Finite Group Databasebeta

← #25148799

Subgroups — #25148799

Order 11008.

1194 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583130C212yesmaximal
2#19142926C211yesmaximal, characteristic
3#19135925C211yesmaximal, characteristic, complemented
4#19135838C211yesmaximal, characteristic, complemented
5#19135728C211yesmaximal, characteristic, complemented
6#19135678C211yesmaximal, characteristic, complemented
7#19135019C212yesmaximal, complemented
8#19134950C212yesmaximal, complemented
9#19134863C212yesmaximal, complemented
10C2×#14582654C211yesmaximal, characteristic, complemented
11C2×C43×#533C211yesmaximal, characteristic, complemented
12C22×#10621884C2212yes—
13C23×C43⋊C8C2212yes—
14C2×#13063308—21no—
15C2×#13063299C2211yescharacteristic
16#14583130—28no—
17C2×#13063256C2212yes—
18C2×#13063249C2212yes—
19C2×#13063249C2212yes—
20C2×#13063249C2212yes—
21C2×#13063245C2212yes—
22#14582801C2211yescharacteristic
23#14582801C2211yescharacteristic
24#14582797C2211yescharacteristic
25#14582797C2211yescharacteristic
26#14582790—21no—
27#14582790—21no—
28#14582778—21no—
29#14582759C2211yescharacteristic
30#14582661C2212yes—
31#14582661C2212yes—
32#14582654C2211yescharacteristic
33#14582654C2212yes—
34#14582654C2211yescharacteristic
35C43×#533—28no—
36C2×C4⋊Q8×C43C2211yescharacteristic
37C2×C4⋊Q8×C43C2211yescharacteristic
38C2×#125×C43—21no—
39C2×C22⋊Q8×C43—21no—
40C2×C22⋊Q8×C43C2212yes—
41C2×C4×Q8×C43—21no—
42C2×C4×Q8×C43C2212yes—
43C2×#117×C43—21no—
44C22×C42×C43C2211yescharacteristic
45C22×D172C2311yescharacteristic
46C22×C22⋊D43—21no—
47C2×#10621884—24no—
48C2×#10621884—24no—
49C2×#10621884—42no—
50C22×C43⋊C8—24no—
51C22×C43⋊C8—24no—
52C22×C43⋊C8—42no—
53C22×C43⋊C8C2312yes—
54C22×C43⋊C8C2312yes—
55#13063308—44no—
56#13063299—24no—
57C2×C4⋊Dic43C2311yescharacteristic
58C2×C4⋊Dic43C2311yescharacteristic
59C2×C4⋊Dic43C2311yescharacteristic
60C2×Dic43⋊C4—21no—
61C2×Dic43⋊C4—21no—
62C2×C22⋊Dic43—21no—
63C2×(C2×D43)⋊C4—21no—
64C2×(C2×D43)⋊C4—21no—
65C2×(C2×D43)⋊C4—21no—
66C2×(C2×D43)⋊C4—21no—
67C2×(C2×D43)⋊C4—21no—
68#13063256—24no—
69#13063249—24no—
70#13063249—24no—
71#13063249—42no—
72#13063245—24no—
73C43⋊#95—21no—
74C43⋊#95—21no—
75C43⋊#95—21no—
76C22×Q8×C43—21no—
77C22×Q8×C43C2312yes—
78C23×C4×C43D411yescharacteristic
79C23×C4×C43D411yescharacteristic
80C23×C4×C43C2311yescharacteristic
81C4⋊Q8×C43—24no—
82C4⋊Q8×C43—24no—
83#125×C43—28no—
84C22⋊Q8×C43—28no—
85C22⋊Q8×C43—24no—
86C22⋊Q8×C43D418yes—
87C4×Q8×C43—28no—
88C4×Q8×C43—24no—
89C4×Q8×C43—24no—
90#117×C43—28no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—22no—
95C2×C4⋊C4×C43—22no—
96C2×C4⋊C4×C43C2312yes—
97C2×C22⋊C4×C43—22no—
98C2×C42×C43—24no—
99C2×C42×C43—22no—
100C2×C42×C43D411yescharacteristic
101C2×C42×C43D411yescharacteristic
102C2×C42×C43C2311yescharacteristic
103C2×C42×C43C2311yescharacteristic
104C24×C43C2×D411yescharacteristic
105C23×D43—21no—
106C2×Q8×C43—24no—
107C2×Q8×C43—22no—
108C2×Q8×C43—22no—
109C2×Q8×C43—22no—
110C2×Q8×C43—22no—
