Finite Group Databasebeta

← #25160055

Subgroups — #25160055

Order 11008.

732 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144442C211yesmaximal, characteristic, complemented
2#19143427C211yesmaximal, characteristic
3#19143187C211yesmaximal, characteristic, complemented
4#19136118C211yesmaximal, characteristic, complemented
5#19136105C211yesmaximal, characteristic, complemented
6#19135955C211yesmaximal, characteristic, complemented
7#19135942C211yesmaximal, characteristic, complemented
8#19135377C211yesmaximal, characteristic, complemented
9#19135196C211yesmaximal, characteristic, complemented
10#19135106C211yesmaximal, characteristic
11#19134968C211yesmaximal, characteristic
12#19134869C211yesmaximal, characteristic, complemented
13#19134825C211yesmaximal, characteristic, complemented
14#19134805C211yesmaximal, characteristic, complemented
15C43×#3081C211yesmaximal, characteristic, complemented
16C2×#13063351C2211yescharacteristic
17C2×#13063331C2211yescharacteristic
18#14583379C2211yescharacteristic
19#14583379C2211yescharacteristic
20#14583203—21no—
21#14583196—21no—
22#14583191—21no—
23#14583176—21no—
24#14583009—21no—
25#14582999—21no—
26C4×#10621883—21no—
27C4×#10621882—21no—
28C2×#13063260C2211yescharacteristic
29#14582942C2211yescharacteristic
30#14582942C2211yescharacteristic
31#14582942C2211yescharacteristic
32#14582942C2211yescharacteristic
33#14582940—21no—
34#14582940—21no—
35#14582934—21no—
36C2×#13063258C2211yescharacteristic
37C2×#13063257C2211yescharacteristic
38#106×D43—21no—
39#14582926C2211yescharacteristic
40C2×#13063251C2211yescharacteristic
41#14582898C2211yescharacteristic
42#14582893C2211yescharacteristic
43C2×#13063246C2211yescharacteristic
44C2×#13063242C2211yescharacteristic
45#14582855C2211yescharacteristic
46#14582802C2211yescharacteristic
47#14582764C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582667C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582664C2211yescharacteristic
52#14582658C2211yescharacteristic
53#14582658C2211yescharacteristic
54#14582658C2211yescharacteristic
55#14582653C2211yescharacteristic
56C43×#544C2211yescharacteristic
57C43×#518C2211yescharacteristic
58C43×#478—21no—
59C43×#478—21no—
60C43×#476—21no—
61C43×#474—21no—
62C43×#428C2211yescharacteristic
63C43×#427C2211yescharacteristic
64C43×#424C2211yescharacteristic
65C43×#418C2211yescharacteristic
66C2×#102×C43C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063351—22no—
69#13063351Q814yescomplemented
70C2×#10621883—21no—
71C2×#10621882—21no—
72#13063331—22no—
73#13063331—22no—
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C2×#10621877C2311yescharacteristic
77C2×#10621872—21no—
78C22×C43⋊C8C2311yescharacteristic
79C2×C8×D43—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×D172—21no—
83C4×D172—21no—
84(C22⋊D43)⋊C4—41no—
85(C22⋊D43)⋊C4—41no—
86#13063283—21no—
87#13063283—21no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C4⋊C4×D43—21no—
91C4⋊C4×D43—21no—
92C2×C22⋊Dic43—41no—
93C2×C4×Dic43C2311yescharacteristic
94#13063260—22no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063258—21no—
99#13063258—21no—
100#13063258—21no—
101#13063257—21no—
102#13063257—21no—
103#13063256—21no—
104#13063256—21no—
105#13063256—21no—
106#13063256—21no—
107C4⋊(C43⋊C8)—21no—
108C4⋊(C43⋊C8)—21no—
109#13063251—22no—
110#13063248—21no—
111#13063248D411yescharacteristic
