Finite Group Databasebeta

← #25196728

Subgroups — #25196728

Order 11008.

776 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140426C211yesmaximal, characteristic, complemented
2#19137291C211yesmaximal, characteristic
3#19136159C211yesmaximal, characteristic, complemented
4#19136123C211yesmaximal, characteristic, complemented
5#19135930C211yesmaximal, characteristic, complemented
6#19135185C211yesmaximal, characteristic, complemented
7#19135164C211yesmaximal, characteristic, complemented
8#19135030C211yesmaximal, characteristic
9#19135020C211yesmaximal, characteristic
10#19134854C211yesmaximal, characteristic, complemented
11#19134840C211yesmaximal, characteristic, complemented
12#19134627C211yesmaximal, characteristic, complemented
13#19134623C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C43×#2025C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×#13063282C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27#14582832—21no—
28#14582832—21no—
29#14582821—21no—
30#14582821—21no—
31#14582799—21no—
32#14582797C2211yescharacteristic
33#14582795C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582787—21no—
36#14582776—21no—
37#14582771—21no—
38#14582769C2211yescharacteristic
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#125×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C22⋊D43—21no—
60C23×Dic43—21no—
61C22×C4×D43C2311yescharacteristic
62C2×#10621872—22no—
63C2×#10621872—22no—
64C2×#10621872—41no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C2×C8×D43—22no—
68C2×C8×D43—22no—
69C2×C8×D43—41no—
70#13063296—22no—
71#13063296Q814yes—
72D4×Dic43—41no—
73D4×Dic43—41no—
74#13063282—41no—
75#13063282—41no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4D411yescharacteristic
86C2×Dic43⋊C4D411yescharacteristic
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4D411yescharacteristic
93C2×(C2×D43)⋊C4D411yescharacteristic
94C2×C4×Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96#13063258—22no—
97#13063258—22no—
98#13063258—41no—
99#13063256—41no—
100#13063246—22no—
101#13063246—22no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×D4×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112#125×C43—41no—
113#125×C43—41no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C42×C43C2311yescharacteristic
122#102×C43—41no—
123#102×C43—41no—
124C24×C43—21no—
125C23×D43C2×D411yescharacteristic
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43C2×Q812yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C2×C22⋊D43—24no—
139C2×C22⋊D43—81no—
140C2×C22⋊D43—81no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—42no—
146C22×Dic43—81no—
147C22×Dic43—81no—
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43C2×Q812yes—
156C2×C4×D43#4112yes—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—42no—
170C4⋊C4×C43—42no—
171C22⋊C4×C43—81no—
172C22⋊C4×C43—81no—
173C42×C43—21no—
174C42×C43—21no—
175C22⋊Dic43—24no—
176C22⋊Dic43—42no—
177(C2×D43)⋊C4—41no—
178(C2×D43)⋊C4—41no—
179(C2×D43)⋊C4—81no—
180(C2×D43)⋊C4—81no—
181(C2×D43)⋊C4—81no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—81no—
190C4⋊Dic43—81no—
191C4⋊Dic43C2×Q812yes—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194Dic43⋊C4—81no—
195Dic43⋊C4—81no—
196Dic43⋊C4—81no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—81no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8#4112yes—
205C2×C43⋊C8#4112yes—
206#10621872—44no—
207C8×D43—44no—
208C23×C43—22no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43C22×D411yescharacteristic
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43C22⋊Q812yes—
223D4×C43—22no—
224D4×C43—22no—
225D4×C43—41no—
226D4×C43—41no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43C22×Q811yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C2×C4×C43H(5,𝔽2)11yescharacteristic
248C22⋊D43—84no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—22no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—84no—
270C2×Dic43C22⋊Q812yes—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—22no—
275C8×C43—41no—
276C8×C43—41no—
277C43⋊C8—22no—
278C43⋊C8—22no—
279#29169—431nomaximal, Sylow
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43C2×C22⋊Q811yescharacteristic
288C22×C43#53211yescharacteristic
289C22×C43#53411yescharacteristic
290C22×C43#57611yescharacteristic
291C22×C43#57611yescharacteristic
292C22×C43#57711yescharacteristic
293C22×C43#57811yescharacteristic
294C2×D43—22no—
295C2×D43—22no—
296C2×D43—22no—
297C2×D43—41no—
298C2×D43—41no—
299C2×D43—41no—
300C2×D43—41no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—81no—
304C4×C43—81no—
305C4×C43—81no—
306C4×C43#55111yescharacteristic
307C4×C43#55111yescharacteristic
308C4×C43#55411yescharacteristic
309C4×C43#55411yescharacteristic
310Dic43—22no—
311Dic43—42no—
312Dic43—41no—
313Dic43—41no—
314Dic43—81no—
315Dic43—81no—
316Dic43—81no—
317#2629—431no—
318#2324—431no—
319#2100—431no—
320#2093—431no—
321#2059—431no—
322#2025D4311yescharacteristic, complemented
323#1921—431no—
324#1918—431no—
325#1895—431no—
326#1893—431no—
327#1864—431no—
328#1862—431no—
329#1809—431no—
330#1808—431no—
331#1729—431no—
332C2×C43—82no—
333C2×C43#256411yescharacteristic
334C2×C43#308111yescharacteristic
335C2×C43#308311yescharacteristic
336C2×C43#317611yescharacteristic
337C2×C43#317811yescharacteristic
