Finite Group Databasebeta

← #25062745

Subgroups — #25062745

Order 11008.

952 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583496C211yesmaximal, characteristic
2#19143634C211yesmaximal, characteristic, complemented
3#19143622C211yesmaximal, characteristic, complemented
4#19132963C212yesmaximal, complemented
5#19132957C212yesmaximal, complemented
6#19132949C212yesmaximal, complemented
7#19132942C212yesmaximal, complemented
8#19132931C211yesmaximal, characteristic, complemented
9#19132931C211yesmaximal, characteristic, complemented
10#19132925C211yesmaximal, characteristic, complemented
11C43×#1463C211yesmaximal, characteristic, complemented
12#14583496—22no—
13#14583496—22no—
14#14583496—22no—
15#14583496—22no—
16C2×#13063320C411yescharacteristic
17C2×#13063320C2211yescharacteristic
18C2×#13063315C411yescharacteristic
19C2×#13063315C2211yescharacteristic
20C2×#13063310C411yescharacteristic
21C2×#13063310C2211yescharacteristic
22C2×#13063308C411yescharacteristic
23C2×#13063308C411yescharacteristic
24C2×#13063304C411yescharacteristic
25C2×#13063303C411yescharacteristic
26C2×#13063303C2211yescharacteristic
27C2×#13063299C411yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×C4×C22⋊D43C2211yescharacteristic
30#14582975—22no—
31#14582974—22no—
32#14582973—22no—
33#14582968—22no—
34#14582953C2212yes—
35#14582949C2212yes—
36#14582863C2211yescharacteristic
37#14582863C2211yescharacteristic
38#14582861C2212yes—
39C22⋊C8×D43C2212yes—
40#14582625C2212yes—
41#14582625C2212yes—
42#14582624C2212yes—
43#14582624C2212yes—
44#14582622C2212yes—
45#14582622C2212yes—
46C22×C4⋊C4×C43C2211yescharacteristic
47C43×#407C2211yescharacteristic
48C43×#407C2211yescharacteristic
49C43×#324C2212yes—
50C43×#324C2212yes—
51C22×Dic86C2×C411yescharacteristic
52C22×D172C2×C411yescharacteristic
53C22×C22⋊D43C2×C411yescharacteristic
54C22×C22⋊D43C2×C411yescharacteristic
55C22×C4×D43C2×C411yescharacteristic
56C22×C4×D43C2311yescharacteristic
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621872—22no—
60C2×C8×D43—22no—
61#13063320—22no—
62#13063320—22no—
63#13063320—22no—
64#13063320—22no—
65#13063315—22no—
66#13063315—22no—
67#13063315—22no—
68#13063315—22no—
69#13063310—22no—
70#13063310—22no—
71#13063310—22no—
72#13063310—22no—
73#13063308—22no—
74#13063308—22no—
75#13063308—22no—
76#13063308—22no—
77#13063304—22no—
78#13063304—22no—
79#13063303—22no—
80#13063303—22no—
81#13063303—22no—
82#13063303—22no—
83#13063299—22no—
84#13063299—22no—
85C4×C22⋊D43—21no—
86C4×C22⋊D43—21no—
87C4×C22⋊D43—21no—
88C4×C22⋊D43—21no—
89C4×C22⋊D43D412yes—
90C4×C22⋊D43D412yes—
91C4×C22⋊D43D412yes—
92C4×C22⋊D43D412yes—
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×C4⋊Dic43C2×C411yescharacteristic
95C2×Dic43⋊C4C2×C411yescharacteristic
96C2×Dic43⋊C4C2×C411yescharacteristic
97C2×Dic43⋊C4C2×C411yescharacteristic
98C2×Dic43⋊C4C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×Dic43⋊C4C2×C411yescharacteristic
101C2×Dic43⋊C4C2×C411yescharacteristic
102C2×Dic43⋊C4C2311yescharacteristic
103C2×C22⋊Dic43C2×C411yescharacteristic
104C2×C22⋊Dic43C2×C411yescharacteristic
105C2×(C2×D43)⋊C4C2×C411yescharacteristic
106C2×(C2×D43)⋊C4C2×C411yescharacteristic
107C2×(C2×D43)⋊C4C2×C411yescharacteristic
108C2×(C2×D43)⋊C4C2×C411yescharacteristic
109C2×(C2×D43)⋊C4C2×C411yescharacteristic
110C2×(C2×D43)⋊C4C2×C411yescharacteristic
111C2×(C2×D43)⋊C4C2×C411yescharacteristic
112C2×(C2×D43)⋊C4C2311yescharacteristic
113C2×C4×Dic43C2×C411yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)—21no—
119C22⋊(C43⋊C8)C2312yes—
120C22⋊(C43⋊C8)C2312yes—
121(C2×D43)⋊C8—22no—
122(C2×D43)⋊C8—22no—
123#13063235—22no—
124C8×Dic43—22no—
125C23×C4×C43C2×C411yescharacteristic
126C23×C4×C43C2×C411yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C2×M16×C43—21no—
129C2×M16×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2×C411yescharacteristic
135C2×C4⋊C4×C43C2×C411yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C22⋊C8×C43C2312yes—
141C22⋊C8×C43C2312yes—
142C24×C43C22×C411yescharacteristic
143C23×D43C22×C411yescharacteristic
144C23×D43C22×C411yescharacteristic
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—42no—
150C22×C4×C43—81no—
