Finite Group Databasebeta

← #15866010

Subgroups — #15866010

Order 3328.

938 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718675C211yesmaximal, characteristic
2#13117480C211yesmaximal, characteristic, complemented
3#13115463C211yesmaximal, characteristic, complemented
4#13115456C211yesmaximal, characteristic, complemented
5#13115421C211yesmaximal, characteristic, complemented
6#13115414C211yesmaximal, characteristic, complemented
7#13115184C211yesmaximal, characteristic
8#13115184C211yesmaximal, characteristic
9#13115097C211yesmaximal, characteristic, complemented
10#13115083C211yesmaximal, characteristic, complemented
11#13114734C211yesmaximal, characteristic, complemented
12C4×#88049C211yesmaximal, characteristic, complemented
13C4×#88072C211yesmaximal, characteristic, complemented
14#13114588C211yesmaximal, characteristic, complemented
15C13×#2275C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C22×#6104C2211yescharacteristic
20C2×C4×D52C2211yescharacteristic
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—
27C13×#376C2211yescharacteristic
28C2×C13×#95—21no—
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32#11718675C418yescomplemented
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39#11718600C2211yescharacteristic
40#11718600C2211yescharacteristic
41C4×C4⋊Dic13C2211yescharacteristic
42#11718589C2211yescharacteristic
43#11718589C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45C2×C4×#1055C2211yescharacteristic
46#11718330—21no—
47#11718330—21no—
48#11718328—21no—
49#11718325—21no—
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C23×C4×C13—21no—
63C23×C4×C13—21no—
64C22×D52C2311yescharacteristic
65C22×C4×D13—21no—
66C4×D4×C13—22no—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C4×D4×C13—22no—
71C4×D4×C13C2×C414yes—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C42×C13—21no—
79C2×C42×C13—21no—
80C2×C42×C13—21no—
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×#6104—22no—
85C2×#6104—22no—
86C2×#6104C2×C414yes—
87C2×#6103—21no—
88C2×#6103—21no—
89C2×#6103—21no—
90C2×#6103—21no—
91C2×#6103—21no—
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×#6101—21no—
96C2×#6101—21no—
97C2×C4×Dic13—21no—
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C4×D52—22no—
103C4×D52C2×C414yescomplemented
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95D411yescharacteristic
108C13×#95D411yescharacteristic
109C13×#95D411yescharacteristic
110C13×#95D411yescharacteristic
111#88072—22no—
112#88072—22no—
113#88072C2×C414yes—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88049—22no—
118#88049—22no—
119#88049C2×C414yescomplemented
120#88048—22no—
121#88048C2×C414yescomplemented
122#88047—22no—
123#88043C2×C414yescomplemented
124C4×#1055—22no—
125#21126—131nomaximal, Sylow
126C24×C13—21no—
127C23×D13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13C22×C412yes—
132C2×D4×C13#4112yes—
133C2×D4×C13#4112yes—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—24no—
138C22×C4×C13—24no—
139C22×C4×C13—24no—
140C22×C4×C13—81no—
141C22×C4×C13—81no—
142C22×C4×C13—81no—
143C22×C4×C13—81no—
144C22×C4×C13—81no—
