Finite Group Databasebeta

← #25103989

Subgroups — #25103989

Order 11008.

768 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144508C211yesmaximal, characteristic
2#19143294C211yesmaximal, characteristic
3#19143014C211yesmaximal, characteristic, complemented
4#19135241C211yesmaximal, characteristic, complemented
5#19135241C211yesmaximal, characteristic, complemented
6#19135192C211yesmaximal, characteristic, complemented
7#19135192C211yesmaximal, characteristic, complemented
8#19134895C211yesmaximal, characteristic
9#19134799C211yesmaximal, characteristic, complemented
10#19134478C211yesmaximal, characteristic, complemented
11#19134473C211yesmaximal, characteristic, complemented
12#19134436C211yesmaximal, characteristic, complemented
13#19134429C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15C43×#1826C211yesmaximal, characteristic, complemented
16C2×#13063333C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19#14583410C2211yescharacteristic
20#14583240C411yescharacteristic, complemented
21#14583240C411yescharacteristic, complemented
22#14583234C411yescharacteristic, complemented
23#14583229C411yescharacteristic, complemented
24#14583223C411yescharacteristic, complemented
25#14583223C411yescharacteristic, complemented
26#14583217C411yescharacteristic, complemented
27#14583212C411yescharacteristic, complemented
28#14582974—21no—
29#14582974—21no—
30#14582973—21no—
31#14582973—21no—
32C2×#13063260C2211yescharacteristic
33C2×#13063260C2211yescharacteristic
34#14582935C2211yescharacteristic
35#14582935C2211yescharacteristic
36#14582927C2211yescharacteristic
37C2×#13063253C2211yescharacteristic
38C2×#13063253C2211yescharacteristic
39#14582893C2211yescharacteristic
40#14582893C2211yescharacteristic
41#14582867C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43#14582857C2211yescharacteristic
44#14582855—21no—
45#14582855—21no—
46#14582855C2211yescharacteristic
47#14582855C2211yescharacteristic
48#14582855C2211yescharacteristic
49#14582855C2211yescharacteristic
50C4×#10621877—21no—
51C4×#10621877—21no—
52C2×#13063236C2211yescharacteristic
53C2×C4×C43⋊C8C2211yescharacteristic
54#14582663C2211yescharacteristic
55#14582663C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582659C2211yescharacteristic
58#14582654C2211yescharacteristic
59#14582654C2211yescharacteristic
60C2×#117×C43C2211yescharacteristic
61C43×#407C2211yescharacteristic
62C4×C22⋊C4×C43C2211yescharacteristic
63C43×#339C2211yescharacteristic
64C43×#339C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#339C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063333—22no—
69#13063333—22no—
70C2×#10621877—21no—
71C2×#10621877—22no—
72C2×#10621877—22no—
73C2×#10621877—22no—
74C2×#10621877—22no—
75C2×#10621877D411yescharacteristic
76C2×#10621877D411yescharacteristic
77C2×#10621877D411yescharacteristic
78C2×#10621877D411yescharacteristic
79C2×#10621877C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81C2×#10621872—21no—
82C22×C43⋊C8—21no—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C2×C8×D43—21no—
88#13063308—21no—
89#13063304C2×C411yescharacteristic
