Finite Group Databasebeta

← #15869956

Subgroups — #15869956

Order 3328.

906 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×D52C211yesmaximal, characteristic
2C2×#11718350C211yesmaximal, characteristic, complemented
3#13118099C211yesmaximal, characteristic
4#13115448C211yesmaximal, characteristic, complemented
5#13115447C211yesmaximal, characteristic, complemented
6#13115403C211yesmaximal, characteristic, complemented
7#13115402C211yesmaximal, characteristic, complemented
8#13115132C211yesmaximal, characteristic
9#13115017C211yesmaximal, characteristic, complemented
10#13114906C211yesmaximal, characteristic, complemented
11C8×#6101C211yesmaximal, characteristic, complemented
12C8×#6103C211yesmaximal, characteristic, complemented
13C8×#6103C211yesmaximal, characteristic, complemented
14C8×#6103C211yesmaximal, characteristic, complemented
15C8×C13×C4⋊C4C211yesmaximal, characteristic, complemented
16C22×#6094C2211yescharacteristic
17C22×C8×D13C2211yescharacteristic
18C22×C8×D13C2211yescharacteristic
19C2×C4×D52C2211yescharacteristic
20C2×#88126C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C2×C4×C8×C13C2211yescharacteristic
24C2×C4×C8×C13C2211yescharacteristic
25C4×C13×C4⋊C4C2211yescharacteristic
26C2×#88060C2211yescharacteristic
27C2×#88060C2211yescharacteristic
28C2×#88060C2211yescharacteristic
29C2×#88060C2211yescharacteristic
30C2×#88060C2211yescharacteristic
31C2×#88055C2211yescharacteristic
32C2×#88054C2211yescharacteristic
33C2×C8×Dic13C2211yescharacteristic
34C2×C8×Dic13C2211yescharacteristic
35#11718654C411yescharacteristic
36#11718653C411yescharacteristic
37#11718652C411yescharacteristic
38#11718645C411yescharacteristic
39C4×#6103C2211yescharacteristic
40C4×#6103C2211yescharacteristic
41C4×#6103C2211yescharacteristic
42C4×#6101C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45#11718350—24no—
46C8×D52—24no—
47#11718336C411yescharacteristic
48#11718336C411yescharacteristic
49#11718333C411yescharacteristic
50#11718321C411yescharacteristic
51C13×#336C2211yescharacteristic
52C13×#336C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×D52C2×C411yescharacteristic
62C22×C4×D13C2311yescharacteristic
63C22×C4×D13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C2×C13×C4⋊C4C2×C411yescharacteristic
69C2×C13×C4⋊C4C2×C411yescharacteristic
70C2×C42×C13C2311yescharacteristic
71C2×C42×C13C2311yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×#6103C2×C411yescharacteristic
74C2×#6103C2×C411yescharacteristic
75C2×#6103C2×C411yescharacteristic
76C2×#6103C2×C411yescharacteristic
77C2×#6103C2×C411yescharacteristic
78C2×#6103C2×C411yescharacteristic
79C2×#6103C2×C411yescharacteristic
80C2×#6103C2×C411yescharacteristic
81C2×#6103C2×C411yescharacteristic
82C2×#6103C2×C411yescharacteristic
83C2×C4⋊Dic13C2×C411yescharacteristic
84C2×#6101C2×C411yescharacteristic
85C2×#6101C2×C411yescharacteristic
86C2×#6101C2×C411yescharacteristic
87C2×#6101C2×C411yescharacteristic
88C2×C4×Dic13C2311yescharacteristic
89C2×C4×Dic13C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C2×#6094—22no—
95C2×#6094—22no—
96C2×#6094—22no—
97C2×C8×D13—22no—
98C2×C8×D13—22no—
99C2×C8×D13—22no—
100C2×C8×D13—22no—
101C2×C8×D13—22no—
102C2×C8×D13D414yes—
103C4×D52—22no—
104C4×D52—22no—
105#88126—22no—
106#88126—22no—
107C13×C4⋊C8—22no—
108C4×C8×C13—22no—
109C4×C8×C13—22no—
110C4×C8×C13—22no—
111C13×#95C2×C411yescharacteristic
112C13×#95C2×C411yescharacteristic
113#88071C2×C411yescharacteristic
114#88071C2×C411yescharacteristic
115#88071C2×C411yescharacteristic
116#88071C2×C411yescharacteristic
