Finite Group Databasebeta

← #25018702

Subgroups — #25018702

Order 11008.

1602 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582766C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊Dic43C211yesmaximal, characteristic
3#19132842C212yesmaximal
4#19132838C212yesmaximal
5#19132828C212yesmaximal, complemented
6Dic43⋊#95C211yesmaximal, characteristic, complemented
7#19132822C212yesmaximal, complemented
8#19132820C211yesmaximal, characteristic, complemented
9#19132819C211yesmaximal, characteristic, complemented
10#19132818C211yesmaximal, characteristic
11C2×C4×C22⋊C4×C43C211yesmaximal, characteristic
12C22×Dic43⋊C4C2212yes—
13C22×C22⋊Dic43C2211yescharacteristic
14C22×C22⋊Dic43C2211yescharacteristic
15C22×C22⋊Dic43C2212yes—
16C22×C4×Dic43C2211yescharacteristic
17C22×C4×Dic43C2211yescharacteristic
18#14582766—24no—
19C4×C22⋊Dic43C418yescomplemented
20C2×C43⋊#95C2211yescharacteristic
21C2×C43⋊#95C2212yes—
22C2×C43⋊#95C2211yescharacteristic
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2211yescharacteristic
31C2×C43⋊#95C2211yescharacteristic
32C24×C4×C43C2211yescharacteristic
33C22×C22⋊C4×C43C2212yes—
34C22×C42×C43C2212yes—
35C4×C22⋊C4×C43—24no—
36C2×#95×C43C2211yescharacteristic
37C2×#95×C43C2211yescharacteristic
38C23×Dic43C2312yes—
39C23×Dic43C2312yes—
40C23×Dic43C2311yescharacteristic
41C23×Dic43C2311yescharacteristic
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2311yescharacteristic
44C2×Dic43⋊C4—24no—
45C2×Dic43⋊C4—24no—
46C2×Dic43⋊C4—42no—
47C2×C22⋊Dic43—24no—
48C2×C22⋊Dic43—22no—
49C2×C22⋊Dic43—22no—
50C2×C22⋊Dic43—24no—
51C2×C22⋊Dic43—42no—
52C2×C22⋊Dic43—42no—
53C2×C22⋊Dic43C2×C414yes—
54C2×C22⋊Dic43C2×C414yes—
55C2×C4×Dic43—22no—
56C2×C4×Dic43—22no—
57C2×C4×Dic43—42no—
58C2×C4×Dic43C2×C414yes—
59C2×C4×Dic43C2×C414yes—
60C43⋊#95—24no—
61C43⋊#95—24no—
62C43⋊#95—22no—
63C43⋊#95—24no—
64C43⋊#95—22no—
65C43⋊#95—24no—
66C43⋊#95—24no—
67C43⋊#95—42no—
68C43⋊#95—42no—
69C43⋊#95—42no—
70C43⋊#95C2×C414yes—
71C43⋊#95C2×C414yes—
72C25×C43C2311yescharacteristic
73C23×C4×C43—22no—
74C23×C4×C43—22no—
75C23×C4×C43—24no—
76C23×C4×C43—42no—
77C23×C4×C43C2×C414yes—
78C23×C4×C43C2312yes—
79C23×C4×C43C2312yes—
80C23×C4×C43C2311yescharacteristic
81C23×C4×C43C2311yescharacteristic
82C2×C22⋊C4×C43—24no—
83C2×C22⋊C4×C43—24no—
84C2×C22⋊C4×C43—24no—
85C2×C42×C43—24no—
86C2×C42×C43—24no—
87C2×C42×C43—42no—
88#95×C43—22no—
89#95×C43D414yes—
90C24×C43—21no—
91C24×C43—22no—
92C24×C43—22no—
93C24×C43—21no—
94C24×C43—21no—
95C24×C43—21no—
96C24×C43—22no—
97C24×C43—21no—
98C24×C43—21no—
99C24×C43C22×C412yes—
100C24×C43#4114yes—
101C24×C43C2411yescharacteristic
102C22×C4×C43—28no—
103C22×C4×C43—28no—
104C22×C4×C43—21no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—21no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
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—44no—
122C22×C4×C43—48no—
123C22×C4×C43—48no—
124C22×C4×C43C22×C412yes—
125C22×C4×C43C22×C412yes—
