Finite Group Databasebeta

← #25099034

Subgroups — #25099034

Order 11008.

1126 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582942C211yesmaximal, characteristic, complemented
2C2×#14582898C211yesmaximal, characteristic
3C2×#14582893C211yesmaximal, characteristic
4#19137183C211yesmaximal, characteristic
5#19135236C212yesmaximal, complemented
6#19135229C212yesmaximal, complemented
7#19135222C212yesmaximal, complemented
8#19135215C212yesmaximal, complemented
9C2×#14582661C211yesmaximal, characteristic, complemented
10#19134292C211yesmaximal, characteristic, complemented
11C43×#2274C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C22×#10621877C2211yescharacteristic
14C23×C43⋊C8C2211yescharacteristic
15C22×C4⋊Dic43C2211yescharacteristic
16#14582942—24no—
17C2×#13063258C2212yes—
18C2×#13063256C2212yes—
19#14582898C418yescomplemented
20#14582893—24no—
21C2×#13063248C2211yescharacteristic
22C2×#13063248C2211yescharacteristic
23C2×#13063248C2212yes—
24C2×#13063245C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2212yes—
27#14582805C2212yes—
28#14582801C2212yes—
29#14582776—22no—
30#14582756—21no—
31#14582756—21no—
32#14582661C2212yes—
33#14582661C2212yes—
34#14582654C2212yes—
35#14582654C2212yes—
36C2×#117×C43C2211yescharacteristic
37C2×#117×C43C2211yescharacteristic
38C22×C4⋊C4×C43C2211yescharacteristic
39C4×C4⋊C4×C43—21no—
40C4×C4⋊C4×C43—21no—
41C4×C4⋊C4×C43C2212yes—
42C4×C4⋊C4×C43C2212yes—
43C4×C22⋊C4×C43—22no—
44C2×#10621898—22no—
45C2×#10621898—22no—
46C2×#10621898—22no—
47C2×#10621898—22no—
48C2×#10621898—22no—
49C2×#10621898C2×C414yes—
50C22×Dic86C2311yescharacteristic
51C22×D172C2311yescharacteristic
52C22×C22⋊D43—21no—
53C23×Dic43—21no—
54C22×C4×D43—21no—
55C2×#10621877—22no—
56C2×#10621877—22no—
57C2×#10621877C2×C414yes—
58C22×C43⋊C8—22no—
59C22×C43⋊C8—22no—
60C22×C43⋊C8—22no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2312yes—
64C2×C4⋊Dic43—22no—
65C2×C4⋊Dic43—22no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43C2312yes—
68C2×(C2×D43)⋊C4—22no—
69C2×(C2×D43)⋊C4—22no—
70#13063258—24no—
71#13063256—24no—
72#13063248—22no—
73#13063248—22no—
74#13063248C2×C418yescomplemented
75#13063245—22no—
76#13063245—22no—
77#13063245C2×C418yescomplemented
78C43⋊#95—22no—
79C43⋊#95—22no—
80C23×C4×C43—21no—
81C23×C4×C43C2311yescharacteristic
82#117×C43—22no—
83#117×C43—22no—
84#117×C43—22no—
85#117×C43D414yes—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43—22no—
88C2×C4⋊C4×C43C2×C414yes—
89C2×C4⋊C4×C43D411yescharacteristic
90C2×C4⋊C4×C43D411yescharacteristic
91C2×C4⋊C4×C43C2312yes—
92C2×C4⋊C4×C43C2311yescharacteristic
93C2×C4⋊C4×C43C2311yescharacteristic
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43D412yes—
96C2×C42×C43—21no—
97C2×C42×C43—22no—
98C2×C42×C43—22no—
99C2×C42×C43C2312yes—
100#95×C43—22no—
101#95×C43—22no—
102C24×C43C2×D411yescharacteristic
103C23×D43—21no—
104C22×C4×C43—24no—
105C22×C4×C43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—22no—
108C22×C4×C43—81no—
109C22×C4×C43—81no—
110C22×C4×C43C22×C412yes—
111C22×C4×C43C2×D412yes—
112C22×C4×C43C2×D412yes—
113C22×C4×C43C2×D412yes—
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43#4112yes—
