Finite Group Databasebeta

← #25106335

Subgroups — #25106335

Order 11008.

1234 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583434C211yesmaximal, characteristic
2C2×#14582954C211yesmaximal, characteristic, complemented
3#384×D43C211yesmaximal, characteristic, complemented
4#19135565C211yesmaximal, characteristic, complemented
5#19135411C211yesmaximal, characteristic, complemented
6#19135409C211yesmaximal, characteristic, complemented
7#19134911C212yesmaximal
8#19134901C212yesmaximal, complemented
9#19134599C212yesmaximal, complemented
10#19134594C212yesmaximal, complemented
11C43×#1992C211yesmaximal, characteristic, complemented
12#14583434—24no—
13#14583434C418yescomplemented
14C2×#13063320—21no—
15C2×#13063313C2211yescharacteristic
16C2×#13063310—21no—
17C2×#13063305C2211yescharacteristic
18C2×#13063300C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×#13063287—21no—
21C2×#13063287C2211yescharacteristic
22C2×#13063283—21no—
23C2×C4⋊C4×D43—21no—
24C2×C4⋊C4×D43—21no—
25C2×C4⋊C4×D43C2212yes—
26C2×C42×D43C2211yescharacteristic
27#14582954—24no—
28C2×Dic43⋊C8C2212yes—
29C2×#13063250C2212yes—
30C2×#13063248C2212yes—
31C2×#13063247C2212yes—
32C2×#13063245C2212yes—
33C2×(C2×D43)⋊C8C2212yes—
34C2×#13063236C2211yescharacteristic
35#14582769C2211yescharacteristic
36#14582768—21no—
37#14582768—21no—
38#14582768C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C2×#125×C43C2211yescharacteristic
42C2×#97×C43C2211yescharacteristic
43C43×#384C2211yescharacteristic
44C43×#340C2212yes—
45C43×#340C2212yes—
46C22×Dic86C2311yescharacteristic
47C22×D172—21no—
48C22×D172C2311yescharacteristic
49C22×C4×D43—21no—
50C22×C4×D43—22no—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C22×C43⋊C8C2312yes—
55#13063320—28no—
56#13063313—22no—
57#13063313C2×C414yescomplemented
58#13063310—28no—
59#13063305—22no—
60#13063305C2×C414yes—
61#13063300—22no—
62#13063300C2×C414yes—
63#13063290—22no—
64#13063290C2×C414yescomplemented
65#13063287—28no—
66#13063287—22no—
67#13063287C2×C414yescomplemented
68#13063283—28no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2312yes—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—22no—
75C2×Dic43⋊C4—22no—
76C2×Dic43⋊C4—22no—
77C4⋊C4×D43—42no—
78C4⋊C4×D43—42no—
79C4⋊C4×D43—44no—
80C4⋊C4×D43—44no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43D411yescharacteristic
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90C42×D43C2×C414yes—
91C42×D43D414yes—
92Dic43⋊C8—24no—
93#13063250—42no—
94#13063248—42no—
95#13063247—42no—
96#13063245—42no—
97(C2×D43)⋊C8—24no—
98#13063236—22no—
99C22×C8×C43C2312yes—
100#125×C43—22no—
101#125×C43C2×C414yescomplemented
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43C2312yes—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C42×C43C2311yescharacteristic
110#97×C43—22no—
111C23×D43—21no—
112C23×D43C2×D411yescharacteristic
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—22no—
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2411yescharacteristic
119C22×Dic43—21no—
120C22×Dic43—22no—
121C22×Dic43C2×D411yescharacteristic
