Finite Group Databasebeta

← #25200124

Subgroups — #25200124

Order 11008.

766 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142933C211yesmaximal, characteristic
2C4×#13063305C211yesmaximal, characteristic
3#19136024C211yesmaximal, characteristic
4#19135801C211yesmaximal, characteristic
5#19135801C211yesmaximal, characteristic
6#19135606C211yesmaximal, characteristic
7#19135454C211yesmaximal, characteristic, complemented
8#19135327C211yesmaximal, characteristic, complemented
9#19135272C211yesmaximal, characteristic, complemented
10#19135269C211yesmaximal, characteristic, complemented
11#19135236C211yesmaximal, characteristic, complemented
12#19134935C211yesmaximal, characteristic, complemented
13#19134848C211yesmaximal, characteristic, complemented
14#19134352C211yesmaximal, characteristic
15C43×#1921C211yesmaximal, characteristic, complemented
16C22×Dic172C2211yescharacteristic
17C2×#13063305C2211yescharacteristic
18C2×#13063305C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C42×D43C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582805C2211yescharacteristic
34#14582804C2211yescharacteristic
35#14582804C2211yescharacteristic
36#14582798C2211yescharacteristic
37#14582795C2211yescharacteristic
38#14582786—21no—
39#14582785—21no—
40#14582784—21no—
41#14582773—21no—
42#14582770—21no—
43#14582761—21no—
44#14582756C2211yescharacteristic
45#14582756C2211yescharacteristic
46C4×C4⋊Dic43—21no—
47C4×(C2×D43)⋊C4—21no—
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43D411yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C2×Dic172—22no—
65C2×Dic172—22no—
66C2×Dic172—41no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063305—22no—
70#13063305—22no—
71#13063305—41no—
72#13063305—41no—
73C4×Dic86—41no—
74C4×Dic86—41no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43D411yescharacteristic
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90C42×D43—41no—
91C42×D43—41no—
92#13063258—22no—
93#13063258—41no—
94#13063250—22no—
95#13063250—41no—
96#13063248—22no—
97#13063248—22no—
98#13063248—22no—
99#13063248—41no—
100(C2×D43)⋊C8—22no—
101(C2×D43)⋊C8—22no—
102C8×Dic43—41no—
103C8×Dic43—41no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C42×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#107×C43—22no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43C2×D411yescharacteristic
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C2×C4×D43—21no—
142C2×C4×D43—21no—
143C2×C4×D43—21no—
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—22no—
148C2×C4×D43—41no—
149C2×C4×D43—41no—
150C2×C4×D43—41no—
151C2×C4×D43—41no—
152C2×C4×D43Q1614yescomplemented
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86#4112yes—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43#4112yes—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—42no—
179C4⋊C4×C43#4112yes—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—42no—
183(C2×D43)⋊C4—24no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—42no—
187C4⋊Dic43—24no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—42no—
193C4⋊Dic43—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4—42no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—41no—
199C4×Dic43—41no—
200C4×Dic43—42no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8#4112yes—
207Dic172—44no—
208C23×C43C22×D411yescharacteristic
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43—21no—
215C22×D43C2×Q1612yes—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
