Finite Group Databasebeta

← #25118667

Subgroups — #25118667

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#19144381C211yesmaximal, characteristic
2#19143539C211yesmaximal, characteristic, complemented
3#19143162C211yesmaximal, characteristic
4#19135570C211yesmaximal, characteristic, complemented
5#19135369C211yesmaximal, characteristic, complemented
6#19135344C211yesmaximal, characteristic, complemented
7#19135340C211yesmaximal, characteristic, complemented
8#19135197C211yesmaximal, characteristic, complemented
9#19134873C211yesmaximal, characteristic
10#19134871C211yesmaximal, characteristic
11#19134443C211yesmaximal, characteristic, complemented
12#19134434C211yesmaximal, characteristic
13#19134431C211yesmaximal, characteristic
14#19134399C211yesmaximal, characteristic
15C43×#1922C211yesmaximal, characteristic, complemented
16C2×#13063333C2211yescharacteristic
17C2×#13063331C2211yescharacteristic
18#14583452C2211yescharacteristic
19#14583367C2211yescharacteristic
20#14583209C411yescharacteristic, complemented
21#14583205C411yescharacteristic, complemented
22#14583202C411yescharacteristic, complemented
23#14583198C411yescharacteristic, complemented
24#14583193C411yescharacteristic, complemented
25#14583188C411yescharacteristic, complemented
26#14583183C411yescharacteristic, complemented
27#14583178C411yescharacteristic, complemented
28#14583029—21no—
29#14583027—21no—
30#14583027—21no—
31C8×Dic86—21no—
32C2×#13063261C2211yescharacteristic
33C2×#13063260C2211yescharacteristic
34#14582935C2211yescharacteristic
35#14582926C2211yescharacteristic
36#14582926C2211yescharacteristic
37#14582925C2211yescharacteristic
38#14582924—21no—
39#14582924—21no—
40#14582922C2211yescharacteristic
41#14582921—21no—
42C2×Dic43⋊C8C2211yescharacteristic
43C2×Dic43⋊C8C2211yescharacteristic
44C4⋊C8×D43—21no—
45C2×#13063253C2211yescharacteristic
46C2×#13063251C2211yescharacteristic
47#14582896C2211yescharacteristic
48#14582893C2211yescharacteristic
49#14582857C2211yescharacteristic
50M16×Dic43C2211yescharacteristic
51C2×C8×Dic43C2211yescharacteristic
52C2×C8×Dic43C2211yescharacteristic
53C42×Dic43C2211yescharacteristic
54#14582663C2211yescharacteristic
55#14582660C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582658C2211yescharacteristic
58#14582658C2211yescharacteristic
59#14582654C2211yescharacteristic
60C43×#427C2211yescharacteristic
61C43×#424C2211yescharacteristic
62C43×#405C2211yescharacteristic
63C43×#341C2211yescharacteristic
64C43×#339C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#336C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063333—22no—
69#13063333—41no—
70#13063331—22no—
71#13063331—41no—
72C2×#10621877C2311yescharacteristic
73C2×#10621877C2311yescharacteristic
74C2×#10621872—21no—
75C2×#10621872—21no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80#13063324C2×C411yescharacteristic
81#13063324C2×C411yescharacteristic
82#13063316C2×C411yescharacteristic
83#13063316C2×C411yescharacteristic
84#13063302—21no—
85#13063302—21no—
86C4×Dic86—21no—
87C4×Dic86—21no—
88#13063290C2×C411yescharacteristic
89#13063290C2×C411yescharacteristic
90#13063287C2×C411yescharacteristic
91#13063287C2×C411yescharacteristic
92(C22⋊D43)⋊C4—21no—
93(C22⋊D43)⋊C4—21no—
94#13063284C2311yescharacteristic
95#13063282—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100C42×D43—21no—
101#13063261—41no—
102#13063260—41no—
103#13063258C2×C411yescharacteristic
104#13063258C2×C411yescharacteristic
105#13063256C2×C411yescharacteristic
106#13063256C2×C411yescharacteristic
107C4⋊(C43⋊C8)—21no—
108C4⋊(C43⋊C8)—21no—
109C4⋊(C43⋊C8)—21no—
110C4⋊(C43⋊C8)—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115Dic43⋊C8C2×C411yescharacteristic
116Dic43⋊C8C2×C411yescharacteristic
117Dic43⋊C8C2×C411yescharacteristic
118Dic43⋊C8C2×C411yescharacteristic
119Dic43⋊C8D411yescharacteristic
120Dic43⋊C8D411yescharacteristic
121Dic43⋊C8D411yescharacteristic
122Dic43⋊C8D411yescharacteristic
123#13063253—22no—
124#13063251Q814yescomplemented
125#13063250C2×C411yescharacteristic
126#13063250C2×C411yescharacteristic
127#13063248C2×C411yescharacteristic
128#13063248C2×C411yescharacteristic
129#13063247C2×C411yescharacteristic
130#13063247C2×C411yescharacteristic
131#13063245C2×C411yescharacteristic
132#13063245C2×C411yescharacteristic
133#13063235—21no—
134#13063235—21no—
135C8×Dic43—21no—
136C8×Dic43—21no—
137C8×Dic43—41no—
