Finite Group Databasebeta

← #25062750

Subgroups — #25062750

Order 11008.

952 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583490C211yesmaximal, characteristic
2#19143635C211yesmaximal, characteristic, complemented
3#19143623C211yesmaximal, characteristic, complemented
4#19132964C211yesmaximal, characteristic, complemented
5#19132957C212yesmaximal, complemented
6#19132952C211yesmaximal, characteristic, complemented
7#19132950C211yesmaximal, characteristic, complemented
8#19132940C212yesmaximal, complemented
9#19132930C212yesmaximal, complemented
10#19132923C212yesmaximal, complemented
11C43×#1473C211yesmaximal, characteristic, complemented
12#14583490—22no—
13#14583490—22no—
14#14583490—22no—
15#14583490—22no—
16C2×#13063320C411yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×#13063316C411yescharacteristic
19C2×#13063310C411yescharacteristic
20C2×#13063309C411yescharacteristic
21C2×#13063307C411yescharacteristic
22C2×#13063307C2211yescharacteristic
23C2×#13063305C411yescharacteristic
24C2×#13063303C2211yescharacteristic
25C2×#13063302C411yescharacteristic
26C2×#13063298C411yescharacteristic
27C2×C4×D172C2211yescharacteristic
28C2×(C22⋊D43)⋊C4C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30#14582978—22no—
31#14582976—22no—
32#14582972—22no—
33#14582969—22no—
34#14582956C2211yescharacteristic
35#14582952C2211yescharacteristic
36#14582861C2212yes—
37#14582861C2212yes—
38#14582861C2212yes—
39C22⋊C8×D43C2212yes—
40#14582625C2212yes—
41#14582624C2212yes—
42#14582624C2212yes—
43#14582624C2212yes—
44#14582624C2212yes—
45#14582623C2212yes—
46C2×#126×C43C2211yescharacteristic
47C43×#432C2211yescharacteristic
48C43×#431C2211yescharacteristic
49C43×#324C2212yes—
50C43×#323C2212yes—
51C22×Dic86C2×C411yescharacteristic
52C22×D172C2×C411yescharacteristic
53C22×C22⋊D43C2×C411yescharacteristic
54C22×C22⋊D43C2×C411yescharacteristic
55C23×Dic43C2×C411yescharacteristic
56C22×C4×D43C2×C411yescharacteristic
57C22×C4×D43C2×C411yescharacteristic
58C22×C4×D43C2311yescharacteristic
59C22×C4×D43C2311yescharacteristic
60C2×#10621872—22no—
61C2×#10621872—22no—
62C2×#10621872—22no—
63C2×C8×D43—22no—
64#13063320—22no—
65#13063320—22no—
66#13063317—21no—
67#13063317—21no—
68#13063317—21no—
69#13063317—21no—
70#13063316—22no—
71#13063316—22no—
72#13063310—22no—
73#13063310—22no—
74#13063309—22no—
75#13063309—22no—
76#13063307—22no—
77#13063307—22no—
78#13063307—22no—
79#13063307—22no—
80#13063305—22no—
81#13063305—22no—
82#13063303—22no—
83#13063303—22no—
84#13063302—22no—
85#13063302—22no—
86#13063298—22no—
87#13063298—22no—
88C4×D172D412yes—
89C4×D172D412yes—
90C4×D172D412yes—
91C4×D172D412yes—
92(C22⋊D43)⋊C4—22no—
93(C22⋊D43)⋊C4—22no—
94C2×C4⋊Dic43C2×C411yescharacteristic
95C2×C4⋊Dic43C2×C411yescharacteristic
96C2×C4⋊Dic43C2×C411yescharacteristic
97C2×C4⋊Dic43C2×C411yescharacteristic
98C2×C4⋊Dic43C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×Dic43⋊C4C2×C411yescharacteristic
101C2×Dic43⋊C4C2×C411yescharacteristic
102C2×Dic43⋊C4C2×C411yescharacteristic
103C2×Dic43⋊C4C2311yescharacteristic
104C2×Dic43⋊C4C2311yescharacteristic
105C4⋊C4×D43—22no—
106C4⋊C4×D43—22no—
107C2×C22⋊Dic43C2×C411yescharacteristic
108C2×(C2×D43)⋊C4C2×C411yescharacteristic
109C2×(C2×D43)⋊C4C2×C411yescharacteristic
110C2×(C2×D43)⋊C4C2×C411yescharacteristic
111C2×(C2×D43)⋊C4C2×C411yescharacteristic
