Finite Group Databasebeta

← #25130547

Subgroups — #25130547

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×#14583615C211yesmaximal, characteristic
2C2×C4×#10621884C211yesmaximal, characteristic, complemented
3#19139513C211yesmaximal, characteristic, complemented
4#19135779C212yesmaximal, complemented
5#19135597C212yesmaximal, complemented
6#19135557C211yesmaximal, characteristic, complemented
7#19135388C211yesmaximal, characteristic, complemented
8#19134904C212yesmaximal, complemented
9#19134791C212yesmaximal, complemented
10#19134596C211yesmaximal, characteristic, complemented
11C2×C43×#477C211yesmaximal, characteristic, complemented
12C22×#10621884C2211yescharacteristic
13#14583615—24no—
14#14583615—24no—
15C2×#13063314—22no—
16C2×#13063301C2212yes—
17C2×#13063300—21no—
18C2×#13063300C2212yes—
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063283—21no—
22C2×#13063283C2212yes—
23C4×#10621884—24no—
24C2×#13063256C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063247C2212yes—
27C2×#13063245C2211yescharacteristic
28C2×(C2×D43)⋊C8C2212yes—
29C2×(C2×D43)⋊C8C2212yes—
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582821—22no—
32#14582801—21no—
33#14582797—21no—
34#14582769C2211yescharacteristic
35#14582756C2212yes—
36#14582662C2212yes—
37#14582661C2212yes—
38#14582661C2212yes—
39C2×C4⋊Q8×C43C2211yescharacteristic
40C2×C4×Q8×C43C2211yescharacteristic
41C43×#477—24no—
42C2×#107×C43C2212yes—
43C2×C4⋊C8×C43C2211yescharacteristic
44C2×#103×C43C2212yes—
45C22×D172—22no—
46C22×D172D411yescharacteristic
47C22×D172C2311yescharacteristic
48C22×C4×D43—21no—
49C22×C4×D43C2312yes—
50C2×#10621884—22no—
51C2×#10621884—22no—
52C2×#10621884—22no—
53C22×C43⋊C8C2311yescharacteristic
54C22×C43⋊C8C2311yescharacteristic
55#13063314—216no—
56#13063301—24no—
57#13063301—42no—
58#13063300—28no—
59#13063300—24no—
60#13063300—24no—
61C4×D172—22no—
62C4×D172—22no—
63C4×D172—22no—
64C4×D172D414yes—
65#13063283—28no—
66#13063283—24no—
67#13063283—24no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43D411yescharacteristic
71C2×C4⋊Dic43C2312yes—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—22no—
74C2×(C2×D43)⋊C4—22no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—22no—
77C2×(C2×D43)⋊C4—22no—
78C2×(C2×D43)⋊C4—22no—
79C2×(C2×D43)⋊C4D412yes—
80C2×C4×Dic43—22no—
81#13063256—22no—
82#13063249—22no—
83#13063247—42no—
84#13063245—22no—
85(C2×D43)⋊C8—24no—
86(C2×D43)⋊C8—42no—
87C4×C43⋊C8—22no—
88C43⋊#95—22no—
89C22×Q8×C43—21no—
90C22×Q8×C43C2311yescharacteristic
91C22×C8×C43C2312yes—
92C4⋊Q8×C43—22no—
93C4⋊Q8×C43D414yes—
94C4×Q8×C43—22no—
95C4×Q8×C43—22no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2312yes—
100C2×C42×C43—21no—
101C2×C42×C43C2311yescharacteristic
102#107×C43—24no—
103C4⋊C8×C43—22no—
104#103×C43—24no—
105C23×D43—21no—
106C23×D43C2×D412yes—
107C2×Q8×C43—24no—
108C2×Q8×C43—21no—
109C2×Q8×C43—21no—
110C2×Q8×C43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—21no—
113C2×Q8×C43—81no—
114C2×Q8×C43—81no—
115C2×Q8×C43#4112yes—
116C22×C4×C43—21no—
