Finite Group Databasebeta

← #25112758

Subgroups — #25112758

Order 11008.

1068 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×#14583588C211yesmaximal, characteristic
2#19143327C212yesmaximal
3#19135586C212yesmaximal, complemented
4#19135062C212yesmaximal, complemented
5#19135061C212yesmaximal, complemented
6#19134674C211yesmaximal, characteristic, complemented
7#19134590C211yesmaximal, characteristic, complemented
8#19134390C211yesmaximal, characteristic, complemented
9#19134334C211yesmaximal, characteristic, complemented
10#343×D43C211yesmaximal, characteristic, complemented
11C43×#1822C211yesmaximal, characteristic, complemented
12C22×#10621877C2212yes—
13C2×M16×D43C2212yes—
14#14583588—22no—
15#14583588—22no—
16#14583588—22no—
17#14583588—22no—
18C2×#13063318C412yes—
19C2×#13063317C412yes—
20C2×#13063316C2211yescharacteristic
21C2×#13063307C412yes—
22C2×#13063305C2211yescharacteristic
23C2×#13063304C2211yescharacteristic
24C2×#13063290C2211yescharacteristic
25C2×C4×C22⋊D43C2211yescharacteristic
26C2×#13063282C412yes—
27C2×C4⋊C4×D43C2211yescharacteristic
28#14582974—22no—
29#14582973—22no—
30#14582967—22no—
31(C22⋊D43)⋊C8—22no—
32#14582922C2212yes—
33C2×#13063243C2212yes—
34C2×#13063243C2212yes—
35#14582862C2212yes—
36M16×Dic43C2212yes—
37#14582668C2212yes—
38#14582668C2211yescharacteristic
39#14582668C2211yescharacteristic
40#14582667C2212yes—
41#14582667C2212yes—
42C2×#117×C43C2211yescharacteristic
43C43×#407C2212yes—
44C43×#343C2212yes—
45C43×#343C2211yescharacteristic
46C43×#343C2211yescharacteristic
47C22×Dic86C2311yescharacteristic
48C22×C22⋊D43C2×C411yescharacteristic
49C22×C4×D43C2×C412yes—
50C22×C4×D43C2311yescharacteristic
51C2×#10621877—22no—
52C2×#10621877—24no—
53C2×#10621877—42no—
54C2×#10621877C2312yes—
55C2×#10621877C2312yes—
56C2×#10621872—22no—
57M16×D43—24no—
58M16×D43—42no—
59C22×C43⋊C8—22no—
60C2×C8×D43—22no—
61#13063318—24no—
62#13063318—24no—
63#13063317—24no—
64#13063317—24no—
65#13063316—22no—
66#13063316—22no—
67#13063307—24no—
68#13063307—24no—
69#13063305—22no—
70#13063305—22no—
71#13063304—22no—
72#13063304—22no—
73#13063290—22no—
74#13063290—22no—
75C4×C22⋊D43D412yes—
76C4×C22⋊D43D412yes—
77C4×C22⋊D43D412yes—
78C4×C22⋊D43D412yes—
79#13063282—22no—
80#13063282—22no—
81#13063282—22no—
82#13063282—22no—
83C2×C4⋊Dic43C2×C412yes—
84C2×C4⋊Dic43C2×C412yes—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4C2×C412yes—
87C2×Dic43⋊C4C2×C412yes—
88C2×Dic43⋊C4C2×C412yes—
89C2×Dic43⋊C4C2×C412yes—
90C2×Dic43⋊C4C2×C411yescharacteristic
91C4⋊C4×D43—22no—
92C4⋊C4×D43—22no—
93C2×C22⋊Dic43C2×C412yes—
94C2×C22⋊Dic43C2×C411yescharacteristic
95C2×(C2×D43)⋊C4C2×C412yes—
96C2×(C2×D43)⋊C4C2×C411yescharacteristic
97C2×C4×Dic43C2×C412yes—
98C2×C4×Dic43C2311yescharacteristic
99Dic43⋊C8—22no—
100Dic43⋊C8—22no—
101#13063243—24no—
102#13063243—42no—
103(C2×D43)⋊C8—22no—
104(C2×D43)⋊C8—22no—
105#13063235—22no—
106C8×Dic43—22no—
107C23×C4×C43C2311yescharacteristic
108C2×M16×C43C2312yes—
109C2×M16×C43C2312yes—
110#117×C43—22no—
111#117×C43—22no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C22⋊C4×C43C2×C412yes—
