Finite Group Databasebeta

← #25101796

Subgroups — #25101796

Order 11008.

1218 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583434C211yesmaximal, characteristic
2C2×#14582851C211yesmaximal, characteristic, complemented
3#19137000C211yesmaximal, characteristic, complemented
4#19135565C211yesmaximal, characteristic, complemented
5#19135411C211yesmaximal, characteristic, complemented
6#19135409C211yesmaximal, characteristic, complemented
7#19135032C212yesmaximal
8#19135027C212yesmaximal, complemented
9#19134414C212yesmaximal, complemented
10#19134409C212yesmaximal, complemented
11C43×#1992C211yesmaximal, characteristic, complemented
12C22×#10621872C2212yes—
13#14583434—24no—
14#14583434C418yescomplemented
15C2×#13063320—21no—
16C2×#13063313C2211yescharacteristic
17C2×#13063310—21no—
18C2×#13063305C2211yescharacteristic
19C2×#13063300C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063287—21no—
22C2×#13063287C2211yescharacteristic
23C2×#13063283—21no—
24C2×#13063283—21no—
25C2×C42×D43C2211yescharacteristic
26C2×#13063250C2212yes—
27C2×#13063248C2212yes—
28C2×#13063247C2212yes—
29C2×#13063245C2212yes—
30#14582851—24no—
31C2×#13063236C2211yescharacteristic
32C2×C8×Dic43C2212yes—
33#14582769C2211yescharacteristic
34#14582764—21no—
35#14582756—21no—
36#14582756C2212yes—
37C4⋊C4×Dic43—21no—
38C4⋊C4×Dic43C2212yes—
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×D43D411yescharacteristic
51C22×C4×D43D411yescharacteristic
52C22×C4×D43C2311yescharacteristic
53C2×#10621872—24no—
54C2×#10621872—24no—
55C2×#10621872—24no—
56C22×C43⋊C8C2312yes—
57#13063320—28no—
58#13063313—22no—
59#13063313C2×C414yes—
60#13063310—28no—
61#13063305—22no—
62#13063305C2×C414yes—
63#13063300—22no—
64#13063300C2×C414yes—
65#13063290—22no—
66#13063290C2×C414yes—
67#13063287—28no—
68#13063287—22no—
69#13063287C2×C414yes—
70#13063283—28no—
71#13063283—44no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43C2312yes—
76C2×Dic43⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—22no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—22no—
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88C42×D43C2×C414yes—
89C42×D43D414yes—
90#13063250—24no—
91#13063248—24no—
92#13063247—24no—
93#13063245—24no—
94#13063236—22no—
95C8×Dic43—24no—
96C43⋊#95—22no—
97C43⋊#95—22no—
98C22×C8×C43C2312yes—
99#125×C43—22no—
100#125×C43C2×C414yes—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43C2312yes—
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C42×C43C2311yescharacteristic
109#97×C43—22no—
110C23×D43—21no—
111C23×D43C2×D411yescharacteristic
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—22no—
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2411yescharacteristic
118C22×Dic43—21no—
119C22×Dic43—22no—
120C22×Dic43C2×D411yescharacteristic
121C22×Dic43C2×D411yescharacteristic
122C22×Dic43C2×D411yescharacteristic
123C2×D172—21no—
124C2×D172—24no—
125C2×D172—22no—
126C2×D172—22no—
127C2×D172—42no—