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×C43C2×Q1612yes—
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C2×C4×C43H(5,𝔽2)11yescharacteristic
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43C2×Q1612yes—
260C2×Dic43#13512yes—
261C4×D43—44no—
262C4×D43—44no—
263C4×D43—41no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—41no—
267Dic86—22no—
268Dic86—22no—
269Dic86—41no—
270Dic86—41no—
271Dic86—41no—
272Dic86—41no—
273Dic86—41no—
274Dic86—41no—
275C8×C43—22no—
276C8×C43—41no—
277C43⋊C8—22no—
278C43⋊C8—41no—
279#29462—431nomaximal, Sylow
280C22×C43#52511yescharacteristic
281C22×C43#53211yescharacteristic
282C22×C43#53411yescharacteristic
283C22×C43C22×Q1611yescharacteristic
284C22×C43C2×#13511yescharacteristic
285C22×C43#57511yescharacteristic
286C22×C43#57511yescharacteristic
287C2×D43—22no—
288C2×D43—22no—
289C2×D43—22no—
290C2×D43—41no—
291C2×D43—41no—
292C2×D43—41no—
293C2×D43—41no—
294C4×C43—22no—
295C4×C43—42no—
296C4×C43—41no—
297C4×C43—81no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43#55111yescharacteristic
301C4×C43#55311yescharacteristic
302C4×C43#55311yescharacteristic
303C4×C43#55911yescharacteristic
304Dic43—22no—
305Dic43—22no—
306Dic43—42no—
307Dic43—41no—
308Dic43—81no—
309Dic43—81no—
310Dic43—81no—
311#2855—431no—
312C4×C22⋊Q8—431no—
313#2076—431no—
314#2036—431no—
315#2036—431no—
316#2001—431no—
317#1969—431no—
318#1942—431no—
319#1933—431no—
320#1933—431no—
321#1928—431no—
322#1921D4311yescharacteristic, complemented
323#1878—431no—
324#1863—431no—
325C4×C22⋊C8—431no—
326C2×C43#260211yescharacteristic
327C2×C43#310211yescharacteristic
328C2×C43#310411yescharacteristic
329C2×C43#317011yescharacteristic
330C2×C43#318311yescharacteristic
331C2×C43#318911yescharacteristic
332C2×C43#319111yescharacteristic
333D43—42no—
334C22×Q16—431no—
335C2×C22⋊Q8—431no—
336C2×C22⋊Q8—431no—
337C2×C4×Q8—431no—
338C22×C42—431no—
339C2×#107—431no—
340C2×#107—431no—
341C2×#107C2×D4311yescharacteristic
342C2×#103—431no—
343C2×#103—431no—
344C2×#103—431no—
345C2×#103—431no—
346C2×#103—431no—
347C2×#103—431no—
348C2×C22⋊C8—431no—
349C2×C22⋊C8—431no—
350C2×C4×C8—431no—
351C2×C4×C8—431no—
352#391—431no—
353#391—431no—
354#391—431no—
355#389—431no—
356#389—431no—
357#389C2×D4311yescharacteristic
358#387—861no—
359#387—861no—
360#387—861no—
361#385—861no—
362#385—861no—
363#381—861no—
364#380—431no—
365#380—431no—
366C4×C4⋊C4—861no—
367C4×C4⋊C4C2×D4311yescharacteristic
368C4×C22⋊C4—861no—
369#340—431no—
370#340—431no—
371#340—431no—
372#340C2×D4311yescharacteristic
373#340C2×D4311yescharacteristic
374#340C2×D4311yescharacteristic
375#336—431no—
376#336C2×D4311yescharacteristic
377C43#2946211yescharacteristic, complemented, Sylow
378C22×Q8—431no—
379C22×Q8—431no—
380C23×C4—431no—
381C23×C4—431no—
382C23×C4—431no—
383C2×Q16—862no—
384C2×Q16—862no—
385C2×Q16—1721no—
386C22×C8—431no—
387C22×C8—431no—
388C22×C8C22×D4311yescharacteristic
389C22×C8C22×D4311yescharacteristic
390C22⋊Q8—862no—
391C22⋊Q8—862no—
392C22⋊Q8—1721no—
393C22⋊Q8—1721no—
394C4×Q8—1721no—
395C4×Q8—1721no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C42—21no—
413C2×C42—431no—
414C2×C42—431no—
415C2×C42—431no—
416C2×C42—861no—
417C2×C42—1721no—
418C2×C42—1721no—
419C2×C42C22×D4311yescharacteristic
420#107—22no—
421#107—862no—
422#107—1721no—
423#103—862no—
424#103—862no—
425#103—862no—
426#103—862no—
427#103—1721no—
428#103—1721no—
429C22⋊C8—862no—
430C22⋊C8—862no—
431C4×C8—1721no—
432C4×C8—1721no—
433#95—21no—