126C22×C4×C43C2×D414yes—
127C22×C4×C43C2×D412yes—
128C22×C4×C43#4114yes—
129C22×C4×C43#4112yes—
130C22×C4×C43#4114yes—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—22no—
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—21no—
153C22×Dic43—21no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43C22×C412yes—
162C22×Dic43C22×C412yes—
163C22×Dic43C22×C412yes—
164C22×Dic43C22×C412yes—
165C22×Dic43#4112yes—
166C22×Dic43#4112yes—
167C22⋊C4×C43—216no—
168C42×C43—48no—
169C22⋊Dic43—28no—
170C22⋊Dic43—28no—
171C22⋊Dic43—48no—
172Dic43⋊C4—48no—
173C4×Dic43—28no—
174C4×Dic43—44no—
175C23×C43—22no—
176C23×C43—22no—
177C23×C43—22no—
178C23×C43—22no—
179C23×C43—22no—
180C23×C43—22no—
181C23×C43—24no—
182C23×C43—24no—
183C23×C43—24no—
184C23×C43—24no—
185C23×C43—24no—
186C23×C43—24no—
187C23×C43—42no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—42no—
197C23×C43#11714yes—
198C23×C43C23×C411yescharacteristic
199C23×C43C22×D411yescharacteristic
200C23×C43C2×#4111yescharacteristic
201C23×C43C2×#4111yescharacteristic
202C23×C43C2×#4112yes—
203C23×C43C2×#4112yes—
204C23×C43C2×#4111yescharacteristic
205C23×C43C2×#4112yes—
206C23×C43H(5,𝔽2)12yes—
207C23×C43H(5,𝔽2)11yescharacteristic
208C23×C432−1+411yescharacteristic
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—24no—
214C2×C4×C43—24no—
215C2×C4×C43—24no—
216C2×C4×C43—24no—
217C2×C4×C43—24no—
218C2×C4×C43—24no—
219C2×C4×C43—24no—
220C2×C4×C43—24no—
221C2×C4×C43—24no—
222C2×C4×C43—24no—
223C2×C4×C43—416no—
224C2×C4×C43—42no—
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#11714yes—
233C2×C4×C43C4×D414yes—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—24no—
237C2×Dic43—24no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—42no—
256C2×Dic43—42no—
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×Dic43#11714yes—
270#13892—431nomaximal, Sylow
271C22×C43—24no—
272C22×C43—24no—
273C22×C43—24no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—44no—
279C22×C43—44no—
280C22×C43—44no—
281C22×C43—44no—
282C22×C43C2×#11711yescharacteristic
283C22×C43C2×#11711yescharacteristic
284C22×C43C2×#11711yescharacteristic
285C22×C43C2×C4×D411yescharacteristic
286C22×C43C4×#4111yescharacteristic
287C22×C43#51811yescharacteristic
288C22×C43#52011yescharacteristic
289C22×C43#52512yes—
290C22×C43#52912yes—
291C22×C43#52912yes—
292C22×C43#52912yes—
293C22×C43#53812yes—
294C22×C43#53912yes—
295C22×C43#54612yes—
296C22×C43#54711yescharacteristic
297C22×C43#55011yescharacteristic
298C22×C43#55112yes—
299C22×C43#55112yes—
300C22×C43#55312yes—
301C22×C43#55312yes—
302C22×C43#55511yescharacteristic
303C22×C43#55611yescharacteristic
304C22×C43#55612yes—
305C4×C43—24no—
306C4×C43—24no—
307C4×C43—44no—
308C4×C43—44no—
309Dic43—24no—
310Dic43—42no—
311Dic43—42no—
312Dic43—42no—
313Dic43—82no—
314Dic43—82no—
315C2×#383—431no—
316C2×C4×C22⋊C4—431no—
317C2×C4×C22⋊C4D4311yescharacteristic
318#1440—432no—
319#1439—432no—
320#1436—432no—
