Finite Group Databasebeta

← #15870683

Subgroups — #15870683

Order 3328.

876 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718745C211yesmaximal, characteristic
2#13117198C211yesmaximal, characteristic
3#13115789C211yesmaximal, characteristic, complemented
4#13115602C211yesmaximal, characteristic, complemented
5#13115418C211yesmaximal, characteristic, complemented
6#13115411C211yesmaximal, characteristic, complemented
7#13115096C211yesmaximal, characteristic
8#13115082C211yesmaximal, characteristic
9#13114843C211yesmaximal, characteristic
10#13114734C211yesmaximal, characteristic, complemented
11C4×#88048C211yesmaximal, characteristic, complemented
12#13114693C211yesmaximal, characteristic, complemented
13#13114664C211yesmaximal, characteristic
14C4×#88049C211yesmaximal, characteristic
15C13×#2331C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C2×C4×D52C2211yescharacteristic
19C2×C4×D52C2211yescharacteristic
20C13×#391—21no—
21C13×#391—21no—
22C13×#389C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#387—21no—
25C13×#387—21no—
26C13×#382C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C13×#376C2211yescharacteristic
30#11718745C418yescomplemented
31C2×#88049C2211yescharacteristic
32C2×#88049C2211yescharacteristic
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40C4×C4⋊Dic13C2211yescharacteristic
41C4×C4⋊Dic13C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45C2×C4×#1055C2211yescharacteristic
46#11718327—21no—
47#11718327—21no—
48#11718327—21no—
49D13×#95—21no—
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×Q8×C13—21no—
61C22×D52C2311yescharacteristic
62C22×C4×D13—21no—
63C22×C4×D13—21no—
64C22×C4×D13—21no—
65C13×C4⋊Q8—22no—
66C13×C4⋊Q8C2×C414yescomplemented
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C42×C13—21no—
75C2×C42×C13—21no—
76C2×C42×C13C2311yescharacteristic
77C2×C42×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×#6103—21no—
80C2×#6103—21no—
81C2×#6103—21no—
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4×Dic13—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C22×#1055C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C4×D52—22no—
93C4×D52—22no—
94C4×D52—22no—
95C4×D52—22no—
96C4×D52C2×C414yes—
97C4×D52Q814yescomplemented
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95D411yescharacteristic
105C13×#95D411yescharacteristic
106C13×#95D411yescharacteristic
107C13×#95D411yescharacteristic
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88049—22no—
112#88049—22no—
113#88049C2×C414yes—
114#88049C2×C414yes—
115#88048—22no—
116#88048C2×C414yescomplemented
117#88048C2×C414yescomplemented
118#88047—22no—
119C4⋊#1055—22no—
120C4⋊#1055C2×C414yescomplemented
121#88043—22no—
122C4×#1055—22no—
123#21623—131nomaximal, Sylow
124C23×D13—21no—
125C2×Q8×C13—24no—
126C2×Q8×C13—81no—
127C2×Q8×C13—81no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2411yescharacteristic
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C2×D52—21no—
143C2×D52—21no—
144C2×D52—21no—
145C2×D52C22×C412yes—
146C2×D52C2×Q812yes—
147C2×D52#4112yes—
148C2×C4×D13—24no—
149C2×C4×D13—24no—
150C2×C4×D13—24no—
151C2×C4×D13—81no—
152C2×C4×D13—81no—
153C2×C4×D13—81no—
154C2×C4×D13—81no—
155C2×C4×D13—81no—
156C2×C4×D13—81no—
157C13×C4⋊C4—24no—
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—81no—
165C13×C4⋊C4—81no—
166C13×C4⋊C4C22×C412yes—
167C13×C4⋊C4C22×C412yes—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—81no—
171C42×C13—81no—
172C42×C13C22×C412yes—
173C42×C13C2×Q812yes—
174C42×C13#4112yes—
175C42×C13#4112yes—
176#6103—24no—
177#6103—24no—
178#6103—24no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13C22×C412yes—
183C4⋊Dic13C2×Q812yes—
184C4⋊Dic13#4112yes—
185C4×Dic13—81no—
186C4×Dic13—81no—
187C4×Dic13—81no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055C22×C412yes—