90#13063304C2×C411yescharacteristic
91#13063299C2×C411yescharacteristic
92#13063299C2×C411yescharacteristic
93#13063294—21no—
94C4×C22⋊D43—21no—
95C4×C22⋊D43—21no—
96#13063284C2311yescharacteristic
97#13063260—22no—
98#13063260—22no—
99#13063258C2×C411yescharacteristic
100#13063258C2×C411yescharacteristic
101#13063258C2×C411yescharacteristic
102#13063258C2×C411yescharacteristic
103#13063256C2×C411yescharacteristic
104#13063256C2×C411yescharacteristic
105#13063256C2×C411yescharacteristic
106#13063256C2×C411yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109#13063253—22no—
110#13063253—22no—
111#13063248C2×C411yescharacteristic
112#13063248C2×C411yescharacteristic
113#13063248C2×C411yescharacteristic
114#13063248C2×C411yescharacteristic
115#13063245C2×C411yescharacteristic
116#13063245C2×C411yescharacteristic
117#13063245C2×C411yescharacteristic
118#13063245C2×C411yescharacteristic
119C22⋊(C43⋊C8)C2×C411yescharacteristic
120C22⋊(C43⋊C8)C2×C411yescharacteristic
121C22⋊(C43⋊C8)C2×C411yescharacteristic
122C22⋊(C43⋊C8)C2×C411yescharacteristic
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125#13063236—21no—
126#13063236—21no—
127#13063236—21no—
128#13063236—21no—
129#13063236—22no—
130#13063235—21no—
131C4×C43⋊C8—21no—
132C4×C43⋊C8—21no—
133C4×C43⋊C8—21no—
134C4×C43⋊C8—21no—
135C4×C43⋊C8—22no—
136C8×Dic43—21no—
137C23×C4×C43C2311yescharacteristic
138C2×M16×C43C2311yescharacteristic
139C2×M16×C43C2311yescharacteristic
140#117×C43—21no—
141#117×C43—21no—
142#117×C43C2×C411yescharacteristic
143#117×C43C2×C411yescharacteristic
144#117×C43C2311yescharacteristic
145#117×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2×C411yescharacteristic
147C2×C4⋊C4×C43C2×C411yescharacteristic
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43—21no—
150C2×C42×C43—21no—
151C2×C42×C43C2311yescharacteristic
152C2×C42×C43C2311yescharacteristic
153C22⋊C8×C43—21no—
154C22⋊C8×C43—21no—
155#95×C43—21no—
156C24×C43#4111yescharacteristic
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43C22×C411yescharacteristic
166C22×C4×C43C22×C411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43#4111yescharacteristic
170C22×C4×C43C2411yescharacteristic
171C2×C22⋊D43—21no—
172C2×C22⋊D43—21no—
173C2×C22⋊D43—21no—
174#10621898—21no—
175#10621898—21no—
176#10621898—21no—
177#10621898—21no—
178C2×D172C22×C411yescharacteristic
179C2×C4×D43—21no—
180C2×Dic86C22×C411yescharacteristic
181M16×C43—21no—
182M16×C43—21no—
183M16×C43—21no—
184M16×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43C22×C411yescharacteristic
190C4⋊C4×C43C22×C411yescharacteristic
191C4⋊C4×C43C22×C411yescharacteristic
192C4⋊C4×C43C22×C411yescharacteristic
193C22⋊C4×C43—21no—
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—21no—
197C22⋊C4×C43—42no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—21no—
205C42×C43—21no—
206C22⋊Dic43—21no—
207C22⋊Dic43—21no—
208C22⋊Dic43—21no—
209(C2×D43)⋊C4—21no—
210(C2×D43)⋊C4—21no—
211C4⋊Dic43C22×C411yescharacteristic
212C4⋊Dic43C22×C411yescharacteristic
213Dic43⋊C4—21no—
214Dic43⋊C4—21no—
215C4×Dic43—21no—
216#10621877—24no—
217#10621877—21no—
