Finite Group Databasebeta

← #25118681

Subgroups — #25118681

Order 11008.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144379C211yesmaximal, characteristic
2#19143541C211yesmaximal, characteristic, complemented
3#19143161C211yesmaximal, characteristic
4#19135574C211yesmaximal, characteristic, complemented
5#19135367C211yesmaximal, characteristic, complemented
6#19135346C211yesmaximal, characteristic, complemented
7#19135340C211yesmaximal, characteristic, complemented
8#19135195C211yesmaximal, characteristic, complemented
9#19135192C211yesmaximal, characteristic, complemented
10#19134868C211yesmaximal, characteristic
11#19134451C211yesmaximal, characteristic, complemented
12#19134442C211yesmaximal, characteristic
13#19134430C211yesmaximal, characteristic
14#19134407C211yesmaximal, characteristic
15C43×#1866C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17#14583452C2211yescharacteristic
18#41×Dic43C2211yescharacteristic
19#14583208C411yescharacteristic, complemented
20#14583204C411yescharacteristic, complemented
21#14583201C411yescharacteristic, complemented
22#14583197C411yescharacteristic, complemented
23#14583192C411yescharacteristic, complemented
24#14583187C411yescharacteristic, complemented
25#14583182C411yescharacteristic, complemented
26#14583177C411yescharacteristic, complemented
27#14583028—21no—
28#14583028—21no—
29#14583026—21no—
30#14583023—21no—
31C2×#13063260C2211yescharacteristic
32#14582937C2211yescharacteristic
33#14582935C2211yescharacteristic
34#14582927—21no—
35#14582927C2211yescharacteristic
36#14582927C2211yescharacteristic
37#14582925—21no—
38#14582925C2211yescharacteristic
39#14582922—21no—
40#14582922C2211yescharacteristic
41C2×Dic43⋊C8—21no—
42C2×Dic43⋊C8C2211yescharacteristic
43C2×Dic43⋊C8C2211yescharacteristic
44C2×#13063252C2211yescharacteristic
45#14582895C2211yescharacteristic
46#14582855C2211yescharacteristic
47#14582854C2211yescharacteristic
48M16×Dic43C2211yescharacteristic
49C2×#13063235C2211yescharacteristic
50C2×C8×Dic43C2211yescharacteristic
51#14582745C2211yescharacteristic
52#14582664C2211yescharacteristic
53#14582663C2211yescharacteristic
54#14582660C2211yescharacteristic
55#14582660C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582659C2211yescharacteristic
58#14582658C2211yescharacteristic
59#14582654C2211yescharacteristic
60C2×#131×C43C2211yescharacteristic
61C2×#108×C43C2211yescharacteristic
62C43×#424C2211yescharacteristic
63C2×#104×C43C2211yescharacteristic
64C43×#416C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#336C2211yescharacteristic
67#13063332—22no—
68#13063332—41no—
69C2×#10621877—21no—
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C22×C43⋊C8—21no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063324C2×C411yescharacteristic
76#13063324C2×C411yescharacteristic
77#13063316C2×C411yescharacteristic
78#13063316C2×C411yescharacteristic
79#13063302—21no—
80#13063302—21no—
81Q8×Dic43C2×C411yescharacteristic
82Q8×Dic43C2×C411yescharacteristic
83C4×Dic86—21no—
84C4×Dic86—21no—
85D4×Dic43—21no—
86D4×Dic43—21no—
87D4×Dic43C2×C411yescharacteristic
88D4×Dic43C2×C411yescharacteristic
89#13063284—21no—
90#13063284C2311yescharacteristic
91#13063284C2311yescharacteristic
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063260—41no—
96#13063259C2×C411yescharacteristic
97#13063259C2×C411yescharacteristic
98#13063258C2×C411yescharacteristic
99#13063258C2×C411yescharacteristic
100#13063257C2×C411yescharacteristic
101#13063257C2×C411yescharacteristic
102#13063256C2×C411yescharacteristic
103#13063256C2×C411yescharacteristic