128C2×D172—42no—
129C2×D172C22×C412yes—
130C2×C4×D43—22no—
131C2×C4×D43—22no—
132C2×C4×D43—22no—
133C2×C4×D43—22no—
134C2×C4×D43—24no—
135C2×C4×D43—41no—
136C2×C4×D43—41no—
137C2×C4×D43—42no—
138C2×C4×D43—42no—
139C2×C4×D43C22⋊C414yes—
140C2×C4×D43C22⋊C414yes—
141C2×C4×D43C22×C412yes—
142C2×C4×D43C2×D412yes—
143C2×Dic86—22no—
144C2×Dic86—22no—
145C2×Dic86—21no—
146C2×Dic86C22×C412yes—
147C2×C8×C43—22no—
148C2×C8×C43—22no—
149C2×C8×C43#4114yes—
150C4⋊C4×C43—24no—
151C4⋊C4×C43—24no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—42no—
157C4⋊C4×C43—42no—
158C4⋊C4×C43C22×C412yes—
159C4⋊C4×C43C22×C412yes—
160C42×C43C22×C412yes—
161C42×C43C2×D412yes—
162(C2×D43)⋊C4—24no—
163(C2×D43)⋊C4—24no—
164(C2×D43)⋊C4—24no—
165(C2×D43)⋊C4—24no—
166(C2×D43)⋊C4—24no—
167(C2×D43)⋊C4—44no—
168C4⋊Dic43—24no—
169C4⋊Dic43—22no—
170C4⋊Dic43—22no—
171C4⋊Dic43—42no—
172C4⋊Dic43—42no—
173Dic43⋊C4—24no—
174C4×Dic43—24no—
175C4×Dic43—44no—
176C4×Dic43C22⋊C414yes—
177C4×Dic43C22⋊C414yes—
178C4×Dic43C22×C412yes—
179C4×Dic43C2×D412yes—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—22no—
182C2×C43⋊C8#4114yes—
183#10621872—216no—
184C23×C43C22×D411yescharacteristic
185C22×D43—21no—
186C22×D43—21no—
187C22×D43—21no—
188C22×D43—21no—
189C22×D43—21no—
190C22×D43—21no—
191C22×D43—22no—
192C22×D43—41no—
193C22×D43—41no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43C2×C22⋊C412yes—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—22no—
204C2×C4×C43—22no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43C2×C22⋊C412yes—
213C2×C4×C43C2×C22⋊C412yes—
214C2×C4×C43C23×C411yescharacteristic
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C2×#4112yes—
217C2×C4×C43C2×#4112yes—
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—22no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—42no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C2×Dic43C2×C22⋊C412yes—
229C2×Dic43C2×C22⋊C412yes—
230C2×Dic43C2×C22⋊C412yes—
231C2×Dic43AGL(1,ℤ/8)12yes—
232C2×Dic43#13712yes—
233D172—24no—
234D172—48no—
235D172—42no—
236C4×D43—24no—
237C4×D43—24no—
238C4×D43—28no—
239C4×D43—44no—
240C4×D43—48no—
241Dic86—24no—
242Dic86—42no—
243C8×C43—24no—
244C43⋊C8—24no—
245#21403—431nomaximal, Sylow
246C22×C43C22×C22⋊C411yescharacteristic
247C22×C43#53211yescharacteristic
248C22×C43#53211yescharacteristic
249C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
250C22×C43C2×#13711yescharacteristic
251C22×C43#57511yescharacteristic
252C22×C43#57511yescharacteristic
253C2×D43—22no—
254C2×D43—22no—
255C2×D43—22no—
256C2×D43—41no—
257C2×D43—41no—
258C2×D43—41no—
259C2×D43—41no—
260C2×D43—42no—
261C2×D43—42no—
262C2×D43—42no—
263C2×D43—81no—
264C2×D43—81no—
265C2×D43—81no—
266C2×D43—81no—
267C4×C43—22no—
268C4×C43—22no—
269C4×C43—42no—
270C4×C43—42no—
271C4×C43—82no—
272C4×C43C4×#4112yes—
273C4×C43#52512yes—
274Dic43—22no—
275Dic43—22no—
276Dic43—42no—
277Dic43—82no—
278Dic43#41714yes—
279C2×#529—431no—
280C2×C4×M16—431no—
