Finite Group Databasebeta

← #25129339

Subgroups — #25129339

Order 11008.

1468 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583215C211yesmaximal, characteristic, complemented
2C2×#14583210C211yesmaximal, characteristic, complemented
3#19137187C211yesmaximal, characteristic, complemented
4#19135781C212yesmaximal, complemented
5#19135774C212yesmaximal, complemented
6#19134918C211yesmaximal, characteristic, complemented
7#19134918C211yesmaximal, characteristic, complemented
8#19134794C212yesmaximal, complemented
9#19134526C212yesmaximal, complemented
10#19134507C211yesmaximal, characteristic, complemented
11C2×C43×#535C211yesmaximal, characteristic
12C2×#13063284C2211yescharacteristic, complemented
13C22×C4⋊Dic43C2211yescharacteristic, complemented
14#14583215—24no—
15#14583210—24no—
16C2×#13063258C2212yescomplemented
17C2×#13063256C2212yescomplemented
18C2×#13063246C2212yes—
19C2×#13063246C2212yes—
20C2×#13063246C2212yes—
21C2×#13063246C2212yes—
22C2×C22⋊(C43⋊C8)C2212yes—
23C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
24C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
25C2×C22⋊(C43⋊C8)C2212yescomplemented
26#14582806—21no—
27#14582802—21no—
28#14582779—21no—
29#14582779—21no—
30#14582759C2212yes—
31#14582759C2212yescomplemented
32#14582661C2212yescomplemented
33#14582661C2212yescomplemented
34C22×#41×C43C2211yescharacteristic
35C23×D4×C43C2211yescharacteristic
36C43×#535—24no—
37C43×#535—24no—
38C2×#127×C43—21no—
39C2×#124×C43—21no—
40C2×#121×C43C2211yescharacteristic
41C2×#121×C43C2211yescharacteristic
42C2×#121×C43C2211yescharacteristic
43C2×#121×C43C2211yescharacteristic
44C2×#120×C43—21no—
45C2×#120×C43—21no—
46C2×#117×C43C2211yescharacteristic
47C23×Dic43—21no—
48C22×C43⋊C8C2312yes—
49C22×C43⋊C8C2312yes—
50#13063284—42no—
51C2×C4⋊Dic43—22no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43C2312yes—
55C2×C4⋊Dic43C2312yes—
56C2×C22⋊Dic43—21no—
57C2×C22⋊Dic43—22no—
58C2×C22⋊Dic43—22no—
59C2×C4×Dic43—21no—
60#13063258—24no—
61#13063256—24no—
62#13063246—24no—
63#13063246—24no—
64#13063246—42no—
65#13063246—42no—
66C22⋊(C43⋊C8)—22no—
67C22⋊(C43⋊C8)—22no—
68C22⋊(C43⋊C8)—24no—
69C22⋊(C43⋊C8)—42no—
70C43⋊#95—22no—
71C43⋊#95—22no—
72C25×C43—21no—
73C2×#41×C43—22no—
74C2×#41×C43—22no—
75C2×#41×C43—24no—
76C2×#41×C43—42no—
77C22×Q8×C43D411yescharacteristic
78C22×D4×C43—21no—
79C22×D4×C43—21no—
80C22×D4×C43—21no—
81C22×D4×C43—21no—
82C22×D4×C43—22no—
83C22×D4×C43—22no—
84C22×D4×C43—21no—
85C22×D4×C43—24no—
86C22×D4×C43—42no—
87C22×D4×C43D411yescharacteristic
88C22×D4×C43D411yescharacteristic
89C22×D4×C43D411yescharacteristic
90C22×D4×C43C2311yescharacteristic
91C22×D4×C43C2311yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2311yescharacteristic
94C23×C4×C43C2311yescharacteristic
95#127×C43—28no—
96#124×C43—28no—
97#121×C43—22no—
98#121×C43—22no—
99#121×C43—22no—
100#121×C43—22no—
101#121×C43—22no—
102#121×C43—22no—
103#121×C43D414yes—
104#121×C43D414yes—
105#120×C43—28no—
106#120×C43—28no—
107#117×C43—22no—
108#117×C43—22no—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C42×C43—21no—
117C24×C43—24no—
118C24×C43—21no—
119C24×C43—21no—
120C24×C43—42no—
121C24×C43—42no—
122C24×C43—82no—
123C24×C43—82no—
124C24×C43C2×D411yescharacteristic
125C24×C43C2×D411yescharacteristic
126C24×C43C2×D411yescharacteristic
127#41×C43—48no—
