Finite Group Databasebeta

← #25130541

Subgroups — #25130541

Order 11008.

1154 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583614C211yesmaximal, characteristic
2C2×#14583194C211yesmaximal, characteristic, complemented
3C2×C4×#10621884C211yesmaximal, characteristic, complemented
4#19135777C212yesmaximal, complemented
5#19135596C212yesmaximal, complemented
6#19135555C211yesmaximal, characteristic, complemented
7#19135390C211yesmaximal, characteristic, complemented
8#19134908C212yesmaximal, complemented
9#19134792C212yesmaximal, complemented
10#19134592C211yesmaximal, characteristic, complemented
11C43×#2538C211yesmaximal, characteristic, complemented
12C22×#10621884C2211yescharacteristic
13#14583614—24no—
14#14583614—24no—
15C2×#13063325C2211yescharacteristic
16C2×#13063311—22no—
17C2×#13063299C2212yes—
18C2×#13063296—21no—
19C2×C4×D172C2211yescharacteristic
20C2×#13063284C2212yes—
21C2×#13063283—21no—
22#14583194—24no—
23C4×#10621884—24no—
24C2×#13063258C2212yes—
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063249C2212yes—
28C2×#13063249C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2212yes—
31C2×C22⋊(C43⋊C8)C2212yes—
32C2×C22⋊(C43⋊C8)C2212yes—
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582661C2212yes—
35#14582661C2212yes—
36#14582661C2212yes—
37C2×C22⋊Q8×C43C2212yes—
38C2×C4×Q8×C43C2211yescharacteristic
39C2×C4×D4×C43C2211yescharacteristic
40C43×#396—22no—
41C43×#390—21no—
42C43×#389—21no—
43C43×#384C2211yescharacteristic
44C43×#380C2212yes—
45C22×Dic86—21no—
46C22×D172C2311yescharacteristic
47C22×C22⋊D43—22no—
48C22×C4×D43—21no—
49C2×#10621884—22no—
50C2×#10621884—22no—
51C2×#10621884—22no—
52C22×C43⋊C8C2311yescharacteristic
53C22×C43⋊C8C2312yes—
54C22×C43⋊C8C2311yescharacteristic
55#13063325—22no—
56#13063325D414yes—
57#13063311—216no—
58#13063299—24no—
59#13063299—24no—
60#13063296—28no—
61C4×D172—22no—
62C4×D172D414yes—
63#13063284—24no—
64#13063284—24no—
65#13063283—28no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2312yes—
69C2×C22⋊Dic43—22no—
70C2×(C2×D43)⋊C4—22no—
71C2×(C2×D43)⋊C4—21no—
72C2×C4×Dic43—22no—
73#13063258—24no—
74#13063256—22no—
75C4⋊(C43⋊C8)—22no—
76#13063249—24no—
77#13063249—22no—
78#13063245—22no—
79#13063245—42no—
80C22⋊(C43⋊C8)—24no—
81C22⋊(C43⋊C8)—42no—
82C4×C43⋊C8—22no—
83C22×Q8×C43C2311yescharacteristic
84C22×D4×C43D411yescharacteristic
85C23×C4×C43C2312yes—
86C22⋊Q8×C43—24no—
87C22⋊Q8×C43—42no—
88C4×Q8×C43—22no—
89C4×Q8×C43—22no—
90C4×D4×C43—22no—
91C4×D4×C43—22no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43D411yescharacteristic
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43C2312yes—
99C2×C22⋊C4×C43—22no—
100C2×C22⋊C4×C43—22no—
101C2×C22⋊C4×C43D412yes—
102C2×C42×C43—21no—
103C2×C42×C43C2311yescharacteristic
104#95×C43—22no—
105C24×C43C2×D412yes—
106C23×D43—21no—
107C2×Q8×C43—21no—
108C2×Q8×C43—21no—
109C2×Q8×C43—21no—
110C2×Q8×C43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43#4112yes—