145C22×C4×C13—81no—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2411yescharacteristic
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C2×D52—21no—
157C2×D52—21no—
158C2×D52—21no—
159C2×D52—21no—
160C2×D52—21no—
161C2×D52C22×C412yes—
162C2×C4×D13—24no—
163C2×C4×D13—81no—
164C2×C4×D13—81no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4C22×C412yes—
169C13×C4⋊C4#4112yes—
170C13×C4⋊C4#4112yes—
171C13×C22⋊C4—24no—
172C13×C22⋊C4—24no—
173C13×C22⋊C4—24no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13—81no—
179C42×C13—81no—
180C42×C13—81no—
181C42×C13C22×C412yes—
182C42×C13#4112yes—
183#6104—28no—
184#6103—24no—
185#6103—81no—
186#6103—81no—
187#6103—81no—
188#6103—81no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13C22×C412yes—
195#6101—81no—
196#6101—81no—
197C4×Dic13—81no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055C22×C412yes—
209C2×#1055C22×C412yes—
210C2×#442—131no—
211#2319—131no—
212#2275D1311yescharacteristic, complemented
213#1926—131no—
214#1925—131no—
215#1920—131no—
216#1919—131no—
217#1879—131no—
218#1879—131no—
219#1864—131no—
220#1862—131no—
221#1776—131no—
222C4×#102—131no—
223C4×#102—131no—
224#1746—131no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—41no—
229C23×C13—41no—
230C23×C13—41no—
231C23×C13—41no—
232C23×C13C22×D411yescharacteristic
233C22×D13—22no—
234C22×D13—41no—
235C22×D13—41no—
236C22×D13—41no—
237C22×D13—41no—
238C22×D13—41no—
239C22×D13—41no—
240D4×C13—22no—
241D4×C13—22no—
242D4×C13—22no—
243D4×C13#11714yes—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—22no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—84no—
270C2×C4×C13—84no—
271C2×C4×C13—84no—
272C2×C4×C13C4×D412yes—
273C2×C4×C13C4×D412yes—
274C2×C4×C13C23×C411yescharacteristic
275C2×C4×C13C2×#4111yescharacteristic
276C2×C4×C13C2×#4111yescharacteristic
277C2×C4×C13C2×#4111yescharacteristic
278C2×C4×C13C2×#4111yescharacteristic
279C2×C4×C13C2×#4111yescharacteristic
280C2×Dic13—22no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289D52—22no—
290D52—22no—
291D52—41no—
292D52—41no—
293C4×D13—84no—
294#1055—22no—
295#1055—22no—
296#1055—41no—
297#1055—41no—
298C22×D8—131no—
299C2×C4×D4—131no—
300C2×C4×D4C2×D1311yescharacteristic
301C2×C4×D4C2×D1311yescharacteristic
302C2×C4×D4C2×D1311yescharacteristic
303#442—138no—
304C2×#107—131no—
305C2×#106—131no—
306C2×#106—131no—
307C2×#102—131no—
308C2×#102—131no—
309C2×#102—131no—
310C2×#102—131no—
311C2×#102—131no—
312C2×#102—131no—
313C2×#97—131no—
314C2×C4×C8—131no—
315#390—131no—
316#390—131no—
317#389—131no—
318#389—131no—
319#388—261no—
320#388—261no—
321#381—261no—
322#380—261no—
323C4×C4⋊C4—131no—
324C4×C4⋊C4C2×D1311yescharacteristic
325C4×C4⋊C4C2×D1311yescharacteristic
326C4×C4⋊C4C2×D1311yescharacteristic
327C4×C22⋊C4—21no—
328C4×C22⋊C4—21no—
329C4×C22⋊C4—21no—
330#376C2×D1311yescharacteristic
331C2×#95—21no—
332#340—131no—
333#340—131no—
334#340—131no—
335#340—131no—
336#340—131no—
337#340—131no—
338#336—131no—
339#336—131no—
340#336—131no—
341#336—131no—
342C22×C13—24no—
343C22×C13—42no—
344C22×C13—42no—
345C22×C13—42no—
346C22×C13—42no—
347C22×C13—42no—
348C22×C13—42no—
349C22×C13C2×C4×D411yescharacteristic
350C22×C13#52511yescharacteristic
