Finite Group Databasebeta

← #25130367

Subgroups — #25130367

Order 11008.

1126 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583210C211yesmaximal, characteristic, complemented
2C2×#14582942C211yesmaximal, characteristic, complemented
3#19138912C211yesmaximal, characteristic, complemented
4#19135920C212yesmaximal, complemented
5#19135774C212yesmaximal, complemented
6#19135034C211yesmaximal, characteristic, complemented
7#19134893C211yesmaximal, characteristic, complemented
8#19134856C212yesmaximal, complemented
9#19134794C212yesmaximal, complemented
10#19134690C211yesmaximal, characteristic, complemented
11C2×C43×#555C211yesmaximal, characteristic
12C22×#10621877C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14#14583210—24no—
15#14582942—24no—
16C2×#13063258C2212yes—
17C2×#13063258C2212yes—
18C2×#13063256C2212yes—
19C2×#13063246C2212yes—
20C2×#13063246C2212yes—
21C2×C22⋊(C43⋊C8)C2211yescharacteristic
22C2×C22⋊(C43⋊C8)C2212yes—
23#14582838—21no—
24#14582835—21no—
25#14582797C2212yes—
26#14582779—21no—
27#14582771—21no—
28#14582759C2212yes—
29#14582759C2211yescharacteristic
30#14582661C2212yes—
31#14582661C2212yes—
32#14582661C2212yes—
33#14582654C2212yes—
34C43×#555—24no—
35C43×#555—24no—
36C2×C4⋊Q8×C43C2211yescharacteristic
37C2×#124×C43—21no—
38C2×#124×C43—21no—
39C2×#121×C43—21no—
40C2×#121×C43C2211yescharacteristic
41C2×#121×C43C2211yescharacteristic
42C2×C4×D4×C43C2211yescharacteristic
43C2×C4×D4×C43C2211yescharacteristic
44C2×#117×C43—21no—
45C2×#117×C43C2211yescharacteristic
46C2×#117×C43C2211yescharacteristic
47C23×Dic43—21no—
48C2×#10621877—22no—
49C2×#10621877—24no—
50C22×C43⋊C8C2312yes—
51C22×C43⋊C8C2312yes—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43C2312yes—
56C2×C4⋊Dic43C2312yes—
57C2×Dic43⋊C4—22no—
58C2×C22⋊Dic43—21no—
59C2×C22⋊Dic43—22no—
60#13063258—24no—
61#13063258—24no—
62#13063256—24no—
63#13063246—24no—
64#13063246—24no—
65C22⋊(C43⋊C8)—22no—
66C22⋊(C43⋊C8)—24no—
67C43⋊#95—22no—
68C43⋊#95—21no—
69C43⋊#95—22no—
70C22×Q8×C43—21no—
71C22×D4×C43—21no—
72C22×D4×C43—21no—
73C22×D4×C43D411yescharacteristic
74C22×D4×C43C2311yescharacteristic
75C23×C4×C43—21no—
76C23×C4×C43C2311yescharacteristic
77C23×C4×C43C2311yescharacteristic
78C4⋊Q8×C43—22no—
79C4⋊Q8×C43—22no—
80#124×C43—28no—
81#124×C43—28no—
82#121×C43—28no—
83#121×C43—22no—
84#121×C43—22no—
85#121×C43—22no—
86#121×C43D414yes—
87C4×D4×C43—22no—
88C4×D4×C43—22no—
89C4×D4×C43—22no—
90C4×D4×C43—22no—
91#117×C43—28no—
92#117×C43—22no—
93#117×C43—22no—
94#117×C43—22no—
95#117×C43D414yes—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43D411yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43D411yescharacteristic
107C2×C22⋊C4×C43D411yescharacteristic
108C2×C42×C43—21no—
109C2×C42×C43—21no—
110C2×C42×C43C2311yescharacteristic
111C24×C43—21no—
112C24×C43C2×D411yescharacteristic
113C24×C43C2×D411yescharacteristic
114C2×Q8×C43—24no—
115C2×Q8×C43—82no—
116C2×D4×C43—24no—
117C2×D4×C43—22no—
118C2×D4×C43—21no—
119C2×D4×C43—22no—
120C2×D4×C43—24no—
121C2×D4×C43—22no—
122C2×D4×C43—22no—
123C2×D4×C43—41no—
124C2×D4×C43—82no—
125C2×D4×C43—82no—
126C2×D4×C43C2×D412yes—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—24no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—42no—
138C22×C4×C43—42no—
139C22×C4×C43C2×D412yes—
140C22×C4×C43C2×D412yes—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—42no—
149C22×Dic43—82no—
150C4⋊C4×C43—24no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43C2×D412yes—
156C4⋊C4×C43C2×D412yes—
157C4⋊C4×C43C2×D412yes—
158C22⋊C4×C43—24no—
159C22⋊C4×C43—24no—
160C22⋊C4×C43—24no—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—24no—
164C22⋊C4×C43—22no—
165C42×C43—24no—
166C42×C43—24no—
167C42×C43—21no—
168C42×C43—21no—
169C22⋊Dic43—42no—
170C22⋊Dic43—82no—
