Finite Group Databasebeta

← #25019292

Subgroups — #25019292

Order 11008.

1862 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063281C211yesmaximal, characteristic
2C2×#14582763C211yesmaximal, characteristic, complemented
3C2×#14582745C211yesmaximal, characteristic, complemented
4#19132846C212yesmaximal, complemented
5#19132838C212yesmaximal
6#19132832C211yesmaximal, characteristic
7#19132830C211yesmaximal, characteristic, complemented
8#19132828C211yesmaximal, characteristic, complemented
9#19132821C212yesmaximal, complemented
10#19132817C212yesmaximal
11C43×#1437C211yesmaximal, characteristic
12C24×Dic43C2211yescharacteristic
13C2×#13063281—24no—
14C2×#13063281—24no—
15C2×#13063281C418yescomplemented
16C22×Dic43⋊C4C2211yescharacteristic
17C22×Dic43⋊C4C2211yescharacteristic
18C22×Dic43⋊C4C2212yes—
19C22×C22⋊Dic43C2212yes—
20C22×C22⋊Dic43C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22C22×C4×Dic43C2211yescharacteristic
23C22×C4×Dic43C2211yescharacteristic
24#14582763—24no—
25#14582745—24no—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2212yes—
35C22×C22⋊C4×C43C2212yes—
36C22×C22⋊C4×C43C2211yescharacteristic
37C22×C42×C43C2211yescharacteristic
38C2×#95×C43C2211yescharacteristic
39C2×#95×C43C2212yes—
40C23×Dic43—24no—
41C23×Dic43—22no—
42C23×Dic43—22no—
43C23×Dic43—24no—
44C23×Dic43C2×C414yes—
45C23×Dic43C2312yes—
46C23×Dic43C2311yescharacteristic
47C23×Dic43C2312yes—
48C23×Dic43C2311yescharacteristic
49C23×Dic43C2311yescharacteristic
50C23×Dic43C2311yescharacteristic
51#13063281—232no—
52C2×Dic43⋊C4—22no—
53C2×Dic43⋊C4—22no—
54C2×Dic43⋊C4—22no—
55C2×Dic43⋊C4—22no—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—42no—
58C2×Dic43⋊C4—42no—
59C2×Dic43⋊C4C2×C414yes—
60C2×Dic43⋊C4C2×C414yes—
61C2×C22⋊Dic43—22no—
62C2×C22⋊Dic43—22no—
63C2×C22⋊Dic43—24no—
64C2×C22⋊Dic43—24no—
65C2×C22⋊Dic43—42no—
66C2×C22⋊Dic43C2×C414yes—
67C2×C4×Dic43—22no—
68C2×C4×Dic43—22no—
69C2×C4×Dic43—22no—
70C2×C4×Dic43—24no—
71C2×C4×Dic43C2×C414yes—
72C2×C4×Dic43C2×C414yes—
73C2×C4×Dic43D414yes—
74C2×C4×Dic43D414yes—
75C43⋊#95—22no—
76C43⋊#95—24no—
77C43⋊#95—24no—
78C43⋊#95—24no—
79C43⋊#95—24no—
80C43⋊#95—24no—
81C43⋊#95—24no—
82C43⋊#95—24no—
83C43⋊#95—42no—
84C25×C43C2311yescharacteristic
85C23×C4×C43C2312yes—
86C23×C4×C43C2311yescharacteristic
87C23×C4×C43C2312yes—
88C23×C4×C43C2311yescharacteristic
89C2×C22⋊C4×C43—22no—
90C2×C22⋊C4×C43—22no—
91C2×C22⋊C4×C43—24no—
92C2×C22⋊C4×C43—24no—
93C2×C22⋊C4×C43—42no—
94C2×C22⋊C4×C43C2×C414yes—
95C2×C42×C43—22no—
96C2×C42×C43—24no—
97#95×C43—22no—
98#95×C43—42no—
99C24×C43—21no—
100C24×C43—21no—
101C24×C43—22no—
102C24×C43—22no—
103C24×C43—22no—
104C24×C43—22no—
105C24×C43—22no—
106C24×C43C22×C412yes—
107C24×C43#4114yes—
108C24×C43C2411yescharacteristic
109C22×C4×C43—22no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43C22×C412yes—
129C22×C4×C43C22×C412yes—