113C2×D4×C43—22no—
114C2×D4×C43—22no—
115C2×D4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43C2×D412yes—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2411yescharacteristic
129C2×C22⋊D43—28no—
130C2×C22⋊D43—82no—
131C2×C22⋊D43—82no—
132C22×Dic43—21no—
133C22×Dic43—22no—
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172C2×D412yes—
140C2×C4×D43—24no—
141C2×C4×D43—42no—
142C2×C4×D43—42no—
143C2×Dic86—24no—
144C2×Dic86—81no—
145C2×Dic86—81no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—44no—
152C4⋊C4×C43—42no—
153C4⋊C4×C43—42no—
154C4⋊C4×C43—81no—
155C22⋊C4×C43—24no—
156C22⋊C4×C43—44no—
157C22⋊C4×C43—82no—
158C42×C43—42no—
159C42×C43C2×D412yes—
160C42×C43C2×D412yes—
161C22⋊Dic43—28no—
162#10621884—28no—
163(C2×D43)⋊C4—28no—
164(C2×D43)⋊C4—24no—
165C4⋊Dic43—24no—
166C4⋊Dic43—21no—
167C4⋊Dic43—22no—
168C4⋊Dic43C2×D412yes—
169C4⋊Dic43C2×D414yes—
170C4×Dic43—28no—
171C2×C43⋊C8—21no—
172C2×C43⋊C8—21no—
173C2×C43⋊C8—21no—
174C2×C43⋊C8—22no—
175C2×C43⋊C8—22no—
176C2×C43⋊C8—21no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—21no—
179C2×C43⋊C8#4112yes—
180C23×C43—22no—
181C23×C43—22no—
182C23×C43—22no—
183C23×C43—22no—
184C23×C43—22no—
185C23×C43—22no—
186C23×C43—22no—
187C23×C43C22×D411yescharacteristic
188C22×D43—22no—
189C22×D43—41no—
190C22×D43—41no—
191C22×D43—41no—
192C22×D43—41no—
193C22×D43—41no—
194C22×D43—41no—
195Q8×C43—22no—
196Q8×C43—22no—
197Q8×C43—41no—
198Q8×C43—41no—
199D4×C43—44no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—41no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—41no—
216C2×C4×C43—42no—
217C2×C4×C43—41no—
218C2×C4×C43#12012yes—
219C2×C4×C43#12012yes—
220C2×C4×C43#13512yes—
221C2×C4×C43#13712yes—
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43H(5,𝔽2)11yescharacteristic
227C2×C4×C432−1+411yescharacteristic
228C22⋊D43—88no—
229C2×Dic43—22no—
230C2×Dic43—24no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235D172—22no—
236D172—22no—
237D172—41no—
238D172—41no—
239C4×D43—48no—
240Dic86—84no—
241C43⋊C8—22no—
242C43⋊C8—41no—
243C43⋊C8—42no—
244#24121—431nomaximal, Sylow
245C22×C43—42no—
246C22×C43—42no—
247C22×C43—42no—
248C22×C43—42no—
249C22×C43—42no—
250C22×C43—42no—
251C22×C43—42no—
252C22×C43C2×#12011yescharacteristic
253C22×C43#54611yescharacteristic
254C22×C43#54711yescharacteristic
255C22×C43C2×#13511yescharacteristic
256C22×C43C2×#13711yescharacteristic
257C22×C43#57611yescharacteristic
258C22×C43#57711yescharacteristic
259C2×D43—42no—
260C2×D43—42no—
261C2×D43—42no—
262C2×D43—81no—
263C2×D43—81no—
264C2×D43—81no—
265C2×D43—81no—
266C4×C43—22no—
267C4×C43—42no—
268C4×C43—42no—
269C4×C43—81no—
270C4×C43—82no—
271C4×C43#45214yes—
272C4×C43#52511yescharacteristic
273C4×C43#53711yescharacteristic
274C4×C43#54811yescharacteristic
275C4×C43#55011yescharacteristic
276Dic43—42no—
277Dic43—44no—
278C2×#555—431no—
279C2×#477—431no—
280C2×C4×SD16—431no—
281#2538D4311yescharacteristic, complemented