117#88071C2×C411yescharacteristic
118#88071C2×C411yescharacteristic
119#88071C2×C411yescharacteristic
120#88071C2×C411yescharacteristic
121#88060—22no—
122#88060—22no—
123#88060—22no—
124#88060—22no—
125#88060—22no—
126#88055—22no—
127#88054—22no—
128C8×Dic13—22no—
129C8×Dic13—22no—
130C4⋊#1055—22no—
131#88043—22no—
132#21566—131nomaximal, Sylow
133C23×D13C22×C411yescharacteristic
134C23×D13C22×C411yescharacteristic
135C22×C4×C13C22×C411yescharacteristic
136C22×C4×C13C22×C411yescharacteristic
137C22×C4×C13C22×C411yescharacteristic
138C22×C4×C13C22×C411yescharacteristic
139C22×C4×C13C22×C411yescharacteristic
140C22×C4×C13C22×C411yescharacteristic
141C22×C4×C13C2411yescharacteristic
142C22×Dic13C22×C411yescharacteristic
143C22×Dic13C22×C411yescharacteristic
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C411yescharacteristic
148C2×D52—22no—
149C2×D52—22no—
150C2×D52—22no—
151C2×C4×D13—21no—
152C2×C4×D13—21no—
153C2×C4×D13—21no—
154C2×C4×D13—21no—
155C2×C4×D13—21no—
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13C2×D412yes—
162C2×C4×D13#4112yes—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13C2×D412yes—
172C2×C8×C13#4112yes—
173C2×C8×C13#4112yes—
174C2×C8×C13#4112yes—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—21no—
182C42×C13—21no—
183#6103—22no—
184#6103—22no—
185#6103—22no—
186#6103—22no—
187#6103—22no—
188#6103—22no—
189#6103—22no—
190#6103—22no—
191#6103—22no—
192#6103—22no—
193C4⋊Dic13—22no—
194#6101—22no—
195#6101—22no—
196#6101—22no—
197#6101—22no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055C2×D412yes—
213C2×#1055#4112yes—
214#6094—28no—
215C8×D13—28no—
216C8×D13—44no—
217C2×C8×D4—131no—
218C2×#405—131no—
219#2395—131no—
220#1924—131no—
221#1924—131no—
222#1917—131no—
223#1917—131no—
224#1870—131no—
225#1851—131no—
226#1818—131no—
227C8×C4⋊C4—131no—
228C8×C4⋊C4D1311yescharacteristic, complemented
229C8×C22⋊C4—131no—
230C8×C22⋊C4—131no—
231C8×C22⋊C4—131no—
232C23×C13C23×C411yescharacteristic
233C22×D13—21no—
234C22×D13—21no—
235C22×D13—21no—
236C22×D13—21no—
237C22×D13—21no—
238C22×D13—21no—
239C22×D13—21no—
240C22×D13—21no—
241C22×D13—21no—
242C22×D13—21no—
243C22×D13—21no—
244C22×D13—21no—
245C22×D13C4×D412yes—
246C22×D13#13112yes—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
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#13112yes—
264C2×C4×C13#13112yes—
265C2×C4×C13C22×D411yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×C4×C13C2×#4111yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
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—21no—
283C2×Dic13—21no—
284C2×Dic13—21no—
285C2×Dic13—21no—
286C2×Dic13—21no—
287C2×Dic13C4×D412yes—
288C2×Dic13#13112yes—
289D52—28no—
290C4×D13—22no—
291C4×D13—22no—
292C4×D13—22no—
293C4×D13—22no—
294C4×D13—41no—
295C4×D13—41no—
296C4×D13—41no—
297C4×D13—41no—
298C8×C13—22no—
299C8×C13—41no—
300C8×C13—41no—
301C8×C13#12314yes—
302#1055—22no—
303#1055—22no—
304#1055—41no—
305#1055—41no—
306C22×M16—131no—
307C23×C8—131no—
308C23×C8—131no—
309C2×C4×D4—131no—
310C2×#117—131no—
311C8×D4—264no—
312C2×C4⋊C8—131no—
313C2×C4⋊C8—131no—
314C2×C4⋊C8C2×D1311yescharacteristic
315C2×C22⋊C8—131no—
316C2×C22⋊C8—131no—
317C2×C22⋊C8—131no—
318C2×C22⋊C8—131no—
319C2×C22⋊C8—131no—
320#405—264no—
321C2×#97—131no—
322C2×#97—131no—
323C2×C4×C8—131no—
324C2×C4×C8—131no—
325C2×C4×C8C2×D1311yescharacteristic
326C2×C4×C8C2×D1311yescharacteristic
327C2×C4×C8C2×D1311yescharacteristic
328#400—131no—
329#399—131no—
330#398—131no—
331#397—131no—
332#397—131no—
333#397—131no—