321C4⋊#95—431no—
322#1434—432no—
323#1434—431no—
324#1434—431no—
325C22⋊#95—431no—
326C2×C43—44no—
327C2×C43#228311yescharacteristic
328C2×C43#229011yescharacteristic
329C2×C43#231811yescharacteristic
330C2×C43#234211yescharacteristic
331C2×C43#234711yescharacteristic
332C2×C43#235311yescharacteristic
333C2×C43#235411yescharacteristic
334C2×C43#246612yes—
335C2×C43#246712yes—
336C2×C43#251812yes—
337C2×C43#252312yes—
338C24×C4C2×D4311yescharacteristic
339C22×C4⋊C4—432no—
340C22×C22⋊C4—431no—
341C22×C22⋊C4—431no—
342C22×C22⋊C4—432no—
343C22×C22⋊C4C2×D4312yes—
344C22×C42—431no—
345C22×C42—431no—
346C22×C42C2×D4312yes—
347#383—864no—
348C4×C22⋊C4—24no—
349C4×C22⋊C4—438no—
350C2×#95—431no—
351C2×#95—431no—
352C2×#95—431no—
353C2×#95—432no—
354C2×#95—431no—
355C2×#95—432no—
356C2×#95—432no—
357C2×#95—432no—
358C2×#95—432no—
359C2×#95—432no—
360C2×#95—432no—
361C2×#95—432no—
362C2×#95C2×D4311yescharacteristic
363C2×#95C2×D4311yescharacteristic
364C43#1389211yescharacteristic, complemented, Sylow
365C25C22×D4311yescharacteristic
366C23×C4—22no—
367C23×C4—24no—
368C23×C4—22no—
369C23×C4—42no—
370C23×C4—431no—
371C23×C4—431no—
372C23×C4—431no—
373C23×C4—431no—
374C23×C4—432no—
375C23×C4—432no—
376C23×C4C4×D4314yes—
377C23×C4C22×D4312yes—
378C23×C4C22×D4312yes—
379C23×C4C22×D4311yescharacteristic
380C23×C4C22×D4311yescharacteristic
381C2×C4⋊C4—864no—
382C2×C4⋊C4—864no—
383C2×C4⋊C4—1722no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—434no—
388C2×C22⋊C4—434no—
389C2×C22⋊C4—862no—
390C2×C22⋊C4—862no—
391C2×C22⋊C4—864no—
392C2×C22⋊C4—864no—
393C2×C22⋊C4—1722no—
394C2×C22⋊C4—1722no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—42no—
398C2×C42—434no—
399C2×C42—434no—
400C2×C42—862no—
401C2×C42—862no—
402C2×C42—1722no—
403#95—22no—
404#95—434no—
405#95—434no—
406#95—864no—
407#95—864no—
408#95—862no—
409#95—864no—
410#95—864no—
411#95—864no—
412#95—862no—
413#95—1722no—
414#95—1722no—
415#95—1722no—
416#95C22⋊D4314yes—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—22no—
422C24—21no—
423C24—22no—
424C24—21no—
425C24—21no—
426C24C2×C4×D4312yes—
427C24#1062189814yes—
428C24C23×D4311yescharacteristic
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
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—28no—
447C22×C4—28no—
448C22×C4—44no—
449C22×C4—48no—
450C22×C4—48no—
451C22×C4—432no—
452C22×C4—432no—
453C22×C4—432no—
454C22×C4—432no—
455C22×C4—432no—
456C22×C4—432no—
457C22×C4—862no—
458C22×C4—862no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—862no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—862no—
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×C4C2×C4×D4312yes—
488C22×C4C2×C4×D4312yes—
489C22×C4#1062189814yes—
490C22×C4#1062189812yes—
491C22×C4#1062190014yes—
492C22×C4C2×C22⋊D4314yes—
493C22×C4C2×C22⋊D4312yes—
494C4⋊C4—1728no—
495C22⋊C4—216no—
496C22⋊C4—868no—
497C22⋊C4—868no—
498C22⋊C4—1728no—
499C42—48no—
500C42—868no—