282#2033—432no—
283#2000—432no—
284#1990—431no—
285#1954—431no—
286#1873—432no—
287#1854—432no—
288#1802—431no—
289C2×C43—82no—
290C2×C43#240711yescharacteristic
291C2×C43C2×#45211yescharacteristic
292C2×C43#301211yescharacteristic
293C2×C43#330511yescharacteristic
294C2×C43#332911yescharacteristic
295C2×C43#334011yescharacteristic
296C2×C43#335711yescharacteristic
297D43—82no—
298C22×SD16—431no—
299#555—864no—
300#555—864no—
301C2×C4⋊Q8—431no—
302C2×#124—862no—
303C2×C22⋊Q8C2×D4312yes—
304C2×#121—432no—
305C2×#121—861no—
306C2×C4×Q8C2×D4311yescharacteristic
307C2×C4×D4—431no—
308C2×C4×D4C2×D4311yescharacteristic
309C2×#117—432no—
310C2×#117—861no—
311#477—864no—
312C4×SD16—864no—
313C2×#107—432no—
314C2×#106—431no—
315C2×C4⋊C8—431no—
316C2×#103—432no—
317C2×#103—431no—
318C2×#102—431no—
319C2×#102—432no—
320C2×C22⋊C8—432no—
321C2×C22⋊C8—432no—
322C2×C4×C8—431no—
323#396—22no—
324#390—21no—
325#389—21no—
326#384C2×D4311yescharacteristic
327#380C2×D4312yes—
328#340—432no—
329#340—432no—
330#340—432no—
331C43#2412111yescharacteristic, complemented, Sylow
332C22×Q8—861no—
333C22×Q8C22×D4311yescharacteristic
334C22×D4—431no—
335C22×D4—862no—
336C22×D4C22⋊D4311yescharacteristic
337C23×C4—861no—
338C23×C4C22×D4312yes—
339C2×SD16—862no—
340C2×SD16—862no—
341C2×SD16—862no—
342C22×C8—431no—
343C22×C8—431no—
344C22×C8—432no—
345C4⋊Q8—434no—
346C4⋊Q8—862no—
347#124—8616no—
348C22⋊Q8—24no—
349C22⋊Q8—42no—
350#121—864no—
351#121—864no—
352#121—868no—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—434no—
358C4×D4—862no—
359#117—868no—
360#117—864no—
361#117—864no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—432no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4C22⋊D4311yescharacteristic
370C2×C4⋊C4C22×D4311yescharacteristic
371C2×C4⋊C4C22×D4312yes—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—862no—
375C2×C22⋊C4—862no—
376C2×C22⋊C4—861no—
377C2×C22⋊C4C22⋊D4312yes—
378C2×C42—21no—
379C2×C42—862no—
380C2×C42C22×D4311yescharacteristic
381#107—864no—
382#106—862no—
383C4⋊C8—862no—
384#103—862no—
385#103—864no—
386#102—862no—
387#102—1722no—
388C22⋊C8—864no—
389C22⋊C8—1722no—
390C4×C8—862no—
391#95—22no—
392C24—861no—
393C24C2×C22⋊D4312yes—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—864no—
400C2×Q8—3441no—
401C2×Q8—3441no—
402C2×Q8#1062190012yes—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—432no—
407C2×D4—868no—
408C2×D4—861no—
409C2×D4—861no—
410C2×D4—861no—
411C2×D4—861no—
412C2×D4—861no—
413C2×D4—3442no—
414C2×D4—3442no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—861no—
425C22×C4—862no—
426C22×C4—864no—
427C22×C4—1722no—
428C22×C4—1722no—
429C22×C4C2×C22⋊D4312yes—
430C22×C4C2×C22⋊D4311yescharacteristic
431C22×C4C2×C22⋊D4311yescharacteristic
432C22×C4C23×D4311yescharacteristic
433SD16—868no—
434C2×C8—432no—
435C2×C8—861no—
436C2×C8—861no—
437C2×C8—861no—
438C2×C8—862no—
439C2×C8—862no—
440C2×C8—861no—
441C2×C8—862no—
