Finite Group Databasebeta

← #25200778

Subgroups — #25200778

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140555C211yesmaximal, characteristic
2#19136077C211yesmaximal, characteristic, complemented
3#19136009C211yesmaximal, characteristic
4#19135838C211yesmaximal, characteristic, complemented
5#19135678C211yesmaximal, characteristic
6#19135479C211yesmaximal, characteristic
7#19135452C211yesmaximal, characteristic
8#19135288C211yesmaximal, characteristic, complemented
9#19135274C211yesmaximal, characteristic, complemented
10#19134950C211yesmaximal, characteristic
11#19134950C211yesmaximal, characteristic
12#19134863C211yesmaximal, characteristic, complemented
13#19134849C211yesmaximal, characteristic, complemented
14#19134347C211yesmaximal, characteristic, complemented
15C43×#2327C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×#13063249C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063236C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30#14582828—21no—
31#14582828—21no—
32#14582828—21no—
33#14582823—21no—
34#14582801C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582801C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C4⋊Q8×C43C2211yescharacteristic
49C2×C4×Q8×C43C2211yescharacteristic
50C2×C4×Q8×C43C2211yescharacteristic
51C43×#391C2211yescharacteristic
52C43×#391C2211yescharacteristic
53C43×#387—21no—
54C43×#387—21no—
55C43×#387—21no—
56C43×#387—21no—
57C43×#382C2211yescharacteristic
58C43×#376C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C2×#10621884—22no—
61C2×#10621884—22no—
62C2×#10621884—22no—
63C2×#10621884—22no—
64C2×#10621884—41no—
65C2×#10621884—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82#13063258—41no—
83#13063256—41no—
84#13063249—22no—
85#13063249—22no—
86#13063249—22no—
87#13063249—22no—
88#13063249—41no—
89#13063249—41no—
90#13063245—41no—
91#13063245—41no—
92#13063236—22no—
93C4×C43⋊C8—22no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C22×Q8×C43C2311yescharacteristic
98C22×Q8×C43C2311yescharacteristic
99C4⋊Q8×C43—22no—
100C4⋊Q8×C43—22no—
101C4×Q8×C43—41no—
102C4×Q8×C43—41no—
103C4×Q8×C43—41no—
104C4×Q8×C43—41no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C42×C43—21no—
112C2×C42×C43—21no—
113C2×C42×C43C2311yescharacteristic
114C2×C42×C43C2311yescharacteristic
115C2×C42×C43C2311yescharacteristic
116#95×C43—21no—
117#95×C43—21no—
118#95×C43—21no—
119#95×C43—21no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124#95×C43D411yescharacteristic
125#95×C43D411yescharacteristic
126C23×D43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43#4112yes—
138C2×Q8×C43#4112yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C4⋊C4×C43—24no—
160C4⋊C4×C43—24no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—42no—
166C4⋊C4×C43—42no—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—42no—
174C42×C43—42no—
175#10621884—44no—
176#10621884—44no—
177(C2×D43)⋊C4—81no—
178(C2×D43)⋊C4—81no—
179(C2×D43)⋊C4—81no—
180(C2×D43)⋊C4—81no—
181(C2×D43)⋊C4—81no—
182(C2×D43)⋊C4—81no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189Dic43⋊C4—81no—
190Dic43⋊C4—81no—
191Dic43⋊C4—81no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8#4112yes—
203C2×C43⋊C8#4112yes—
204C23×C43C22×D411yescharacteristic
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212Q8×C43—22no—
213Q8×C43—22no—
214Q8×C43—22no—
215Q8×C43—22no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
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—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—41no—
241C2×C4×C43—41no—
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×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265D172—41no—
266D172—41no—
267D172—41no—
268D172—41no—
269C43⋊C8—22no—
270C43⋊C8—22no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273#29508—431nomaximal, Sylow
274C22×C43#52511yescharacteristic
275C22×C43#53211yescharacteristic
276C22×C43#53511yescharacteristic
277C22×C43#57711yescharacteristic
278C22×C43#57711yescharacteristic
279C22×C43#57711yescharacteristic
280C22×C43#57811yescharacteristic
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—81no—
284C2×D43—81no—
285C2×D43—81no—
286C2×D43—81no—
287C2×D43—81no—
288C4×C43—42no—
289C4×C43—42no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43#55111yescharacteristic
299C4×C43#55111yescharacteristic
300C4×C43#55311yescharacteristic
301C4×C43#55311yescharacteristic
302Dic43—81no—
303Dic43—81no—
304Dic43—81no—
305#2644—431no—
306#2327D4311yescharacteristic, complemented
307#2085—431no—
308#2073—431no—
309#2043—431no—
310#2013—431no—
311#1973—431no—
312#1968—431no—
313#1935—431no—
314#1933—431no—
315#1880—431no—
316#1880—431no—
317#1865—431no—
318#1863—431no—
319#1746—431no—
320C2×C43#260311yescharacteristic
321C2×C43#312111yescharacteristic
322C2×C43#312611yescharacteristic
323C2×C43#317411yescharacteristic
324C2×C43#317811yescharacteristic
325C2×C43#322111yescharacteristic
326C2×C43#322511yescharacteristic
