Finite Group Databasebeta

← #25019125

Subgroups — #25019125

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×#13063283C211yesmaximal, characteristic
2C2×#14582766C211yesmaximal, characteristic, complemented
3C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
4#19132847C212yesmaximal, complemented
5#19132839C212yesmaximal
6#19132833C211yesmaximal, characteristic
7#19132831C211yesmaximal, characteristic
8#19132827C211yesmaximal, characteristic, complemented
9#19132821C212yesmaximal, complemented
10(C2×D43)⋊#95C212yesmaximal
11C43×#1436C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C2×#13063283—24no—
14C2×#13063283—24no—
15C2×#13063283C418yescomplemented
16C22×C4⋊Dic43C2211yescharacteristic
17C22×Dic43⋊C4C2212yes—
18C22×(C2×D43)⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2212yes—
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×C4×Dic43C2211yescharacteristic
23C22×C4×Dic43C2211yescharacteristic
24C22×C4×Dic43C2211yescharacteristic
25#14582766—24no—
26C4×Dic43⋊C4—24no—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C42×C43C2211yescharacteristic
37C2×#95×C43C2212yes—
38C2×#95×C43C2211yescharacteristic
39C2×#95×C43C2212yes—
40C24×D43C2311yescharacteristic
41C23×Dic43C2312yes—
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2312yes—
44C23×Dic43C2311yescharacteristic
45C23×Dic43C2311yescharacteristic
46C22×C4×D43—24no—
47C22×C4×D43—24no—
48C22×C4×D43—22no—
49C22×C4×D43—22no—
50C22×C4×D43C2×C414yes—
51#13063283—232no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43C2×C414yes—
55C2×Dic43⋊C4—24no—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—24no—
58C2×(C2×D43)⋊C4—22no—
59C2×(C2×D43)⋊C4—22no—
60C2×(C2×D43)⋊C4—22no—
61C2×(C2×D43)⋊C4—22no—
62C2×(C2×D43)⋊C4—24no—
63C2×(C2×D43)⋊C4—24no—
64C2×(C2×D43)⋊C4—24no—
65C2×(C2×D43)⋊C4—24no—
66C2×(C2×D43)⋊C4—42no—
67C2×(C2×D43)⋊C4—42no—
68C2×(C2×D43)⋊C4C2×C414yes—
69C2×(C2×D43)⋊C4C2×C414yes—
70C2×C4×Dic43—22no—
71C2×C4×Dic43—22no—
72C2×C4×Dic43—22no—
73C2×C4×Dic43—42no—
74C2×C4×Dic43C2×C414yes—
75C2×C4×Dic43C2×C414yes—
76C2×C4×Dic43D414yes—
77C2×C4×Dic43D414yes—
78C43⋊#95—22no—
79C43⋊#95—24no—
80C43⋊#95—24no—
81C43⋊#95—24no—
82C43⋊#95—24no—
83C43⋊#95—24no—
84C43⋊#95—24no—
85C43⋊#95—42no—
86C23×C4×C43C2312yes—
87C23×C4×C43C2311yescharacteristic
88C23×C4×C43C2312yes—
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2311yescharacteristic
91C2×C4⋊C4×C43—22no—
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43C2×C414yes—
94C2×C42×C43—22no—
95C2×C42×C43—42no—
96#95×C43—22no—
97#95×C43—24no—
98#95×C43—42no—
99C24×C43C2411yescharacteristic
100C23×D43—21no—
101C23×D43—21no—
102C23×D43—22no—
103C23×D43—22no—
104C23×D43—22no—
105C23×D43—22no—
106C23×D43—22no—
107C23×D43C22×C412yes—
108C23×D43#4114yes—
109C22×C4×C43—21no—
110C22×C4×C43—21no—
111C22×C4×C43—22no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
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×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43C22×C412yes—
