Finite Group Databasebeta

← #25169729

Subgroups — #25169729

Order 11008.

902 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139179C211yesmaximal, characteristic, complemented
2#19137660C211yesmaximal, characteristic, complemented
3#19136121C211yesmaximal, characteristic, complemented
4#19135903C211yesmaximal, characteristic, complemented
5#19135826C211yesmaximal, characteristic, complemented
6#19135462C211yesmaximal, characteristic, complemented
7#19135218C211yesmaximal, characteristic, complemented
8#19135212C211yesmaximal, characteristic, complemented
9#19135167C211yesmaximal, characteristic, complemented
10#19135151C211yesmaximal, characteristic, complemented
11#19134945C211yesmaximal, characteristic, complemented
12#19134945C211yesmaximal, characteristic, complemented
13#19134593C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#2011C211yesmaximal, characteristic
16C2×#13063318—21no—
17C2×D4×Dic43—21no—
18C2×D4×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582827—21no—
31#14582822—21no—
32#14582802—21no—
33#14582802C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582793—21no—
39#14582779—21no—
40#14582779—21no—
41#14582768C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×D8×C43C2211yescharacteristic
53C22×D8×C43C2211yescharacteristic
54C2×#127×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C23×Dic43—21no—
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063318—44no—
64D4×Dic43—22no—
65D4×Dic43—22no—
66D4×Dic43—41no—
67D4×Dic43—41no—
68D4×Dic43—44no—
69C2×C4⋊Dic43D411yescharacteristic
70C2×C4⋊Dic43D411yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43C2311yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92#13063259—22no—
93#13063258—41no—
94Dic43⋊C8—41no—
95#13063246—22no—
96#13063246—22no—
97#13063246—22no—
98#13063246—41no—
99#13063246—41no—
100#13063246—41no—
101C8×Dic43—41no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C22×D4×C43—21no—
108C22×D4×C43—21no—
109C22×D4×C43C2311yescharacteristic
110C22×D4×C43C2311yescharacteristic
111C22×D4×C43C2311yescharacteristic
112C2×D8×C43—22no—
113C2×D8×C43—22no—
114C2×D8×C43—22no—
115C2×D8×C43—41no—
116C2×D8×C43—41no—
117C2×D8×C43—41no—
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120#127×C43—22no—
121#127×C43—22no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C42×C43C2311yescharacteristic
126#102×C43—22no—
127#102×C43—41no—
128C24×C43—21no—
129C24×C43—21no—
130C24×C43—21no—
131C2×D4×C43—24no—
132C2×D4×C43—24no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—42no—
150C2×D4×C43—42no—
151C2×D4×C43—81no—
152C2×D4×C43—81no—
153C2×D4×C43#4112yes—
154C2×D4×C43#4112yes—
155C22×C4×C43—21no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—42no—
164C22×Dic43—42no—
165C22×Dic43—42no—
166C22×Dic43—42no—
167C22×Dic43—81no—
168C22×Dic43—81no—
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173D8×C43—44no—
174D8×C43—44no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43#4112yes—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C22⋊C4×C43—42no—
184C22⋊C4×C43—81no—
185C42×C43—21no—
186C42×C43—21no—
187C22⋊Dic43—42no—
188C22⋊Dic43—42no—
189C22⋊Dic43—42no—
190C22⋊Dic43—42no—
191C22⋊Dic43—42no—
192C22⋊Dic43—42no—
193C22⋊Dic43—42no—
194C22⋊Dic43—81no—
195C22⋊Dic43—81no—
196C22⋊Dic43—81no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—41no—
205C4⋊Dic43D814yescomplemented
206C4⋊Dic43#4112yes—
207Dic43⋊C4—42no—
208Dic43⋊C4—42no—
209Dic43⋊C4—81no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—42no—
215C4×Dic43—42no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C23×C43—22no—
223C23×C43—22no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43C22×D411yescharacteristic
244D4×C43—22no—
245D4×C43—22no—
246D4×C43—22no—
247D4×C43—22no—
248D4×C43—48no—
249D4×C43—41no—
250D4×C43—41no—
251D4×C43—41no—
252D4×C43—41no—
253D4×C43—41no—
254D4×C43—41no—
255D4×C43—41no—