111C2×Q8×C43—22no—
112C2×Q8×C43—42no—
113C2×Q8×C43—42no—
114C2×Q8×C43C2×D414yes—
115C22×C4×C43—22no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—41no—
125C22×C4×C43SD1614yescomplemented
126C22×C4×C43C2×D414yes—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C2×C22⋊D43—42no—
134C2×C22⋊D43—42no—
135C2×C22⋊D43—42no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C2×D172—22no—
140C2×D172—22no—
141C2×D172—21no—
142C2×D172—21no—
143C4⋊C4×C43—24no—
144C4⋊C4×C43—24no—
145C4⋊C4×C43—28no—
146C4⋊C4×C43—24no—
147C4⋊C4×C43—28no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43C2×D414yes—
150C22⋊C4×C43—28no—
151C42×C43—28no—
152C42×C43—22no—
153C42×C43—22no—
154C42×C43—22no—
155C42×C43—22no—
156C22⋊Dic43—42no—
157#10621884—48no—
158(C2×D43)⋊C4—42no—
159(C2×D43)⋊C4—42no—
160(C2×D43)⋊C4—42no—
161(C2×D43)⋊C4—42no—
162(C2×D43)⋊C4—42no—
163C4⋊Dic43—22no—
164C4⋊Dic43—22no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167Dic43⋊C4—42no—
168Dic43⋊C4—42no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—22no—
171C2×C43⋊C8—22no—
172C2×C43⋊C8—22no—
173C2×C43⋊C8—22no—
174C2×C43⋊C8—48no—
175C2×C43⋊C8#4114yes—
176C23×C43—21no—
177C23×C43—21no—
178C23×C43—21no—
179C23×C43—21no—
180C23×C43#12012yes—
181C23×C43C2×SD1612yes—
182C23×C43#13712yes—
183C23×C43C22×D411yescharacteristic
184C22×D43—41no—
185C22×D43—41no—
186C22×D43—41no—
187C22×D43—41no—
188C22×D43—41no—
189C22×D43—41no—
190C22×D43—41no—
191Q8×C43—24no—
192Q8×C43—24no—
193Q8×C43—48no—
194Q8×C43—42no—
195Q8×C43—42no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—28no—
205C2×C4×C43—24no—
206C2×C4×C43—24no—
207C2×C4×C43—21no—
208C2×C4×C43—24no—
209C2×C4×C43—24no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—44no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43#12012yes—
218C2×C4×C43C2×SD1612yes—
219C2×C4×C43C2×SD1612yes—
220C2×C4×C43#13512yes—
221C2×C4×C43C22×D412yes—
222C2×C4×C43C2×#4112yes—
223C2×C4×C43H(5,𝔽2)11yescharacteristic
224C2×C4×C432−1+411yescharacteristic
225C22⋊D43—84no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235D172—42no—
236D172—42no—
237C43⋊C8—24no—
238C43⋊C8—42no—
239#25497—431nomaximal, Sylow
240C22×C43—22no—
241C22×C43—22no—
242C22×C43—22no—
243C22×C43—22no—
244C22×C43—22no—
245C22×C43—22no—
246C22×C43#44814yes—
247C22×C43C2×#12011yescharacteristic
248C22×C43#53211yescharacteristic
249C22×C43#53711yescharacteristic
250C22×C43C22×SD1611yescharacteristic
251C22×C43C2×#13511yescharacteristic
252C22×C43C2×#13711yescharacteristic
253C22×C43#57511yescharacteristic
254C2×D43—81no—
255C2×D43—81no—
256C2×D43—81no—
257C2×D43—81no—
258C2×D43—81no—
259C2×D43—81no—
260C2×D43—81no—
261C4×C43—22no—
262C4×C43—22no—
263C4×C43—22no—
264C4×C43—22no—
265C4×C43—44no—
266C4×C43—41no—
267C4×C43—44no—
268C4×C43#54612yes—
269C4×C43#54712yes—
270Dic43—81no—
271Dic43—81no—
272Dic43—81no—
273C2×#533D4311yescharacteristic, complemented
274C2×#465—432no—
275#2854—431no—
276#2058—431no—
277#2043—431no—
278#2023—431no—