115C2×C42×C43C2×C412yes—
116C22⋊C8×C43—22no—
117C22⋊C8×C43—22no—
118C24×C43C22×C411yescharacteristic
119C23×D43C22×C411yescharacteristic
120C22×C4×C43—22no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43C22×C411yescharacteristic
124C22×C4×C43C22×C412yes—
125C22×C4×C43C22×C412yes—
126C22×C4×C43C2×D412yes—
127C22×C4×C43C2×D412yes—
128C22×C4×C43C2411yescharacteristic
129C2×C22⋊D43—42no—
130C2×C22⋊D43C22⋊C412yes—
131C2×C22⋊D43C22⋊C412yes—
132C22×Dic43C22×C412yes—
133C22×Dic43C22×C411yescharacteristic
134C22×Dic43C22×C412yes—
135C22×Dic43C22×C411yescharacteristic
136C22×Dic43C22×C411yescharacteristic
137C2×C4×D43—22no—
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×C4×D43—22no—
141C2×C4×D43—22no—
142C2×C4×D43—44no—
143C2×C4×D43C2×D412yes—
144C2×C4×D43C2×D412yes—
145C2×Dic86—22no—
146C2×Dic86—22no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149M16×C43—22no—
150M16×C43—22no—
151M16×C43—22no—
152M16×C43—22no—
153C2×C8×C43—22no—
154C2×C8×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C22⋊C4×C43—24no—
158C42×C43—22no—
159C42×C43—22no—
160C22⋊Dic43—24no—
161C22⋊Dic43C22⋊C412yes—
162C22⋊Dic43C22⋊C412yes—
163(C2×D43)⋊C4—22no—
164(C2×D43)⋊C4—22no—
165(C2×D43)⋊C4C22⋊C411yescharacteristic
166(C2×D43)⋊C4C22⋊C411yescharacteristic
167(C2×D43)⋊C4C22⋊C411yescharacteristic
168(C2×D43)⋊C4C22⋊C411yescharacteristic
169C4⋊Dic43—22no—
170C4⋊Dic43—24no—
171C4⋊Dic43—24no—
172Dic43⋊C4—22no—
173Dic43⋊C4—22no—
174Dic43⋊C4—24no—
175Dic43⋊C4—22no—
176Dic43⋊C4—22no—
177Dic43⋊C4—24no—
178Dic43⋊C4C22⋊C412yes—
179Dic43⋊C4C22⋊C412yes—
180C4×Dic43—22no—
181C4×Dic43—22no—
182C4×Dic43C2×D412yes—
183C4×Dic43C2×D412yes—
184#10621877—22no—
185#10621877—22no—
186#10621877—22no—
187#10621877—44no—
188#10621877#4114yes—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—44no—
192#10621872—44no—
193C8×D43—44no—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43C2×C22⋊C412yes—
199C23×C43C23×C411yescharacteristic
200C22×D43—21no—
201C22×D43—21no—
202C22×D43—22no—
203C22×D43—41no—
204C22×D43C2×C22⋊C411yescharacteristic
205C22×D43C2×C22⋊C411yescharacteristic
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43C2×C22⋊C411yescharacteristic
217C2×C4×C43C2×C22⋊C411yescharacteristic
218C2×C4×C43C22×D412yes—
219C2×C4×C43C2×#4112yes—
220C2×C4×C43H(5,𝔽2)11yescharacteristic
221C2×C4×C432−1+411yescharacteristic
222C22⋊D43—24no—
223C22⋊D43—42no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—22no—
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—42no—
233C2×Dic43C2×C22⋊C411yescharacteristic
234C2×Dic43C2×C22⋊C411yescharacteristic
235C2×Dic43C2×C22⋊C412yes—
236C2×Dic43C2×C22⋊C412yes—
237C4×D43—22no—
238C4×D43—22no—
239C4×D43—22no—
240C4×D43—22no—
241C4×D43—44no—
242C4×D43—44no—
243Dic86—42no—
244Dic86—42no—
245C8×C43—42no—
246C8×C43—42no—
247C43⋊C8—24no—
248C43⋊C8—42no—
249#22480—431nomaximal, Sylow
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—22no—
253C22×C43—22no—
254C22×C43—22no—
255C22×C43—81no—
256C22×C43—81no—
257C22×C43C22×C22⋊C411yescharacteristic
258C22×C43C4×#4111yescharacteristic
259C22×C43#52011yescharacteristic
