Finite Group Databasebeta

← #25964315

Subgroups — #25964315

Order 11008.

1970 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148421C211yesmaximal, characteristic, complemented
2C4×#13063372C211yesmaximal, characteristic
3#19144459C213yesmaximal, complemented
4#19144448C213yesmaximal, complemented
5#19144438C213yesmaximal, complemented
6#19144438C213yesmaximal, complemented
7#19144418C213yesmaximal, complemented
8#19144402C213yesmaximal, complemented
9#19144385C213yesmaximal, complemented
10C2×#14583207C213yesmaximal, complemented
11#19143195C211yesmaximal, characteristic, complemented
12#19143190C211yesmaximal, characteristic, complemented
13#19143129C211yesmaximal, characteristic
14#19143129C211yesmaximal, characteristic
15C43×#2906C211yesmaximal, characteristic, complemented
16C2×#13063372C2211yescharacteristic
17#14583625—21no—
18#14583625—21no—
19#14583608—23no—
20#14583608—23no—
21#14583527C2213yes—
22#14583527C2213yes—
23#14583456C2213yes—
24C2×#13063317C2213yes—
25#14583382C2211yescharacteristic
26#14583382C2211yescharacteristic
27#14583382C2211yescharacteristic
28#14583379C2213yes—
29#14583378—23no—
30#14583376C2213yes—
31#14583375—21no—
32C4×#10621898C2213yes—
33C4×#10621900—23no—
34C2×C4×Dic86C2213yes—
35C4×Q8×D43—21no—
36#14583207C2216yes—
37#14583207C2216yes—
38#14583207C2213yes—
39#14583207C2216yes—
40#14583207C2213yes—
41#14583207C2216yes—
42#14583200C2216yes—
43#14583200C2211yescharacteristic
44#14583200C2213yes—
45#14583195C2216yes—
46#14583195C2213yes—
47#14583190C2213yes—
48#14583185C2216yes—
49#14583185C2213yes—
50#14583180C2213yes—
51#14582941C2213yes—
52#14582941C2213yes—
53#14582941C2213yes—
54#14582941C2213yes—
55#14582937C2213yes—
56#14582937C2213yes—
57C2×#13063259C2213yes—
58C2×#13063257C2213yes—
59#14582909C2213yes—
60#14582909C2213yes—
61#14582901C2213yes—
62#14582901C2213yes—
63#14582896C2213yes—
64#14582896C2213yes—
65C2×#13063250C2213yes—
66C2×#13063250C2213yes—
67C2×#131×C43C2211yescharacteristic
68C2×#131×C43C2211yescharacteristic
69C4×#41×C43C2211yescharacteristic
70C43×#424C2213yes—
71C43×#424C2213yes—
72C43×#423C2213yes—
73C2×C4⋊C8×C43C2213yes—
74#13063372—24no—
75#13063372Q818yescomplemented
76C2×#10621898C2313yes—
77C2×#10621900—23no—
78C22×Dic86C2313yes—
79C2×Q8×D43—21no—
80#13063325C2313yes—
81#13063325C2313yes—
82#13063324—23no—
83#13063324—23no—
84#13063317—23no—
85#13063317—23no—
86#13063317C2313yes—
87#13063317C2316yes—
88#13063317C2311yescharacteristic
89#13063316—23no—
90#13063316—23no—
91#13063304—23no—
92#13063304—23no—
93#13063302—26no—
94#13063302—26no—
95Q8×Dic43—21no—
96Q8×Dic43—21no—
97Q8×Dic43—21no—
98C4×Dic86—23no—
99C4×Dic86—23no—
100C4×Dic86—23no—
101C4×Dic86—23no—
102C4×Dic86C2313yes—
