Finite Group Databasebeta

← #15870599

Subgroups — #15870599

Order 3328.

936 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718670C211yesmaximal, characteristic
2C4×#88124C211yesmaximal, characteristic, complemented
3#13115793C211yesmaximal, characteristic, complemented
4#13115604C211yesmaximal, characteristic, complemented
5#13115421C211yesmaximal, characteristic, complemented
6#13115407C211yesmaximal, characteristic, complemented
7#13115097C211yesmaximal, characteristic
8#13115083C211yesmaximal, characteristic
9#13114846C211yesmaximal, characteristic
10#13114734C211yesmaximal, characteristic, complemented
11#13114734C211yesmaximal, characteristic, complemented
12#13114689C211yesmaximal, characteristic, complemented
13#13114661C211yesmaximal, characteristic
14#13114661C211yesmaximal, characteristic
15C42×D4×C13C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C22×C42×C13—21no—
20C2×#88124C2211yescharacteristic
21C4×C13×C4⋊C4C2211yescharacteristic
22C4×C13×C4⋊C4C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24C4×C13×C22⋊C4—21no—
25C4×C13×C22⋊C4—21no—
26C4×C13×C22⋊C4—21no—
27C43×C13C2211yescharacteristic
28C2×#88072C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32#11718670C418yescomplemented
33C2×#88048C2211yescharacteristic
34C2×#88048C2211yescharacteristic
35C2×#88047C2211yescharacteristic
36C2×#88047C2211yescharacteristic
37#11718597C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40#11718594—21no—
41#11718594—21no—
42C4×#6101—21no—
43C4×#6101—21no—
44#11718589C2211yescharacteristic
45#11718589C2211yescharacteristic
46C2×C4⋊#1055C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49C2×#88043C2211yescharacteristic
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—
64C4×D4×C13—22no—
65C4×D4×C13—22no—
66C4×D4×C13—22no—
67C4×D4×C13—22no—
68C4×D4×C13C2×C414yes—
69C4×D4×C13Q814yes—
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4—21no—
76C2×C42×C13—21no—
77C2×C42×C13—21no—
78C2×C42×C13—21no—
79C2×C42×C13—44no—
80C2×C42×C13D411yescharacteristic
81C2×C42×C13D411yescharacteristic
82C2×C42×C13D411yescharacteristic
83C2×C42×C13D411yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101#88124—22no—
102#88124C2×C414yescomplemented
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106#88072—22no—
107#88072—22no—
108#88072C2×C414yes—
109#88072C2×C414yes—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88048—22no—
117#88048C2×C414yescomplemented
118#88047—22no—
119#88047C2×C414yescomplemented
120C4⋊#1055—22no—
121C4⋊#1055C2×C414yescomplemented
122#88043—22no—
123#88043—22no—
124#21617—131nomaximal, Sylow
125C24×C13—21no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13C22×C412yes—
130C2×D4×C13C2×Q812yes—
131C2×D4×C13#4112yes—
132C22×C4×C13—24no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—24no—
137C22×C4×C13—24no—
138C22×C4×C13—42no—
139C22×C4×C13—42no—
140C22×C4×C13—42no—
141C22×C4×C13—42no—
142C22×C4×C13—42no—
143C22×C4×C13—42no—
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2411yescharacteristic
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4C22×C412yes—
159C13×C4⋊C4C2×Q812yes—
160C13×C4⋊C4#4112yes—
161C13×C22⋊C4—24no—
162C13×C22⋊C4—24no—
163C13×C22⋊C4—24no—
164C42×C13—22no—
165C42×C13—21no—
166C42×C13—21no—
167C42×C13—41no—
168C42×C13—41no—
169C42×C13—41no—
170C42×C13—42no—
171C42×C13—42no—
172C42×C13—42no—
173C42×C13C22×C412yes—
174C42×C13C2×Q812yes—
175C42×C13#4112yes—
176C42×C13#4112yes—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13C22×C412yes—
184C4⋊Dic13C22×C412yes—
185#6101—24no—
186#6101—24no—
187#6101—42no—
188#6101—42no—
189C4×Dic13—42no—
