Finite Group Databasebeta

← #25113885

Subgroups — #25113885

Order 11008.

1038 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582899C211yesmaximal, characteristic
2#19137463C211yesmaximal, characteristic, complemented
3#19137424C211yesmaximal, characteristic
4#19135287C211yesmaximal, characteristic, complemented
5#19135239C211yesmaximal, characteristic, complemented
6#19135226C211yesmaximal, characteristic, complemented
7#19134857C211yesmaximal, characteristic, complemented
8#19134841C211yesmaximal, characteristic, complemented
9#19134684C211yesmaximal, characteristic, complemented
10#19134627C211yesmaximal, characteristic, complemented
11#19134534C211yesmaximal, characteristic
12#19134419C211yesmaximal, characteristic, complemented
13C4×#13063247C211yesmaximal, characteristic, complemented
14#19134378C211yesmaximal, characteristic, complemented
15C43×#1933C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063283—21no—
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24#14582899C418yescomplemented
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582786—21no—
36#14582780—21no—
37#14582777—21no—
38#14582777—21no—
39#14582761—21no—
40#14582761—21no—
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45C4×(C2×D43)⋊C4C2211yescharacteristic
46#95×D43—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#103×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C2×#10621902—22no—
61C2×#10621902—22no—
62C2×#10621902—22no—
63C2×#10621902—41no—
64C2×#10621902—41no—
65C2×#10621902C2×C414yes—
66C22×D172—21no—
67C22×D172C2311yescharacteristic
68C22×C4×D43—21no—
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43C2311yescharacteristic
73C2×#10621872—41no—
74C2×#10621872—41no—
75C2×#10621872C2×C414yescomplemented
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C4×D172—22no—
79C4×D172—41no—
80#13063287—22no—
81#13063287—41no—
82#13063283—44no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C4⋊C4×D43—22no—
89C4⋊C4×D43C2×C414yescomplemented
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4D411yescharacteristic
95C2×(C2×D43)⋊C4D411yescharacteristic
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99#13063258—41no—
100#13063256—41no—
101#13063249—41no—
102#13063249C2×C414yescomplemented
103#13063247—22no—
104#13063247C2×C414yes—
105#13063245—22no—
106#13063245C2×C414yes—
107(C2×D43)⋊C8—22no—
108#13063235—41no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95D411yescharacteristic
117C43⋊#95D411yescharacteristic
118C22×Q8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126#103×C43—41no—
127#103×C43C2×C414yescomplemented
128C4×C8×C43—41no—
129#95×C43—21no—
130#95×C43—21no—
131#95×C43—21no—
132C23×D43—21no—
133C23×D43C2×D411yescharacteristic
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43C22×C412yes—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153#10621902—28no—
154#10621902—44no—
155#10621902—44no—
156#10621902—44no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—24no—
161C2×D172—42no—
162C2×D172—42no—
163C2×D172C22×C412yes—
164C2×D172#4112yes—
165C2×D172#4112yes—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—24no—
171C2×C4×D43—24no—
172C2×C4×D43—42no—
173C2×C4×D43—42no—
174C2×C4×D43—42no—
175C2×C4×D43—42no—
176C2×C4×D43—42no—
177C2×C4×D43—42no—
178C2×C4×D43—42no—
179C2×C4×D43—42no—
180C2×C4×D43—81no—
181C2×C4×D43—81no—
182C2×C4×D43C22×C412yes—
183C2×C4×D43#4112yes—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43C22×C412yes—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—42no—
196C4⋊C4×C43C22×C412yes—
197C42×C43—21no—
198C42×C43—21no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—41no—
201(C2×D43)⋊C4—42no—
202(C2×D43)⋊C4—42no—
203(C2×D43)⋊C4—42no—
204(C2×D43)⋊C4—81no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—42no—
211C4⋊Dic43C22×C412yes—
212Dic43⋊C4—24no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—42no—
216C4×Dic43—42no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8C22×C412yes—
223#10621872—44no—
224C23×C43C22×D411yescharacteristic
225C22×D43—22no—
226C22×D43—22no—
227C22×D43—22no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—21no—
232C22×D43—21no—
233C22×D43—21no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238C22×D43C4×D412yes—
239Q8×C43—22no—
240Q8×C43—22no—