103C4×Dic86C2316yes—
104C4×Dic86C2313yes—
105#13063290—23no—
106#13063290—23no—
107C4×D172C2311yescharacteristic
108C4×D172C2313yes—
109D4×Dic43—23no—
110D4×Dic43—23no—
111D4×Dic43—23no—
112C4×C22⋊D43—23no—
113C4×C22⋊D43—23no—
114(C22⋊D43)⋊C4—26no—
115#13063284C2313yes—
116#13063284C2313yes—
117#13063284C2313yes—
118#13063283—23no—
119#13063282—23no—
120#13063281—26no—
121C2×C4⋊Dic43C2313yes—
122C2×C4⋊Dic43C2313yes—
123C2×C4⋊Dic43C2313yes—
124C2×Dic43⋊C4—23no—
125C2×Dic43⋊C4—23no—
126C2×Dic43⋊C4—23no—
127C4⋊C4×D43—23no—
128C2×C4×Dic43—23no—
129C42×D43—23no—
130#13063259C2313yes—
131#13063259C2313yes—
132#13063259C2316yes—
133#13063259C2311yescharacteristic
134#13063259C2313yes—
135#13063257C2311yescharacteristic
136#13063257C2313yes—
137#13063257C2316yes—
138#13063257C2313yes—
139#13063257C2313yes—
140#13063250C2313yes—
141#13063250C2313yes—
142#13063250C2316yes—
143#13063250C2316yes—
144#13063250C2313yes—
145#13063250C2313yes—
146#13063247C2311yescharacteristic
147#13063247C2311yescharacteristic
148#13063247C2313yes—
149#13063247C2313yes—
150C2×#41×C43C2311yescharacteristic
151#131×C43—24no—
152#131×C43—24no—
153C2×M16×C43C2313yes—
154C2×M16×C43C2313yes—
155C22×C8×C43C2313yes—
156C22×C8×C43C2313yes—
157C4×Q8×C43D411yescharacteristic
158C4×Q8×C43D411yescharacteristic
159C4×D4×C43D413yes—
160C4×D4×C43D413yes—
161#117×C43C2313yes—
162C2×C42×C43C2313yes—
163C4⋊C8×C43C2313yes—
164C4⋊C8×C43C2313yes—
165C4⋊C8×C43C2316yes—
166C4⋊C8×C43C2311yescharacteristic
167C4⋊C8×C43C2313yes—
168#41×C43C2×Q814yes—
169#41×C43#4114yes—
170C2×Q8×C43C2×D411yescharacteristic
171C2×D4×C43C2×D413yes—
172C22×C4×C43C2×D413yes—
173C22×C4×C43C2×D413yes—
174C22×C4×C43C2413yes—
175C2×C22⋊D43—23no—
176C22×Dic43—23no—
177C22×Dic43—23no—
178C22×Dic43—23no—
179C22×Dic43—23no—
180Q8×D43—28no—
181#10621900—224no—
182#10621898—26no—
183#10621898C2×Q8112yes—
184C2×D172C2411yescharacteristic
185C2×C4×D43—23no—
186C2×C4×D43—21no—
187C2×C4×D43—23no—
188C2×Dic86—23no—
189C2×Dic86—26no—
190C2×Dic86—23no—
191C2×Dic86—23no—
192C2×Dic86C2×Q8112yes—
193C2×Dic86C2413yes—
194M16×C43—26no—
195M16×C43—26no—
196C2×C8×C43—26no—
197C2×C8×C43—26no—
198C2×C8×C43C2411yescharacteristic
199C2×C8×C43C2411yescharacteristic
200C2×C8×C43C2413yes—
201C2×C8×C43C2413yes—
202C4⋊C4×C43C2×D413yes—
203C4⋊C4×C43C2×D413yes—
204C22⋊C4×C43C2×D416yes—
205C42×C43C2×D413yes—
206C42×C43C2×D413yes—
207C42×C43C2411yescharacteristic
208C42×C43C2413yes—
209C22⋊Dic43—23no—
210C22⋊Dic43—23no—
211C22⋊Dic43—23no—
212(C2×D43)⋊C4—21no—
213(C2×D43)⋊C4—23no—
214C4⋊Dic43—23no—
215C4⋊Dic43—23no—
216C4⋊Dic43—23no—
217C4⋊Dic43—23no—
218C4⋊Dic43—23no—
219C4⋊Dic43C2413yes—
220C4⋊Dic43C2411yescharacteristic
221C4⋊Dic43C2413yes—
222C4⋊Dic43C2411yescharacteristic