279#2013—431no—
280#1892—432no—
281#1880—432no—
282#1865—432no—
283C2×#336—431no—
284C2×C43—24no—
285C2×C43#243011yescharacteristic
286C2×C43C2×#44811yescharacteristic
287C2×C43#300211yescharacteristic
288C2×C43#316711yescharacteristic
289C2×C43#318111yescharacteristic
290C2×C43#324611yescharacteristic
291C2×C43#324811yescharacteristic
292D43—161no—
293C22×SD16—432no—
294C23×C8—432no—
295#533—28no—
296C2×C4⋊Q8C2×D4311yescharacteristic
297C2×C4⋊Q8C2×D4311yescharacteristic
298C2×#125—21no—
299C2×#123—861no—
300C2×C22⋊Q8—21no—
301C2×C22⋊Q8C2×D4312yes—
302C2×#121—431no—
303C2×C4×Q8—21no—
304C2×C4×Q8C2×D4312yes—
305C2×#117—21no—
306C22×C42C2×D4311yescharacteristic
307#465—868no—
308C2×#106—432no—
309C2×#103—432no—
310C2×#103—432no—
311C2×#103—432no—
312C2×#102—432no—
313#390—431no—
314#390—431no—
315#389—431no—
316#389—431no—
317#388—861no—
318#388—861no—
319#386—861no—
320#380—431no—
321#340—432no—
322#340—432no—
323#336—431no—
324#336—432no—
325#336—431no—
326C43#2549711yescharacteristic, complemented, Sylow
327C22×Q8—21no—
328C22×Q8C22×D4312yes—
329C22×D4—431no—
330C22×D4—861no—
331C23×C4C22⋊D4311yescharacteristic
332C23×C4C22⋊D4311yescharacteristic
333C23×C4C22×D4311yescharacteristic
334C2×SD16—864no—
335C2×SD16—864no—
336C2×SD16—1722no—
337C22×C8—432no—
338C22×C8—432no—
339C22×C8—864no—
340C22×C8—864no—
341C22×C8—1722no—
342C4⋊Q8—24no—
343C4⋊Q8—24no—
344#125—28no—
345#123—1724no—
346C22⋊Q8—28no—
347C22⋊Q8—24no—
348C22⋊Q8C22⋊D4318yes—
349#121—864no—
350C4×Q8—28no—
351C4×Q8—24no—
352C4×Q8—24no—
353#117—28no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—431no—
360C2×C4⋊C4—431no—
361C2×C4⋊C4—431no—
362C2×C4⋊C4—861no—
363C2×C4⋊C4—861no—
364C2×C4⋊C4C22×D4312yes—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—861no—
367C2×C22⋊C4—861no—
368C2×C22⋊C4—861no—
369C2×C22⋊C4—861no—
370C2×C22⋊C4—861no—
371C2×C22⋊C4—861no—
372C2×C42—22no—
373C2×C42—24no—
374C2×C42C22⋊D4311yescharacteristic
375C2×C42C22⋊D4311yescharacteristic
376C2×C42C22×D4311yescharacteristic
377C2×C42C22×D4311yescharacteristic
378#106—864no—
379#103—864no—
380#103—864no—
381#103—1722no—
382#102—864no—
383#95—861no—
384#95—861no—
385#95—861no—
386C24—861no—
387C24C2×C22⋊D4311yescharacteristic
388C2×Q8—24no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—42no—
395C2×Q8—42no—
396C2×Q8C2×C22⋊D4314yes—
397C2×D4—862no—
398C2×D4—862no—
399C2×D4—861no—
400C2×D4—861no—
401C2×D4—1722no—
402C2×D4—1722no—
403C2×D4—1722no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—41no—
414C22×C4—861no—
415C22×C4—861no—
416C22×C4—861no—
417C22×C4#1062188414yescomplemented
418C22×C4C2×C22⋊D4311yescharacteristic
419C22×C4C2×C22⋊D4311yescharacteristic
420C22×C4C2×C22⋊D4314yes—
421C22×C4C2×C22⋊D4311yescharacteristic
422C22×C4C2×C22⋊D4311yescharacteristic
423C22×C4C2×C22⋊D4311yescharacteristic
424C22×C4C23×D4311yescharacteristic
425SD16—1728no—
426C2×C8—434no—
427C2×C8—862no—
428C2×C8—862no—
429C2×C8—862no—
430C2×C8—862no—
431C2×C8—862no—
432C2×C8—1728no—
