Finite Group Databasebeta

← #25096668

Subgroups — #25096668

Order 11008.

1338 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×C4×#10621900C211yesmaximal, characteristic
2C2×#14582955C211yesmaximal, characteristic, complemented
3#19136988C211yesmaximal, characteristic, complemented
4#19134688C212yesmaximal, complemented
5#19134611C211yesmaximal, characteristic, complemented
6#19134607C211yesmaximal, characteristic, complemented
7#19134605C211yesmaximal, characteristic, complemented
8#19134532C212yesmaximal
9#19134424C212yesmaximal, complemented
10#19134422C212yesmaximal, complemented
11C43×#1804C211yesmaximal, characteristic, complemented
12C22×#10621900C2211yescharacteristic
13C4×#10621900—24no—
14C4×#10621900C418yescomplemented
15C2×C4×Dic86C2211yescharacteristic
16C2×#13063290C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×C4×C22⋊D43—21no—
19C2×(C22⋊D43)⋊C4—21no—
20C2×#13063283C2211yescharacteristic
21C2×#13063281—21no—
22C22×C4×Dic43—21no—
23C2×C42×D43C2211yescharacteristic
24#14582955—24no—
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063250C2212yes—
27C2×#13063248C2212yes—
28C2×#13063246C2212yes—
29C2×(C2×D43)⋊C8C2212yes—
30C2×#13063235C2212yes—
31#14582766—21no—
32#14582765C2211yescharacteristic
33#14582761—21no—
34#14582756C2212yes—
35C4⋊C4×Dic43C2212yes—
36#14582746—21no—
37#14582744—21no—
38#14582662C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C2×C4×D4×C43C2211yescharacteristic
42C2×C4⋊C8×C43C2211yescharacteristic
43C2×#102×C43C2212yes—
44C43×#382C2211yescharacteristic
45C43×#340C2212yes—
46C2×#10621900—22no—
47C2×#10621900—22no—
48C2×#10621900—22no—
49C2×#10621900—22no—
50C2×#10621900—22no—
51C2×#10621900C2×C414yes—
52C22×Dic86C2311yescharacteristic
53C22×C22⋊D43—21no—
54C23×Dic43—21no—
55C23×Dic43—21no—
56C22×C4×D43D411yescharacteristic
57C22×C4×D43D411yescharacteristic
58C22×C4×D43C2311yescharacteristic
59C22×C43⋊C8C2312yes—
60C4×Dic86—22no—
61C4×Dic86C2×C414yes—
62#13063290—22no—
63#13063290C2×C414yes—
64D4×Dic43—22no—
65D4×Dic43C2×C414yes—
66C4×C22⋊D43—28no—
67(C22⋊D43)⋊C4—28no—
68#13063283—22no—
69#13063283C2×C414yes—
70#13063281—28no—
71C2×C4⋊Dic43C2312yes—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—22no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—28no—
82C2×C4×Dic43—22no—
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86C42×D43C2×C414yes—
87C42×D43D414yes—
88C4⋊(C43⋊C8)—22no—
89#13063250—24no—
90#13063248—24no—
91#13063246—24no—
92(C2×D43)⋊C8—24no—
93#13063235—24no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—22no—
97C43⋊#95—22no—
98C22×D4×C43C2311yescharacteristic
99C23×C4×C43—21no—
100C22×C8×C43C2312yes—
101C4×D4×C43—22no—
102C4×D4×C43C2×C414yes—
103C2×C4⋊C4×C43C2312yes—
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C22⋊C4×C43—21no—
106C2×C42×C43C2311yescharacteristic
107C4⋊C8×C43—22no—
108#102×C43—24no—
109#95×C43—21no—
110#95×C43—21no—
111C24×C43—21no—
112C23×D43C2×D411yescharacteristic
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43C22×C412yes—
117C2×D4×C43#4112yes—
118C2×D4×C43#4112yes—