281#2285—431no—
282#1992—431no—
283#1992D4311yescharacteristic, complemented
284#1959—431no—
285#1959—431no—
286#1895—432no—
287#1894—432no—
288C4×#103—432no—
289C4×#102—432no—
290C2×C43#229711yescharacteristic
291C2×C43C2×#41711yescharacteristic
292C2×C43#289611yescharacteristic
293C2×C43#317111yescharacteristic
294C2×C43#317111yescharacteristic
295C2×C43#317211yescharacteristic
296C2×C43#317211yescharacteristic
297D43—42no—
298D43—82no—
299C22×M16—432no—
300#529—438no—
301#529—864no—
302C2×#126—861no—
303C2×#125C2×D4311yescharacteristic
304C2×#124—431no—
305C2×#123—861no—
306C2×C22⋊Q8—431no—
307C2×#121—431no—
308C2×C4×Q8—431no—
309C2×C4×D4—431no—
310C2×C4×D4—861no—
311C2×#117—861no—
312C2×#117—861no—
313C22×C42—431no—
314C2×#103—432no—
315C2×#103—432no—
316C2×#102—432no—
317C2×#102—432no—
318C4×M16—864no—
319C2×#97—431no—
320C2×#97C2×D4311yescharacteristic
321C2×C4×C8—432no—
322#384—431no—
323#384C2×D4311yescharacteristic
324#382—861no—
325#380—432no—
326#380—861no—
327C4×C4⋊C4—432no—
328C4×C4⋊C4—861no—
329#340—432no—
330#340—432no—
331#340C2×D4312yes—
332#340C2×D4312yes—
333C43#2140311yescharacteristic, complemented, Sylow
334C22×Q8—431no—
335C22×D4—431no—
336C22×D4—861no—
337C23×C4—431no—
338C23×C4—431no—
339C23×C4—431no—
340C23×C4—861no—
341C2×M16—864no—
342C2×M16—864no—
343C2×M16—864no—
344C22×C8—432no—
345C22×C8C22×D4312yes—
346#126—868no—
347#125—22no—
348#125C4×D4314yes—
349#124—434no—
350#124—862no—
351#123—868no—
352C22⋊Q8—434no—
353C22⋊Q8—862no—
354#121—434no—
355#121—862no—
356C4×Q8—434no—
357C4×Q8—862no—
358C4×D4—434no—
359C4×D4—862no—
360C4×D4—868no—
361#117—868no—
362#117—1724no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—432no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4C22×D4312yes—
373C2×C4⋊C4C22×D4311yescharacteristic
374C2×C4⋊C4C22×D4311yescharacteristic
375C2×C22⋊C4—861no—
376C2×C22⋊C4—861no—
377C2×C22⋊C4—861no—
378C2×C22⋊C4—861no—
379C2×C22⋊C4—861no—
380C2×C22⋊C4—862no—
381C2×C42—431no—
382C2×C42—431no—
383C2×C42—431no—
384C2×C42—434no—
385C2×C42—434no—
386C2×C42—861no—
387C2×C42—862no—
388C2×C42C22×D4311yescharacteristic
389#103—864no—
390#103—864no—
391#102—864no—
392#102—864no—
393#97—22no—
394#97—862no—
395C4×C8—864no—
396#95—862no—
397#95—862no—
398C24—431no—
399C24—861no—
400C2×Q8—432no—
401C2×Q8—861no—
402C2×Q8—862no—
403C2×Q8—862no—
404C2×D4—432no—
405C2×D4—864no—
406C2×D4—861no—
407C2×D4—862no—
408C2×D4—862no—
409C2×D4—1722no—
410C2×D4—1722no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—431no—
415C22×C4—431no—
416C22×C4—431no—
417C22×C4—434no—
418C22×C4—432no—
419C22×C4—432no—
420C22×C4—434no—
421C22×C4—862no—
422C22×C4—862no—
423C22×C4—864no—
424C22×C4—862no—
425C22×C4—862no—
426C22×C4—861no—
427C22×C4—862no—
428C22×C4—1721no—
429C22×C4—1721no—
430C22×C4—1722no—
431C22×C4—1722no—
432C22×C4D4×D4311yescharacteristic
433C22×C4D4×D4311yescharacteristic
434C22×C4C23×D4311yescharacteristic
435M16—8616no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—434no—
