Finite Group Databasebeta

← #25200771

Subgroups — #25200771

Order 11008.

758 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137306C211yesmaximal, characteristic, complemented
2#19136066C211yesmaximal, characteristic, complemented
3#19135998C211yesmaximal, characteristic, complemented
4#19135836C211yesmaximal, characteristic, complemented
5#19135671C211yesmaximal, characteristic
6#19135475C211yesmaximal, characteristic, complemented
7#19135460C211yesmaximal, characteristic
8#19135291C211yesmaximal, characteristic, complemented
9#19135270C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic, complemented
11#19134946C211yesmaximal, characteristic
12#19134848C211yesmaximal, characteristic, complemented
13#19134841C211yesmaximal, characteristic, complemented
14#19134347C211yesmaximal, characteristic, complemented
15C43×#2644C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063236C2211yescharacteristic
32C2×C4×C43⋊C8C2211yescharacteristic
33#14582805C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582791—21no—
36#14582791—21no—
37#14582773—21no—
38#14582773—21no—
39#14582769C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C43×#397—21no—
49C43×#397—21no—
50C43×#397—21no—
51C43×#396—21no—
52C43×#390C2211yescharacteristic
53C43×#390C2211yescharacteristic
54C43×#390C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#376C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C2×#10621883—22no—
63C2×#10621883—22no—
64C2×#10621883—41no—
65C2×#10621882—22no—
66C2×#10621882—22no—
67C2×#10621882—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063313—22no—
73#13063313—22no—
74C4×Dic86—41no—
75C4×Dic86—41no—
76C4×D172—41no—
77C4×D172—41no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89#13063258—41no—
90#13063258—41no—
91#13063248—22no—
92#13063248—22no—
93#13063248—41no—
94#13063246—41no—
95#13063246—41no—
96#13063245—22no—
97#13063245—22no—
98#13063245—41no—
99#13063236—22no—
100C4×C43⋊C8—22no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C22×D4×C43C2311yescharacteristic
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C42×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119#95×C43—21no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124#95×C43D411yescharacteristic
125#95×C43D411yescharacteristic
126C24×C43—21no—
127C23×D43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172#4112yes—
153C2×C4×D43—42no—
154C2×C4×D43—81no—
155C2×C4×D43—81no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86#4112yes—
162C4⋊C4×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—81no—
169C4⋊C4×C43—81no—
170C4⋊C4×C43—81no—
171C22⋊C4×C43—81no—
172C22⋊C4×C43—81no—
173C22⋊C4×C43—81no—
174C22⋊C4×C43—81no—
175C22⋊C4×C43—81no—
176C22⋊C4×C43—81no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183#10621883—44no—
184#10621882—44no—
185(C2×D43)⋊C4—24no—
186(C2×D43)⋊C4—24no—
187(C2×D43)⋊C4—42no—
188(C2×D43)⋊C4—81no—
189(C2×D43)⋊C4—81no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—81no—
195C4⋊Dic43—81no—
196Dic43⋊C4—42no—
197C4×Dic43—42no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8#4112yes—
209C2×C43⋊C8#4112yes—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43C22×D411yescharacteristic
218C22×D43—22no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
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×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C2×C4×C43H(5,𝔽2)11yescharacteristic
262C2×Dic43—22no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271D172—22no—
272D172—22no—
273D172—41no—
274D172—41no—
275C4×D43—84no—
276Dic86—22no—
277Dic86—22no—
278Dic86—41no—
279Dic86—41no—
280C43⋊C8—22no—
281C43⋊C8—22no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#29507—431nomaximal, Sylow
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43#52511yescharacteristic
293C22×C43#53211yescharacteristic
294C22×C43#53511yescharacteristic
295C22×C43#57611yescharacteristic
296C22×C43#57611yescharacteristic
297C22×C43#57711yescharacteristic
298C22×C43#57811yescharacteristic
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—81no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C4×C43—41no—
307C4×C43—41no—
308C4×C43—41no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43—81no—
313C4×C43—81no—
314C4×C43—81no—
315C4×C43#55111yescharacteristic
316C4×C43#55111yescharacteristic
317C4×C43#55311yescharacteristic
318C4×C43#55311yescharacteristic
319Dic43—42no—
320Dic43—81no—
321Dic43—81no—
322#2644D4311yescharacteristic, complemented
323#2326—431no—
324#2083—431no—
325#2071—431no—
326#2042—431no—
327#2012—431no—
328#1973—431no—
329#1970—431no—
330#1936—431no—
331#1933—431no—
332#1880—431no—
333#1879—431no—
334#1863—431no—
335#1862—431no—
336#1746—431no—
337C2×C43—161no—
338C2×C43#260311yescharacteristic
339C2×C43#311911yescharacteristic
340C2×C43#312411yescharacteristic
341C2×C43#317511yescharacteristic
342C2×C43#317911yescharacteristic
343C2×C43#322011yescharacteristic
344C2×C43#322511yescharacteristic
345D43—82no—
346C22×SD16—431no—
347C22×D8—431no—
348C2×#124—431no—
349C2×C4×Q8—431no—
350C2×C4×D4—431no—
351C2×#107—431no—
