Finite Group Databasebeta

← #25118659

Subgroups — #25118659

Order 11008.

720 conjugacy classes of subgroups.

The subgroup lattice has 640 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#19135570C211yesmaximal, characteristic, complemented
5#19135367C211yesmaximal, characteristic, complemented
6#19135341C211yesmaximal, characteristic, complemented
7#19135340C211yesmaximal, characteristic, complemented
8#19135195C211yesmaximal, characteristic, complemented
9#19135192C211yesmaximal, characteristic, complemented
10#19134868C211yesmaximal, characteristic
11#19134443C211yesmaximal, characteristic, complemented
12#19134435C211yesmaximal, characteristic
13#19134430C211yesmaximal, characteristic
14#104×Dic43C211yesmaximal, 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×C8×Dic43C2211yescharacteristic
50C2×C8×Dic43C2211yescharacteristic
51C42×Dic43C2211yescharacteristic
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×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97#13063260—41no—
98#13063259C2×C411yescharacteristic
99#13063259C2×C411yescharacteristic
100#13063258C2×C411yescharacteristic
101#13063258C2×C411yescharacteristic
102#13063257C2×C411yescharacteristic
103#13063257C2×C411yescharacteristic
104#13063256C2×C411yescharacteristic
105#13063256C2×C411yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8C2×C411yescharacteristic
115Dic43⋊C8C2×C411yescharacteristic
116Dic43⋊C8C2×C411yescharacteristic
117Dic43⋊C8C2×C411yescharacteristic
118Dic43⋊C8D411yescharacteristic
119Dic43⋊C8D411yescharacteristic
120Dic43⋊C8D411yescharacteristic
121Dic43⋊C8D411yescharacteristic
122#13063252Q814yescomplemented
123#13063249C2×C411yescharacteristic
124#13063249C2×C411yescharacteristic
125#13063246C2×C411yescharacteristic
126#13063246C2×C411yescharacteristic
127#13063236—21no—
128#13063235—21no—
129#13063235—21no—
130C4×C43⋊C8—21no—
131C8×Dic43—21no—
132C8×Dic43—21no—
133C8×Dic43—41no—
134C8×Dic43—41no—
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—24no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—42no—
216C4×Dic43C22×C411yescharacteristic
217C4×Dic43C22×C411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219C4×Dic43C2×D411yescharacteristic
220C4×Dic43C2×Q812yes—
221#10621877—21no—
222#10621877—21no—
223#10621877—21no—
224#10621877—42no—
225#10621877C2×Q812yes—
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—42no—
233C2×C43⋊C8C22×C411yescharacteristic
234C2×C43⋊C8C22×C411yescharacteristic
235C2×C43⋊C8C2×D411yescharacteristic
236C2×C43⋊C8C2×D411yescharacteristic
237C23×C43—21no—
238C23×C43C2×#4111yescharacteristic
239Q8×C43—21no—
240Q8×C43C4×Q812yes—
241D4×C43—22no—
242D4×C43—22no—
243D4×C43—21no—
244D4×C43C4×Q812yes—
245C2×C4×C43—21no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43C23×C411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C22×Q811yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C2×C4×C432−1+411yescharacteristic
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—41no—
268C2×Dic43—42no—
269C2×Dic43—81no—
270C2×Dic43C4×D411yescharacteristic
271C2×Dic43C4×D411yescharacteristic
272C2×Dic43C4×D411yescharacteristic
273C2×Dic43C4×D411yescharacteristic
274Dic86—42no—
275Dic86—81no—
276C8×C43—21no—
277C8×C43—21no—
278C8×C43—21no—
279C8×C43—21no—
280C8×C43—41no—
281C8×C43—41no—
282C43⋊C8—21no—
283C43⋊C8—21no—
284C43⋊C8—21no—
285C43⋊C8—21no—
286C43⋊C8—22no—
287C43⋊C8—41no—
288#22982—431nomaximal, Sylow