433C4⋊C4—24no—
434C4⋊C4—24no—
435C4⋊C4—28no—
436C4⋊C4—24no—
437C4⋊C4—28no—
438C4⋊C4—22no—
439C4⋊C4—862no—
440C4⋊C4—862no—
441C4⋊C4—861no—
442C4⋊C4—861no—
443C4⋊C4—1722no—
444C4⋊C4—1722no—
445C4⋊C4C2×C22⋊D4314yes—
446C22⋊C4—28no—
447C22⋊C4—1722no—
448C22⋊C4—1722no—
449C22⋊C4—1722no—
450C22⋊C4—1722no—
451C22⋊C4—1722no—
452C22⋊C4—1722no—
453C42—28no—
454C42—22no—
455C42—22no—
456C42—22no—
457C42—22no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—1721no—
463C23—1721no—
464C23—1721no—
465C23—1721no—
466C23—1721no—
467C23—1721no—
468C23—1721no—
469C23#1306329412yes—
470C23C2×#1062188412yes—
471C23#1306335612yes—
472C23C22×C22⋊D4311yescharacteristic
473Q8—24no—
474Q8—24no—
475Q8—48no—
476Q8—42no—
477Q8—42no—
478D4—3444no—
479D4—1722no—
480D4—1722no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—28no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—44no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—1721no—
503C2×C4—1721no—
504C2×C4—1721no—
505C2×C4—1721no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4—1721no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4#1306329412yes—
512C2×C4C2×#1062188412yes—
513C2×C4C2×#1062188412yes—
514C2×C4#1306334512yes—
515C2×C4C22×C22⋊D4312yes—
516C2×C4#41×D4312yes—
517C2×C4#1306337111yescharacteristic
518C2×C4#1306337211yescharacteristic
519C8—864no—
520C8—1722no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—3441no—
528C22—3441no—
529C22—3441no—
530C22—3441no—
531C22—3441no—
532C22—3441no—
533C22—3441no—
534C22#1458303814yes—
535C22C2×#1306329411yescharacteristic
536C22#1458344511yescharacteristic
537C22#1458347711yescharacteristic
538C22C22×#1062188411yescharacteristic
539C22C2×#1306334511yescharacteristic
540C22C2×#1306335611yescharacteristic
541C22#1458369711yescharacteristic
542C4—22no—
543C4—22no—
544C4—22no—
545C4—22no—
546C4—41no—
547C4—44no—
548C4—44no—
549C4—3441no—
550C4—3441no—
551C4—3441no—
552C4#1458353712yes—
553C4#1458354812yes—
554C2—24no—
555C2—6881no—
556C2#1913819911yescharacteristic
557C2C2×#1458303811yescharacteristic
558C2#1914381311yescharacteristic
559C2#1914515511yescharacteristic
560C2#1914529811yescharacteristic
561C2#1914590711yescharacteristic
562C2#1914592611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#533C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenterC2×#533D43
hypocenterC43#25497
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
3. #19135925C2semidirect
4. #19135838C2semidirect
5. #19135728C2semidirect
6. #19135678C2semidirect
7. #19135019C2semidirect
8. #19134950C2semidirect
9. #19134863C2semidirect
10. C2×#14582654C2semidirect
11. C2×C43×#533C2semidirect
125. C22×C4×C43SD16semidirect
273. C2×#533D43semidirect
326. C43#25497semidirect
417. C22×C4#10621884semidirect

Maximal subgroups

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

subgroupindex
C2×#145831302
#191429262
#191359252
#191358382
#191357282
#191356782
#191350192
#191349502
#191348632
C2×#145826542
C2×C43×#5332
#2549743