132C22×C4×C43C22×C412yes—
133C22×C4×C43C22×C412yes—
134C22×C4×C43C2×D412yes—
135C22×C4×C43C2×D412yes—
136C22×C4×C43#4114yes—
137C22×C4×C43#4114yes—
138C22×Dic43—22no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—22no—
142C22×Dic43—22no—
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×Dic43C22×C412yes—
160C22×Dic43C22×C412yes—
161C22×Dic43C22×C412yes—
162C22×Dic43C2×D412yes—
163C22×Dic43C2×D412yes—
164C22×Dic43C2×D412yes—
165C22×Dic43C2×D412yes—
166C22×Dic43#4114yes—
167C2×C4×D43—216no—
168C2×C4×D43—216no—
169C2×C4×D43—28no—
170C2×C4×D43—28no—
171C2×C4×D43—28no—
172C4⋊C4×C43—28no—
173C42×C43—44no—
174(C2×D43)⋊C4—28no—
175(C2×D43)⋊C4—28no—
176(C2×D43)⋊C4—48no—
177(C2×D43)⋊C4—48no—
178C4⋊Dic43—28no—
179Dic43⋊C4—216no—
180C4×Dic43—28no—
181C4×Dic43—44no—
182C4×Dic43C22⋊C4116yescomplemented
183C23×C43C23×C411yescharacteristic
184C23×C43C22×D411yescharacteristic
185C23×C43C22×D411yescharacteristic
186C23×C43C2×#4112yes—
187C23×C43C2×#4112yes—
188C23×C43C2×#4112yes—
189C23×C43C2×#4112yes—
190C23×C43H(5,𝔽2)12yes—
191C23×C432−1+412yes—
192C22×D43—22no—
193C22×D43—22no—
194C22×D43—24no—
195C22×D43—24no—
196C22×D43—24no—
197C22×D43—24no—
198C22×D43—24no—
199C22×D43—24no—
200C22×D43—24no—
201C22×D43—24no—
202C22×D43—42no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—42no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C22×D43—42no—
212C22×D43#11714yes—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—24no—
216C2×C4×C43—24no—
217C2×C4×C43—24no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—24no—
221C2×C4×C43—22no—
222C2×C4×C43—24no—
223C2×C4×C43—24no—
224C2×C4×C43—24no—
225C2×C4×C43—24no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
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×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43C2×C22⋊C414yes—
241C2×C4×C43#11714yes—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—24no—
245C2×Dic43—24no—
246C2×Dic43—24no—
247C2×Dic43—24no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—24no—
252C2×Dic43—24no—
253C2×Dic43—24no—
254C2×Dic43—24no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—41no—
258C2×Dic43—41no—
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—
271C4×D43—232no—
272#13938—431nomaximal, Sylow
273C22×C43C22×C22⋊C411yescharacteristic
274C22×C43C2×#11711yescharacteristic
275C22×C43C2×#11711yescharacteristic
276C22×C43C4×#4112yes—
277C22×C43#52012yes—
278C22×C43#52512yes—
279C22×C43#52512yes—
280C22×C43#52512yes—
281C22×C43#53211yescharacteristic
282C22×C43#53211yescharacteristic
283C22×C43#53511yescharacteristic
284C22×C43#53611yescharacteristic
285C22×C43#53712yes—
286C22×C43#55112yes—
287C22×C43#55112yes—
288C22×C43#55212yes—
289C22×C43#55212yes—
290C22×C43#55312yes—
291C22×C43#55312yes—
292C22×C43#55612yes—
293C22×C43#55612yes—
294C2×D43—28no—
295C2×D43—24no—
296C2×D43—42no—
297C2×D43—44no—
298C2×D43—44no—
299C2×D43—44no—
300C2×D43—44no—
301C2×D43—44no—
302C2×D43—42no—
303C4×C43—24no—
304C4×C43—24no—