112C2×(C2×D43)⋊C4C2×C411yescharacteristic
113C2×(C2×D43)⋊C4C2×C411yescharacteristic
114C2×C4×Dic43C2×C411yescharacteristic
115C4⋊(C43⋊C8)—21no—
116C4⋊(C43⋊C8)—21no—
117C22⋊(C43⋊C8)C2312yes—
118C22⋊(C43⋊C8)C2312yes—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—22no—
122(C2×D43)⋊C8—22no—
123#13063236—21no—
124C4×C43⋊C8—21no—
125#126×C43—21no—
126#126×C43—21no—
127#126×C43—21no—
128#126×C43—21no—
129C2×C4⋊C4×C43C2×C411yescharacteristic
130C2×C4⋊C4×C43C2×C411yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43C2×C411yescharacteristic
133C2×C22⋊C4×C43C2×C411yescharacteristic
134C2×C22⋊C4×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43—21no—
138C22⋊C8×C43C2312yes—
139C22⋊C8×C43C2312yes—
140#97×C43—21no—
141C4×C8×C43—21no—
142C24×C43C22×C411yescharacteristic
143C23×D43C22×C411yescharacteristic
144C23×D43C22×C411yescharacteristic
145C22×C4×C43C22×C411yescharacteristic
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C2×C22⋊D43—22no—
152C2×C22⋊D43—22no—
153C2×C22⋊D43—42no—
154C2×C22⋊D43—81no—
155C22×Dic43—22no—
156C22×Dic43—81no—
157C22×Dic43C22×C411yescharacteristic
158C22×Dic43C22×C411yescharacteristic
159C22×Dic43C22×C411yescharacteristic
160C22×Dic43C22×C411yescharacteristic
161C22×Dic43C22×C411yescharacteristic
162C22×Dic43C22×C411yescharacteristic
163C2×D172—42no—
164C2×D172C22⋊C412yes—
165C2×D172C22⋊C412yes—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—42no—
169C2×C4×D43—81no—
170C2×C4×D43—81no—
171C2×C4×D43—81no—
172C2×C4×D43C2×D412yes—
173C2×C4×D43C2×D412yes—
174C2×C4×D43C2×D412yes—
175C2×C4×D43C2×D412yes—
176C2×Dic86—22no—
177C2×Dic86—81no—
178C2×C8×C43—22no—
179C2×C8×C43—22no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C22⋊C4×C43—21no—
190C22⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C42×C43C2×D411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C42×C43C2×D411yescharacteristic
195C42×C43C2×D411yescharacteristic
196C22⋊Dic43—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4C22⋊C412yes—
202(C2×D43)⋊C4C22⋊C412yes—
203(C2×D43)⋊C4C22⋊C412yes—
204(C2×D43)⋊C4C22⋊C412yes—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—22no—
210C4⋊Dic43—22no—
211C4⋊Dic43C22⋊C412yes—
212C4⋊Dic43C22⋊C412yes—
213Dic43⋊C4—21no—
214Dic43⋊C4—21no—
215Dic43⋊C4—21no—
216Dic43⋊C4—21no—
217Dic43⋊C4—21no—
218Dic43⋊C4—21no—
219Dic43⋊C4—21no—
220Dic43⋊C4—21no—
221Dic43⋊C4—22no—
222Dic43⋊C4—22no—
223C4×Dic43—22no—
224C2×C43⋊C8—22no—
225C2×C43⋊C8—22no—
226#10621872—82no—
227#10621872—82no—
228#10621872—82no—
229C8×D43—82no—
230C23×C43—21no—
231C23×C43—22no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43C23×C411yescharacteristic
235C22×D43—22no—
236C22×D43—22no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—41no—
240C22×D43—41no—
241C22×D43C2×C22⋊C412yes—
242C22×D43C2×C22⋊C412yes—
243C2×C4×C43—22no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—22no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43C2×C22⋊C411yescharacteristic
254C2×C4×C43C2×C22⋊C411yescharacteristic
255C2×C4×C43C2×C22⋊C411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C22⋊D43—44no—
259C22⋊D43—82no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—82no—
271C2×Dic43C2×C22⋊C412yes—
272C2×Dic43C2×C22⋊C412yes—
273D172—42no—
274D172—42no—
275C4×D43—42no—
276C4×D43—42no—
277C4×D43—42no—
278C4×D43—42no—
279C4×D43—44no—
