Finite Group Databasebeta

← #25160037

Subgroups — #25160037

Order 11008.

714 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144455C211yesmaximal, characteristic
2#19144437C211yesmaximal, characteristic, complemented
3#19143188C211yesmaximal, characteristic
4#19136136C211yesmaximal, characteristic, complemented
5#19136108C211yesmaximal, characteristic, complemented
6#19135960C211yesmaximal, characteristic, complemented
7#19135938C211yesmaximal, characteristic, complemented
8#19135375C211yesmaximal, characteristic, complemented
9#19135194C211yesmaximal, characteristic, complemented
10#19135112C211yesmaximal, characteristic
11#19134966C211yesmaximal, characteristic
12#19134872C211yesmaximal, characteristic
13#19134821C211yesmaximal, characteristic
14#19134810C211yesmaximal, characteristic, complemented
15C43×#2947C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17#14583527C2211yescharacteristic
18#14583382C2211yescharacteristic
19#14583206—21no—
20#14583206—21no—
21#14583204—21no—
22#14583201—21no—
23#14583194—21no—
24#14583187—21no—
25#14583184—21no—
26#14583182—21no—
27C2×#13063261C2211yescharacteristic
28#14582942—21no—
29#14582942C2211yescharacteristic
30#14582942C2211yescharacteristic
31#14582942C2211yescharacteristic
32#14582939—21no—
33#14582939C2211yescharacteristic
34#14582935—21no—
35#14582935C2211yescharacteristic
36C2×#13063257C2211yescharacteristic
37C2×#13063256—21no—
38C2×#13063256C2211yescharacteristic
39#14582926C2211yescharacteristic
40#14582925C2211yescharacteristic
41C2×#13063252C2211yescharacteristic
42#14582908C2211yescharacteristic
43#14582900C2211yescharacteristic
44C2×#13063249C2211yescharacteristic
45C2×#13063244C2211yescharacteristic
46#14582806C2211yescharacteristic
47#14582768C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582667C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582663C2211yescharacteristic
52#14582660C2211yescharacteristic
53#14582658C2211yescharacteristic
54#14582658C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×#137×C43C2211yescharacteristic
57C43×#520C2211yescharacteristic
58C43×#519C2211yescharacteristic
59C43×#441—21no—
60C43×#440—21no—
61C4×Q16×C43—21no—
62C4×SD16×C43—21no—
63C43×#428C2211yescharacteristic
64C43×#416C2211yescharacteristic
65C2×#103×C43C2211yescharacteristic
66C43×#405C2211yescharacteristic
67#13063332—22no—
68#13063332—22no—
69C2×#10621877—21no—
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C2×#10621877C2311yescharacteristic
73C22×C43⋊C8—21no—
74C22×C43⋊C8C2311yescharacteristic
75#13063325—21no—
76#13063324—21no—
77#13063317—21no—
78#13063316—21no—
79#13063302—41no—
80Q8×Dic43—21no—
81D4×Dic43—21no—
82D4×Dic43—41no—
83#13063284—21no—
84#13063284C2311yescharacteristic
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—41no—
89C2×C4×Dic43C2311yescharacteristic
90#13063261—22no—
91#13063258—21no—
92#13063258—21no—
93#13063258—21no—
94#13063258—21no—
95#13063258D411yescharacteristic
96#13063258D411yescharacteristic
97#13063257—21no—
98#13063257—21no—
99#13063256—21no—
100#13063256—21no—
101#13063256—21no—
102#13063256—21no—
103#13063256—21no—
104#13063256—21no—
105#13063256D411yescharacteristic
106#13063256D411yescharacteristic
107C4⋊(C43⋊C8)—21no—
108C4⋊(C43⋊C8)—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063252—22no—
