Finite Group Databasebeta

← #15921778

Subgroups — #15921778

Order 3328.

818 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718517C211yesmaximal, characteristic, complemented
2C2×#11718782C211yesmaximal, characteristic
3#13118550C211yesmaximal, characteristic
4#13118539C211yesmaximal, characteristic
5#13116316C211yesmaximal, characteristic, complemented
6#13116311C211yesmaximal, characteristic, complemented
7#13116177C211yesmaximal, characteristic, complemented
8#13116168C211yesmaximal, characteristic, complemented
9#13115575C211yesmaximal, characteristic, complemented
10#13115567C211yesmaximal, characteristic, complemented
11#13115033C211yesmaximal, characteristic
12#13115028C211yesmaximal, characteristic
13#13114991C211yesmaximal, characteristic, complemented
14#13114617C211yesmaximal, characteristic
15C13×#1809C211yesmaximal, characteristic
16C22×C13×M16C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C2×#88144C2211yescharacteristic
20C2×#88142C2211yescharacteristic
21C2×#88132—21no—
22C2×C13×#107C2211yescharacteristic
23C2×C13×#106C2211yescharacteristic
24C13×#380C2211yescharacteristic
25C13×#380C2211yescharacteristic
26C4×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊#1055C2211yescharacteristic
28#11718782—24no—
29C2×#88058C2211yescharacteristic
30C2×#88058C2211yescharacteristic
31C2×#88057C2211yescharacteristic
32C2×#88057C2211yescharacteristic
33C2×#88055C2211yescharacteristic
34C2×C8×Dic13C2211yescharacteristic
35#11718646C2211yescharacteristic
36#11718646C2211yescharacteristic
37#11718637C2211yescharacteristic
38#11718637C2211yescharacteristic
39#11718634C2211yescharacteristic
40#11718634C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45#11718610—21no—
46#11718609—21no—
47#11718607—21no—
48#11718517—24no—
49#11718318—21no—
50#11718317—21no—
51#11718316—21no—
52#11718308—21no—
53C13×#340C2211yescharacteristic
54C13×#340C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×Dic13—21no—
63C22×Dic26—21no—
64C2×C13×M16—22no—
65C2×C13×M16—22no—
66C2×C13×M16Q814yescomplemented
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4—21no—
75C2×C22⋊Dic13—21no—
76C2×C22⋊Dic13D411yescharacteristic
77C2×C22⋊Dic13D411yescharacteristic
78#88180—22no—
79#88180—41no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13—41no—
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13C2311yescharacteristic
100C2×C4×Dic13C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103#88144—22no—
104#88144—41no—
105#88142—22no—
106#88142—41no—
107#88132—44no—
108C13×#107—22no—
109C13×#106—22no—
110C13×#95—21no—
111C13×#95—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071D411yescharacteristic
117#88071D411yescharacteristic
118C22⋊#1055Q814yescomplemented
119#88058—22no—
120#88058D414yes—
121#88057—22no—
122#88057—22no—
123#88055—22no—
124C8×Dic13—22no—
125#88048—22no—
126#88048—41no—
127#88048—41no—
128#88047—22no—
129#26078—131nomaximal, Sylow
130C24×C13C2×D411yescharacteristic
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×C13C2×D411yescharacteristic
140C22×C4×C13C2×Q812yes—
141C22×C4×C13C2×Q812yes—
142C22×C4×C13C2411yescharacteristic
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—42no—
148C22×Dic13—42no—
149C22×Dic13—81no—
150C22×Dic13C2×D411yescharacteristic
151C22×Dic13C2×D411yescharacteristic
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154C2×Dic26—42no—
155C2×Dic26—42no—
156C2×Dic26—81no—
157C13×M16—28no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13C2×D412yes—
161C2×C8×C13C2×Q812yes—
162C2×C8×C13C2×Q812yes—
163C2×C8×C13#4112yes—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C22⋊C4—42no—
173C13×C22⋊C4—81no—
174C22⋊Dic13—22no—
175C22⋊Dic13—22no—
176C22⋊Dic13—42no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—42no—
184C4⋊Dic13—42no—
185C4⋊Dic13—42no—
186C4⋊Dic13—81no—
187C4⋊Dic13C2×D412yes—
188C4⋊Dic13C2×D412yes—
189#6101—42no—
190#6101—42no—
191#6101—42no—
192#6101—42no—