112#13063248D411yescharacteristic
113#13063246—21no—
114#13063246—21no—
115#13063245—21no—
116#13063245D411yescharacteristic
117#13063245D411yescharacteristic
118#13063242—22no—
119#13063236—21no—
120C4×C43⋊C8—21no—
121C43⋊#95—41no—
122C22×D4×C43C2311yescharacteristic
123C2×M16×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C4⋊Q8×C43—21no—
126C4⋊Q8×C43—21no—
127#125×C43—21no—
128#125×C43—21no—
129C22⋊Q8×C43—41no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43—21no—
133C4×D4×C43—21no—
134#117×C43C2311yescharacteristic
135#117×C43C2311yescharacteristic
136#117×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—41no—
139#107×C43—21no—
140#107×C43D411yescharacteristic
141#107×C43D411yescharacteristic
142#106×C43—21no—
143#106×C43D411yescharacteristic
144#106×C43D411yescharacteristic
145C4⋊C8×C43—21no—
146C4⋊C8×C43—21no—
147#102×C43—21no—
148#102×C43—21no—
149#102×C43—21no—
150#102×C43—21no—
151C24×C43—21no—
152C2×Q8×C43—41no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43C2×Q812yes—
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C22×C4×C43—41no—
162C22×C4×C43C2411yescharacteristic
163C2×C22⋊D43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167#10621898—21no—
168#10621898—21no—
169#10621898C2×Q812yes—
170#10621898#4112yes—
171C2×D172C2×D411yescharacteristic
172C2×C4×D43—21no—
173C2×C4×D43—41no—
174C2×C4×D43—41no—
175C2×Dic86C2×D411yescharacteristic
176M16×C43—21no—
177M16×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43—41no—
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C4⋊C4×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—21no—
197C22⋊C4×C43—41no—
198C22⋊C4×C43—41no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C22⋊Dic43—82no—
203#10621883—24no—
204#10621882—24no—
205(C2×D43)⋊C4—41no—
206(C2×D43)⋊C4—41no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211Dic43⋊C4—41no—
212Dic43⋊C4—41no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—41no—
216C4×Dic43—41no—
217#10621877—21no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877C2×Q812yes—
222#10621877#4112yes—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8C2×D411yescharacteristic
229C2×C43⋊C8C2×D411yescharacteristic
230#10621872—24no—
231C8×D43—24no—
232C23×C43—22no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—81no—
236C23×C43—81no—
237C23×C43H(5,𝔽2)11yescharacteristic
238C22×D43—21no—
239Q8×C43—161no—
240D4×C43—22no—
241D4×C43—22no—
242D4×C43—41no—
243D4×C43—41no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—81no—
252C2×C4×C43—161no—
253C2×C4×C43—161no—
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×Q811yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C432−1+411yescharacteristic
260C22⋊D43—22no—
261C22⋊D43—22no—
262C2×Dic43—21no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—81no—
269C2×Dic43—81no—
270D172—21no—
271D172C22⋊Q812yes—
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—161no—
275C4×D43—161no—
276Dic86—21no—
277Dic86C22⋊Q812yes—
278C8×C43—21no—
279C8×C43—21no—
280C8×C43—41no—
281C43⋊C8—22no—
282C43⋊C8—22no—
283C43⋊C8—21no—
284C43⋊C8—21no—
285C43⋊C8—41no—
286#26402—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—42no—
290C22×C43—82no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—161no—
294C22×C43#53911yescharacteristic
295C22×C43D4211yescharacteristic
296C22×C43#55411yescharacteristic
297C2×D43—22no—
298C2×D43—41no—
