Finite Group Databasebeta

← #25101792

Subgroups — #25101792

Order 11008.

1218 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583428C211yesmaximal, characteristic
2C2×#14582851C211yesmaximal, characteristic, complemented
3#19137000C211yesmaximal, characteristic, complemented
4#19135564C211yesmaximal, characteristic, complemented
5#19135563C211yesmaximal, characteristic, complemented
6#19135412C211yesmaximal, characteristic, complemented
7#19135030C212yesmaximal
8#19135025C212yesmaximal, complemented
9#103×Dic43C212yesmaximal, complemented
10#102×Dic43C212yesmaximal, complemented
11C43×#1959C211yesmaximal, characteristic, complemented
12C22×#10621872C2212yes—
13#14583428—24no—
14#14583428C418yescomplemented
15C2×#13063318—21no—
16C2×#13063317C2211yescharacteristic
17C2×#13063307—21no—
18C2×#13063301C2211yescharacteristic
19C2×#13063296C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C2×(C22⋊D43)⋊C4—21no—
23C2×#13063283—21no—
24C2×#13063281—21no—
25C2×C42×D43C2211yescharacteristic
26C2×#13063249C2212yes—
27C2×#13063246C2212yes—
28#14582851—24no—
29C2×#13063236C2211yescharacteristic
30C2×C8×Dic43C2212yes—
31#14582769C2211yescharacteristic
32#14582764—21no—
33#14582756—21no—
34#14582756C2212yes—
35C4⋊C4×Dic43—21no—
36C4⋊C4×Dic43C2212yes—
37#14582662C2212yes—
38#14582662C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C2×#124×C43C2211yescharacteristic
42C2×#103×C43C2212yes—
43C2×#102×C43C2212yes—
44C2×#97×C43C2211yescharacteristic
45C43×#384C2211yescharacteristic
46C22×C22⋊D43—21no—
47C23×Dic43—21no—
48C22×C4×D43D411yescharacteristic
49C22×C4×D43D411yescharacteristic
50C22×C4×D43C2311yescharacteristic
51C2×#10621872—24no—
52C2×#10621872—24no—
53C2×#10621872—24no—
54C22×C43⋊C8C2312yes—
55#13063318—28no—
56#13063317—22no—
57#13063317C2×C414yes—
58#13063307—28no—
59#13063301—22no—
60#13063301C2×C414yes—
61#13063296—22no—
62#13063296C2×C414yes—
63Q8×Dic43—22no—
64Q8×Dic43C2×C414yes—
65D4×Dic43—22no—
66D4×Dic43C2×C414yes—
67(C22⋊D43)⋊C4—28no—
68#13063283—44no—
69#13063281—28no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2312yes—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—22no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—22no—
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88C42×D43C2×C414yes—
89C42×D43D414yes—
90#13063249—24no—
91#13063246—24no—
92#13063236—22no—
93C8×Dic43—24no—
94C43⋊#95—22no—
95C43⋊#95—22no—
96C22×Q8×C43C2311yescharacteristic
97C22×D4×C43C2311yescharacteristic
98C22×C8×C43C2312yes—
99#124×C43—22no—
100#124×C43C2×C414yes—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43C2312yes—
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C42×C43C2311yescharacteristic
107#103×C43—24no—
108#102×C43—24no—
109#97×C43—22no—
110C24×C43—21no—
111C23×D43C2×D411yescharacteristic
112C2×Q8×C43—21no—
113C2×Q8×C43—22no—
114C2×Q8×C43—22no—
115C2×Q8×C43C22×C412yes—
116C2×D4×C43—21no—
117C2×D4×C43—22no—
118C2×D4×C43—22no—
119C2×D4×C43C22×C412yes—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2411yescharacteristic
125C2×C22⋊D43—24no—