122C22×Dic43C2×D411yescharacteristic
123C22×Dic43C2×D411yescharacteristic
124C2×D172—21no—
125C2×D172—24no—
126C2×D172—22no—
127C2×D172—22no—
128C2×D172—42no—
129C2×D172—42no—
130C2×D172C22×C412yes—
131C2×C4×D43—22no—
132C2×C4×D43—22no—
133C2×C4×D43—22no—
134C2×C4×D43—22no—
135C2×C4×D43—24no—
136C2×C4×D43—22no—
137C2×C4×D43—22no—
138C2×C4×D43—44no—
139C2×C4×D43—44no—
140C2×C4×D43—42no—
141C2×C4×D43—42no—
142C2×C4×D43—44no—
143C2×C4×D43C22⋊C414yes—
144C2×C4×D43C22⋊C414yes—
145C2×C4×D43C22×C412yes—
146C2×C4×D43C2×D412yes—
147C2×Dic86—22no—
148C2×Dic86—22no—
149C2×Dic86—21no—
150C2×Dic86C22×C412yes—
151C2×C8×C43—22no—
152C2×C8×C43—22no—
153C2×C8×C43—22no—
154C4⋊C4×C43—24no—
155C4⋊C4×C43—24no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—42no—
161C4⋊C4×C43—42no—
162C4⋊C4×C43C22×C412yes—
163C4⋊C4×C43C22×C412yes—
164C42×C43C22×C412yes—
165C42×C43C2×D412yes—
166(C2×D43)⋊C4—24no—
167(C2×D43)⋊C4—24no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—24no—
170(C2×D43)⋊C4—24no—
171C4⋊Dic43—24no—
172C4⋊Dic43—22no—
173C4⋊Dic43—22no—
174C4⋊Dic43—42no—
175C4⋊Dic43—42no—
176Dic43⋊C4—24no—
177Dic43⋊C4—44no—
178Dic43⋊C4—44no—
179Dic43⋊C4—44no—
180C4×Dic43—24no—
181C4×Dic43C22⋊C414yes—
182C4×Dic43C22⋊C414yes—
183C4×Dic43C22×C412yes—
184C4×Dic43C2×D412yes—
185C2×C43⋊C8—22no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C23×C43C22×D411yescharacteristic
189C22×D43—21no—
190C22×D43—21no—
191C22×D43—21no—
192C22×D43—21no—
193C22×D43—22no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43—41no—
200C22×D43C2×C22⋊C412yes—
201C22×D43AGL(1,ℤ/8)12yes—
202C22×D43#13712yes—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43C2×C22⋊C412yes—
217C2×C4×C43C2×C22⋊C412yes—
218C2×C4×C43C23×C411yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43H(5,𝔽2)12yes—
221C2×C4×C432−1+412yes—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—22no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—42no—
230C2×Dic43—42no—
231C2×Dic43—42no—
232C2×Dic43C2×C22⋊C412yes—
233C2×Dic43C2×C22⋊C412yes—
234C2×Dic43C2×C22⋊C412yes—
235C2×Dic43AGL(1,ℤ/8)12yes—
236C2×Dic43#13712yes—
237D172—24no—
238D172—48no—
239D172—42no—
240C4×D43—28no—
241C4×D43—24no—
242C4×D43—24no—
243C4×D43—28no—
244C4×D43—48no—
245C4×D43—88no—
246Dic86—24no—
247Dic86—42no—
248C8×C43—42no—
249C43⋊C8—42no—
250#21867—431nomaximal, Sylow
251C22×C43C22×C22⋊C411yescharacteristic
252C22×C43#53511yescharacteristic
253C22×C43#53611yescharacteristic
254C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
255C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
256C22×C43C2×#13711yescharacteristic
257C22×C43C2×#13711yescharacteristic
258C2×D43—22no—
259C2×D43—22no—
260C2×D43—22no—
261C2×D43—22no—
262C2×D43—22no—
263C2×D43—22no—
264C2×D43—42no—
265C2×D43—42no—
266C2×D43—42no—
267C2×D43—81no—
268C2×D43—81no—
269C2×D43—81no—
270C2×D43—81no—
271C2×D43#41714yes—
272C4×C43—22no—
273C4×C43—22no—
274C4×C43—42no—
275C4×C43—42no—
276C4×C43—82no—
277C4×C43#52012yes—
278C4×C43#53712yes—
279Dic43—22no—
280Dic43—22no—
281Dic43—42no—
282Dic43—82no—
283Dic43#41714yes—