119C22×C4×C43—24no—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—44no—
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2411yescharacteristic
126C2×C22⋊D43—24no—
127C2×C22⋊D43—24no—
128C2×C22⋊D43—24no—
129C22×Dic43—24no—
130C22×Dic43—24no—
131C22×Dic43—24no—
132C22×Dic43—24no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—22no—
136C22×Dic43—44no—
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140#10621900—28no—
141#10621900—28no—
142#10621900—28no—
143#10621900—28no—
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—42no—
149C2×C4×D43—42no—
150C2×C4×D43C22⋊C414yes—
151C2×C4×D43C22⋊C414yes—
152C2×C4×D43C22×C412yes—
153C2×C4×D43C2×D412yes—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86C22×C412yes—
158C2×Dic86#4112yes—
159C2×Dic86#4112yes—
160C2×C8×C43—22no—
161C2×C8×C43—22no—
162C2×C8×C43—22no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43C22×C412yes—
167C22⋊C4×C43—24no—
168C42×C43C22×C412yes—
169C42×C43C2×D412yes—
170C22⋊Dic43—24no—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—44no—
173C4⋊Dic43—21no—
174C4⋊Dic43—22no—
175C4⋊Dic43—22no—
176C4⋊Dic43C22×C412yes—
177Dic43⋊C4—24no—
178Dic43⋊C4—24no—
179C4×Dic43—24no—
180C4×Dic43—24no—
181C4×Dic43—24no—
182C4×Dic43—44no—
183C4×Dic43C22⋊C414yes—
184C4×Dic43C22⋊C414yes—
185C4×Dic43C22×C412yes—
186C4×Dic43C2×D412yes—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—22no—
189C2×C43⋊C8—22no—
190C23×C43—22no—
191C23×C43—22no—
192C23×C43—22no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43C22×D411yescharacteristic
196C22×D43—21no—
197C22×D43—21no—
198C22×D43—22no—
199C22×D43—22no—
200C22×D43C2×C22⋊C412yes—
201D4×C43—22no—
202D4×C43—22no—
203D4×C43—22no—
204D4×C43#11714yes—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—48no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43C2×C22⋊C412yes—
214C2×C4×C43C2×C22⋊C412yes—
215C2×C4×C43C23×C411yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C2×#4111yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C22⋊D43—216no—
222C2×Dic43—216no—
223C2×Dic43—22no—
224C2×Dic43—22no—
225C2×Dic43—22no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—48no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43C2×C22⋊C412yes—
237C2×Dic43C2×C22⋊C412yes—
238C2×Dic43C2×C22⋊C412yes—
239C4×D43—22no—
240C4×D43—22no—
241C4×D43—22no—
242C4×D43—22no—
243C4×D43—44no—
244C4×D43—44no—
245Dic86—22no—
246Dic86—22no—
247Dic86—22no—
248Dic86#11714yes—
249C8×C43—42no—
250C43⋊C8—42no—
251#20742—431nomaximal, Sylow
252C22×C43—24no—
253C22×C43—44no—
254C22×C43—44no—
255C22×C43—42no—
256C22×C43—42no—
257C22×C43C22×C22⋊C411yescharacteristic
258C22×C43#52511yescharacteristic
259C22×C43#52511yescharacteristic
260C22×C43#57512yes—
261C22×C43#57512yes—
262C2×D43—22no—
263C2×D43—22no—
264C2×D43—22no—
265C2×D43—42no—
266C2×D43—42no—
267C4×C43—22no—
268C4×C43—22no—
269C4×C43—42no—
270C4×C43—82no—
271C4×C43C2×#11711yescharacteristic
272C4×C43C2×#11711yescharacteristic
273C4×C43#52511yescharacteristic
274C4×C43#52511yescharacteristic
275Dic43—22no—
276Dic43—22no—
277Dic43—24no—