256D4×C43—41no—
257D4×C43—84no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43C2×D812yes—
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C43H(5,𝔽2)11yescharacteristic
272C2×C4×C43H(5,𝔽2)11yescharacteristic
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—22no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—84no—
296C2×Dic43—84no—
297C2×Dic43C2×D812yes—
298C2×Dic43C2×D812yes—
299C8×C43—22no—
300C8×C43—41no—
301C43⋊C8—41no—
302C43⋊C8—41no—
303#27062—431nomaximal, Sylow
304C22×C43—42no—
305C22×C43—42no—
306C22×C43—42no—
307C22×C43—42no—
308C22×C43—42no—
309C22×C43—42no—
310C22×C43—81no—
311C22×C43—81no—
312C22×C43—81no—
313C22×C43—81no—
314C22×C43—81no—
315C22×C43—81no—
316C22×C43—81no—
317C22×C43—81no—
318C22×C43—81no—
319C22×C43—81no—
320C22×C43—81no—
321C22×C43—81no—
322C22×C43—81no—
323C22×C43—81no—
324C22×C43—81no—
325C22×C43#52511yescharacteristic
326C22×C43#54611yescharacteristic
327C22×C43#55011yescharacteristic
328C22×C43C22×D811yescharacteristic
329C22×C43#57511yescharacteristic
330C22×C43#57611yescharacteristic
331C22×C43#57711yescharacteristic
332C4×C43—22no—
333C4×C43—41no—
334C4×C43—81no—
335C4×C43#52911yescharacteristic
336C4×C43#53811yescharacteristic
337C4×C43#55111yescharacteristic
338C4×C43#55311yescharacteristic
339Dic43—22no—
340Dic43—22no—
341Dic43—42no—
342Dic43—41no—
343Dic43—41no—
344Dic43—81no—
345Dic43—81no—
346Dic43—81no—
347#2512—431no—
348#2366—431no—
349#2093—431no—
350#2054—431no—
351#2041—431no—
352#2011D4311yescharacteristic
353#1970—431no—
354#1925—431no—
355#1925—431no—
356#1918—431no—
357#1916—431no—
358#1879—431no—
359#1879—431no—
360#1802—431no—
361C4×#102—431no—
362C2×C43—82no—
363C2×C43—82no—
364C2×C43—161no—
365C2×C43#246711yescharacteristic
366C2×C43#310011yescharacteristic
367C2×C43#311811yescharacteristic
368C2×C43#329411yescharacteristic
369C2×C43#330911yescharacteristic
370C2×C43#339111yescharacteristic
371C2×C43#340111yescharacteristic
372C22×D8C2×D4311yescharacteristic
373C22×D8C2×D4311yescharacteristic
374C2×#127C2×D4311yescharacteristic
375C2×#126—861no—
376C2×C4×D4—431no—
377C2×C4×D4—431no—
378C2×C4×D4—861no—
379C2×#107—431no—
380C2×#107—431no—
381C2×C4⋊C8—431no—
382C2×#102—431no—
383C2×#102—431no—
384C2×#102—431no—
385C2×#102—431no—
386C2×#102—431no—
387C2×#102—431no—
388C2×#102C2×D4311yescharacteristic
389C2×#102C2×D4311yescharacteristic
390C2×C4×C8—431no—
391#397—861no—
392#396—861no—
393#390—431no—
394#390—431no—
395#390—431no—
396#390—431no—
397#390—861no—
398#390C2×D4311yescharacteristic
399#389—431no—
400#388—861no—
401#386—861no—
402#386—861no—
403#384—431no—
404C4×C4⋊C4—431no—
405C4×C4⋊C4—431no—
406C4×C4⋊C4—431no—
407#340—431no—
408#340—431no—
409#340—431no—
410#340—431no—
411#336—431no—
412#336—431no—
413#336—431no—
414#336C2×D4311yescharacteristic
415C43#2706211yescharacteristic, complemented, Sylow
416C22×D4—21no—
417C22×D4—21no—
418C22×D4C22×D4311yescharacteristic
419C22×D4C22×D4311yescharacteristic
420C22×D4C22×D4311yescharacteristic
421C23×C4—861no—
422C23×C4—861no—
423C2×D8—22no—
424C2×D8—22no—
425C2×D8—22no—
426C2×D8—41no—
427C2×D8—41no—
428C2×D8—41no—
429C22×C8—431no—
430C22×C8—431no—
431C22×C8C22×D4311yescharacteristic
432C22×C8C22×D4311yescharacteristic
433#127—22no—
434#127—22no—
435#126—1724no—
436C4×D4—862no—
437C4×D4—862no—
438C4×D4—1721no—
439C4×D4—1721no—
440C4×D4—1724no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—431no—
445C2×C4⋊C4—431no—
446C2×C4⋊C4—431no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4C22×D4311yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C22⋊C4—861no—
460C2×C22⋊C4—861no—
461C2×C22⋊C4—861no—
462C2×C22⋊C4—861no—
463C2×C42—431no—
464C2×C42—431no—
465C2×C42—861no—
466C2×C42—861no—
467C2×C42C22×D4311yescharacteristic
468#107—862no—
469#107—1721no—
470C4⋊C8—1721no—
471#102—22no—
472#102—41no—
473#102—862no—
474#102—862no—
475#102—862no—
476#102—1721no—
