Finite Group Databasebeta

← #25200726

Subgroups — #25200726

Order 11008.

788 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137320C211yesmaximal, characteristic
2#19136076C211yesmaximal, characteristic, complemented
3#19136013C211yesmaximal, characteristic, complemented
4#19135829C211yesmaximal, characteristic
5#19135682C211yesmaximal, characteristic
6#19135479C211yesmaximal, characteristic, complemented
7#19135452C211yesmaximal, characteristic, complemented
8#19135291C211yesmaximal, characteristic, complemented
9#19135277C211yesmaximal, characteristic, complemented
10#19134932C211yesmaximal, characteristic, complemented
11#19134932C211yesmaximal, characteristic, complemented
12#19134855C211yesmaximal, characteristic, complemented
13#19134841C211yesmaximal, characteristic, complemented
14#19134347C211yesmaximal, characteristic, complemented
15C43×#2645C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063322C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063236C2211yescharacteristic
32C2×C4×C43⋊C8C2211yescharacteristic
33#14582801C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582777—21no—
36#14582777—21no—
37#14582777—21no—
38#14582777—21no—
39#14582765C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C43×#401—21no—
49C43×#400—21no—
50C43×#400—21no—
51C43×#400—21no—
52C43×#391C2211yescharacteristic
53C43×#391C2211yescharacteristic
54C43×#391C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#376C2211yescharacteristic
59C22×D172—21no—
60C22×D172—21no—
61C22×D172C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621884—22no—
69C2×#10621884—41no—
70C2×#10621884—41no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063322—22no—
76#13063322—22no—
77C4×D172—41no—
78C4×D172—41no—
79C4×D172—41no—
80C4×D172—41no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
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×(C2×D43)⋊C4—21no—
89#13063258—41no—
90#13063256—41no—
91#13063249—41no—
92#13063249—41no—
93#13063245—22no—
94#13063245—22no—
95#13063245—22no—
96#13063245—22no—
97#13063245—41no—
98#13063245—41no—
99#13063236—22no—
100C4×C43⋊C8—22no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C22×Q8×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×C42×C43C2311yescharacteristic
111C2×C42×C43C2311yescharacteristic
112C2×C42×C43C2311yescharacteristic
113#95×C43—21no—
114#95×C43—21no—
115#95×C43—21no—
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—
127C23×D43—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—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—21no—
146C22×Dic43—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—24no—
150C2×D172—24no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—81no—
160C2×D172—81no—
161C2×D172—81no—
162C2×D172—81no—
163C2×D172#4112yes—
164C2×D172#4112yes—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
167C2×C4×D43—81no—
168C2×C4×D43—81no—
169C2×C4×D43—81no—
170C2×C4×D43—81no—
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—81no—
178C4⋊C4×C43—81no—
179C4⋊C4×C43—81no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186#10621884—44no—
187#10621884—44no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—81no—
191(C2×D43)⋊C4—81no—
192(C2×D43)⋊C4—81no—
193(C2×D43)⋊C4—81no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
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×C43C22×D411yescharacteristic
211C22×D43—22no—
212C22×D43—22no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×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×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43H(5,𝔽2)11yescharacteristic