193#6101—42no—
194#6101—42no—
195#6101—81no—
196#6101—81no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C4×Dic13—42no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055C2×Q812yes—
207C2×#1055C2×Q812yes—
208C2×#501—131no—
209C2×#428—131no—
210#2441—131no—
211#2440—131no—
212#2084—131no—
213#2083—131no—
214#2059—131no—
215#2058—131no—
216#1943—131no—
217#1942—131no—
218#1854—131no—
219#1853—131no—
220#1844—131no—
221#1809D1311yescharacteristic
222#1753—131no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13C4⋊Q812yes—
230C23×C13C22×D411yescharacteristic
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—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13C4⋊Q812yes—
250C2×C4×C13C22×D411yescharacteristic
251C2×C4×C13C22×Q811yescharacteristic
252C2×C4×C13C22×Q811yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×C4×C13H(5,𝔽2)11yescharacteristic
255C2×C4×C132−1+411yescharacteristic
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—22no—
263C2×Dic13—22no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—21no—
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—
277C2×Dic13—41no—
278C2×Dic13—84no—
279C2×Dic13AGL(1,ℤ/8)12yes—
280C2×Dic13#13712yes—
281Dic26—84no—
282C8×C13—22no—
283C8×C13C22⋊Q814yescomplemented
284#1055—22no—
285#1055—22no—
286C22×M16C2×D1311yescharacteristic
287C2×C4⋊Q8—131no—
288C2×#125—131no—
289C2×C22⋊Q8—261no—
290C2×#117—131no—
291C22×C4⋊C4—131no—
292#501—264no—
293#428—264no—
294C2×#107—131no—
295C2×#107—131no—
296C2×#107—131no—
297C2×#107C2×D1311yescharacteristic
298C2×#106—131no—
299C2×#106—131no—
300C2×#106—131no—
301C2×#106—131no—
302C2×#106—131no—
303C2×#106C2×D1311yescharacteristic
304C2×C22⋊C8—131no—
305C2×#97—131no—
306C2×C4×C8—131no—
307#399—261no—
308#398—261no—
309#396—261no—
310#395—261no—
311#389—131no—
312#389—131no—
313#389—131no—
314#389—131no—
315#389—261no—
316#387—261no—
317#385—261no—
318#384—131no—
319#384—131no—
320#380C2×D1311yescharacteristic
321#380C2×D1311yescharacteristic
322C4×C22⋊C4—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#340C2×D1311yescharacteristic
328#340C2×D1311yescharacteristic
329#336—131no—
330#336—131no—
331C22×C13—22no—
332C22×C13—22no—
333C22×C13—22no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13C2×C4⋊Q811yescharacteristic
339C22×C13D4211yescharacteristic
340C22×C13#54711yescharacteristic
341C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
342C22×C13C2×#13711yescharacteristic
343C22×C13#57711yescharacteristic
344C22×C13#57711yescharacteristic
345C4×C13—22no—
346C4×C13—81no—
347C4×C13—81no—
348C4×C13—81no—
349C4×C13—81no—
350C4×C13C2×C22⋊Q811yescharacteristic
351C4×C13#54411yescharacteristic
352C4×C13D4×Q811yescharacteristic
353C4×C13#55411yescharacteristic
354Dic13—22no—
355Dic13—22no—
356Dic13—41no—
357Dic13—42no—
358Dic13—42no—
359Dic13—41no—
360Dic13—81no—
361Dic13—81no—
362C22×Q8—261no—
363C23×C4—261no—
364C23×C4C22×D1311yescharacteristic
365C2×M16—22no—
366C2×M16—22no—
367C2×M16Dic2614yescomplemented
368C22×C8—131no—
369C22×C8—131no—
370C22×C8C22×D1311yescharacteristic
371C22×C8C22×D1311yescharacteristic
372C4⋊Q8—262no—
373C4⋊Q8—521no—
374#125—262no—
375#125—521no—
376C22⋊Q8—524no—
377#117—262no—
378#117—521no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—262no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—261no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4—261no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4—261no—
396C2×C4⋊C4—521no—
397C2×C4⋊C4C22×D1311yescharacteristic
398C2×C4⋊C4C22×D1311yescharacteristic
399C2×C4⋊C4C22×D1311yescharacteristic
400C2×C4⋊C4C22×D1311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—131no—
404C2×C22⋊C4—131no—
405C2×C22⋊C4—261no—
406C2×C42—131no—
407C2×C42—131no—
408C2×C42—261no—
409#107—22no—
410#107—134no—
411#107—262no—
412#107—262no—
413#106—22no—
414#106—262no—
415#106—262no—
416#106—262no—
417#106—521no—
418#106—521no—
419C22⋊C8—134no—
420#97—262no—
