Finite Group Databasebeta

← #25106172

Subgroups — #25106172

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147998C211yesmaximal, characteristic
2#19143231C211yesmaximal, characteristic
3#19137088C211yesmaximal, characteristic
4#19135574C212yesmaximal, complemented
5#19135570C212yesmaximal, complemented
6#19135540C211yesmaximal, characteristic, complemented
7#19135539C211yesmaximal, characteristic, complemented
8#19135538C211yesmaximal, characteristic, complemented
9#19134693C212yesmaximal
10#19134693C212yesmaximal
11C43×#1986C211yesmaximal, characteristic, complemented
12#14583529C412yescomplemented
13#14583529C412yescomplemented
14#14583528—21no—
15#14583528—21no—
16#14583526C412yescomplemented
17#14583526C412yescomplemented
18#14583524—21no—
19#14583524—21no—
20#14583456C2211yescharacteristic
21#14583453—22no—
22#14583453—22no—
23#14583452C2212yes—
24C2×#13063282C2211yescharacteristic
25#117×D43C2212yes—
26#14582961—22no—
27#14582958—22no—
28#14582922C2212yes—
29#14582862C2212yes—
30C4×#10621877C2211yescharacteristic
31#14582791—21no—
32#14582789—21no—
33#14582786—21no—
34#14582780—21no—
35C4×C4⋊Dic43C2211yescharacteristic
36C4×(C2×D43)⋊C4C2211yescharacteristic
37C4×(C2×D43)⋊C4C2211yescharacteristic
38#14582745C2211yescharacteristic
39C42×Dic43C2211yescharacteristic
40#14582660C2212yes—
41#14582660C2212yes—
42#14582659C2212yes—
43#14582659C2212yes—
44#14582658C2212yes—
45#14582658C2212yes—
46C43×#533C2211yescharacteristic
47C4×M16×C43C2211yescharacteristic
48C4×C4⋊C4×C43C2211yescharacteristic
49C43×#339C2212yes—
50C43×#339C2212yes—
51C22×C4×D43C2311yescharacteristic
52C2×#10621877C2312yes—
53#13063325C2×C411yescharacteristic
54#13063325C2×C411yescharacteristic
55#13063324—22no—
56#13063324—22no—
57#13063324C2×C412yes—
58#13063324C2×C412yes—
59#13063323—22no—
60#13063323—22no—
61#13063317C2×C412yes—
62#13063316C2×C412yes—
63#13063316C2×C412yes—
64#13063315—22no—
65#13063315—22no—
66#13063315—22no—
67#13063315—22no—
68#13063305—22no—
69#13063305—22no—
70#13063304—21no—
71#13063304—21no—
72#13063303—22no—
73#13063303—22no—
74#13063303—22no—
75#13063303—22no—
76#13063302—22no—
77#13063302—22no—
78#13063301—22no—
79#13063301—22no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84#13063284C2312yes—
85#13063283C2×C412yes—
86#13063283C2×C412yes—
87#13063282—22no—
88#13063282C2×C412yes—
89#13063282C2×C412yes—
90#13063282D412yes—
91#13063282D412yes—
92#13063281—22no—
93C2×C4⋊Dic43—21no—
94C2×Dic43⋊C4D411yescharacteristic
95C2×Dic43⋊C4D411yescharacteristic
96C4⋊C4×D43C2×C412yes—
97C4⋊C4×D43C2×C412yes—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4D411yescharacteristic
101C2×(C2×D43)⋊C4D411yescharacteristic
102C22⋊C4×D43—22no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43C2311yescharacteristic
106C2×C4×Dic43C2311yescharacteristic
107C2×C4×Dic43C2311yescharacteristic
108C42×D43—22no—
109Dic43⋊C8—24no—
110(C2×D43)⋊C8—24no—
111#13063236—21no—
112C4×C43⋊C8—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C2×M16×C43C2312yes—
