Finite Group Databasebeta

← #15867830

Subgroups — #15867830

Order 3328.

826 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117445C211yesmaximal, characteristic
2#13117192C211yesmaximal, characteristic
3#13115606C211yesmaximal, characteristic, complemented
4#13115606C211yesmaximal, characteristic, complemented
5#13115600C211yesmaximal, characteristic, complemented
6#13115595C211yesmaximal, characteristic, complemented
7#13115037C211yesmaximal, characteristic
8#13115037C211yesmaximal, characteristic
9#13115031C211yesmaximal, characteristic
10#13115026C211yesmaximal, characteristic
11#13114733C211yesmaximal, characteristic, complemented
12#13114733C211yesmaximal, characteristic, complemented
13C4×#88058C211yesmaximal, characteristic, complemented
14C4×#88057C211yesmaximal, characteristic, complemented
15C2×C13×#433C211yesmaximal, characteristic
16C2×C13×#117C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C13×#433C418yescomplemented
20C2×C13×C4⋊C8C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C13×C22⋊C8C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C2×C13×#97C2211yescharacteristic
25C2×C4×C8×C13C2211yescharacteristic
26#11718873C2211yescharacteristic
27#11718873C2211yescharacteristic
28C2×#88058C2211yescharacteristic
29C2×#88058C2211yescharacteristic
30C2×#88058C2211yescharacteristic
31C2×#88058C2211yescharacteristic
32C2×#88057C2211yescharacteristic
33C2×#88057C2211yescharacteristic
34C2×#88057C2211yescharacteristic
35C2×#88057C2211yescharacteristic
36#11718642—21no—
37#11718642—21no—
38C4⋊C4×Dic13—21no—
39C4⋊C4×Dic13—21no—
40#11718612—21no—
41#11718612—21no—
42C22⋊C4×Dic13—21no—
43C22⋊C4×Dic13—21no—
44#11718597C2211yescharacteristic
45#11718596C2211yescharacteristic
46C4×C4⋊Dic13C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48C4×C4⋊Dic13C2211yescharacteristic
49C4×C4⋊Dic13C2211yescharacteristic
50C4×C4⋊Dic13C2211yescharacteristic
51C4×C4⋊Dic13C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—21no—
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C13×#117C2×C414yes—
67C13×#117Q814yes—
68C2×C13×C4⋊C4D411yescharacteristic
69C2×C13×C4⋊C4D411yescharacteristic
70C2×C13×C22⋊C4D411yescharacteristic
71C2×C13×C22⋊C4D411yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76C2×C22⋊Dic13—21no—
77#88180—22no—
78#88180—22no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—22no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4×Dic13—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C13×C4⋊C8C2×C414yescomplemented
100C13×C4⋊C8C2×C414yescomplemented
101C13×C22⋊C8C2×C414yes—
102C13×C22⋊C8C2×C414yes—
103C13×#97C2×C414yescomplemented
104C4×C8×C13C2×C414yescomplemented
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88058—22no—
116#88058—22no—
117#88058—22no—
118#88058—22no—
119#88057—22no—
120#88057—22no—
121#88057—22no—
122#88057—22no—
123#21367—131nomaximal, Sylow
124C24×C13C2×D411yescharacteristic
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13C22×C412yes—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×Q812yes—
136C22×C4×C13C2411yescharacteristic
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—24no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—81no—
147C22×Dic13—81no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13C22×C412yes—
157C2×C8×C13C22×C412yes—
158C2×C8×C13C22×C412yes—
159C2×C8×C13C22×C412yes—
160C13×C4⋊C4C4⋊C414yes—
161C13×C4⋊C4C4⋊C414yes—
162C13×C22⋊C4C4⋊C414yes—
163C13×C22⋊C4C4⋊C414yes—
164C42×C13C22×C412yes—
165C42×C13C22×C412yes—
166C42×C13C2×Q812yes—
167C42×C13C2×Q812yes—
168C22⋊Dic13—24no—
169C22⋊Dic13—81no—
170C22⋊Dic13—81no—
171C4⋊Dic13—24no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—81no—
185C4⋊Dic13—81no—
186C4⋊Dic13#4112yes—
187C4⋊Dic13#4112yes—
188C4⋊Dic13#4112yes—
189C4⋊Dic13#4112yes—
190C4×Dic13—24no—
191C4×Dic13—81no—
192C4×Dic13—81no—
193C4×Dic13—81no—
194C4×Dic13—81no—
195C4×Dic13—81no—