117C22×C4×C43—22no—
118C22×C4×C43—21no—
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2411yescharacteristic
122C22×Dic43—21no—
123C22×Dic43—22no—
124C22×Dic43C2×D412yes—
125C2×D172—22no—
126C2×D172—22no—
127C2×D172—22no—
128C2×D172—21no—
129C2×D172—28no—
130C2×D172—21no—
131C2×D172—21no—
132C2×D172—21no—
133C2×D172—21no—
134C2×D172—82no—
135C2×D172—82no—
136C2×D172C2×D412yes—
137C2×C4×D43—24no—
138C2×C4×D43—22no—
139C2×C4×D43—22no—
140C2×C4×D43—22no—
141C2×C4×D43—22no—
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—42no—
145C2×C4×D43—42no—
146C2×C8×C43—22no—
147C2×C8×C43—22no—
148C2×C8×C43—22no—
149C4⋊C4×C43—24no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—42no—
154C4⋊C4×C43C2×D414yes—
155C42×C43—42no—
156C42×C43C2×D412yes—
157C42×C43C2×D412yes—
158#10621884—28no—
159(C2×D43)⋊C4—28no—
160(C2×D43)⋊C4—28no—
161(C2×D43)⋊C4—24no—
162(C2×D43)⋊C4—24no—
163(C2×D43)⋊C4—44no—
164(C2×D43)⋊C4—82no—
165C4⋊Dic43—22no—
166C4⋊Dic43—21no—
167C4⋊Dic43—22no—
168C4⋊Dic43—22no—
169C4⋊Dic43—42no—
170C4⋊Dic43—81no—
171C4⋊Dic43C2×D412yes—
172Dic43⋊C4—44no—
173C4×Dic43—28no—
174C2×C43⋊C8—21no—
175C2×C43⋊C8—21no—
176C2×C43⋊C8—21no—
177C2×C43⋊C8—21no—
178C2×C43⋊C8—21no—
179C2×C43⋊C8#4112yes—
180C23×C43C22×D411yescharacteristic
181C22×D43—22no—
182C22×D43—22no—
183C22×D43—22no—
184C22×D43—22no—
185C22×D43—22no—
186C22×D43—22no—
187C22×D43—22no—
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—
199Q8×C43—84no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—24no—
203C2×C4×C43—22no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43#12012yes—
212C2×C4×C43#12012yes—
213C2×C4×C43#13512yes—
214C2×C4×C43#13712yes—
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C2×#4111yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C2×C4×C43H(5,𝔽2)11yescharacteristic
220C2×C4×C432−1+411yescharacteristic
221C2×Dic43—22no—
222C2×Dic43—22no—
223C2×Dic43—22no—
224C2×Dic43—22no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—42no—
228C2×Dic43—42no—
229C2×Dic43—42no—
230D172—22no—
231D172—22no—
232D172—41no—
233D172—41no—
234D172—44no—
235D172—88no—
236C4×D43—42no—
237C4×D43—42no—
238C4×D43—42no—
239C4×D43—42no—
240C4×D43—48no—
241C8×C43—42no—
242C43⋊C8—22no—
243C43⋊C8—41no—
244#24121—431nomaximal, Sylow
245C22×C43C2×#12011yescharacteristic
246C22×C43#54611yescharacteristic
247C22×C43#54711yescharacteristic
248C22×C43C2×#13511yescharacteristic
249C22×C43C2×#13711yescharacteristic
250C22×C43#57611yescharacteristic
251C22×C43#57711yescharacteristic
252C2×D43—42no—
253C2×D43—42no—
254C2×D43—42no—
255C2×D43—42no—
256C2×D43—42no—
257C2×D43—42no—
258C2×D43—42no—
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—44no—
269C4×C43—81no—
270C4×C43#45214yes—
271C4×C43#52511yescharacteristic
272C4×C43#53711yescharacteristic
273C4×C43#54811yescharacteristic
274C4×C43#55011yescharacteristic
275Dic43—42no—
276Dic43—42no—
277Dic43—82no—
278C2×#555—431no—
279C2×#477D4311yescharacteristic, complemented
280C2×C4×SD16—431no—
281#2538—431no—
282#2033—432no—
283#2000—432no—
284#1990—431no—