439C2×C8—862no—
440C2×C8—862no—
441C2×C8#1062190214yes—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—42no—
449C4⋊C4—42no—
450C4⋊C4—864no—
451C4⋊C4—864no—
452C4⋊C4—862no—
453C4⋊C4—862no—
454C4⋊C4—1722no—
455C4⋊C4—1722no—
456C4⋊C4C2×C4×D4312yes—
457C4⋊C4C2×C4×D4312yes—
458C22⋊C4—864no—
459C22⋊C4—864no—
460C22⋊C4—864no—
461C22⋊C4—864no—
462C22⋊C4—864no—
463C22⋊C4—1724no—
464C42—434no—
465C42—434no—
466C42—432no—
467C42—432no—
468C42—864no—
469C42—1724no—
470C42C2×C4×D4312yes—
471C42D4×D4312yes—
472C23—432no—
473C23—861no—
474C23—861no—
475C23—861no—
476C23—861no—
477C23—861no—
478C23—861no—
479C23—862no—
480C23—1721no—
481C23—1721no—
482C23—1721no—
483C23—1721no—
484C23—1721no—
485C23—1721no—
486C23C2×D4×D4311yescharacteristic
487Q8—864no—
488Q8—1722no—
489D4—864no—
490D4—1728no—
491D4—1722no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—432no—
506C2×C4—432no—
507C2×C4—432no—
508C2×C4—432no—
509C2×C4—432no—
510C2×C4—868no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—864no—
516C2×C4—864no—
517C2×C4—862no—
518C2×C4—1724no—
519C2×C4—1728no—
520C2×C4—1722no—
521C2×C4—1722no—
522C2×C4—1722no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4C22⋊C4×D4312yes—
526C2×C4C22⋊C4×D4312yes—
527C2×C4C22×C4×D4311yescharacteristic
528C2×C4C2×D4×D4311yescharacteristic
529C2×C4#41×D4312yes—
530C2×C4C2×#1062190212yes—
531C8—24no—
532C8—864no—
533C22—862no—
534C22—862no—
535C22—862no—
536C22—3441no—
537C22—3441no—
538C22—3441no—
539C22—3441no—
540C22—1722no—
541C22—1722no—
542C22—1722no—
543C22—1721no—
544C22—1721no—
545C22—1721no—
546C22—1721no—
547C22C2×C22⋊C4×D4311yescharacteristic
548C22#1458344811yescharacteristic
549C22#1458345011yescharacteristic
550C22AGL(1,ℤ/8)×D4311yescharacteristic
551C22#137×D4311yescharacteristic
552C22#1458369511yescharacteristic
553C22#1458369811yescharacteristic
554C4—22no—
555C4—22no—
556C4—42no—
557C4—42no—
558C4—82no—
559C4—434no—
560C4—862no—
561C4—862no—
562C4—3442no—
563C4—1722no—
564C4C4×#1062190212yes—
565C4#1458341212yes—
566C2—3442no—
567C2—1722no—
568C2#1913708411yescharacteristic
569C2#417×D4311yescharacteristic
570C2#1914311111yescharacteristic
571C2#1914518911yescharacteristic
572C2#1914519211yescharacteristic
573C2#1914520011yescharacteristic
574C2#1914520311yescharacteristic
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#21403
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×#14582851C2semidirect
3. #19137000C2semidirect
4. #19135565C2semidirect
5. #19135411C2semidirect
6. #19135409C2semidirect
8. #19135027C2semidirect
9. #19134414C2semidirect
10. #19134409C2semidirect
11. C43×#1992C2semidirect
14. #14583434C4semidirect
283. #1992D43semidirect
333. C43#21403semidirect

Maximal subgroups

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

subgroupindex
C2×#145834342
C2×#145828512
#191370002
#191355652
#191354112
#191354092
#191350322
#191350272
#191344142
#191344092
C43×#19922
#2140343