Finite Group Databasebeta

← #25108899

Subgroups — #25108899

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#19144381C211yesmaximal, characteristic
2#19143528C211yesmaximal, characteristic, complemented
3#19143238C211yesmaximal, characteristic
4#19135537C211yesmaximal, characteristic, complemented
5#19135367C211yesmaximal, characteristic, complemented
6#19135340C211yesmaximal, characteristic, complemented
7#19135299C211yesmaximal, characteristic
8#19135298C211yesmaximal, characteristic
9#19135242C211yesmaximal, characteristic
10#19135241C211yesmaximal, characteristic
11#19135197C211yesmaximal, characteristic, complemented
12#19135196C211yesmaximal, characteristic, complemented
13#19134614C211yesmaximal, characteristic
14C8×Dic43⋊C4C211yesmaximal, characteristic, complemented
15C43×#1945C211yesmaximal, characteristic, complemented
16#14583452C2211yescharacteristic
17#14583367C2211yescharacteristic
18#14583209C411yescharacteristic, complemented
19#14583205C411yescharacteristic, complemented
20#14583202C411yescharacteristic, complemented
21#14583198C411yescharacteristic, complemented
22#14583193C411yescharacteristic, complemented
23#14583188C411yescharacteristic, complemented
24#14583183C411yescharacteristic, complemented
25#14583178C411yescharacteristic, complemented
26#14583028—21no—
27#14583028—21no—
28#14583023—21no—
29#14583023—21no—
30#14582959—21no—
31#14582959—21no—
32#14582951—21no—
33#14582951—21no—
34C2×#13063260C2211yescharacteristic
35#14582935C2211yescharacteristic
36#14582926C2211yescharacteristic
37#14582925C2211yescharacteristic
38#14582922C2211yescharacteristic
39C2×Dic43⋊C8C2211yescharacteristic
40C2×#13063253C2211yescharacteristic
41C2×#13063251C2211yescharacteristic
42#14582896C2211yescharacteristic
43#14582893C2211yescharacteristic
44#14582867C2211yescharacteristic
45#14582865C2211yescharacteristic
46#14582857C2211yescharacteristic
47#14582855C2211yescharacteristic
48M16×Dic43C2211yescharacteristic
49C2×C8×Dic43C2211yescharacteristic
50C2×C8×Dic43C2211yescharacteristic
51C4×Dic43⋊C4C2211yescharacteristic
52#14582664C2211yescharacteristic
53#14582663C2211yescharacteristic
54#14582660C2211yescharacteristic
55#14582659C2211yescharacteristic
56#14582658C2211yescharacteristic
57#14582658C2211yescharacteristic
58#14582654C2211yescharacteristic
59#14582653C2211yescharacteristic
60C2×#108×C43C2211yescharacteristic
61C43×#427C2211yescharacteristic
62C43×#424C2211yescharacteristic
63C43×#424C2211yescharacteristic
64C2×C4×C8×C43C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#339C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68C2×#10621877C2311yescharacteristic
69C2×#10621877C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063324C2×C411yescharacteristic
73#13063324C2×C411yescharacteristic
74#13063316C2×C411yescharacteristic
75#13063316C2×C411yescharacteristic
76#13063302—21no—
77#13063302—21no—
78C4×Dic86—21no—
79C4×Dic86—21no—
80#13063290C2×C411yescharacteristic
81#13063290C2×C411yescharacteristic
82#13063287C2×C411yescharacteristic
83#13063287C2×C411yescharacteristic
84(C22⋊D43)⋊C4—21no—
85(C22⋊D43)⋊C4—21no—
86#13063284C2311yescharacteristic
87#13063282—21no—
88C2×Dic43⋊C4—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91C42×D43—21no—
92#13063260—41no—
93#13063258C2×C411yescharacteristic
94#13063258C2×C411yescharacteristic
95#13063256C2×C411yescharacteristic
96#13063256C2×C411yescharacteristic
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)—21no—
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8C2×C411yescharacteristic
104Dic43⋊C8C2×C411yescharacteristic
105Dic43⋊C8C2×C411yescharacteristic
106Dic43⋊C8C2×C411yescharacteristic
107#13063253—41no—
108#13063251—41no—
109#13063250C2×C411yescharacteristic
110#13063250C2×C411yescharacteristic
111#13063248C2×C411yescharacteristic
112#13063248C2×C411yescharacteristic
113#13063247C2×C411yescharacteristic
114#13063247C2×C411yescharacteristic