477#102—1721no—
478#102—1721no—
479C4×C8—1721no—
480#95—431no—
481#95—431no—
482#95—861no—
483#95—861no—
484#95—861no—
485C24—21no—
486C24—21no—
487C24—21no—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—81no—
509C2×D4—81no—
510C2×D4#1062190012yes—
511C2×D4#1062190012yes—
512C22×C4—21no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—3441no—
522C22×C4—3441no—
523C22×C4—1722no—
524C22×C4—1722no—
525C22×C4—1722no—
526C22×C4—1722no—
527C22×C4D4×D4311yescharacteristic
528C22×C4D4×D4311yescharacteristic
529C22×C4C23×D4311yescharacteristic
530D8—44no—
531D8—44no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—861no—
538C2×C8—861no—
539C2×C8—861no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8#1062190012yes—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—434no—
547C4⋊C4—432no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—3441no—
556C4⋊C4—1721no—
557C4⋊C4—1722no—
558C4⋊C4—1722no—
559C22⋊C4—42no—
560C22⋊C4—81no—
561C22⋊C4—3441no—
562C22⋊C4—3441no—
563C22⋊C4—3441no—
564C22⋊C4—1722no—
565C22⋊C4—1722no—
566C22⋊C4—1722no—
567C22⋊C4—1722no—
568C22⋊C4—1722no—
569C22⋊C4—1722no—
570C22⋊C4—1722no—
571C42—21no—
572C42—21no—
573C42—861no—
574C42—861no—
575C42—861no—
576C42—861no—
577C42—1722no—
578C42—1722no—
579C23—22no—
580C23—22no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C2×D4×D4311yescharacteristic
601D4—22no—
602D4—22no—
603D4—22no—
604D4—22no—
605D4—48no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—84no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—432no—
624C2×C4—432no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—861no—
631C2×C4—861no—
632C2×C4—861no—
633C2×C4—861no—
634C2×C4—861no—
635C2×C4—862no—
636C2×C4—3444no—
637C2×C4—3444no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4—1721no—
647C2×C4—1721no—
648C2×C4—1721no—
649C2×C4D8×D4312yes—
650C2×C4#41×D4311yescharacteristic
651C2×C4C2×#1062190011yescharacteristic
652C2×C4C2×#1062190011yescharacteristic
653C2×C4C2×#1062190011yescharacteristic
654C2×C4#1306337011yescharacteristic
655C2×C4#1306337011yescharacteristic
656C8—22no—
657C8—41no—
658C8—1721no—
659C8—1721no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22#1458340511yescharacteristic
682C22#1458354611yescharacteristic
683C22#1458356911yescharacteristic
684C22C2×D8×D4311yescharacteristic
685C22#1458369511yescharacteristic
686C22#1458370011yescharacteristic
687C22#1458370911yescharacteristic
688C4—22no—
689C4—41no—
690C4—81no—
691C4—862no—
692C4—862no—
693C4—3441no—
694C4—3441no—
695C4—3441no—
696C4—1721no—
697C4—1721no—
698C4—1722no—
699C4#1458343011yescharacteristic
700C4#1458348411yescharacteristic
701C4#1458358011yescharacteristic
702C4#1458359211yescharacteristic
703C2—82no—
704C2—82no—
705C2—161no—
706C2#1913864111yescharacteristic
707C2#1914459011yescharacteristic
708C2#1914477211yescharacteristic
709C2#1914641111yescharacteristic
710C2#1914660811yescharacteristic
711C2#1914756811yescharacteristic
712C2#1914765611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#2011C2
socleC23×C43C22×D4
hypercenter#2011D43
hypocenterC43#27062
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2011

Complements

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

NH ≅ G/Ntype
1. #19139179C2semidirect
2. #19137660C2semidirect
3. #19136121C2semidirect
4. #19135903C2semidirect
5. #19135826C2semidirect
6. #19135462C2semidirect
7. #19135218C2semidirect
8. #19135212C2semidirect
9. #19135167C2semidirect
10. #19135151C2semidirect
11. #19134945C2semidirect
12. #19134945C2semidirect
13. #19134593C2semidirect
14. #102×Dic43C2semidirect
205. C4⋊Dic43D8semidirect
415. C43#27062semidirect

Maximal subgroups

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

subgroupindex
#191391792
#191376602
#191361212
#191359032
#191358262
#191354622
#191352182
#191352122
#191351672
#191351512
#191349452
#191345932
#102×Dic432
C43×#20112
#2706243