Finite Group Databasebeta

← #25103994

Subgroups — #25103994

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#19144506C211yesmaximal, characteristic
2#19143296C211yesmaximal, characteristic
3#19143011C211yesmaximal, characteristic, complemented
4#19135246C211yesmaximal, characteristic, complemented
5#19135245C211yesmaximal, characteristic, complemented
6#19135193C211yesmaximal, characteristic, complemented
7#19135192C211yesmaximal, characteristic, complemented
8#19134894C211yesmaximal, characteristic
9#19134801C211yesmaximal, characteristic, complemented
10#19134693C211yesmaximal, characteristic, complemented
11#19134479C211yesmaximal, characteristic, complemented
12#19134475C211yesmaximal, characteristic, complemented
13#19134430C211yesmaximal, characteristic, complemented
14#19134380C211yesmaximal, characteristic, complemented
15C43×#1765C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C2×M16×D43C2211yescharacteristic
18#14583406C2211yescharacteristic
19#117×D43C2211yescharacteristic
20#14583239C411yescharacteristic, complemented
21#14583238C411yescharacteristic, complemented
22#14583233C411yescharacteristic, complemented
23#14583228C411yescharacteristic, complemented
24#14583222C411yescharacteristic, complemented
25#14583221C411yescharacteristic, complemented
26#14583216C411yescharacteristic, complemented
27#14583211C411yescharacteristic, complemented
28#14582975—21no—
29#14582975—21no—
30#14582970—21no—
31#14582970—21no—
32C2×#13063261C2211yescharacteristic
33C2×#13063260C2211yescharacteristic
34#14582937C2211yescharacteristic
35#14582935C2211yescharacteristic
36#14582927C2211yescharacteristic
37C2×#13063252C2211yescharacteristic
38#14582895C2211yescharacteristic
39#14582866C2211yescharacteristic
40#14582862C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42#14582857C2211yescharacteristic
43#14582856—21no—
44#14582855C2211yescharacteristic
45#14582854C2211yescharacteristic
46#14582854C2211yescharacteristic
47#14582853—21no—
48#14582851—21no—
49C4×#10621872—21no—
50C2×C8×Dic43C2211yescharacteristic
51C4×(C2×D43)⋊C4C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582660C2211yescharacteristic
54#14582660C2211yescharacteristic
55#14582659C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582658C2211yescharacteristic
58#14582654C2211yescharacteristic
59#14582653C2211yescharacteristic
60C2×#131×C43C2211yescharacteristic
61C2×#104×C43C2211yescharacteristic
62C43×#416C2211yescharacteristic
63C43×#405C2211yescharacteristic
64C2×#97×C43C2211yescharacteristic
65C43×#341C2211yescharacteristic
66C43×#339C2211yescharacteristic
67C22×C4×D43C2311yescharacteristic
68C2×#10621877C2311yescharacteristic
69C2×#10621877C2311yescharacteristic
70C2×#10621872—21no—
71C2×#10621872—22no—
72C2×#10621872—22no—
73C2×#10621872D411yescharacteristic
74C2×#10621872D411yescharacteristic
75C2×#10621872D411yescharacteristic
76C2×#10621872D411yescharacteristic
77M16×D43—22no—
78M16×D43—22no—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C2×C8×D43—21no—
82#13063306—21no—
83#13063301C2×C411yescharacteristic
84#13063301C2×C411yescharacteristic
