Finite Group Databasebeta

← #25108901

Subgroups — #25108901

Order 11008.

648 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144379C211yesmaximal, characteristic
2#19143527C211yesmaximal, characteristic, complemented
3#19143235C211yesmaximal, characteristic
4#19135537C211yesmaximal, characteristic, complemented
5#19135367C211yesmaximal, characteristic, complemented
6#19135342C211yesmaximal, characteristic, complemented
7#19135341C211yesmaximal, characteristic, complemented
8#19135301C211yesmaximal, characteristic
9#19135296C211yesmaximal, characteristic
10#19135240C211yesmaximal, characteristic
11#19135195C211yesmaximal, characteristic, complemented
12#19135194C211yesmaximal, characteristic, complemented
13#19134613C211yesmaximal, characteristic
14#19134456C211yesmaximal, characteristic, complemented
15C43×#1929C211yesmaximal, characteristic
16#14583452C2211yescharacteristic
17#41×Dic43C2211yescharacteristic
18#14583208C411yescharacteristic, complemented
19#14583204C411yescharacteristic, complemented
20#14583201C411yescharacteristic, complemented
21#14583197C411yescharacteristic, complemented
22#14583192C411yescharacteristic, complemented
23#14583187C411yescharacteristic, complemented
24#14583182C411yescharacteristic, complemented
25#14583177C411yescharacteristic, complemented
26#14583027—21no—
27#14583027—21no—
28C8×Dic86—21no—
29C8×Dic86—21no—
30#14582957—21no—
31#14582957—21no—
32#14582949—21no—
33#14582949—21no—
34C2×#13063260C2211yescharacteristic
35#14582937C2211yescharacteristic
36#14582935C2211yescharacteristic
37#14582927C2211yescharacteristic
38#14582927C2211yescharacteristic
39#14582926C2211yescharacteristic
40#14582925C2211yescharacteristic
41#14582922C2211yescharacteristic
42C2×Dic43⋊C8C2211yescharacteristic
43C2×#13063252C2211yescharacteristic
44#14582895C2211yescharacteristic
45#14582866C2211yescharacteristic
46#14582854C2211yescharacteristic
47M16×Dic43C2211yescharacteristic
48C2×C4×C43⋊C8C2211yescharacteristic
49C2×C8×Dic43C2211yescharacteristic
50C2×C8×Dic43C2211yescharacteristic
51C4×Dic43⋊C4C2211yescharacteristic
52#14582664C2211yescharacteristic
53#14582663C2211yescharacteristic
54#14582660C2211yescharacteristic
55#14582660C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582659C2211yescharacteristic
58#14582658C2211yescharacteristic
59#14582653C2211yescharacteristic
60C2×#108×C43C2211yescharacteristic
61C2×#104×C43C2211yescharacteristic
62C43×#416C2211yescharacteristic
63C43×#408C2211yescharacteristic
64C43×#405C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#336C2211yescharacteristic
67C2×#10621877C2311yescharacteristic
68C2×#10621877C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063324C2×C411yescharacteristic
72#13063324C2×C411yescharacteristic
73#13063316C2×C411yescharacteristic
74#13063316C2×C411yescharacteristic
75#13063302—21no—
76#13063302—21no—
77Q8×Dic43C2×C411yescharacteristic
78Q8×Dic43C2×C411yescharacteristic
79C4×Dic86—21no—
80C4×Dic86—21no—
81D4×Dic43—21no—
82D4×Dic43—21no—
83D4×Dic43C2×C411yescharacteristic
84D4×Dic43C2×C411yescharacteristic
85#13063284—21no—
86#13063284C2311yescharacteristic
87#13063284C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43C2311yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92#13063260—41no—
93#13063259C2×C411yescharacteristic
94#13063259C2×C411yescharacteristic
95#13063258C2×C411yescharacteristic
96#13063258C2×C411yescharacteristic
97#13063257C2×C411yescharacteristic
98#13063257C2×C411yescharacteristic
