Finite Group Databasebeta

← #15866014

Subgroups — #15866014

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
1#13117479C211yesmaximal, characteristic, complemented
2#13117197C211yesmaximal, characteristic, complemented
3#13115465C211yesmaximal, characteristic, complemented
4#13115458C211yesmaximal, characteristic, complemented
5#13115423C211yesmaximal, characteristic, complemented
6#13115416C211yesmaximal, characteristic, complemented
7#13115186C211yesmaximal, characteristic
8#13115186C211yesmaximal, characteristic
9#13115099C211yesmaximal, characteristic, complemented
10#13115085C211yesmaximal, characteristic, complemented
11#13114733C211yesmaximal, characteristic, complemented
12C4×#88072C211yesmaximal, characteristic, complemented
13C4×#88072C211yesmaximal, characteristic, complemented
14#13114589C211yesmaximal, characteristic, complemented
15C2×C13×#442C211yesmaximal, characteristic
16C22×C13×D8C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C2×D4×Dic13C2211yescharacteristic
20C2×D4×Dic13C2211yescharacteristic
21C13×#442C418yescomplemented
22C2×C13×#106C2211yescharacteristic
23C2×C13×#102C2211yescharacteristic
24C2×C13×#102C2211yescharacteristic
25C2×C13×#97C2211yescharacteristic
26#11718882C2211yescharacteristic
27#11718882C2211yescharacteristic
28C2×#88072C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32#11718873—21no—
33#11718872—21no—
34C4×C22⋊Dic13—21no—
35C2×#88071—21no—
36C2×#88058C2211yescharacteristic
37C2×#88057C2211yescharacteristic
38#11718646C2211yescharacteristic
39#11718646C2211yescharacteristic
40C4⋊C4×Dic13C2211yescharacteristic
41C4⋊C4×Dic13C2211yescharacteristic
42#11718612—21no—
43#11718612—21no—
44C22⋊C4×Dic13—21no—
45C22⋊C4×Dic13—21no—
46C4×C4⋊Dic13C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48#11718593C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C23×C4×C13—21no—
64C23×Dic13—21no—
65C23×Dic13—21no—
66C2×C13×D8—22no—
67C2×C13×D8—22no—
68C2×C13×D8C2×C414yes—
69C22×C8×C13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C4×D4×C13—22no—
72C4×D4×C13—22no—
73C4×D4×C13C2×C414yes—
74C4×D4×C13C2×C414yescomplemented
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C42×C13C2311yescharacteristic
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13—21no—
82C2×C22⋊Dic13—21no—
83C2×C22⋊Dic13—21no—
84C2×C22⋊Dic13—21no—
85C2×C22⋊Dic13—21no—
86D4×Dic13—22no—
87D4×Dic13—22no—
88D4×Dic13—22no—
89D4×Dic13—22no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4×Dic13—21no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13C2311yescharacteristic
101C2×C4×Dic13C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C13×#106C2×C414yescomplemented
105C13×#102C2×C414yes—
106C13×#102C2×C414yescomplemented
107C13×#97C2×C414yescomplemented
108#88072—22no—
109#88072—22no—
110#88072—22no—
111#88072—22no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071D411yescharacteristic
119#88071D411yescharacteristic
120#88071D411yescharacteristic
121#88071D411yescharacteristic
122#88058—22no—
123#88057—22no—
124C4×#1055—22no—
125#21126—131nomaximal, Sylow
126C24×C13—21no—
127C24×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13C22×C412yes—
137C2×D4×C13C22×C412yes—
138C2×D4×C13#4112yes—
139C2×D4×C13#4112yes—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—24no—
143C22×C4×C13—24no—
144C22×C4×C13—81no—
145C22×C4×C13—81no—
146C22×C4×C13—81no—
147C22×C4×C13—81no—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2411yescharacteristic
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—24no—
154C22×Dic13—24no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—81no—
158C22×Dic13—81no—
159C22×Dic13—81no—
160C22×Dic13—81no—
161C22×Dic13C2×D411yescharacteristic
162C22×Dic13C2×D411yescharacteristic
163C22×Dic13C2×D411yescharacteristic
164C22×Dic13C2×D411yescharacteristic
165C13×D8—28no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13C22×C412yes—
171C2×C8×C13C22×C412yes—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4C22×C412yes—
175C13×C4⋊C4C22×C412yes—
176C13×C22⋊C4—24no—
177C13×C22⋊C4—24no—
178C42×C13C22×C412yes—
179C42×C13#4112yes—
180C22⋊Dic13—24no—
181C22⋊Dic13—24no—
182C22⋊Dic13—81no—
183C22⋊Dic13—81no—
184C22⋊Dic13—81no—