241Q8×C43—41no—
242Q8×C43—41no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43AGL(1,ℤ/8)12yes—
261C2×C4×C43C23×C411yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—22no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43C4×D412yes—
285D172—22no—
286D172—22no—
287D172—22no—
288D172—48no—
289D172#11714yescomplemented
290C4×D43—22no—
291C4×D43—22no—
292C4×D43—22no—
293C4×D43—22no—
294C4×D43—48no—
295C4×D43—48no—
296C4×D43—84no—
297C4×D43—84no—
298C8×C43—22no—
299C8×C43—41no—
300C43⋊C8—22no—
301C43⋊C8—41no—
302#22582—431nomaximal, Sylow
303C22×C43C2×C4×D411yescharacteristic
304C22×C43#54611yescharacteristic
305C22×C43#54611yescharacteristic
306C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C43#57511yescharacteristic
308C22×C43#57711yescharacteristic
309C22×C43#57811yescharacteristic
310C2×D43—24no—
311C2×D43—22no—
312C2×D43—22no—
313C2×D43—22no—
314C2×D43—41no—
315C2×D43—42no—
316C2×D43—42no—
317C2×D43—42no—
318C2×D43—41no—
319C2×D43—42no—
320C2×D43—41no—
321C2×D43—42no—
322C2×D43—41no—
323C2×D43—42no—
324C4×C43—22no—
325C4×C43—42no—
326C4×C43—42no—
327C4×C43—41no—
328C4×C43—81no—
329C4×C43—81no—
330C4×C43C2×#11711yescharacteristic
331C4×C43#51811yescharacteristic
332C4×C43#55111yescharacteristic
333C4×C43#55111yescharacteristic
334Dic43—22no—
335Dic43—41no—
336Dic43—42no—
337Dic43—41no—
338Dic43—81no—
339Dic43—81no—
340C2×#417—431no—
341#2344—431no—
342#2339—431no—
343#1935—431no—
344#1933D4311yescharacteristic, complemented
345#1928—431no—
346#1927—431no—
347#1864—431no—
348#1862—431no—
349#1824—431no—
350#1809—431no—
351#1788—431no—
352#1762—431no—
353C4×#102—431no—
354#1753—431no—
355C2×C43#234211yescharacteristic
356C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
357C2×C43#294711yescharacteristic
358C2×C43#330611yescharacteristic
359C2×C43#331511yescharacteristic
360C2×C43#332311yescharacteristic
361C2×C43#333011yescharacteristic
362D43—42no—
363D43—44no—
364C22×#41—431no—
365C22×M16—431no—
366C2×C4×D4—431no—
367C2×C4×D4—431no—
368C2×#117—861no—
369C22×C4⋊C4—431no—
370C2×#107—431no—
371C2×#106—431no—
372#417—438no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#103C2×D4311yescharacteristic
376C2×#103C2×D4311yescharacteristic
377C2×#102—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×C22⋊C8—431no—
382C2×#97—431no—
383C2×C4×C8C2×D4311yescharacteristic
384#391—431no—
385#391C2×D4311yescharacteristic
386#389—431no—
387#389C2×D4311yescharacteristic
388#387—861no—
389#387—861no—
390#386—861no—
391#386—861no—
392#381—861no—
393#381—861no—
394#380—431no—
395#380—431no—
396C4×C4⋊C4—431no—
397C4×C4⋊C4—431no—
398C4×C22⋊C4—431no—
399C2×#95—861no—
400#340—431no—
401#340—431no—
402#340—431no—
403#340—431no—
404#340C2×D4311yescharacteristic
405#340C2×D4311yescharacteristic
406#336—431no—
407#336—431no—
408C43#2258211yescharacteristic, complemented, Sylow
409C2×#41—434no—
410C2×#41—862no—
411C2×#41—862no—
412C2×#41—862no—
413C2×#41—1721no—
414C2×#41—1721no—
415C22×Q8C22×D4311yescharacteristic
416C22×D4—431no—
417C22×D4—861no—
418C23×C4—431no—
419C23×C4—861no—
420C23×C4—861no—
421C23×C4—861no—
422C23×C4—861no—
423C2×M16—434no—
424C2×M16—1721no—
425C2×M16—1721no—
426C22×C8—431no—
427C22×C8—431no—
428C22×C8C22×D4311yescharacteristic
429C22×C8C22×D4311yescharacteristic
430C4×D4—862no—
431C4×D4—862no—
432C4×D4—1721no—
433C4×D4—1721no—
434#117—1724no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—434no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—862no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4C22×D4311yescharacteristic
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C22⋊C4—431no—
447C2×C22⋊C4—431no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C42—431no—
453C2×C42—861no—
454C2×C42—861no—
455C2×C42C22×D4311yescharacteristic
456#107—1721no—
457#106—1721no—
458#103—41no—
459#103—434no—
460#103—1721no—
461#103C4×D4314yescomplemented
462#102—434no—
463#102—434no—
464#102—862no—
465#102—862no—
466C22⋊C8—862no—
467#97—1721no—
468C4×C8—41no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—431no—
473#95—431no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479#95—861no—
480#95—861no—
481C24—431no—
482C24—861no—
483#41—868no—
484#41—1724no—
485#41—1724no—
486#41—1724no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8C2×C4×D4312yes—