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2×D412yes—
132C22×C4×C43#4114yes—
133C22×Dic43—216no—
134C22×Dic43—216no—
135C22×Dic43—28no—
136C22×Dic43—28no—
137C22×Dic43—28no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—22no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43C22×C412yes—
163C22×Dic43C22×C412yes—
164C22×Dic43C22×C412yes—
165C22×Dic43C22×C412yes—
166C22×Dic43C2×D412yes—
167C22×Dic43C2×D412yes—
168C22×Dic43C2×D412yes—
169C22×Dic43C2×D412yes—
170C22×Dic43#4114yes—
171C22×Dic43#4114yes—
172C22⋊C4×C43—28no—
173C22⋊C4×C43—48no—
174C42×C43—28no—
175C22⋊Dic43—28no—
176C22⋊Dic43—48no—
177Dic43⋊C4—28no—
178Dic43⋊C4—28no—
179Dic43⋊C4—48no—
180C4×Dic43—28no—
181C4×Dic43—28no—
182C4×Dic43C22⋊C4116yescomplemented
183C23×C43—22no—
184C23×C43—22no—
185C23×C43—24no—
186C23×C43—24no—
187C23×C43—24no—
188C23×C43—24no—
189C23×C43—24no—
190C23×C43—24no—
191C23×C43—24no—
192C23×C43—24no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—42no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43—42no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43#11714yes—
204C23×C43C23×C411yescharacteristic
205C23×C43C22×D411yescharacteristic
206C23×C43C22×D411yescharacteristic
207C23×C43C2×#4112yes—
208C23×C43C2×#4112yes—
209C23×C43C2×#4112yes—
210C23×C43C2×#4112yes—
211C23×C43H(5,𝔽2)12yes—
212C23×C432−1+412yes—
213C2×C4×C43—24no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—24no—
217C2×C4×C43—22no—
218C2×C4×C43—24no—
219C2×C4×C43—24no—
220C2×C4×C43—24no—
221C2×C4×C43—24no—
222C2×C4×C43—42no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43C2×C22⋊C414yes—
237C2×Dic43—232no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—24no—
243C2×Dic43—24no—
244C2×Dic43—24no—
245C2×Dic43—24no—
246C2×Dic43—24no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—24no—
250C2×Dic43—22no—
251C2×Dic43—24no—
252C2×Dic43—24no—
253C2×Dic43—24no—
254C2×Dic43—24no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43C2×C22⋊C414yes—
270C2×Dic43C2×C22⋊C414yes—
271C2×Dic43#11714yes—
272#13957—431nomaximal, Sylow
273C22×C43—28no—
274C22×C43—24no—
275C22×C43—42no—
276C22×C43—44no—
277C22×C43—44no—
278C22×C43—44no—
279C22×C43—44no—
280C22×C43—44no—
281C22×C43—42no—
282C22×C43C22×C22⋊C411yescharacteristic
283C22×C43C2×#11711yescharacteristic
284C22×C43C2×#11711yescharacteristic
285C22×C43C4×#4112yes—
286C22×C43#52012yes—
287C22×C43#52511yescharacteristic
288C22×C43#52511yescharacteristic
289C22×C43#52512yes—
290C22×C43#52512yes—
291C22×C43#53212yes—
292C22×C43#53511yescharacteristic
293C22×C43#53611yescharacteristic
294C22×C43#53712yes—
295C22×C43#55112yes—
296C22×C43#55112yes—
297C22×C43#55212yes—
298C22×C43#55212yes—
299C22×C43#55212yes—
300C22×C43#55212yes—
301C22×C43#55512yes—
302C22×C43#55512yes—
303C4×C43—24no—
304C4×C43—42no—
305C4×C43—44no—
306C4×C43—82no—
307Dic43—24no—
308Dic43—24no—
309Dic43—24no—
310Dic43—44no—