128#41×C43—48no—
129C2×Q8×C43—22no—
130C2×Q8×C43—22no—
131C2×Q8×C43—41no—
132C2×D4×C43—24no—
133C2×D4×C43—24no—
134C2×D4×C43—24no—
135C2×D4×C43—22no—
136C2×D4×C43—22no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—22no—
140C2×D4×C43—22no—
141C2×D4×C43—24no—
142C2×D4×C43—24no—
143C2×D4×C43—22no—
144C2×D4×C43—22no—
145C2×D4×C43—22no—
146C2×D4×C43—22no—
147C2×D4×C43—22no—
148C2×D4×C43—22no—
149C2×D4×C43—41no—
150C2×D4×C43—41no—
151C2×D4×C43—41no—
152C2×D4×C43—48no—
153C2×D4×C43—48no—
154C2×D4×C43—42no—
155C2×D4×C43—42no—
156C2×D4×C43—82no—
157C2×D4×C43—82no—
158C2×D4×C43—82no—
159C2×D4×C43—82no—
160C2×D4×C43C2×D412yes—
161C2×D4×C43C2×D412yes—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43C2×D412yes—
174C22×C4×C43C2×D412yes—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43#4114yes—
179C22×C4×C43C2411yescharacteristic
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—42no—
183C22×Dic43—82no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43C2×D412yes—
187C4⋊C4×C43C2×D412yes—
188C22⋊C4×C43—24no—
189C22⋊C4×C43—24no—
190C22⋊C4×C43—24no—
191C22⋊C4×C43—24no—
192C22⋊C4×C43—24no—
193C42×C43—24no—
194C22⋊Dic43—42no—
195C22⋊Dic43—82no—
196C22⋊Dic43—82no—
197C4⋊Dic43—22no—
198C4⋊Dic43—22no—
199C4⋊Dic43—22no—
200C4⋊Dic43—22no—
201C4⋊Dic43—42no—
202C4×Dic43—42no—
203C2×C43⋊C8—22no—
204C2×C43⋊C8—22no—
205C2×C43⋊C8—22no—
206C2×C43⋊C8—22no—
207C2×C43⋊C8—22no—
208C2×C43⋊C8—22no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—22no—
214C23×C43—22no—
215C23×C43—22no—
216C23×C43—22no—
217C23×C43—22no—
218C23×C43—22no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—22no—
223C23×C43—22no—
224C23×C43—48no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—42no—
230C23×C43—42no—
231C23×C43—42no—
232C23×C43—42no—
233C23×C43—88no—
234C23×C43—84no—
235C23×C43—84no—
236C23×C43—88no—
237C23×C43#12012yes—
238C23×C43#12312yes—
239C23×C43C22×D411yescharacteristic
240Q8×C43—44no—
241D4×C43—24no—
242D4×C43—24no—
243D4×C43—44no—
244D4×C43—44no—
245D4×C43—48no—
246D4×C43—44no—
247D4×C43—42no—
248D4×C43—42no—
249D4×C43—84no—
250D4×C43—84no—
251D4×C43—84no—
252D4×C43—84no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—24no—
258C2×C4×C43—24no—
259C2×C4×C43—24no—
260C2×C4×C43—24no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—42no—
267C2×C4×C43—42no—
268C2×C4×C43—42no—
269C2×C4×C43—42no—
270C2×C4×C43#12012yes—
271C2×C4×C43#12312yes—
272C2×C4×C43C22×D411yescharacteristic
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C2×#4112yes—
275C2×C4×C43H(5,𝔽2)12yes—
276C2×Dic43—42no—
277C2×Dic43—42no—
278C2×Dic43—42no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—42no—
282C2×Dic43—84no—
283C43⋊C8—42no—
284C43⋊C8—42no—
285#24013—431nomaximal, Sylow
286C22×C43—24no—
287C22×C43—22no—
288C22×C43—22no—
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—42no—
297C22×C43—41no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—42no—
301C22×C43—41no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—41no—
305C22×C43—42no—
306C22×C43—42no—
307C22×C43—816no—
308C22×C43—82no—
309C22×C43—82no—
310C22×C43—82no—
311C22×C43—82no—
312C22×C43C2×#12011yescharacteristic
313C22×C43C2×#12311yescharacteristic
314C22×C43#53411yescharacteristic
315C22×C43#57612yes—
316C22×C43#57712yes—
317C4×C43—22no—
318C4×C43—22no—
319C4×C43—41no—
320C4×C43—42no—