119C4⋊Q8×C43C2×C411yescharacteristic
120C4⋊Q8×C43C2×C411yescharacteristic
121#125×C43C2×C412yes—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—21no—
124C4×Q8×C43—21no—
125C4×Q8×C43—21no—
126#117×C43C2312yes—
127C2×C4⋊C4×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C2×C42×C43C2311yescharacteristic
130C2×C42×C43C2311yescharacteristic
131#97×C43—21no—
132C4×C8×C43—21no—
133#95×C43—21no—
134C23×D43C2×D411yescharacteristic
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×C4×D43C22×C412yes—
152C2×C4×D43C2×D412yes—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—22no—
156C2×Dic86—22no—
157M16×C43—22no—
158M16×C43—22no—
159C2×C8×C43—22no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—22no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—42no—
165C4⋊C4×C43C22×C412yes—
166C4⋊C4×C43C22×C412yes—
167C22⋊C4×C43—22no—
168C42×C43—22no—
169C42×C43—22no—
170C42×C43—22no—
171C42×C43C22×C411yescharacteristic
172C42×C43C22×C411yescharacteristic
173C42×C43C2×D411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C22⋊Dic43—22no—
176(C2×D43)⋊C4—22no—
177(C2×D43)⋊C4—22no—
178(C2×D43)⋊C4—42no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4C22⋊C412yes—
181(C2×D43)⋊C4C22⋊C412yes—
182(C2×D43)⋊C4C22⋊C412yes—
183(C2×D43)⋊C4C22⋊C412yes—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—22no—
187C4⋊Dic43—22no—
188C4⋊Dic43—42no—
189C4⋊Dic43C22×C412yes—
190C4⋊Dic43C22×C412yes—
191Dic43⋊C4—22no—
192Dic43⋊C4—22no—
193Dic43⋊C4—22no—
194Dic43⋊C4—22no—
195Dic43⋊C4—22no—
196Dic43⋊C4—22no—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4C22⋊C412yes—
200Dic43⋊C4C22⋊C412yes—
201Dic43⋊C4C22⋊C412yes—
202Dic43⋊C4C22⋊C412yes—
203C4×Dic43—22no—
204C4×Dic43—22no—
205C4×Dic43—22no—
206C4×Dic43—22no—
207C4×Dic43—22no—
208C4×Dic43—42no—
209C4×Dic43—42no—
210C4×Dic43C22×C412yes—
211C4×Dic43C2×D412yes—
212#10621877—22no—
213#10621877—22no—
214C2×C43⋊C8—22no—
215C23×C43C22×D411yescharacteristic
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43C2×C22⋊C412yes—
221Q8×C43—81no—
222Q8×C43—81no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43C2×C22⋊C411yescharacteristic
234C2×C4×C43C2×C22⋊C411yescharacteristic
235C2×C4×C43C2×C22⋊C411yescharacteristic
236C2×C4×C43C2×C22⋊C411yescharacteristic
237C2×C4×C43C23×C411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C432−1+412yes—
240C2×C4×C432−1+412yes—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43C2×C22⋊C412yes—
254C2×Dic43C2×C22⋊C412yes—
255C2×Dic43C2×C22⋊C412yes—
256C4×D43—24no—
257C4×D43—24no—
258C4×D43—82no—
259C4×D43—82no—
260Dic86—82no—
261Dic86—82no—
262Dic86—81no—
263Dic86—81no—
264C8×C43—42no—
265C43⋊C8—42no—
266#21846—431nomaximal, Sylow
267C22×C43—21no—
268C22×C43—21no—
269C22×C43C22×C22⋊C411yescharacteristic
270C22×C43#53611yescharacteristic
271C22×C43#53611yescharacteristic
272C2×D43—22no—
273C2×D43—22no—
274C2×D43—22no—
275C2×D43—81no—
276C2×D43—81no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—42no—
282C4×C43—42no—
283C4×C43—42no—
284C4×C43—81no—
285C4×C43#51912yes—
286C4×C43#53612yes—