112#13063249—21no—
113#13063249—21no—
114#13063249—21no—
115#13063249—21no—
116#13063249—21no—
117#13063246—21no—
118#13063244—22no—
119C43⋊#95—41no—
120C2×#41×C43C2311yescharacteristic
121C22×Q8×C43C2311yescharacteristic
122#137×C43—22no—
123#137×C43Q814yescomplemented
124C2×Q16×C43—21no—
125C2×SD16×C43—21no—
126C2×M16×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×Q8×C43—21no—
131C4×Q8×C43—21no—
132C4×Q8×C43—21no—
133C4×D4×C43—21no—
134C4×D4×C43—41no—
135#117×C43—21no—
136#117×C43—41no—
137#117×C43C2311yescharacteristic
138#117×C43C2311yescharacteristic
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43C2311yescharacteristic
141#107×C43—21no—
142#106×C43—21no—
143#103×C43—21no—
144#103×C43—21no—
145#103×C43D411yescharacteristic
146#103×C43D411yescharacteristic
147#102×C43D411yescharacteristic
148#102×C43D411yescharacteristic
149#97×C43—21no—
150C4×C8×C43—21no—
151#41×C43—21no—
152#41×C43—21no—
153#41×C43C2×Q812yes—
154#41×C43#4112yes—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43C2×D411yescharacteristic
161C2×Q8×C43C2×Q812yes—
162C2×D4×C43—21no—
163C2×D4×C43C2×D411yescharacteristic
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—41no—
168C22×C4×C43C2411yescharacteristic
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—41no—
173C2×Dic86—41no—
174Q16×C43—24no—
175SD16×C43—24no—
176M16×C43—21no—
177M16×C43C2×Q812yes—
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
192C22⋊C4×C43—21no—
193C22⋊C4×C43—21no—
194C22⋊C4×C43—41no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43—41no—
198C42×C43—41no—
199C42×C43—41no—
200C22⋊Dic43—21no—
201C22⋊Dic43—41no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—41no—
207C4⋊Dic43—41no—
208C4⋊Dic43C2×D411yescharacteristic
209C4⋊Dic43C2×D411yescharacteristic
210Dic43⋊C4—41no—
211Dic43⋊C4—41no—
212Dic43⋊C4—82no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—41no—
217#10621877—24no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877—21no—
222#10621877—21no—
223#10621877#4112yes—
224C2×C43⋊C8—24no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8C2×D411yescharacteristic
231C2×C43⋊C8C2×D411yescharacteristic
232C23×C43—21no—
233C23×C43H(5,𝔽2)11yescharacteristic
234Q8×C43—21no—
235Q8×C43—22no—
236Q8×C43—22no—
237Q8×C43—41no—
238Q8×C43—41no—
239Q8×C43C22⋊Q812yes—
240D4×C43—22no—
241D4×C43—22no—
242D4×C43—21no—
243D4×C43C22⋊Q812yes—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—22no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—81no—
256C2×C4×C43—161no—
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×Q811yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C432−1+411yescharacteristic
263C2×Dic43—22no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—81no—
271C2×Dic43—81no—
272C2×Dic43—161no—
273Dic86—161no—
274C8×C43—22no—
275C8×C43—21no—
276C8×C43—21no—
277C43⋊C8—21no—
278C43⋊C8—22no—
279C43⋊C8—21no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282#26401—431nomaximal, Sylow
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—22no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43#53911yescharacteristic
289C22×C43D4211yescharacteristic
290C22×C43#55411yescharacteristic
291C4×C43—22no—
292C4×C43—42no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—81no—
