Finite Group Databasebeta

← #25199447

Subgroups — #25199447

Order 11008.

868 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063305C211yesmaximal, characteristic, complemented
2#19137111C211yesmaximal, characteristic
3#19136025C211yesmaximal, characteristic, complemented
4#19135800C211yesmaximal, characteristic, complemented
5#19135782C211yesmaximal, characteristic
6#19135599C211yesmaximal, characteristic
7#19135227C211yesmaximal, characteristic, complemented
8#19135180C211yesmaximal, characteristic, complemented
9#19135168C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic, complemented
11#19134927C211yesmaximal, characteristic, complemented
12#19134852C211yesmaximal, characteristic, complemented
13#19134844C211yesmaximal, characteristic, complemented
14#19134662C211yesmaximal, characteristic, complemented
15C43×#1925C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C2×#13063305C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21C2×(C22⋊D43)⋊C4—21no—
22C2×C42×D43C2211yescharacteristic
23C2×#13063259C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31#14582804C2211yescharacteristic
32#14582798C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582793—21no—
35#14582784—21no—
36#14582775—21no—
37#14582773—21no—
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4×C4⋊Dic43—21no—
42C22⋊C4×Dic43—21no—
43C4×(C2×D43)⋊C4—21no—
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×C22⋊D43—21no—
61C23×Dic43—21no—
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C2×#10621883—22no—
66C2×#10621883—22no—
67C2×#10621883—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063305—22no—
71#13063305—22no—
72#13063296—22no—
73#13063296—22no—
74C4×Dic86—41no—
75C4×Dic86—41no—
76D4×Dic43—41no—
77D4×Dic43—41no—
78(C22⋊D43)⋊C4—44no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43D411yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96C42×D43—41no—
97C42×D43—41no—
98#13063259—41no—
99#13063256—22no—
100#13063250—22no—
101#13063250—41no—
102#13063248—22no—
103#13063246—41no—
104(C2×D43)⋊C8—41no—
105(C2×D43)⋊C8—41no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C22×D4×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C42×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#107×C43—22no—
124#102×C43—22no—
125#102×C43—22no—
126#95×C43—21no—
127C24×C43—21no—
128C23×D43C2×D411yescharacteristic
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43#4112yes—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C2×C22⋊D43—24no—
142C2×C22⋊D43—42no—
143C2×C22⋊D43—42no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—42no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C2×C4×D43—22no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—22no—
162C2×C4×D43—22no—
163C2×C4×D43—41no—
164C2×C4×D43—41no—
165C2×C4×D43—41no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86#4112yes—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43#4112yes—
184C22⋊C4×C43—42no—
185C22⋊C4×C43—42no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—42no—
189C22⋊Dic43—24no—
190C22⋊Dic43—42no—
191#10621883—44no—
192(C2×D43)⋊C4—24no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—42no—
195C4⋊Dic43—24no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—42no—
202C4⋊Dic43#4112yes—
203Dic43⋊C4—42no—
204Dic43⋊C4—42no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—41no—
208C4×Dic43—41no—
209C4×Dic43—42no—
210C4×Dic43—42no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C23×C43—22no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43C22×D411yescharacteristic
225C22×D43—21no—
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43#13712yes—