126C2×C22⋊D43—42no—
127C2×C22⋊D43—42no—
128C22×Dic43—24no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—22no—
132C22×Dic43—42no—
133C22×Dic43—42no—
134C22×Dic43C2×D411yescharacteristic
135C22×Dic43C2×D411yescharacteristic
136C22×Dic43C2×D411yescharacteristic
137C2×C4×D43—22no—
138C2×C4×D43—22no—
139C2×C4×D43—22no—
140C2×C4×D43—22no—
141C2×C4×D43—41no—
142C2×C4×D43—41no—
143C2×C4×D43C22⋊C414yes—
144C2×C4×D43C22⋊C414yes—
145C2×C4×D43C22×C412yes—
146C2×C4×D43C2×D412yes—
147C2×C8×C43—22no—
148C2×C8×C43—22no—
149C2×C8×C43#4114yes—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—42no—
153C4⋊C4×C43—42no—
154C22⋊C4×C43—24no—
155C22⋊C4×C43—24no—
156C42×C43C22×C412yes—
157C42×C43C2×D412yes—
158C22⋊Dic43—24no—
159C22⋊Dic43—24no—
160(C2×D43)⋊C4—24no—
161(C2×D43)⋊C4—44no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43—24no—
165C4⋊Dic43—22no—
166C4⋊Dic43—22no—
167C4⋊Dic43—42no—
168C4⋊Dic43—42no—
169C4⋊Dic43C22×C412yes—
170C4⋊Dic43C22×C412yes—
171Dic43⋊C4—24no—
172Dic43⋊C4—24no—
173Dic43⋊C4—24no—
174C4×Dic43—24no—
175C4×Dic43—44no—
176C4×Dic43C22⋊C414yes—
177C4×Dic43C22⋊C414yes—
178C4×Dic43C22×C412yes—
179C4×Dic43C2×D412yes—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—22no—
182C2×C43⋊C8#4114yes—
183#10621872—216no—
184C23×C43—22no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43C22×D411yescharacteristic
192C22×D43—21no—
193C22×D43—21no—
194C22×D43—21no—
195C22×D43—21no—
196C22×D43—21no—
197C22×D43—21no—
198C22×D43C2×C22⋊C412yes—
199Q8×C43—24no—
200Q8×C43—42no—
201D4×C43—24no—
202D4×C43—42no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—22no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43C2×C22⋊C412yes—
214C2×C4×C43C2×C22⋊C412yes—
215C2×C4×C43C23×C411yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C2×#4112yes—
218C2×C4×C43C2×#4112yes—
219C22⋊D43—48no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—22no—
225C2×Dic43—22no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—48no—
231C2×Dic43—42no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43C2×C22⋊C412yes—
235C2×Dic43C2×C22⋊C412yes—
236C2×Dic43C2×C22⋊C412yes—
237C2×Dic43AGL(1,ℤ/8)12yes—
238C2×Dic43#13712yes—
239C4×D43—24no—
240C4×D43—24no—
241C4×D43—28no—
242C4×D43—44no—
243C8×C43—24no—
244C43⋊C8—24no—
245#21403—431nomaximal, Sylow
246C22×C43—42no—
247C22×C43—42no—
248C22×C43—42no—
249C22×C43—81no—
250C22×C43—81no—
251C22×C43—81no—
252C22×C43—81no—
253C22×C43C22×C22⋊C411yescharacteristic
254C22×C43#53211yescharacteristic
255C22×C43#53211yescharacteristic
256C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
257C22×C43C2×#13711yescharacteristic
258C22×C43#57511yescharacteristic
259C22×C43#57511yescharacteristic
260C2×D43—22no—
261C2×D43—22no—
262C2×D43—22no—
263C2×D43—41no—
264C2×D43—41no—
265C2×D43—41no—
266C2×D43—41no—
267C4×C43—22no—
268C4×C43—22no—
269C4×C43—42no—
270C4×C43—82no—
271C4×C43C4×#4112yes—
272C4×C43#52512yes—
273Dic43—22no—
274Dic43—22no—
275Dic43—42no—
276Dic43—42no—
277Dic43—82no—
278Dic43#41714yes—
279C2×#529—431no—
280C2×C4×M16—431no—
281#2285—431no—
282#1992—431no—