287Dic43—22no—
288Dic43—22no—
289Dic43—22no—
290Dic43—42no—
291Dic43—42no—
292Dic43—42no—
293Dic43—81no—
294#3458—431no—
295#2921—431no—
296#2298—431no—
297#1995—432no—
298#1994—432no—
299#1986—431no—
300#1986—431no—
301#1986—431no—
302#1986D4311yescharacteristic, complemented
303#1826—432no—
304#1826—432no—
305C2×C43—21no—
306C2×C43—21no—
307C2×C43#231011yescharacteristic
308C2×C43#290111yescharacteristic
309C2×C43#290111yescharacteristic
310D43—42no—
311#544—432no—
312#544—432no—
313#544—432no—
314#544—432no—
315#544—861no—
316#544—861no—
317#543—861no—
318#543—861no—
319#533—432no—
320#533—431no—
321#533—862no—
322#533—862no—
323#533C2×D4311yescharacteristic
324C2×#117—431no—
325C2×#117—432no—
326#433—862no—
327#433—862no—
328#423—432no—
329#407—432no—
330C4×M16—431no—
331C4×M16C2×D4311yescharacteristic
332#388—861no—
333#388—861no—
334#387—861no—
335#387—861no—
336C4×C4⋊C4—431no—
337C4×C4⋊C4C2×D4311yescharacteristic
338C4×C22⋊C4—431no—
339C4×C22⋊C4—431no—
340#376—431no—
341C43—431no—
342#339—432no—
343#339—432no—
344#339—432no—
345#339—432no—
346#339—432no—
347#339—432no—
348#339C2×D4312yes—
349#339C2×D4312yes—
350C43#2184611yescharacteristic, complemented, Sylow
351C23×C4—431no—
352C2×M16—432no—
353C2×M16C22×D4312yes—
354C4⋊Q8—432no—
355C4⋊Q8—432no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
358C4⋊Q8—862no—
359C4⋊Q8—862no—
360C4⋊Q8—862no—
361C4⋊Q8—862no—
362C4⋊Q8C4×D4311yescharacteristic
363C4⋊Q8C4×D4311yescharacteristic
364#125—432no—
365#125—432no—
366#125—432no—
367#125—862no—
368#125—862no—
369#125—862no—
370#125—862no—
371#125C4×D4312yes—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—862no—
375C22⋊Q8—862no—
376C22⋊Q8—862no—
377C22⋊Q8—862no—
378C22⋊Q8—862no—
379C22⋊Q8—862no—
380C22⋊Q8—862no—
381C22⋊Q8—862no—
382C22⋊Q8—862no—
383C22⋊Q8—862no—
384C22⋊Q8—861no—
385C22⋊Q8—861no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—862no—
389C4×Q8—862no—
390C4×Q8—861no—
391C4×Q8—861no—
392#117—432no—
393#117—432no—
394#117—432no—
395#117—432no—
396#117—432no—
397#117—432no—
398#117—432no—
399#117—862no—
400#117—862no—
401#117C22×D4312yes—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—432no—
406C2×C4⋊C4—432no—
407C2×C4⋊C4—861no—
408C2×C22⋊C4—431no—
409C2×C22⋊C4—431no—
410C2×C22⋊C4—862no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C42—431no—
414C2×C42—431no—
415C2×C42—431no—
416C2×C42—862no—
417C2×C42—861no—
418C2×C42—861no—
419C2×C42C22×D4311yescharacteristic
420C2×C42C22×D4311yescharacteristic
421C2×C42C22×D4311yescharacteristic
422C4⋊C8—864no—
423C22⋊C8—864no—
424#97—21no—
425#97—861no—
426C4×C8—21no—
427C4×C8—861no—
428#95—21no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434C24—431no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—862no—
438C2×Q8—862no—
439C2×Q8—861no—
440C2×Q8—861no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—432no—
447C22×C4—432no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4D4×D4311yescharacteristic
455C22×C4D4×D4311yescharacteristic
456C22×C4C23×D4311yescharacteristic