327D43—161no—
328C22×SD16—431no—
329C22×SD16—431no—
330C2×C4⋊Q8C2×D4311yescharacteristic
331C2×C4×Q8C2×D4311yescharacteristic
332C2×C4×Q8C2×D4311yescharacteristic
333C2×#107—431no—
334C2×#106—431no—
335C2×#103—431no—
336C2×#103—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#103—431no—
340C2×#103—431no—
341C2×#102—431no—
342C2×#102—431no—
343C2×#97—431no—
344C2×C4×C8—431no—
345#397—861no—
346#397—861no—
347#397—861no—
348#396—861no—
349#391C2×D4311yescharacteristic
350#391C2×D4311yescharacteristic
351#390—431no—
352#390—431no—
353#390—431no—
354#389—431no—
355#389—431no—
356#389—431no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#382C2×D4311yescharacteristic
362#376C2×D4311yescharacteristic
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#336—431no—
368#336—431no—
369#336—431no—
370#336—431no—
371C43#2950811yescharacteristic, complemented, Sylow
372C22×Q8C22×D4311yescharacteristic
373C22×Q8C22×D4311yescharacteristic
374C22×D4—431no—
375C2×SD16—862no—
376C2×SD16—862no—
377C2×SD16—862no—
378C2×SD16—862no—
379C2×SD16—1721no—
380C2×SD16—1721no—
381C22×C8—431no—
382C22×C8—431no—
383C22×C8—431no—
384C22×C8—431no—
385C4⋊Q8—22no—
386C4⋊Q8—22no—
387C4×Q8—41no—
388C4×Q8—41no—
389C4×Q8—41no—
390C4×Q8—41no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42C22×D4311yescharacteristic
412C2×C42C22×D4311yescharacteristic
413C2×C42C22×D4311yescharacteristic
414#107—1721no—
415#106—1721no—
416#103—862no—
417#103—862no—
418#103—862no—
419#103—862no—
420#103—1721no—
421#103—1721no—
422#102—1721no—
423#102—1721no—
424#97—862no—
425C4×C8—862no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95C22⋊D4311yescharacteristic
436#95C22⋊D4311yescharacteristic
437#95C22⋊D4311yescharacteristic
438#95C22⋊D4311yescharacteristic
439C24—861no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8#1062189812yes—
451C2×Q8#1062189812yes—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4C2×C22⋊D4311yescharacteristic
466C22×C4C2×C22⋊D4311yescharacteristic
467C22×C4C2×C22⋊D4311yescharacteristic
468C22×C4C2×C22⋊D4311yescharacteristic
469C22×C4C2×C22⋊D4311yescharacteristic
470C22×C4C2×C22⋊D4311yescharacteristic
471C22×C4C23×D4311yescharacteristic
472SD16—1724no—
473SD16—1724no—
474C2×C8—432no—
475C2×C8—432no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C4⋊C4—24no—
487C4⋊C4—24no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—3441no—
501C4⋊C4—3441no—
502C4⋊C4—3441no—
503C22⋊C4—3441no—
504C22⋊C4—3441no—
505C22⋊C4—3441no—
506C22⋊C4—3441no—
507C22⋊C4—3441no—
508C22⋊C4—3441no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—42no—
516C42—42no—
517C23—1721no—
518C23—1721no—
519C23—1721no—
520C23—1721no—
521C23—1721no—
522C23—1721no—
523C23—1721no—
524C23C22×C22⋊D4311yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—22no—
528Q8—22no—
529Q8—41no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533D4—1721no—
534D4—1721no—
535D4—1721no—
536D4—1721no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
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#41×D4311yescharacteristic
577C2×C4#41×D4311yescharacteristic
578C2×C4C2×#1062189811yescharacteristic
579C2×C4C2×#1062189811yescharacteristic
580C2×C4#1306337011yescharacteristic
581C2×C4#1306337011yescharacteristic
582C8—862no—
583C8—862no—
584C8—1721no—
585C8—1721no—
586C22—3441no—
587C22—3441no—
588C22—3441no—
589C22—3441no—
590C22—3441no—
591C22—3441no—
592C22—3441no—
593C22#1458341011yescharacteristic
594C22#1458344511yescharacteristic
595C22#1458346611yescharacteristic
596C22#1458370711yescharacteristic
597C22#1458370711yescharacteristic
598C22#1458370711yescharacteristic
599C22#1458371411yescharacteristic
600C4—41no—
601C4—41no—
602C4—42no—
603C4—42no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—81no—
609C4—81no—
610C4—3441no—
611C4—3441no—
612C4—3441no—
613C4#1458357811yescharacteristic
614C4#1458357811yescharacteristic
615C4#1458359811yescharacteristic
616C4#1458359811yescharacteristic
617C2—6881no—
618C2#1914021611yescharacteristic
619C2#1914482411yescharacteristic
620C2#1914488611yescharacteristic
621C2#1914522411yescharacteristic
622C2#1914526511yescharacteristic
623C2#1914565611yescharacteristic
624C2#1914570411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2327C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2327D43
hypocenterC43#29508
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #2327

Complements

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

NH ≅ G/Ntype
2. #19136077C2semidirect
4. #19135838C2semidirect
8. #19135288C2semidirect
9. #19135274C2semidirect
12. #19134863C2semidirect
13. #19134849C2semidirect
14. #19134347C2semidirect
15. C43×#2327C2semidirect
306. #2327D43semidirect
371. C43#29508semidirect

Maximal subgroups

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

subgroupindex
#191405552
#191360772
#191360092
#191358382
#191356782
#191354792
#191354522
#191352882
#191352742
#191349502
#191348632
#191348492
#191343472
C43×#23272
#2950843