196C4×Dic13—81no—
197C2×#433D1311yescharacteristic
198#2314—131no—
199#2274—131no—
200#1949—131no—
201#1949—131no—
202#1948—131no—
203#1947—131no—
204#1854—131no—
205#1854—131no—
206#1853—131no—
207#1852—131no—
208#1776—131no—
209#1776—131no—
210C4×#107—131no—
211C4×#106—131no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13—21no—
218C23×C13C2×C4⋊C412yes—
219C23×C13C22×D411yescharacteristic
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
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—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13C2×C4⋊C412yes—
235C2×C4×C13C2×C4⋊C412yes—
236C2×C4×C13C2×C4⋊C412yes—
237C2×C4×C13C2×C4⋊C412yes—
238C2×C4×C13C2×C4⋊C412yes—
239C2×C4×C13C23×C411yescharacteristic
240C2×C4×C13C22×Q811yescharacteristic
241C2×C4×C13C2×#4111yescharacteristic
242C2×C4×C13C2×#4111yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—84no—
270C8×C13—22no—
271C8×C13—22no—
272C8×C13—22no—
273C8×C13—22no—
274C2×#117—131no—
275C2×#117C2×D1311yescharacteristic
276C22×C4⋊C4—131no—
277#433Dic1318yescomplemented
278C2×#107—131no—
279C2×#107—131no—
280C2×#107—131no—
281C2×#107—131no—
282C2×#106—131no—
283C2×#106—131no—
284C2×#106—131no—
285C2×#106—131no—
286C2×C4⋊C8C2×D1311yescharacteristic
287C2×C4⋊C8C2×D1311yescharacteristic
288C2×C22⋊C8C2×D1311yescharacteristic
289C2×C22⋊C8C2×D1311yescharacteristic
290C2×#97C2×D1311yescharacteristic
291C2×C4×C8C2×D1311yescharacteristic
292#388—261no—
293#388—261no—
294#387—261no—
295#387—261no—
296#384—131no—
297#382—131no—
298#380—131no—
299#380—131no—
300C4×C4⋊C4—131no—
301C4×C4⋊C4—131no—
302C4×C4⋊C4—131no—
303C4×C4⋊C4—131no—
304C4×C4⋊C4—131no—
305C4×C4⋊C4—131no—
306C4×C4⋊C4—261no—
307C4×C4⋊C4—261no—
308C4×C22⋊C4—261no—
309C4×C22⋊C4—261no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318C22×C13—22no—
319C22×C13—22no—
320C22×C13—22no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13—41no—
325C22×C13C22×C4⋊C411yescharacteristic
326C22×C13#52511yescharacteristic
327C22×C13#52511yescharacteristic
328C22×C13#57611yescharacteristic
329C22×C13#57711yescharacteristic
330C22×C13#57711yescharacteristic
331C22×C13#57811yescharacteristic
332C4×C13—22no—
333C4×C13—22no—
334C4×C13—22no—
335C4×C13—22no—
336C4×C13—22no—
337C4×C13C4×#4111yescharacteristic
338C4×C13C4×#4111yescharacteristic
339C4×C13#53311yescharacteristic
340C4×C13#53311yescharacteristic
341Dic13—42no—
342Dic13—42no—
343Dic13—42no—
344Dic13—42no—
345Dic13—81no—
346Dic13—81no—
347Dic13—81no—
348Dic13—81no—
349C23×C4—261no—
350C23×C4C22×D1311yescharacteristic
351C22×C8C22×D1311yescharacteristic
352C22×C8C22×D1311yescharacteristic
353C22×C8C22×D1311yescharacteristic
354C22×C8C22×D1311yescharacteristic
355#117—262no—
356#117—262no—
357#117Dic2614yes—
358#117C2×Dic1314yes—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—262no—
368C2×C4⋊C4—262no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4D5211yescharacteristic
373C2×C4⋊C4D5211yescharacteristic
374C2×C22⋊C4—261no—
375C2×C22⋊C4—261no—
376C2×C22⋊C4—261no—
377C2×C22⋊C4D5211yescharacteristic
378C2×C22⋊C4D5211yescharacteristic
379C2×C42—261no—
380C2×C42—261no—
381C2×C42—261no—
382C2×C42—261no—
383C2×C42—261no—
384C2×C42—261no—
385C2×C42—261no—
386C2×C42C22×D1311yescharacteristic
387C2×C42C22×D1311yescharacteristic
388#107—262no—
389#107—262no—
390#107—262no—
391#107—262no—
392#106—262no—
393#106—262no—
394#106—262no—
395#106—262no—
396C4⋊C8C2×Dic1314yescomplemented
397C4⋊C8C2×Dic1314yescomplemented
398C22⋊C8C2×Dic1314yes—
399C22⋊C8C2×Dic1314yes—
400#97C2×Dic1314yescomplemented
401C4×C8C2×Dic1314yescomplemented
402#95—261no—
403#95—261no—
404#95—261no—
405#95—261no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95—261no—
410#95—261no—
411#95—261no—
412C2×C13—42no—
413C2×C13#229611yescharacteristic
414C2×C13#291211yescharacteristic
415C2×C13#291311yescharacteristic
416C2×C13#311811yescharacteristic
