Finite Group Databasebeta

← #25169269

Subgroups — #25169269

Order 11008.

784 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139000C211yesmaximal, characteristic, complemented
2#19137607C211yesmaximal, characteristic
3#19136011C211yesmaximal, characteristic, complemented
4#19135967C211yesmaximal, characteristic, complemented
5#19135783C211yesmaximal, characteristic
6#19135775C211yesmaximal, characteristic
7#19135362C211yesmaximal, characteristic, complemented
8#19135323C211yesmaximal, characteristic, complemented
9#19135201C211yesmaximal, characteristic, complemented
10#19135171C211yesmaximal, characteristic, complemented
11#19135166C211yesmaximal, characteristic, complemented
12#19134856C211yesmaximal, characteristic, complemented
13#19134789C211yesmaximal, characteristic, complemented
14#19134684C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C2×#13063296C2211yescharacteristic
17C2×C4×C22⋊D43—21no—
18C2×C4⋊C4×D43C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28#14582840—21no—
29#14582828—21no—
30#14582802C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582795C2211yescharacteristic
34#14582793—21no—
35#14582790—21no—
36#14582775—21no—
37#14582772—21no—
38#14582767—21no—
39#14582764C2211yescharacteristic
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×(C2×D43)⋊C4C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×C22⋊D43—21no—
60C22×C4×D43—21no—
61C22×C4×D43C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063296—22no—
65#13063296—22no—
66C4×C22⋊D43—44no—
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C4⋊C4×D43—22no—
76C4⋊C4×D43—41no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4D411yescharacteristic
83C2×(C2×D43)⋊C4D411yescharacteristic
84C2×C4×Dic43—21no—
85C2×C4×Dic43C2311yescharacteristic
86#13063258—22no—
87#13063257—22no—
88#13063257—41no—
89#13063256—22no—
90Dic43⋊C8—22no—
91#13063246—22no—
92#13063246—41no—
93(C2×D43)⋊C8—22no—
94(C2×D43)⋊C8—41no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95D411yescharacteristic
104C43⋊#95D411yescharacteristic
105C22×D4×C43C2311yescharacteristic
106C23×C4×C43—21no—
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C4×D4×C43—22no—
110C4×D4×C43—41no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C22⋊C4×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#102×C43—22no—
118#102×C43—22no—
119C4×C8×C43—41no—
120#95×C43—21no—
121C24×C43—21no—
122C23×D43C2×D411yescharacteristic
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43#4112yes—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—42no—
133C22×C4×C43—42no—
134C22×C4×C43—81no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C2×C22⋊D43—24no—
139C2×C22⋊D43—42no—
140C2×C22⋊D43—42no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C4×D43—81no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43#4112yes—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43#4112yes—
169C22⋊C4×C43—42no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—42no—
173C22⋊Dic43—24no—
174C22⋊Dic43—42no—
175C22⋊Dic43—81no—
176(C2×D43)⋊C4—22no—
177(C2×D43)⋊C4—22no—
178(C2×D43)⋊C4—42no—
179(C2×D43)⋊C4—81no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43#4112yes—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190Dic43⋊C4—81no—
191Dic43⋊C4—81no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—42no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C23×C43—22no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43C22×D411yescharacteristic
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43—21no—
215C22×D43#13512yes—
216D4×C43—22no—
217D4×C43—22no—
218D4×C43—41no—
219D4×C43—41no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—22no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—84no—
235C2×C4×C43AGL(1,ℤ/8)12yes—
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43H(5,𝔽2)11yescharacteristic
241C2×C4×C432−1+411yescharacteristic
242C22⋊D43—48no—
243C2×Dic43—22no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—41no—
267C4×D43—41no—
268C4×D43—84no—
269C8×C43—22no—
270C8×C43—41no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273#27031—431nomaximal, Sylow
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—42no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43#52511yescharacteristic
282C22×C43#54611yescharacteristic
283C22×C43#54711yescharacteristic
284C22×C43C2×#13511yescharacteristic
285C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C43#57711yescharacteristic
287C22×C43#57711yescharacteristic
288C2×D43—22no—
289C2×D43—22no—
290C2×D43—22no—
291C2×D43—41no—
292C2×D43—41no—
293C2×D43—41no—
294C2×D43—41no—
295C4×C43—22no—
296C4×C43—41no—
297C4×C43—42no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43#52911yescharacteristic
301C4×C43#53911yescharacteristic
302C4×C43#55311yescharacteristic
303C4×C43#55611yescharacteristic
304Dic43—41no—
305Dic43—41no—
306Dic43—42no—
307Dic43—41no—
308Dic43—81no—
309Dic43—81no—
310Dic43—81no—
311#2495—431no—
312#2361—431no—
313#2073—431no—
314#2065—431no—
315#2034—431no—
316#2033—431no—
317#1949—431no—
318#1941—431no—
319#1923—431no—
320#1919—431no—
321#1918—431no—
322#1864—431no—
323#1853—431no—
324#1824—431no—
325C4×#102D4311yescharacteristic, complemented
326C2×C43—82no—
327C2×C43#246611yescharacteristic
328C2×C43#310511yescharacteristic