85#13063296C2×C411yescharacteristic
86#13063296C2×C411yescharacteristic
87#13063293—21no—
88C4×C22⋊D43—21no—
89C4×C22⋊D43—21no—
90#13063284C2311yescharacteristic
91#13063284C2311yescharacteristic
92#13063283C2×C411yescharacteristic
93#13063283C2×C411yescharacteristic
94#13063282—21no—
95#13063281—21no—
96C4⋊C4×D43C2×C411yescharacteristic
97C4⋊C4×D43C2×C411yescharacteristic
98C2×(C2×D43)⋊C4—21no—
99C22⋊C4×D43—21no—
100C2×C4×Dic43C2311yescharacteristic
101C42×D43—21no—
102#13063261—22no—
103#13063260—22no—
104#13063259C2×C411yescharacteristic
105#13063259C2×C411yescharacteristic
106#13063258C2×C411yescharacteristic
107#13063258C2×C411yescharacteristic
108#13063257C2×C411yescharacteristic
109#13063257C2×C411yescharacteristic
110#13063256C2×C411yescharacteristic
111#13063256C2×C411yescharacteristic
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114#13063252—22no—
115#13063249C2×C411yescharacteristic
116#13063249C2×C411yescharacteristic
117#13063246C2×C411yescharacteristic
118#13063246C2×C411yescharacteristic
119C22⋊(C43⋊C8)—21no—
120C22⋊(C43⋊C8)—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8C2×C411yescharacteristic
124(C2×D43)⋊C8C2×C411yescharacteristic
125(C2×D43)⋊C8C2×C411yescharacteristic
126(C2×D43)⋊C8C2×C411yescharacteristic
127#13063236—21no—
128#13063235—21no—
129#13063235—21no—
130#13063235—21no—
131C4×C43⋊C8—21no—
132C8×Dic43—21no—
133C8×Dic43—21no—
134C8×Dic43—22no—
135C8×Dic43—21no—
136C43⋊#95—21no—
137C2×#41×C43C2311yescharacteristic
138#131×C43—22no—
139#131×C43—22no—
140C2×M16×C43—21no—
141C2×M16×C43C2311yescharacteristic
142C2×M16×C43C2311yescharacteristic
143C22×C8×C43—21no—
144C22×C8×C43C2311yescharacteristic
145C22×C8×C43C2311yescharacteristic
146#117×C43C2311yescharacteristic
147C2×C42×C43C2311yescharacteristic
148#104×C43—22no—
149#103×C43C2×C411yescharacteristic
150#103×C43C2×C411yescharacteristic
151#102×C43C2×C411yescharacteristic
152#102×C43C2×C411yescharacteristic
153#97×C43—21no—
154#97×C43—22no—
155C4×C8×C43—21no—
156C23×D43#4111yescharacteristic
157#41×C43—21no—
158#41×C43—21no—
159#41×C43—21no—
160#41×C43—21no—
161C2×Q8×C43C22×C411yescharacteristic
162C2×D4×C43—21no—
163C2×D4×C43C22×C411yescharacteristic
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43C2411yescharacteristic
167C2×C22⋊D43—21no—
168C2×C22⋊D43—21no—
169C22×Dic43—21no—
170C22×Dic43#4111yescharacteristic
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43C22×C411yescharacteristic
178C2×C4×D43C22×C411yescharacteristic
179C2×C4×D43C2×D411yescharacteristic
180C2×C4×D43C2×D411yescharacteristic
181M16×C43—21no—
182M16×C43—21no—
183M16×C43—21no—
184M16×C43—42no—
185M16×C43#4112yes—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—42no—
191C2×C8×C43C22×C411yescharacteristic
192C2×C8×C43C22×C411yescharacteristic
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×D411yescharacteristic
195C2×C8×C43#4112yes—
196C2×C8×C43#4112yes—
197C4⋊C4×C43C22×C411yescharacteristic
198C4⋊C4×C43C22×C411yescharacteristic
199C22⋊C4×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43—21no—
203C22⋊Dic43—21no—
204C22⋊Dic43—21no—
