Finite Group Databasebeta

← #25106171

Subgroups — #25106171

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148000C211yesmaximal, characteristic
2#19143230C211yesmaximal, characteristic
3#19137091C211yesmaximal, characteristic
4#19135574C212yesmaximal, complemented
5#19135570C212yesmaximal, complemented
6#19135537C212yesmaximal, complemented
7#19135537C212yesmaximal, complemented
8#19134695C211yesmaximal, characteristic
9#19134694C211yesmaximal, characteristic
10#19134692C211yesmaximal, characteristic
11C43×#1826C211yesmaximal, characteristic
12#14583530C412yescomplemented
13#14583530C412yescomplemented
14#14583527—21no—
15#14583527—21no—
16#14583527C412yescomplemented
17#14583527C412yescomplemented
18#14583525—21no—
19#14583525—21no—
20#14583456—22no—
21#14583452—22no—
22#14583452C2212yes—
23#14583452C2212yes—
24C2×#13063284C2211yescharacteristic
25C2×#13063284C2211yescharacteristic
26#14582957—22no—
27#14582957—22no—
28#14582922C2212yes—
29#14582863C2211yescharacteristic
30M16×Dic43C2212yes—
31#14582793—21no—
32#14582787—21no—
33#14582784—21no—
34#14582782—21no—
35C4×Dic43⋊C4C2211yescharacteristic
36C4×Dic43⋊C4C2211yescharacteristic
37C4×C22⋊Dic43C2211yescharacteristic
38#14582745C2211yescharacteristic
39C42×Dic43C2211yescharacteristic
40#14582660C2212yes—
41#14582660C2212yes—
42#14582659C2212yes—
43#14582659C2212yes—
44#14582658C2212yes—
45#14582658C2212yes—
46C2×#117×C43C2211yescharacteristic
47C43×#407C2211yescharacteristic
48C4×C22⋊C4×C43C2211yescharacteristic
49C43×#339C2212yes—
50C43×#339C2212yes—
51C2×#10621877C2312yes—
52#13063325—22no—
53#13063325—22no—
54#13063324—22no—
55#13063324—22no—
56#13063324C2×C412yes—
57#13063324C2×C412yes—
58#13063324C2×C412yes—
59#13063324C2×C412yes—
60#13063317—22no—
61#13063317—22no—
62#13063316—22no—
63#13063316—22no—
64#13063316C2×C412yes—
65#13063316C2×C412yes—
66#13063316C2×C412yes—
67#13063316C2×C412yes—
68#13063304—22no—
69#13063304—22no—
70#13063304—22no—
71#13063304—22no—
72#13063302—22no—
73#13063302—22no—
74#13063302—22no—
75#13063302—22no—
76#13063302—22no—
77#13063302—22no—
78#13063302—22no—
79#13063302—22no—
80C4×Dic86—22no—
81C4×Dic86—22no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84#13063284—21no—
85#13063284—21no—
86#13063284C2×C412yes—
87#13063284C2×C412yes—
88#13063284C2×C412yes—
89#13063284D412yes—
90#13063284D412yes—
91#13063284C2312yes—
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×C4⋊Dic43D411yescharacteristic
95C2×C4⋊Dic43D411yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43D411yescharacteristic
101C2×C22⋊Dic43D411yescharacteristic
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43C2311yescharacteristic
106C2×C4×Dic43C2311yescharacteristic
107C2×C4×Dic43C2311yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109Dic43⋊C8—24no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112#13063235—22no—
113C8×Dic43—22no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C23×C4×C43C2311yescharacteristic
120C2×M16×C43C2312yes—
121#117×C43—21no—
122#117×C43—21no—
123#117×C43C2×C412yes—
124#117×C43C2312yes—
125C2×C4⋊C4×C43C2×C411yescharacteristic
126C2×C4⋊C4×C43C2×C411yescharacteristic
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132C22⋊C8×C43—21no—
133C22⋊C8×C43—21no—
134#95×C43—21no—
135C24×C43C2×D411yescharacteristic
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C22×C411yescharacteristic
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C2×Dic86—22no—
157C2×Dic86—22no—
158C2×Dic86—22no—
159C2×Dic86—22no—
160M16×C43—22no—
161M16×C43—22no—
162C2×C8×C43—22no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43C22×C412yes—
166C4⋊C4×C43C22×C412yes—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—22no—
169C22⋊C4×C43—42no—
170C42×C43—22no—
171C42×C43—22no—
172C42×C43—22no—
