Finite Group Databasebeta

← #15921776

Subgroups — #15921776

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×#11718363C211yesmaximal, characteristic, complemented
2C2×#11718782C211yesmaximal, characteristic
3#13118549C211yesmaximal, characteristic
4#13118538C211yesmaximal, characteristic
5#13116314C211yesmaximal, characteristic, complemented
6#13116309C211yesmaximal, characteristic, complemented
7#13116175C211yesmaximal, characteristic, complemented
8#13116170C211yesmaximal, characteristic, complemented
9#13115574C211yesmaximal, characteristic, complemented
10#13115569C211yesmaximal, characteristic, complemented
11#13115037C211yesmaximal, characteristic
12#13115031C211yesmaximal, characteristic
13#13114993C211yesmaximal, characteristic, complemented
14#13114869C211yesmaximal, characteristic
15C13×#1753C211yesmaximal, characteristic
16C22×C13×M16C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C2×#88132—21no—
20C2×#88124C2211yescharacteristic
21C2×#88123C2211yescharacteristic
22C2×C13×C22⋊C8C2211yescharacteristic
23C2×C13×#97C2211yescharacteristic
24C2×C4×C8×C13C2211yescharacteristic
25C4×C13×C22⋊C4C2211yescharacteristic
26#11718873C2211yescharacteristic
27#11718873C2211yescharacteristic
28#11718782—24no—
29C2×#88058C2211yescharacteristic
30C2×#88058C2211yescharacteristic
31C2×#88058C2211yescharacteristic
32C2×#88058C2211yescharacteristic
33C2×#88057C2211yescharacteristic
34C2×#88057C2211yescharacteristic
35C2×#88057C2211yescharacteristic
36C2×#88057C2211yescharacteristic
37C2×#88057C2211yescharacteristic
38C2×#88057C2211yescharacteristic
39#11718611—21no—
40#11718610—21no—
41#11718609—21no—
42#11718596C2211yescharacteristic
43#11718596C2211yescharacteristic
44#11718589C2211yescharacteristic
45#11718589C2211yescharacteristic
46#11718589C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718363—24no—
49#11718322—21no—
50#11718317—21no—
51#11718315—21no—
52#11718308—21no—
53C13×#336C2211yescharacteristic
54C13×#336C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60#11718143C2211yescharacteristic
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
69C22×C8×C13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C2×C13×C22⋊C4D411yescharacteristic
72C2×C13×C22⋊C4D411yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×C22⋊Dic13—21no—
76C2×C22⋊Dic13—21no—
77C2×C22⋊Dic13—21no—
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—21no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13—41no—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×#6101—21no—
101C2×#6101—21no—
102C2×C4×Dic13—21no—
103#88132—44no—
104#88124—22no—
105#88124—41no—
106#88123—22no—
107#88123—41no—
108C13×C22⋊C8Q814yescomplemented
109C13×#97—22no—
110C4×C8×C13—22no—
111C13×#95D411yescharacteristic
112C13×#95D411yescharacteristic
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88058—22no—
120#88058—22no—
121#88058—22no—
122#88058D414yes—
123#88057—22no—
124#88057—22no—
125#88057—22no—
126#88057—22no—
127#88057—41no—
128#88057—41no—
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×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
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—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—42no—
152C22×Dic13—42no—
153C22×Dic13—81no—
154C2×Dic26—42no—
155C2×Dic26—42no—
156C2×Dic26—81no—
157C13×M16—28no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13C2×D412yes—
165C2×C8×C13C2×Q812yes—
166C2×C8×C13C2×Q812yes—
167C2×C8×C13C2×Q812yes—
168C2×C8×C13C2×Q812yes—
169C2×C8×C13#4112yes—
170C13×C22⋊C4—22no—
171C13×C22⋊C4—22no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—21no—
176C22⋊Dic13—42no—
177C22⋊Dic13—42no—
178C22⋊Dic13—81no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—42no—
194C4⋊Dic13—42no—
195C4⋊Dic13—42no—
196C4⋊Dic13—42no—
197C4⋊Dic13—81no—
198C4⋊Dic13—81no—
199C4⋊Dic13C2×D412yes—
200C4⋊Dic13C2×D412yes—
201#6101—42no—
202#6101—42no—
203#6101—42no—
204#6101—42no—
205#6101—42no—
206#6101—81no—
207C4×Dic13—42no—
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#1809—131no—
222#1753D1311yescharacteristic
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—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13C4⋊Q812yes—
248C2×C4×C13AGL(1,ℤ/8)12yes—
249C2×C4×C13#13712yes—
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—22no—
257C2×Dic13—22no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
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—41no—
279C2×Dic13—41no—
280C2×Dic13—84no—
281Dic26—84no—
282C8×C13—22no—
283C8×C13—22no—
284C8×C13—22no—
285C8×C13C22⋊Q814yescomplemented
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×#107—131no—
298C2×#106—131no—
299C2×#106—131no—
300C2×#106—131no—
301C2×#106—131no—
302C2×#106—131no—
303C2×#106—131no—
304C2×C22⋊C8C2×D1311yescharacteristic
305C2×#97C2×D1311yescharacteristic
306C2×C4×C8C2×D1311yescharacteristic
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#380—131no—
321#380—131no—
322C4×C22⋊C4C2×D1311yescharacteristic
