Finite Group Databasebeta

← #15870689

Subgroups — #15870689

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×#11718669C211yesmaximal, characteristic
2#13117584C211yesmaximal, characteristic, complemented
3#13115788C211yesmaximal, characteristic, complemented
4#13115604C211yesmaximal, characteristic, complemented
5#13115421C211yesmaximal, characteristic, complemented
6#13115414C211yesmaximal, characteristic, complemented
7#13115097C211yesmaximal, characteristic
8#13115083C211yesmaximal, characteristic
9#13114846C211yesmaximal, characteristic
10#13114734C211yesmaximal, characteristic, complemented
11C4×#88048C211yesmaximal, characteristic, complemented
12#13114693C211yesmaximal, characteristic, complemented
13#13114661C211yesmaximal, characteristic
14C4×#88072C211yesmaximal, characteristic
15C13×#2275C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C2×#88123C2211yescharacteristic
20C4×C13×C4⋊C4C2211yescharacteristic
21C4×C13×C4⋊C4C2211yescharacteristic
22C4×C13×C4⋊C4C2211yescharacteristic
23C4×C13×C22⋊C4—21no—
24C4×C13×C22⋊C4—21no—
25C4×C13×C22⋊C4—21no—
26C13×#376C2211yescharacteristic
27C2×C13×#95—21no—
28C2×#88072C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32#11718669C418yescomplemented
33C2×#88048C2211yescharacteristic
34C2×#88048C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C2×#88047C2211yescharacteristic
37#11718597C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40#11718589C2211yescharacteristic
41#11718589C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45C2×C4×#1055C2211yescharacteristic
46#11718315—21no—
47#11718315—21no—
48#11718307—21no—
49#11718307—21no—
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C23×C4×C13—21no—
63C23×C4×C13—21no—
64C22×Dic26—21no—
65C4×D4×C13—22no—
66C4×D4×C13—22no—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13C2×C414yes—
70C4×D4×C13Q814yescomplemented
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C42×C13—21no—
78C2×C42×C13—21no—
79C2×C42×C13—21no—
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×#6101—21no—
89C2×#6101—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96#88123—22no—
97#88123C2×C414yescomplemented
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95D411yescharacteristic
102C13×#95D411yescharacteristic
103C13×#95D411yescharacteristic
104C13×#95D411yescharacteristic
105#88072—22no—
106#88072—22no—
107#88072C2×C414yes—
108#88072C2×C414yes—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
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
124C24×C13—21no—
125C2×D4×C13—21no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13C22×C412yes—
129C2×D4×C13C2×Q812yes—
130C2×D4×C13#4112yes—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—24no—
135C22×C4×C13—24no—
136C22×C4×C13—24no—
137C22×C4×C13—81no—
138C22×C4×C13—81no—
139C22×C4×C13—81no—
140C22×C4×C13—81no—
141C22×C4×C13—81no—
142C22×C4×C13—81no—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2411yescharacteristic
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C2×Dic26—24no—
155C2×Dic26—81no—
156C2×Dic26—81no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4C22×C412yes—
161C13×C4⋊C4C2×Q812yes—
162C13×C4⋊C4#4112yes—
163C13×C22⋊C4—24no—
164C13×C22⋊C4—24no—
165C13×C22⋊C4—24no—
166C42×C13—21no—
167C42×C13—21no—
168C42×C13—81no—
169C42×C13—81no—
170C42×C13—81no—
171C42×C13C22×C412yes—
172C42×C13C2×Q812yes—
173C42×C13#4112yes—
174C42×C13#4112yes—
175C4⋊Dic13—24no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13C22×C412yes—
183C4⋊Dic13C22×C412yes—
184#6101—81no—
185#6101—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#2331—131no—
202#2275D1311yescharacteristic
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×C13—22no—
216C23×C13—22no—
217C23×C13—22no—
218C23×C13—41no—
219C23×C13—41no—
220C23×C13—41no—
221C23×C13—41no—
222C23×C13C22×D411yescharacteristic
223D4×C13—22no—
224D4×C13—22no—
225D4×C13—22no—
226D4×C13C4×Q814yes—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—22no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
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×C13—84no—
251C2×C4×C13—84no—
252C2×C4×C13—84no—
253C2×C4×C13C4×D412yes—
254C2×C4×C13C4×D412yes—
255C2×C4×C13C22⋊Q812yes—
256C2×C4×C13C22⋊Q812yes—
257C2×C4×C13C23×C411yescharacteristic
258C2×C4×C13C22×Q811yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13C2×#4111yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×Dic13—22no—
264C2×Dic13—22no—
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—
275Dic26—84no—
276#1055—22no—
277#1055—22no—
278#1055—41no—
279#1055—41no—
280C2×C4⋊Q8—131no—
281C2×C4×D4C2×D1311yescharacteristic
282C2×C4×D4C2×D1311yescharacteristic
283C2×C4×D4C2×D1311yescharacteristic
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—261no—
298#391—261no—
299#389—131no—
300#389—131no—
301#387—261no—
302#387—261no—
303#382—131no—
304C4×C4⋊C4—131no—
305C4×C4⋊C4—131no—
306C4×C4⋊C4C2×D1311yescharacteristic
307C4×C4⋊C4C2×D1311yescharacteristic
308C4×C4⋊C4C2×D1311yescharacteristic
309C4×C22⋊C4—21no—
310C4×C22⋊C4—21no—
311C4×C22⋊C4—21no—
312#376C2×D1311yescharacteristic
313C2×#95—21no—