285#1954—431no—
286#1873—432no—
287#1854—432no—
288#1802—431no—
289C2×C43#240711yescharacteristic
290C2×C43C2×#45211yescharacteristic
291C2×C43#301211yescharacteristic
292C2×C43#330511yescharacteristic
293C2×C43#332911yescharacteristic
294C2×C43#334011yescharacteristic
295C2×C43#335711yescharacteristic
296D43—82no—
297D43—82no—
298C22×SD16—431no—
299#555—864no—
300#555—864no—
301C2×C4⋊Q8C2×D4311yescharacteristic
302C2×#124—862no—
303C2×C22⋊Q8—432no—
304C2×#121—432no—
305C2×#121—861no—
306C2×C4×Q8C2×D4311yescharacteristic
307C2×C4×D4—431no—
308C2×C4×D4—431no—
309C2×#117—432no—
310C2×#117—861no—
311#477—24no—
312C4×SD16—864no—
313C2×#107C2×D4312yes—
314C2×#106—431no—
315C2×C4⋊C8C2×D4311yescharacteristic
316C2×#103—431no—
317C2×#103C2×D4312yes—
318C2×#102—431no—
319C2×#102—432no—
320C2×C22⋊C8—432no—
321C2×C22⋊C8—432no—
322C2×C4×C8—431no—
323#396—862no—
324#390—861no—
325#389—861no—
326#384—431no—
327#380—432no—
328#340—432no—
329#340—432no—
330#340—432no—
331C43#2412111yescharacteristic, complemented, Sylow
332C22×Q8—21no—
333C22×Q8C22×D4311yescharacteristic
334C22×D4—431no—
335C22×D4—431no—
336C22×D4—862no—
337C23×C4—432no—
338C23×C4—861no—
339C2×SD16—862no—
340C2×SD16—862no—
341C2×SD16—862no—
342C22×C8—431no—
343C22×C8—431no—
344C22×C8C22×D4312yes—
345C4⋊Q8—22no—
346C4⋊Q8C22⋊D4314yes—
347#124—8616no—
348C22⋊Q8—864no—
349C22⋊Q8—1722no—
350#121—864no—
351#121—868no—
352#121—864no—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×D4—434no—
356C4×D4—862no—
357C4×D4—862no—
358C4×D4—862no—
359#117—864no—
360#117—868no—
361#117—864no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—431no—
365C2×C4⋊C4—431no—
366C2×C4⋊C4—432no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4—862no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4C22×D4311yescharacteristic
371C2×C4⋊C4C22×D4312yes—
372C2×C22⋊C4—432no—
373C2×C22⋊C4—862no—
374C2×C22⋊C4—862no—
375C2×C22⋊C4—861no—
376C2×C22⋊C4—862no—
377C2×C22⋊C4—862no—
378C2×C42—21no—
379C2×C42—862no—
380C2×C42C22×D4311yescharacteristic
381#107—24no—
382#106—862no—
383C4⋊C8—22no—
384#103—24no—
385#103—862no—
386#102—862no—
387#102—1722no—
388C22⋊C8—864no—
389C22⋊C8—1722no—
390C4×C8—862no—
391#95—862no—
392C24—432no—
393C24—861no—
394C2×Q8—24no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—81no—
401C2×Q8—81no—
402C2×Q8#1062190212yes—
403C2×D4—432no—
404C2×D4—868no—
405C2×D4—862no—
406C2×D4—862no—
407C2×D4—862no—
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—21no—
418C22×C4—432no—
419C22×C4—861no—
420C22×C4—864no—
421C22×C4—862no—
422C22×C4—862no—
423C22×C4—862no—
424C22×C4—862no—
425C22×C4—862no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—1722no—
429C22×C4—1722no—
430C22×C4D4×D4311yescharacteristic
431C22×C4D4×D4311yescharacteristic
432C22×C4C23×D4311yescharacteristic
433SD16—868no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—432no—
438C2×C8—861no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—861no—
442C2×C8—861no—
443C4⋊C4—24no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—42no—
448C4⋊C4—432no—