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8C2×C411yescharacteristic
113Dic43⋊C8C2×C411yescharacteristic
114Dic43⋊C8C2×C411yescharacteristic
115Dic43⋊C8C2×C411yescharacteristic
116Dic43⋊C8D411yescharacteristic
117Dic43⋊C8D411yescharacteristic
118Dic43⋊C8D411yescharacteristic
119Dic43⋊C8D411yescharacteristic
120#13063252Q814yescomplemented
121#13063249C2×C411yescharacteristic
122#13063249C2×C411yescharacteristic
123#13063246C2×C411yescharacteristic
124#13063246C2×C411yescharacteristic
125#13063236—21no—
126#13063235—21no—
127#13063235—21no—
128#13063235—41no—
129C4×C43⋊C8—21no—
130C8×Dic43—21no—
131C8×Dic43—21no—
132C8×Dic43—41no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C2×#41×C43C2311yescharacteristic
136#131×C43—22no—
137#131×C43—41no—
138C2×M16×C43—21no—
139C2×M16×C43C2311yescharacteristic
140C2×M16×C43C2311yescharacteristic
141C22×C8×C43—21no—
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144#117×C43C2311yescharacteristic
145C2×C42×C43C2311yescharacteristic
146#108×C43—41no—
147C4⋊C8×C43—21no—
148C4⋊C8×C43—21no—
149#104×C43—22no—
150#103×C43C2×C411yescharacteristic
151#103×C43C2×C411yescharacteristic
152#102×C43C2×C411yescharacteristic
153#102×C43C2×C411yescharacteristic
154#41×C43—21no—
155#41×C43—21no—
156#41×C43C2×Q812yes—
157#41×C43#4112yes—
158C2×Q8×C43C22×C411yescharacteristic
159C2×D4×C43—21no—
160C2×D4×C43C22×C411yescharacteristic
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43C2411yescharacteristic
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43#4111yescharacteristic
168C22×Dic43#4111yescharacteristic
169C2×Dic86—21no—
170C2×Dic86—21no—
171M16×C43—21no—
172M16×C43—21no—
173M16×C43—21no—
174M16×C43—21no—
175M16×C43—42no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—42no—
183C2×C8×C43C22×C411yescharacteristic
184C2×C8×C43C22×C411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43C2×D411yescharacteristic
187C4⋊C4×C43C22×C411yescharacteristic
188C4⋊C4×C43C22×C411yescharacteristic
189C22⋊C4×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—21no—
193C22⋊Dic43—21no—
194C22⋊Dic43—21no—
195C22⋊Dic43—21no—
196C22⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43C22×C411yescharacteristic
202C4⋊Dic43C22×C411yescharacteristic
203C4⋊Dic43C22×C411yescharacteristic
204C4⋊Dic43C22×C411yescharacteristic
205Dic43⋊C4—21no—
206Dic43⋊C4—21no—
207Dic43⋊C4—21no—
208Dic43⋊C4—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43C22×C411yescharacteristic
215C4×Dic43C22×C411yescharacteristic
216C4×Dic43C2×D411yescharacteristic
217C4×Dic43C2×D411yescharacteristic
218C4×Dic43C2×Q812yes—
219#10621877—21no—
220#10621877—21no—
221#10621877—21no—
222#10621877—42no—
223#10621877C2×Q812yes—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—42no—
231C2×C43⋊C8C22×C411yescharacteristic
232C2×C43⋊C8C22×C411yescharacteristic
233C2×C43⋊C8C2×D411yescharacteristic
234C2×C43⋊C8C2×D411yescharacteristic
235C23×C43—21no—
236C23×C43C2×#4111yescharacteristic
237Q8×C43—21no—
238Q8×C43C4×Q812yes—
239D4×C43—22no—
240D4×C43—22no—
241D4×C43—21no—
242D4×C43C4×Q812yes—
243C2×C4×C43—21no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43C23×C411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×Q811yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C2×C4×C432−1+411yescharacteristic
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—22no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—42no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—81no—
268C2×Dic43C4×D411yescharacteristic
269C2×Dic43C4×D411yescharacteristic
270C2×Dic43C4×D411yescharacteristic
271C2×Dic43C4×D411yescharacteristic
272Dic86—42no—
273Dic86—81no—