232D4×C43—22no—
233D4×C43—22no—
234D4×C43—41no—
235D4×C43—41no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—22no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43#13512yes—
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C2×C4×C43H(5,𝔽2)11yescharacteristic
257C22⋊D43—48no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—84no—
279C2×Dic43AGL(1,ℤ/8)12yes—
280C4×D43—44no—
281C4×D43—44no—
282C4×D43—41no—
283C4×D43—41no—
284C4×D43—41no—
285C4×D43—41no—
286Dic86—22no—
287Dic86—22no—
288Dic86—41no—
289Dic86—41no—
290C8×C43—41no—
291C8×C43—41no—
292C43⋊C8—41no—
293C43⋊C8—41no—
294#29414—431nomaximal, Sylow
295C22×C43—42no—
296C22×C43—42no—
297C22×C43—42no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43#52511yescharacteristic
303C22×C43#52511yescharacteristic
304C22×C43#53411yescharacteristic
305C22×C43C2×#13511yescharacteristic
306C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C43C2×#13711yescharacteristic
308C22×C43#57511yescharacteristic
309C2×D43—22no—
310C2×D43—22no—
311C2×D43—22no—
312C2×D43—41no—
313C2×D43—41no—
314C2×D43—41no—
315C2×D43—41no—
316C4×C43—22no—
317C4×C43—42no—
318C4×C43—41no—
319C4×C43—81no—
320C4×C43—81no—
321C4×C43#55111yescharacteristic
322C4×C43#55311yescharacteristic
323C4×C43#55311yescharacteristic
324C4×C43#55911yescharacteristic
325Dic43—22no—
326Dic43—42no—
327Dic43—42no—
328Dic43—41no—
329Dic43—41no—
330Dic43—81no—
331Dic43—81no—
332C4×C22⋊Q8—431no—
333C4×#121—431no—
334#2076—431no—
335#2036—431no—
336#2034—431no—
337#2000—431no—
338#1927—431no—
339#1925D4311yescharacteristic, complemented
340#1920—431no—
341#1918—431no—
342#1880—431no—
343#1877—431no—
344#1863—431no—
345#1862—431no—
346#1817—431no—
347C2×C43—82no—
348C2×C43#260011yescharacteristic
349C2×C43#310211yescharacteristic
350C2×C43#310611yescharacteristic
351C2×C43#311011yescharacteristic
352C2×C43#311711yescharacteristic
353C2×C43#319011yescharacteristic
354C2×C43#319411yescharacteristic
355D43—42no—
356C22×SD16—431no—
357C2×C22⋊Q8—431no—
358C2×#121—431no—
359C2×C4×Q8—431no—
360C2×C4×D4—431no—
361C2×C4×D4—861no—
362C22×C42—431no—
363C2×#107—431no—
364C2×#107C2×D4311yescharacteristic
365C2×#106—431no—
366C2×#103—431no—
367C2×#103—431no—
368C2×#103—431no—
369C2×#102—431no—
370C2×#102C2×D4311yescharacteristic
371C2×#102C2×D4311yescharacteristic
372C2×C22⋊C8—431no—
373C2×C22⋊C8—431no—
374#391—431no—
375#390C2×D4311yescharacteristic
376#389—431no—
377#389—431no—
378#388—861no—
379#387—861no—
380#386—861no—
381#385—861no—
382#380—431no—
383#380—431no—
384C4×C4⋊C4—431no—
385C4×C4⋊C4—861no—
386C4×C4⋊C4C2×D4311yescharacteristic
387C4×C22⋊C4—861no—
388C4×C22⋊C4—861no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340C2×D4311yescharacteristic
395#336—431no—
396#336—431no—
397#336—431no—
398#336C2×D4311yescharacteristic
399C43#2941411yescharacteristic, complemented, Sylow
400C22×Q8—431no—
401C22×D4—861no—
402C22×D4C22×D4311yescharacteristic
403C23×C4—431no—
404C23×C4—431no—
405C23×C4—431no—
406C23×C4—861no—
407C2×SD16—862no—
408C2×SD16—862no—
409C2×SD16—1721no—
410C22×C8—431no—
411C22×C8—431no—
412C22×C8C22×D4311yescharacteristic
413C22×C8C22×D4311yescharacteristic
414C22⋊Q8—862no—
415C22⋊Q8—862no—
416#121—862no—
417#121—862no—
418C4×Q8—1721no—
419C4×Q8—1721no—
420C4×D4—1721no—
421C4×D4—1721no—
422C4×D4—1724no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C42—21no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—861no—
445C2×C42—861no—
446C2×C42—1721no—
447C2×C42—1721no—
448C2×C42C22×D4311yescharacteristic
449#107—22no—
450#107—1721no—
451#106—862no—
452#103—862no—
453#103—862no—
454#103—1721no—
455#102—22no—
456#102—22no—