329C2×C43#312511yescharacteristic
330C2×C43#330111yescharacteristic
331C2×C43#331011yescharacteristic
332C2×C43#333711yescharacteristic
333C2×C43#335411yescharacteristic
334D43—42no—
335C2×#121—431no—
336C2×C4×D4—861no—
337C2×C4×D4C2×D4311yescharacteristic
338C22×C4⋊C4—431no—
339C2×#107—431no—
340C2×#106—431no—
341C2×#106—431no—
342C2×#106—431no—
343C2×C4⋊C8—431no—
344C2×#102—431no—
345C2×#102—431no—
346C2×#102C2×D4311yescharacteristic
347C2×#102C2×D4311yescharacteristic
348C2×C22⋊C8—431no—
349C2×C22⋊C8—431no—
350C2×C4×C8C2×D4311yescharacteristic
351#400—861no—
352#397—861no—
353#390—431no—
354#389—431no—
355#389—431no—
356#389—431no—
357#388—861no—
358#388—861no—
359#386—861no—
360#385—861no—
361#383—861no—
362#382—431no—
363#380—431no—
364#380—431no—
365C4×C4⋊C4—431no—
366C4×C4⋊C4C2×D4311yescharacteristic
367C4×C22⋊C4—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#340C2×D4311yescharacteristic
375#340C2×D4311yescharacteristic
376#336—431no—
377#336—431no—
378C43#2703111yescharacteristic, complemented, Sylow
379C22×D4—861no—
380C22×D4C22×D4311yescharacteristic
381C23×C4—21no—
382C23×C4—431no—
383C23×C4—861no—
384C22×C8—431no—
385C22×C8—431no—
386C22×C8C22×D4311yescharacteristic
387C22×C8C22×D4311yescharacteristic
388#121—862no—
389#121—862no—
390C4×D4—22no—
391C4×D4—41no—
392C4×D4—1724no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—862no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—1721no—
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—431no—
408C2×C22⋊C4—431no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C42—21no—
415C2×C42—431no—
416C2×C42—861no—
417C2×C42C22×D4311yescharacteristic
418#107—862no—
419#106—862no—
420#106—862no—
421#106—1721no—
422C4⋊C8—862no—
423#102—22no—
424#102—22no—
425#102—862no—
426#102—1721no—
427C22⋊C8—862no—
428C22⋊C8—1721no—
429C4×C8—41no—
430#95—21no—
431#95—431no—
432#95—431no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441C24—21no—
442C24—431no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—864no—
449C2×D4—1722no—
450C2×D4—1722no—
451C2×D4#1062189812yes—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—81no—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—3441no—
472C22×C4—1722no—
473C22×C4—1722no—
474C22×C4D4×D4311yescharacteristic
475C22×C4D4×D4311yescharacteristic
476C22×C4C23×D4311yescharacteristic
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8#1062189812yes—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—432no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—3441no—
503C4⋊C4—3441no—
504C4⋊C4—1722no—
505C4⋊C4—1722no—
506C4⋊C4#1062189812yes—
507C22⋊C4—42no—
508C22⋊C4—862no—
509C22⋊C4—864no—
510C22⋊C4—862no—
511C22⋊C4—3441no—
512C22⋊C4—3441no—
513C22⋊C4—1722no—
514C22⋊C4—1722no—
515C42—21no—
516C42—21no—
517C42—42no—
518C42—861no—
519C42—861no—
520C42—1722no—
521C23—22no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—432no—
529C23—861no—
530C23—861no—
531C23—861no—
532C23—861no—
533C23—861no—
534C23—861no—
535C23C2×D4×D4311yescharacteristic
536D4—22no—
537D4—22no—
538D4—41no—
539D4—41no—
540D4—1728no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—84no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—862no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—3444no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4#1306334912yes—
583C2×C4#41×D4311yescharacteristic
584C2×C4C2×#1062189811yescharacteristic
585C2×C4C2×#1062189811yescharacteristic
586C2×C4C2×#1062189811yescharacteristic
587C2×C4#1306337011yescharacteristic
588C2×C4#1306337211yescharacteristic
589C8—22no—
590C8—41no—
591C8—1721no—
592C8—1721no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—862no—
601C22—862no—
602C22—862no—
603C22—1721no—
604C22—1721no—
605C22—1721no—
606C22—1721no—
607C22#1458340811yescharacteristic
608C22#1458353911yescharacteristic
609C22#1458355411yescharacteristic
610C22#135×D4311yescharacteristic
611C22C2×#1306334911yescharacteristic
612C22#1458370511yescharacteristic
613C22#1458370611yescharacteristic
614C4—22no—
615C4—41no—
616C4—42no—
617C4—81no—
618C4—81no—
619C4—3441no—
620C4—3441no—
621C4—3441no—
622C4—1721no—
623C4—1721no—
624C4—1722no—
625C4—1721no—
626C4#1458343311yescharacteristic
627C4#1458349111yescharacteristic
628C4#1458359811yescharacteristic
629C4#1458361711yescharacteristic
630C2—82no—
631C2—1722no—
632C2#1913863111yescharacteristic
633C2#1914464011yescharacteristic
634C2#1914486811yescharacteristic
635C2#1914649811yescharacteristic
636C2#1914661211yescharacteristic
637C2#1914697911yescharacteristic
638C2#1914719211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenterC4×#102D43
hypocenterC43#27031
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. #19139000C2semidirect
3. #19136011C2semidirect
4. #19135967C2semidirect
7. #19135362C2semidirect
8. #19135323C2semidirect
9. #19135201C2semidirect
10. #19135171C2semidirect
11. #19135166C2semidirect
12. #19134856C2semidirect
13. #19134789C2semidirect
14. #19134684C2semidirect
15. C4×#102×C43C2semidirect
325. C4×#102D43semidirect
378. C43#27031semidirect

Maximal subgroups

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

subgroupindex
#191390002
#191376072
#191360112
#191359672
#191357832
#191357752
#191353622
#191353232
#191352012
#191351712
#191351662
#191348562
#191347892
#191346842
C4×#102×C432
#2703143