205C22⋊Dic43—21no—
206C22⋊Dic43—21no—
207(C2×D43)⋊C4—21no—
208(C2×D43)⋊C4—21no—
209(C2×D43)⋊C4—21no—
210(C2×D43)⋊C4—21no—
211(C2×D43)⋊C4—42no—
212C4⋊Dic43C22×C411yescharacteristic
213C4⋊Dic43C22×C411yescharacteristic
214C4⋊Dic43C22×C411yescharacteristic
215C4⋊Dic43C22×C411yescharacteristic
216Dic43⋊C4—21no—
217Dic43⋊C4—21no—
218Dic43⋊C4—21no—
219Dic43⋊C4—21no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43—21no—
226#10621877—21no—
227#10621877—21no—
228#10621877—21no—
229#10621877#4112yes—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8C22×C411yescharacteristic
237C2×C43⋊C8C22×C411yescharacteristic
238C2×C43⋊C8C2×D411yescharacteristic
239C2×C43⋊C8C2×D411yescharacteristic
240#10621872—24no—
241#10621872—22no—
242#10621872—22no—
243#10621872—22no—
244#10621872—22no—
245C8×D43—24no—
246C23×C43—21no—
247C23×C43C2×#4111yescharacteristic
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43C4×D411yescharacteristic
253C22×D43C4×D411yescharacteristic
254Q8×C43—21no—
255Q8×C43—21no—
256D4×C43—21no—
257D4×C43—21no—
258D4×C43—41no—
259D4×C43—41no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43C23×C411yescharacteristic
269C2×C4×C43C22×D411yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C43C2×#4111yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C22⋊D43—81no—
275C22⋊D43—81no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—22no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43C4×D411yescharacteristic
286C2×Dic43C4×D411yescharacteristic
287C4×D43—21no—
288C4×D43—21no—
289C4×D43—21no—
290C4×D43—21no—
291C4×D43—21no—
292C4×D43—21no—
293C4×D43—21no—
294C4×D43—21no—
295C4×D43—81no—
296C4×D43—81no—
297C8×C43—21no—
298C8×C43—21no—
299C8×C43—22no—
300C8×C43—41no—
301C8×C43#12312yes—
302C8×C43#12312yes—
303C43⋊C8—21no—
304C43⋊C8—21no—
305C43⋊C8—21no—
306C43⋊C8—21no—
307C43⋊C8—22no—
308C43⋊C8—41no—
309#21594—431nomaximal, Sylow
310C22×C43—21no—
311C22×C43—21no—
312C22×C43—41no—
313C22×C43—41no—
314C22×C43—41no—
315C22×C43C2×C4×D411yescharacteristic
316C22×C43#52911yescharacteristic
317C22×C43#52911yescharacteristic
318C2×D43—21no—
319C2×D43—21no—
320C2×D43—21no—
321C2×D43—21no—
322C2×D43—21no—
323C2×D43—21no—
324C2×D43—81no—
325C2×D43—81no—
326C4×C43—41no—
327C4×C43—41no—
328C4×C43—41no—
329C4×C43—81no—
330C4×C43C4×#4111yescharacteristic
331C4×C43C4×#4111yescharacteristic
332C4×C43C2×#12311yescharacteristic
333C4×C43#52511yescharacteristic
334Dic43—21no—
335Dic43—21no—
336Dic43—42no—
337Dic43—41no—
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#1826—431no—
351#1773—431no—
352#1772—431no—
353#1765D4311yescharacteristic, complemented
354#1764—431no—
355#1753—431no—
356C2×C43—21no—
357C2×C43—21no—
358C2×C43—81no—
359C2×C43C4×#12311yescharacteristic
360C2×C43#295611yescharacteristic
361C2×C43#295711yescharacteristic
362D43—41no—
363D43—41no—
364C2×#131C2×D4311yescharacteristic
365C22×M16—431no—
366C22×M16—431no—
367#525—431no—
368C2×#117—431no—
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×#104C2×D4311yescharacteristic
388#416—431no—
389#416C2×D4311yescharacteristic
390#408—431no—
391#407—431no—