289C22×C43—21no—
290C22×C43—21no—
291C22×C43—22no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43C2×C4×D411yescharacteristic
295C22×C43#55211yescharacteristic
296C22×C43#55411yescharacteristic
297C4×C43—22no—
298C4×C43—42no—
299C4×C43—41no—
300C4×C43—41no—
301C4×C43C2×C4×Q811yescharacteristic
302C4×C43#52011yescharacteristic
303C4×C43#54611yescharacteristic
304C4×C43D4×Q811yescharacteristic
305Dic43—24no—
306Dic43—21no—
307Dic43—21no—
308Dic43—21no—
309Dic43—41no—
310Dic43—41no—
311Dic43—41no—
312Dic43—41no—
313Dic43#44312yes—
314#3076—431no—
315#2962—431no—
316#2906—431no—
317#1994—431no—
318#1950—431no—
319#1945—431no—
320#1945—431no—
321#1922—431no—
322#1922—431no—
323#1866—431no—
324#1866D4311yescharacteristic
325C4×C4⋊C8—431no—
326#1764—431no—
327#1764—431no—
328C4×#104—431no—
329C2×C43—21no—
330C2×C43—21no—
331C2×C43—42no—
332C2×C43#236011yescharacteristic
333C2×C43C2×#44311yescharacteristic
334C2×C43#295611yescharacteristic
335C2×#131—431no—
336C2×#131C2×D4311yescharacteristic
337#533—431no—
338C4×#41—431no—
339#479—431no—
340#479—431no—
341#478—431no—
342#478—431no—
343#477—431no—
344#476—431no—
345#475—431no—
346#474—431no—
347#446—861no—
348#446—861no—
349#446—861no—
350C8×Q8—861no—
351C2×#108—431no—
352C2×#108C2×D4311yescharacteristic
353#427—431no—
354#427—431no—
355#424—431no—
356#424—431no—
357#424—431no—
358#424—861no—
359#424—861no—
360#424C2×D4311yescharacteristic
361#423—431no—
362#423—861no—
363C2×C4⋊C8—431no—
364C2×C4⋊C8—431no—
365C2×C4⋊C8—861no—
366C2×#104—431no—
367C2×#104C2×D4311yescharacteristic
368#416—431no—
369#416C2×D4311yescharacteristic
370#405—431no—
371#405—431no—
372C4×M16—431no—
373C2×C4×C8—431no—
374C2×C4×C8—431no—
375C43—431no—
376#341—431no—
377#341—431no—
378#339—431no—
379#339—431no—
380#339—431no—
381#339—431no—
382#339—431no—
383#339C2×D4311yescharacteristic
384#336—431no—
385#336C2×D4311yescharacteristic
386C43#2298211yescharacteristic, complemented, Sylow
387C2×#41C22×D4311yescharacteristic
388#131—22no—
389#131—41no—
390#131—862no—
391#131—1721no—
392C2×M16—21no—
393C2×M16—431no—
394C2×M16—431no—
395C2×M16—861no—
396C2×M16C22×D4311yescharacteristic
397C2×M16C22×D4311yescharacteristic
398C22×C8—21no—
399C22×C8—431no—
400C22×C8—431no—
401C22×C8—861no—
402C22×C8C22×D4311yescharacteristic
403C22×C8C22×D4311yescharacteristic
404C4⋊Q8—431no—
405C4⋊Q8—431no—
406#125—431no—
407#125—431no—
408C22⋊Q8—861no—
409C22⋊Q8—861no—
410C4×Q8—431no—
411C4×Q8—431no—
412C4×Q8—861no—
413C4×Q8—861no—
414C4×D4—431no—
415C4×D4—431no—
416C4×D4—861no—
417C4×D4—861no—
418#117—431no—
419#117—431no—
420#117—861no—
421#117C22×D4311yescharacteristic
422C2×C42—431no—
423C2×C42—431no—
424C2×C42—861no—
425C2×C42—861no—
426C2×C42—861no—
427C2×C42C22×D4311yescharacteristic
428#108—41no—
429#108—1721no—
430#107—431no—
431#107—431no—
432#107—431no—
433#107—431no—
434#106—431no—
435#106—431no—
436#106—431no—
437#106—431no—
438C4⋊C8—21no—
439C4⋊C8—21no—
440C4⋊C8—431no—
441C4⋊C8—431no—
442C4⋊C8—431no—
443C4⋊C8—431no—
444C4⋊C8—431no—
445C4⋊C8—431no—
446C4⋊C8—431no—
447C4⋊C8—431no—
448C4⋊C8—861no—
449C4⋊C8—861no—
450C4⋊C8—861no—
451C4⋊C8—861no—
452C4⋊C8—861no—
453C4⋊C8—861no—
454C4⋊C8—861no—
455C4⋊C8—861no—
456#104—22no—
457#104—434no—
458#103—431no—
459#103—431no—
460#103C4×D4311yescharacteristic
461#103C4×D4311yescharacteristic
462#102—431no—
463#102—431no—
464#102C4×D4311yescharacteristic
465#102C4×D4311yescharacteristic
466#97—861no—
467#97—861no—