352C2×#107—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#103—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102—431no—
361C2×#97—431no—
362C2×C4×C8—431no—
363#397—21no—
364#397—21no—
365#397—21no—
366#396—21no—
367#391—431no—
368#390—431no—
369#390C2×D4311yescharacteristic
370#390C2×D4311yescharacteristic
371#390C2×D4311yescharacteristic
372#389C2×D4311yescharacteristic
373#389C2×D4311yescharacteristic
374#389C2×D4311yescharacteristic
375#388—861no—
376#388—861no—
377#385—861no—
378#385—861no—
379#384—431no—
380#376C2×D4311yescharacteristic
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#336—431no—
386#336—431no—
387#336—431no—
388#336—431no—
389C43#2950711yescharacteristic, complemented, Sylow
390C22×Q8—431no—
391C22×D4—431no—
392C22×D4C22×D4311yescharacteristic
393C23×C4—861no—
394C2×SD16—862no—
395C2×SD16—862no—
396C2×SD16—1721no—
397C2×D8—862no—
398C2×D8—862no—
399C2×D8—1721no—
400C22×C8—431no—
401C22×C8—431no—
402C22×C8—431no—
403C22×C8—431no—
404#124—862no—
405#124—862no—
406C4×Q8—1721no—
407C4×Q8—1721no—
408C4×D4—1721no—
409C4×D4—1721no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C42—861no—
433C2×C42C22×D4311yescharacteristic
434C2×C42C22×D4311yescharacteristic
435C2×C42C22×D4311yescharacteristic
436#107—1721no—
437#107—1721no—
438#103—862no—
439#103—862no—
440#103—1721no—
441#102—862no—
442#102—862no—
443#102—1721no—
444#102—1721no—
445#102—1721no—
446#97—862no—
447C4×C8—862no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—861no—
452#95—861no—
453#95C22⋊D4311yescharacteristic
454#95C22⋊D4311yescharacteristic
455#95C22⋊D4311yescharacteristic
456#95C22⋊D4311yescharacteristic
457C24—21no—
458C24—861no—
459C2×Q8—432no—
460C2×Q8—861no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—432no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—3441no—
484C22×C4—3441no—
485C22×C4—1722no—
486C22×C4C2×C22⋊D4311yescharacteristic
487C22×C4C2×C22⋊D4311yescharacteristic
488C22×C4C2×C22⋊D4311yescharacteristic
489C22×C4C2×C22⋊D4311yescharacteristic
490C22×C4C2×C22⋊D4311yescharacteristic
491C22×C4C2×C22⋊D4311yescharacteristic
492C22×C4C23×D4311yescharacteristic
493SD16—1724no—
494D8—1724no—
495C2×C8—432no—
496C2×C8—432no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—81no—
514C4⋊C4—81no—
515C4⋊C4—81no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—3441no—
521C4⋊C4—3441no—
522C4⋊C4—1722no—
523C22⋊C4—81no—
524C22⋊C4—81no—
525C22⋊C4—81no—
526C22⋊C4—81no—
527C22⋊C4—81no—
528C22⋊C4—81no—
529C22⋊C4—864no—
530C22⋊C4—864no—
531C22⋊C4—3441no—
532C22⋊C4—3441no—
533C22⋊C4—1722no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—1722no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—862no—
549C23—1721no—
550C23—1721no—
551C23—1721no—
552C23—1721no—
553C23—1721no—
554C23—1721no—
555C23C22×C22⋊D4311yescharacteristic
556Q8—862no—
557Q8—862no—
558Q8—1721no—
559Q8—1721no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—862no—
565D4—862no—
566D4—1721no—
567D4—1721no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—862no—
596C2×C4—3444no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4#41×D4311yescharacteristic
606C2×C4#41×D4311yescharacteristic
607C2×C4#41×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4#1306337111yescharacteristic
610C2×C4#1306337111yescharacteristic
611C8—862no—
612C8—862no—
613C8—1721no—
614C8—1721no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—3441no—
623C22—3441no—
624C22—3441no—
625C22—3441no—
626C22—1722no—
627C22—1722no—
628C22—1722no—
629C22#1458340611yescharacteristic
630C22#1458344511yescharacteristic
631C22#1458346311yescharacteristic
632C22#1458370211yescharacteristic
633C22#1458370211yescharacteristic
634C22#1458371011yescharacteristic
635C22#1458371411yescharacteristic
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—81no—
643C4—81no—
644C4—81no—
645C4—3441no—
646C4—3441no—
647C4—1722no—
648C4#1458357411yescharacteristic
649C4#1458357411yescharacteristic
650C4#1458360011yescharacteristic
651C4#1458360011yescharacteristic
652C2—161no—
653C2—3442no—
654C2#1914022411yescharacteristic
655C2#1914478811yescharacteristic
656C2#1914485111yescharacteristic
657C2#1914522811yescharacteristic
658C2#1914528011yescharacteristic
659C2#1914563911yescharacteristic
660C2#1914569811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2644C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenter#2644D43
hypocenterC43#29507
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #2644

Complements

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

NH ≅ G/Ntype
1. #19137306C2semidirect
2. #19136066C2semidirect
3. #19135998C2semidirect
4. #19135836C2semidirect
6. #19135475C2semidirect
8. #19135291C2semidirect
9. #19135270C2semidirect
10. #19134953C2semidirect
12. #19134848C2semidirect
13. #19134841C2semidirect
14. #19134347C2semidirect
15. C43×#2644C2semidirect
322. #2644D43semidirect
389. C43#29507semidirect

Maximal subgroups

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

subgroupindex
#191373062
#191360662
#191359982
#191358362
#191356712
#191354752
#191354602
#191352912
#191352702
#191349532
#191349462
#191348482
#191348412
#191343472
C43×#26442
#2950743