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×C13—24no—
325C22×C13—42no—
326C22×C13—42no—
327C22×C13—42no—
328C22×C13—42no—
329C22×C13—42no—
330C22×C13—42no—
331C22×C13C2×C4×D411yescharacteristic
332C22×C13C2×C22⋊Q811yescharacteristic
333C22×C13#52511yescharacteristic
334C22×C13#57611yescharacteristic
335C22×C13#57711yescharacteristic
336C22×C13#57711yescharacteristic
337C22×C13#57711yescharacteristic
338C4×C13—22no—
339C4×C13—22no—
340C4×C13—22no—
341C4×C13—22no—
342C4×C13—42no—
343C4×C13—41no—
344C4×C13—42no—
345C4×C13—41no—
346C4×C13—42no—
347C4×C13C2×C4×Q811yescharacteristic
348C4×C13C4×#4111yescharacteristic
349C4×C13#52911yescharacteristic
350C4×C13#53311yescharacteristic
351Dic13—42no—
352Dic13—42no—
353Dic13—81no—
354Dic13—81no—
355C22×Q8—261no—
356C22×D4C22×D1311yescharacteristic
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—21no—
360C22×C8—131no—
361C22×C8—131no—
362C22×C8—131no—
363C22×C8—131no—
364C4⋊Q8—134no—
365C4⋊Q8—262no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4Dic2614yescomplemented
371C4×D4C4×D1314yes—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
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—261no—
409#95—261no—
410#95—261no—
411#95—261no—
412#95—261no—
413#95—261no—
414#95C22⋊D1311yescharacteristic
415#95C22⋊D1311yescharacteristic
416#95C22⋊D1311yescharacteristic
417#95C22⋊D1311yescharacteristic
418C2×C13—44no—
419C2×C13C4×C22⋊Q811yescharacteristic
420C2×C13#294611yescharacteristic
421C2×C13#294911yescharacteristic
422C2×C13#308111yescharacteristic
423C2×C13#308411yescharacteristic
424C2×C13#311811yescharacteristic
425C2×C13#312511yescharacteristic
426C24—21no—
427C2×Q8—264no—
428C2×Q8—1041no—
429C2×Q8—1041no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4C2×Dic2612yes—
434C2×D4C2×C4×D1312yes—
435C2×D4#612712yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—81no—
443C22×C4—81no—
444C22×C4—81no—
445C22×C4—81no—
446C22×C4—81no—
447C22×C4—81no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
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—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—132no—
475C4⋊C4—132no—
476C4⋊C4—264no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—1041no—
484C4⋊C4—1041no—
485C4⋊C4C2×Dic2612yes—
486C4⋊C4C2×C4×D1312yes—
487C4⋊C4#612712yes—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—24no—
491C42—21no—
492C42—21no—
493C42—81no—
494C42—81no—
495C42—81no—
496C42—1041no—
497C42—1041no—
498C42C2×Dic2612yes—
499C42C2×C4×D1312yes—
500C42#612712yes—
501C42#612712yes—
502C13#2162311yescharacteristic, complemented, Sylow
503C23—22no—
504C23—22no—
505C23—22no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23C22×C22⋊D1311yescharacteristic
511Q8—1044no—
512D4—22no—
513D4—22no—
514D4—22no—
515D4C4×Dic2614yes—
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—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—84no—
540C2×C4—84no—
541C2×C4—84no—
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#8817812yes—
555C2×C4#8817812yes—
556C2×C4C4×C22⋊D1312yes—
557C2×C4C4×C22⋊D1312yes—
558C2×C4C22×Dic2611yescharacteristic
559C2×C4C22×C4×D1311yescharacteristic
560C2×C4C2×#612711yescharacteristic
561C2×C4C2×#612711yescharacteristic
562C2×C4C2×#612711yescharacteristic
563C2×C4C2×#612711yescharacteristic
564C8—262no—
565C8—262no—
566C8—521no—
567C8—521no—
568C22—24no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22C2×#8817811yescharacteristic
576C22C2×C4×C22⋊D1311yescharacteristic
577C22#1171949611yescharacteristic
578C22#1171954011yescharacteristic
579C22#1171954111yescharacteristic
580C22#1171954111yescharacteristic
581C22#1171954211yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—22no—
586C4—42no—
587C4—42no—
588C4—41no—
589C4—42no—
590C4—41no—
591C4—522no—
592C4—522no—
593C4—1041no—
594C4—1041no—
595C4C2×C4×Dic2611yescharacteristic
596C4#1171917511yescharacteristic
597C4C4×#612711yescharacteristic
598C4#1171918411yescharacteristic
599C2—44no—
600C2C4×#8817811yescharacteristic
601C2#1312366411yescharacteristic
602C2#1312369311yescharacteristic
603C2#1312466711yescharacteristic
604C2#1312469811yescharacteristic
605C2#1312502011yescharacteristic
606C2#1312511311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2275C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenter#2275D13
hypocenterC13#21623
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ #376 ◁ #2275

Complements

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

NH ≅ G/Ntype
2. #13117584C2semidirect
3. #13115788C2semidirect
4. #13115604C2semidirect
5. #13115421C2semidirect
6. #13115414C2semidirect
10. #13114734C2semidirect
11. C4×#88048C2semidirect
12. #13114693C2semidirect
32. #11718669C4semidirect
70. C4×D4×C13Q8semidirect
97. #88123C2×C4semidirect
116. #88048C2×C4semidirect
117. #88048C2×C4semidirect
120. C4⋊#1055C2×C4semidirect
370. C4×D4Dic26semidirect
502. C13#21623semidirect

Maximal subgroups

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

subgroupindex
C2×#117186692
#131175842
#131157882
#131156042
#131154212
#131154142
#131150972
#131150832
#131148462
#131147342
C4×#880482
#131146932
#131146612
C4×#880722
C13×#22752
#2162313