173C42×C43—22no—
174C22⋊Dic43—22no—
175C22⋊Dic43—22no—
176C22⋊Dic43—42no—
177C22⋊Dic43C22⋊C412yes—
178C22⋊Dic43C22⋊C412yes—
179C22⋊Dic43C22⋊C412yes—
180C22⋊Dic43C22⋊C412yes—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—22no—
184C4⋊Dic43—22no—
185C4⋊Dic43—22no—
186C4⋊Dic43—22no—
187C4⋊Dic43C22⋊C412yes—
188C4⋊Dic43C22⋊C412yes—
189C4⋊Dic43C22⋊C412yes—
190C4⋊Dic43C22⋊C412yes—
191C4⋊Dic43C22×C412yes—
192C4⋊Dic43C22×C412yes—
193Dic43⋊C4—22no—
194Dic43⋊C4—22no—
195Dic43⋊C4—22no—
196Dic43⋊C4—22no—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203C4×Dic43—22no—
204C4×Dic43—22no—
205C4×Dic43—22no—
206C4×Dic43—22no—
207C4×Dic43—42no—
208C4×Dic43—42no—
209C4×Dic43C22×C412yes—
210C4×Dic43C22×C412yes—
211C4×Dic43C2×D412yes—
212C4×Dic43C2×D412yes—
213#10621877—22no—
214#10621877—22no—
215C2×C43⋊C8—22no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43C2×C22⋊C411yescharacteristic
221C23×C43C2×C22⋊C411yescharacteristic
222C23×C43C22×D411yescharacteristic
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—81no—
238C2×C4×C43—81no—
239C2×C4×C43C2×C22⋊C411yescharacteristic
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43C23×C411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C432−1+412yes—
244C2×C4×C432−1+412yes—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—81no—
258C2×Dic43—81no—
259C2×Dic43C2×C22⋊C412yes—
260C2×Dic43C2×C22⋊C412yes—
261C2×Dic43C2×C22⋊C412yes—
262C2×Dic43C2×C22⋊C412yes—
263Dic86—82no—
264Dic86—82no—
265Dic86—82no—
266Dic86—82no—
267C8×C43—42no—
268C43⋊C8—42no—
269#21846—431nomaximal, Sylow
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—21no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43C22×C22⋊C411yescharacteristic
281C22×C43#53611yescharacteristic
282C22×C43#53611yescharacteristic
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—42no—
286C4×C43—42no—
287C4×C43—42no—
288C4×C43—81no—
289C4×C43#51912yes—
290C4×C43#53612yes—
291Dic43—22no—
292Dic43—22no—
293Dic43—22no—
294Dic43—22no—
295Dic43—42no—
296Dic43—42no—
297Dic43—42no—
298Dic43—81no—
299#3458—431no—
300#2921—431no—
301#2298—431no—
302#1995—432no—
303#1994—432no—
304#1986—432no—
305#1986—432no—
306#1826—431no—
307#1826—431no—
308#1826—431no—
309#1826D4311yescharacteristic
310C2×C43—21no—
311C2×C43—21no—
312C2×C43—41no—
313C2×C43—41no—
314C2×C43#231011yescharacteristic
315C2×C43#290111yescharacteristic
316C2×C43#290111yescharacteristic
317#544—432no—
318#544—432no—
319#544—432no—
320#544—432no—
321#544—861no—
322#544—861no—
323#543—861no—
324#543—861no—
325#533—432no—
326#533—432no—
327#533—862no—
328#533—862no—
329C2×#117—431no—
330C2×#117—431no—
331C2×#117C2×D4311yescharacteristic
332#433—862no—
333#433—862no—
334#423—432no—
335#407—431no—
336#407C2×D4311yescharacteristic
337C4×M16—432no—
338#388—861no—
339#388—861no—
340#387—861no—
341#387—861no—
342C4×C4⋊C4—431no—
343C4×C4⋊C4—431no—
344C4×C22⋊C4—431no—
345C4×C22⋊C4C2×D4311yescharacteristic
346#376—431no—
347C43—431no—
348#339—432no—
349#339—432no—
350#339—432no—
351#339—432no—
352#339—432no—
353#339—432no—
354#339C2×D4312yes—
355#339C2×D4312yes—
356C43#2184611yescharacteristic, complemented, Sylow
357C23×C4C22×D4311yescharacteristic
358C2×M16—432no—
359C2×M16C22×D4312yes—
360C4⋊Q8—432no—
361C4⋊Q8—432no—
362C4⋊Q8—432no—
363C4⋊Q8—432no—
364C4⋊Q8—862no—
365C4⋊Q8—862no—
366C4⋊Q8—862no—
367C4⋊Q8—862no—
368#125—432no—
369#125—432no—
370#125—432no—
371#125—432no—
372#125—862no—
373#125—862no—
374#125—862no—
375#125—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—862no—
385C22⋊Q8—862no—
386C22⋊Q8—862no—
387C22⋊Q8—862no—
388C4×Q8—862no—
389C4×Q8—862no—
390C4×Q8—862no—
391C4×Q8—862no—
392#117—21no—
393#117—21no—
394#117—432no—
395#117—432no—
396#117—432no—
397#117—432no—
398#117—432no—
399#117—432no—
400#117—861no—
401#117—861no—