185C22⋊Dic13—81no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—81no—
193C4⋊Dic13—81no—
194C4⋊Dic13#4112yes—
195C4⋊Dic13#4112yes—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—81no—
201C4×Dic13—81no—
202C4×Dic13—81no—
203C4×Dic13—81no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#442D1311yescharacteristic
211#2319—131no—
212#2275—131no—
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—22no—
229C23×C13—41no—
230C23×C13—41no—
231C23×C13—41no—
232C23×C13—41no—
233C23×C13—41no—
234C23×C13—41no—
235C23×C13—41no—
236C23×C13—41no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13C22×D411yescharacteristic
240D4×C13—22no—
241D4×C13—22no—
242D4×C13—22no—
243D4×C13—22no—
244D4×C13—22no—
245D4×C13—41no—
246D4×C13—41no—
247D4×C13#11714yes—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—84no—
259C2×C4×C13—84no—
260C2×C4×C13C4×D412yes—
261C2×C4×C13C4×D412yes—
262C2×C4×C13C23×C411yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13C2×#4111yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—21no—
280C2×Dic13—21no—
281C2×Dic13—21no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—84no—
293C2×Dic13—84no—
294C8×C13—22no—
295C8×C13—22no—
296#1055—41no—
297#1055—41no—
298C22×D8C2×D1311yescharacteristic
299C2×C4×D4—131no—
300C2×C4×D4—131no—
301C2×C4×D4C2×D1311yescharacteristic
302C2×C4×D4C2×D1311yescharacteristic
303#442Dic1318yescomplemented
304C2×#107—131no—
305C2×#106—131no—
306C2×#106C2×D1311yescharacteristic
307C2×#102—131no—
308C2×#102—131no—
309C2×#102—131no—
310C2×#102—131no—
311C2×#102C2×D1311yescharacteristic
312C2×#102C2×D1311yescharacteristic
313C2×#97C2×D1311yescharacteristic
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⋊C4—131no—
325C4×C4⋊C4—131no—
326C4×C4⋊C4—131no—
327C4×C22⋊C4—261no—
328C4×C22⋊C4—261no—
329C4×C22⋊C4—261no—
330#376—131no—
331C2×#95—261no—
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×C13—42no—
350C22×C13—42no—
351C22×C13—42no—
352C22×C13—81no—
353C22×C13—81no—
354C22×C13—81no—
355C22×C13—81no—
356C22×C13C2×C4×D411yescharacteristic
357C22×C13#52511yescharacteristic
358C22×C13#52511yescharacteristic
359C22×C13#57611yescharacteristic
360C22×C13#57611yescharacteristic
361C22×C13#57711yescharacteristic
362C22×C13#57711yescharacteristic
363C4×C13—22no—
364C4×C13—22no—
365C4×C13—42no—
366C4×C13—42no—
367C4×C13C2×#11711yescharacteristic
368C4×C13C4×#4111yescharacteristic
369C4×C13#52911yescharacteristic
370C4×C13#52911yescharacteristic
371Dic13—41no—
372Dic13—42no—
373Dic13—41no—
374Dic13—41no—
375Dic13—42no—
376Dic13—41no—
377Dic13—81no—
378Dic13—81no—
379C22×D4C22×D1311yescharacteristic
380C22×D4C22×D1311yescharacteristic
381C23×C4—21no—
382C23×C4—21no—
383C23×C4—261no—
384C23×C4—261no—
385C2×D8—22no—
386C2×D8—22no—
387C2×D8C2×Dic1314yes—
388C22×C8—131no—
389C22×C8—131no—
390C22×C8C22×D1311yescharacteristic
391C22×C8C22×D1311yescharacteristic
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—262no—
395C4×D4—262no—
396C4×D4—262no—
397C4×D4—262no—
398C4×D4C2×Dic1314yes—
399C4×D4C2×Dic1314yescomplemented
400C2×C4⋊C4—131no—
401C2×C4⋊C4—131no—
402C2×C4⋊C4—131no—
403C2×C4⋊C4—131no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4—261no—
406C2×C4⋊C4C22×D1311yescharacteristic
407C2×C4⋊C4C22×D1311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—261no—
411C2×C22⋊C4—261no—
412C2×C22⋊C4—261no—
413C2×C22⋊C4—261no—
414C2×C22⋊C4—261no—
415C2×C22⋊C4—261no—
416C2×C42—131no—
417C2×C42—131no—
418C2×C42—261no—
419C2×C42—261no—
420C2×C42—261no—
421C2×C42—261no—
422C2×C42C22×D1311yescharacteristic
423#107—262no—
424#106—262no—
425#106C2×Dic1314yescomplemented
426#102—262no—
427#102—262no—
428#102—262no—
429#102—262no—
430#102C2×Dic1314yes—
431#102C2×Dic1314yescomplemented
432#97C2×Dic1314yescomplemented
433C4×C8—262no—
434#95—131no—
435#95—131no—
436#95—131no—
437#95—131no—
438#95—261no—
439#95—261no—
440#95—261no—
441#95—261no—
442#95—261no—
443#95—261no—
444C2×C13—44no—
445C2×C13—82no—
446C2×C13#229011yescharacteristic
447C2×C13#294611yescharacteristic
448C2×C13#294611yescharacteristic
449C2×C13#311811yescharacteristic
450C2×C13#311911yescharacteristic
451C2×C13#312211yescharacteristic
452C2×C13#312511yescharacteristic
453C24—21no—