223C4⋊Dic43C2413yes—
224C4⋊Dic43C2411yescharacteristic
225Dic43⋊C4—26no—
226Dic43⋊C4—23no—
227Dic43⋊C4—23no—
228Dic43⋊C4—23no—
229Dic43⋊C4—26no—
230Dic43⋊C4—26no—
231Dic43⋊C4—23no—
232Dic43⋊C4—21no—
233Dic43⋊C4—21no—
234C4×Dic43—23no—
235C4×Dic43—23no—
236C4×Dic43—23no—
237C4×Dic43—26no—
238C4×Dic43—23no—
239C4×Dic43—23no—
240C23×C43C22×D413yes—
241C22×D43—21no—
242Q8×C43C22⋊Q814yes—
243D4×C43C22⋊Q8112yes—
244C2×C4×C43—43no—
245C2×C4×C43—43no—
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D413yes—
248C2×C4×C43C22×D413yes—
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C22×D413yes—
251C2×C4×C43C22×Q816yes—
252C2×C4×C43C2×#4116yes—
253C2×C4×C43C2511yescharacteristic
254C22⋊D43—212no—
255C2×Dic43—212no—
256C2×Dic43—23no—
257C2×Dic43—21no—
258C2×Dic43—23no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—23no—
262C2×Dic43—23no—
263C2×Dic43—83no—
264C2×Dic43—83no—
265C2×Dic43—83no—
266D172—21no—
267D172C22×Q812yes—
268C4×D43—212no—
269C4×D43—42no—
270C4×D43—83no—
271Dic86—212no—
272Dic86—23no—
273Dic86—83no—
274Dic86—83no—
275Dic86C22×Q816yes—
276C8×C43—21no—
277C8×C43—21no—
278C8×C43—23no—
279C8×C43—23no—
280#60499—431nomaximal, Sylow
281C22×C43—23no—
282C22×C43—23no—
283C22×C43C2×C22⋊Q816yes—
284C22×C43C23×D411yescharacteristic
285C2×D43—22no—
286C2×D43—41no—
287C2×D43—41no—
288C4×C43—23no—
289C4×C43—21no—
290C4×C43—23no—
291C4×C43—21no—
292C4×C43C2×C22⋊Q816yes—
293C4×C43C23×Q811yescharacteristic
294C4×C43C22×#4111yescharacteristic
295Dic43—26no—
296Dic43—41no—
297Dic43—43no—
298Dic43—43no—
299Dic43—41no—
300Dic43—43no—
301Dic43—41no—
302#3504—431no—
303C4×2−1+4—431no—
304#3084—433no—
305#3083—433no—
306#3082—433no—
307#3082—433no—
308#3080—433no—
309#3078—433no—
310#3076—433no—
311C2×#479—433no—
312#2913—431no—
313#2912—431no—
314#2906D4311yescharacteristic, complemented
315#2898—431no—
316#2898—431no—
317C2×C43—26no—
318C2×C43C22×C22⋊Q811yescharacteristic
319C2×C43#358411yescharacteristic
320C2×C43#358611yescharacteristic
321D43—42no—
322C2×2−1+4—431no—
323C2×#131C2×D4311yescharacteristic
324C2×#131C2×D4311yescharacteristic
325#557—861no—
326#557—861no—
327#554—863no—
328#554—863no—
329#544—433no—
330#544—433no—
331#533—433no—
332C2×#125—433no—
333#520—431no—
334#520—431no—
335#520—431no—
336#520—433no—
337#520—863no—
338#519—433no—
339#519—861no—
340C4×#41—433no—
341C4×#41—863no—
342C4×#41C2×D4311yescharacteristic
343C2×C4×Q8—433no—
344C2×C4×Q8—861no—
345#479—433no—
346#479—436no—
347#479—436no—
348#479—436no—
349#479—433no—
350#479—436no—
351#478—431no—
352#478—433no—
353#478—436no—
354#477—433no—
355#477—436no—
356#476—433no—
357#475—433no—
358#475—436no—
359#474—433no—
360#428—433no—
361#428—433no—
362#428—433no—
363#428—433no—