493C2×D4—432no—
494C2×D4—432no—
495C2×D4—432no—
496C2×D4—864no—
497C2×D4—861no—
498C2×D4—861no—
499C2×D4—861no—
500C2×D4—1722no—
501C2×D4—1722no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—431no—
507C22×C4—432no—
508C22×C4—432no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—864no—
512C22×C4—864no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—3441no—
521C22×C4—3441no—
522C22×C4—1722no—
523C22×C4—1722no—
524C22×C4—1722no—
525C22×C4—1722no—
526C22×C4—1722no—
527C22×C4—1722no—
528C22×C4—1722no—
529C22×C4—1722no—
530C22×C4D4×D4311yescharacteristic
531C22×C4D4×D4311yescharacteristic
532C22×C4C23×D4311yescharacteristic
533M16—1724no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—432no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8C2×C4×D4312yes—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4—432no—
553C4⋊C4—864no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—861no—
558C4⋊C4—861no—
559C4⋊C4—1722no—
560C4⋊C4C2×C4×D4312yes—
561C22⋊C4—862no—
562C22⋊C4—3441no—
563C22⋊C4—1721no—
564C22⋊C4—1722no—
565C22⋊C4—1722no—
566C22⋊C4—1722no—
567C42—21no—
568C42—21no—
569C42—861no—
570C42—861no—
571C42—1722no—
572C42—1722no—
573C23—432no—
574C23—862no—
575C23—861no—
576C23—861no—
577C23—861no—
578C23—861no—
579C23—862no—
580C23—861no—
581C23—862no—
582C23—861no—
583C23—1721no—
584C23—1721no—
585C23—1721no—
586C23—1721no—
587C23C2×D4×D4311yescharacteristic
588Q8—22no—
589Q8—22no—
590Q8—41no—
591Q8—41no—
592D4—434no—
593D4—862no—
594D4—862no—
595D4—862no—
596D4—1728no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—432no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—862no—
618C2×C4—862no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—862no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—3444no—
629C2×C4—3444no—
630C2×C4—1728no—
631C2×C4—1728no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4#1306335212yes—
641C2×C4C22×C4×D4311yescharacteristic
642C2×C4#41×D4311yescharacteristic
643C2×C4#41×D4311yescharacteristic
644C2×C4#41×D4311yescharacteristic
645C2×C4#1306337011yescharacteristic
646C2×C4#1306337111yescharacteristic
647C8—22no—
648C8—41no—
649C8—862no—
650C8—1721no—
651C22—862no—
652C22—862no—
653C22—864no—
654C22—862no—
655C22—1722no—
656C22—1722no—
657C22—1721no—
658C22—1722no—
659C22—1721no—
660C22—1721no—
661C22—1722no—
662C22—1721no—
663C22—1722no—
664C22—1722no—
665C22C4×D4×D4311yescharacteristic
666C22#1458353811yescharacteristic
667C22#1458354211yescharacteristic
668C22C2×#1306335211yescharacteristic
669C22#1458369611yescharacteristic
670C22#1458370611yescharacteristic
671C22#1458371211yescharacteristic
672C4—22no—
673C4—42no—
674C4—41no—
675C4—42no—
676C4—81no—
677C4—81no—
678C4—862no—
679C4—3441no—
680C4—3441no—
681C4—1721no—
682C4—1721no—
683C4—1722no—
684C4#117×D4311yescharacteristic
685C4#1458337111yescharacteristic
686C4#1458357411yescharacteristic
687C4#1458357711yescharacteristic
688C2—1722no—
689C2—1724no—
690C2#1913744311yescharacteristic
691C2C4×#1306335211yescharacteristic
692C2#1914343311yescharacteristic
693C2#1914656211yescharacteristic
694C2#1914669711yescharacteristic
695C2#1914681011yescharacteristic
696C2#1914689911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1933C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
cosocleC22×C4×C43C24
hypercenter#1933D43
hypocenterC43#22582
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1933

Complements

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

NH ≅ G/Ntype
2. #19137463C2semidirect
4. #19135287C2semidirect
5. #19135239C2semidirect
6. #19135226C2semidirect
7. #19134857C2semidirect
8. #19134841C2semidirect
9. #19134684C2semidirect
10. #19134627C2semidirect
12. #19134419C2semidirect
13. C4×#13063247C2semidirect
14. #19134378C2semidirect
15. C43×#1933C2semidirect
24. #14582899C4semidirect
75. C2×#10621872C2×C4semidirect
89. C4⋊C4×D43C2×C4semidirect
102. #13063249C2×C4semidirect
127. #103×C43C2×C4semidirect
289. D172#117semidirect
344. #1933D43semidirect
408. C43#22582semidirect
461. #103C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828992
#191374632
#191374242
#191352872
#191352392
#191352262
#191348572
#191348412
#191346842
#191346272
#191345342
#191344192
C4×#130632472
#191343782
C43×#19332
#2258243