Finite Group Databasebeta

← #25138111

Subgroups — #25138111

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#19144418C211yesmaximal, characteristic
2C2×#14583207C211yesmaximal, characteristic, complemented
3C4×#13063358C211yesmaximal, characteristic
4#19143260C211yesmaximal, characteristic
5#19136042C211yesmaximal, characteristic
6#19136037C211yesmaximal, characteristic
7#19135896C211yesmaximal, characteristic
8#19135896C211yesmaximal, characteristic
9#19135588C211yesmaximal, characteristic, complemented
10#19135381C211yesmaximal, characteristic, complemented
11#19135376C211yesmaximal, characteristic, complemented
12#19135251C211yesmaximal, characteristic, complemented
13#19135251C211yesmaximal, characteristic, complemented
14#19134588C211yesmaximal, characteristic, complemented
15C43×#1950C211yesmaximal, characteristic, complemented
16C2×#13063358C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C4×#10621898C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20#14583207—21no—
21#14583207—21no—
22#14583207—21no—
23#14583207—21no—
24#14583207—21no—
25#14583207—21no—
26#14583200—21no—
27#14583200—21no—
28#14583007—21no—
29#14583001—21no—
30C4×Dic172—21no—
31C4×#10621873—21no—
32#14582959—21no—
33#14582959—21no—
34#14582955—21no—
35#14582951—21no—
36#14582941C2211yescharacteristic
37#14582941C2211yescharacteristic
38#14582941C2211yescharacteristic
39C2×#13063259C2211yescharacteristic
40C2×#13063257C2211yescharacteristic
41#14582923C2211yescharacteristic
42#14582909C2211yescharacteristic
43#14582901C2211yescharacteristic
44#14582901C2211yescharacteristic
45#14582901C2211yescharacteristic
46C2×#13063250C2211yescharacteristic
47C2×#13063250C2211yescharacteristic
48C2×#13063243C2211yescharacteristic
49C2×#13063243C2211yescharacteristic
50#14582865C2211yescharacteristic
51#14582865C2211yescharacteristic
52#14582854C2211yescharacteristic
53#14582854C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582667C2211yescharacteristic
60C2×#108×C43C2211yescharacteristic
61C2×#108×C43C2211yescharacteristic
62C43×#423C2211yescharacteristic
63C2×C4⋊C8×C43C2211yescharacteristic
64C4×M16×C43C2211yescharacteristic
65C43×#341C2211yescharacteristic
66C43×#341C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68C22×Dic86C2311yescharacteristic
69#13063358—22no—
70#13063358—22no—
71C2×Dic172—21no—
72C2×#10621873—21no—
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75#13063317—21no—
76#13063317—21no—
77#13063317—21no—
78#13063317—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86D411yescharacteristic
84C4×Dic86D411yescharacteristic
85C4×D172D411yescharacteristic
86C4×D172D411yescharacteristic
87C4×C22⋊D43—21no—
88C4×C22⋊D43—21no—
89#13063284C2311yescharacteristic
90#13063282—21no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×C4×Dic43—21no—
98C42×D43—21no—
99#13063259—21no—
100#13063259—21no—
101#13063259—21no—
102#13063259—21no—
103#13063259—21no—
104#13063257—21no—
105#13063257—21no—
106#13063257—21no—
107#13063257—21no—
108#13063257—21no—
109C4⋊(C43⋊C8)—21no—
110C4⋊(C43⋊C8)—21no—
111#13063250—21no—
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063250—21no—
116#13063250—21no—
117#13063250—21no—
118#13063250—21no—
119#13063250—21no—
120#13063247—21no—
121#13063247—21no—
122#13063247—21no—
123#13063243—22no—
124#13063243—22no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127(C2×D43)⋊C8—21no—
128(C2×D43)⋊C8—21no—
129#13063235—21no—
130#13063235—21no—
131C8×Dic43—21no—
132C8×Dic43—21no—
133C2×M16×C43C2311yescharacteristic
134C2×M16×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C2×M16×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C2×C42×C43C2311yescharacteristic
140#108×C43—22no—
141#108×C43—22no—
142C4⋊C8×C43—21no—
143C4⋊C8×C43—21no—
144C4⋊C8×C43D411yescharacteristic
145C4⋊C8×C43D411yescharacteristic
146C4⋊C8×C43D411yescharacteristic
147C4⋊C8×C43D411yescharacteristic