434#95—21no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445C24—431no—
446C2×Q8—432no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8—861no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—434no—
465C22×C4—431no—
466C22×C4—862no—
467C22×C4—861no—
468C22×C4—861no—
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—1721no—
478C22×C4—1721no—
479C22×C4—1721no—
480C22×C4—1721no—
481C22×C4D4×D4311yescharacteristic
482C22×C4D4×D4311yescharacteristic
483C22×C4C23×D4311yescharacteristic
484Q16—1724no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—432no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8#1062189812yes—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—42no—
505C4⋊C4—864no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—1722no—
511C4⋊C4—1722no—
512C4⋊C4—1722no—
513C4⋊C4—1722no—
514C4⋊C4#1062190212yes—
515C22⋊C4—864no—
516C22⋊C4—1722no—
517C22⋊C4—1722no—
518C22⋊C4—1722no—
519C42—21no—
520C42—21no—
521C42—42no—
522C42—861no—
523C42—861no—
524C42—1721no—
525C42—1721no—
526C42—1722no—
527C23—432no—
528C23—861no—
529C23—861no—
530C23—861no—
531C23—861no—
532C23—861no—
533C23—861no—
534C23C2×D4×D4311yescharacteristic
535Q8—862no—
536Q8—862no—
537Q8—1721no—
538Q8—1721no—
539Q8—1721no—
540Q8—1721no—
541Q8—1721no—
542Q8—1721no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—432no—
561C2×C4—432no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—862no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—1724no—
571C2×C4—1724no—
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—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4Q16×D4312yes—
588C2×C4#41×D4311yescharacteristic
589C2×C4#41×D4311yescharacteristic
590C2×C4C2×#1062189811yescharacteristic
591C2×C4C2×#1062190211yescharacteristic
592C2×C4#1306337111yescharacteristic
593C2×C4#1306337111yescharacteristic
594C8—22no—
595C8—41no—
596C8—862no—
597C8—1721no—
598C22—862no—
599C22—862no—
600C22—862no—
601C22—1721no—
602C22—1721no—
603C22—1721no—
604C22—1721no—
605C22#1458341211yescharacteristic
606C22#1458344611yescharacteristic
607C22#1458346011yescharacteristic
608C22C2×Q16×D4311yescharacteristic
609C22#135×D4311yescharacteristic
610C22#1458369511yescharacteristic
611C22#1458369511yescharacteristic
612C4—22no—
613C4—42no—
614C4—41no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—862no—
619C4—862no—
620C4—3441no—
621C4—3441no—
622C4—3441no—
623C4—1721no—
624C4—1722no—
625C4#1458357311yescharacteristic
626C4#1458360011yescharacteristic
627C4#1458360211yescharacteristic
628C4#1458363411yescharacteristic
629C2—1722no—
630C2#1914020511yescharacteristic
631C2#1914461811yescharacteristic
632C2#1914463611yescharacteristic
633C2#1914517811yescharacteristic
634C2#1914532211yescharacteristic
635C2#1914536911yescharacteristic
636C2#1914538611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1921C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1921D43
hypocenterC43#29462
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
7. #19135454C2semidirect
8. #19135327C2semidirect
9. #19135272C2semidirect
10. #19135269C2semidirect
11. #19135236C2semidirect
12. #19134935C2semidirect
13. #19134848C2semidirect
15. C43×#1921C2semidirect
152. C2×C4×D43Q16semidirect
322. #1921D43semidirect
377. C43#29462semidirect

Maximal subgroups

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

subgroupindex
#191429332
C4×#130633052
#191360242
#191358012
#191356062
#191354542
#191353272
#191352722
#191352692
#191352362
#191349352
#191348482
#191343522
C43×#19212
#2946243