449C4⋊C4—862no—
450C4⋊C4—861no—
451C4⋊C4—862no—
452C4⋊C4—862no—
453C4⋊C4—3441no—
454C4⋊C4—1724no—
455C4⋊C4—1722no—
456C4⋊C4C2×C22⋊D4314yes—
457C22⋊C4—868no—
458C22⋊C4—868no—
459C22⋊C4—864no—
460C22⋊C4—864no—
461C22⋊C4—3442no—
462C22⋊C4—1724no—
463C42—42no—
464C42—868no—
465C42D4×D4312yes—
466C42C2×C22⋊D4312yes—
467C23—862no—
468C23—862no—
469C23—862no—
470C23—862no—
471C23—862no—
472C23—862no—
473C23—862no—
474C23—862no—
475C23—1721no—
476C23—1721no—
477C23—1721no—
478C23—1721no—
479C23—1721no—
480C23—1721no—
481C23C2×D4×D4311yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—41no—
485Q8—41no—
486Q8—84no—
487D4—862no—
488D4—862no—
489D4—3448no—
490D4—1721no—
491D4—1721no—
492D4—1724no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—862no—
505C2×C4—862no—
506C2×C4—862no—
507C2×C4—862no—
508C2×C4—1722no—
509C2×C4—1722no—
510C2×C4—1722no—
511C2×C4—1721no—
512C2×C4—1721no—
513C2×C4—1722no—
514C2×C4—1722no—
515C2×C4—1728no—
516C2×C4—1722no—
517C2×C4—1722no—
518C2×C4#1306329312yes—
519C2×C4#1306329312yes—
520C2×C4#1306334812yes—
521C2×C4#1306335712yes—
522C2×C4C2×D4×D4311yescharacteristic
523C2×C4C22×C22⋊D4311yescharacteristic
524C2×C4#41×D4311yescharacteristic
525C2×C4C2×#1062190211yescharacteristic
526C2×C4#1306337111yescharacteristic
527C2×C4#1306337311yescharacteristic
528C8—42no—
529C8—862no—
530C8—1721no—
531C22—3441no—
532C22—3441no—
533C22—3441no—
534C22—3441no—
535C22—1722no—
536C22—1722no—
537C22—1722no—
538C22—1722no—
539C22—1722no—
540C22—1722no—
541C22—1722no—
542C22—1722no—
543C22—1722no—
544C22—1722no—
545C22C2×#1306329311yescharacteristic
546C22#1458354011yescharacteristic
547C22#1458355111yescharacteristic
548C22C2×#1306334811yescharacteristic
549C22C2×#1306335711yescharacteristic
550C22#1458370311yescharacteristic
551C22#1458370911yescharacteristic
552C4—22no—
553C4—42no—
554C4—44no—
555C4—81no—
556C4—3442no—
557C4—1722no—
558C4—1722no—
559C4#1458306014yes—
560C4#1458341211yescharacteristic
561C4#1458347911yescharacteristic
562C4#1458356011yescharacteristic
563C4#1458356811yescharacteristic
564C2—3442no—
565C2—3442no—
566C2#1913794211yescharacteristic
567C2C2×#1458306011yescharacteristic
568C2#1914389811yescharacteristic
569C2#1914654211yescharacteristic
570C2#1914688611yescharacteristic
571C2#1914701111yescharacteristic
572C2#1914721811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#477C2
socleC23×C43C22×D4
prime radicalC2×#14583615C2
hypercenterC2×#477D43
hypocenterC43#24121
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621884C2semidirect
3. #19139513C2semidirect
4. #19135779C2semidirect
5. #19135597C2semidirect
6. #19135557C2semidirect
7. #19135388C2semidirect
8. #19134904C2semidirect
9. #19134791C2semidirect
10. #19134596C2semidirect
11. C2×C43×#477C2semidirect
279. C2×#477D43semidirect
331. C43#24121semidirect

Maximal subgroups

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

subgroupindex
C2×#145836152
C2×C4×#106218842
#191395132
#191357792
#191355972
#191355572
#191353882
#191349042
#191347912
#191345962
C2×C43×#4772
#2412143