148#97×C43—21no—
149C4×C8×C43—21no—
150C22×C4×C43#4111yescharacteristic
151C22×C4×C43#4111yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C2×C22⋊D43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158#10621898—21no—
159#10621898—21no—
160#10621898—21no—
161#10621898—21no—
162C2×D172C2×D411yescharacteristic
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86C2×D411yescharacteristic
172C2×Dic86#4112yes—
173M16×C43—21no—
174M16×C43—21no—
175M16×C43—21no—
176M16×C43—21no—
177M16×C43—21no—
178M16×C43—21no—
179M16×C43—21no—
180M16×C43#4112yes—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43C2×D411yescharacteristic
190C2×C8×C43C2×D411yescharacteristic
191C2×C8×C43C2×D411yescharacteristic
192C2×C8×C43C2×D411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C42×C43C2×D411yescharacteristic
195C42×C43C2×D411yescharacteristic
196C42×C43C2×D411yescharacteristic
197C22⋊Dic43—21no—
198(C2×D43)⋊C4—21no—
199(C2×D43)⋊C4—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43C2×D411yescharacteristic
207C4⋊Dic43C2×D411yescharacteristic
208Dic43⋊C4—21no—
209Dic43⋊C4—21no—
210Dic43⋊C4—41no—
211Dic43⋊C4—41no—
212Dic43⋊C4—41no—
213Dic43⋊C4—41no—
214Dic43⋊C4—41no—
215Dic43⋊C4—41no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—41no—
220C4×Dic43—41no—
221#10621877—21no—
222#10621877—21no—
223#10621877—21no—
224#10621877—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227Dic172—24no—
228#10621873—24no—
229C23×C43C2×#4111yescharacteristic
230C22×D43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43#12111yescharacteristic
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C432−1+411yescharacteristic
242C2×C4×C432−1+411yescharacteristic
243C22⋊D43—41no—
244C22⋊D43—41no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—22no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—81no—
255C2×Dic43—81no—
256C2×Dic43—81no—
257D172—21no—
258D172—21no—
259C4×D43—42no—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43—81no—
263Dic86—22no—
264Dic86—21no—
265Dic86—21no—
266Dic86—22no—
267Dic86—41no—
268Dic86—41no—
269C8×C43—22no—
270C8×C43—21no—
271C8×C43—21no—
272C8×C43—21no—
273C8×C43—21no—
274C8×C43—41no—
275C8×C43—41no—
276C8×C43—41no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279#24725—431nomaximal, Sylow
280C22×C43—21no—
281C22×C43—21no—
282C22×C43C2×#12111yescharacteristic
283C22×C43#55211yescharacteristic
284C22×C43#55611yescharacteristic
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—41no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43#52511yescharacteristic
293C4×C43#53611yescharacteristic
294C4×C43#54711yescharacteristic
295C4×C43#54811yescharacteristic
296Dic43—42no—
297Dic43—41no—
298Dic43—41no—
299Dic43—41no—
300Dic43—81no—
301Dic43—81no—
302Dic43—81no—
303#3080—431no—
304C2×#479—431no—
305C4×#137—431no—
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#1950D4311yescharacteristic, complemented
315#1930—431no—
316#1930—431no—
317#1801—431no—
318C2×C43—21no—
319C2×C43—21no—
320C2×C43#241511yescharacteristic
321C2×C43#306711yescharacteristic
322C2×C43#306911yescharacteristic
323D43—81no—
324C2×#137—431no—
325C2×#125—431no—
326C4×#41—431no—
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—861no—
341#433—861no—
342#432—861no—
343#431—861no—
344C2×#108C2×D4311yescharacteristic
345C2×#108C2×D4311yescharacteristic
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#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#341C2×D4311yescharacteristic
374#341C2×D4311yescharacteristic
375C43#2472511yescharacteristic, complemented, Sylow
376C2×#41—431no—
377C22×Q8—431no—
378#137—862no—
379#137—862no—
380C2×Q16—861no—
381C2×SD16—861no—
382C2×M16—431no—
383C2×M16—431no—
384C2×M16C22×D4311yescharacteristic
385C2×M16C22×D4311yescharacteristic
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—431no—
395C4×Q8—431no—
396C4×Q8—861no—