171C4⋊Dic43—22no—
172C4⋊Dic43—22no—
173C4⋊Dic43—22no—
174C4⋊Dic43—22no—
175C4⋊Dic43—42no—
176Dic43⋊C4—82no—
177#10621877—28no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—22no—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—22no—
182C2×C43⋊C8—22no—
183C2×C43⋊C8#4114yes—
184C23×C43—22no—
185C23×C43—21no—
186C23×C43—21no—
187C23×C43—22no—
188C23×C43—21no—
189C23×C43—22no—
190C23×C43—22no—
191C23×C43—21no—
192C23×C43—21no—
193C23×C43—22no—
194C23×C43—42no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—42no—
198C23×C43#12012yes—
199C23×C43C22×D411yescharacteristic
200Q8×C43—84no—
201D4×C43—24no—
202D4×C43—44no—
203D4×C43—41no—
204D4×C43—41no—
205D4×C43—84no—
206D4×C43—84no—
207C2×C4×C43—21no—
208C2×C4×C43—22no—
209C2×C4×C43—21no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—24no—
213C2×C4×C43—21no—
214C2×C4×C43—22no—
215C2×C4×C43—21no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—48no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—42no—
228C2×C4×C43#12012yes—
229C2×C4×C43#13712yes—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4112yes—
233C2×C4×C432−1+412yes—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—84no—
241C43⋊C8—24no—
242C43⋊C8—42no—
243#24105—431nomaximal, Sylow
244C22×C43—22no—
245C22×C43—22no—
246C22×C43—22no—
247C22×C43—42no—
248C22×C43—42no—
249C22×C43—42no—
250C22×C43—42no—
251C22×C43—41no—
252C22×C43—42no—
253C22×C43—41no—
254C22×C43—42no—
255C22×C43—41no—
256C22×C43—42no—
257C22×C43—82no—
258C22×C43—82no—
259C22×C43C2×#12011yescharacteristic
260C22×C43#54712yes—
261C22×C43C2×#13711yescharacteristic
262C22×C43#57511yescharacteristic
263C22×C43#57612yes—
264C4×C43—22no—
265C4×C43—22no—
266C4×C43—41no—
267C4×C43—42no—
268C4×C43—41no—
269C4×C43—42no—
270C4×C43—42no—
271C4×C43#52511yescharacteristic
272C4×C43#53611yescharacteristic
273C4×C43#54712yes—
274Dic43—82no—
275Dic43—82no—
276C2×#555D4311yescharacteristic
277C2×#480—431no—
278C2×#428—431no—
279#2487—431no—
280#2057—432no—
281#2033—432no—
282#1895—431no—
283#1870—431no—
284#1864—432no—
285#1854—432no—
286#1825—431no—
287C2×C43—42no—
288C2×C43—81no—
289C2×C43—82no—
290C2×C43#240611yescharacteristic
291C2×C43#300711yescharacteristic
292C2×C43#300811yescharacteristic
293C2×C43#334712yes—
294C2×C43#335712yes—
295C22×M16—431no—
296#555—24no—
297#555—24no—
298C2×C4⋊Q8C2×D4311yescharacteristic
299C2×#124—21no—
300C2×#124—21no—
301C2×#121—21no—
302C2×#121C2×D4311yescharacteristic
303C2×#121C2×D4311yescharacteristic
304C2×C4×D4C2×D4311yescharacteristic
305C2×C4×D4C2×D4311yescharacteristic
306C2×#117—21no—
307C2×#117C2×D4311yescharacteristic
308C2×#117C2×D4311yescharacteristic
309C22×C4⋊C4—431no—
310#480—864no—
311#428—864no—
312C2×#107—432no—
313C2×#107—432no—
314C2×#106—432no—
315C2×#102—432no—
316C2×#102—432no—
317C2×C22⋊C8—431no—
318C2×C22⋊C8—432no—
319#400—861no—
320#399—861no—
321#389—432no—
322#386—861no—
323#385—861no—
324#380—431no—
325#380—432no—
326#340—432no—
327#340—432no—
328#340—432no—
329#336—432no—
330C43#2410511yescharacteristic, complemented, Sylow
331C22×Q8—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4C22⋊D4311yescharacteristic
335C22×D4C22×D4311yescharacteristic
336C23×C4—21no—
337C23×C4—861no—
338C23×C4C22×D4311yescharacteristic
339C23×C4C22×D4311yescharacteristic
340C2×M16—864no—
341C2×M16—862no—
342C22×C8—432no—
343C22×C8—432no—
344C4⋊Q8—22no—
345C4⋊Q8—22no—
346#124—28no—
347#124—28no—
348#121—28no—
349#121—22no—
350#121—22no—
351#121—22no—
352#121C22⋊D4314yes—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—22no—
357#117—28no—
358#117—22no—
359#117—22no—
360#117—22no—
361#117C22⋊D4314yes—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—432no—
364C2×C4⋊C4—432no—
365C2×C4⋊C4—862no—
366C2×C4⋊C4—862no—