298C4×C43C2×C22⋊Q811yescharacteristic
299C4×C43#52511yescharacteristic
300C4×C43#54711yescharacteristic
301C4×C43D4×Q811yescharacteristic
302Dic43—42no—
303Dic43—41no—
304Dic43—41no—
305Dic43—81no—
306Dic43—81no—
307#3084—431no—
308#3082—431no—
309#2947D4311yescharacteristic
310#2912—431no—
311#2096—431no—
312#2090—431no—
313#2064—431no—
314#2060—431no—
315#1951—431no—
316#1922—431no—
317#1908—431no—
318#1882—431no—
319#1866—431no—
320#1859—431no—
321#1857—431no—
322C2×C43—21no—
323C2×C43—21no—
324C2×C43—42no—
325C2×C43#244911yescharacteristic
326C2×C43#328911yescharacteristic
327C2×C43#329111yescharacteristic
328C2×#137C2×D4311yescharacteristic
329C2×#131—431no—
330#544—431no—
331#520—431no—
332#520C2×D4311yescharacteristic
333#519C2×D4311yescharacteristic
334#479—861no—
335#479—861no—
336#479—861no—
337#478—861no—
338#477—861no—
339#476—861no—
340#475—861no—
341#475—861no—
342#441—21no—
343#440—21no—
344C4×Q16—21no—
345C4×SD16—21no—
346C2×#108—431no—
347#428—431no—
348#428—431no—
349#428—431no—
350#428—431no—
351#428—861no—
352#428—861no—
353#428C2×D4311yescharacteristic
354#427—431no—
355#427—861no—
356C2×#106—431no—
357C2×#106—431no—
358C2×#106—861no—
359#424—431no—
360#424—431no—
361C2×#104—431no—
362#419—431no—
363#417—431no—
364#416C2×D4311yescharacteristic
365C2×#103—431no—
366C2×#103C2×D4311yescharacteristic
367C2×#101—431no—
368#405C2×D4311yescharacteristic
369#391—431no—
370#384—431no—
371#343—431no—
372#343—431no—
373#343—431no—
374#341—431no—
375#339—431no—
376#339—431no—
377#339—431no—
378#336—431no—
379C43#2640111yescharacteristic, complemented, Sylow
380C2×#41C22×D4311yescharacteristic
381C22×Q8C22×D4311yescharacteristic
382#137—22no—
383#137Dic8614yescomplemented
384C2×Q16—21no—
385C2×SD16—21no—
386#131—862no—
387#131—862no—
388C2×M16—431no—
389C2×M16—431no—
390C2×M16—431no—
391C2×M16—861no—
392C2×M16C22×D4311yescharacteristic
393C22×C8—431no—
394C22×C8—861no—
395C22×C8C22×D4311yescharacteristic
396C4⋊Q8—861no—
397C4⋊Q8—861no—
398#125—861no—
399#125—861no—
400C22⋊Q8—1721no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—861no—
407C4×D4—21no—
408C4×D4—41no—
409C4×D4—861no—
410C4×D4—1721no—
411#117—21no—
412#117—41no—
413#117—431no—
414#117—861no—
415#117C22×D4311yescharacteristic
416#117C22×D4311yescharacteristic
417C2×C4⋊C4—21no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—1721no—
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C42—431no—
424#108—862no—
425#107—21no—
426#107—431no—
427#107—431no—
428#107—861no—
429#107—861no—
430#107—861no—
431#107—861no—
432#106—21no—
433#106—431no—
434#106—431no—
435#106—861no—
436#106—861no—
437#106—861no—
438#106—861no—
439#106—861no—
440#106—861no—
441#106—861no—
442#106—861no—
443C4⋊C8—861no—
444C4⋊C8—861no—
445C4⋊C8—861no—
446C4⋊C8—861no—
447#104—862no—
448#103—21no—
449#103—21no—
450#103—861no—
451#103—861no—
452#103—861no—
453#103—861no—
454#103—861no—
455#103C22⋊D4311yescharacteristic
456#103C22⋊D4311yescharacteristic
457#102—861no—
458#102C22⋊D4311yescharacteristic
459#102C22⋊D4311yescharacteristic
460#101—862no—
461#97—21no—
462C4×C8—21no—
463#95—1721no—
464#41—21no—
465#41—21no—
466#41C2×Dic8612yes—
467#41#1062189812yes—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—1721no—
474C2×Q8C2×Dic8612yes—
475C2×Q8C2×C22⋊D4311yescharacteristic