402#117C4×D4312yes—
403#117C22×D4312yes—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4C4×D4311yescharacteristic
411C2×C4⋊C4C4×D4311yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—431no—
415C2×C22⋊C4—431no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C42—21no—
419C2×C42—431no—
420C2×C42—431no—
421C2×C42—431no—
422C2×C42—431no—
423C2×C42—861no—
424C2×C42—861no—
425C2×C42—861no—
426C2×C42C22×D4311yescharacteristic
427C2×C42C22×D4311yescharacteristic
428C4⋊C8—864no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433#97—862no—
434C4×C8—862no—
435#95—21no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441C24D4×D4311yescharacteristic
442C2×Q8—862no—
443C2×Q8—862no—
444C2×Q8—862no—
445C2×Q8—862no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4C2×C4×D4311yescharacteristic
461C22×C4C2×C4×D4311yescharacteristic
462C22×C4D4×D4311yescharacteristic
463C22×C4D4×D4311yescharacteristic
464C22×C4D4×D4311yescharacteristic
465C22×C4C23×D4311yescharacteristic
466M16—22no—
467M16—22no—
468M16—862no—
469M16—862no—
470C2×C8—22no—
471C2×C8—862no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—432no—
475C4⋊C4—432no—
476C4⋊C4—432no—
477C4⋊C4—432no—
478C4⋊C4—432no—
479C4⋊C4—432no—
480C4⋊C4—862no—
481C4⋊C4—862no—
482C4⋊C4—862no—
483C4⋊C4—862no—
484C4⋊C4—862no—
485C4⋊C4—862no—
486C4⋊C4—862no—
487C4⋊C4—862no—
488C4⋊C4—862no—
489C4⋊C4—862no—
490C4⋊C4—862no—
491C4⋊C4—862no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—1722no—
495C4⋊C4—1722no—
496C4⋊C4C2×C4×D4312yes—
497C4⋊C4C2×C4×D4312yes—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—42no—
501C22⋊C4—432no—
502C22⋊C4—432no—
503C22⋊C4—432no—
504C22⋊C4—432no—
505C22⋊C4—862no—
506C22⋊C4—862no—
507C22⋊C4—1722no—
508C42—22no—
509C42—22no—
510C42—22no—
511C42—22no—
512C42—432no—
513C42—432no—
514C42—432no—
515C42—432no—
516C42—862no—
517C42—862no—
518C42—862no—
519C42—862no—
520C42—1722no—
521C42—1722no—
522C23—21no—
523C23—21no—
524C23—41no—
525C23—41no—
526C23C22⋊C4×D4311yescharacteristic
527C23C22⋊C4×D4311yescharacteristic
528C23C2×D4×D4311yescharacteristic
529Q8—3442no—
530Q8—3442no—
531Q8—3442no—
532Q8—3442no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4—432no—
550C2×C4—432no—
551C2×C4—432no—
552C2×C4—432no—
553C2×C4—862no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—3441no—
557C2×C4—3441no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4C22⋊C4×D4311yescharacteristic
568C2×C4C22⋊C4×D4311yescharacteristic
569C2×C4C22×C4×D4311yescharacteristic
570C2×C4C2×D4×D4311yescharacteristic
571C2×C4#1306337212yes—
572C2×C4#1306337212yes—
573C8—42no—
574C8—1722no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—81no—
584C22—81no—
585C22C2×C22⋊C4×D4311yescharacteristic
586C22#1458347111yescharacteristic
587C22#1458347111yescharacteristic
588C4—21no—
589C4—21no—
590C4—42no—
591C4—42no—
592C4—42no—
593C4—81no—
594C4—862no—
595C4—862no—
596C4—862no—
597C4—862no—
598C4—3441no—
599C4—1722no—
600C4—1722no—
601C4—1722no—
602C4#1458337612yes—
603C4#1458347112yes—
604C2—21no—
605C2—21no—
606C2—41no—
607C2—41no—
608C2#1913718011yescharacteristic
609C2#1914313911yescharacteristic
610C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1826C2
socleC22×C43C22×C22⋊C4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#1826D43
hypocenterC43#21846
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
4. #19135574C2semidirect
5. #19135570C2semidirect
6. #19135537C2semidirect
7. #19135537C2semidirect
12. #14583530C4semidirect
13. #14583530C4semidirect
16. #14583527C4semidirect
17. #14583527C4semidirect
356. C43#21846semidirect

Maximal subgroups

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

subgroupindex
#191480002
#191432302
#191370912
#191355742
#191355702
#191355372
#191346952
#191346942
#191346922
C43×#18262
#2184643