Finite Group Databasebeta

← #25138107

Subgroups — #25138107

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×#14583207C211yesmaximal, characteristic, complemented
3C4×#13063355C211yesmaximal, characteristic
4#19136040C211yesmaximal, characteristic
5#19136035C211yesmaximal, characteristic
6#19135893C211yesmaximal, characteristic
7#19135893C211yesmaximal, characteristic
8#19135587C211yesmaximal, characteristic, complemented
9#19135380C211yesmaximal, characteristic, complemented
10#19135375C211yesmaximal, characteristic, complemented
11#19135371C211yesmaximal, characteristic, complemented
12#19135250C211yesmaximal, characteristic, complemented
13#19135250C211yesmaximal, characteristic, complemented
14#19134588C211yesmaximal, characteristic, complemented
15C43×#2925C211yesmaximal, characteristic
16C2×#13063355C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19#14583207—21no—
20#14583207—21no—
21#14583207—21no—
22#14583207—21no—
23#14583206—21no—
24#14583206—21no—
25#14583199—21no—
26#14583199—21no—
27#14583004—21no—
28#14582999—21no—
29C4×#10621885—21no—
30C4×#10621883—21no—
31C2×#13063261C2211yescharacteristic
32C2×#13063261C2211yescharacteristic
33#14582942C2211yescharacteristic
34#14582942C2211yescharacteristic
35#14582942C2211yescharacteristic
36C2×#13063259C2211yescharacteristic
37C2×#13063257C2211yescharacteristic
38#14582923C2211yescharacteristic
39#14582907C2211yescharacteristic
40#14582900C2211yescharacteristic
41#14582900C2211yescharacteristic
42#14582900C2211yescharacteristic
43C2×#13063250C2211yescharacteristic
44C2×#13063250C2211yescharacteristic
45C2×#13063243C2211yescharacteristic
46C2×#13063243C2211yescharacteristic
47C4×#10621877C2211yescharacteristic
48#14582667C2211yescharacteristic
49#14582667C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582667C2211yescharacteristic
52#14582667C2211yescharacteristic
53#14582667C2211yescharacteristic
54#14582664C2211yescharacteristic
55#14582664C2211yescharacteristic
56C4×#41×C43C2211yescharacteristic
57C43×#433—21no—
58C43×#433—21no—
59C43×#432—21no—
60C43×#431—21no—
61C43×#423C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#408C2211yescharacteristic
64C43×#408C2211yescharacteristic
65C43×#405C2211yescharacteristic
66C43×#405C2211yescharacteristic
67C22×Dic86C2311yescharacteristic
68#13063355—22no—
69#13063355—22no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72C2×#10621877C2311yescharacteristic
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76#13063317—21no—
77#13063317—21no—
78#13063317—21no—
79#13063317—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86—21no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×C4×Dic43—21no—
91#13063261—22no—
92#13063261—22no—
93#13063259—21no—
94#13063259—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063257—21no—
99#13063257—21no—
100#13063256—21no—
101#13063256—21no—
102#13063256—21no—
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)—21no—
105#13063250—21no—
106#13063250—21no—
107#13063250—21no—
108#13063250—21no—
109#13063249—21no—
110#13063249—21no—
111#13063249—21no—
112#13063248—21no—
113#13063248—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117#13063243—22no—
118#13063243—22no—
119#13063236—21no—
120C4×C43⋊C8—21no—
121C2×#41×C43C2311yescharacteristic
122C2×M16×C43C2311yescharacteristic
123C2×M16×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C4×Q8×C43D411yescharacteristic
127C4×Q8×C43D411yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43D411yescharacteristic
131C4×D4×C43D411yescharacteristic
132#117×C43—21no—
133#117×C43C2311yescharacteristic
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43D411yescharacteristic
139C4⋊C8×C43D411yescharacteristic
140C4⋊C8×C43D411yescharacteristic
141C4⋊C8×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C22⋊C8×C43—21no—
144C22⋊C8×C43—21no—
145C22⋊C8×C43—21no—
146#97×C43—21no—
147#97×C43—21no—
148C4×C8×C43—21no—
149C4×C8×C43—21no—
150#41×C43—21no—