392C2×C22⋊C8—431no—
393#405—431no—
394#405—431no—
395#405—431no—
396#405—431no—
397#405—861no—
398#405—861no—
399#405C2×D4311yescharacteristic
400C4×M16—861no—
401C4×M16—861no—
402C2×#97C2×D4311yescharacteristic
403C2×C4×C8—431no—
404C4×C22⋊C4—431no—
405#341—431no—
406#341C2×D4311yescharacteristic
407#339—431no—
408#339—431no—
409#339—431no—
410#339—431no—
411#339—431no—
412#339C2×D4311yescharacteristic
413#336—431no—
414#336—431no—
415C43#2159411yescharacteristic, complemented, Sylow
416C2×#41C22×D4311yescharacteristic
417C23×C4—431no—
418#131—22no—
419#131—22no—
420C2×M16—21no—
421C2×M16—431no—
422C2×M16—431no—
423C2×M16—431no—
424C2×M16—431no—
425C2×M16—431no—
426C2×M16—431no—
427C2×M16—861no—
428C2×M16—862no—
429C2×M16—862no—
430C2×M16—862no—
431C2×M16—862no—
432C2×M16C22×D4311yescharacteristic
433C2×M16C22×D4311yescharacteristic
434C22×C8—21no—
435C22×C8—431no—
436C22×C8—431no—
437C22×C8—861no—
438C22×C8C22×D4311yescharacteristic
439C22×C8C22×D4311yescharacteristic
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—431no—
449#117—431no—
450#117—431no—
451#117—431no—
452#117—861no—
453#117—861no—
454#117C22×D4311yescharacteristic
455C2×C4⋊C4—431no—
456C2×C4⋊C4—431no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C42—431no—
460C2×C42—861no—
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—22no—
475#104—862no—
476#103—431no—
477#103—431no—
478#103C4×D4311yescharacteristic
479#103C4×D4311yescharacteristic
480#102—431no—
481#102—431no—
482#102C4×D4311yescharacteristic
483#102C4×D4311yescharacteristic
484C22⋊C8—431no—
485C22⋊C8—431no—
486C22⋊C8—431no—
487C22⋊C8—431no—
488C22⋊C8—861no—
489C22⋊C8—861no—
490C22⋊C8—861no—
491C22⋊C8—861no—
492#97—21no—
493#97—22no—
494#97—861no—
495#97—861no—
496#97—861no—
497#97—861no—
498C4×C8—21no—
499C4×C8—861no—
500C4×C8—861no—
501C4×C8—862no—
502C4×C8—861no—
503C4×C8—861no—
504#95—861no—
505C24—431no—
506#41—21no—
507#41—21no—
508#41—21no—
509#41—21no—
510C2×Q8C2×C4×D4311yescharacteristic
511C2×D4—21no—
512C2×D4—861no—
513C2×D4—861no—
514C2×D4C2×C4×D4311yescharacteristic
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—431no—
518C22×C4—431no—
519C22×C4—431no—
520C22×C4—431no—
521C22×C4—431no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4C23×D4311yescharacteristic
530M16—21no—
531M16—21no—
532M16—21no—
533M16—42no—
534M16—432no—
535M16—864no—
536M16—861no—
537M16—862no—
538M16—862no—
539M16—862no—
540M16—862no—
541M16—861no—
542M16—861no—
543M16#1062189812yes—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—42no—
549C2×C8—431no—
550C2×C8—431no—
551C2×C8—431no—
552C2×C8—431no—
553C2×C8—864no—
554C2×C8—861no—
555C2×C8—861no—
556C2×C8—861no—
557C2×C8—861no—
558C2×C8—861no—
559C2×C8—861no—
560C2×C8C2×C4×D4311yescharacteristic
561C2×C8C2×C4×D4311yescharacteristic
562C2×C8#1062189812yes—
563C2×C8D4×D4311yescharacteristic
564C2×C8D4×D4311yescharacteristic
565C2×C8#1062190012yes—
566C4⋊C4—431no—
567C4⋊C4—431no—
568C4⋊C4—431no—
569C4⋊C4—431no—
570C4⋊C4—861no—
571C4⋊C4—861no—
572C4⋊C4—861no—
573C4⋊C4—861no—
574C4⋊C4C2×C4×D4311yescharacteristic
575C4⋊C4C2×C4×D4311yescharacteristic
