Finite Group Databasebeta

← #25138113

Subgroups — #25138113

Order 11008.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144417C211yesmaximal, characteristic
2C2×#14583206C211yesmaximal, characteristic, complemented
3#19143261C211yesmaximal, characteristic
4#19136043C211yesmaximal, characteristic
5#19136038C211yesmaximal, characteristic
6#19135891C211yesmaximal, characteristic
7#19135891C211yesmaximal, characteristic
8#19135588C211yesmaximal, characteristic, complemented
9#19135377C211yesmaximal, characteristic, complemented
10#19135372C211yesmaximal, characteristic, complemented
11#19135370C211yesmaximal, characteristic, complemented
12#19135253C211yesmaximal, characteristic, complemented
13#19135253C211yesmaximal, characteristic, complemented
14#19134591C211yesmaximal, characteristic, complemented
15C4×#137×C43C211yesmaximal, characteristic
16C2×#13063317C2211yescharacteristic
17#14583206—21no—
18#14583206—21no—
19#14583206—21no—
20#14583206—21no—
21#14583206—21no—
22#14583206—21no—
23#14583199—21no—
24#14583199—21no—
25#14582960—21no—
26#14582960—21no—
27#14582956—21no—
28#14582952—21no—
29C2×#13063260C2211yescharacteristic
30C2×#13063260C2211yescharacteristic
31#14582942C2211yescharacteristic
32#14582942C2211yescharacteristic
33C2×#13063258C2211yescharacteristic
34C2×#13063256C2211yescharacteristic
35#14582923C2211yescharacteristic
36#14582923C2211yescharacteristic
37C2×C4⋊(C43⋊C8)C2211yescharacteristic
38#14582900C2211yescharacteristic
39#14582900C2211yescharacteristic
40C2×#13063249C2211yescharacteristic
41C2×#13063249C2211yescharacteristic
42C2×#13063244C2211yescharacteristic
43C2×#13063244C2211yescharacteristic
44#14582866C2211yescharacteristic
45#14582866C2211yescharacteristic
46#14582855C2211yescharacteristic
47#14582855C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582668C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582667C2211yescharacteristic
52#14582667C2211yescharacteristic
53#14582667C2211yescharacteristic
54#14582663C2211yescharacteristic
55#14582663C2211yescharacteristic
56C2×#137×C43C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C2×C4×Q8×C43C2211yescharacteristic
59C43×#441—21no—
60C43×#440—21no—
61C4×Q16×C43—21no—
62C4×SD16×C43—21no—
63C43×#428C2211yescharacteristic
64C43×#419C2211yescharacteristic
65C43×#417C2211yescharacteristic
66C4×M16×C43C2211yescharacteristic
67C2×#10621877C2311yescharacteristic
68C2×#10621877C2311yescharacteristic
69C2×#10621877C2311yescharacteristic
70C2×#10621877C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063317—21no—
74#13063317—21no—
75#13063317—21no—
76#13063317—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81#13063260—22no—
82#13063260—22no—
83#13063258—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063256—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256—21no—
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)D411yescharacteristic
96C4⋊(C43⋊C8)D411yescharacteristic
97C4⋊(C43⋊C8)D411yescharacteristic
98C4⋊(C43⋊C8)D411yescharacteristic
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063249—21no—
105#13063246—21no—
106#13063246—21no—
107#13063244—22no—
108#13063244—22no—
109C22⋊(C43⋊C8)—21no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113#13063236—21no—
114#13063236—21no—
115C4×C43⋊C8—21no—
116C4×C43⋊C8—21no—
117C2×#41×C43C2311yescharacteristic
118C22×Q8×C43C2311yescharacteristic
119#137×C43—22no—
120#137×C43—22no—
121C2×Q16×C43—21no—
122C2×SD16×C43—21no—
123C2×M16×C43C2311yescharacteristic
124C2×M16×C43C2311yescharacteristic
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43D411yescharacteristic
130C4×Q8×C43D411yescharacteristic
131C4×D4×C43—21no—
132C4×D4×C43—21no—
133C4×D4×C43D411yescharacteristic
134C4×D4×C43D411yescharacteristic
135#117×C43—21no—
136#117×C43C2311yescharacteristic
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C42×C43—21no—
140C2×C42×C43—21no—
141C2×C42×C43C2311yescharacteristic
142#107×C43—21no—
143#106×C43—21no—
144#103×C43—21no—
145#103×C43—21no—
146#103×C43—21no—
147#102×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×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43C2×D411yescharacteristic
160C2×Q8×C43#4112yes—
161C2×D4×C43—21no—