190C4×Dic13—42no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055C22×C412yes—
202C2×#1055C22×C412yes—
203C2×#478—131no—
204C4×#125—131no—
205C42×D4D1311yescharacteristic
206#1989—131no—
207#1949—131no—
208#1920—131no—
209#1918—131no—
210#1864—131no—
211#1862—131no—
212#1804—131no—
213#1776—131no—
214#1776—131no—
215#1767—131no—
216#1762—131no—
217#1762—131no—
218C23×C13—22no—
219C23×C13—22no—
220C23×C13—22no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13C22×D411yescharacteristic
226D4×C13—22no—
227D4×C13—22no—
228D4×C13—22no—
229D4×C13C4×Q814yes—
230C2×C4×C13—21no—
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—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—21no—
243C2×C4×C13—22no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—48no—
247C2×C4×C13—48no—
248C2×C4×C13—48no—
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×C13C4×D412yes—
256C2×C4×C13C4×D412yes—
257C2×C4×C13C22⋊Q812yes—
258C2×C4×C13C22⋊Q812yes—
259C2×C4×C13AGL(1,ℤ/8)12yes—
260C2×C4×C13C23×C411yescharacteristic
261C2×C4×C13C22×Q811yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13C2×#4111yescharacteristic
266C2×Dic13—22no—
267C2×Dic13—22no—
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—
278#1055—22no—
279#1055—22no—
280#1055—41no—
281#1055—41no—
282C2×#125—131no—
283C2×C4×D4C2×D1311yescharacteristic
284C2×C4×D4C2×D1311yescharacteristic
285C2×C4×D4C2×D1311yescharacteristic
286C22×C42—21no—
287#478—138no—
288C2×#107—131no—
289C2×#107—131no—
290C2×#106—131no—
291C2×#106—131no—
292C2×C4⋊C8—131no—
293C2×C4⋊C8—131no—
294C2×#102—131no—
295C2×#102—131no—
296C2×#102—131no—
297C2×#102—131no—
298C2×#97—131no—
299C2×#97—131no—
300#389—131no—
301#389—131no—
302#387—261no—
303#387—261no—
304#382—131no—
305C4×C4⋊C4—131no—
306C4×C4⋊C4—131no—
307C4×C4⋊C4—261no—
308C4×C4⋊C4—261no—
309C4×C4⋊C4C2×D1311yescharacteristic
310C4×C4⋊C4C2×D1311yescharacteristic
311C4×C4⋊C4C2×D1311yescharacteristic
312C4×C22⋊C4—21no—
313C4×C22⋊C4—21no—
314C4×C22⋊C4—21no—
315C43C2×D1311yescharacteristic
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#336—131no—
325#336—131no—
326C22×C13—24no—
327C22×C13—42no—
328C22×C13—42no—
329C22×C13—42no—
330C22×C13—42no—
331C22×C13—42no—
332C22×C13—42no—
333C22×C13C2×C4×D411yescharacteristic
334C22×C13C2×C22⋊Q811yescharacteristic
335C22×C13#52511yescharacteristic
336C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
337C22×C13#57511yescharacteristic
338C22×C13#57511yescharacteristic
339C22×C13#57511yescharacteristic
340C4×C13—22no—
341C4×C13—22no—
342C4×C13—22no—
343C4×C13—22no—
344C4×C13—22no—
345C4×C13—42no—
346C4×C13—41no—
347C4×C13—42no—
348C4×C13—42no—
349C4×C13C2×C4×Q811yescharacteristic
350C4×C13C4×#4111yescharacteristic
351C4×C13#52911yescharacteristic
352C4×C13#53311yescharacteristic
353Dic13—42no—
354Dic13—42no—
355Dic13—81no—
356Dic13—81no—
357C22×D4C22×D1311yescharacteristic
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—21no—
361C22×C8—131no—
362C22×C8—131no—
363C22×C8—131no—
364C22×C8—131no—
365#125—134no—
366#125—262no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4Dic2614yes—
372C4×D4C4×D1314yes—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C4⋊C4C22×D1311yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—44no—
391C2×C42—261no—
392C2×C42—261no—
393C2×C42C22⋊D1311yescharacteristic
394C2×C42C22⋊D1311yescharacteristic
395C2×C42C22⋊D1311yescharacteristic
396C2×C42C22⋊D1311yescharacteristic
397C2×C42C22×D1311yescharacteristic
398C2×C42C22×D1311yescharacteristic
399C2×C42C22×D1311yescharacteristic
400#107—134no—
401#107—262no—
402#106—134no—
403#106—262no—
404C4⋊C8—134no—
405C4⋊C8—262no—
406#102—134no—
407#102—134no—