199C2×#1055C22×C412yes—
200C2×#476—131no—
201#2331D1311yescharacteristic, complemented
202#2275—131no—
203#1988—131no—
204#1949—131no—
205#1920—131no—
206#1919—131no—
207#1864—131no—
208#1862—131no—
209#1804—131no—
210#1776—131no—
211C4×#106—131no—
212#1768—131no—
213#1762—131no—
214C4×#102—131no—
215C23×C13C22×D411yescharacteristic
216C22×D13—22no—
217C22×D13—22no—
218C22×D13—22no—
219C22×D13—41no—
220C22×D13—41no—
221C22×D13—41no—
222C22×D13—41no—
223Q8×C13—84no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
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×C13—41no—
250C2×C4×C13C4×D412yes—
251C2×C4×C13C4×D412yes—
252C2×C4×C13C22⋊Q812yes—
253C2×C4×C13C22⋊Q812yes—
254C2×C4×C13C23×C411yescharacteristic
255C2×C4×C13C22×Q811yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269D52—22no—
270D52—22no—
271D52—22no—
272D52C4×Q814yes—
273C4×D13—84no—
274C4×D13—84no—
275C4×D13—84no—
276#1055—22no—
277#1055—22no—
278#1055—41no—
279#1055—41no—
280C2×C4⋊Q8C2×D1311yescharacteristic
281C2×C4×D4—131no—
282C2×C4×D4—131no—
283C2×C4×D4—131no—
284#476—138no—
285C2×#107—131no—
286C2×#106—131no—
287C2×#106—131no—
288C2×#106—131no—
289C2×C4⋊C8—131no—
290C2×C4⋊C8—131no—
291C2×#102—131no—
292C2×#102—131no—
293C2×#102—131no—
294C2×#102—131no—
295C2×#97—131no—
296C2×C4×C8—131no—
297#391—21no—
298#391—21no—
299#389C2×D1311yescharacteristic
300#389C2×D1311yescharacteristic
301#387—21no—
302#387—21no—
303#382C2×D1311yescharacteristic
304C4×C4⋊C4—131no—
305C4×C4⋊C4—131no—
306C4×C4⋊C4—131no—
307C4×C4⋊C4C2×D1311yescharacteristic
308C4×C4⋊C4C2×D1311yescharacteristic
309C4×C22⋊C4—261no—
310C4×C22⋊C4—261no—
311C4×C22⋊C4—261no—
312#376C2×D1311yescharacteristic
313C2×#95—261no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#336—131no—
323#336—131no—
324C22×C13C2×C4×D411yescharacteristic
325C22×C13C2×C22⋊Q811yescharacteristic
326C22×C13#52511yescharacteristic
327C22×C13#57611yescharacteristic
328C22×C13#57711yescharacteristic
329C22×C13#57711yescharacteristic
330C22×C13#57711yescharacteristic
331C2×D13—24no—
332C2×D13—42no—
333C2×D13—42no—
334C2×D13—42no—
335C2×D13—42no—
336C2×D13—42no—
337C2×D13—42no—
338C4×C13—22no—
339C4×C13—22no—
340C4×C13—22no—
341C4×C13—22no—
342C4×C13—41no—
343C4×C13—41no—
344C4×C13—42no—
345C4×C13—42no—
346C4×C13—81no—
347C4×C13—81no—
348C4×C13C2×C4×Q811yescharacteristic
349C4×C13C4×#4111yescharacteristic
350C4×C13#52911yescharacteristic
351C4×C13#53311yescharacteristic
352Dic13—42no—
353Dic13—42no—
354Dic13—42no—
355C22×Q8—21no—
356C22×D4—131no—
357C23×C4—261no—
358C23×C4—261no—
359C23×C4—261no—
360C22×C8—131no—
361C22×C8—131no—
362C22×C8—131no—
363C22×C8—131no—
364C4⋊Q8—22no—
365C4⋊Q8C4×D1314yescomplemented
366C4×D4—134no—
367C4×D4—134no—
368C4×D4—262no—
369C4×D4—262no—
370C4×D4—262no—
371C4×D4—262no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4C22×D1311yescharacteristic
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C22⋊C4—261no—
383C2×C22⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—261no—
388C2×C42—261no—
389C2×C42—261no—
390C2×C42C22×D1311yescharacteristic
391C2×C42C22×D1311yescharacteristic
392C2×C42C22×D1311yescharacteristic
393#107—262no—
394#106—134no—
395#106—134no—
396#106—262no—
397C4⋊C8—134no—
398C4⋊C8—262no—
399#102—134no—
400#102—134no—
401#102—262no—
402#102—262no—
403#97—262no—
404C4×C8—262no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—261no—
412#95—261no—
413#95—261no—
414#95C22⋊D1311yescharacteristic
415#95C22⋊D1311yescharacteristic
416#95C22⋊D1311yescharacteristic
417#95C22⋊D1311yescharacteristic
418C2×C13C4×C22⋊Q811yescharacteristic
419C2×C13#294611yescharacteristic
420C2×C13#294911yescharacteristic
421C2×C13#308111yescharacteristic
422C2×C13#308411yescharacteristic
423C2×C13#311811yescharacteristic
424C2×C13#312511yescharacteristic
425D13—44no—
426C24—261no—
427C2×Q8—24no—
428C2×Q8—81no—