99#13063256C2×C411yescharacteristic
100#13063256C2×C411yescharacteristic
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8C2×C411yescharacteristic
112Dic43⋊C8C2×C411yescharacteristic
113Dic43⋊C8C2×C411yescharacteristic
114Dic43⋊C8C2×C411yescharacteristic
115#13063252—41no—
116#13063249C2×C411yescharacteristic
117#13063249C2×C411yescharacteristic
118#13063246C2×C411yescharacteristic
119#13063246C2×C411yescharacteristic
120C22⋊(C43⋊C8)—21no—
121C22⋊(C43⋊C8)—21no—
122#13063235—21no—
123#13063235—21no—
124C4×C43⋊C8—41no—
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43—41no—
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C8×Dic43D411yescharacteristic
131C8×Dic43D411yescharacteristic
132C43⋊#95—21no—
133C2×#41×C43C2311yescharacteristic
134C2×M16×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138#117×C43C2311yescharacteristic
139C2×C42×C43C2311yescharacteristic
140#108×C43—41no—
141#104×C43—41no—
142#103×C43C2×C411yescharacteristic
143#103×C43C2×C411yescharacteristic
144#102×C43C2×C411yescharacteristic
145#102×C43C2×C411yescharacteristic
146C22⋊C8×C43—21no—
147C22⋊C8×C43—21no—
148#97×C43—21no—
149C4×C8×C43—21no—
150#41×C43—21no—
151#41×C43—21no—
152#41×C43—21no—
153#41×C43—21no—
154C2×Q8×C43C22×C411yescharacteristic
155C2×D4×C43—21no—
156C2×D4×C43C22×C411yescharacteristic
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43C2411yescharacteristic
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43#4111yescharacteristic
164C22×Dic43#4111yescharacteristic
165C2×Dic86—21no—
166C2×Dic86—21no—
167M16×C43—21no—
168M16×C43—21no—
169M16×C43—21no—
170M16×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43C22×C411yescharacteristic
178C2×C8×C43C22×C411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C4⋊C4×C43C22×C411yescharacteristic
182C4⋊C4×C43C22×C411yescharacteristic
183C22⋊C4×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C22⋊Dic43—21no—
188C22⋊Dic43—21no—
189C22⋊Dic43—21no—
190C22⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43C22×C411yescharacteristic
196C4⋊Dic43C22×C411yescharacteristic
197C4⋊Dic43C22×C411yescharacteristic
198C4⋊Dic43C22×C411yescharacteristic
199Dic43⋊C4—24no—
200Dic43⋊C4—21no—
201Dic43⋊C4—21no—
202Dic43⋊C4—21no—
203Dic43⋊C4—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43C22×C411yescharacteristic
211C4×Dic43C22×C411yescharacteristic
212C4×Dic43C2×D411yescharacteristic
213C4×Dic43C2×D411yescharacteristic
214#10621877—21no—
215#10621877—21no—
216#10621877—21no—
217#10621877—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8C22×C411yescharacteristic
225C2×C43⋊C8C22×C411yescharacteristic
226C2×C43⋊C8C2×D411yescharacteristic
227C2×C43⋊C8C2×D411yescharacteristic
228C23×C43—21no—
229C23×C43C2×#4111yescharacteristic
230Q8×C43—21no—
231Q8×C43—21no—
232D4×C43—21no—
233D4×C43—21no—
234D4×C43—41no—
235D4×C43—41no—
236C2×C4×C43—22no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C2×C4×C432−1+411yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—41no—
257C2×Dic43—42no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—42no—
261C2×Dic43C4×D411yescharacteristic
262C2×Dic43C4×D411yescharacteristic
263C2×Dic43C4×D411yescharacteristic
264C2×Dic43C4×D411yescharacteristic
265Dic86—42no—
266Dic86—42no—
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—21no—
271C8×C43—41no—
272C8×C43—41no—
273C43⋊C8—21no—
274C43⋊C8—21no—
275C43⋊C8—21no—
276C43⋊C8—21no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279#22130—431nomaximal, Sylow