338C2×C43#319811yescharacteristic
339C2×C43#320311yescharacteristic
340D43—42no—
341C22×M16—431no—
342C23×C8—431no—
343C2×#125C2×D4311yescharacteristic
344C2×#121—431no—
345C2×C4×D4—431no—
346C2×#117—431no—
347C2×#107—431no—
348C2×#107—431no—
349C2×#107—431no—
350C2×#106—431no—
351C2×#102—431no—
352C2×#102—431no—
353C2×#102C2×D4311yescharacteristic
354C2×#102C2×D4311yescharacteristic
355#398—861no—
356#398—861no—
357#396—861no—
358#396—861no—
359#390—861no—
360#390C2×D4311yescharacteristic
361#389—431no—
362#389—431no—
363#389—431no—
364#388—861no—
365#386—861no—
366#385—861no—
367#384—431no—
368#380—431no—
369#380—431no—
370#380—431no—
371C4×C4⋊C4—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#340—431no—
378#340C2×D4311yescharacteristic
379#340C2×D4311yescharacteristic
380#336—431no—
381#336—431no—
382#336—431no—
383#336C2×D4311yescharacteristic
384C43#2916911yescharacteristic, complemented, Sylow
385C22×D4—861no—
386C22×D4C22×D4311yescharacteristic
387C23×C4—431no—
388C23×C4—861no—
389C2×M16—862no—
390C2×M16—862no—
391C2×M16—1721no—
392C22×C8—431no—
393C22×C8—431no—
394C22×C8—862no—
395C22×C8—862no—
396C22×C8—1721no—
397C22×C8C22×D4311yescharacteristic
398C22×C8C22×D4311yescharacteristic
399#125—41no—
400#125—41no—
401#121—434no—
402#121—862no—
403C4×D4—1721no—
404C4×D4—1721no—
405#117—1721no—
406#117—1721no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—431no—
426C2×C22⋊C4—431no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C42—431no—
433C2×C42—861no—
434C2×C42C22×D4311yescharacteristic
435#107—862no—
436#107—862no—
437#107—1721no—
438#106—1721no—
439#102—41no—
440#102—41no—
441#102—862no—
442#102—862no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450C24—21no—
451C24—431no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—864no—
458C2×D4—3441no—
459C2×D4—3441no—
460C2×D4Q8×D4312yes—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—431no—
465C22×C4—432no—
466C22×C4—432no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—3441no—
478C22×C4—3441no—
479C22×C4—1722no—
480C22×C4D4×D4311yescharacteristic
481C22×C4D4×D4311yescharacteristic
482C22×C4C23×D4311yescharacteristic
483M16—1724no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—432no—
491C2×C8—432no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—1724no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—432no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—3441no—
514C4⋊C4—3441no—
515C4⋊C4—3441no—
516C4⋊C4—3441no—
517C4⋊C4—3441no—
518C4⋊C4—1721no—
519C4⋊C4—1721no—
520C22⋊C4—81no—
521C22⋊C4—81no—
522C22⋊C4—864no—
523C22⋊C4—3441no—
524C22⋊C4—3441no—
525C22⋊C4—3441no—
526C22⋊C4—1721no—
527C22⋊C4—1721no—
528C22⋊C4—1722no—
529C42—21no—
530C42—21no—
531C42—861no—
532C42—861no—
533C42—3441no—
534C23—22no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—432no—
542C23—861no—
543C23—861no—
544C23—861no—
545C23—861no—
546C23—861no—
547C23—861no—
548C23C2×D4×D4311yescharacteristic
549D4—22no—
550D4—22no—
551D4—41no—
552D4—41no—
553D4—3444no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—432no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—3444no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4C2×Q8×D4311yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C2×C4#41×D4311yescharacteristic
598C2×C4#41×D4311yescharacteristic
599C2×C4#1306337011yescharacteristic
600C2×C4#1306337011yescharacteristic
601C8—41no—
602C8—41no—
603C8—862no—
604C8—862no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—862no—
613C22—862no—
614C22—862no—
615C22—1721no—
616C22—1721no—
617C22—1721no—
618C22—1721no—
619C22C22⋊Q8×D4311yescharacteristic
620C22#1458344811yescharacteristic
621C22#1458345911yescharacteristic
622C22#1458370311yescharacteristic
623C22#1458370311yescharacteristic
624C22#1458370611yescharacteristic
625C22#1458371311yescharacteristic
626C4—41no—
627C4—41no—
628C4—81no—
629C4—81no—
630C4—81no—
631C4—862no—
632C4—3441no—
633C4—3441no—
634C4—3441no—
635C4—1721no—
636C4—1721no—
637C4—1722no—
638C4#1458357911yescharacteristic
639C4#1458357911yescharacteristic
640C4#1458360311yescharacteristic
641C4#1458360311yescharacteristic
642C2—82no—
643C2—1722no—
644C2#1913977211yescharacteristic
645C2#1914442511yescharacteristic
646C2#1914444711yescharacteristic
647C2#1914524411yescharacteristic
648C2#1914526211yescharacteristic
649C2#1914544611yescharacteristic
650C2#1914549411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2025C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenter#2025D43
hypocenterC43#29169
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2025

Complements

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

NH ≅ G/Ntype
1. #19140426C2semidirect
3. #19136159C2semidirect
4. #19136123C2semidirect
5. #19135930C2semidirect
6. #19135185C2semidirect
7. #19135164C2semidirect
10. #19134854C2semidirect
11. #19134840C2semidirect
12. #19134627C2semidirect
13. #19134623C2semidirect
14. #19134290C2semidirect
15. C43×#2025C2semidirect
322. #2025D43semidirect
384. C43#29169semidirect

Maximal subgroups

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

subgroupindex
#191404262
#191372912
#191361592
#191361232
#191359302
#191351852
#191351642
#191350302
#191350202
#191348542
#191348402
#191346272
#191346232
#191342902
C43×#20252
#2916943