218#10621877—21no—
219#10621877—22no—
220#10621877—22no—
221#10621877—22no—
222#10621877—22no—
223#10621877#4112yes—
224#10621877#4112yes—
225C2×C43⋊C8—24no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8C22×C411yescharacteristic
235C2×C43⋊C8C22×C411yescharacteristic
236C2×C43⋊C8C22×C411yescharacteristic
237C2×C43⋊C8C22×C411yescharacteristic
238C2×C43⋊C8C2×D411yescharacteristic
239C2×C43⋊C8C2×D411yescharacteristic
240C2×C43⋊C8C2×D411yescharacteristic
241C2×C43⋊C8C2×D411yescharacteristic
242C2×C43⋊C8#4112yes—
243C2×C43⋊C8#4112yes—
244#10621872—42no—
245C8×D43—42no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43C4×D411yescharacteristic
251C23×C43C4×D411yescharacteristic
252C23×C43C2×#4111yescharacteristic
253C22×D43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—22no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—81no—
275C2×C4×C43—81no—
276C2×C4×C43C4×D411yescharacteristic
277C2×C4×C43C4×D411yescharacteristic
278C2×C4×C43C23×C411yescharacteristic
279C2×C4×C43C22×D411yescharacteristic
280C2×C4×C43C2×#4111yescharacteristic
281C2×C4×C43C2×#4111yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C22⋊D43—41no—
285C22⋊D43—41no—
286C22⋊D43—81no—
287C22⋊D43—81no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291D172—21no—
292D172—21no—
293C4×D43—41no—
294C4×D43—41no—
295Dic86—21no—
296Dic86—21no—
297C8×C43—41no—
298C8×C43—41no—
299C43⋊C8—21no—
300C43⋊C8—21no—
301C43⋊C8—21no—
302C43⋊C8—21no—
303C43⋊C8—21no—
304C43⋊C8—21no—
305C43⋊C8—22no—
306C43⋊C8—22no—
307C43⋊C8#12312yes—
308C43⋊C8#12312yes—
309#21594—431nomaximal, Sylow
310C22×C43—21no—
311C22×C43—21no—
312C22×C43—21no—
313C22×C43—21no—
314C22×C43—21no—
315C22×C43—21no—
316C22×C43—21no—
317C22×C43—21no—
318C22×C43—81no—
319C22×C43—81no—
320C22×C43C2×C4×D411yescharacteristic
321C22×C43#52911yescharacteristic
322C22×C43#52911yescharacteristic
323C2×D43—41no—
324C2×D43—41no—
325C2×D43—41no—
326C4×C43—21no—
327C4×C43—21no—
328C4×C43—42no—
329C4×C43—41no—
330C4×C43—41no—
331C4×C43—41no—
332C4×C43—41no—
333C4×C43—81no—
334C4×C43C4×#4111yescharacteristic
335C4×C43C4×#4111yescharacteristic
336C4×C43C2×#12311yescharacteristic
337C4×C43#52511yescharacteristic
338Dic43—41no—
339Dic43—41no—
340Dic43—41no—
341#3091—431no—
342#2930—431no—
343#2873—431no—
344#1929—431no—
345#1929—431no—
346#1922—431no—
347#1922—431no—
348#1871—431no—
349#1855—431no—
350#1826D4311yescharacteristic, complemented
351#1773—431no—
352#1772—431no—
353#1765—431no—
354#1764—431no—
355#1753—431no—
356C2×C43—21no—
357C2×C43—21no—
358C2×C43—41no—
359C2×C43—41no—
360C2×C43C4×#12311yescharacteristic
361C2×C43#295611yescharacteristic
362C2×C43#295711yescharacteristic
363D43—81no—
364C2×#131—431no—
365C22×M16—431no—
366C22×M16—431no—
367#525—431no—
368C2×#117C2×D4311yescharacteristic
369#485—431no—
370#485—431no—
371#484—431no—
372#483—431no—
373#482—431no—
374#482—431no—
375#481—431no—
376#480—431no—
377#436—861no—
378#436—861no—
379#435—861no—
380#435—861no—
381C2×#108—431no—
382C2×#108—431no—
383#427—431no—
384#427—431no—
385#424—431no—
386C2×#104—431no—
387C2×#104—431no—
388#416—431no—
389#416—431no—
390#408—431no—