138C8×Dic43—41no—
139C2×M16×C43C2311yescharacteristic
140C2×M16×C43C2311yescharacteristic
141C22×C8×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143#117×C43C2311yescharacteristic
144#117×C43C2311yescharacteristic
145C2×C42×C43C2311yescharacteristic
146#107×C43C2×C411yescharacteristic
147#107×C43C2×C411yescharacteristic
148#106×C43C2×C411yescharacteristic
149#106×C43C2×C411yescharacteristic
150C4⋊C8×C43—21no—
151C4⋊C8×C43—21no—
152#97×C43—21no—
153C4×C8×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—21no—
157C22×Dic43—21no—
158C22×Dic43#4111yescharacteristic
159C22×Dic43#4111yescharacteristic
160#10621898—21no—
161#10621898—21no—
162#10621898C2×Q812yes—
163#10621898#4112yes—
164C2×D172C22×C411yescharacteristic
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86C22×C411yescharacteristic
171M16×C43—21no—
172M16×C43—21no—
173M16×C43—21no—
174M16×C43C2×Q812yes—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43C22×C411yescharacteristic
182C2×C8×C43C22×C411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C2×C8×C43C2×D411yescharacteristic
185C4⋊C4×C43C22×C411yescharacteristic
186C4⋊C4×C43C22×C411yescharacteristic
187C4⋊C4×C43C22×C411yescharacteristic
188C4⋊C4×C43C22×C411yescharacteristic
189C22⋊C4×C43—21no—
190C22⋊C4×C43—21no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—21no—
195C22⋊Dic43—21no—
196(C2×D43)⋊C4—21no—
197(C2×D43)⋊C4—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43C22×C411yescharacteristic
201C4⋊Dic43C22×C411yescharacteristic
202Dic43⋊C4—21no—
203Dic43⋊C4—21no—
204Dic43⋊C4—21no—
205Dic43⋊C4—21no—
206Dic43⋊C4—21no—
207Dic43⋊C4—21no—
208C4×Dic43—24no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—42no—
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—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8C22×C411yescharacteristic
230C2×C43⋊C8C22×C411yescharacteristic
231C2×C43⋊C8C2×D411yescharacteristic
232C2×C43⋊C8C2×D411yescharacteristic
233#10621872—42no—
234#10621872—42no—
235C8×D43—42no—
236C8×D43—42no—
237C23×C43C2×#4111yescharacteristic
238C22×D43—21no—
239C2×C4×C43—22no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43C23×C411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×Q811yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C2×C4×C432−1+411yescharacteristic
252C22⋊D43—22no—
253C22⋊D43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—21no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—41no—
262C2×Dic43C4×D411yescharacteristic
263C2×Dic43C4×D411yescharacteristic
264C2×Dic43C4×D411yescharacteristic
265C2×Dic43C4×D411yescharacteristic
266D172—21no—
267D172C4×Q812yes—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—42no—
271C4×D43—81no—
272Dic86—21no—
273Dic86—42no—
274Dic86—81no—
275Dic86C4×Q812yes—
276C8×C43—21no—
277C8×C43—21no—
278C8×C43—21no—
279C8×C43—21no—
280C8×C43—22no—
281C8×C43—41no—
282C43⋊C8—21no—
283C43⋊C8—21no—
284C43⋊C8—21no—
285C43⋊C8—21no—
286C43⋊C8—41no—
287C43⋊C8—41no—
288#22982—431nomaximal, Sylow
289C22×C43—21no—
290C22×C43—21no—
291C22×C43C2×C4×D411yescharacteristic
292C22×C43#55211yescharacteristic
293C22×C43#55411yescharacteristic
294C2×D43—22no—
295C2×D43—41no—
296C2×D43—41no—
297C4×C43—42no—
298C4×C43—41no—
299C4×C43—41no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43C2×C4×Q811yescharacteristic
303C4×C43#52011yescharacteristic
304C4×C43#54611yescharacteristic
305C4×C43D4×Q811yescharacteristic
306Dic43—24no—
307Dic43—22no—
308Dic43—21no—
309Dic43—21no—
310Dic43—21no—
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#1922D4311yescharacteristic, complemented
323#1866—431no—
324#1866—431no—
325C4×C4⋊C8—431no—
326#1764—431no—
327#1764—431no—
328C4×#104—431no—
329C2×C43—21no—
330C2×C43—21no—
331C2×C43#236011yescharacteristic
332C2×C43C2×#44311yescharacteristic
333C2×C43#295611yescharacteristic
334D43—42no—
335C2×#131—431no—
336C2×#131—431no—
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×#108—431no—
353#427—431no—
354#427C2×D4311yescharacteristic
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×#104—431no—
368#416—431no—
369#416—431no—
370#405—431no—
371#405C2×D4311yescharacteristic
372C4×M16—431no—
373C2×C4×C8—431no—
374C2×C4×C8—431no—
375C43—431no—
376#341—431no—
377#341C2×D4311yescharacteristic
378#339—431no—
379#339—431no—
380#339—431no—
381#339—431no—
382#339C2×D4311yescharacteristic
383#339C2×D4311yescharacteristic
384#336—431no—
385#336C2×D4311yescharacteristic