576C22⋊C4—21no—
577C22⋊C4—861no—
578C22⋊C4—861no—
579C22⋊C4—861no—
580C22⋊C4—861no—
581C22⋊C4—861no—
582C22⋊C4—861no—
583C22⋊C4—861no—
584C22⋊C4—861no—
585C22⋊C4—1722no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—861no—
590C42—861no—
591C42—861no—
592C42—861no—
593C42—861no—
594C42—861no—
595C23—21no—
596C23—431no—
597C23—431no—
598C23—861no—
599C23—861no—
600C23—1721no—
601C23—1721no—
602C23#41×D4311yescharacteristic
603Q8—21no—
604Q8—21no—
605D4—21no—
606D4—21no—
607D4—41no—
608D4—41no—
609D4—3441no—
610D4—3441no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—431no—
620C2×C4—431no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—861no—
631C2×C4—862no—
632C2×C4—861no—
633C2×C4—861no—
634C2×C4—861no—
635C2×C4—861no—
636C2×C4—3441no—
637C2×C4—3441no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4C22×C4×D4311yescharacteristic
641C2×C4C2×D4×D4311yescharacteristic
642C2×C4#41×D4311yescharacteristic
643C2×C4C2×#1062190011yescharacteristic
644C2×C4C2×#1062189811yescharacteristic
645C2×C4C2×#1062189811yescharacteristic
646C8—21no—
647C8—21no—
648C8—22no—
649C8—41no—
650C8—861no—
651C8—861no—
652C8—861no—
653C8—861no—
654C8—862no—
655C8—1721no—
656C8#1306330712yes—
657C8#1306330712yes—
658C22—21no—
659C22—21no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—861no—
664C22—861no—
665C22—861no—
666C22—861no—
667C22—861no—
668C22—861no—
669C22—3441no—
670C22—3441no—
671C22C4×D4×D4311yescharacteristic
672C22#1458342711yescharacteristic
673C22#1458343111yescharacteristic
674C4—41no—
675C4—41no—
676C4—41no—
677C4—81no—
678C4—861no—
679C4—861no—
680C4—1722no—
681C4—1721no—
682C4—1721no—
683C4—1721no—
684C4—1721no—
685C4C4×#1062190011yescharacteristic
686C4C4×#1062189811yescharacteristic
687C4C2×#1306330711yescharacteristic
688C4#1458340811yescharacteristic
689C2—21no—
690C2—21no—
691C2—81no—
692C2—1721no—
693C2—1721no—
694C2C4×#1306330711yescharacteristic
695C2#1914350311yescharacteristic
696C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1765C2
socleC22×C43C2×C4×D4
prime radical#14583406C22
cosocleC22×C4×C43C24
hypercenter#1765D43
hypocenterC43#21594
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1765

Complements

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

NH ≅ G/Ntype
3. #19143011C2semidirect
4. #19135246C2semidirect
5. #19135245C2semidirect
6. #19135193C2semidirect
7. #19135192C2semidirect
9. #19134801C2semidirect
10. #19134693C2semidirect
11. #19134479C2semidirect
12. #19134475C2semidirect
13. #19134430C2semidirect
14. #19134380C2semidirect
15. C43×#1765C2semidirect
20. #14583239C4semidirect
21. #14583238C4semidirect
22. #14583233C4semidirect
23. #14583228C4semidirect
24. #14583222C4semidirect
25. #14583221C4semidirect
26. #14583216C4semidirect
27. #14583211C4semidirect
353. #1765D43semidirect
415. C43#21594semidirect

Maximal subgroups

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

subgroupindex
#191445062
#191432962
#191430112
#191352462
#191352452
#191351932
#191351922
#191348942
#191348012
#191346932
#191344792
#191344752
#191344302
#191343802
C43×#17652
#2159443