421C4×C8—262no—
422#95—21no—
423#95—21no—
424#95—131no—
425#95—131no—
426#95—261no—
427#95—261no—
428#95—261no—
429#95—261no—
430C2×C13—42no—
431C2×C13#244011yescharacteristic
432C2×C13#316311yescharacteristic
433C2×C13#316511yescharacteristic
434C2×C13#327211yescharacteristic
435C2×C13#327811yescharacteristic
436C2×C13#334411yescharacteristic
437C2×C13#334511yescharacteristic
438C24D4×D1311yescharacteristic
439C2×Q8—522no—
440C2×Q8—522no—
441C2×Q8—1041no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—131no—
453C22×C4—131no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—522no—
459C22×C4—522no—
460C22×C4—1041no—
461C22×C4C2×Dic2612yes—
462C22×C4D4×D1311yescharacteristic
463C22×C4Q8×D1312yes—
464C22×C4C23×D1311yescharacteristic
465M16—28no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—132no—
469C2×C8—132no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8C2×Dic2612yes—
475C2×C8C2×Dic2612yes—
476C2×C8D4×D1312yes—
477C2×C8#612912yes—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—132no—
487C4⋊C4—132no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—522no—
495C4⋊C4—522no—
496C4⋊C4—522no—
497C4⋊C4—522no—
498C4⋊C4—522no—
499C4⋊C4—522no—
500C4⋊C4—522no—
501C4⋊C4—522no—
502C4⋊C4—522no—
503C4⋊C4—1041no—
504C4⋊C4—1041no—
505C4⋊C4—1041no—
506C22⋊C4—42no—
507C22⋊C4—81no—
508C22⋊C4—262no—
509C22⋊C4—262no—
510C22⋊C4—522no—
511C42—261no—
512C42—261no—
513C42—261no—
514C42—261no—
515C42—522no—
516C13#2607811yescharacteristic, complemented, Sylow
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23#8814212yes—
524C23C2×D4×D1311yescharacteristic
525Q8—1044no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—132no—
545C2×C4—132no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—261no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—261no—
553C2×C4—261no—
554C2×C4—261no—
555C2×C4—261no—
556C2×C4—262no—
557C2×C4—262no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—1044no—
569C2×C4#8814212yes—
570C2×C4C22×Dic2611yescharacteristic
571C2×C4C2×D4×D1311yescharacteristic
572C2×C4C2×#612911yescharacteristic
573C2×C4C2×Q8×D1311yescharacteristic
574C2×C4#8825611yescharacteristic
575C2×C4#8825711yescharacteristic
576C8—22no—
577C8—262no—
578C8—262no—
579C8#8813214yescomplemented
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22C2×#8814211yescharacteristic
588C22#1171931411yescharacteristic
589C22#1171931611yescharacteristic
590C22D13×AGL(1,ℤ/8)11yescharacteristic
591C22#1171948011yescharacteristic
592C22D13×#13711yescharacteristic
593C22#1171948311yescharacteristic
594C4—22no—
595C4—81no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4—262no—
600C4—262no—
601C4—521no—
602C4—522no—
603C4—522no—
604C4—521no—
605C4—1041no—
606C4—1041no—
607C4C2×#8813211yescharacteristic
608C4#1171922411yescharacteristic
609C4#1171933711yescharacteristic
610C4#1171934011yescharacteristic
611C2—42no—
612C2#1311853911yescharacteristic
613C2#1312536611yescharacteristic
614C2#1312538011yescharacteristic
615C2#1312643311yescharacteristic
616C2#1312649911yescharacteristic
617C2#1312728611yescharacteristic
618C2#1312730111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1809C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1809D13
hypocenterC13#26078
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
1. C2×#11718517C2semidirect
5. #13116316C2semidirect
6. #13116311C2semidirect
7. #13116177C2semidirect
8. #13116168C2semidirect
9. #13115575C2semidirect
10. #13115567C2semidirect
13. #13114991C2semidirect
66. C2×C13×M16Q8semidirect
118. C22⋊#1055Q8semidirect
283. C8×C13C22⋊Q8semidirect
367. C2×M16Dic26semidirect
516. C13#26078semidirect
579. C8#88132semidirect

Maximal subgroups

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

subgroupindex
C2×#117185172
C2×#117187822
#131185502
#131185392
#131163162
#131163112
#131161772
#131161682
#131155752
#131155672
#131150332
#131150282
#131149912
#131146172
C13×#18092
#2607813