284C2×#529—431no—
285C2×#432—431no—
286C2×#384—431no—
287#1992—431no—
288#1992D4311yescharacteristic, complemented
289#1959—431no—
290#1959—431no—
291#1874—432no—
292#1872—432no—
293#1803—432no—
294#1802—432no—
295C2×C43#231111yescharacteristic
296C2×C43C2×#41711yescharacteristic
297C2×C43C2×#41711yescharacteristic
298C2×C43#321711yescharacteristic
299C2×C43#321811yescharacteristic
300C2×C43#323811yescharacteristic
301C2×C43#323911yescharacteristic
302D43—24no—
303D43—82no—
304#529—438no—
305#529—864no—
306C2×#126—861no—
307C2×#125C2×D4311yescharacteristic
308C2×#124—431no—
309C2×#123—861no—
310C2×C22⋊Q8—431no—
311C2×#121—431no—
312C2×C4×Q8—431no—
313C2×C4×D4—431no—
314C2×C4×D4—861no—
315C2×#117—861no—
316C22×C4⋊C4—432no—
317C22×C4⋊C4—861no—
318C22×C4⋊C4—861no—
319C22×C42—431no—
320#432—864no—
321C2×C4⋊C8—432no—
322C2×#103—432no—
323C2×#103—432no—
324C2×#102—432no—
325C2×#102—432no—
326C2×C22⋊C8—432no—
327C2×#97—431no—
328C2×#97C2×D4311yescharacteristic
329#384—432no—
330#384—431no—
331#384—861no—
332#384—861no—
333#384C2×D4311yescharacteristic
334#340—432no—
335#340—432no—
336#340C2×D4312yes—
337#340C2×D4312yes—
338C43#2186711yescharacteristic, complemented, Sylow
339C22×Q8—431no—
340C22×D4—431no—
341C22×D4—861no—
342C23×C4—431no—
343C23×C4—431no—
344C23×C4—431no—
345C23×C4—861no—
346C23×C4—862no—
347C22×C8—432no—
348C22×C8C22×D4312yes—
349#126—868no—
350#125—22no—
351#125C4×D4314yescomplemented
352#124—434no—
353#124—862no—
354#123—868no—
355C22⋊Q8—434no—
356C22⋊Q8—862no—
357#121—434no—
358#121—862no—
359C4×Q8—434no—
360C4×Q8—862no—
361C4×D4—434no—
362C4×D4—862no—
363C4×D4—868no—
364#117—868no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—432no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—862no—
373C2×C4⋊C4—862no—
374C2×C4⋊C4—862no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—1722no—
378C2×C4⋊C4—1722no—
379C2×C4⋊C4—1724no—
380C2×C4⋊C4—1724no—
381C2×C4⋊C4C22×D4312yes—
382C2×C4⋊C4C22×D4311yescharacteristic
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C42—431no—
390C2×C42—431no—
391C2×C42—431no—
392C2×C42—434no—
393C2×C42—434no—
394C2×C42—861no—
395C2×C42C22×D4311yescharacteristic
396C4⋊C8—864no—
397#103—1722no—
398#103—1722no—
399#102—1722no—
400#102—1722no—
401C22⋊C8—864no—
402#97—22no—
403#97—862no—
404C24—431no—
405C24—861no—
406C2×Q8—432no—
407C2×Q8—861no—
408C2×Q8—862no—
409C2×Q8—862no—
410C2×D4—432no—
411C2×D4—864no—
412C2×D4—861no—
413C2×D4—862no—
414C2×D4—862no—
415C2×D4—1722no—
416C2×D4—1722no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—431no—
421C22×C4—431no—
422C22×C4—431no—
423C22×C4—434no—
424C22×C4—434no—
425C22×C4—432no—
426C22×C4—432no—
427C22×C4—862no—
428C22×C4—862no—
429C22×C4—864no—
430C22×C4—862no—
431C22×C4—862no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—861no—
435C22×C4—862no—
436C22×C4—1722no—
437C22×C4—1722no—
438C22×C4—1724no—
439C22×C4—1724no—
440C22×C4—1724no—
441C22×C4D4×D4311yescharacteristic
442C22×C4D4×D4311yescharacteristic
443C22×C4C23×D4311yescharacteristic
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—862no—