408#102—262no—
409#102—262no—
410#97—262no—
411#97—262no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—261no—
416#95—261no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95—261no—
421C2×C13—44no—
422C2×C13C4×C22⋊Q811yescharacteristic
423C2×C13#294311yescharacteristic
424C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
425C2×C13#307711yescharacteristic
426C2×C13#308011yescharacteristic
427C2×C13#311111yescharacteristic
428C2×C13#311411yescharacteristic
429C24—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4C2×Dic2612yes—
434C2×D4C2×C4×D1312yes—
435C2×D4#612712yes—
436C22×C4—24no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
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—264no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—522no—
485C4⋊C4—522no—
486C4⋊C4C2×Dic2612yes—
487C4⋊C4C2×C4×D1312yes—
488C4⋊C4#612712yes—
489C22⋊C4—24no—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C42—22no—
493C42—21no—
494C42—21no—
495C42—41no—
496C42—41no—
497C42—41no—
498C42—42no—
499C42—42no—
500C42—42no—
501C42—522no—
502C42—522no—
503C42C2×Dic2612yes—
504C42C2×C4×D1312yes—
505C42#612712yes—
506C42#612712yes—
507C13#2161711yescharacteristic, complemented, Sylow
508C23—22no—
509C23—22no—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23C22×C22⋊D1311yescharacteristic
516D4—22no—
517D4—22no—
518D4—22no—
519D4C4×Dic2614yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—48no—
537C2×C4—48no—
538C2×C4—48no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—262no—
546C2×C4—262no—
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#8817812yes—
558C2×C4#8817812yes—
559C2×C4C4×C22⋊D1312yes—
560C2×C4C4×C22⋊D1312yes—
561C2×C4#8818612yes—
562C2×C4C22×Dic2611yescharacteristic
563C2×C4C22×C4×D1311yescharacteristic
564C2×C4C2×#612711yescharacteristic
565C2×C4C2×#612711yescharacteristic
566C2×C4C2×#612711yescharacteristic
567C2×C4C2×#612711yescharacteristic
568C8—262no—
569C8—262no—
570C8—521no—
571C8—521no—
572C22—24no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22C2×#8817811yescharacteristic
580C22C2×C4×C22⋊D1311yescharacteristic
581C22#1171949611yescharacteristic
582C22C2×#8818611yescharacteristic
583C22#1171952711yescharacteristic
584C22#1171952711yescharacteristic
585C22#1171952711yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—22no—
590C4—22no—
591C4—42no—
592C4—42no—
593C4—41no—
594C4—42no—
595C4—522no—
596C4—522no—
597C4—1041no—
598C4—1041no—
599C4C2×C4×Dic2611yescharacteristic
600C4#1171917511yescharacteristic
601C4C4×#612711yescharacteristic
602C4#1171918411yescharacteristic
603C2—44no—
604C2C4×#8817811yescharacteristic
605C2#1312363411yescharacteristic
606C2C4×#8818611yescharacteristic
607C2#1312463311yescharacteristic
608C2#1312465811yescharacteristic
609C2#1312494511yescharacteristic
610C2#1312497411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC42×D4×C13C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenterC42×D4D13
hypocenterC13#21617
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
2. C4×#88124C2semidirect
3. #13115793C2semidirect
4. #13115604C2semidirect
5. #13115421C2semidirect
6. #13115407C2semidirect
10. #13114734C2semidirect
11. #13114734C2semidirect
12. #13114689C2semidirect
32. #11718670C4semidirect
102. #88124C2×C4semidirect
117. #88048C2×C4semidirect
119. #88047C2×C4semidirect
121. C4⋊#1055C2×C4semidirect
507. C13#21617semidirect

Maximal subgroups

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

subgroupindex
C2×#117186702
C4×#881242
#131157932
#131156042
#131154212
#131154072
#131150972
#131150832
#131148462
#131147342
#131146892
#131146612
C42×D4×C132
#2161713