280C4×D43—82no—
281Dic86—82no—
282C8×C43—42no—
283C8×C43—42no—
284C43⋊C8—42no—
285C43⋊C8—42no—
286#17406—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—82no—
293C22×C43C22×C22⋊C411yescharacteristic
294C22×C43#56812yes—
295C2×D43—22no—
296C2×D43—22no—
297C2×D43—22no—
298C2×D43—22no—
299C2×D43—22no—
300C2×D43—22no—
301C2×D43—44no—
302C2×D43—82no—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—21no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—41no—
312Dic43—22no—
313Dic43—22no—
314Dic43—41no—
315Dic43—41no—
316Dic43—41no—
317Dic43—41no—
318C2×#539—431no—
319#2975—431no—
320#2973—431no—
321#1473—431no—
322#1473D4311yescharacteristic, complemented
323#1472—432no—
324#1470—431no—
325#1470—431no—
326#1468—432no—
327#1465—432no—
328#1463—432no—
329C2×C43—22no—
330C2×C43—81no—
331C2×C43#287911yescharacteristic
332C2×C43#288311yescharacteristic
333C2×C43#288911yescharacteristic
334D43—42no—
335D43—42no—
336#539—862no—
337#539—862no—
338#539—862no—
339#539—862no—
340C2×#126—431no—
341C2×#126C2×D4311yescharacteristic
342C2×#125—431no—
343C2×#125—431no—
344C2×#123—431no—
345C2×#123—431no—
346C2×#123—431no—
347C2×#123—431no—
348C2×C22⋊Q8—431no—
349C2×C22⋊Q8—431no—
350C2×C22⋊Q8—431no—
351C2×#121—431no—
352C2×C4×D4—431no—
353C2×C4×D4—431no—
354C22×C4⋊C4—431no—
355#436—862no—
356#436—862no—
357#435—862no—
358#435—862no—
359#432—431no—
360#432C2×D4311yescharacteristic
361#431—431no—
362#431C2×D4311yescharacteristic
363#407—432no—
364#407—432no—
365#407—432no—
366C2×C22⋊C8—432no—
367#324—432no—
368#324—432no—
369#324—432no—
370#324—432no—
371#324—432no—
372#324C2×D4312yes—
373#323—432no—
374#323C2×D4312yes—
375C43#1740611yescharacteristic, complemented, Sylow
376C22×Q8—431no—
377C22×D4—431no—
378C22×D4—431no—
379C22×D4—431no—
380C23×C4—431no—
381C23×C4—431no—
382C23×C4—431no—
383C23×C4—431no—
384C23×C4—431no—
385C2×M16—862no—
386C2×M16—862no—
387C2×M16—862no—
388C22×C8—862no—
389#126—21no—
390#126—21no—
391#126—21no—
392#126—21no—
393#126—862no—
394#126—862no—
395#125—862no—
396#125—862no—
397#125—861no—
398#125—861no—
399#125—861no—
400#125—861no—
401#123—862no—
402#123—862no—
403#123—862no—
404#123—862no—
405#123—862no—
406#123—862no—
407#123—862no—
408#123—862no—
409C22⋊Q8—862no—
410C22⋊Q8—862no—
411C22⋊Q8—862no—
412C22⋊Q8—862no—
413C22⋊Q8—862no—
414C22⋊Q8—862no—
415#121—862no—
416#121—862no—
417C4×D4—432no—
418C4×D4—432no—
419C4×D4—432no—
420C4×D4—432no—
421C4×D4—862no—
422C4×D4—862no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—862no—
435C2×C4⋊C4—862no—
436C2×C4⋊C4C4×D4311yescharacteristic
437C2×C4⋊C4C4×D4311yescharacteristic
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C22⋊C4—431no—
440C2×C22⋊C4—431no—
441C2×C22⋊C4—431no—
442C2×C22⋊C4—431no—
443C2×C22⋊C4—431no—
444C2×C22⋊C4—431no—
445C2×C22⋊C4—431no—
446C2×C22⋊C4C4×D4311yescharacteristic
447C2×C22⋊C4C4×D4311yescharacteristic
448C2×C22⋊C4C22×D4311yescharacteristic
449C2×C42—431no—
450C2×C42C22×D4311yescharacteristic
451C4⋊C8—21no—
452C4⋊C8—21no—
453C4⋊C8—861no—
454C4⋊C8—861no—
455C22⋊C8—432no—
456C22⋊C8—432no—
457C22⋊C8—862no—
458C22⋊C8—862no—
459C22⋊C8—862no—
460C22⋊C8—862no—
461C22⋊C8C22×D4312yes—
462C22⋊C8C22×D4312yes—
463#97—21no—
464#97—861no—
465C4×C8—21no—
466C4×C8—861no—
467C24—431no—
468C24—431no—
469C24C2×C4×D4311yescharacteristic
470C2×Q8—862no—
471C2×Q8—3441no—