321C4×C43—42no—
322C4×C43#54612yes—
323C4×C43#54612yes—
324Dic43—82no—
325Dic43—82no—
326C2×#535D4311yescharacteristic
327C2×#481—431no—
328C2×#480—431no—
329#2311—431no—
330#2034—432no—
331#2033—432no—
332#1875—431no—
333#1875—431no—
334#1854—432no—
335#1786—432no—
336#1780—431no—
337C2×C43—42no—
338C2×C43—42no—
339C2×C43—81no—
340C2×C43—82no—
341C2×C43—82no—
342C2×C43#240511yescharacteristic
343C2×C43#300811yescharacteristic
344C2×C43#300911yescharacteristic
345C2×C43#309612yes—
346C2×C43#319812yes—
347C22×#41C2×D4311yescharacteristic
348C23×D4C2×D4311yescharacteristic
349#535—24no—
350#535—24no—
351C2×#127—21no—
352C2×#124—21no—
353C2×#121C2×D4311yescharacteristic
354C2×#121C2×D4311yescharacteristic
355C2×#121C2×D4311yescharacteristic
356C2×#121C2×D4311yescharacteristic
357C2×#120—21no—
358C2×#120—21no—
359C2×#117—431no—
360C2×#117C2×D4311yescharacteristic
361C22×C4⋊C4—431no—
362#481—864no—
363#480—864no—
364C2×#107—432no—
365C2×#106—432no—
366C2×#102—432no—
367C2×#102—432no—
368C2×#102—432no—
369C2×#102—432no—
370C2×C22⋊C8—431no—
371C2×C22⋊C8—431no—
372C2×C22⋊C8—432no—
373C2×C22⋊C8—432no—
374#391—861no—
375#390—861no—
376#386—861no—
377#386—861no—
378#380—432no—
379#380—432no—
380#340—432no—
381#340—432no—
382C43#2401311yescharacteristic, complemented, Sylow
383C25—21no—
384C2×#41—24no—
385C2×#41—22no—
386C2×#41—22no—
387C2×#41—42no—
388C22×Q8C22⋊D4311yescharacteristic
389C22×D4—21no—
390C22×D4—21no—
391C22×D4—21no—
392C22×D4—21no—
393C22×D4—22no—
394C22×D4—22no—
395C22×D4—24no—
396C22×D4—21no—
397C22×D4—42no—
398C22×D4C22⋊D4311yescharacteristic
399C22×D4C22⋊D4311yescharacteristic
400C22×D4C22⋊D4311yescharacteristic
401C22×D4C22×D4311yescharacteristic
402C22×D4C22×D4311yescharacteristic
403C23×C4—861no—
404C23×C4C22×D4311yescharacteristic
405C23×C4C22×D4311yescharacteristic
406C23×C4C22×D4311yescharacteristic
407C22×C8—432no—
408C22×C8—432no—
409#127—28no—
410#124—28no—
411#121—22no—
412#121—22no—
413#121—22no—
414#121—22no—
415#121—22no—
416#121—22no—
417#121C22⋊D4314yes—
418#121C22⋊D4314yes—
419#120—28no—
420#120—28no—
421#117—22no—
422#117—22no—
423#117—1722no—
424C2×C4⋊C4—432no—
425C2×C4⋊C4—432no—
426C2×C4⋊C4—862no—
427C2×C4⋊C4—862no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—862no—
437C2×C22⋊C4—862no—
438C2×C22⋊C4—861no—
439C2×C42—21no—
440C2×C42—861no—
441#107—864no—
442#106—864no—
443#102—864no—
444#102—864no—
445#102—1722no—
446#102—1722no—
447C22⋊C8—864no—
448C22⋊C8—862no—
449C22⋊C8—862no—
450C22⋊C8—1722no—
451#95—862no—
452#95—862no—
453C24—24no—
454C24—21no—
455C24—21no—
456C24—42no—
457C24—42no—
458C24—82no—
459C24—82no—
460C24C2×C22⋊D4311yescharacteristic
461C24C2×C22⋊D4311yescharacteristic
462C24C2×C22⋊D4311yescharacteristic
463#41—48no—
464#41—48no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—41no—
468C2×D4—24no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—24no—
474C2×D4—24no—
475C2×D4—24no—
476C2×D4—24no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—82no—
493C2×D4—82no—
494C2×D4—82no—
495C2×D4—82no—
496C2×D4C2×C22⋊D4312yes—
497C2×D4C2×C22⋊D4312yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—862no—
510C22×C4—862no—
511C22×C4—3442no—
512C22×C4—1722no—
513C22×C4#1062190014yes—
514C22×C4C2×C22⋊D4311yescharacteristic
515C22×C4C2×C22⋊D4311yescharacteristic
516C22×C4C2×C22⋊D4312yes—