115#13063245C2×C411yescharacteristic
116#13063245C2×C411yescharacteristic
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063236—21no—
122#13063235—21no—
123#13063235—21no—
124C4×C43⋊C8—21no—
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43—41no—
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C8×Dic43D411yescharacteristic
131C8×Dic43D411yescharacteristic
132C43⋊#95—21no—
133C2×M16×C43C2311yescharacteristic
134C2×M16×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137#117×C43C2311yescharacteristic
138#117×C43C2311yescharacteristic
139C2×C42×C43C2311yescharacteristic
140#108×C43—41no—
141#107×C43C2×C411yescharacteristic
142#107×C43C2×C411yescharacteristic
143#106×C43C2×C411yescharacteristic
144#106×C43C2×C411yescharacteristic
145C4⋊C8×C43—21no—
146C4⋊C8×C43—21no—
147C4⋊C8×C43—21no—
148C4⋊C8×C43—21no—
149C4×C8×C43—41no—
150C22×C4×C43—21no—
151C22×C4×C43C2411yescharacteristic
152C2×C22⋊D43—21no—
153C22×Dic43—21no—
154C22×Dic43#4111yescharacteristic
155C22×Dic43#4111yescharacteristic
156#10621898—21no—
157#10621898—21no—
158#10621898—21no—
159#10621898—21no—
160C2×D172C22×C411yescharacteristic
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86C22×C411yescharacteristic
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
183C4⋊C4×C43C22×C411yescharacteristic
184C4⋊C4×C43C22×C411yescharacteristic
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C22⋊Dic43—21no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43C22×C411yescharacteristic
197C4⋊Dic43C22×C411yescharacteristic
198Dic43⋊C4—24no—
199Dic43⋊C4—21no—
200Dic43⋊C4—21no—
201Dic43⋊C4—21no—
202Dic43⋊C4—21no—
203Dic43⋊C4—21no—
204Dic43⋊C4—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×C43C2×#4111yescharacteristic
229C22×D43—21no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43C23×C411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43H(5,𝔽2)11yescharacteristic
240C2×C4×C432−1+411yescharacteristic
241C2×C4×C432−1+411yescharacteristic
242C2×C4×C432−1+411yescharacteristic
243C22⋊D43—41no—
244C22⋊D43—41no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43C4×D411yescharacteristic
254C2×Dic43C4×D411yescharacteristic
255C2×Dic43C4×D411yescharacteristic
256C2×Dic43C4×D411yescharacteristic
257D172—21no—
258D172—21no—
259C4×D43—42no—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43—42no—
263Dic86—21no—
264Dic86—21no—
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×C43C2×C4×D411yescharacteristic
283C22×C43#54111yescharacteristic
284C22×C43#54211yescharacteristic
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—41no—
288C4×C43—42no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43#51911yescharacteristic
294C4×C43#52011yescharacteristic
295C4×C43#53611yescharacteristic
296C4×C43#53711yescharacteristic
297Dic43—21no—
298Dic43—21no—
299Dic43—21no—
300Dic43—42no—
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#1945D4311yescharacteristic, complemented
312#1937—431no—
313#1937—431no—
314#1929—431no—
315#1929—431no—
316#1922—431no—
317#1922—431no—
318#1806—431no—
319C8×C4⋊C4—431no—
320C2×C43—21no—
321C2×C43—21no—
322C2×C43#232311yescharacteristic
323C2×C43C2×#44311yescharacteristic
324C2×C43#295511yescharacteristic
325D43—81no—
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#427C2×D4311yescharacteristic
348#424—431no—
349#424—431no—
350#424C2×D4311yescharacteristic
351#424C2×D4311yescharacteristic
352#423—431no—
353C2×C4⋊C8—431no—
354C2×#104—431no—
355C2×#104—431no—
356#416—431no—
357#416—431no—
358#408—431no—
359#408—431no—
360#405—431no—
361#405—431no—
362C4×M16—431no—
363C2×C4×C8—431no—
364C2×C4×C8—431no—
365C2×C4×C8C2×D4311yescharacteristic
366C4×C4⋊C4—431no—
367#341—431no—
368#341—431no—
369#339—431no—
370#339—431no—
371#339—431no—
372#339—431no—
373#339C2×D4311yescharacteristic
374#339C2×D4311yescharacteristic
375#336—431no—
376#336—431no—
377C43#2213011yescharacteristic, complemented, Sylow