397C4×Q8—861no—
398C4×Q8—861no—
399C4×Q8—861no—
400C4×D4—431no—
401C4×D4—431no—
402C4×D4—861no—
403C4×D4—861no—
404#117—431no—
405#117—861no—
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—861no—
413C2×C42—861no—
414C2×C42C22×D4311yescharacteristic
415#108—22no—
416#108—22no—
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⋊C8D17211yescharacteristic
432C4⋊C8D17211yescharacteristic
433C4⋊C8D17211yescharacteristic
434C4⋊C8D17211yescharacteristic
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—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—861no—
460#41—861no—
461#41—861no—
462#41—861no—
463C2×Q8—431no—
464C2×Q8—432no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×D4—431no—
471C2×D4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4#1062190211yescharacteristic
480C22×C4#1062190211yescharacteristic
481C22×C4C23×D4311yescharacteristic
482Q16—864no—
483SD16—864no—
484M16—21no—
485M16—21no—
486M16—21no—
487M16—21no—
488M16—21no—
489M16—21no—
490M16—21no—
491M16—861no—
492M16—861no—
493M16—861no—
494M16—861no—
495M16#1062190012yes—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8C2×D17211yescharacteristic
507C2×C8C2×D17211yescharacteristic
508C2×C8C2×D17211yescharacteristic
509C2×C8C2×D17211yescharacteristic
510C4⋊C4—431no—
511C4⋊C4—431no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
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⋊C4—1721no—
525C4⋊C4—1721no—
526C22⋊C4—861no—
527C22⋊C4—861no—
528C22⋊C4—861no—
529C42—861no—
530C42—861no—
531C42—861no—
532C42—1721no—
533C42—1721no—
534C42C2×D17211yescharacteristic
535C42C2×D17211yescharacteristic
536C42D4×D4311yescharacteristic
537C42D4×D4311yescharacteristic
538C23—861no—
539C23C2×#1062190211yescharacteristic
540Q8—862no—
541Q8—862no—
542Q8—861no—
543Q8—861no—
544Q8—1721no—
545Q8—1721no—
546D4—861no—
547D4—861no—
548D4—1721no—
549D4—1721no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—862no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—3441no—
557C2×C4—3441no—
558C2×C4—3441no—
559C2×C4—3441no—
560C2×C4—1722no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4#1306330011yescharacteristic
569C2×C4#1306330011yescharacteristic
570C2×C4#1306330011yescharacteristic
571C2×C4#1306330011yescharacteristic
572C2×C4C2×D4×D4311yescharacteristic
573C2×C4C22×D17211yescharacteristic
574C2×C4#41×D4311yescharacteristic
575C2×C4C2×#1062190011yescharacteristic
576C2×C4#1306337211yescharacteristic
577C2×C4#1306337311yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—22no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—1721no—
587C8—1721no—
588C22—21no—
589C22—21no—
590C22—1721no—
591C22—1721no—
592C22—1721no—
593C22C2×#1306330011yescharacteristic
594C22#1458358711yescharacteristic
595C22#1458362311yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—3441no—
601C4—3441no—
602C4—3441no—
603C4—1721no—
604C4—1721no—
605C4—1721no—
606C4—1722no—
607C4#1458340911yescharacteristic
608C4#1458347211yescharacteristic
609C4#1458355311yescharacteristic
610C4#1458356111yescharacteristic
611C2—21no—
612C2—21no—
613C2—3441no—
614C2#1913802211yescharacteristic
615C2#1914431611yescharacteristic
616C2#1914433311yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1950C2
socleC22×C43C2×#121
prime radicalC2×#10621898C23
hypercenter#1950D43
hypocenterC43#24725
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
2. C2×#14583207C2semidirect
9. #19135588C2semidirect
10. #19135381C2semidirect
11. #19135376C2semidirect
12. #19135251C2semidirect
13. #19135251C2semidirect
14. #19134588C2semidirect
15. C43×#1950C2semidirect
314. #1950D43semidirect
375. C43#24725semidirect

Maximal subgroups

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

subgroupindex
#191444182
C2×#145832072
C4×#130633582
#191432602
#191360422
#191360372
#191358962
#191355882
#191353812
#191353762
#191352512
#191345882
C43×#19502
#2472543