299C2×D43—41no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—81no—
307C4×C43C2×C22⋊Q811yescharacteristic
308C4×C43#52511yescharacteristic
309C4×C43#54711yescharacteristic
310C4×C43D4×Q811yescharacteristic
311Dic43—22no—
312Dic43—81no—
313Dic43—81no—
314Dic43—81no—
315#3083—431no—
316#3081D4311yescharacteristic, complemented
317#2946—431no—
318#2912—431no—
319#2092—431no—
320#2090—431no—
321#2063—431no—
322#2061—431no—
323#1952—431no—
324#1922—431no—
325#1907—431no—
326#1883—431no—
327#1866—431no—
328#1860—431no—
329#1856—431no—
330C2×C43—21no—
331C2×C43—21no—
332C2×C43—82no—
333C2×C43#244911yescharacteristic
334C2×C43#328811yescharacteristic
335C2×C43#329011yescharacteristic
336D43—42no—
337C2×AGL(1,ℤ/8)—431no—
338C2×#131—431no—
339#544C2×D4311yescharacteristic
340#520—431no—
341#520—431no—
342#518C2×D4311yescharacteristic
343#479—861no—
344#478—21no—
345#478—21no—
346#478—861no—
347#477—861no—
348#476—21no—
349#474—21no—
350#474—861no—
351#442—861no—
352#440—861no—
353C4×SD16—861no—
354C4×D8—861no—
355C2×#108—431no—
356#428—431no—
357#428—431no—
358#428—431no—
359#428—431no—
360#428—861no—
361#428—861no—
362#428C2×D4311yescharacteristic
363#427—861no—
364#427C2×D4311yescharacteristic
365C2×#107—431no—
366C2×#106—431no—
367C2×#106—861no—
368#424—431no—
369#424C2×D4311yescharacteristic
370C2×#104—431no—
371#418C2×D4311yescharacteristic
372#417—431no—
373#416—431no—
374C2×#102—431no—
375C2×#102C2×D4311yescharacteristic
376C2×#100—431no—
377#405—431no—
378#390—431no—
379#382—431no—
380#343—431no—
381#343—431no—
382#343—431no—
383#341—431no—
384#339—431no—
385#339—431no—
386#339—431no—
387#336—431no—
388C43#2640211yescharacteristic, complemented, Sylow
389C2×#41—431no—
390C22×D4C22×D4311yescharacteristic
391AGL(1,ℤ/8)—434no—
392AGL(1,ℤ/8)—862no—
393C2×SD16—861no—
394C2×D8—861no—
395#131—862no—
396#131—862no—
397C2×M16—431no—
398C2×M16—431no—
399C2×M16—431no—
400C2×M16—861no—
401C2×M16C22×D4311yescharacteristic
402C22×C8—431no—
403C22×C8—861no—
404C22×C8C22×D4311yescharacteristic
405C4⋊Q8—21no—
406C4⋊Q8—21no—
407#125—21no—
408#125—21no—
409C22⋊Q8—41no—
410C4×Q8—861no—
411C4×Q8—861no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—861no—
417C4×D4—861no—
418C4×D4—1721no—
419C4×D4—1721no—
420#117—861no—
421#117—861no—
422#117C22×D4311yescharacteristic
423#117C22×D4311yescharacteristic
424#117C22×D4311yescharacteristic
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C22⋊C4—41no—
431C2×C22⋊C4—1721no—
432C2×C42—431no—
433#108—862no—
434#107—21no—
435#107—861no—
436#107—861no—
437#107—861no—
438#107—861no—
439#107—861no—
440#107—861no—
441#107C22⋊D4311yescharacteristic
442#107C22⋊D4311yescharacteristic
443#106—21no—
444#106—861no—
445#106—861no—
446#106—861no—
447#106—861no—
448#106—861no—
449#106—861no—
450#106C22⋊D4311yescharacteristic
451#106C22⋊D4311yescharacteristic
452C4⋊C8—21no—
453C4⋊C8—21no—
454C4⋊C8—861no—
455C4⋊C8—861no—
456#104—862no—
457#103—431no—
458#103—431no—
459#103—861no—
460#102—21no—
461#102—21no—
462#102—21no—
463#102—21no—
464#102—431no—
465#102—431no—
466#102—861no—
467#102—861no—
468#102—861no—
469#100—862no—
470#97—861no—
471C4×C8—861no—
472#95—1721no—
473C24—21no—
474#41—432no—
475#41—432no—
476#41—861no—
477#41—861no—
478C2×Q8—41no—
479C2×Q8—431no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—431no—
486C2×D4—861no—
487C2×D4Q8×D4312yes—
488C22×C4—21no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—1721no—