476C2×D4—21no—
477C2×D4C2×C22⋊D4311yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—41no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—1721no—
486C22×C4C23×D4311yescharacteristic
487Q16—24no—
488SD16—24no—
489M16—21no—
490M16—432no—
491M16—864no—
492M16—861no—
493M16—861no—
494M16—861no—
495M16—861no—
496M16—861no—
497M16C2×Dic8612yes—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—431no—
502C2×C8—431no—
503C2×C8—864no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8C2×C22⋊D4311yescharacteristic
510C2×C8C2×C22⋊D4311yescharacteristic
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—431no—
517C4⋊C4—431no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—3442no—
523C4⋊C4—1721no—
524C4⋊C4—1721no—
525C4⋊C4—1721no—
526C4⋊C4—1721no—
527C4⋊C4D4×D4311yescharacteristic
528C4⋊C4D4×D4311yescharacteristic
529C4⋊C4C2×C22⋊D4311yescharacteristic
530C4⋊C4C2×C22⋊D4311yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—41no—
534C22⋊C4—861no—
535C22⋊C4—1721no—
536C42—21no—
537C42—21no—
538C42—41no—
539C42—41no—
540C42—41no—
541C42—861no—
542C42—861no—
543C42—861no—
544C42—1721no—
545C23—21no—
546C23#1306337011yescharacteristic
547Q8—21no—
548Q8—22no—
549Q8—22no—
550Q8—41no—
551Q8—41no—
552Q8—6881no—
553Q8#1306330412yes—
554D4—22no—
555D4—22no—
556D4—21no—
557D4#1306330412yes—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—81no—
570C2×C4—161no—
571C2×C4—862no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—3441no—
575C2×C4—3441no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—6881no—
581C2×C4C2×D4×D4311yescharacteristic
582C2×C4C22×C22⋊D4311yescharacteristic
583C2×C4C22×Dic8611yescharacteristic
584C2×C4#41×D4311yescharacteristic
585C2×C4C2×#1062189811yescharacteristic
586C2×C4#1306337211yescharacteristic
587C8—22no—
588C8—21no—
589C8—21no—
590C8—861no—
591C8—861no—
592C8—862no—
593C8—1721no—
594C8—1721no—
595C22—21no—
596C22—21no—
597C22—22no—
598C22—41no—
599C22—41no—
600C22#1458349111yescharacteristic
601C22D4×C22⋊D4311yescharacteristic
602C22#1458360811yescharacteristic
603C4—22no—
604C4—42no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—81no—
610C4—3441no—
611C4—3441no—
612C4—1722no—
613C4—1721no—
614C4—1721no—
615C4C2×#1306330411yescharacteristic
616C4#1458340811yescharacteristic
617C4#1458354811yescharacteristic
618C4D4×Dic8611yescharacteristic
619C2—21no—
620C2—21no—
621C2—42no—
622C2#1913839811yescharacteristic
623C2#1914636611yescharacteristic
624C2#1914638611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2947C2
socleC22×C43D42
prime radicalC2×#41×C43C23
hypercenter#2947D43
hypocenterC43#26401
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2947

Complements

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

NH ≅ G/Ntype
2. #19144437C2semidirect
4. #19136136C2semidirect
5. #19136108C2semidirect
6. #19135960C2semidirect
7. #19135938C2semidirect
8. #19135375C2semidirect
9. #19135194C2semidirect
14. #19134810C2semidirect
123. #137×C43Q8semidirect
379. C43#26401semidirect
383. #137Dic86semidirect

Maximal subgroups

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

subgroupindex
#191444552
#191444372
#191431882
#191361362
#191361082
#191359602
#191359382
#191353752
#191351942
#191351122
#191349662
#191348722
#191348212
#191348102
C43×#29472
#2640143