151#41×C43—21no—
152#41×C43—21no—
153#41×C43—21no—
154C2×Q8×C43C2×D411yescharacteristic
155C2×D4×C43—21no—
156C2×D4×C43C2×D411yescharacteristic
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43#4111yescharacteristic
161C22×C4×C43#4111yescharacteristic
162C22×C4×C43C2411yescharacteristic
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86#4112yes—
173M16×C43—21no—
174M16×C43—21no—
175M16×C43—21no—
176M16×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43C2×D411yescharacteristic
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43C2×D411yescharacteristic
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43C2×D411yescharacteristic
190C4⋊C4×C43C2×D411yescharacteristic
191C22⋊C4×C43—21no—
192C22⋊C4×C43—21no—
193C22⋊C4×C43—21no—
194C42×C43—21no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43C2×D411yescharacteristic
198C42×C43C2×D411yescharacteristic
199C42×C43C2×D411yescharacteristic
200C42×C43C2×D411yescharacteristic
201#10621885—24no—
202#10621883—24no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209Dic43⋊C4—41no—
210Dic43⋊C4—41no—
211Dic43⋊C4—41no—
212Dic43⋊C4—41no—
213Dic43⋊C4—41no—
214Dic43⋊C4—41no—
215C4×Dic43—41no—
216C4×Dic43—41no—
217#10621877—21no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877—21no—
222#10621877—21no—
223#10621877—21no—
224#10621877#4112yes—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C23×C43—21no—
230C23×C43C2×#4111yescharacteristic
231Q8×C43—21no—
232Q8×C43—21no—
233D4×C43—21no—
234D4×C43—21no—
235D4×C43—41no—
236D4×C43—41no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—42no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—81no—
246C2×C4×C43#12111yescharacteristic
247C2×C4×C43#12111yescharacteristic
248C2×C4×C43#12111yescharacteristic
249C2×C4×C43#12111yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C432−1+411yescharacteristic
255C2×C4×C432−1+411yescharacteristic
256C2×Dic43—22no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—81no—
263C2×Dic43—81no—
264C2×Dic43—81no—
265Dic86—22no—
266Dic86—22no—
267Dic86—41no—
268Dic86—41no—
269C8×C43—21no—
270C8×C43—21no—
271C8×C43—21no—
272C8×C43—21no—
273C8×C43—41no—
274C8×C43—41no—
275C43⋊C8—22no—
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—41no—
294C4×C43—41no—
295C4×C43#52511yescharacteristic
296C4×C43#53611yescharacteristic
297C4×C43#54711yescharacteristic
298C4×C43#54811yescharacteristic
299Dic43—42no—
300Dic43—81no—
301Dic43—81no—
302Dic43—81no—
303#3080—431no—
304C2×#479—431no—
305C4×#137—431no—
306#2925D4311yescharacteristic
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×#137—431no—
325C2×#125—431no—
326C4×#41C2×D4311yescharacteristic
327C2×C4×Q8—431no—
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—861no—
337#440—861no—
338C4×Q16—861no—
339C4×SD16—861no—
340#433—21no—
341#433—21no—
342#432—21no—
343#431—21no—
344C2×#108—431no—
345C2×#108—431no—
346#428—431no—
347#428—431no—
348#428—431no—
349C2×#107—431no—
350C2×#106—431no—
351#423—431no—
352#423C2×D4311yescharacteristic
353C2×C4⋊C8C2×D4311yescharacteristic
354#419—431no—
355#417—431no—
356#417—431no—
357#417—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#101—431no—
361C2×#101—431no—
362#408C2×D4311yescharacteristic
363#408C2×D4311yescharacteristic
364#405C2×D4311yescharacteristic
365#405C2×D4311yescharacteristic
366C4×M16—431no—
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×Q8—431no—
378#137—862no—
379#137—862no—
380C2×Q16—861no—
381C2×SD16—861no—
382C2×M16—431no—
383C2×M16—431no—
384C2×M16—431no—
385C2×M16—431no—
386C2×M16C22×D4311yescharacteristic
387C2×M16C22×D4311yescharacteristic
388C22×C8C22×D4311yescharacteristic
389C22×C8C22×D4311yescharacteristic
390#125—861no—
391#125—861no—
392#125—861no—
393#125—861no—
394C4×Q8—861no—
395C4×Q8—861no—
396C4×Q8—861no—
397C4×Q8—861no—
398C4×Q8D17211yescharacteristic
399C4×Q8D17211yescharacteristic
400C4×D4—21no—
401C4×D4—21no—
402C4×D4D17211yescharacteristic
403C4×D4D17211yescharacteristic