311Dic43—42no—
312Dic43—82no—
313C22×#117—431no—
314C2×#382—431no—
315C2×#376—431no—
316#1441—432no—
317#1439—432no—
318#1437—431no—
319#1437D4311yescharacteristic
320#1436—431no—
321#1436—431no—
322#1434—432no—
323C22⋊#95—432no—
324C2×C43—44no—
325C2×C43#228011yescharacteristic
326C2×C43#229711yescharacteristic
327C2×C43#231111yescharacteristic
328C2×C43#234312yes—
329C2×C43#234612yes—
330C2×C43#260912yes—
331C2×C43#260912yes—
332C2×C43#261012yes—
333C2×C43#261112yes—
334C24×C4—431no—
335C2×#117—438no—
336C2×#117—864no—
337C2×#117—864no—
338C22×C4⋊C4—431no—
339C22×C4⋊C4—431no—
340C22×C4⋊C4—432no—
341C22×C22⋊C4—431no—
342C22×C22⋊C4—432no—
343C22×C22⋊C4C2×D4312yes—
344C22×C22⋊C4C2×D4311yescharacteristic
345C22×C42—431no—
346C22×C42—431no—
347C22×C42—431no—
348C22×C42C2×D4311yescharacteristic
349#382—864no—
350#376—864no—
351C2×#95—432no—
352C2×#95—432no—
353C2×#95—432no—
354C2×#95—432no—
355C2×#95—432no—
356C2×#95—432no—
357C2×#95—431no—
358C2×#95—432no—
359C2×#95—432no—
360C2×#95C2×D4311yescharacteristic
361C2×#95C2×D4312yes—
362C43#1395711yescharacteristic, complemented, Sylow
363C25C22×D4311yescharacteristic
364C23×C4—431no—
365C23×C4—431no—
366C23×C4—431no—
367C23×C4—434no—
368C23×C4—431no—
369C23×C4—432no—
370C23×C4—432no—
371C23×C4—862no—
372C23×C4—862no—
373C23×C4—864no—
374C23×C4—864no—
375C23×C4C22×D4312yes—
376C23×C4C22×D4311yescharacteristic
377C23×C4C22×D4312yes—
378C23×C4C22×D4311yescharacteristic
379#117—8632no—
380C2×C4⋊C4—434no—
381C2×C4⋊C4—434no—
382C2×C4⋊C4—862no—
383C2×C4⋊C4—862no—
384C2×C4⋊C4—862no—
385C2×C4⋊C4—862no—
386C2×C4⋊C4—864no—
387C2×C4⋊C4—1722no—
388C2×C4⋊C4—1722no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—434no—
395C2×C22⋊C4—862no—
396C2×C22⋊C4—862no—
397C2×C22⋊C4—864no—
398C2×C22⋊C4—864no—
399C2×C22⋊C4—1722no—
400C2×C22⋊C4C4×D4314yes—
401C2×C42—22no—
402C2×C42—24no—
403C2×C42—434no—
404C2×C42—434no—
405C2×C42—434no—
406C2×C42—434no—
407C2×C42—862no—
408C2×C42—862no—
409C2×C42—864no—
410C2×C42—862no—
411#95—22no—
412#95—42no—
413#95—864no—
414#95—864no—
415#95—864no—
416#95—864no—
417#95—864no—
418#95—864no—
419#95—862no—
420#95—864no—
421#95—1722no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24C2×C4×D4312yes—
430C24#1062189814yes—
431C24C23×D4311yescharacteristic
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—432no—
452C22×C4—432no—
453C22×C4—432no—
454C22×C4—432no—
455C22×C4—432no—
456C22×C4—432no—
457C22×C4—432no—
458C22×C4—434no—
459C22×C4—432no—
460C22×C4—434no—
461C22×C4—868no—
462C22×C4—868no—
463C22×C4—8616no—
464C22×C4—8616no—
465C22×C4—868no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4C2×C4×D4312yes—
491C22×C4C2×C4×D4312yes—
492C22×C4D4×D4312yes—
493C22×C4D4×D4312yes—
494C22×C4#1062190014yes—
495C4⋊C4—868no—
496C4⋊C4—868no—
497C4⋊C4—1728no—
498C22⋊C4—28no—
499C22⋊C4—48no—
500C22⋊C4—868no—
501C22⋊C4—1728no—
502C42—28no—
503C42—4316no—