274C8×C43—21no—
275C8×C43—21no—
276C8×C43—21no—
277C8×C43—21no—
278C8×C43—41no—
279C8×C43—41no—
280C43⋊C8—21no—
281C43⋊C8—21no—
282C43⋊C8—21no—
283C43⋊C8—21no—
284C43⋊C8—22no—
285C43⋊C8—41no—
286#22984—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—22no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43C2×C4×D411yescharacteristic
293C22×C43#55211yescharacteristic
294C22×C43#55411yescharacteristic
295C4×C43—22no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—81no—
299C4×C43C2×C4×Q811yescharacteristic
300C4×C43#52011yescharacteristic
301C4×C43#54611yescharacteristic
302C4×C43D4×Q811yescharacteristic
303Dic43—21no—
304Dic43—21no—
305Dic43—21no—
306Dic43—21no—
307Dic43—42no—
308Dic43—41no—
309Dic43—41no—
310Dic43—41no—
311Dic43—41no—
312#3076—431no—
313#2962—431no—
314#2906—431no—
315#1995—431no—
316#1950—431no—
317#1946—431no—
318#1945—431no—
319#1922—431no—
320#1922—431no—
321#1866—431no—
322#1866D4311yescharacteristic
323#1768—431no—
324#1765—431no—
325#1764—431no—
326#1759—431no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43—42no—
330C2×C43#236011yescharacteristic
331C2×C43#295511yescharacteristic
332C2×C43#295711yescharacteristic
333C2×#131—431no—
334C2×#131C2×D4311yescharacteristic
335#533—431no—
336C4×#41—431no—
337#479—431no—
338#479—431no—
339#478—431no—
340#478—431no—
341#477—431no—
342#476—431no—
343#475—431no—
344#474—431no—
345#446—861no—
346#446—861no—
347#446—861no—
348C8×Q8—861no—
349C2×#108—431no—
350C2×#108C2×D4311yescharacteristic
351#427—431no—
352#427—431no—
353#424—431no—
354#424—431no—
355#424—431no—
356#424—861no—
357#424—861no—
358#424C2×D4311yescharacteristic
359#423—431no—
360#423—861no—
361C2×C4⋊C8—431no—
362C2×C4⋊C8—431no—
363C2×C4⋊C8—861no—
364C2×#104—431no—
365C2×#104C2×D4311yescharacteristic
366#416—431no—
367#416C2×D4311yescharacteristic
368#405—431no—
369#405—431no—
370C4×M16—431no—
371C2×#97—431no—
372C2×C4×C8—431no—
373#376—431no—
374#341—431no—
375#341—431no—
376#339—431no—
377#339—431no—
378#339—431no—
379#339—431no—
380#339—431no—
381#339C2×D4311yescharacteristic
382#336—431no—
383#336C2×D4311yescharacteristic
384C43#2298411yescharacteristic, complemented, Sylow
385C2×#41C22×D4311yescharacteristic
386#131—22no—
387#131—41no—
388#131—862no—
389#131—1721no—
390C2×M16—21no—
391C2×M16—431no—
392C2×M16—431no—
393C2×M16—861no—
394C2×M16C22×D4311yescharacteristic
395C2×M16C22×D4311yescharacteristic
396C22×C8—21no—
397C22×C8—431no—
398C22×C8—431no—
399C22×C8—861no—
400C22×C8C22×D4311yescharacteristic
401C22×C8C22×D4311yescharacteristic
402C4⋊Q8—431no—
403C4⋊Q8—431no—
404#125—431no—
405#125—431no—
406C22⋊Q8—861no—
407C22⋊Q8—861no—
408C4×Q8—431no—
409C4×Q8—431no—
410C4×Q8—861no—
411C4×Q8—861no—
412C4×D4—431no—
413C4×D4—431no—
414C4×D4—861no—
415C4×D4—861no—
416#117—431no—
417#117—431no—
418#117—861no—
419#117C22×D4311yescharacteristic
420C2×C42—431no—
421C2×C42—431no—
422C2×C42—861no—
423C2×C42C22×D4311yescharacteristic
424#108—41no—
425#108—1721no—
426#107—431no—
427#107—431no—
428#107—431no—
429#107—431no—
430#106—431no—
431#106—431no—
432#106—431no—
433#106—431no—
434C4⋊C8—21no—
435C4⋊C8—21no—
436C4⋊C8—431no—
437C4⋊C8—431no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—431no—
442C4⋊C8—431no—
443C4⋊C8—431no—
444C4⋊C8—861no—
445C4⋊C8—861no—
446C4⋊C8—861no—
447C4⋊C8—861no—
448C4⋊C8—861no—
449C4⋊C8—861no—
450C4⋊C8—861no—
451C4⋊C8—861no—
452#104—22no—
453#104—434no—
454#103—431no—
455#103—431no—
456#103C4×D4311yescharacteristic
457#103C4×D4311yescharacteristic
458#102—431no—
459#102—431no—
460#102C4×D4311yescharacteristic
461#102C4×D4311yescharacteristic
462#97—861no—