116C22×C4×C43#4112yes—
117C22×C4×C43#4112yes—
118C22×C4×C43#4112yes—
119C22×C4×C43C2411yescharacteristic
120C2×C22⋊D43—24no—
121C2×C22⋊D43—42no—
122C2×C22⋊D43—42no—
123C22×Dic43—21no—
124C22×Dic43—22no—
125C22×Dic43—42no—
126C22×Dic43—81no—
127C22×Dic43—81no—
128#10621898—28no—
129#10621898—28no—
130#10621898—44no—
131#10621898—44no—
132C2×D172—21no—
133C2×D172—21no—
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172C22×C412yes—
138C2×C4×D43—24no—
139C2×C4×D43—42no—
140C2×C4×D43—42no—
141C2×Dic86—21no—
142C2×Dic86—21no—
143C2×Dic86—21no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86C22×C412yes—
147C4⋊C4×C43—24no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43C22×C414yes—
154C4⋊C4×C43C2×D412yes—
155C4⋊C4×C43C2×D412yes—
156C22⋊C4×C43—24no—
157C22⋊C4×C43—24no—
158C42×C43—24no—
159C42×C43—22no—
160C42×C43—22no—
161C42×C43—82no—
162C42×C43—82no—
163(C2×D43)⋊C4—82no—
164(C2×D43)⋊C4—82no—
165C4⋊Dic43—22no—
166C4⋊Dic43—22no—
167C4⋊Dic43—42no—
168#10621877—28no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—22no—
171C2×C43⋊C8—21no—
172C2×C43⋊C8—21no—
173C2×C43⋊C8—21no—
174C2×C43⋊C8—21no—
175C2×C43⋊C8—21no—
176C2×C43⋊C8—21no—
177C2×C43⋊C8—44no—
178C2×C43⋊C8C22×C414yes—
179C23×C43—21no—
180C23×C43—21no—
181C23×C43—21no—
182C23×C43—21no—
183C23×C43C4×D412yes—
184C23×C43#12112yes—
185C23×C43#12312yes—
186C23×C43C22×D411yescharacteristic
187C22×D43—22no—
188C22×D43—41no—
189C22×D43—41no—
190C22×D43—41no—
191C22×D43—41no—
192C22×D43—41no—
193C22×D43—41no—
194C2×C4×C43—24no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—22no—
201C2×C4×C43—22no—
202C2×C4×C43—22no—
203C2×C4×C43—41no—
204C2×C4×C43—42no—
205C2×C4×C43—41no—
206C2×C4×C43—42no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—84no—
210C2×C4×C43#11714yes—
211C2×C4×C43C4×D412yes—
212C2×C4×C43C4×D414yes—
213C2×C4×C43#12112yes—
214C2×C4×C43#12312yes—
215C2×C4×C43#12414yes—
216C2×C4×C43#12614yes—
217C2×C4×C43C23×C411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C22⋊D43—48no—
224C2×Dic43—22no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—42no—
228C2×Dic43—42no—
229C2×Dic43—42no—
230C2×Dic43—84no—
231D172—22no—
232D172—22no—
233D172—41no—
234D172—41no—
235C4×D43—48no—
236Dic86—22no—
237Dic86—22no—
238Dic86—41no—
239Dic86—41no—
240C43⋊C8—24no—
241C43⋊C8—41no—
242C43⋊C8—41no—
243#21062—431nomaximal, Sylow
244C22×C43—22no—
245C22×C43—22no—
246C22×C43—22no—
247C22×C43—22no—
248C22×C43—22no—
249C22×C43—22no—
250C22×C43#38814yes—
251C22×C43C2×C4×D411yescharacteristic
252C22×C43C2×#12111yescharacteristic
253C22×C43C2×#12311yescharacteristic
254C22×C43#57611yescharacteristic
255C22×C43#57711yescharacteristic
256C22×C43#57711yescharacteristic
257C22×C43#57811yescharacteristic
258C2×D43—42no—
259C2×D43—42no—
260C2×D43—42no—
261C2×D43—81no—
262C2×D43—81no—
263C2×D43—81no—
264C2×D43—81no—
265C4×C43—42no—
266C4×C43—42no—
267C4×C43—44no—
268C4×C43—42no—
269C4×C43—42no—
270C4×C43#38814yes—
271C4×C43C2×#11711yescharacteristic
272C4×C43C2×C4×D411yescharacteristic
273C4×C43C2×#12411yescharacteristic
274C4×C43C2×#12611yescharacteristic
275Dic43—42no—
276Dic43—82no—
277C2×#428—431no—
278C2×#417—431no—
279C2×#416—431no—
280#2311—431no—