260C2×D43—21no—
261C2×D43—21no—
262C2×D43—21no—
263C2×D43—21no—
264C2×D43—21no—
265C2×D43—42no—
266C2×D43—42no—
267C2×D43#41312yes—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—42no—
271C4×C43—42no—
272C4×C43#54612yes—
273C4×C43#54712yes—
274Dic43—22no—
275Dic43—22no—
276Dic43—21no—
277Dic43—21no—
278Dic43—42no—
279Dic43—42no—
280C2×#552—431no—
281D4×M16—432no—
282#1998—432no—
283#1901—432no—
284#1901—432no—
285#1822D4311yescharacteristic, complemented
286#1821—431no—
287#1801—431no—
288C4×#101—431no—
289#1742—431no—
290C2×#343—431no—
291C2×C43—21no—
292C2×C43—21no—
293C2×C43—42no—
294C2×C43#233911yescharacteristic
295C2×C43C2×#41311yescharacteristic
296C2×C43#288911yescharacteristic
297D43—22no—
298D43—41no—
299C22×M16—432no—
300C22×M16—432no—
301#552—862no—
302#552—862no—
303#552—862no—
304#552—862no—
305C2×#126—432no—
306C2×#125—431no—
307C2×#125—432no—
308C2×#123—432no—
309C2×C22⋊Q8—431no—
310C2×C22⋊Q8—431no—
311C2×C4×Q8—431no—
312C2×C4×D4—431no—
313C2×#117—432no—
314C2×#117C2×D4311yescharacteristic
315C22×C4⋊C4—431no—
316#436—862no—
317#435—862no—
318#435—862no—
319C8×D4—862no—
320#423—432no—
321C2×#101—432no—
322C2×#101—432no—
323#407—432no—
324#407C2×D4312yes—
325C4×M16—432no—
326#343—432no—
327#343—432no—
328#343—431no—
329#343—432no—
330#343—431no—
331#343C2×D4311yescharacteristic
332#343C2×D4311yescharacteristic
333#343C2×D4312yes—
334C43#2248011yescharacteristic, complemented, Sylow
335C22×Q8—431no—
336C22×D4—431no—
337C23×C4—431no—
338C23×C4—432no—
339C23×C4C22×D4311yescharacteristic
340C2×M16—432no—
341C2×M16—432no—
342C2×M16—862no—
343C2×M16—862no—
344C2×M16—864no—
345C2×M16—864no—
346C2×M16—1722no—
347C2×M16—1722no—
348C2×M16C22×D4312yes—
349C2×M16C22×D4312yes—
350C22×C8—862no—
351C22×C8—862no—
352#126—864no—
353#126—864no—
354#125—864no—
355#125—864no—
356#125—862no—
357#125—862no—
358#123—864no—
359#123—864no—
360C22⋊Q8—862no—
361C22⋊Q8—862no—
362C22⋊Q8—862no—
363C22⋊Q8—862no—
364C4×Q8—862no—
365C4×Q8—862no—
366C4×D4—432no—
367C4×D4—432no—
368C4×D4—432no—
369C4×D4—432no—
370#117—22no—
371#117—22no—
372#117—862no—
373#117—862no—
374#117—862no—
375#117—862no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—432no—
378C2×C4⋊C4—432no—
379C2×C4⋊C4—432no—
380C2×C4⋊C4—432no—
381C2×C4⋊C4—432no—
382C2×C4⋊C4—432no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—862no—
385C2×C4⋊C4—862no—
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C22⋊C4—431no—
389C2×C22⋊C4—431no—
390C2×C22⋊C4—432no—
391C2×C22⋊C4—432no—
392C2×C22⋊C4C4×D4312yes—
393C2×C42—431no—
394C2×C42—432no—
395C2×C42C4×D4312yes—
396C4⋊C8—862no—
397C4⋊C8—862no—
398#101—864no—
399#101—1722no—
400C22⋊C8—22no—
401C22⋊C8—22no—
402C22⋊C8—862no—
403C22⋊C8—862no—
404#97—862no—
405C4×C8—862no—
406C24—431no—
407C24C2×C4×D4311yescharacteristic
408C2×Q8—862no—
409C2×Q8—862no—
410C2×Q8—861no—
411C2×Q8—861no—
412C2×D4—432no—
413C2×D4—432no—
414C2×D4—1722no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—431no—
419C22×C4—431no—
420C22×C4—431no—
421C22×C4—432no—
422C22×C4—432no—
423C22×C4—432no—
424C22×C4—432no—
425C22×C4—862no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—1724no—