364#427—433no—
365#427—433no—
366C2×#107—433no—
367C2×#106—433no—
368#424C2×D4313yes—
369#424C2×D4313yes—
370#423C2×D4313yes—
371C2×C4⋊C8C2×D4313yes—
372#419—433no—
373#419—433no—
374#417—433no—
375#417—433no—
376#416—433no—
377#416—433no—
378C2×#103—433no—
379C2×#103—433no—
380C43#6049911yescharacteristic, complemented, Sylow
3812−1+4—438no—
3822−1+4—864no—
383C2×#41—433no—
384C2×#41—863no—
385C2×#41C22×D4311yescharacteristic
386C22×Q8—433no—
387C22×Q8—861no—
388#131—24no—
389#131—24no—
390C2×M16C22×D4313yes—
391C2×M16C22×D4313yes—
392C22×C8C22×D4313yes—
393C22×C8C22×D4313yes—
394C4⋊Q8—433no—
395C4⋊Q8—433no—
396C4⋊Q8—863no—
397C4⋊Q8—863no—
398#125—433no—
399#125—436no—
400#125—431no—
401#125—863no—
402#125—863no—
403#125—863no—
404#125—863no—
405C22⋊Q8—863no—
406C22⋊Q8—863no—
407C22⋊Q8—866no—
408C22⋊Q8—866no—
409C4×Q8—433no—
410C4×Q8—436no—
411C4×Q8—433no—
412C4×Q8—861no—
413C4×Q8—861no—
414C4×Q8—861no—
415C4×Q8—863no—
416C4×Q8—863no—
417C4×Q8—863no—
418C4×Q8—863no—
419C4×Q8—863no—
420C4×Q8—863no—
421C4×Q8D17211yescharacteristic
422C4×Q8D17211yescharacteristic
423C4×D4—431no—
424C4×D4—433no—
425C4×D4—863no—
426C4×D4—863no—
427C4×D4—863no—
428C4×D4—863no—
429C4×D4—863no—
430C4×D4—866no—
431C4×D4D17213yes—
432C4×D4D17213yes—
433#117—433no—
434#117—433no—
435#117—433no—
436#117—863no—
437#117—866no—
438#117—863no—
439#117C22×D4313yes—
440C2×C4⋊C4—433no—
441C2×C4⋊C4—433no—
442C2×C4⋊C4—433no—
443C2×C4⋊C4—863no—
444C2×C4⋊C4—863no—
445C2×C4⋊C4—863no—
446C2×C4⋊C4—863no—
447C2×C42—863no—
448C2×C42—863no—
449C2×C42C22×D4313yes—
450#107—433no—
451#107—436no—
452#107—431no—
453#107—433no—
454#107—433no—
455#106—433no—
456#106—436no—
457#106—431no—
458#106—433no—
459#106—433no—
460C4⋊C8C22×D4311yescharacteristic
461C4⋊C8C22×D4313yes—
462C4⋊C8C22×D4313yes—
463C4⋊C8C22×D4313yes—
464C4⋊C8C22×D4316yes—
465#103—433no—
466#103—433no—
467#103—436no—
468#103—436no—
469#103—433no—
470#103—433no—
471#102—431no—
472#102—431no—
473#102—433no—
474#102—433no—
475#41—4312no—
476#41—8624no—
477#41—866no—
478#41#1062190014yes—
479#41Q8×D4314yes—
480C2×Q8—4312no—
481C2×Q8—433no—
482C2×Q8—868no—
483C2×Q8—863no—
484C2×Q8—863no—
485C2×Q8—863no—
486C2×Q8—866no—
487C2×Q8C2×D17211yescharacteristic
488C2×D4—431no—
489C2×D4—863no—
490C2×D4C2×D17213yes—
491C22×C4—863no—
492C22×C4—863no—
493C22×C4—863no—
494C22×C4—863no—
495C22×C4—863no—
496C22×C4—863no—
497C22×C4—861no—
498C22×C4C2×D17213yes—
499C22×C4C2×D17213yes—
500C22×C4C23×D4313yes—
501M16—26no—
502M16—26no—
503C2×C8—26no—
504C2×C8—26no—
505C2×C8C23×D4311yescharacteristic
506C2×C8C23×D4313yes—
507C2×C8C23×D4313yes—
508C2×C8C23×D4311yescharacteristic
509C4⋊C4—433no—
510C4⋊C4—431no—
511C4⋊C4—433no—
512C4⋊C4—431no—
513C4⋊C4—433no—
514C4⋊C4—431no—