378C2×#41—431no—
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—861no—
403#117C22×D4311yescharacteristic
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#107C4×D4311yescharacteristic
415#107C4×D4311yescharacteristic
416#106—431no—
417#106—431no—
418#106C4×D4311yescharacteristic
419#106C4×D4311yescharacteristic
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—431no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—861no—
429C4⋊C8—861no—
430C4⋊C8—861no—
431C4⋊C8—861no—
432C4⋊C8—861no—
433C4⋊C8—861no—
434#104—1721no—
435#104—1721no—
436#103—431no—
437#103—431no—
438#103—431no—
439#103—431no—
440#102—431no—
441#102—431no—
442#102—431no—
443#102—431no—
444C22⋊C8—861no—
445C22⋊C8—861no—
446C22⋊C8—861no—
447C22⋊C8—861no—
448#97—861no—
449#97—861no—
450#97—861no—
451C4×C8—41no—
452C4×C8—431no—
453C4×C8—431no—
454C4×C8—431no—
455C4×C8—431no—
456C4×C8—861no—
457C4×C8—861no—
458C4×C8—861no—
459C4×C8—1721no—
460#95—861no—
461#41—861no—
462#41—861no—
463#41—861no—
464#41—861no—
465C2×Q8—431no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×D4—431no—
469C2×D4—861no—
470C22×C4—21no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—861no—
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—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—864no—
517C4⋊C4C2×C4×D4311yescharacteristic
518C4⋊C4C2×C4×D4311yescharacteristic
519C4⋊C4C2×C4×D4311yescharacteristic
520C4⋊C4C2×C4×D4311yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—861no—
524C22⋊C4—861no—
525C22⋊C4—861no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—861no—
535C42—861no—
536C42—861no—
537C42—861no—
538C42—861no—
539C23—861no—
540C23#41×D4311yescharacteristic
541Q8—861no—
542Q8—861no—
543Q8—1722no—
544Q8—1722no—
545D4—861no—
546D4—861no—
547D4—1721no—
548D4—1721no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—431no—
557C2×C4—431no—
558C2×C4—431no—
559C2×C4—431no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—1722no—
566C2×C4—1722no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4C22×C4×D4311yescharacteristic
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4#1306337011yescharacteristic
575C2×C4#1306337211yescharacteristic
576C2×C4#1306337311yescharacteristic
577C2×C4#1306337311yescharacteristic
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—1721no—
593C22—1721no—
594C22—1721no—
595C22C4×D4×D4311yescharacteristic
596C22#1458350811yescharacteristic
597C22#1458351911yescharacteristic
598C4—42no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—432no—
604C4—861no—
605C4—861no—
606C4—861no—
607C4—1722no—
608C4—1721no—
609C4—1721no—
610C4—1721no—
611C4#1458337511yescharacteristic
612C4#1458338011yescharacteristic
613C4#1458347411yescharacteristic
614C4#1458347611yescharacteristic
615C2—21no—
616C2—21no—
617C2—3441no—
618C2#1913727211yescharacteristic
619C2#443×D4311yescharacteristic
620C2#1914349311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1945C2
socleC22×C43C2×C4×D4
prime radicalC2×#10621898C23
cosocleC22×C4×C43C24
hypercenter#1945D43
hypocenterC43#22130
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1945

Complements

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

NH ≅ G/Ntype
2. #19143528C2semidirect
4. #19135537C2semidirect
5. #19135367C2semidirect
6. #19135340C2semidirect
11. #19135197C2semidirect
12. #19135196C2semidirect
14. C8×Dic43⋊C4C2semidirect
15. C43×#1945C2semidirect
18. #14583209C4semidirect
19. #14583205C4semidirect
20. #14583202C4semidirect
21. #14583198C4semidirect
22. #14583193C4semidirect
23. #14583188C4semidirect
24. #14583183C4semidirect
25. #14583178C4semidirect
311. #1945D43semidirect
377. C43#22130semidirect

Maximal subgroups

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

subgroupindex
#191443812
#191435282
#191432382
#191355372
#191353672
#191353402
#191352992
#191352982
#191352422
#191352412
#191351972
#191351962
#191346142
C8×Dic43⋊C42
C43×#19452
#2213043