351C22×C13#52511yescharacteristic
352C22×C13#57611yescharacteristic
353C22×C13#57611yescharacteristic
354C22×C13#57711yescharacteristic
355C22×C13#57711yescharacteristic
356C2×D13—42no—
357C2×D13—42no—
358C2×D13—42no—
359C2×D13—81no—
360C2×D13—81no—
361C2×D13—81no—
362C2×D13—81no—
363C4×C13—22no—
364C4×C13—22no—
365C4×C13—41no—
366C4×C13—42no—
367C4×C13—41no—
368C4×C13—41no—
369C4×C13—42no—
370C4×C13—41no—
371C4×C13—42no—
372C4×C13C2×#11711yescharacteristic
373C4×C13C4×#4111yescharacteristic
374C4×C13#52911yescharacteristic
375C4×C13#52911yescharacteristic
376Dic13—42no—
377Dic13—81no—
378Dic13—81no—
379C22×D4—131no—
380C22×D4C22×D1311yescharacteristic
381C23×C4—21no—
382C23×C4—21no—
383C23×C4—21no—
384C23×C4—261no—
385C2×D8—134no—
386C2×D8—262no—
387C2×D8—262no—
388C22×C8—131no—
389C22×C8—131no—
390C22×C8—131no—
391C22×C8—131no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—134no—
398C4×D4—262no—
399C4×D4C4×D1314yes—
400C2×C4⋊C4—131no—
401C2×C4⋊C4—131no—
402C2×C4⋊C4—131no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4C22×D1311yescharacteristic
406C2×C4⋊C4C22×D1311yescharacteristic
407C2×C4⋊C4C22×D1311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—261no—
412C2×C22⋊C4—261no—
413C2×C22⋊C4—261no—
414C2×C22⋊C4—261no—
415C2×C22⋊C4—261no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—261no—
420C2×C42C22×D1311yescharacteristic
421C2×C42C22×D1311yescharacteristic
422C2×C42C22×D1311yescharacteristic
423#107—262no—
424#106—134no—
425#106—262no—
426#102—134no—
427#102—134no—
428#102—262no—
429#102—262no—
430#102—262no—
431#102—262no—
432#97—134no—
433C4×C8—262no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—261no—
438#95—261no—
439#95—261no—
440#95C22⋊D1311yescharacteristic
441#95C22⋊D1311yescharacteristic
442#95C22⋊D1311yescharacteristic
443#95C22⋊D1311yescharacteristic
444C2×C13—44no—
445C2×C13#229011yescharacteristic
446C2×C13#294611yescharacteristic
447C2×C13#294611yescharacteristic
448C2×C13#311811yescharacteristic
449C2×C13#311911yescharacteristic
450C2×C13#312211yescharacteristic
451C2×C13#312511yescharacteristic
452D13—82no—
453C24—21no—
454C24—261no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—132no—
459C2×D4—261no—
460C2×D4—261no—
461C2×D4—261no—
462C2×D4—261no—
463C2×D4—261no—
464C2×D4C2×C4×D1312yes—
465C2×D4#612712yes—
466C2×D4#612712yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—81no—
474C22×C4—81no—
475C22×C4—81no—
476C22×C4—81no—
477C22×C4—81no—
478C22×C4—81no—
479C22×C4—261no—
480C22×C4—264no—
481C22×C4—261no—
482C22×C4—261no—
483C22×C4—1041no—
484C22×C4—1041no—
485C22×C4C2×C22⋊D1311yescharacteristic
486C22×C4C2×C22⋊D1311yescharacteristic
487C22×C4C2×C22⋊D1311yescharacteristic
488C22×C4C2×C22⋊D1311yescharacteristic
489C22×C4C2×C22⋊D1311yescharacteristic
490C22×C4C2×C22⋊D1311yescharacteristic
491C22×C4C23×D1311yescharacteristic
492D8—268no—
493C2×C8—132no—
494C2×C8—132no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—261no—
503C2×C8—261no—
504C2×C8—261no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—132no—
509C4⋊C4—261no—
510C4⋊C4—261no—
511C4⋊C4—261no—
512C4⋊C4—261no—
513C4⋊C4—261no—
514C4⋊C4—1041no—
515C4⋊C4—1041no—