457M16—22no—
458M16—22no—
459M16—862no—
460M16—862no—
461C2×C8—22no—
462C2×C8—862no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—42no—
468C4⋊C4—432no—
469C4⋊C4—432no—
470C4⋊C4—432no—
471C4⋊C4—432no—
472C4⋊C4—432no—
473C4⋊C4—432no—
474C4⋊C4—862no—
475C4⋊C4—862no—
476C4⋊C4—862no—
477C4⋊C4—862no—
478C4⋊C4—862no—
479C4⋊C4—862no—
480C4⋊C4—862no—
481C4⋊C4—862no—
482C4⋊C4—862no—
483C4⋊C4—862no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—1722no—
487C4⋊C4C2×C4×D4312yes—
488C4⋊C4C2×C4×D4312yes—
489C22⋊C4—22no—
490C22⋊C4—432no—
491C22⋊C4—432no—
492C22⋊C4—432no—
493C22⋊C4—432no—
494C22⋊C4—862no—
495C22⋊C4—862no—
496C22⋊C4—862no—
497C22⋊C4—1722no—
498C22⋊C4—1722no—
499C42—22no—
500C42—22no—
501C42—22no—
502C42—432no—
503C42—432no—
504C42—862no—
505C42—862no—
506C42—862no—
507C42—862no—
508C42—862no—
509C42—1722no—
510C42—1722no—
511C42C2×C4×D4311yescharacteristic
512C42C2×C4×D4311yescharacteristic
513C42D4×D4311yescharacteristic
514C42D4×D4311yescharacteristic
515C23—432no—
516C23—861no—
517C23—861no—
518C23—1721no—
519C23—1721no—
520C23C2×D4×D4311yescharacteristic
521Q8—81no—
522Q8—81no—
523Q8—3441no—
524Q8—3441no—
525Q8—3442no—
526Q8—3442no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—432no—
538C2×C4—432no—
539C2×C4—432no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—864no—
543C2×C4—864no—
544C2×C4—862no—
545C2×C4—862no—
546C2×C4—862no—
547C2×C4—3442no—
548C2×C4—3442no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4C22⋊C4×D4311yescharacteristic
557C2×C4C22⋊C4×D4311yescharacteristic
558C2×C4C22⋊C4×D4311yescharacteristic
559C2×C4C22⋊C4×D4311yescharacteristic
560C2×C4C22×C4×D4311yescharacteristic
561C2×C4C2×D4×D4311yescharacteristic
562C2×C4#1306337212yes—
563C2×C4#1306337312yes—
564C8—42no—
565C8—1722no—
566C22—21no—
567C22—21no—
568C22—862no—
569C22—862no—
570C22—862no—
571C22—3441no—
572C22—3441no—
573C22C2×C22⋊C4×D4311yescharacteristic
574C22#1458346911yescharacteristic
575C22#1458347411yescharacteristic
576C4—21no—
577C4—21no—
578C4—21no—
579C4—21no—
580C4—42no—
581C4—42no—
582C4—42no—
583C4—81no—
584C4—862no—
585C4—862no—
586C4—862no—
587C4—3441no—
588C4—1722no—
589C4—1722no—
590C4—1722no—
591C4#1458337512yes—
592C4#1458347212yes—
593C2—21no—
594C2—21no—
595C2—1722no—
596C2#1913717811yescharacteristic
597C2#1914313911yescharacteristic
598C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1986C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1986D43
hypocenterC43#21846
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
4. #19135574C2semidirect
5. #19135570C2semidirect
6. #19135540C2semidirect
7. #19135539C2semidirect
8. #19135538C2semidirect
11. C43×#1986C2semidirect
12. #14583529C4semidirect
13. #14583529C4semidirect
16. #14583526C4semidirect
17. #14583526C4semidirect
302. #1986D43semidirect
350. C43#21846semidirect

Maximal subgroups

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

subgroupindex
#191479982
#191432312
#191370882
#191355742
#191355702
#191355402
#191355392
#191355382
#191346932
C43×#19862
#2184643