162C2×D4×C43C2×D411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43#4111yescharacteristic
169C22×C4×C43#4111yescharacteristic
170C22×C4×C43C2411yescharacteristic
171C22×Dic43—21no—
172C22×Dic43—21no—
173Q16×C43—24no—
174SD16×C43—24no—
175M16×C43—21no—
176M16×C43—21no—
177M16×C43—21no—
178M16×C43#4112yes—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43C2×D411yescharacteristic
188C4⋊C4×C43C2×D411yescharacteristic
189C22⋊C4×C43—21no—
190C22⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—21no—
195C42×C43—41no—
196C42×C43—41no—
197C42×C43C2×D411yescharacteristic
198C42×C43C2×D411yescharacteristic
199C42×C43C2×D411yescharacteristic
200C42×C43C2×D411yescharacteristic
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205Dic43⋊C4—41no—
206Dic43⋊C4—41no—
207Dic43⋊C4—41no—
208Dic43⋊C4—41no—
209#10621877—21no—
210#10621877—21no—
211#10621877—21no—
212#10621877—21no—
213#10621877—21no—
214#10621877—21no—
215#10621877—21no—
216#10621877—21no—
217C2×C43⋊C8—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⋊C8—21no—
225C2×C43⋊C8C2×D411yescharacteristic
226C2×C43⋊C8C2×D411yescharacteristic
227C2×C43⋊C8C2×D411yescharacteristic
228C2×C43⋊C8C2×D411yescharacteristic
229C23×C43—21no—
230C23×C43C2×#4111yescharacteristic
231Q8×C43—22no—
232Q8×C43—21no—
233Q8×C43—21no—
234Q8×C43—22no—
235Q8×C43—41no—
236Q8×C43—41no—
237D4×C43—21no—
238D4×C43—21no—
239D4×C43—41no—
240D4×C43—41no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—22no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—42no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—81no—
254C2×C4×C43—81no—
255C2×C4×C43#12111yescharacteristic
256C2×C4×C43#12111yescharacteristic
257C2×C4×C43#12111yescharacteristic
258C2×C4×C43#12111yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C432−1+411yescharacteristic
264C2×C4×C432−1+411yescharacteristic
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—81no—
268C2×Dic43—81no—
269C8×C43—22no—
270C8×C43—41no—
271C43⋊C8—21no—
272C43⋊C8—21no—
273C43⋊C8—21no—
274C43⋊C8—21no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279#24725—431nomaximal, Sylow
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43C2×#12111yescharacteristic
286C22×C43#55211yescharacteristic
287C22×C43#55611yescharacteristic
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—41no—
293C4×C43—42no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—81no—
297C4×C43#52511yescharacteristic
298C4×C43#53611yescharacteristic
299C4×C43#54711yescharacteristic
300C4×C43#54811yescharacteristic
301Dic43—81no—
302Dic43—81no—
303#3080—431no—
304C2×#479—431no—
305C4×#137D4311yescharacteristic
306#2925—431no—
307#2079—431no—
308#2078—431no—
309#2052—431no—
310#2052—431no—
311#1998—431no—
312#1952—431no—
313#1951—431no—
314#1950—431no—
315#1930—431no—
316#1930—431no—
317#1801—431no—
318C2×C43—21no—
319C2×C43—21no—
320C2×C43—81no—
321C2×C43#241511yescharacteristic
322C2×C43#306711yescharacteristic
323C2×C43#306911yescharacteristic
324C2×#137C2×D4311yescharacteristic
325C2×#125—431no—
326C4×#41C2×D4311yescharacteristic
327C2×C4×Q8C2×D4311yescharacteristic
328#479—861no—
329#479—861no—
330#479—861no—
331#479—861no—
332#479—861no—
333#479—861no—
334#478—861no—
335#478—861no—
336#441—21no—
337#440—21no—
338C4×Q16—21no—
339C4×SD16—21no—
340#433—861no—
341#433—861no—
342#432—861no—
343#431—861no—
344C2×#108—431no—
345C2×#108—431no—
346#428—431no—
347#428—431no—
348#428C2×D4311yescharacteristic
349C2×#107—431no—
350C2×#106—431no—
351#423—431no—
352#423—431no—
353C2×C4⋊C8—431no—
354#419C2×D4311yescharacteristic
355#417—431no—
356#417—431no—
357#417C2×D4311yescharacteristic
358C2×#103—431no—
359C2×#103—431no—
360C2×#101—431no—
361C2×#101—431no—
362#408—431no—
363#408—431no—
364#405—431no—
365#405—431no—
366C4×M16C2×D4311yescharacteristic
367#343—431no—
368#343—431no—
369#343—431no—
370#343—431no—
371#343—431no—
372#343—431no—
373#341—431no—
374#341—431no—
375C43#2472511yescharacteristic, complemented, Sylow
376C2×#41C22×D4311yescharacteristic
377C22×Q8C22×D4311yescharacteristic
378#137—22no—
379#137—22no—
380C2×Q16—21no—
381C2×SD16—21no—
382C2×M16—431no—
383C2×M16—431no—
384C2×M16—431no—
385C2×M16—431no—
386C2×M16C22×D4311yescharacteristic