278Dic43—22no—
279Dic43—42no—
280Dic43—82no—
281C2×C4×#41—431no—
282C2×#432—431no—
283#2283—431no—
284#1825—432no—
285#1805—431no—
286#1805—431no—
287#1804—431no—
288#1804D4311yescharacteristic, complemented
289#1788—432no—
290#1763—432no—
291#1762—432no—
292C2×C43—44no—
293C2×C43#228011yescharacteristic
294C2×C43#289611yescharacteristic
295C2×C43#289611yescharacteristic
296C2×C43#311112yes—
297C2×C43#311112yes—
298D43—42no—
299C22×#41—431no—
300C4×#41—438no—
301C4×#41—864no—
302C2×C4×Q8—431no—
303C2×C4×Q8—431no—
304C2×C4×D4—431no—
305C2×C4×D4—861no—
306C2×C4×D4—861no—
307C2×C4×D4C2×D4311yescharacteristic
308C2×#117—431no—
309C2×#117—861no—
310C22×C42—431no—
311C22×C42—861no—
312#432—864no—
313C2×C4⋊C8—431no—
314C2×C4⋊C8C2×D4311yescharacteristic
315C2×#103—432no—
316C2×#103—432no—
317C2×#102—432no—
318C2×#102C2×D4312yes—
319C2×C22⋊C8—432no—
320C2×#97—432no—
321#383—861no—
322#382—431no—
323#382C2×D4311yescharacteristic
324#381—861no—
325#380—432no—
326C4×C4⋊C4—432no—
327C4×C22⋊C4—861no—
328#376—861no—
329#340—432no—
330#340—432no—
331#340—432no—
332#340C2×D4312yes—
333C43#2074211yescharacteristic, complemented, Sylow
334C2×#41—434no—
335C2×#41—862no—
336C2×#41—862no—
337C2×#41—862no—
338C2×#41—862no—
339C2×#41—862no—
340C22×Q8—431no—
341C22×D4—861no—
342C22×D4C22×D4311yescharacteristic
343C23×C4—21no—
344C23×C4—431no—
345C23×C4—431no—
346C23×C4—431no—
347C23×C4—861no—
348C23×C4—861no—
349C22×C8—432no—
350C22×C8C22×D4312yes—
351C4×Q8—434no—
352C4×Q8—434no—
353C4×Q8—862no—
354C4×Q8—862no—
355C4×D4—22no—
356C4×D4—434no—
357C4×D4—862no—
358C4×D4—868no—
359C4×D4—868no—
360C4×D4C4×D4314yes—
361#117—434no—
362#117—868no—
363#117—862no—
364C2×C4⋊C4—431no—
365C2×C4⋊C4—432no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4C22×D4312yes—
369C2×C4⋊C4C22×D4311yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—861no—
372C2×C22⋊C4—861no—
373C2×C22⋊C4—862no—
374C2×C42—431no—
375C2×C42—431no—
376C2×C42—431no—
377C2×C42—434no—
378C2×C42—434no—
379C2×C42—868no—
380C2×C42—861no—
381C2×C42—861no—
382C2×C42—861no—
383C2×C42—862no—
384C2×C42C22×D4311yescharacteristic
385C4⋊C8—22no—
386C4⋊C8—862no—
387#103—864no—
388#103—864no—
389#102—24no—
390#102—864no—
391C22⋊C8—864no—
392#97—864no—
393#95—21no—
394#95—21no—
395#95—862no—
396#95—862no—
397#95—861no—
398#95—861no—
399C24—21no—
400C24—431no—
401#41—868no—
402#41—868no—
403#41—868no—
404#41—868no—
405C2×Q8—432no—
406C2×Q8—432no—
407C2×Q8—432no—
408C2×Q8—861no—
409C2×Q8—861no—
410C2×Q8—861no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—864no—
415C2×D4—864no—
416C2×D4—864no—
417C2×D4C2×C4×D4312yes—
418C2×D4#1062190012yes—
419C2×D4#1062190212yes—
420C22×C4—21no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—44no—
424C22×C4—431no—
425C22×C4—431no—
426C22×C4—431no—
427C22×C4—432no—
428C22×C4—432no—
429C22×C4—434no—
430C22×C4—434no—
431C22×C4—864no—
432C22×C4—864no—
433C22×C4—864no—
434C22×C4—864no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—862no—
442C22×C4—1722no—
443C22×C4—1722no—
444C22×C4—1724no—
445C22×C4D4×D4311yescharacteristic