457#102—1721no—
458C22⋊C8—1721no—
459C22⋊C8—1721no—
460#95—21no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468C24—21no—
469C24—431no—
470C2×Q8—432no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—864no—
482C2×D4—1722no—
483C2×D4—1722no—
484C2×D4#1062189812yes—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—862no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—1721no—
505C22×C4—1721no—
506C22×C4—1721no—
507C22×C4—1722no—
508C22×C4—1722no—
509C22×C4—1722no—
510C22×C4D4×D4311yescharacteristic
511C22×C4D4×D4311yescharacteristic
512C22×C4C23×D4311yescharacteristic
513SD16—1724no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—432no—
532C4⋊C4—864no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—1722no—
539C4⋊C4—1722no—
540C4⋊C4—1722no—
541C4⋊C4#1062190012yes—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—864no—
545C22⋊C4—864no—
546C22⋊C4—1722no—
547C22⋊C4—1722no—
548C22⋊C4—1722no—
549C42—21no—
550C42—21no—
551C42—42no—
552C42—861no—
553C42—861no—
554C42—1721no—
555C42—1721no—
556C42—1722no—
557C42—1722no—
558C23—22no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—432no—
566C23—861no—
567C23—861no—
568C23—861no—
569C23—861no—
570C23—861no—
571C23—861no—
572C23C2×D4×D4311yescharacteristic
573Q8—862no—
574Q8—862no—
575Q8—1721no—
576Q8—1721no—
577D4—22no—
578D4—22no—
579D4—41no—
580D4—41no—
581D4—1728no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—432no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—3444no—
608C2×C4—1724no—
609C2×C4—1724no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4#1306334412yes—
625C2×C4#41×D4311yescharacteristic
626C2×C4#41×D4311yescharacteristic
627C2×C4C2×#1062190011yescharacteristic
628C2×C4C2×#1062189811yescharacteristic
629C2×C4#1306337111yescharacteristic
630C2×C4#1306337111yescharacteristic
631C8—41no—
632C8—41no—
633C8—1721no—
634C8—1721no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—862no—
643C22—862no—
644C22—862no—
645C22—1721no—
646C22—1721no—
647C22—1721no—
648C22—1721no—
649C22#1458340811yescharacteristic
650C22#1458340911yescharacteristic
651C22#1458346011yescharacteristic
652C22C2×#1306334411yescharacteristic
653C22AGL(1,ℤ/8)×D4311yescharacteristic
654C22#137×D4311yescharacteristic
655C22#1458369611yescharacteristic
656C4—22no—
657C4—41no—
658C4—42no—
659C4—81no—
660C4—81no—
661C4—862no—
662C4—3441no—
663C4—3441no—
664C4—1721no—
665C4—1722no—
666C4—1721no—
667C4—1722no—
668C4#1458357311yescharacteristic
669C4#1458359511yescharacteristic
670C4#1458360011yescharacteristic
671C4#1458363111yescharacteristic
672C2—82no—
673C2—1722no—
674C2#1914018011yescharacteristic
675C2#1914460911yescharacteristic
676C2#1914465211yescharacteristic
677C2#1914469211yescharacteristic
678C2#1914476511yescharacteristic
679C2#1914537511yescharacteristic
680C2#1914541311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1925C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenter#1925D43
hypocenterC43#29414
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
1. C4×#13063305C2semidirect
3. #19136025C2semidirect
4. #19135800C2semidirect
7. #19135227C2semidirect
8. #19135180C2semidirect
9. #19135168C2semidirect
10. #19134953C2semidirect
11. #19134927C2semidirect
12. #19134852C2semidirect
13. #19134844C2semidirect
14. #19134662C2semidirect
15. C43×#1925C2semidirect
339. #1925D43semidirect
399. C43#29414semidirect

Maximal subgroups

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

subgroupindex
C4×#130633052
#191371112
#191360252
#191358002
#191357822
#191355992
#191352272
#191351802
#191351682
#191349532
#191349272
#191348522
#191348442
#191346622
C43×#19252
#2941443