367C2×C4⋊C4—862no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4C22⋊D4311yescharacteristic
370C2×C4⋊C4C22×D4311yescharacteristic
371C2×C4⋊C4C22×D4311yescharacteristic
372C2×C4⋊C4C22×D4311yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—862no—
379C2×C22⋊C4—861no—
380C2×C22⋊C4C22⋊D4311yescharacteristic
381C2×C22⋊C4C22⋊D4311yescharacteristic
382C2×C42—21no—
383C2×C42—21no—
384C2×C42C22×D4311yescharacteristic
385#107—864no—
386#107—864no—
387#106—864no—
388#102—864no—
389#102—864no—
390C22⋊C8—864no—
391C22⋊C8—862no—
392#95—862no—
393#95—861no—
394#95—862no—
395C24—21no—
396C24C2×C22⋊D4311yescharacteristic
397C24C2×C22⋊D4311yescharacteristic
398C2×Q8—24no—
399C2×Q8—82no—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—41no—
408C2×D4—82no—
409C2×D4—82no—
410C2×D4C2×C22⋊D4312yes—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—862no—
424C22×C4—862no—
425C22×C4—3442no—
426C22×C4—1722no—
427C22×C4C2×C22⋊D4311yescharacteristic
428C22×C4C2×C22⋊D4311yescharacteristic
429C22×C4C2×C22⋊D4311yescharacteristic
430C22×C4C2×C22⋊D4312yes—
431C22×C4C2×C22⋊D4312yes—
432C22×C4C2×C22⋊D4311yescharacteristic
433C22×C4C23×D4311yescharacteristic
434M16—868no—
435C2×C8—434no—
436C2×C8—862no—
437C2×C8—862no—
438C2×C8—862no—
439C2×C8—862no—
440C2×C8—862no—
441C4⋊C4—24no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—862no—
447C4⋊C4—862no—
448C4⋊C4—862no—
449C4⋊C4—862no—
450C4⋊C4—3442no—
451C4⋊C4—1722no—
452C4⋊C4C2×C22⋊D4312yes—
453C4⋊C4C2×C22⋊D4312yes—
454C4⋊C4C2×C22⋊D4312yes—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—22no—
460C22⋊C4—24no—
461C22⋊C4—22no—
462C22⋊C4—3442no—
463C22⋊C4—1722no—
464C42—24no—
465C42—24no—
466C42—21no—
467C42—21no—
468C23—21no—
469C23—21no—
470C23—22no—
471C23—22no—
472C23—21no—
473C23—22no—
474C23—21no—
475C23—21no—
476C23—22no—
477C23—22no—
478C23—41no—
479C23—41no—
480C23—42no—
481C23—42no—
482C23#1306329412yes—
483C23C22×C22⋊D4311yescharacteristic
484Q8—84no—
485D4—24no—
486D4—44no—
487D4—41no—
488D4—41no—
489D4—84no—
490D4—84no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—48no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—3444no—
513C2×C4—1722no—
514C2×C4—1722no—
515C2×C4—1722no—
516C2×C4—1722no—
517C2×C4—1722no—
518C2×C4—1722no—
519C2×C4#1306329412yes—
520C2×C4#1306335512yes—
521C2×C4C22×C22⋊D4311yescharacteristic
522C2×C4C22×C22⋊D4311yescharacteristic
523C2×C4#41×D4312yes—
524C2×C4#1306337212yes—
525C8—864no—
526C8—1722no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—41no—
534C22—42no—
535C22—42no—
536C22—41no—
537C22—41no—
538C22—42no—
539C22—42no—
540C22—82no—
541C22—82no—
542C22C2×#1306329411yescharacteristic
543C22#1458354812yes—
544C22C2×#1306335511yescharacteristic
545C22#1458369711yescharacteristic
546C22#1458370212yes—
547C4—22no—
548C4—22no—
549C4—41no—
550C4—42no—
551C4—41no—
552C4—42no—
553C4—42no—
554C4—3442no—
555C4—3442no—
556C4#1458340611yescharacteristic
557C4#1458347011yescharacteristic
558C4#1458354812yes—
559C2—42no—
560C2—81no—
561C2—82no—
562C2#1913792611yescharacteristic
563C2#1914385511yescharacteristic
564C2#1914386311yescharacteristic
565C2#1914709512yes—
566C2#1914721512yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#555C2
socleC23×C43C22×D4
hypercenterC2×#555D43
hypocenterC43#24105
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#14583210C2semidirect
2. C2×#14582942C2semidirect
3. #19138912C2semidirect
4. #19135920C2semidirect
5. #19135774C2semidirect
6. #19135034C2semidirect
7. #19134893C2semidirect
8. #19134856C2semidirect
9. #19134794C2semidirect
10. #19134690C2semidirect
330. C43#24105semidirect

Maximal subgroups

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

subgroupindex
C2×#145832102
C2×#145829422
#191389122
#191359202
#191357742
#191350342
#191348932
#191348562
#191347942
#191346902
C2×C43×#5552
#2410543