454C24—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4#612712yes—
464C2×D4#612712yes—
465C2×D4C22×Dic1312yes—
466C2×D4C22×Dic1312yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—81no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—81no—
475C22×C4—131no—
476C22×C4—131no—
477C22×C4—131no—
478C22×C4—131no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4—264no—
482C22×C4—264no—
483C22×C4—261no—
484C22×C4—261no—
485C22×C4—1041no—
486C22×C4—1041no—
487C22×C4—1041no—
488C22×C4—1041no—
489C22×C4D4×D1311yescharacteristic
490C22×C4D4×D1311yescharacteristic
491C22×C4C23×D1311yescharacteristic
492D8—28no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—261no—
503C2×C8C22×Dic1312yes—
504C2×C8C22×Dic1312yes—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—132no—
508C4⋊C4—132no—
509C4⋊C4—261no—
510C4⋊C4—261no—
511C4⋊C4—261no—
512C4⋊C4—261no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—1041no—
516C4⋊C4—1041no—
517C4⋊C4C22×Dic1312yes—
518C4⋊C4C22×Dic1312yes—
519C22⋊C4—24no—
520C22⋊C4—24no—
521C22⋊C4—264no—
522C22⋊C4—264no—
523C22⋊C4—1041no—
524C22⋊C4—1041no—
525C22⋊C4—1041no—
526C22⋊C4—1041no—
527C42—261no—
528C42—261no—
529C42—261no—
530C42—261no—
531C42—1041no—
532C42—1041no—
533C42—1041no—
534C42—1041no—
535C42#612912yes—
536C42C22×Dic1312yes—
537C13#2112611yescharacteristic, complemented, Sylow
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23C2×D4×D1311yescharacteristic
553D4—22no—
554D4—22no—
555D4—22no—
556D4—22no—
557D4—22no—
558D4—41no—
559D4—41no—
560D4#8818014yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—84no—
572C2×C4—84no—
573C2×C4—261no—
574C2×C4—261no—
575C2×C4—261no—
576C2×C4—261no—
577C2×C4—261no—
578C2×C4—261no—
579C2×C4—261no—
580C2×C4—261no—
581C2×C4—261no—
582C2×C4—261no—
583C2×C4—261no—
584C2×C4—261no—
585C2×C4—262no—
586C2×C4—262no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4—521no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—1044no—
598C2×C4—1044no—
599C2×C4D4×Dic1312yes—
600C2×C4D4×Dic1312yes—
601C2×C4C2×#612711yescharacteristic
602C2×C4C2×#612711yescharacteristic
603C2×C4C2×#612911yescharacteristic
604C2×C4#41×D1311yescharacteristic
605C2×C4#41×D1311yescharacteristic
606C2×C4C23×Dic1311yescharacteristic
607C8—22no—
608C8—22no—
609C8—521no—
610C8—521no—
611C22—24no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22#1171925211yescharacteristic
626C22#1171925211yescharacteristic
627C22#1171947911yescharacteristic
628C22#1171947911yescharacteristic
629C22#1171948011yescharacteristic
630C22#1171948011yescharacteristic
631C22C2×D4×Dic1311yescharacteristic
632C4—22no—
633C4—22no—
634C4—42no—
635C4—42no—
636C4—521no—
637C4—522no—
638C4—521no—
639C4—521no—
640C4—522no—
641C4—521no—
642C4—1041no—
643C4—1041no—
644C4#1171924311yescharacteristic
645C4#1171924311yescharacteristic
646C4C2×#8818011yescharacteristic
647C4#41×Dic1311yescharacteristic
648C2—44no—
649C2—82no—
650C2#1311728111yescharacteristic
651C2#1312366911yescharacteristic
652C2#1312366911yescharacteristic
653C2#1312501811yescharacteristic
654C2#1312503911yescharacteristic
655C2#1312507811yescharacteristic
656C2#1312511711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#442C2
socleC23×C13C22×D4
prime radicalC22×C13×D8C22
cosocleC22×C4×C13C24
hypercenterC2×#442D13
hypocenterC13#21126
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. #13117479C2semidirect
2. #13117197C2semidirect
3. #13115465C2semidirect
4. #13115458C2semidirect
5. #13115423C2semidirect
6. #13115416C2semidirect
9. #13115099C2semidirect
10. #13115085C2semidirect
11. #13114733C2semidirect
12. C4×#88072C2semidirect
13. C4×#88072C2semidirect
14. #13114589C2semidirect
21. C13×#442C4semidirect
74. C4×D4×C13C2×C4semidirect
104. C13×#106C2×C4semidirect
106. C13×#102C2×C4semidirect
107. C13×#97C2×C4semidirect
303. #442Dic13semidirect
399. C4×D4C2×Dic13semidirect
425. #106C2×Dic13semidirect
431. #102C2×Dic13semidirect
432. #97C2×Dic13semidirect
537. C13#21126semidirect

Maximal subgroups

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

subgroupindex
#131174792
#131171972
#131154652
#131154582
#131154232
#131154162
#131151862
#131150992
#131150852
#131147332
C4×#880722
#131145892
C2×C13×#4422
#2112613