305C4×C43—42no—
306C4×C43—44no—
307C4×C43—82no—
308Dic43—24no—
309Dic43—24no—
310Dic43—44no—
311Dic43—42no—
312Dic43—82no—
313C22×#117—431no—
314C2×#383—431no—
315C2×C4×C4⋊C4—431no—
316#1441—432no—
317#1439—432no—
318#1437—431no—
319#1437—431no—
320#1436—431no—
321#1436D4311yescharacteristic, complemented
322#1434—432no—
323C22⋊#95—432no—
324C2×C43#228011yescharacteristic
325C2×C43#229711yescharacteristic
326C2×C43#231111yescharacteristic
327C2×C43#234312yes—
328C2×C43#234712yes—
329C2×C43#259812yes—
330C2×C43#259912yes—
331C2×C43#260112yes—
332C2×C43#260112yes—
333D43—44no—
334C24×C4—431no—
335C2×#117—438no—
336C2×#117—864no—
337C2×#117—864no—
338C22×C4⋊C4—431no—
339C22×C4⋊C4—432no—
340C22×C4⋊C4C2×D4311yescharacteristic
341C22×C22⋊C4—431no—
342C22×C22⋊C4—431no—
343C22×C22⋊C4—432no—
344C22×C22⋊C4—432no—
345C22×C42—431no—
346C22×C42—431no—
347C22×C42—431no—
348C22×C42C2×D4311yescharacteristic
349#383—864no—
350C4×C4⋊C4—864no—
351C2×#95—432no—
352C2×#95—432no—
353C2×#95—432no—
354C2×#95—432no—
355C2×#95—432no—
356C2×#95—431no—
357C2×#95—432no—
358C2×#95—432no—
359C2×#95C2×D4312yes—
360C2×#95C2×D4311yescharacteristic
361C2×#95C2×D4312yes—
362C43#1393811yescharacteristic, complemented, Sylow
363C25—431no—
364C23×C4—431no—
365C23×C4—431no—
366C23×C4—431no—
367C23×C4—432no—
368C23×C4—434no—
369C23×C4—432no—
370C23×C4—862no—
371C23×C4—862no—
372C23×C4—864no—
373C23×C4—864no—
374C23×C4C22×D4312yes—
375C23×C4C22×D4311yescharacteristic
376C23×C4C22×D4312yes—
377C23×C4C22×D4311yescharacteristic
378C23×C4C22×D4311yescharacteristic
379#117—8632no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—434no—
383C2×C4⋊C4—862no—
384C2×C4⋊C4—862no—
385C2×C4⋊C4—864no—
386C2×C4⋊C4—864no—
387C2×C4⋊C4—864no—
388C2×C4⋊C4C4×D4314yes—
389C2×C22⋊C4—434no—
390C2×C22⋊C4—434no—
391C2×C22⋊C4—862no—
392C2×C22⋊C4—862no—
393C2×C22⋊C4—862no—
394C2×C22⋊C4—862no—
395C2×C22⋊C4—864no—
396C2×C22⋊C4—864no—
397C2×C22⋊C4—864no—
398C2×C22⋊C4—864no—
399C2×C22⋊C4—1722no—
400C2×C22⋊C4—1722no—
401C2×C42—22no—
402C2×C42—42no—
403C2×C42—434no—
404C2×C42—434no—
405C2×C42—434no—
406C2×C42—434no—
407C2×C42—862no—
408C2×C42—862no—
409C2×C42—862no—
410C2×C42—1722no—
411#95—24no—
412#95—22no—
413#95—42no—
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—432no—
423C24—434no—
424C24—861no—
425C24—861no—
426C24—862no—
427C24—862no—
428C24—862no—
429C24—862no—
430C24—862no—
431C24C23×D4311yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
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—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—432no—
455C22×C4—432no—
456C22×C4—432no—
457C22×C4—432no—
458C22×C4—432no—
459C22×C4—432no—
460C22×C4—432no—
461C22×C4—434no—
462C22×C4—868no—
463C22×C4—868no—
464C22×C4—8616no—
465C22×C4—8616no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—868no—
471C22×C4—862no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—862no—
475C22×C4—862no—
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×C4C2×C4×D4312yes—