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#336C2×D1311yescharacteristic
330#336C2×D1311yescharacteristic
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—22no—
347C4×C13—22no—
348C4×C13—41no—
349C4×C13—41no—
350C4×C13C2×C22⋊Q811yescharacteristic
351C4×C13#54411yescharacteristic
352C4×C13D4×Q811yescharacteristic
353C4×C13#55411yescharacteristic
354Dic13—42no—
355Dic13—42no—
356Dic13—81no—
357Dic13—81no—
358Dic13—81no—
359Dic13—81no—
360Dic13—81no—
361Dic13—81no—
362C22×Q8—261no—
363C23×C4—261no—
364C23×C4C22×D1311yescharacteristic
365C2×M16—22no—
366C2×M16—22no—
367C2×M16Dic2614yescomplemented
368C22×C8C22×D1311yescharacteristic
369C22×C8C22×D1311yescharacteristic
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—131no—
384C2×C4⋊C4—131no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—262no—
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—261no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4—521no—
401C2×C22⋊C4—261no—
402C2×C22⋊C4—261no—
403C2×C22⋊C4—261no—
404C2×C22⋊C4D5211yescharacteristic
405C2×C22⋊C4D5211yescharacteristic
406C2×C42—261no—
407C2×C42C22×D1311yescharacteristic
408C2×C42C22×D1311yescharacteristic
409#107—134no—
410#107—262no—
411#107—262no—
412#107—262no—
413#106—262no—
414#106—262no—
415#106—262no—
416#106—262no—
417#106—521no—
418#106—521no—
419C22⋊C8Dic2614yescomplemented
420#97—22no—
421C4×C8—22no—
422#95—261no—
423#95—261no—
424#95—261no—
425#95—261no—
426#95—261no—
427#95—261no—
428#95D5211yescharacteristic
429#95D5211yescharacteristic
430C2×C13—42no—
431C2×C13#244011yescharacteristic
432C2×C13#316311yescharacteristic
433C2×C13#316511yescharacteristic
434C2×C13#327211yescharacteristic
435C2×C13#327811yescharacteristic
436C2×C13#334411yescharacteristic
437C2×C13#334511yescharacteristic
438C24C2×D5211yescharacteristic
439C2×Q8—522no—
440C2×Q8—522no—
441C2×Q8—1041no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—261no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—522no—
455C22×C4—522no—
456C22×C4—1041no—
457C22×C4C2×Dic2612yes—
458C22×C4C2×Dic2612yes—
459C22×C4C2×D5211yescharacteristic
460C22×C4C2×D5211yescharacteristic
461C22×C4C2×D5211yescharacteristic
462C22×C4C2×D5211yescharacteristic
463C22×C4C2×D5211yescharacteristic
464C22×C4C23×D1311yescharacteristic
465M16—28no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8C2×Dic2612yes—
473C2×C8C2×Dic2612yes—
474C2×C8C2×Dic2612yes—
475C2×C8C2×Dic2612yes—
476C2×C8D4×D1312yes—
477C2×C8#612912yes—
478C4⋊C4—132no—
479C4⋊C4—132no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
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—22no—
507C22⋊C4—22no—
508C22⋊C4—522no—
509C22⋊C4—522no—
510C22⋊C4—1041no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—522no—
516C13#2607811yescharacteristic, complemented, Sylow
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23#8812312yes—
524C23C22×D5211yescharacteristic
525Q8—1044no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—262no—
543C2×C4—262no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
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—1044no—
567C2×C4#8812312yes—
568C2×C4#8816212yes—
569C2×C4#8816312yes—
570C2×C4C22×Dic2611yescharacteristic
571C2×C4C22×Dic2611yescharacteristic
572C2×C4C2×D4×D1311yescharacteristic
573C2×C4C2×#612911yescharacteristic
574C2×C4#8825611yescharacteristic
575C2×C4#8825711yescharacteristic
576C8—22no—
577C8—22no—
578C8—22no—
579C8#8813214yescomplemented
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22C2×#8812311yescharacteristic
588C22D4×D5211yescharacteristic
589C22#1171926011yescharacteristic
590C22C2×#8816211yescharacteristic
591C22C2×#8816311yescharacteristic
592C22#1171945611yescharacteristic
593C22#1171945611yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—41no—
598C4—41no—
599C4—522no—
600C4—522no—
601C4—1041no—
602C4—1041no—
603C4—1041no—
604C4—1041no—
605C4—1041no—
606C4—1041no—
607C4C2×#8813211yescharacteristic
608C4#1171922411yescharacteristic
609C4D4×Dic2611yescharacteristic
610C4#1171924811yescharacteristic
611C2—42no—
612C2#1311853811yescharacteristic
613C2#1312536711yescharacteristic
614C2#1312538211yescharacteristic
615C2#1312643811yescharacteristic
616C2#1312650411yescharacteristic
617C2#1312729311yescharacteristic
618C2#1312730811yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1753C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1753D13
hypocenterC13#26078
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#11718363C2semidirect
5. #13116314C2semidirect
6. #13116309C2semidirect
7. #13116175C2semidirect
8. #13116170C2semidirect
9. #13115574C2semidirect
10. #13115569C2semidirect
13. #13114993C2semidirect
66. C2×C13×M16Q8semidirect
108. C13×C22⋊C8Q8semidirect
285. C8×C13C22⋊Q8semidirect
367. C2×M16Dic26semidirect
419. C22⋊C8Dic26semidirect
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×#117183632
C2×#117187822
#131185492
#131185382
#131163142
#131163092
#131161752
#131161702
#131155742
#131155692
#131150372
#131150312
#131149932
#131148692
C13×#17532
#2607813