504C42—868no—
505C42—868no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—22no—
511C23—22no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—41no—
521C23—41no—
522C23—42no—
523C23—41no—
524C23—41no—
525C23—42no—
526C23#1306328214yes—
527C23C22×C4×D4311yescharacteristic
528C23C2×D4×D4311yescharacteristic
529C23C2×D4×D4311yescharacteristic
530C23#41×D4312yes—
531C23#41×D4312yes—
532C23C2×#1062190012yes—
533C23C2×#1062189812yes—
534C23#1306337012yes—
535C23#1306337212yes—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—434no—
560C2×C4—434no—
561C2×C4—434no—
562C2×C4—8632no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—864no—
568C2×C4—864no—
569C2×C4—864no—
570C2×C4—864no—
571C2×C4—864no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—864no—
575C2×C4—864no—
576C2×C4—864no—
577C2×C4—862no—
578C2×C4—864no—
579C2×C4—864no—
580C2×C4—1722no—
581C2×C4—1722no—
582C2×C4—1722no—
583C2×C4—1722no—
584C2×C4—1722no—
585C2×C4—1722no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4—1722no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1722no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4C22⋊C4×D4314yes—
595C22—28no—
596C22—24no—
597C22—42no—
598C22—42no—
599C22—44no—
600C22—44no—
601C22—44no—
602C22—44no—
603C22—44no—
604C22C2×C22⋊C4×D4311yescharacteristic
605C22#117×D4311yescharacteristic
606C22C2×#1306328211yescharacteristic
607C22C4×#1062190012yes—
608C22#1458337812yes—
609C22#1458340511yescharacteristic
610C22#1458340711yescharacteristic
611C22#1458340812yes—
612C22#1458340812yes—
613C22#1458344412yes—
614C22#1458346211yescharacteristic
615C22#1458346911yescharacteristic
616C22#1458347812yes—
617C22#1458357512yes—
618C22#1458357812yes—
619C22#1458358212yes—
620C22#1458358512yes—
621C22#1458358612yes—
622C22#1458358912yes—
623C22#1458361112yes—
624C22#1458361312yes—
625C4—24no—
626C4—42no—
627C4—44no—
628C4—82no—
629C4—864no—
630C4—864no—
631C4—864no—
632C4—3442no—
633C4—1722no—
634C4—1724no—
635C2—44no—
636C2#1913697611yescharacteristic
637C2#1913708011yescharacteristic
638C2#1913718511yescharacteristic
639C2#1913744912yes—
640C2#1913747712yes—
641C2#1914026912yes—
642C2#1914027012yes—
643C2#1914027912yes—
644C2#1914029012yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1437C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenter#1437D43
hypocenterC43#13957
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#14582763C2semidirect
3. C2×#14582745C2semidirect
4. #19132846C2semidirect
7. #19132830C2semidirect
8. #19132828C2semidirect
9. #19132821C2semidirect
15. C2×#13063281C4semidirect
182. C4×Dic43C22⋊C4semidirect
362. C43#13957semidirect

Maximal subgroups

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

subgroupindex
C22×#130632812
C2×#145827632
C2×#145827452
#191328462
#191328382
#191328322
#191328302
#191328282
#191328212
#191328172
C43×#14372
#1395743