429C2×Q8—81no—
430C2×D4—132no—
431C2×D4—132no—
432C2×D4—132no—
433C2×D4—261no—
434C2×D4—261no—
435C2×D4—261no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—264no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—264no—
445C22×C4—264no—
446C22×C4—1041no—
447C22×C4—1041no—
448C22×C4—1041no—
449C22×C4—1041no—
450C22×C4—1041no—
451C22×C4—1041no—
452C22×C4C2×C22⋊D1311yescharacteristic
453C22×C4C2×C22⋊D1311yescharacteristic
454C22×C4C2×C22⋊D1311yescharacteristic
455C22×C4C2×C22⋊D1311yescharacteristic
456C22×C4C2×C22⋊D1311yescharacteristic
457C22×C4C2×C22⋊D1311yescharacteristic
458C22×C4C23×D1311yescharacteristic
459C2×C8—132no—
460C2×C8—132no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C4⋊C4—24no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—132no—
481C4⋊C4—132no—
482C4⋊C4—132no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4C2×C4×D1312yes—
487C4⋊C4C2×C4×D1312yes—
488C22⋊C4—264no—
489C22⋊C4—264no—
490C22⋊C4—264no—
491C42—21no—
492C42—21no—
493C42—81no—
494C42—81no—
495C42—1041no—
496C42—1041no—
497C42—1041no—
498C42C2×C4×D1312yes—
499C42#612712yes—
500C42Q8×D1312yes—
501C42#613112yes—
502C13#2162311yescharacteristic, complemented, Sylow
503C23—262no—
504C23—262no—
505C23—262no—
506C23—521no—
507C23—521no—
508C23—521no—
509C23—521no—
510C23C22×C22⋊D1311yescharacteristic
511Q8—84no—
512D4—134no—
513D4—262no—
514D4—262no—
515D4—262no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
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—262no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—1044no—
552C2×C4—1044no—
553C2×C4—1044no—
554C2×C4C4×C22⋊D1312yes—
555C2×C4C4×C22⋊D1312yes—
556C2×C4#8820012yes—
557C2×C4#8820012yes—
558C2×C4C22×C4×D1311yescharacteristic
559C2×C4C2×#612711yescharacteristic
560C2×C4C2×Q8×D1311yescharacteristic
561C2×C4C2×#613111yescharacteristic
562C2×C4#41×D1311yescharacteristic
563C2×C4#41×D1311yescharacteristic
564C8—262no—
565C8—262no—
566C8—521no—
567C8—521no—
568C22—264no—
569C22—522no—
570C22—522no—
571C22—522no—
572C22—522no—
573C22—522no—
574C22—522no—
575C22C2×C4×C22⋊D1311yescharacteristic
576C22C2×#8820011yescharacteristic
577C22#1171953311yescharacteristic
578C22#1171954011yescharacteristic
579C22#1171954111yescharacteristic
580C22#1171954211yescharacteristic
581C22#1171954211yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—22no—
586C4—42no—
587C4—42no—
588C4—41no—
589C4—41no—
590C4—81no—
591C4—81no—
592C4—522no—
593C4—522no—
594C4—522no—
595C4C4×Q8×D1311yescharacteristic
596C4C4×#613111yescharacteristic
597C4#1171928311yescharacteristic
598C4#1171928511yescharacteristic
599C2—524no—
600C2C4×#8820011yescharacteristic
601C2#1312366811yescharacteristic
602C2#1312369511yescharacteristic
603C2#1312466111yescharacteristic
604C2#1312469411yescharacteristic
605C2#1312501411yescharacteristic
606C2#1312510711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2331C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#2331D13
hypocenterC13#21623
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ #376 ◁ #2331

Complements

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

NH ≅ G/Ntype
3. #13115789C2semidirect
4. #13115602C2semidirect
5. #13115418C2semidirect
6. #13115411C2semidirect
10. #13114734C2semidirect
11. C4×#88048C2semidirect
12. #13114693C2semidirect
15. C13×#2331C2semidirect
30. #11718745C4semidirect
66. C13×C4⋊Q8C2×C4semidirect
97. C4×D52Q8semidirect
116. #88048C2×C4semidirect
117. #88048C2×C4semidirect
120. C4⋊#1055C2×C4semidirect
201. #2331D13semidirect
365. C4⋊Q8C4×D13semidirect
502. C13#21623semidirect

Maximal subgroups

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

subgroupindex
C2×#117187452
#131171982
#131157892
#131156022
#131154182
#131154112
#131150962
#131150822
#131148432
#131147342
C4×#880482
#131146932
#131146642
C4×#880492
C13×#23312
#2162313