Finite Group Databasebeta

← #15921773

Subgroups — #15921773

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×#11718741C211yesmaximal, characteristic, complemented
2C2×#11718625C211yesmaximal, characteristic
3#13118549C211yesmaximal, characteristic
4#13116312C211yesmaximal, characteristic, complemented
5#13116308C211yesmaximal, characteristic, complemented
6#13116174C211yesmaximal, characteristic, complemented
7#13116166C211yesmaximal, characteristic, complemented
8#13115571C211yesmaximal, characteristic, complemented
9#13115566C211yesmaximal, characteristic, complemented
10#13115033C211yesmaximal, characteristic
11#13115029C211yesmaximal, characteristic
12#13114992C211yesmaximal, characteristic, complemented
13#13114867C211yesmaximal, characteristic
14#13114620C211yesmaximal, characteristic
15C13×#2440C211yesmaximal, characteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8—21no—
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C22×#6099C2211yescharacteristic
21C2×#88124C2211yescharacteristic
22C13×#398—21no—
23C13×#395—21no—
24C13×#389C2211yescharacteristic
25C13×#389C2211yescharacteristic
26C13×#385—21no—
27C13×#384C2211yescharacteristic
28C13×#380C2211yescharacteristic
29C4×C13×C22⋊C4C2211yescharacteristic
30#11718873C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32#11718741—24no—
33#11718625—24no—
34C2×#88048C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718610—21no—
45#11718609—21no—
46#11718596C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×#88043C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51#11718315—21no—
52#11718308—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13—21no—
62C23×C4×C13—21no—
63C23×C4×C13C2311yescharacteristic
64C13×C4⋊Q8—22no—
65C13×C4⋊Q8—41no—
66C13×C22⋊Q8—44no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—41no—
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4D411yescharacteristic
81C2×C13×C22⋊C4D411yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×C22⋊Dic13—21no—
85C2×C22⋊Dic13—21no—
86#88180—22no—
87#88180—41no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×C4×Dic13—21no—
99C2×#6099—22no—
100C2×#6099—22no—
101C2×#6099Q814yescomplemented
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106#88124—22no—
107#88124—41no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95D411yescharacteristic
112C13×#95D411yescharacteristic
113#88071—21no—
114#88071—21no—
115#88071—21no—
116C22⋊#1055Q814yescomplemented
117#88048—22no—
118#88048—22no—
119#88048—22no—
120#88048—22no—
121#88048—41no—
122#88048—41no—
123#88047—22no—
124#88047—22no—
125#88047—22no—
126#88047D414yes—
127#88043—22no—
128C4×#1055—22no—
129#26078—131nomaximal, Sylow
130C24×C13C2×D411yescharacteristic
131C2×Q8×C13—42no—
132C2×Q8×C13—42no—
133C2×Q8×C13—81no—
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—21no—
142C22×C4×C13—42no—
143C22×C4×C13—42no—
144C22×C4×C13—81no—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×Q812yes—
151C22×C4×C13C2×Q812yes—
152C22×C4×C13C2411yescharacteristic
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—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×C4⋊C4—42no—
168C13×C4⋊C4—42no—
169C13×C4⋊C4—81no—
170C13×C4⋊C4C2×D412yes—
171C13×C22⋊C4—22no—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—42no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—21no—
178C22⋊Dic13—42no—
179C22⋊Dic13—81no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—42no—
188C4⋊Dic13—81no—
189C4⋊Dic13C2×D412yes—
190#6101—42no—
191#6101—42no—
192#6101—42no—
193#6101—81no—
194C4×Dic13—42no—
195#6099—28no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055C2×D412yes—
203C2×#1055C2×Q812yes—
204C2×#1055C2×Q812yes—
205C2×#1055C2×Q812yes—
206C2×#1055C2×Q812yes—
207C2×#1055#4112yes—
208C2×#501—131no—
209C2×#428—131no—
210#2441—131no—
211#2440D1311yescharacteristic
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#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
231Q8×C13—84no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—22no—
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—84no—
261C2×C4×C13C4⋊Q812yes—
262C2×C4×C13AGL(1,ℤ/8)12yes—
263C2×C4×C13#13712yes—
264C2×C4×C13C22×D411yescharacteristic
265C2×C4×C13C22×Q811yescharacteristic
266C2×C4×C13C22×Q811yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×C4×C13H(5,𝔽2)11yescharacteristic
269C2×C4×C132−1+411yescharacteristic
270C2×Dic13—22no—
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—41no—
281C2×Dic13—41no—
282#1055—22no—
283#1055—22no—
284#1055—22no—
285#1055C22⋊Q814yescomplemented
286C22×M16—131no—
287C2×C4⋊Q8C2×D1311yescharacteristic
288C2×#125—131no—
289C2×C22⋊Q8—21no—
290C2×#117—131no—
291C22×C4⋊C4C2×D1311yescharacteristic
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⋊C8—131no—
305C2×#97—131no—
306C2×C4×C8—131no—
307#399—261no—
308#398—21no—
309#396—261no—
310#395—21no—
311#389—131no—