334#394—131no—
335#394—131no—
336C4×C4⋊C4—131no—
337C4×C4⋊C4C2×D1311yescharacteristic
338C4×C22⋊C4—131no—
339C4×C22⋊C4—131no—
340C4×C22⋊C4—131no—
341#336—131no—
342#336—131no—
343#336—131no—
344#336—131no—
345#336—131no—
346#336—131no—
347#336—131no—
348#336—131no—
349#336C2×D1311yescharacteristic
350#336C2×D1311yescharacteristic
351C22×C13C2×C4×D411yescharacteristic
352C22×C13C4×#4111yescharacteristic
353C22×C13C4×#4111yescharacteristic
354C22×C13C2×#13111yescharacteristic
355C22×C13C2×#13111yescharacteristic
356C22×C13C2×#13111yescharacteristic
357C22×C13C2×#13111yescharacteristic
358C2×D13—22no—
359C2×D13—22no—
360C2×D13—22no—
361C2×D13—22no—
362C2×D13—22no—
363C2×D13—22no—
364C2×D13—41no—
365C2×D13—41no—
366C2×D13—41no—
367C2×D13—41no—
368C2×D13—41no—
369C2×D13—41no—
370C2×D13—41no—
371C2×D13—41no—
372C4×C13—22no—
373C4×C13—22no—
374C4×C13—41no—
375C4×C13—41no—
376C4×C13—41no—
377C4×C13—41no—
378C4×C13C2×#12311yescharacteristic
379C4×C13#52511yescharacteristic
380C4×C13#52911yescharacteristic
381C4×C13#52911yescharacteristic
382Dic13—22no—
383Dic13—22no—
384Dic13—41no—
385Dic13—41no—
386Dic13—41no—
387Dic13—41no—
388C22×D4—131no—
389C23×C4—131no—
390C23×C4—131no—
391C2×M16—262no—
392C2×M16—262no—
393C2×M16—262no—
394C22×C8—131no—
395C22×C8—131no—
396C22×C8—134no—
397C22×C8—131no—
398C22×C8—131no—
399C22×C8—262no—
400C22×C8—262no—
401C22×C8—262no—
402C22×C8—262no—
403C22×C8—262no—
404C22×C8C22×D1311yescharacteristic
405C22×C8C22×D1311yescharacteristic
406C22×C8C22×D1311yescharacteristic
407C22×C8C22×D1311yescharacteristic
408C4×D4—262no—
409C4×D4—262no—
410#117—262no—
411#117—262no—
412C2×C4⋊C4—131no—
413C2×C4⋊C4—131no—
414C2×C4⋊C4—131no—
415C2×C4⋊C4—131no—
416C2×C4⋊C4—131no—
417C2×C4⋊C4C4×D1311yescharacteristic
418C2×C4⋊C4C4×D1311yescharacteristic
419C2×C22⋊C4—131no—
420C2×C22⋊C4—131no—
421C2×C22⋊C4—131no—
422C2×C22⋊C4—131no—
423C2×C22⋊C4—131no—
424C2×C22⋊C4—131no—
425C2×C22⋊C4—131no—
426C2×C22⋊C4—131no—
427C2×C22⋊C4—131no—
428C2×C22⋊C4—131no—
429C2×C42—131no—
430C2×C42—131no—
431C2×C42C22×D1311yescharacteristic
432C2×C42C22×D1311yescharacteristic
433C2×C42C22×D1311yescharacteristic
434C4⋊C8—22no—
435C4⋊C8—262no—
436C4⋊C8—262no—
437C22⋊C8—262no—
438C22⋊C8—262no—
439C22⋊C8—262no—
440C22⋊C8—262no—
441C22⋊C8—262no—
442#97—262no—
443#97—262no—
444C4×C8—22no—
445C4×C8—22no—
446C4×C8—22no—
447C4×C8—262no—
448C4×C8—262no—
449#95—131no—
450#95—131no—
451#95—131no—
452#95—131no—
453#95—131no—
454#95—131no—
455#95—131no—
456#95—131no—
457#95C4×D1311yescharacteristic
458#95C4×D1311yescharacteristic
459C2×C13C4×#12311yescharacteristic
460C2×C13#292911yescharacteristic
461C2×C13#293111yescharacteristic
462C2×C13#296611yescharacteristic
463C2×C13#296611yescharacteristic
464C2×C13#296611yescharacteristic
465C2×C13#296611yescharacteristic
466D13—42no—
467D13—42no—
468C24—131no—
469C24—131no—
470C2×D4—262no—
471C2×D4—262no—
472C2×D4—262no—
473C22×C4—131no—
474C22×C4—131no—
475C22×C4—132no—
476C22×C4—132no—
477C22×C4—131no—
478C22×C4—131no—
479C22×C4—131no—
480C22×C4—131no—
481C22×C4—261no—
482C22×C4—261no—
483C22×C4—261no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4C2×C4×D1311yescharacteristic
492C22×C4C2×C4×D1311yescharacteristic
493C22×C4C2×C4×D1311yescharacteristic
494C22×C4C2×C4×D1311yescharacteristic
495C22×C4C2×C4×D1311yescharacteristic
496C22×C4C2×C4×D1311yescharacteristic
497C22×C4C23×D1311yescharacteristic
498M16—268no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—132no—
508C2×C8—132no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—268no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—524no—