501C42—1724no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—41no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—41no—
520C23—41no—
521C23—42no—
522C23—42no—
523C23—41no—
524C23#1306328214yes—
525C23C22×C4×D4311yescharacteristic
526C23C22×C22⋊D4311yescharacteristic
527C23#41×D4311yescharacteristic
528C23#41×D4311yescharacteristic
529C23C2×#1062190012yes—
530C23C2×#1062189811yescharacteristic
531C23C2×#1062189812yes—
532C23C2×#1062189812yes—
533C23#1306337012yes—
534C23#1306337111yescharacteristic
535C23#1306337211yescharacteristic
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—416no—
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—864no—
561C2×C4—864no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4—1722no—
576C2×C4—1722no—
577C2×C4—1722no—
578C2×C4—1722no—
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—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1722no—
591C2×C4—1722no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1721no—
595C2×C4#1306328114yes—
596C2×C4C4×C22⋊D4314yes—
597C22—24no—
598C22—24no—
599C22—24no—
600C22—42no—
601C22—42no—
602C22—44no—
603C22—44no—
604C22—42no—
605C22—44no—
606C22—42no—
607C22—44no—
608C22#117×D4311yescharacteristic
609C22C2×#1306328111yescharacteristic
610C22C2×#1306328211yescharacteristic
611C22C2×C4×C22⋊D4311yescharacteristic
612C22C4×#1062189811yescharacteristic
613C22#1458337211yescharacteristic
614C22#1458337911yescharacteristic
615C22#1458341012yes—
616C22#1458342912yes—
617C22#1458342912yes—
618C22#1458343312yes—
619C22#1458348212yes—
620C22#1458349112yes—
621C22#1458354312yes—
622C22#1458354811yescharacteristic
623C22#1458356811yescharacteristic
624C22#1458357512yes—
625C22#1458357812yes—
626C22#1458359512yes—
627C22#1458359912yes—
628C22#1458361211yescharacteristic
629C22#1458361711yescharacteristic
630C22#1458361912yes—
631C4—24no—
632C4—24no—
633C4—44no—
634C4—44no—
635C4—864no—
636C4—3442no—
637C4—3442no—
638C4—1722no—
639C4—1722no—
640C4—1722no—
641C2—44no—
642C2#1913698911yescharacteristic
643C2#1913703811yescharacteristic
644C2#1913722211yescharacteristic
645C2#1913744011yescharacteristic
646C2#1913748611yescharacteristic
647C2#1913753811yescharacteristic
648C2#1913754511yescharacteristic
649C2#1913862512yes—
650C2#1913864012yes—
651C2#1913925312yes—
652C2#1913932212yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C4×C22⋊C4×C43C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×C4×C22⋊C4D43
hypocenterC43#13892
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14582766C2semidirect
5. #19132828C2semidirect
6. Dic43⋊#95C2semidirect
7. #19132822C2semidirect
8. #19132820C2semidirect
9. #19132819C2semidirect
19. C4×C22⋊Dic43C4semidirect
364. C43#13892semidirect

Maximal subgroups

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

subgroupindex
C2×#145827662
C2×C4×C22⋊Dic432
#191328422
#191328382
#191328282
Dic43⋊#952
#191328222
#191328202
#191328192
#191328182
C2×C4×C22⋊C4×C432
#1389243