264C2×C4×C43H(5,𝔽2)11yescharacteristic
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271D172—22no—
272D172—22no—
273D172—22no—
274D172—22no—
275D172—41no—
276D172—41no—
277D172—41no—
278D172—41no—
279D172—84no—
280D172—84no—
281C4×D43—84no—
282C4×D43—84no—
283C43⋊C8—22no—
284C43⋊C8—22no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287#29504—431nomaximal, Sylow
288C22×C43#52511yescharacteristic
289C22×C43#53211yescharacteristic
290C22×C43#53511yescharacteristic
291C22×C43#57611yescharacteristic
292C22×C43#57711yescharacteristic
293C22×C43#57711yescharacteristic
294C22×C43#57711yescharacteristic
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—81no—
302C2×D43—81no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43—41no—
313C4×C43—41no—
314C4×C43—41no—
315C4×C43—81no—
316C4×C43—81no—
317C4×C43—81no—
318C4×C43—81no—
319C4×C43#55111yescharacteristic
320C4×C43#55111yescharacteristic
321C4×C43#55311yescharacteristic
322C4×C43#55311yescharacteristic
323Dic43—81no—
324Dic43—81no—
325#2645D4311yescharacteristic, complemented
326#2328—431no—
327#2085—431no—
328#2074—431no—
329#2041—431no—
330#2014—431no—
331#1973—431no—
332#1968—431no—
333#1936—431no—
334#1934—431no—
335#1877—431no—
336#1877—431no—
337#1864—431no—
338#1862—431no—
339#1746—431no—
340C2×C43#260311yescharacteristic
341C2×C43#311811yescharacteristic
342C2×C43#312311yescharacteristic
343C2×C43#317411yescharacteristic
344C2×C43#317911yescharacteristic
345C2×C43#322211yescharacteristic
346C2×C43#322411yescharacteristic
347D43—82no—
348D43—82no—
349C22×SD16—431no—
350C22×SD16—431no—
351C2×#127—431no—
352C2×C4×D4—431no—
353C2×C4×D4—431no—
354C2×#107—431no—
355C2×#106—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102—431no—
361C2×#102—431no—
362C2×#102—431no—
363C2×#102—431no—
364C2×#97—431no—
365C2×C4×C8—431no—
366#401—21no—
367#400—21no—
368#400—21no—
369#400—21no—
370#391C2×D4311yescharacteristic
371#391C2×D4311yescharacteristic
372#391C2×D4311yescharacteristic
373#390—431no—
374#390—431no—
375#389C2×D4311yescharacteristic
376#389C2×D4311yescharacteristic
377#389C2×D4311yescharacteristic
378#386—861no—
379#386—861no—
380#386—861no—
381#386—861no—
382#382—431no—
383#376C2×D4311yescharacteristic
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#336—431no—
389#336—431no—
390#336—431no—
391#336—431no—
392C43#2950411yescharacteristic, complemented, Sylow
393C22×Q8C22×D4311yescharacteristic
394C22×D4—431no—
395C22×D4—431no—
396C22×D4—861no—
397C22×D4—861no—
398C23×C4—861no—
399C23×C4—861no—
400C2×SD16—862no—
401C2×SD16—862no—
402C2×SD16—862no—
403C2×SD16—862no—
404C2×SD16—1721no—
405C2×SD16—1721no—
406C22×C8—431no—
407C22×C8—431no—
408C22×C8—431no—
409C22×C8—431no—
410#127—862no—
411#127—862no—
412C4×D4—1721no—
413C4×D4—1721no—
414C4×D4—1721no—
415C4×D4—1721no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C42C22×D4311yescharacteristic
431C2×C42C22×D4311yescharacteristic
432C2×C42C22×D4311yescharacteristic
433#107—1721no—
434#106—1721no—
435#103—1721no—
436#103—1721no—
437#102—862no—
438#102—862no—
439#102—862no—
440#102—862no—
441#102—1721no—
442#102—1721no—
443#97—862no—
444C4×C8—862no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—861no—
455#95—861no—
456#95C22⋊D4311yescharacteristic
457#95C22⋊D4311yescharacteristic
458#95C22⋊D4311yescharacteristic
459#95C22⋊D4311yescharacteristic
460C24—861no—
461C24—861no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×D4—432no—
469C2×D4—432no—
470C2×D4—864no—
471C2×D4—864no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—3441no—
483C2×D4—3441no—