446C22×C4D4×D4311yescharacteristic
447C22×C4C23×D4311yescharacteristic
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—862no—
452C2×C8—862no—
453C2×C8—862no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—432no—
458C4⋊C4—864no—
459C4⋊C4—864no—
460C4⋊C4—861no—
461C4⋊C4—862no—
462C4⋊C4—862no—
463C4⋊C4C2×C4×D4312yes—
464C22⋊C4—24no—
465C22⋊C4—864no—
466C22⋊C4—864no—
467C22⋊C4—1724no—
468C42—434no—
469C42—434no—
470C42—432no—
471C42—432no—
472C42—864no—
473C42—864no—
474C42—864no—
475C42—1724no—
476C42C2×C4×D4312yes—
477C42D4×D4312yes—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—42no—
482C23—42no—
483C23—432no—
484C23—861no—
485C23—861no—
486C23—862no—
487C23—862no—
488C23C2×D4×D4311yescharacteristic
489Q8—434no—
490Q8—862no—
491Q8—862no—
492Q8—862no—
493D4—22no—
494D4—22no—
495D4—22no—
496D4—8616no—
497D4#1306328314yes—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—48no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—432no—
507C2×C4—432no—
508C2×C4—432no—
509C2×C4—8616no—
510C2×C4—862no—
511C2×C4—861no—
512C2×C4—862no—
513C2×C4—861no—
514C2×C4—862no—
515C2×C4—862no—
516C2×C4—862no—
517C2×C4—862no—
518C2×C4—862no—
519C2×C4—862no—
520C2×C4—862no—
521C2×C4—862no—
522C2×C4—1724no—
523C2×C4—1724no—
524C2×C4—1728no—
525C2×C4—1722no—
526C2×C4—1722no—
527C2×C4—1722no—
528C2×C4—1722no—
529C2×C4C22⋊C4×D4312yes—
530C2×C4C22⋊C4×D4312yes—
531C2×C4C22×C4×D4311yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4#41×D4311yescharacteristic
534C2×C4#41×D4311yescharacteristic
535C2×C4C2×#1062190011yescharacteristic
536C2×C4C2×#1062190211yescharacteristic
537C8—42no—
538C8—1722no—
539C22—24no—
540C22—44no—
541C22—42no—
542C22—42no—
543C22—44no—
544C22—862no—
545C22—862no—
546C22—862no—
547C22—1722no—
548C22—1722no—
549C22C2×C22⋊C4×D4311yescharacteristic
550C22#1458340911yescharacteristic
551C22#1458341211yescharacteristic
552C22#1458369512yes—
553C22#1458369612yes—
554C4—22no—
555C4—22no—
556C4—42no—
557C4—82no—
558C4—862no—
559C4—862no—
560C4—862no—
561C4—864no—
562C4—3442no—
563C4—1722no—
564C4#117×D4311yescharacteristic
565C4C2×#1306328311yescharacteristic
566C4#1458340911yescharacteristic
567C4#1458341211yescharacteristic
568C2—44no—
569C2—1722no—
570C2#1913697711yescharacteristic
571C2#1914310911yescharacteristic
572C2#1914311011yescharacteristic
573C2#1914470112yes—
574C2#1914470912yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1804C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
cosocleC22×C4×C43C24
hypercenter#1804D43
hypocenterC43#20742
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. C2×#14582955C2semidirect
3. #19136988C2semidirect
4. #19134688C2semidirect
5. #19134611C2semidirect
6. #19134607C2semidirect
7. #19134605C2semidirect
9. #19134424C2semidirect
10. #19134422C2semidirect
11. C43×#1804C2semidirect
14. C4×#10621900C4semidirect
288. #1804D43semidirect
333. C43#20742semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106219002
C2×#145829552
#191369882
#191346882
#191346112
#191346072
#191346052
#191345322
#191344242
#191344222
C43×#18042
#2074243