281#2274D4311yescharacteristic, complemented
282#1928—432no—
283#1927—432no—
284#1926—432no—
285#1925—432no—
286C2×#340—431no—
287#1729—431no—
288C2×C43—24no—
289C2×C43C2×#38811yescharacteristic
290C2×C43#294611yescharacteristic
291C2×C43#294711yescharacteristic
292C2×C43#304511yescharacteristic
293C2×C43#304611yescharacteristic
294C2×C43#309811yescharacteristic
295C2×C43#309911yescharacteristic
296D43—82no—
297C22×#41—431no—
298C22×M16—431no—
299C23×C8—431no—
300C2×#117C2×D4311yescharacteristic
301C2×#117C2×D4311yescharacteristic
302C22×C4⋊C4—431no—
303C22×C4⋊C4C2×D4311yescharacteristic
304#428—864no—
305C2×#107—432no—
306C2×#106—432no—
307#417—438no—
308#416—864no—
309C2×#103—432no—
310C2×#103—431no—
311C2×#103—431no—
312C2×#102—432no—
313C2×#102—431no—
314C2×#102—431no—
315#391—432no—
316#390—432no—
317#386—862no—
318#380—861no—
319#380—861no—
320C4×C4⋊C4—21no—
321C4×C4⋊C4—21no—
322C4×C4⋊C4C2×D4312yes—
323C4×C4⋊C4C2×D4312yes—
324C4×C22⋊C4—22no—
325#340—432no—
326#340—432no—
327#336—432no—
328#336—432no—
329C43#2106211yescharacteristic, complemented, Sylow
330C2×#41—434no—
331C2×#41—862no—
332C2×#41—862no—
333C2×#41—862no—
334C2×#41—862no—
335C2×#41—862no—
336C22×Q8—431no—
337C22×D4—431no—
338C22×D4—861no—
339C23×C4—21no—
340C23×C4—861no—
341C23×C4—861no—
342C23×C4C22×D4311yescharacteristic
343C2×M16—434no—
344C2×M16—862no—
345C2×M16—862no—
346C22×C8—432no—
347C22×C8—431no—
348C22×C8—431no—
349C22×C8—862no—
350C22×C8—862no—
351C22×C8—862no—
352#117—22no—
353#117—22no—
354#117—22no—
355#117D17214yes—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—432no—
359C2×C4⋊C4—862no—
360C2×C4⋊C4—862no—
361C2×C4⋊C4—861no—
362C2×C4⋊C4C4×D4314yes—
363C2×C4⋊C4C22⋊D4311yescharacteristic
364C2×C4⋊C4C22⋊D4311yescharacteristic
365C2×C4⋊C4C22×D4312yes—
366C2×C4⋊C4C22×D4311yescharacteristic
367C2×C4⋊C4C22×D4311yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—862no—
370C2×C22⋊C4—862no—
371C2×C22⋊C4C22⋊D4312yes—
372C2×C42—21no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42C22×D4312yes—
376#107—864no—
377#106—864no—
378#103—438no—
379#103—862no—
380#103—862no—
381#102—438no—
382#102—862no—
383#102—862no—
384#95—22no—
385#95—22no—
386#95—862no—
387#95—862no—
388C24—861no—
389C24C2×C22⋊D4311yescharacteristic
390#41—868no—
391#41—868no—
392#41—1724no—
393#41—1724no—
394C2×Q8—432no—
395C2×Q8—861no—
396C2×Q8—861no—
397C2×Q8—861no—
398C2×Q8—861no—
399C2×Q8—861no—
400C2×D4—432no—
401C2×D4—864no—
402C2×D4—861no—
403C2×D4—861no—
404C2×D4—861no—
405C2×D4—861no—
406C2×D4—861no—
407C2×D4—1722no—
408C2×D4—1722no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—81no—
414C22×C4—81no—
415C22×C4—861no—
416C22×C4—864no—
417C22×C4—862no—
418C22×C4—3441no—
419C22×C4—3441no—
420C22×C4—1722no—
421C22×C4—1722no—
422C22×C4—1722no—
423C22×C4C2×C4×D4312yes—
424C22×C4C2×D17212yes—
425C22×C4#1062189812yes—
426C22×C4#1062189812yes—
427C22×C4#1062189812yes—
428C22×C4#1062189812yes—
429C22×C4C2×C22⋊D4312yes—
430C22×C4C2×C22⋊D4312yes—
431C22×C4C2×C22⋊D4311yescharacteristic
432C22×C4C23×D4311yescharacteristic
433M16—868no—
434C2×C8—434no—
435C2×C8—862no—
436C2×C8—862no—
437C2×C8—861no—
438C2×C8—861no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—861no—