515C4⋊C4—863no—
516C4⋊C4—863no—
517C4⋊C4—863no—
518C4⋊C4—866no—
519C4⋊C4—863no—
520C4⋊C4—863no—
521C4⋊C4—863no—
522C4⋊C4—866no—
523C4⋊C4—866no—
524C4⋊C4—863no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—863no—
528C4⋊C4—863no—
529C4⋊C4C2×D17213yes—
530C4⋊C4C2×D17213yes—
531C22⋊C4—863no—
532C22⋊C4—863no—
533C22⋊C4—863no—
534C22⋊C4—861no—
535C22⋊C4—863no—
536C22⋊C4C2×D17216yes—
537C42—863no—
538C42—863no—
539C42—863no—
540C42—866no—
541C42—863no—
542C42—863no—
543C42C2×D17213yes—
544C42C2×D17213yes—
545C42C23×D4311yescharacteristic
546C42C23×D4313yes—
547C23—861no—
548C23C22×D17213yes—
549Q8—436no—
550Q8—8612no—
551Q8—863no—
552Q8—3443no—
553Q8—3443no—
554Q8#1306330514yes—
555D4—432no—
556D4—8612no—
557D4—861no—
558D4#13063305112yes—
559C2×C4—43no—
560C2×C4—43no—
561C2×C4—8612no—
562C2×C4—863no—
563C2×C4—8612no—
564C2×C4—861no—
565C2×C4—863no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—863no—
569C2×C4—863no—
570C2×C4—3443no—
571C2×C4—3443no—
572C2×C4—3443no—
573C2×C4—3443no—
574C2×C4—1722no—
575C2×C4C22×D17211yescharacteristic
576C2×C4C22×D17213yes—
577C2×C4C22×D17213yes—
578C2×C4C22×D17211yescharacteristic
579C2×C4C22×D17213yes—
580C2×C4C2×Q8×D4316yes—
581C2×C4C2×#1062190016yes—
582C2×C4C24×D4311yescharacteristic
583C8—21no—
584C8—21no—
585C8—23no—
586C8—23no—
587C22—23no—
588C22—23no—
589C22—862no—
590C22—1721no—
591C22—1721no—
592C22C2×#1306330516yes—
593C22C23×D17211yescharacteristic
594C4—21no—
595C4—23no—
596C4—21no—
597C4—23no—
598C4—866no—
599C4—1723no—
600C4—1723no—
601C4—1721no—
602C4—1723no—
603C4—1721no—
604C4—1721no—
605C4C2×#1306330516yes—
606C4C22×Q8×D4311yescharacteristic
607C4C22×#1062190011yescharacteristic
608C2—26no—
609C2—1722no—
610C2C22×#1306330511yescharacteristic
611C2#1914936911yescharacteristic
612C2#1914938311yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2906C2
socleC22×C43C23×D4
prime radicalC2×#13063372C22
hypercenter#2906D43
hypocenterC43#60499
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2906

Complements

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

NH ≅ G/Ntype
1. #19148421C2semidirect
3. #19144459C2semidirect
4. #19144448C2semidirect
5. #19144438C2semidirect
6. #19144438C2semidirect
7. #19144418C2semidirect
8. #19144402C2semidirect
9. #19144385C2semidirect
10. C2×#14583207C2semidirect
11. #19143195C2semidirect
12. #19143190C2semidirect
15. C43×#2906C2semidirect
75. #13063372Q8semidirect
314. #2906D43semidirect
380. C43#60499semidirect

Maximal subgroups

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

subgroupindex
#191484212
C4×#130633722
#191444592
#191444482
#191444382
#191444182
#191444022
#191443852
C2×#145832072
#191431952
#191431902
#191431292
C43×#29062
#6049943