—
176C22⋊Dic13—81no—
177C22⋊Dic13—81no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—42no—
186C4⋊Dic13—81no—
187C4⋊Dic13#4112yes—
188C4×Dic13—42no—
189C4×Dic13—42no—
190C4×Dic13—42no—
191#6099—44no—
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×#1055—21no—
203C2×#1055#4112yes—
204#2486D1311yescharacteristic
205#2354—131no—
206#2100—131no—
207#2084—131no—
208#2077—131no—
209#2076—131no—
210#1918—131no—
211#1918—131no—
212#1870—131no—
213#1854—131no—
214#1854—131no—
215#1825—131no—
216#1824—131no—
217#1809—131no—
218#1736—131no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13#12312yes—
233C23×C13C22×D411yescharacteristic
234D4×C13—44no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
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—21no—
248C2×C4×C13—21no—
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—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—84no—
266C2×C4×C13#12312yes—
267C2×C4×C13AGL(1,ℤ/8)12yes—
268C2×C4×C13C2×#4111yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13H(5,𝔽2)11yescharacteristic
273C2×C4×C132−1+411yescharacteristic
274C2×Dic13—22no—
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—
286#1055—22no—
287#1055—41no—
288#1055—41no—
289#1055—41no—
290C22×M16—131no—
291C2×#123—21no—
292C2×C4×D4C2×D1311yescharacteristic
293C2×#117—131no—
294C2×#117—131no—
295C22×C4⋊C4C2×D1311yescharacteristic
296C2×#107—131no—
297C2×#107—131no—
298C2×#106—131no—
299C2×#106—131no—
300C2×C22⋊C8—131no—
301C2×C22⋊C8—131no—
302C2×C22⋊C8—131no—
303#398—21no—
304#397—21no—
305#390—261no—
306#389C2×D1311yescharacteristic
307#389C2×D1311yescharacteristic
308#388—261no—
309#388—261no—
310#384—131no—
311#381—21no—
312#380—131no—
313#380—131no—
314#380C2×D1311yescharacteristic
315#380C2×D1311yescharacteristic
316#380C2×D1311yescharacteristic
317C4×C4⋊C4—131no—
318C4×C4⋊C4—261no—
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#340—131no—
328#340—131no—
329#340—131no—
330#340—131no—
331#336—131no—
332#336—131no—
333C22×C13—22no—
334C22×C13—22no—
335C22×C13—22no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13—41no—
346C22×C13—41no—
347C22×C13C2×#12311yescharacteristic
348C22×C13#54611yescharacteristic
349C22×C13#54711yescharacteristic
350C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C13#57511yescharacteristic
352C22×C13#57711yescharacteristic
353C22×C13#57811yescharacteristic
354C4×C13—22no—
355C4×C13—22no—
356C4×C13—41no—
357C4×C13—41no—
358C4×C13—81no—
359C4×C13—81no—
360C4×C13—81no—
361C4×C13—81no—
362C4×C13#52911yescharacteristic
363C4×C13#53911yescharacteristic
364C4×C13#55111yescharacteristic
365C4×C13#55211yescharacteristic
366Dic13—42no—
367Dic13—81no—
368Dic13—81no—
369Dic13—81no—
370C22×D4C22⋊D1311yescharacteristic
371C23×C4—21no—
372C23×C4C22×D1311yescharacteristic
373C23×C4C22×D1311yescharacteristic
374C2×M16—262no—
375C2×M16—262no—
376C2×M16—521no—
377C22×C8—131no—
378C22×C8—131no—
379C22×C8—131no—
380C22×C8—131no—
381#123—44no—
382C4×D4—22no—
383C4×D4—22no—
384#117—262no—
385#117—262no—
386#117—521no—
387#117—521no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4—131no—
396C2×C4⋊C4—131no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4C22⋊D1311yescharacteristic
400C2×C4⋊C4C22×D1311yescharacteristic
401C2×C4⋊C4C22×D1311yescharacteristic
402C2×C4⋊C4C22×D1311yescharacteristic
403C2×C4⋊C4C22×D1311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—261no—
408C2×C22⋊C4—261no—
409C2×C22⋊C4—261no—
410C2×C22⋊C4—261no—
411C2×C22⋊C4C22⋊D1311yescharacteristic
412C2×C22⋊C4C22⋊D1311yescharacteristic
413C2×C42—261no—
414C2×C42—261no—
415C2×C42—261no—
416C2×C42C22×D1311yescharacteristic
417#107—262no—
418#107—262no—
419#106—521no—