442C2×C8—861no—
443C2×C8—1724no—
444C4⋊C4—24no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—862no—
451C4⋊C4—862no—
452C4⋊C4—1722no—
453C4⋊C4C2×C4×D4314yes—
454C4⋊C4C2×D17212yes—
455C4⋊C4C2×D17212yes—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—3442no—
459C22⋊C4—3442no—
460C42—24no—
461C42—22no—
462C42—22no—
463C42—82no—
464C42—82no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—862no—
470C23—1721no—
471C23—1721no—
472C23—1721no—
473C23—1721no—
474C23—1721no—
475C23—1721no—
476C23C4×C22⋊D4312yes—
477C23#1306329912yes—
478C23#1306330812yes—
479C23C22×C22⋊D4311yescharacteristic
480Q8—862no—
481Q8—862no—
482Q8—1721no—
483Q8—1721no—
484D4—862no—
485D4—862no—
486D4—1728no—
487D4—1721no—
488D4—1721no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—84no—
505C2×C4—862no—
506C2×C4—3444no—
507C2×C4—1722no—
508C2×C4—1722no—
509C2×C4—1722no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4—1728no—
513C2×C4#1306328214yes—
514C2×C4C4×C22⋊D4312yes—
515C2×C4C4×D17214yes—
516C2×C4#1306329912yes—
517C2×C4#1306330812yes—
518C2×C4#1306331314yes—
519C2×C4#1306331914yes—
520C2×C4C22×C4×D4311yescharacteristic
521C2×C4C22×D17211yescharacteristic
522C2×C4C2×#1062189811yescharacteristic
523C2×C4C2×#1062189811yescharacteristic
524C2×C4C2×#1062189811yescharacteristic
525C2×C4C2×#1062189811yescharacteristic
526C8—864no—
527C8—1721no—
528C8—1721no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—3441no—
536C22—3441no—
537C22—3441no—
538C22—3441no—
539C22—1722no—
540C22—1722no—
541C22—1722no—
542C22#1458279014yes—
543C22C2×C4×C22⋊D4311yescharacteristic
544C22C2×#1306329911yescharacteristic
545C22C2×#1306330811yescharacteristic
546C22#1458370211yescharacteristic
547C22#1458370711yescharacteristic
548C22#1458371011yescharacteristic
549C22#1458371411yescharacteristic
550C4—44no—
551C4—42no—
552C4—42no—
553C4—42no—
554C4—42no—
555C4—3442no—
556C4—1722no—
557C4#1458279014yes—
558C4C2×#1306328211yescharacteristic
559C4C2×C4×D17211yescharacteristic
560C4C2×#1306331311yescharacteristic
561C4C2×#1306331911yescharacteristic
562C2—24no—
563C2—3442no—
564C2C2×#1458279011yescharacteristic
565C2#1914342711yescharacteristic
566C2#1914343811yescharacteristic
567C2#1914413411yescharacteristic
568C2#1914414511yescharacteristic
569C2#1914457311yescharacteristic
570C2#1914458411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2274C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#2274D43
hypocenterC43#21062
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2274

Complements

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

NH ≅ G/Ntype
1. C2×#14582942C2semidirect
5. #19135236C2semidirect
6. #19135229C2semidirect
7. #19135222C2semidirect
8. #19135215C2semidirect
9. C2×#14582661C2semidirect
10. #19134292C2semidirect
11. C43×#2274C2semidirect
19. #14582898C4semidirect
74. #13063248C2×C4semidirect
77. #13063245C2×C4semidirect
281. #2274D43semidirect
329. C43#21062semidirect

Maximal subgroups

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

subgroupindex
C2×#145829422
C2×#145828982
C2×#145828932
#191371832
#191352362
#191352292
#191352222
#191352152
C2×#145826612
#191342922
C43×#22742
#2106243