463#97—861no—
464#97—861no—
465#97—1721no—
466C4×C8—861no—
467C4×C8—861no—
468C4×C8—861no—
469C4×C8—1721no—
470#95—861no—
471#95—861no—
472#41—21no—
473#41—21no—
474#41#1062190012yes—
475#41Q8×D4312yes—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8C2×C4×D4311yescharacteristic
479C2×D4—21no—
480C2×D4C2×C4×D4311yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4C23×D4311yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—42no—
494M16—432no—
495M16—861no—
496M16—861no—
497M16—861no—
498M16—1722no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—42no—
506C2×C8—431no—
507C2×C8—431no—
508C2×C8—431no—
509C2×C8—431no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—1722no—
517C2×C8C2×C4×D4311yescharacteristic
518C2×C8C2×C4×D4311yescharacteristic
519C2×C8D4×D4311yescharacteristic
520C2×C8D4×D4311yescharacteristic
521C4⋊C4—431no—
522C4⋊C4—431no—
523C4⋊C4—431no—
524C4⋊C4—431no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4C2×C4×D4311yescharacteristic
534C4⋊C4C2×C4×D4311yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—861no—
537C22⋊C4—861no—
538C22⋊C4—861no—
539C22⋊C4—861no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—432no—
548C42—861no—
549C42—861no—
550C42—861no—
551C42—861no—
552C42—861no—
553C23—21no—
554C23#41×D4311yescharacteristic
555Q8—21no—
556Q8—3441no—
557Q8—1722no—
558Q8#1306329012yes—
559D4—22no—
560D4—22no—
561D4—21no—
562D4#1306329012yes—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—431no—
572C2×C4—431no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—862no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—3441no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1722no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4C22×C4×D4311yescharacteristic
587C2×C4C2×D4×D4311yescharacteristic
588C2×C4C2×Q8×D4311yescharacteristic
589C2×C4C2×#1062190011yescharacteristic
590C2×C4#1306337011yescharacteristic
591C2×C4#1306337211yescharacteristic
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—862no—
599C8—861no—
600C8—861no—
601C8—861no—
602C8—861no—
603C8—1721no—
604C22—21no—
605C22—21no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22C4×D4×D4311yescharacteristic
610C22#1458358611yescharacteristic
611C22#1458360311yescharacteristic
612C4—22no—
613C4—41no—
614C4—41no—
615C4—81no—
616C4—861no—
617C4—861no—
618C4—861no—
619C4—861no—
620C4—1722no—
621C4—1721no—
622C4—1721no—
623C4—1721no—
624C4—1721no—
625C4C2×#1306329011yescharacteristic
626C4#1458337811yescharacteristic
627C4#1458353611yescharacteristic
628C4#1458356211yescharacteristic
629C2—21no—
630C2—21no—
631C2—42no—
632C2#1913759511yescharacteristic
633C2#1914349311yescharacteristic
634C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1866C2
socleC22×C43C2×C4×D4
prime radicalC2×#41×C43C23
cosocleC22×C4×C43C24
hypercenter#1866D43
hypocenterC43#22984
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
2. #19143541C2semidirect
4. #19135574C2semidirect
5. #19135367C2semidirect
6. #19135346C2semidirect
7. #19135340C2semidirect
8. #19135195C2semidirect
9. #19135192C2semidirect
11. #19134451C2semidirect
19. #14583208C4semidirect
20. #14583204C4semidirect
21. #14583201C4semidirect
22. #14583197C4semidirect
23. #14583192C4semidirect
24. #14583187C4semidirect
25. #14583182C4semidirect
26. #14583177C4semidirect
120. #13063252Q8semidirect
384. C43#22984semidirect

Maximal subgroups

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

subgroupindex
#191443792
#191435412
#191431612
#191355742
#191353672
#191353462
#191353402
#191351952
#191351922
#191348682
#191344512
#191344422
#191344302
#191344072
C43×#18662
#2298443