516C4⋊C4C2×C4×D1312yes—
517C4⋊C4#612712yes—
518C4⋊C4#612712yes—
519C22⋊C4—24no—
520C22⋊C4—24no—
521C22⋊C4—24no—
522C22⋊C4—264no—
523C22⋊C4—1041no—
524C22⋊C4—1041no—
525C22⋊C4—1041no—
526C22⋊C4—1041no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—81no—
532C42—81no—
533C42—81no—
534C42—1041no—
535C42C2×C4×D1312yes—
536C42#612712yes—
537C13#2112611yescharacteristic, complemented, Sylow
538C23—22no—
539C23—22no—
540C23—22no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—262no—
546C23—521no—
547C23—521no—
548C23—521no—
549C23—521no—
550C23—521no—
551C23—521no—
552C23C22×C22⋊D1311yescharacteristic
553D4—22no—
554D4—22no—
555D4—22no—
556D4—262no—
557D4—262no—
558D4—521no—
559D4—521no—
560D4#8812614yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—84no—
587C2×C4—84no—
588C2×C4—84no—
589C2×C4—262no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4—521no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—1044no—
599C2×C4C4×C22⋊D1312yes—
600C2×C4C4×C22⋊D1312yes—
601C2×C4C22×C4×D1311yescharacteristic
602C2×C4C2×#612711yescharacteristic
603C2×C4C2×#612711yescharacteristic
604C2×C4C2×#612711yescharacteristic
605C2×C4C2×#612711yescharacteristic
606C2×C4C2×#612711yescharacteristic
607C8—262no—
608C8—262no—
609C8—521no—
610C8—521no—
611C22—24no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—522no—
619C22—522no—
620C22—522no—
621C22—1041no—
622C22—1041no—
623C22—1041no—
624C22—1041no—
625C22C2×C4×C22⋊D1311yescharacteristic
626C22#1171949611yescharacteristic
627C22#1171949611yescharacteristic
628C22#1171954011yescharacteristic
629C22#1171954011yescharacteristic
630C22#1171954111yescharacteristic
631C22#1171954211yescharacteristic
632C4—22no—
633C4—22no—
634C4—42no—
635C4—41no—
636C4—42no—
637C4—41no—
638C4—41no—
639C4—42no—
640C4—41no—
641C4—522no—
642C4—1041no—
643C4—1041no—
644C4C2×#8812611yescharacteristic
645C4C4×#612711yescharacteristic
646C4#1171918411yescharacteristic
647C4#1171918411yescharacteristic
648C2—44no—
649C2—1042no—
650C2#1311727911yescharacteristic
651C2#1312366411yescharacteristic
652C2#1312366811yescharacteristic
653C2#1312502011yescharacteristic
654C2#1312503511yescharacteristic
655C2#1312507911yescharacteristic
656C2#1312511311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2275C2
socleC23×C13C22×D4
prime radicalC22×#6104C22
cosocleC22×C4×C13C24
hypercenter#2275D13
hypocenterC13#21126
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. #13117480C2semidirect
3. #13115463C2semidirect
4. #13115456C2semidirect
5. #13115421C2semidirect
6. #13115414C2semidirect
9. #13115097C2semidirect
10. #13115083C2semidirect
11. #13114734C2semidirect
12. C4×#88049C2semidirect
13. C4×#88072C2semidirect
14. #13114588C2semidirect
15. C13×#2275C2semidirect
32. #11718675C4semidirect
103. C4×D52C2×C4semidirect
119. #88049C2×C4semidirect
121. #88048C2×C4semidirect
123. #88043C2×C4semidirect
212. #2275D13semidirect
537. C13#21126semidirect

Maximal subgroups

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

subgroupindex
C2×#117186752
#131174802
#131154632
#131154562
#131154212
#131154142
#131151842
#131150972
#131150832
#131147342
C4×#880492
C4×#880722
#131145882
C13×#22752
#2112613