431C22×C4C2×C4×D4311yescharacteristic
432C22×C4C2×C4×D4312yes—
433C22×C4C2×C4×D4312yes—
434C22×C4D4×D4312yes—
435C22×C4D4×D4312yes—
436C22×C4C23×D4311yescharacteristic
437M16—22no—
438M16—22no—
439M16—22no—
440M16—22no—
441M16—434no—
442M16—862no—
443M16—862no—
444M16—862no—
445M16—1724no—
446M16—1724no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—862no—
450C2×C8—862no—
451C2×C8—1724no—
452C2×C8—1724no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—432no—
456C4⋊C4—432no—
457C4⋊C4—864no—
458C4⋊C4—862no—
459C4⋊C4—862no—
460C4⋊C4—864no—
461C4⋊C4—864no—
462C4⋊C4—864no—
463C4⋊C4—862no—
464C4⋊C4—862no—
465C4⋊C4—862no—
466C22⋊C4—24no—
467C22⋊C4—432no—
468C22⋊C4—432no—
469C22⋊C4—431no—
470C22⋊C4—431no—
471C22⋊C4—431no—
472C22⋊C4—431no—
473C22⋊C4—862no—
474C22⋊C4—862no—
475C22⋊C4—864no—
476C42—22no—
477C42—22no—
478C42—432no—
479C42—432no—
480C42—862no—
481C42—862no—
482C23—21no—
483C23—21no—
484C23—41no—
485C23—41no—
486C23—431no—
487C23—431no—
488C23—862no—
489C23—861no—
490C23—861no—
491C23—1721no—
492C23C22⋊C4×D4312yes—
493C23C22×C4×D4311yescharacteristic
494Q8—1722no—
495Q8—1722no—
496D4—864no—
497D4—1722no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—431no—
509C2×C4—431no—
510C2×C4—432no—
511C2×C4—432no—
512C2×C4—861no—
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—1721no—
525C2×C4—1721no—
526C2×C4—1722no—
527C2×C4C22⋊C4×D4311yescharacteristic
528C2×C4C22⋊C4×D4311yescharacteristic
529C2×C4C2×D4×D4312yes—
530C2×C4#41×D4312yes—
531C2×C4#1306337111yescharacteristic
532C2×C4#1306337211yescharacteristic
533C8—42no—
534C8—42no—
535C8—864no—
536C8—1722no—
537C22—21no—
538C22—21no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—81no—
543C22—81no—
544C22—432no—
545C22—861no—
546C22—861no—
547C22—861no—
548C22—861no—
549C22—861no—
550C22—1722no—
551C22—1722no—
552C22C2×C22⋊C4×D4311yescharacteristic
553C22#1458336711yescharacteristic
554C22#1458337911yescharacteristic
555C4—21no—
556C4—21no—
557C4—42no—
558C4—42no—
559C4—862no—
560C4—862no—
561C4—861no—
562C4—861no—
563C4—1722no—
564C4—1722no—
565C4#1458354112yes—
566C4#1458354712yes—
567C2—21no—
568C2—21no—
569C2—42no—
570C2—862no—
571C2—1721no—
572C2#1913741911yescharacteristic
573C2#413×D4311yescharacteristic
574C2#1914307611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1822C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C2×C4
cosocleC22×C4×C43C24
hypercenter#1822D43
hypocenterC43#22480
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1822

Complements

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

NH ≅ G/Ntype
3. #19135586C2semidirect
4. #19135062C2semidirect
5. #19135061C2semidirect
6. #19134674C2semidirect
7. #19134590C2semidirect
8. #19134390C2semidirect
9. #19134334C2semidirect
10. #343×D43C2semidirect
11. C43×#1822C2semidirect
285. #1822D43semidirect
334. C43#22480semidirect

Maximal subgroups

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

subgroupindex
C2×#145835882
#191433272
#191355862
#191350622
#191350612
#191346742
#191345902
#191343902
#191343342
#343×D432
C43×#18222
#2248043