312#389—131no—
313#389—261no—
314#389C2×D1311yescharacteristic
315#389C2×D1311yescharacteristic
316#387—261no—
317#385—21no—
318#384—131no—
319#384C2×D1311yescharacteristic
320#380—131no—
321#380C2×D1311yescharacteristic
322C4×C22⋊C4C2×D1311yescharacteristic
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
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—22no—
347C4×C13—22no—
348C4×C13—41no—
349C4×C13—42no—
350C4×C13—41no—
351C4×C13—81no—
352C4×C13—81no—
353C4×C13—81no—
354C4×C13C2×C22⋊Q811yescharacteristic
355C4×C13#54411yescharacteristic
356C4×C13D4×Q811yescharacteristic
357C4×C13#55411yescharacteristic
358Dic13—42no—
359Dic13—81no—
360Dic13—81no—
361Dic13—81no—
362C22×Q8—21no—
363C23×C4—21no—
364C23×C4C22×D1311yescharacteristic
365C2×M16—134no—
366C2×M16—262no—
367C2×M16—262no—
368C22×C8—131no—
369C22×C8—131no—
370C22×C8—131no—
371C22×C8—131no—
372C4⋊Q8—22no—
373C4⋊Q8—41no—
374#125—262no—
375#125—521no—
376C22⋊Q8—44no—
377#117—262no—
378#117—521no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—41no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—131no—
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⋊C4C22×D1311yescharacteristic
398C2×C4⋊C4C22×D1311yescharacteristic
399C2×C4⋊C4C22×D1311yescharacteristic
400C2×C4⋊C4C22×D1311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—261no—
403C2×C22⋊C4—261no—
404C2×C22⋊C4C22⋊D1311yescharacteristic
405C2×C22⋊C4C22⋊D1311yescharacteristic
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⋊C8—134no—
420#97—262no—
421C4×C8—262no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—261no—
426#95—261no—
427#95—261no—
428#95C22⋊D1311yescharacteristic
429#95C22⋊D1311yescharacteristic
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×C22⋊D1311yescharacteristic
439C2×Q8—42no—
440C2×Q8—42no—
441C2×Q8—81no—
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—42no—
451C22×C4—42no—
452C22×C4—81no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4Q8×D1312yes—
458C22×C4Q8×D1312yes—
459C22×C4C2×C22⋊D1311yescharacteristic
460C22×C4C2×C22⋊D1311yescharacteristic
461C22×C4C2×C22⋊D1311yescharacteristic
462C22×C4C2×C22⋊D1311yescharacteristic
463C22×C4C2×C22⋊D1311yescharacteristic
464C22×C4C23×D1311yescharacteristic
465M16—268no—
466C2×C8—132no—
467C2×C8—132no—
468C2×C8—132no—
469C2×C8—132no—
470C2×C8—132no—
471C2×C8—132no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—81no—
491C4⋊C4—132no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4—522no—
500C4⋊C4—522no—
501C4⋊C4—522no—
502C4⋊C4—522no—
503C4⋊C4—1041no—
504C4⋊C4—1041no—
505C4⋊C4D4×D1312yes—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—42no—
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#8819812yes—
524C23C22×C22⋊D1311yescharacteristic
525Q8—84no—
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—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—84no—
555C2×C4—262no—
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—521no—
567C2×C4#8818612yes—
568C2×C4#8819612yes—
569C2×C4#8819812yes—
570C2×C4C2×D4×D1311yescharacteristic
571C2×C4#8825111yescharacteristic
572C2×C4C2×Q8×D1311yescharacteristic
573C2×C4C2×Q8×D1311yescharacteristic
574C2×C4#41×D1311yescharacteristic
575C2×C4#8825711yescharacteristic
576C8—134no—
577C8—262no—
578C8—262no—
579C8—262no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22C2×#8818611yescharacteristic
588C22D4×C22⋊D1311yescharacteristic
589C22C2×#8819611yescharacteristic
590C22C2×#8819811yescharacteristic
591C22#1171952911yescharacteristic
592C22#1171954111yescharacteristic
593C22#1171954211yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—41no—
598C4—42no—
599C4—41no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4—522no—
604C4—1041no—
605C4—1041no—
606C4—1041no—
607C4#1171932811yescharacteristic
608C4D13×C22⋊Q811yescharacteristic
609C4#1171933711yescharacteristic
610C4#1171934111yescharacteristic
611C2—42no—
612C2#1311853511yescharacteristic
613C2#1312536211yescharacteristic
614C2#1312537811yescharacteristic
615C2#1312643211yescharacteristic
616C2#1312649811yescharacteristic
617C2#1312728511yescharacteristic
618C2#1312730611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2440C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2440D13
hypocenterC13#26078
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
1. C2×#11718741C2semidirect
4. #13116312C2semidirect
5. #13116308C2semidirect
6. #13116174C2semidirect
7. #13116166C2semidirect
8. #13115571C2semidirect
9. #13115566C2semidirect
12. #13114992C2semidirect
101. C2×#6099Q8semidirect
116. C22⋊#1055Q8semidirect
285. #1055C22⋊Q8semidirect
516. C13#26078semidirect

Maximal subgroups

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

subgroupindex
C2×#117187412
C2×#117186252
#131185492
#131163122
#131163082
#131161742
#131161662
#131155712
#131155662
#131150332
#131150292
#131149922
#131148672
#131146202
C13×#24402
#2607813