468#97—861no—
469C4×C8—861no—
470C4×C8—861no—
471C4×C8—861no—
472C4×C8—1721no—
473C4×C8—1721no—
474#41—21no—
475#41—21no—
476#41#1062190012yes—
477#41Q8×D4312yes—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8C2×C4×D4311yescharacteristic
481C2×D4—21no—
482C2×D4C2×C4×D4311yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4C23×D4311yescharacteristic
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—42no—
496M16—432no—
497M16—861no—
498M16—861no—
499M16—861no—
500M16—1722no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—42no—
508C2×C8—431no—
509C2×C8—431no—
510C2×C8—431no—
511C2×C8—431no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—1722no—
519C2×C8C2×C4×D4311yescharacteristic
520C2×C8C2×C4×D4311yescharacteristic
521C2×C8D4×D4311yescharacteristic
522C2×C8D4×D4311yescharacteristic
523C4⋊C4—431no—
524C4⋊C4—431no—
525C4⋊C4—431no—
526C4⋊C4—431no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4C2×C4×D4311yescharacteristic
536C4⋊C4C2×C4×D4311yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—861no—
539C22⋊C4—861no—
540C22⋊C4—861no—
541C22⋊C4—861no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—432no—
550C42—861no—
551C42—861no—
552C42—864no—
553C42—861no—
554C42—861no—
555C42—861no—
556C42—1722no—
557C23—21no—
558C23#41×D4311yescharacteristic
559Q8—21no—
560Q8—3441no—
561Q8—1722no—
562Q8#1306329012yes—
563D4—22no—
564D4—22no—
565D4—21no—
566D4#1306329012yes—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—431no—
576C2×C4—431no—
577C2×C4—431no—
578C2×C4—431no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—3441no—
588C2×C4—1722no—
589C2×C4—1721no—
590C2×C4C22×C4×D4311yescharacteristic
591C2×C4C2×D4×D4311yescharacteristic
592C2×C4C2×Q8×D4311yescharacteristic
593C2×C4C2×#1062190011yescharacteristic
594C2×C4#1306337011yescharacteristic
595C2×C4#1306337211yescharacteristic
596C8—21no—
597C8—21no—
598C8—21no—
599C8—21no—
600C8—41no—
601C8—41no—
602C8—862no—
603C8—861no—
604C8—861no—
605C8—861no—
606C8—861no—
607C8—1721no—
608C22—21no—
609C22—21no—
610C22—22no—
611C22—41no—
612C22—41no—
613C22C4×D4×D4311yescharacteristic
614C22#1458358611yescharacteristic
615C22#1458360311yescharacteristic
616C4—22no—
617C4—42no—
618C4—41no—
619C4—41no—
620C4—432no—
621C4—864no—
622C4—861no—
623C4—861no—
624C4—861no—
625C4—1721no—
626C4—1721no—
627C4—1721no—
628C4—1721no—
629C4C2×#1306329011yescharacteristic
630C4#1458337811yescharacteristic
631C4#1458353611yescharacteristic
632C4#1458356211yescharacteristic
633C2—21no—
634C2—21no—
635C2—42no—
636C2#1913759511yescharacteristic
637C2#443×D4311yescharacteristic
638C2#1914350311yescharacteristic
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#22982
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. #19135570C2semidirect
5. #19135367C2semidirect
6. #19135341C2semidirect
7. #19135340C2semidirect
8. #19135195C2semidirect
9. #19135192C2semidirect
11. #19134443C2semidirect
19. #14583208C4semidirect
20. #14583204C4semidirect
21. #14583201C4semidirect
22. #14583197C4semidirect
23. #14583192C4semidirect
24. #14583187C4semidirect
25. #14583182C4semidirect
26. #14583177C4semidirect
122. #13063252Q8semidirect
386. C43#22982semidirect

Maximal subgroups

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

subgroupindex
#191443792
#191435412
#191431612
#191355702
#191353672
#191353412
#191353402
#191351952
#191351922
#191348682
#191344432
#191344352
#191344302
#104×Dic432
C43×#18662
#2298243