386C43#2298211yescharacteristic, complemented, Sylow
387C2×#41—431no—
388#131—862no—
389#131—862no—
390#131—1721no—
391#131—1721no—
392C2×M16—431no—
393C2×M16—431no—
394C2×M16—861no—
395C2×M16—861no—
396C2×M16C22×D4311yescharacteristic
397C2×M16C22×D4311yescharacteristic
398C22×C8—431no—
399C22×C8—431no—
400C22×C8—861no—
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—861no—
420#117C22×D4311yescharacteristic
421#117C22×D4311yescharacteristic
422C2×C42—431no—
423C2×C42—431no—
424C2×C42—861no—
425C2×C42—861no—
426C2×C42—861no—
427C2×C42C22×D4311yescharacteristic
428#108—1721no—
429#108—1721no—
430#107—431no—
431#107—431no—
432#107C4×D4311yescharacteristic
433#107C4×D4311yescharacteristic
434#106—431no—
435#106—431no—
436#106C4×D4311yescharacteristic
437#106C4×D4311yescharacteristic
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—434no—
457#104—862no—
458#103—431no—
459#103—431no—
460#103—431no—
461#103—431no—
462#102—431no—
463#102—431no—
464#102—431no—
465#102—431no—
466#97—21no—
467#97—861no—
468#97—861no—
469C4×C8—21no—
470C4×C8—861no—
471C4×C8—861no—
472C4×C8—1721no—
473C4×C8—1721no—
474#41—432no—
475#41—432no—
476#41—861no—
477#41—861no—
478C2×Q8—431no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×D4—431no—
482C2×D4—861no—
483C22×C4—21no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4C23×D4311yescharacteristic
491M16—21no—
492M16—21no—
493M16—21no—
494M16—861no—
495M16—861no—
496M16—861no—
497M16—861no—
498M16—1722no—
499M16—1722no—
500M16Q8×D4312yes—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—431no—
508C2×C8—431no—
509C2×C8—431no—
510C2×C8—431no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—1722no—
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—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
535C4⋊C4C2×C4×D4311yescharacteristic
536C4⋊C4C2×C4×D4311yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—861no—
540C22⋊C4—861no—
541C22⋊C4—861no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—431no—
550C42—432no—
551C42—861no—
552C42—861no—
553C42—864no—
554C42—861no—
555C42—861no—
556C42—1722no—
557C23—861no—
558C23#41×D4311yescharacteristic
559Q8—432no—
560Q8—861no—
561Q8—3441no—
562Q8—1722no—
563D4—432no—
564D4—862no—
565D4—862no—
566D4—861no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—431no—
577C2×C4—431no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—861no—
583C2×C4—862no—
584C2×C4—862no—
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×C4#41×D4311yescharacteristic
594C2×C4#1306337111yescharacteristic
595C2×C4#1306337211yescharacteristic
596C8—22no—
597C8—21no—
598C8—21no—
599C8—21no—
600C8—21no—
601C8—41no—
602C8—861no—
603C8—861no—
604C8—861no—
605C8—861no—
606C8—1721no—
607C8—1721no—
608C22—21no—
609C22—21no—
610C22—862no—
611C22—1721no—
612C22—1721no—
613C22C4×D4×D4311yescharacteristic
614C22#1458358511yescharacteristic
615C22#1458360511yescharacteristic
616C4—42no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—432no—
622C4—864no—
623C4—861no—
624C4—862no—
625C4—861no—
626C4—861no—
627C4—1721no—
628C4—1721no—
629C4C4×Q8×D4311yescharacteristic
630C4#1458337911yescharacteristic
631C4#1458354111yescharacteristic
632C4#1458356211yescharacteristic
633C2—21no—
634C2—21no—
635C2—1722no—
636C2#1913760311yescharacteristic
637C2#443×D4311yescharacteristic
638C2#1914350311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1922C2
socleC22×C43C2×C4×D4
prime radicalC2×#10621898C23
cosocleC22×C4×C43C24
hypercenter#1922D43
hypocenterC43#22982
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1922

Complements

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

NH ≅ G/Ntype
2. #19143539C2semidirect
4. #19135570C2semidirect
5. #19135369C2semidirect
6. #19135344C2semidirect
7. #19135340C2semidirect
8. #19135197C2semidirect
11. #19134443C2semidirect
15. C43×#1922C2semidirect
20. #14583209C4semidirect
21. #14583205C4semidirect
22. #14583202C4semidirect
23. #14583198C4semidirect
24. #14583193C4semidirect
25. #14583188C4semidirect
26. #14583183C4semidirect
27. #14583178C4semidirect
124. #13063251Q8semidirect
322. #1922D43semidirect
386. C43#22982semidirect

Maximal subgroups

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

subgroupindex
#191443812
#191435392
#191431622
#191355702
#191353692
#191353442
#191353402
#191351972
#191348732
#191348712
#191344432
#191344342
#191344312
#191343992
C43×#19222
#2298243