484C2×D4—3441no—
485C2×D4—3441no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—3441no—
493C22×C4—3441no—
494C22×C4—3441no—
495C22×C4—3441no—
496C22×C4—1722no—
497C22×C4—1722no—
498C22×C4C2×C22⋊D4311yescharacteristic
499C22×C4C2×C22⋊D4311yescharacteristic
500C22×C4C2×C22⋊D4311yescharacteristic
501C22×C4C2×C22⋊D4311yescharacteristic
502C22×C4C2×C22⋊D4311yescharacteristic
503C22×C4C2×C22⋊D4311yescharacteristic
504C22×C4C23×D4311yescharacteristic
505SD16—1724no—
506SD16—1724no—
507C2×C8—432no—
508C2×C8—432no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—81no—
526C4⋊C4—81no—
527C4⋊C4—81no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C22⋊C4—3441no—
533C22⋊C4—3441no—
534C22⋊C4—3441no—
535C22⋊C4—3441no—
536C22⋊C4—1722no—
537C22⋊C4—1722no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C23—862no—
545C23—862no—
546C23—1721no—
547C23—1721no—
548C23—1721no—
549C23—1721no—
550C23—1721no—
551C23—1721no—
552C23—1721no—
553C23—1721no—
554C23—1721no—
555C23—1721no—
556C23—1721no—
557C23—1721no—
558C23C22×C22⋊D4311yescharacteristic
559Q8—41no—
560Q8—41no—
561Q8—41no—
562Q8—41no—
563D4—862no—
564D4—862no—
565D4—862no—
566D4—862no—
567D4—3444no—
568D4—3444no—
569D4—1721no—
570D4—1721no—
571D4—1721no—
572D4—1721no—
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—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—3444no—
604C2×C4—3444no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4#41×D4311yescharacteristic
612C2×C4#41×D4311yescharacteristic
613C2×C4#41×D4311yescharacteristic
614C2×C4#41×D4311yescharacteristic
615C2×C4#1306337111yescharacteristic
616C2×C4#1306337111yescharacteristic
617C8—862no—
618C8—862no—
619C8—1721no—
620C8—1721no—
621C22—3441no—
622C22—3441no—
623C22—3441no—
624C22—3441no—
625C22—3441no—
626C22—3441no—
627C22—3441no—
628C22—3441no—
629C22—1722no—
630C22—1722no—
631C22—1722no—
632C22—1722no—
633C22—1722no—
634C22—1722no—
635C22#1458340611yescharacteristic
636C22#1458344511yescharacteristic
637C22#1458346311yescharacteristic
638C22#1458370211yescharacteristic
639C22#1458370711yescharacteristic
640C22#1458370711yescharacteristic
641C22#1458370711yescharacteristic
642C4—41no—
643C4—41no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4—81no—
649C4—81no—
650C4—81no—
651C4—81no—
652C4—3441no—
653C4—3441no—
654C4#1458357411yescharacteristic
655C4#1458357411yescharacteristic
656C4#1458360011yescharacteristic
657C4#1458360011yescharacteristic
658C2—3442no—
659C2—3442no—
660C2#1914022411yescharacteristic
661C2#1914477311yescharacteristic
662C2#1914484211yescharacteristic
663C2#1914522411yescharacteristic
664C2#1914527211yescharacteristic
665C2#1914566111yescharacteristic
666C2#1914568311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2645C2
socleC23×C43C22×D4
prime radicalC2×#13063322C22
hypercenter#2645D43
hypocenterC43#29504
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #2645

Complements

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

NH ≅ G/Ntype
2. #19136076C2semidirect
3. #19136013C2semidirect
6. #19135479C2semidirect
7. #19135452C2semidirect
8. #19135291C2semidirect
9. #19135277C2semidirect
10. #19134932C2semidirect
11. #19134932C2semidirect
12. #19134855C2semidirect
13. #19134841C2semidirect
14. #19134347C2semidirect
15. C43×#2645C2semidirect
325. #2645D43semidirect
392. C43#29504semidirect

Maximal subgroups

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

subgroupindex
#191373202
#191360762
#191360132
#191358292
#191356822
#191354792
#191354522
#191352912
#191352772
#191349322
#191348552
#191348412
#191343472
C43×#26452
#2950443