442C2×C8—861no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—44no—
449C4⋊C4—42no—
450C4⋊C4—42no—
451C4⋊C4—81no—
452C4⋊C4—432no—
453C4⋊C4—434no—
454C4⋊C4—864no—
455C4⋊C4—861no—
456C4⋊C4—862no—
457C22⋊C4—24no—
458C22⋊C4—44no—
459C22⋊C4—82no—
460C22⋊C4—868no—
461C22⋊C4—868no—
462C22⋊C4—864no—
463C42—42no—
464C42—868no—
465C42D4×D4312yes—
466C42D4×D4312yes—
467C23—22no—
468C23—22no—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—862no—
475C23—1721no—
476C23—1721no—
477C23—1721no—
478C23—1721no—
479C23—1721no—
480C23—1721no—
481C23C22×C22⋊D4311yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—41no—
485Q8—41no—
486Q8—3444no—
487D4—44no—
488D4—862no—
489D4—862no—
490D4—3448no—
491D4—1721no—
492D4—1721no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—862no—
512C2×C4—864no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4—1722no—
516C2×C4—1722no—
517C2×C4—1728no—
518C2×C4#1306329312yes—
519C2×C4#1306329312yes—
520C2×C4#1306334512yes—
521C2×C4#1306335612yes—
522C2×C4C2×D4×D4311yescharacteristic
523C2×C4C2×D4×D4311yescharacteristic
524C2×C4#41×D4311yescharacteristic
525C2×C4C2×#1062190011yescharacteristic
526C2×C4#1306337011yescharacteristic
527C2×C4#1306337211yescharacteristic
528C8—862no—
529C8—1722no—
530C8—1721no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—3441no—
539C22—3441no—
540C22—3441no—
541C22—3441no—
542C22—1722no—
543C22—1722no—
544C22—1722no—
545C22C2×#1306329311yescharacteristic
546C22#1458354311yescharacteristic
547C22#1458354811yescharacteristic
548C22C2×#1306334511yescharacteristic
549C22C2×#1306335611yescharacteristic
550C22#1458370211yescharacteristic
551C22#1458370711yescharacteristic
552C4—22no—
553C4—42no—
554C4—42no—
555C4—82no—
556C4—81no—
557C4—1722no—
558C4—1724no—
559C4#1458305914yes—
560C4#1458340911yescharacteristic
561C4#1458347811yescharacteristic
562C4#1458355511yescharacteristic
563C4#1458356711yescharacteristic
564C2—82no—
565C2—3442no—
566C2#1913793611yescharacteristic
567C2C2×#1458305911yescharacteristic
568C2#1914389611yescharacteristic
569C2#1914654511yescharacteristic
570C2#1914688911yescharacteristic
571C2#1914700211yescharacteristic
572C2#1914722111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2538C2
socleC23×C43C22×D4
prime radicalC2×#14583614C2
hypercenter#2538D43
hypocenterC43#24121
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

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

NH ≅ G/Ntype
2. C2×#14583194C2semidirect
3. C2×C4×#10621884C2semidirect
4. #19135777C2semidirect
5. #19135596C2semidirect
6. #19135555C2semidirect
7. #19135390C2semidirect
8. #19134908C2semidirect
9. #19134792C2semidirect
10. #19134592C2semidirect
11. C43×#2538C2semidirect
281. #2538D43semidirect
331. C43#24121semidirect

Maximal subgroups

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

subgroupindex
C2×#145836142
C2×#145831942
C2×C4×#106218842
#191357772
#191355962
#191355552
#191353902
#191349082
#191347922
#191345922
C43×#25382
#2412143