420#106—521no—
421C22⋊C8—262no—
422C22⋊C8—262no—
423C22⋊C8—521no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—261no—
430#95—261no—
431#95—261no—
432C2×C13—42no—
433C2×C13—81no—
434C2×C13#241911yescharacteristic
435C2×C13#309411yescharacteristic
436C2×C13#309711yescharacteristic
437C2×C13#331711yescharacteristic
438C2×C13#333011yescharacteristic
439C2×C13#334911yescharacteristic
440C2×C13#335411yescharacteristic
441C24C2×C22⋊D1311yescharacteristic
442C24C2×C22⋊D1311yescharacteristic
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—41no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4#612912yes—
468C22×C4#612912yes—
469C22×C4C2×C22⋊D1311yescharacteristic
470C22×C4C2×C22⋊D1311yescharacteristic
471C22×C4C2×C22⋊D1311yescharacteristic
472C22×C4C2×C22⋊D1311yescharacteristic
473C22×C4C23×D1311yescharacteristic
474M16—524no—
475C2×C8—132no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C4⋊C4—22no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—132no—
500C4⋊C4—261no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—522no—
508C4⋊C4—1041no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—42no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—522no—
515C22⋊C4—522no—
516C22⋊C4—1041no—
517C22⋊C4—1041no—
518C42—21no—
519C42—21no—
520C42—522no—
521C42—522no—
522C42—522no—
523C13#2495811yescharacteristic, complemented, Sylow
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23#8818912yes—
538C23C22×C22⋊D1311yescharacteristic
539D4—44no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
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—84no—
571C2×C4—262no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4#8818612yes—
584C2×C4#8818912yes—
585C2×C4C2×#612911yescharacteristic
586C2×C4C2×#612911yescharacteristic
587C2×C4#41×D1311yescharacteristic
588C2×C4#41×D1311yescharacteristic
589C2×C4#8825611yescharacteristic
590C2×C4#8825711yescharacteristic
591C8—262no—
592C8—521no—
593C8—521no—
594C8—521no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22C2×#8818611yescharacteristic
610C22C2×#8818911yescharacteristic
611C22#1171952711yescharacteristic
612C22#1171952911yescharacteristic
613C22#1171953411yescharacteristic
614C22#1171954211yescharacteristic
615C22#1171954311yescharacteristic
616C4—22no—
617C4—22no—
618C4—41no—
619C4—41no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4—81no—
624C4—522no—
625C4—1041no—
626C4—1041no—
627C4—1041no—
628C4#1171935411yescharacteristic
629C4#1171935511yescharacteristic
630C4#1171936311yescharacteristic
631C4#1171937011yescharacteristic
632C2—42no—
633C2—81no—
634C2#1311830911yescharacteristic
635C2#1312477211yescharacteristic
636C2#1312479911yescharacteristic
637C2#1312695611yescharacteristic
638C2#1312713511yescharacteristic
639C2#1312736611yescharacteristic
640C2#1312743111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2486C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenter#2486D13
hypocenterC13#24958
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2486

Complements

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

NH ≅ G/Ntype
2. #13116399C2semidirect
3. #13116312C2semidirect
4. #13116273C2semidirect
5. #13116267C2semidirect
6. #13115404C2semidirect
7. #13115404C2semidirect
9. #13115033C2semidirect
10. #13115033C2semidirect
11. #13114928C2semidirect
12. #13114926C2semidirect
13. #13114867C2semidirect
14. #13114555C2semidirect
523. C13#24958semidirect

Maximal subgroups

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

subgroupindex
#131177852
#131163992
#131163122
#131162732
#131162672
#131154042
#131151342
#131150332
#131149282
#131149262
#131148672
#131145552
C13×#24862
#2495813