472C2×D4—432no—
473C2×D4—432no—
474C2×D4—862no—
475C2×D4—862no—
476C2×D4—3441no—
477C2×D4—1722no—
478C2×D4—1722no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—432no—
482C22×C4—432no—
483C22×C4—432no—
484C22×C4—432no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—3441no—
493C22×C4—3441no—
494C22×C4—3441no—
495C22×C4—3441no—
496C22×C4—1722no—
497C22×C4C2×C4×D4311yescharacteristic
498C22×C4C2×C4×D4311yescharacteristic
499C22×C4C2×C4×D4311yescharacteristic
500C22×C4C2×C4×D4311yescharacteristic
501C22×C4C2×C4×D4311yescharacteristic
502C22×C4C23×D4311yescharacteristic
503M16—3442no—
504M16—3442no—
505M16—3442no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—862no—
509C2×C8—862no—
510C2×C8—3442no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—432no—
518C4⋊C4—432no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—432no—
542C22⋊C4—432no—
543C22⋊C4—432no—
544C22⋊C4—432no—
545C22⋊C4—862no—
546C22⋊C4—862no—
547C22⋊C4—862no—
548C22⋊C4—862no—
549C22⋊C4—862no—
550C42—862no—
551C42D4×D4311yescharacteristic
552C42D4×D4311yescharacteristic
553C42D4×D4311yescharacteristic
554C42D4×D4311yescharacteristic
555C23—21no—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—432no—
560C23—432no—
561C23—862no—
562C23—862no—
563C23—1721no—
564C23—1721no—
565C23—1721no—
566C23—1721no—
567C23C22×C4×D4311yescharacteristic
568Q8—3442no—
569D4—3442no—
570D4—1722no—
571D4—1722no—
572D4—1724no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—432no—
583C2×C4—432no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—3442no—
591C2×C4—3442no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1724no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4C22⋊C4×D4311yescharacteristic
602C2×C4C22⋊C4×D4311yescharacteristic
603C2×C4C22⋊C4×D4311yescharacteristic
604C2×C4C22⋊C4×D4311yescharacteristic
605C2×C4C2×D4×D4311yescharacteristic
606C2×C4C2×D4×D4311yescharacteristic
607C8—42no—
608C8—42no—
609C8—1722no—
610C8—1722no—
611C22—21no—
612C22—21no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—82no—
617C22—862no—
618C22—862no—
619C22—862no—
620C22—862no—
621C22—862no—
622C22—862no—
623C22—3442no—
624C22—1724no—
625C22C2×C22⋊C4×D4311yescharacteristic
626C22#1458366412yes—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—862no—
637C4—862no—
638C4—1721no—
639C4—1721no—
640C4—1721no—
641C4—1721no—
642C2—22no—
643C2—81no—
644C2—1722no—
645C2—1722no—
646C2#1914303711yescharacteristic
647C2#1914305411yescharacteristic
648C2#1914307611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1473C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063298C4
cosocleC22×C4×C43C24
hypercenter#1473D43
hypocenterC43#17406
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1473

Complements

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

NH ≅ G/Ntype
2. #19143635C2semidirect
3. #19143623C2semidirect
4. #19132964C2semidirect
5. #19132957C2semidirect
6. #19132952C2semidirect
7. #19132950C2semidirect
8. #19132940C2semidirect
9. #19132930C2semidirect
10. #19132923C2semidirect
11. C43×#1473C2semidirect
322. #1473D43semidirect
375. C43#17406semidirect

Maximal subgroups

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

subgroupindex
C2×#145834902
#191436352
#191436232
#191329642
#191329572
#191329522
#191329502
#191329402
#191329302
#191329232
C43×#14732
#1740643