489C22×C4C2×C4×D4312yes—
490C22×C4C2×C4×D4312yes—
491C22×C4#1062189814yes—
492C22×C4D4×D4312yes—
493C22×C4D4×D4312yes—
494C22×C4#1062190214yes—
495C4⋊C4—28no—
496C4⋊C4—868no—
497C4⋊C4—8616no—
498C22⋊C4—868no—
499C22⋊C4—868no—
500C22⋊C4—1728no—
501C22⋊C4—1728no—
502C42—44no—
503C42—4316no—
504C42—868no—
505C42—1724no—
506C23—434no—
507C23—864no—
508C23—864no—
509C23—864no—
510C23—864no—
511C23—862no—
512C23—862no—
513C23—864no—
514C23—864no—
515C23—864no—
516C23—864no—
517C23—1722no—
518C23—1722no—
519C23—1722no—
520C23—1722no—
521C23—1722no—
522C23—1721no—
523C23—1721no—
524C23—1721no—
525C23—1721no—
526C23—1722no—
527C23C22×C4×D4311yescharacteristic
528C23C2×D4×D4311yescharacteristic
529C23C2×D4×D4311yescharacteristic
530C23#41×D4312yes—
531C23#41×D4312yes—
532C23C2×#1062189812yes—
533C23C2×#1062190212yes—
534C23#1306337012yes—
535C23#1306337212yes—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—434no—
564C2×C4—434no—
565C2×C4—8632no—
566C2×C4—862no—
567C2×C4—862no—
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—862no—
577C2×C4—864no—
578C2×C4—864no—
579C2×C4—1722no—
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—1722no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1722no—
593C2×C4C22⋊C4×D4314yes—
594C2×C4#1306328214yes—
595C22—868no—
596C22—864no—
597C22—1722no—
598C22—1724no—
599C22—1724no—
600C22—1724no—
601C22—1724no—
602C22—1722no—
603C22—1724no—
604C22C2×C22⋊C4×D4311yescharacteristic
605C22#117×D4311yescharacteristic
606C22C2×#1306328211yescharacteristic
607C22C4×#1062190212yes—
608C22#1458337812yes—
609C22#1458340812yes—
610C22#1458340812yes—
611C22#1458341212yes—
612C22#1458344811yescharacteristic
613C22#1458345011yescharacteristic
614C22#1458346411yescharacteristic
615C22#1458347111yescharacteristic
616C22#1458347612yes—
617C22#1458357612yes—
618C22#1458357712yes—
619C22#1458358512yes—
620C22#1458358712yes—
621C22#1458359712yes—
622C22#1458359912yes—
623C22#1458361712yes—
624C22#1458362212yes—
625C4—24no—
626C4—24no—
627C4—44no—
628C4—42no—
629C4—82no—
630C4—864no—
631C4—864no—
632C4—3442no—
633C4—1722no—
634C4—1724no—
635C2—1724no—
636C2#1913697611yescharacteristic
637C2#1913708411yescharacteristic
638C2#1913718211yescharacteristic
639C2#1913745412yes—
640C2#1913748412yes—
641C2#1914016012yes—
642C2#1914017112yes—
643C2#1914019112yes—
644C2#1914019912yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1436D43
hypocenterC43#13938
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#14582766C2semidirect
3. C2×C4×Dic43⋊C4C2semidirect
4. #19132847C2semidirect
8. #19132827C2semidirect
9. #19132821C2semidirect
11. C43×#1436C2semidirect
15. C2×#13063283C4semidirect
182. C4×Dic43C22⋊C4semidirect
321. #1436D43semidirect
362. C43#13938semidirect

Maximal subgroups

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

subgroupindex
C22×#130632832
C2×#145827662
C2×C4×Dic43⋊C42
#191328472
#191328392
#191328332
#191328312
#191328272
#191328212
(C2×D43)⋊#952
C43×#14362
#1393843