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43C2×C4×D411yescharacteristic
286C22×C43#54111yescharacteristic
287C22×C43#54211yescharacteristic
288C4×C43—42no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43#51911yescharacteristic
293C4×C43#52011yescharacteristic
294C4×C43#53611yescharacteristic
295C4×C43#53711yescharacteristic
296Dic43—21no—
297Dic43—21no—
298Dic43—21no—
299Dic43—42no—
300Dic43—41no—
301Dic43—41no—
302Dic43—41no—
303Dic43—41no—
304Dic43#44312yes—
305#3076—431no—
306#2960—431no—
307#2922—431no—
308#1986—431no—
309#1950—431no—
310#1945—431no—
311#1945—431no—
312#1937—431no—
313#1937—431no—
314#1929—431no—
315#1929D4311yescharacteristic
316#1922—431no—
317#1922—431no—
318#1806—431no—
319C8×C4⋊C4—431no—
320C2×C43—21no—
321C2×C43—21no—
322C2×C43—81no—
323C2×C43#232311yescharacteristic
324C2×C43C2×#44311yescharacteristic
325C2×C43#295511yescharacteristic
326#533—431no—
327C4×#41—431no—
328#479—431no—
329#479—431no—
330#478—431no—
331#478—431no—
332#477—431no—
333#476—431no—
334#475—431no—
335#474—431no—
336#446—861no—
337#446—861no—
338C8×Q8—861no—
339C8×Q8—861no—
340#433—861no—
341#433—861no—
342#431—861no—
343#431—861no—
344C2×#108—431no—
345C2×#108C2×D4311yescharacteristic
346#427—431no—
347#427—431no—
348#424—431no—
349#424—431no—
350#424—431no—
351#424—431no—
352#423—431no—
353C2×C4⋊C8—431no—
354C2×#104—431no—
355C2×#104C2×D4311yescharacteristic
356#416—431no—
357#416C2×D4311yescharacteristic
358#408—431no—
359#408C2×D4311yescharacteristic
360#405—431no—
361#405C2×D4311yescharacteristic
362C4×M16—431no—
363C2×C4×C8—431no—
364C2×C4×C8—431no—
365C2×C4×C8—431no—
366C4×C4⋊C4—431no—
367#341—431no—
368#341—431no—
369#339—431no—
370#339—431no—
371#339—431no—
372#339—431no—
373#339—431no—
374#339C2×D4311yescharacteristic
375#336—431no—
376#336C2×D4311yescharacteristic
377C43#2213011yescharacteristic, complemented, Sylow
378C2×#41C22×D4311yescharacteristic
379C2×M16—431no—
380C2×M16—431no—
381C2×M16C22×D4311yescharacteristic
382C2×M16C22×D4311yescharacteristic
383C22×C8—431no—
384C22×C8—431no—
385C22×C8C22×D4311yescharacteristic
386C22×C8C22×D4311yescharacteristic
387C4⋊Q8—431no—
388C4⋊Q8—431no—
389#125—431no—
390#125—431no—
391C22⋊Q8—861no—
392C22⋊Q8—861no—
393C4×Q8—431no—
394C4×Q8—431no—
395C4×Q8—861no—
396C4×Q8—861no—
397C4×D4—431no—
398C4×D4—431no—
399C4×D4—861no—
400C4×D4—861no—
401#117—431no—
402#117—431no—
403#117—861no—
404#117C22×D4311yescharacteristic
405C2×C4⋊C4—861no—
406C2×C42—431no—
407C2×C42—431no—
408C2×C42—861no—
409C2×C42C22×D4311yescharacteristic
410#108—41no—
411#108—1721no—
412#107—431no—
413#107—431no—
414#107—431no—
415#107—431no—
416#106—431no—
417#106—431no—
418#106—431no—
419#106—431no—
420C4⋊C8—431no—
421C4⋊C8—431no—
422C4⋊C8—431no—
423C4⋊C8—431no—
424C4⋊C8—861no—
425C4⋊C8—861no—
426C4⋊C8—861no—
427C4⋊C8—861no—
428C4⋊C8—861no—
429C4⋊C8—861no—
430C4⋊C8—861no—
431C4⋊C8—861no—
432C4⋊C8—861no—
433C4⋊C8—861no—
434#104—41no—
435#104—1721no—
436#103—431no—
437#103—431no—
438#103C4×D4311yescharacteristic
439#103C4×D4311yescharacteristic
440#102—431no—
441#102—431no—
442#102C4×D4311yescharacteristic
443#102C4×D4311yescharacteristic
444C22⋊C8—21no—
445C22⋊C8—21no—
446C22⋊C8—861no—
447C22⋊C8—861no—
448#97—21no—
449#97—861no—
450#97—861no—
451C4×C8—21no—
452C4×C8—431no—
453C4×C8—431no—
454C4×C8—431no—
455C4×C8—431no—
456C4×C8—861no—
457C4×C8—861no—
458C4×C8—1721no—
459C4×C8—1721no—
460#95—861no—
461#41—21no—
462#41—21no—
463#41—21no—