517C22×C4C2×C22⋊D4312yes—
518C22×C4C2×C22⋊D4311yescharacteristic
519C22×C4C23×D4311yescharacteristic
520C2×C8—862no—
521C2×C8—862no—
522C2×C8—862no—
523C2×C8—862no—
524C2×C8—862no—
525C2×C8—862no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—862no—
529C4⋊C4—862no—
530C4⋊C4—862no—
531C4⋊C4—862no—
532C4⋊C4—1722no—
533C4⋊C4C2×C22⋊D4312yes—
534C4⋊C4C2×C22⋊D4312yes—
535C22⋊C4—24no—
536C22⋊C4—24no—
537C22⋊C4—24no—
538C22⋊C4—24no—
539C22⋊C4—24no—
540C22⋊C4—3442no—
541C22⋊C4—3442no—
542C22⋊C4—1722no—
543C42—24no—
544C42—1722no—
545C23—21no—
546C23—21no—
547C23—22no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—21no—
552C23—21no—
553C23—22no—
554C23—22no—
555C23—21no—
556C23—21no—
557C23—22no—
558C23—22no—
559C23—21no—
560C23—48no—
561C23—41no—
562C23—41no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—41no—
568C23—41no—
569C23—88no—
570C23—84no—
571C23—84no—
572C23—88no—
573C23#1306329412yes—
574C23#1306330612yes—
575C23C22×C22⋊D4311yescharacteristic
576Q8—44no—
577D4—24no—
578D4—24no—
579D4—44no—
580D4—44no—
581D4—48no—
582D4—44no—
583D4—42no—
584D4—42no—
585D4—84no—
586D4—84no—
587D4—84no—
588D4—84no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—3444no—
607C2×C4—1722no—
608C2×C4—1722no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4—1722no—
612C2×C4—1722no—
613C2×C4#1306329412yes—
614C2×C4#1306330612yes—
615C2×C4C22×C22⋊D4311yescharacteristic
616C2×C4C22×C22⋊D4311yescharacteristic
617C2×C4C2×#1062190012yes—
618C2×C4#1306337012yes—
619C8—1722no—
620C8—1722no—
621C22—24no—
622C22—22no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—42no—
627C22—41no—
628C22—41no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—41no—
633C22—42no—
634C22—42no—
635C22—41no—
636C22—42no—
637C22—42no—
638C22—41no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—816no—
643C22—82no—
644C22—82no—
645C22—82no—
646C22—82no—
647C22C2×#1306329411yescharacteristic
648C22C2×#1306330611yescharacteristic
649C22#1458345811yescharacteristic
650C22#1458370212yes—
651C22#1458371012yes—
652C4—22no—
653C4—22no—
654C4—41no—
655C4—42no—
656C4—42no—
657C4—3442no—
658C4—3442no—
659C4#1458354312yes—
660C4#1458354312yes—
661C2—42no—
662C2—42no—
663C2—81no—
664C2—82no—
665C2—82no—
666C2#1913791811yescharacteristic
667C2#1914386311yescharacteristic
668C2#1914387211yescharacteristic
669C2#1914454712yes—
670C2#1914544712yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#535C2
socleC23×C43C22×D4
hypercenterC2×#535D43
hypocenterC43#24013
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#14583215C2semidirect
2. C2×#14583210C2semidirect
3. #19137187C2semidirect
4. #19135781C2semidirect
5. #19135774C2semidirect
6. #19134918C2semidirect
7. #19134918C2semidirect
8. #19134794C2semidirect
9. #19134526C2semidirect
10. #19134507C2semidirect
12. C2×#13063284C22semidirect
13. C22×C4⋊Dic43C22semidirect
16. C2×#13063258C22semidirect
17. C2×#13063256C22semidirect
23. C2×C22⋊(C43⋊C8)C22semidirect
24. C2×C22⋊(C43⋊C8)C22semidirect
25. C2×C22⋊(C43⋊C8)C22semidirect
31. #14582759C22semidirect
32. #14582661C22semidirect
33. #14582661C22semidirect
382. C43#24013semidirect

Maximal subgroups

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

subgroupindex
C2×#145832152
C2×#145832102
#191371872
#191357812
#191357742
#191349182
#191347942
#191345262
#191345072
C2×C43×#5352
#2401343