391#407C2×D4311yescharacteristic
392C2×C22⋊C8—431no—
393#405—431no—
394#405—431no—
395#405—431no—
396#405—431no—
397#405—431no—
398#405—861no—
399#405—861no—
400C4×M16—861no—
401C4×M16—861no—
402C2×#97—431no—
403C2×C4×C8—431no—
404C4×C22⋊C4C2×D4311yescharacteristic
405#341—431no—
406#341—431no—
407#339—431no—
408#339—431no—
409#339C2×D4311yescharacteristic
410#339C2×D4311yescharacteristic
411#339C2×D4311yescharacteristic
412#339C2×D4311yescharacteristic
413#336—431no—
414#336—431no—
415C43#2159411yescharacteristic, complemented, Sylow
416C2×#41—431no—
417C23×C4C22×D4311yescharacteristic
418#131—862no—
419#131—862no—
420C2×M16—431no—
421C2×M16—431no—
422C2×M16—431no—
423C2×M16—431no—
424C2×M16—431no—
425C2×M16—431no—
426C2×M16—861no—
427C2×M16—862no—
428C2×M16—862no—
429C2×M16—862no—
430C2×M16—862no—
431C2×M16—861no—
432C2×M16C22×D4311yescharacteristic
433C2×M16C22×D4311yescharacteristic
434C22×C8—431no—
435C22×C8—431no—
436C22×C8—431no—
437C22×C8—431no—
438C22×C8—861no—
439C22×C8—861no—
440#123—861no—
441C22⋊Q8—431no—
442C22⋊Q8—431no—
443#121—431no—
444#121—431no—
445#120—861no—
446C4×D4—861no—
447C4×D4—861no—
448#117—21no—
449#117—21no—
450#117—431no—
451#117C4×D4311yescharacteristic
452#117C4×D4311yescharacteristic
453#117C22×D4311yescharacteristic
454#117C22×D4311yescharacteristic
455C2×C4⋊C4C4×D4311yescharacteristic
456C2×C4⋊C4C4×D4311yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C42—21no—
460C2×C42C22×D4311yescharacteristic
461C2×C42C22×D4311yescharacteristic
462#108—862no—
463#108—862no—
464#107—431no—
465#107—431no—
466#107—431no—
467#107—431no—
468#106—431no—
469#106—431no—
470#106—431no—
471#106—431no—
472C4⋊C8—861no—
473C4⋊C8—861no—
474#104—862no—
475#104—862no—
476#103—431no—
477#103—431no—
478#103—431no—
479#103—431no—
480#102—431no—
481#102—431no—
482#102—431no—
483#102—431no—
484C22⋊C8—21no—
485C22⋊C8—21no—
486C22⋊C8—431no—
487C22⋊C8—431no—
488C22⋊C8—431no—
489C22⋊C8—431no—
490C22⋊C8—861no—
491C22⋊C8—861no—
492#97—862no—
493#97—861no—
494#97—861no—
495#97—861no—
496#97—861no—
497#97—861no—
498C4×C8—862no—
499C4×C8—861no—
500C4×C8—861no—
501C4×C8—861no—
502C4×C8—861no—
503C4×C8—861no—
504#95—21no—
505C24#1062190011yescharacteristic
506#41—861no—
507#41—861no—
508#41—861no—
509#41—861no—
510C2×Q8—431no—
511C2×D4—431no—
512C2×D4—861no—
513C2×D4—861no—
514C2×D4—861no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—861no—
524C22×C4C2×C4×D4311yescharacteristic
525C22×C4C2×C4×D4311yescharacteristic
526C22×C4D4×D4311yescharacteristic
527C22×C4D4×D4311yescharacteristic
528C22×C4#1062190011yescharacteristic
529C22×C4C23×D4311yescharacteristic
530M16—21no—
531M16—21no—
532M16—21no—
533M16—21no—
534M16—432no—
535M16—432no—
536M16—862no—
537M16—862no—
538M16—862no—
539M16—862no—
540M16—864no—
541M16—861no—
542M16—861no—
543M16—1722no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—431no—
547C2×C8—431no—
548C2×C8—432no—
549C2×C8—432no—
550C2×C8—431no—
551C2×C8—431no—
552C2×C8—431no—
553C2×C8—431no—
554C2×C8—431no—
555C2×C8—431no—
556C2×C8—864no—
557C2×C8—861no—
558C2×C8—861no—
559C2×C8—861no—
560C2×C8—861no—
561C2×C8—861no—