521C2×C8#612712yes—
522C2×C8#612712yes—
523C2×C8D4×D1312yes—
524C2×C8#613112yes—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—262no—
528C4⋊C4—262no—
529C4⋊C4—262no—
530C4⋊C4—262no—
531C4⋊C4—262no—
532C22⋊C4—262no—
533C22⋊C4—262no—
534C22⋊C4—262no—
535C22⋊C4—262no—
536C22⋊C4—262no—
537C22⋊C4—262no—
538C22⋊C4—262no—
539C22⋊C4—262no—
540C22⋊C4—262no—
541C22⋊C4—262no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—261no—
549C42—261no—
550C42—261no—
551C42—261no—
552C13#2156611yescharacteristic, complemented, Sylow
553C23—132no—
554C23—132no—
555C23—261no—
556C23—261no—
557C23—261no—
558C23—261no—
559C23—261no—
560C23—261no—
561C23—261no—
562C23—261no—
563C23—261no—
564C23—261no—
565C23—261no—
566C23—261no—
567C23C22×C4×D1311yescharacteristic
568D4—268no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
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—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—132no—
586C2×C4—132no—
587C2×C4—261no—
588C2×C4—261no—
589C2×C4—261no—
590C2×C4—261no—
591C2×C4—262no—
592C2×C4—262no—
593C2×C4—262no—
594C2×C4—262no—
595C2×C4—261no—
596C2×C4—261no—
597C2×C4—261no—
598C2×C4—261no—
599C2×C4—261no—
600C2×C4—261no—
601C2×C4—261no—
602C2×C4—261no—
603C2×C4—261no—
604C2×C4—261no—
605C2×C4—261no—
606C2×C4—261no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4#8815512yes—
612C2×C4#8815512yes—
613C2×C4C2×#612711yescharacteristic
614C2×C4C2×#612711yescharacteristic
615C2×C4C2×D4×D1311yescharacteristic
616C2×C4C2×#613111yescharacteristic
617C2×C4#41×D1311yescharacteristic
618C2×C4#41×D1311yescharacteristic
619C8—22no—
620C8—41no—
621C8—41no—
622C8—262no—
623C8—262no—
624C8—521no—
625C8—521no—
626C8#8814814yes—
627C22—262no—
628C22—262no—
629C22—262no—
630C22—262no—
631C22—262no—
632C22—262no—
633C22—521no—
634C22—521no—
635C22—521no—
636C22—521no—
637C22—521no—
638C22—521no—
639C22—521no—
640C22—521no—
641C22C4×#612711yescharacteristic
642C22C4×D4×D1311yescharacteristic
643C22C4×#613111yescharacteristic
644C22C2×#8815511yescharacteristic
645C22C2×#8815511yescharacteristic
646C22D13×#13111yescharacteristic
647C22D13×#13111yescharacteristic
648C4—22no—
649C4—22no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—262no—
655C4—262no—
656C4—521no—
657C4—521no—
658C4—521no—
659C4—521no—
660C4C2×#8814811yescharacteristic
661C4#1171923311yescharacteristic
662C4#1171925211yescharacteristic
663C4#1171928511yescharacteristic
664C2—522no—
665C2—522no—
666C2C4×#8814811yescharacteristic
667C2#1312352511yescharacteristic
668C2#1312354311yescharacteristic
669C2#1312380711yescharacteristic
670C2#1312381111yescharacteristic
671C2#1312381311yescharacteristic
672C2#1312381311yescharacteristic
subgroupG/H
centerC22×C8C22×D13
commutator, socleC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingC8×C13×C4⋊C4C2
prime radicalC22×D52C2×C4
cosocleC22×C4×C13C24
hypercenterC8×C4⋊C4D13
hypocenterC13#21566
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11718350C2semidirect
4. #13115448C2semidirect
5. #13115447C2semidirect
6. #13115403C2semidirect
7. #13115402C2semidirect
9. #13115017C2semidirect
10. #13114906C2semidirect
11. C8×#6101C2semidirect
12. C8×#6103C2semidirect
13. C8×#6103C2semidirect
14. C8×#6103C2semidirect
15. C8×C13×C4⋊C4C2semidirect
228. C8×C4⋊C4D13semidirect
552. C13#21566semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D522
C2×#117183502
#131180992
#131154482
#131154472
#131154032
#131154022
#131151322
#131150172
#131149062
C8×#61012
C8×#61032
C8×C13×C4⋊C42
#2156613