404#117—21no—
405#117C22×D4311yescharacteristic
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C42—21no—
413C2×C42—861no—
414C2×C42C22×D4311yescharacteristic
415#108—862no—
416#108—862no—
417#107—861no—
418#107—861no—
419#107—861no—
420#107—861no—
421#107—861no—
422#106—861no—
423#106—861no—
424#106—861no—
425#106—861no—
426#106—861no—
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8—861no—
430C4⋊C8—861no—
431C4⋊C8C22⋊D4311yescharacteristic
432C4⋊C8C22⋊D4311yescharacteristic
433C4⋊C8C22⋊D4311yescharacteristic
434C4⋊C8C22⋊D4311yescharacteristic
435#103—861no—
436#103—861no—
437#103—861no—
438#103—861no—
439#103—861no—
440#103—861no—
441#103—861no—
442#103—861no—
443#103—861no—
444#102—861no—
445#102—861no—
446#102—861no—
447#101—862no—
448#101—862no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453#97—21no—
454#97—21no—
455#97—861no—
456C4×C8—21no—
457C4×C8—21no—
458C4×C8—861no—
459#41—21no—
460#41—21no—
461#41—21no—
462#41—21no—
463C2×Q8—432no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8C2×D17211yescharacteristic
470C2×D4—21no—
471C2×D4C2×D17211yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4#1062189811yescharacteristic
480C22×C4#1062189811yescharacteristic
481C22×C4C23×D4311yescharacteristic
482Q16—864no—
483SD16—864no—
484M16—21no—
485M16—21no—
486M16—21no—
487M16—21no—
488M16—432no—
489M16—861no—
490M16—861no—
491M16—861no—
492M16—861no—
493M16—861no—
494M16—861no—
495M16—861no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8C2×C22⋊D4311yescharacteristic
507C2×C8C2×C22⋊D4311yescharacteristic
508C2×C8C2×C22⋊D4311yescharacteristic
509C2×C8C2×C22⋊D4311yescharacteristic
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—1721no—
519C4⋊C4—1721no—
520C4⋊C4—1721no—
521C4⋊C4—1721no—
522C4⋊C4—1721no—
523C4⋊C4—1721no—
524C4⋊C4C2×D17211yescharacteristic
525C4⋊C4C2×D17211yescharacteristic
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—1721no—
533C42—1721no—
534C42C2×D17211yescharacteristic
535C42C2×D17211yescharacteristic
536C42C2×C22⋊D4311yescharacteristic
537C42C2×C22⋊D4311yescharacteristic
538C23—21no—
539C23C2×#1062189811yescharacteristic
540Q8—21no—
541Q8—21no—
542Q8—862no—
543Q8—862no—
544Q8—1721no—
545Q8—1721no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—81no—
559C2×C4—862no—
560C2×C4—3441no—
561C2×C4—3441no—
562C2×C4—3441no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4#1306329911yescharacteristic
569C2×C4#1306329911yescharacteristic
570C2×C4#1306329911yescharacteristic
571C2×C4#1306329911yescharacteristic
572C2×C4C22×C22⋊D4311yescharacteristic
573C2×C4C22×D17211yescharacteristic
574C2×C4#41×D4311yescharacteristic
575C2×C4#41×D4311yescharacteristic
576C2×C4#1306337211yescharacteristic
577C2×C4#1306337211yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—862no—
585C8—1721no—
586C8—1721no—
587C8—1721no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C2×#1306329911yescharacteristic
594C22#1458358811yescharacteristic
595C22#1458361711yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—3441no—
604C4—3441no—
605C4—3441no—
606C4—1722no—
607C4#1458341111yescharacteristic
608C4#1458347511yescharacteristic
609C4#1458354811yescharacteristic
610C4#1458355611yescharacteristic
611C2—21no—
612C2—21no—
613C2—81no—
614C2#1913801811yescharacteristic
615C2#1914431511yescharacteristic
616C2#1914433211yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2925C2
socleC22×C43C2×#121
prime radicalC2×#41×C43C23
hypercenter#2925D43
hypocenterC43#24725
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. C2×#14583207C2semidirect
8. #19135587C2semidirect
9. #19135380C2semidirect
10. #19135375C2semidirect
11. #19135371C2semidirect
12. #19135250C2semidirect
13. #19135250C2semidirect
14. #19134588C2semidirect
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×#145832072
C4×#130633552
#191360402
#191360352
#191358932
#191355872
#191353802
#191353752
#191353712
#191352502
#191345882
C43×#29252
#2472543