496C22×C4—1721no—
497C22×C4C23×D4311yescharacteristic
498SD16—864no—
499D8—864no—
500M16—21no—
501M16—21no—
502M16—432no—
503M16—432no—
504M16—864no—
505M16—861no—
506M16—861no—
507M16—861no—
508M16—861no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—431no—
513C2×C8—431no—
514C2×C8—864no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8C2×C22⋊D4311yescharacteristic
521C2×C8C2×C22⋊D4311yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—1721no—
532C4⋊C4—1721no—
533C4⋊C4D4×D4311yescharacteristic
534C4⋊C4D4×D4311yescharacteristic
535C4⋊C4C2×C22⋊D4311yescharacteristic
536C4⋊C4C2×C22⋊D4311yescharacteristic
537C4⋊C4C2×C22⋊D4311yescharacteristic
538C4⋊C4C2×C22⋊D4311yescharacteristic
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—41no—
543C22⋊C4—41no—
544C22⋊C4—3442no—
545C22⋊C4—1721no—
546C22⋊C4—1721no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—861no—
551C42—861no—
552C42—1721no—
553C42—1721no—
554C23—22no—
555C23—41no—
556C23—41no—
557C23—81no—
558C23—81no—
559C23—861no—
560C23#1306337011yescharacteristic
561Q8—161no—
562Q8—432no—
563Q8—861no—
564D4—22no—
565D4—22no—
566D4—41no—
567D4—41no—
568D4—432no—
569D4—862no—
570D4—862no—
571D4—861no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—81no—
580C2×C4—161no—
581C2×C4—161no—
582C2×C4—861no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—3441no—
586C2×C4—3441no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—6881no—
593C2×C4—6881no—
594C2×C4C2×D4×D4311yescharacteristic
595C2×C4C22×C22⋊D4311yescharacteristic
596C2×C4C2×Q8×D4311yescharacteristic
597C2×C4#41×D4311yescharacteristic
598C2×C4#41×D4311yescharacteristic
599C2×C4#1306337311yescharacteristic
600C8—21no—
601C8—21no—
602C8—41no—
603C8—862no—
604C8—862no—
605C8—861no—
606C8—861no—
607C8—1721no—
608C22—21no—
609C22—21no—
610C22—42no—
611C22—82no—
612C22—81no—
613C22—81no—
614C22—161no—
615C22—862no—
616C22—1721no—
617C22—1721no—
618C22#1458349511yescharacteristic
619C22D4×C22⋊D4311yescharacteristic
620C22#1458360311yescharacteristic
621C4—41no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—81no—
628C4—862no—
629C4—3441no—
630C4—3441no—
631C4—3441no—
632C4C22⋊Q8×D4311yescharacteristic
633C4#1458340611yescharacteristic
634C4#1458355111yescharacteristic
635C4Q8×C22⋊D4311yescharacteristic
636C2—21no—
637C2—21no—
638C2—82no—
639C2—1722no—
640C2#1913840111yescharacteristic
641C2#1914635911yescharacteristic
642C2#1914637511yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3081C2
socleC22×C43D42
prime radicalC2×#13063351C22
hypercenter#3081D43
hypocenterC43#26402
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #3081

Complements

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

NH ≅ G/Ntype
1. #19144442C2semidirect
3. #19143187C2semidirect
4. #19136118C2semidirect
5. #19136105C2semidirect
6. #19135955C2semidirect
7. #19135942C2semidirect
8. #19135377C2semidirect
9. #19135196C2semidirect
12. #19134869C2semidirect
13. #19134825C2semidirect
14. #19134805C2semidirect
15. C43×#3081C2semidirect
69. #13063351Q8semidirect
316. #3081D43semidirect
388. C43#26402semidirect

Maximal subgroups

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

subgroupindex
#191444422
#191434272
#191431872
#191361182
#191361052
#191359552
#191359422
#191353772
#191351962
#191351062
#191349682
#191348692
#191348252
#191348052
C43×#30812
#2640243