387C2×M16C22×D4311yescharacteristic
388C22×C8—431no—
389C22×C8—431no—
390#125—861no—
391#125—861no—
392#125—861no—
393#125—861no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8C22⋊D4311yescharacteristic
399C4×Q8C22⋊D4311yescharacteristic
400C4×D4—21no—
401C4×D4—21no—
402C4×D4C22⋊D4311yescharacteristic
403C4×D4C22⋊D4311yescharacteristic
404#117—21no—
405#117C22×D4311yescharacteristic
406C2×C4⋊C4—21no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C42—21no—
413C2×C42—21no—
414C2×C42C22×D4311yescharacteristic
415#108—862no—
416#108—862no—
417#107—21no—
418#107—861no—
419#107—861no—
420#107—861no—
421#107—861no—
422#106—21no—
423#106—861no—
424#106—861no—
425#106—861no—
426#106—861no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—431no—
430C4⋊C8—431no—
431C4⋊C8—861no—
432C4⋊C8—861no—
433C4⋊C8—861no—
434C4⋊C8—861no—
435#103—21no—
436#103—21no—
437#103—21no—
438#103—861no—
439#103—861no—
440#103—861no—
441#103—861no—
442#103—861no—
443#103—861no—
444#102—21no—
445#102—861no—
446#102—861no—
447#101—862no—
448#101—862no—
449C22⋊C8—861no—
450C22⋊C8—861no—
451C22⋊C8—861no—
452C22⋊C8—861no—
453#97—21no—
454#97—861no—
455#97—861no—
456C4×C8—21no—
457C4×C8—861no—
458C4×C8—861no—
459#41—21no—
460#41—21no—
461#41—21no—
462#41—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8#1062189812yes—
469C2×Q8C2×C22⋊D4311yescharacteristic
470C2×D4—21no—
471C2×D4C2×C22⋊D4311yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4#1062190011yescharacteristic
480C22×C4#1062190011yescharacteristic
481C22×C4C23×D4311yescharacteristic
482Q16—24no—
483SD16—24no—
484M16—21no—
485M16—21no—
486M16—21no—
487M16—861no—
488M16—861no—
489M16—861no—
490M16—861no—
491M16—861no—
492M16—861no—
493M16—861no—
494M16—861no—
495M16#1062189812yes—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—431no—
499C2×C8—431no—
500C2×C8—431no—
501C2×C8—431no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—1721no—
521C4⋊C4—1721no—
522C4⋊C4—1721no—
523C4⋊C4—1721no—
524C4⋊C4C2×C22⋊D4311yescharacteristic
525C4⋊C4C2×C22⋊D4311yescharacteristic
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—41no—
533C42—41no—
534C42D4×D4311yescharacteristic
535C42D4×D4311yescharacteristic
536C42C2×C22⋊D4311yescharacteristic
537C42C2×C22⋊D4311yescharacteristic
538C23—21no—
539C23C2×#1062190011yescharacteristic
540Q8—22no—
541Q8—22no—
542Q8—21no—
543Q8—21no—
544Q8—41no—
545Q8—41no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—3441no—
565C2×C4—3441no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4#1306329711yescharacteristic
569C2×C4#1306329711yescharacteristic
570C2×C4#1306329711yescharacteristic
571C2×C4#1306329711yescharacteristic
572C2×C4C2×D4×D4311yescharacteristic
573C2×C4C22×C22⋊D4311yescharacteristic
574C2×C4C2×#1062189811yescharacteristic
575C2×C4C2×#1062189811yescharacteristic
576C2×C4#1306337211yescharacteristic
577C2×C4#1306337211yescharacteristic
578C8—22no—
579C8—41no—
580C8—861no—
581C8—861no—
582C8—861no—
583C8—861no—
584C8—1721no—
585C8—1721no—
586C8—1721no—
587C8—1721no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C2×#1306329711yescharacteristic
594C22#1458358911yescharacteristic
595C22#1458361911yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—42no—
604C4—81no—
605C4—3441no—
606C4—3441no—
607C4#1458341011yescharacteristic
608C4#1458347011yescharacteristic
609C4#1458355411yescharacteristic
610C4#1458355811yescharacteristic
611C2—21no—
612C2—21no—
613C2—81no—
614C2#1913802411yescharacteristic
615C2#1914431211yescharacteristic
616C2#1914432911yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#137×C43C2
socleC22×C43C2×#121
prime radicalC2×#41×C43C23
hypercenterC4×#137D43
hypocenterC43#24725
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
2. C2×#14583206C2semidirect
8. #19135588C2semidirect
9. #19135377C2semidirect
10. #19135372C2semidirect
11. #19135370C2semidirect
12. #19135253C2semidirect
13. #19135253C2semidirect
14. #19134591C2semidirect
375. C43#24725semidirect

Maximal subgroups

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

subgroupindex
#191444172
C2×#145832062
#191432612
#191360432
#191360382
#191358912
#191355882
#191353772
#191353722
#191353702
#191352532
#191345912
C4×#137×C432
#2472543