417C2×C13#311911yescharacteristic
418C2×C13#312011yescharacteristic
419C2×C13#312111yescharacteristic
420C24C2×D5211yescharacteristic
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—261no—
426C22×C4—261no—
427C22×C4—261no—
428C22×C4—261no—
429C22×C4—264no—
430C22×C4—261no—
431C22×C4—261no—
432C22×C4—261no—
433C22×C4—261no—
434C22×C4—1041no—
435C22×C4—1041no—
436C22×C4C2×Dic2612yes—
437C22×C4C2×D5211yescharacteristic
438C22×C4C2×D5211yescharacteristic
439C22×C4C2×D5211yescharacteristic
440C22×C4C2×D5211yescharacteristic
441C22×C4C2×D5211yescharacteristic
442C22×C4C22×Dic1312yes—
443C22×C4C23×D1311yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8C22×Dic1312yes—
453C2×C8C22×Dic1312yes—
454C2×C8C22×Dic1312yes—
455C2×C8C22×Dic1312yes—
456C4⋊C4—132no—
457C4⋊C4—132no—
458C4⋊C4—132no—
459C4⋊C4—132no—
460C4⋊C4—264no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—1041no—
474C4⋊C4—1041no—
475C4⋊C4C4⋊Dic1314yes—
476C4⋊C4C4⋊Dic1314yes—
477C22⋊C4—264no—
478C22⋊C4—1041no—
479C22⋊C4—1041no—
480C22⋊C4C4⋊Dic1314yes—
481C22⋊C4C4⋊Dic1314yes—
482C42—264no—
483C42—1041no—
484C42—1041no—
485C42—1041no—
486C42—1041no—
487C42—1041no—
488C42—1041no—
489C42C2×Dic2612yes—
490C42C2×Dic2612yes—
491C42C22×Dic1312yes—
492C42C22×Dic1312yes—
493C13#2136711yescharacteristic, complemented, Sylow
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23C2×C4⋊Dic1312yes—
501C23C22×D5211yescharacteristic
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—262no—
517C2×C4—262no—
518C2×C4—262no—
519C2×C4—262no—
520C2×C4—521no—
521C2×C4—521no—
522C2×C4—521no—
523C2×C4—521no—
524C2×C4—521no—
525C2×C4—521no—
526C2×C4—521no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—1044no—
541C2×C4C2×C4⋊Dic1312yes—
542C2×C4C2×C4⋊Dic1312yes—
543C2×C4C2×C4⋊Dic1312yes—
544C2×C4C2×C4⋊Dic1312yes—
545C2×C4C2×C4⋊Dic1312yes—
546C2×C4C22×Dic2611yescharacteristic
547C2×C4#41×D1311yescharacteristic
548C2×C4#41×D1311yescharacteristic
549C2×C4#41×D1311yescharacteristic
550C2×C4#41×D1311yescharacteristic
551C2×C4C23×Dic1311yescharacteristic
552C8—22no—
553C8—22no—
554C8—22no—
555C8—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22#1171922911yescharacteristic
564C22#1171922911yescharacteristic
565C22#1171945611yescharacteristic
566C22#1171945611yescharacteristic
567C22#1171945711yescharacteristic
568C22#1171945811yescharacteristic
569C22C22×C4⋊Dic1311yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—22no—
574C4—22no—
575C4—522no—
576C4—522no—
577C4—522no—
578C4—522no—
579C4—1041no—
580C4—1041no—
581C4—1041no—
582C4—1041no—
583C4#1171922211yescharacteristic
584C4#1171922211yescharacteristic
585C4#41×Dic1311yescharacteristic
586C4#41×Dic1311yescharacteristic
587C2—42no—
588C2#1311732011yescharacteristic
589C2#1312343111yescharacteristic
590C2#1312343611yescharacteristic
591C2#1312502211yescharacteristic
592C2#1312503711yescharacteristic
593C2#1312505211yescharacteristic
594C2#1312506711yescharacteristic
subgroupG/H
centerC23C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#433C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenterC2×#433D13
hypocenterC13#21367
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
3. #13115606C2semidirect
4. #13115606C2semidirect
5. #13115600C2semidirect
6. #13115595C2semidirect
11. #13114733C2semidirect
12. #13114733C2semidirect
13. C4×#88058C2semidirect
14. C4×#88057C2semidirect
19. C13×#433C4semidirect
99. C13×C4⋊C8C2×C4semidirect
100. C13×C4⋊C8C2×C4semidirect
103. C13×#97C2×C4semidirect
104. C4×C8×C13C2×C4semidirect
277. #433Dic13semidirect
396. C4⋊C8C2×Dic13semidirect
397. C4⋊C8C2×Dic13semidirect
400. #97C2×Dic13semidirect
401. C4×C8C2×Dic13semidirect
493. C13#21367semidirect

Maximal subgroups

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

subgroupindex
#131174452
#131171922
#131156062
#131156002
#131155952
#131150372
#131150312
#131150262
#131147332
C4×#880582
C4×#880572
C2×C13×#4332
#2136713