562C2×C8—861no—
563C2×C8—861no—
564C2×C8—861no—
565C2×C8—1722no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—431no—
569C4⋊C4—431no—
570C4⋊C4—861no—
571C4⋊C4—861no—
572C4⋊C4C2×C4×D4311yescharacteristic
573C4⋊C4C2×C4×D4311yescharacteristic
574C4⋊C4C2×C4×D4311yescharacteristic
575C4⋊C4C2×C4×D4311yescharacteristic
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—42no—
581C22⋊C4—861no—
582C22⋊C4—861no—
583C22⋊C4—861no—
584C22⋊C4—861no—
585C22⋊C4—861no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—861no—
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—861no—
600C23(C22⋊D43)⋊C411yescharacteristic
601C23(C22⋊D43)⋊C411yescharacteristic
602C23C2×#1062190011yescharacteristic
603Q8—861no—
604Q8—861no—
605D4—861no—
606D4—861no—
607D4—3441no—
608D4—3441no—
609D4—1721no—
610D4—1721no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—81no—
632C2×C4—81no—
633C2×C4—861no—
634C2×C4—861no—
635C2×C4—861no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4(C22⋊D43)⋊C411yescharacteristic
639C2×C4(C22⋊D43)⋊C411yescharacteristic
640C2×C4C22×C4×D4311yescharacteristic
641C2×C4C2×D4×D4311yescharacteristic
642C2×C4#41×D4311yescharacteristic
643C2×C4#41×D4311yescharacteristic
644C2×C4#41×D4311yescharacteristic
645C2×C4#41×D4311yescharacteristic
646C8—41no—
647C8—41no—
648C8—432no—
649C8—432no—
650C8—861no—
651C8—861no—
652C8—861no—
653C8—861no—
654C8—861no—
655C8—861no—
656C8—862no—
657C8—862no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—81no—
667C22—81no—
668C22—1721no—
669C22—1721no—
670C22—1721no—
671C22C2×(C22⋊D43)⋊C411yescharacteristic
672C22#1458342611yescharacteristic
673C22#1458342611yescharacteristic
674C4—21no—
675C4—21no—
676C4—42no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—81no—
682C4—1721no—
683C4—1721no—
684C4—1721no—
685C4#1458336711yescharacteristic
686C4#1458336711yescharacteristic
687C4#123×D4311yescharacteristic
688C4#1458340711yescharacteristic
689C2—21no—
690C2—21no—
691C2—41no—
692C2—41no—
693C2—3441no—
694C2#1913711211yescharacteristic
695C2#1914350111yescharacteristic
696C2#1914350811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1826C2
socleC22×C43C2×C4×D4
prime radical#14583410C22
cosocleC22×C4×C43C24
hypercenter#1826D43
hypocenterC43#21594
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
3. #19143014C2semidirect
4. #19135241C2semidirect
5. #19135241C2semidirect
6. #19135192C2semidirect
7. #19135192C2semidirect
9. #19134799C2semidirect
10. #19134478C2semidirect
11. #19134473C2semidirect
12. #19134436C2semidirect
13. #19134429C2semidirect
14. #19134379C2semidirect
15. C43×#1826C2semidirect
20. #14583240C4semidirect
21. #14583240C4semidirect
22. #14583234C4semidirect
23. #14583229C4semidirect
24. #14583223C4semidirect
25. #14583223C4semidirect
26. #14583217C4semidirect
27. #14583212C4semidirect
350. #1826D43semidirect
415. C43#21594semidirect

Maximal subgroups

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

subgroupindex
#191445082
#191432942
#191430142
#191352412
#191351922
#191348952
#191347992
#191344782
#191344732
#191344362
#191344292
#191343792
C43×#18262
#2159443