283#1992—431no—
284#1959—431no—
285#1959D4311yescharacteristic, complemented
286#1895—432no—
287#1894—432no—
288C4×#103—432no—
289C4×#102—432no—
290C2×C43—82no—
291C2×C43#229711yescharacteristic
292C2×C43C2×#41711yescharacteristic
293C2×C43#289611yescharacteristic
294C2×C43#317111yescharacteristic
295C2×C43#317111yescharacteristic
296C2×C43#317211yescharacteristic
297C2×C43#317211yescharacteristic
298D43—42no—
299C22×M16—432no—
300#529—438no—
301#529—864no—
302C2×#126—861no—
303C2×#125—431no—
304C2×#124C2×D4311yescharacteristic
305C2×#123—861no—
306C2×C22⋊Q8—431no—
307C2×#121—431no—
308C2×C4×Q8—431no—
309C2×C4×D4—431no—
310C2×C4×D4—861no—
311C2×#117—861no—
312C2×#117—861no—
313C22×C42—431no—
314C2×#103—432no—
315C2×#103C2×D4312yes—
316C2×#102—432no—
317C2×#102C2×D4312yes—
318C4×M16—864no—
319C2×#97—431no—
320C2×#97C2×D4311yescharacteristic
321C2×C4×C8—432no—
322#384—431no—
323#384C2×D4311yescharacteristic
324#382—861no—
325#380—432no—
326#380—861no—
327C4×C4⋊C4—432no—
328C4×C4⋊C4—861no—
329#340—432no—
330#340—432no—
331#340—432no—
332#340—432no—
333C43#2140311yescharacteristic, complemented, Sylow
334C22×Q8C22×D4311yescharacteristic
335C22×D4—861no—
336C22×D4C22×D4311yescharacteristic
337C23×C4—431no—
338C23×C4—431no—
339C23×C4—431no—
340C23×C4—861no—
341C2×M16—864no—
342C2×M16—864no—
343C2×M16—864no—
344C22×C8—432no—
345C22×C8C22×D4312yes—
346#126—868no—
347#125—434no—
348#125—862no—
349#124—22no—
350#124C4×D4314yes—
351#123—868no—
352C22⋊Q8—434no—
353C22⋊Q8—862no—
354#121—434no—
355#121—862no—
356C4×Q8—434no—
357C4×Q8—862no—
358C4×D4—434no—
359C4×D4—862no—
360C4×D4—868no—
361#117—868no—
362#117—1724no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—431no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—432no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4C22×D4312yes—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—861no—
378C2×C22⋊C4—861no—
379C2×C22⋊C4—861no—
380C2×C22⋊C4—862no—
381C2×C42—431no—
382C2×C42—431no—
383C2×C42—431no—
384C2×C42—434no—
385C2×C42—434no—
386C2×C42—861no—
387C2×C42—862no—
388C2×C42C22×D4311yescharacteristic
389#103—24no—
390#103—864no—
391#102—24no—
392#102—864no—
393#97—22no—
394#97—862no—
395C4×C8—864no—
396#95—862no—
397#95—862no—
398C24—21no—
399C24—431no—
400C2×Q8—21no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8C2×C4×D4312yes—
404C2×D4—21no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—864no—
408C2×D4—1722no—
409C2×D4—1722no—
410C2×D4C2×C4×D4312yes—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—431no—
414C22×C4—431no—
415C22×C4—431no—
416C22×C4—434no—
417C22×C4—432no—
418C22×C4—432no—
419C22×C4—434no—
420C22×C4—862no—
421C22×C4—862no—
422C22×C4—864no—
423C22×C4—862no—
424C22×C4—862no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—862no—
428C22×C4—1721no—
429C22×C4—1721no—
430C22×C4—1722no—
431C22×C4—1722no—
432C22×C4D4×D4311yescharacteristic
433C22×C4D4×D4311yescharacteristic
434C22×C4C23×D4311yescharacteristic
435M16—8616no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—434no—
439C2×C8—862no—