448C2×C8—862no—
449C2×C8—862no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—42no—
457C4⋊C4—42no—
458C4⋊C4—864no—
459C4⋊C4—864no—
460C4⋊C4—862no—
461C4⋊C4—862no—
462C4⋊C4—1722no—
463C4⋊C4—1722no—
464C4⋊C4—1724no—
465C4⋊C4—1724no—
466C4⋊C4—1724no—
467C4⋊C4C2×C4×D4312yes—
468C4⋊C4C2×C4×D4312yes—
469C22⋊C4—864no—
470C22⋊C4—864no—
471C22⋊C4—864no—
472C22⋊C4—864no—
473C22⋊C4—864no—
474C42—434no—
475C42—434no—
476C42—432no—
477C42—432no—
478C42—864no—
479C42C2×C4×D4312yes—
480C42D4×D4312yes—
481C23—432no—
482C23—432no—
483C23—432no—
484C23—861no—
485C23—861no—
486C23—861no—
487C23—861no—
488C23—862no—
489C23—1721no—
490C23—1721no—
491C23—1721no—
492C23—1721no—
493C23—1721no—
494C23—1721no—
495C23C2×D4×D4311yescharacteristic
496Q8—864no—
497Q8—1722no—
498D4—864no—
499D4—1728no—
500D4—1722no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—432no—
515C2×C4—432no—
516C2×C4—432no—
517C2×C4—432no—
518C2×C4—432no—
519C2×C4—868no—
520C2×C4—868no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—864no—
526C2×C4—864no—
527C2×C4—862no—
528C2×C4—3448no—
529C2×C4—1728no—
530C2×C4—1722no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4C22⋊C4×D4312yes—
536C2×C4C22⋊C4×D4312yes—
537C2×C4C22×C4×D4311yescharacteristic
538C2×C4C2×D4×D4311yescharacteristic
539C2×C4#1306337112yes—
540C2×C4#1306337312yes—
541C8—42no—
542C8—1722no—
543C22—434no—
544C22—862no—
545C22—862no—
546C22—862no—
547C22—862no—
548C22—862no—
549C22—862no—
550C22—3441no—
551C22—3441no—
552C22—3441no—
553C22—3441no—
554C22—1722no—
555C22—1722no—
556C22—1722no—
557C22C2×C22⋊C4×D4311yescharacteristic
558C22#1458346711yescharacteristic
559C22#1458347411yescharacteristic
560C22AGL(1,ℤ/8)×D4311yescharacteristic
561C22AGL(1,ℤ/8)×D4311yescharacteristic
562C22#137×D4311yescharacteristic
563C22#137×D4311yescharacteristic
564C4—22no—
565C4—22no—
566C4—42no—
567C4—42no—
568C4—82no—
569C4—434no—
570C4—862no—
571C4—862no—
572C4—3442no—
573C4—1722no—
574C4#1458338112yes—
575C4#1458347912yes—
576C2—864no—
577C2—3442no—
578C2#1913718611yescharacteristic
579C2#417×D4311yescharacteristic
580C2#417×D4311yescharacteristic
581C2#1914561411yescharacteristic
582C2#1914562311yescharacteristic
583C2#1914581711yescharacteristic
584C2#1914582611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1992C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
cosocleC22×C4×C43C24
hypercenter#1992D43
hypocenterC43#21867
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
2. C2×#14582954C2semidirect
3. #384×D43C2semidirect
4. #19135565C2semidirect
5. #19135411C2semidirect
6. #19135409C2semidirect
8. #19134901C2semidirect
9. #19134599C2semidirect
10. #19134594C2semidirect
11. C43×#1992C2semidirect
13. #14583434C4semidirect
57. #13063313C2×C4semidirect
64. #13063290C2×C4semidirect
67. #13063287C2×C4semidirect
101. #125×C43C2×C4semidirect
288. #1992D43semidirect
338. C43#21867semidirect
351. #125C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834342
C2×#145829542
#384×D432
#191355652
#191354112
#191354092
#191349112
#191349012
#191345992
#191345942
C43×#19922
#2186743