464#41—21no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8C2×C4×D4311yescharacteristic
468C2×D4—21no—
469C2×D4C2×C4×D4311yescharacteristic
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4C23×D4311yescharacteristic
478M16—21no—
479M16—21no—
480M16—21no—
481M16—21no—
482M16—861no—
483M16—861no—
484M16—861no—
485M16—861no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—431no—
493C2×C8—431no—
494C2×C8—431no—
495C2×C8—431no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8C2×C4×D4311yescharacteristic
503C2×C8C2×C4×D4311yescharacteristic
504C2×C8D4×D4311yescharacteristic
505C2×C8D4×D4311yescharacteristic
506C4⋊C4—431no—
507C4⋊C4—431no—
508C4⋊C4—431no—
509C4⋊C4—431no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—864no—
519C4⋊C4C2×C4×D4311yescharacteristic
520C4⋊C4C2×C4×D4311yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—861no—
523C22⋊C4—861no—
524C22⋊C4—861no—
525C22⋊C4—861no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—431no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—861no—
534C42—861no—
535C42—861no—
536C42—861no—
537C42—861no—
538C42—861no—
539C23—21no—
540C23#41×D4311yescharacteristic
541Q8—21no—
542Q8—21no—
543Q8—1722no—
544Q8—1722no—
545D4—21no—
546D4—21no—
547D4—41no—
548D4—41no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—431no—
558C2×C4—431no—
559C2×C4—431no—
560C2×C4—431no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—1722no—
568C2×C4—1721no—
569C2×C4—1722no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4C22×C4×D4311yescharacteristic
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4#1306337011yescharacteristic
575C2×C4#1306337211yescharacteristic
576C2×C4#1306337211yescharacteristic
577C2×C4#1306337211yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—861no—
585C8—861no—
586C8—861no—
587C8—861no—
588C8—1721no—
589C8—1721no—
590C22—21no—
591C22—21no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22C4×D4×D4311yescharacteristic
596C22#1458350611yescharacteristic
597C22#1458351311yescharacteristic
598C4—42no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—432no—
603C4—861no—
604C4—861no—
605C4—861no—
606C4—1722no—
607C4—1721no—
608C4—1721no—
609C4—1721no—
610C4—1721no—
611C4#1458337611yescharacteristic
612C4#1458337811yescharacteristic
613C4#1458347111yescharacteristic
614C4#1458347811yescharacteristic
615C2—21no—
616C2—21no—
617C2—81no—
618C2#1913727411yescharacteristic
619C2#443×D4311yescharacteristic
620C2#1914349511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1929C2
socleC22×C43C2×C4×D4
prime radicalC2×#41×C43C23
cosocleC22×C4×C43C24
hypercenter#1929D43
hypocenterC43#22130
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1929

Complements

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

NH ≅ G/Ntype
2. #19143527C2semidirect
4. #19135537C2semidirect
5. #19135367C2semidirect
6. #19135342C2semidirect
7. #19135341C2semidirect
11. #19135195C2semidirect
12. #19135194C2semidirect
14. #19134456C2semidirect
18. #14583208C4semidirect
19. #14583204C4semidirect
20. #14583201C4semidirect
21. #14583197C4semidirect
22. #14583192C4semidirect
23. #14583187C4semidirect
24. #14583182C4semidirect
25. #14583177C4semidirect
377. C43#22130semidirect

Maximal subgroups

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

subgroupindex
#191443792
#191435272
#191432352
#191355372
#191353672
#191353422
#191353412
#191353012
#191352962
#191352402
#191351952
#191351942
#191346132
#191344562
C43×#19292
#2213043