440C2×C8—862no—
441C2×C8#1062190014yes—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—42no—
445C4⋊C4—42no—
446C4⋊C4—432no—
447C4⋊C4—432no—
448C4⋊C4—864no—
449C4⋊C4—864no—
450C4⋊C4—864no—
451C4⋊C4—864no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—862no—
455C4⋊C4—862no—
456C4⋊C4—1722no—
457C4⋊C4—1722no—
458C22⋊C4—24no—
459C22⋊C4—24no—
460C22⋊C4—864no—
461C22⋊C4—864no—
462C22⋊C4—864no—
463C22⋊C4—1724no—
464C42—434no—
465C42—434no—
466C42—432no—
467C42—432no—
468C42—864no—
469C42—1724no—
470C42C2×C4×D4312yes—
471C42D4×D4312yes—
472C23—22no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—432no—
480C23—861no—
481C23—861no—
482C23—861no—
483C23—861no—
484C23—861no—
485C23—861no—
486C23C2×D4×D4311yescharacteristic
487Q8—24no—
488Q8—42no—
489D4—24no—
490D4—42no—
491D4—1728no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—432no—
503C2×C4—432no—
504C2×C4—432no—
505C2×C4—432no—
506C2×C4—432no—
507C2×C4—868no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—864no—
513C2×C4—864no—
514C2×C4—862no—
515C2×C4—862no—
516C2×C4—1724no—
517C2×C4—1728no—
518C2×C4—1722no—
519C2×C4—1722no—
520C2×C4—1722no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4C22⋊C4×D4312yes—
526C2×C4C22⋊C4×D4312yes—
527C2×C4C22×C4×D4311yescharacteristic
528C2×C4C2×D4×D4311yescharacteristic
529C2×C4#41×D4312yes—
530C2×C4C2×#1062190012yes—
531C8—24no—
532C8—864no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—862no—
541C22—862no—
542C22—862no—
543C22—1721no—
544C22—1721no—
545C22—1721no—
546C22—1721no—
547C22C2×C22⋊C4×D4311yescharacteristic
548C22#1458344711yescharacteristic
549C22#1458344811yescharacteristic
550C22AGL(1,ℤ/8)×D4311yescharacteristic
551C22#137×D4311yescharacteristic
552C22#1458369511yescharacteristic
553C22#1458369811yescharacteristic
554C4—22no—
555C4—22no—
556C4—42no—
557C4—82no—
558C4—434no—
559C4—862no—
560C4—862no—
561C4—3442no—
562C4—1722no—
563C4—1722no—
564C4C4×#1062190012yes—
565C4#1458340912yes—
566C2—82no—
567C2—1722no—
568C2#1913708211yescharacteristic
569C2#417×D4311yescharacteristic
570C2#1914311111yescharacteristic
571C2#1914518711yescharacteristic
572C2#1914519311yescharacteristic
573C2#1914519811yescharacteristic
574C2#1914520411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1959C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
cosocleC22×C4×C43C24
hypercenter#1959D43
hypocenterC43#21403
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1959

Complements

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

NH ≅ G/Ntype
2. C2×#14582851C2semidirect
3. #19137000C2semidirect
4. #19135564C2semidirect
5. #19135563C2semidirect
6. #19135412C2semidirect
8. #19135025C2semidirect
9. #103×Dic43C2semidirect
10. #102×Dic43C2semidirect
11. C43×#1959C2semidirect
14. #14583428C4semidirect
285. #1959D43semidirect
333. C43#21403semidirect

Maximal subgroups

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

subgroupindex
C2×#145834282
C2×#145828512
#191370002
#191355642
#191355632
#191354122
#191350302
#191350252
#103×Dic432
#102×Dic432
C43×#19592
#2140343