151C22×C4×C43—81no—
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C22×C411yescharacteristic
154C22×C4×C43C22×C411yescharacteristic
155C22×C4×C43C22×C411yescharacteristic
156C22×C4×C43C22×C411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C2×C22⋊D43—21no—
163C2×C22⋊D43—21no—
164C2×C22⋊D43—42no—
165C2×C22⋊D43—42no—
166C2×C22⋊D43C22⋊C412yes—
167C2×C22⋊D43C22⋊C412yes—
168C22×Dic43C22×C411yescharacteristic
169C22×Dic43C22×C411yescharacteristic
170C22×Dic43C22×C411yescharacteristic
171C22×Dic43C22×C411yescharacteristic
172C22×Dic43C22×C411yescharacteristic
173C22×Dic43C22×C411yescharacteristic
174C2×D172—22no—
175C2×D172—81no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—81no—
179C2×C4×D43—81no—
180C2×C4×D43C2×D412yes—
181C2×C4×D43C2×D412yes—
182C2×Dic86—22no—
183C2×Dic86—81no—
184M16×C43—81no—
185M16×C43—81no—
186C2×C8×C43—22no—
187C2×C8×C43—22no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C22⋊Dic43—21no—
197C22⋊Dic43—21no—
198C22⋊Dic43C22⋊C412yes—
199C22⋊Dic43C22⋊C412yes—
200(C2×D43)⋊C4—21no—
201(C2×D43)⋊C4—21no—
202(C2×D43)⋊C4—22no—
203(C2×D43)⋊C4—22no—
204(C2×D43)⋊C4—22no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—22no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4C22⋊C412yes—
209(C2×D43)⋊C4C22⋊C412yes—
210C4⋊Dic43—22no—
211C4⋊Dic43—22no—
212Dic43⋊C4—21no—
213Dic43⋊C4—21no—
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217Dic43⋊C4—22no—
218Dic43⋊C4—22no—
219Dic43⋊C4—22no—
220Dic43⋊C4C22⋊C412yes—
221Dic43⋊C4C22⋊C412yes—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43C2×D412yes—
225C4×Dic43C2×D412yes—
226#10621877—81no—
227#10621877—81no—
228C2×C43⋊C8—22no—
229C2×C43⋊C8—22no—
230#10621872—82no—
231C8×D43—82no—
232C23×C43—22no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43C2×C22⋊C411yescharacteristic
236C23×C43C2×C22⋊C411yescharacteristic
237C23×C43C23×C411yescharacteristic
238C22×D43—22no—
239C22×D43—21no—
240C22×D43—22no—
241C22×D43—41no—
242C22×D43—41no—
243C22×D43—41no—
244C22×D43—41no—
245C22×D43C2×C22⋊C412yes—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—42no—
259C2×C4×C43—42no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—81no—
263C2×C4×C43—81no—
264C2×C4×C43C2×C22⋊C411yescharacteristic
265C2×C4×C43C2×C22⋊C411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C22×D411yescharacteristic
268C22⋊D43—42no—
269C22⋊D43—42no—
270C22⋊D43—42no—
271C22⋊D43—42no—
272C2×Dic43—22no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—22no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43C2×C22⋊C412yes—
282C2×Dic43C2×C22⋊C412yes—
283C2×Dic43C2×C22⋊C412yes—
284D172—82no—
285C4×D43—42no—
286C4×D43—42no—
287C4×D43—81no—
288C4×D43—81no—
289Dic86—82no—
290C8×C43—42no—
291C8×C43—42no—
292C43⋊C8—42no—
293C43⋊C8—42no—
294#17406—431nomaximal, Sylow
295C22×C43—21no—
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—21no—
299C22×C43—21no—
300C22×C43—21no—
301C22×C43—21no—
302C22×C43—21no—
303C22×C43—44no—
304C22×C43C22×C22⋊C411yescharacteristic
305C22×C43#56812yes—
306C2×D43—22no—
307C2×D43—22no—
308C2×D43—22no—
309C2×D43—41no—
310C2×D43—41no—
311C2×D43—41no—
312C2×D43—82no—
313C2×D43—82no—
314C4×C43—21no—
315C4×C43—21no—
316C4×C43—21no—
317C4×C43—21no—
318C4×C43—41no—
319C4×C43—41no—
320C4×C43—41no—
321C4×C43—41no—
322Dic43—22no—
323Dic43—22no—
324Dic43—22no—
325Dic43—41no—
326Dic43—41no—
327Dic43—41no—
328C2×#539—431no—
329#2975—431no—
330#2973—431no—
331#1473—432no—
332#1472—432no—
333#1470—432no—
334#1468—432no—
335#1465—431no—
336#1465—431no—
337#1463—431no—
338#1463D4311yescharacteristic, complemented
339C2×C43—22no—
340C2×C43—41no—
341C2×C43—41no—
342C2×C43#287911yescharacteristic
343C2×C43#288311yescharacteristic
344C2×C43#288911yescharacteristic
345D43—42no—
346D43—81no—
347#539—862no—
348#539—862no—
349#539—862no—
350#539—862no—
351C2×#126—431no—
352C2×#126—431no—
353C2×#125—431no—
354C2×#125—431no—
355C2×#123—431no—
356C2×#123—431no—
357C2×#123—431no—
358C2×#123—431no—
359C2×C22⋊Q8—431no—
360C2×C22⋊Q8—431no—
361C2×C22⋊Q8—431no—
362C2×#121—431no—
363C2×C4×D4—431no—
364C2×C4×D4—431no—
365C22×C4⋊C4C2×D4311yescharacteristic
366#436—862no—
367#436—862no—
368#435—862no—
369#435—862no—
370#432—432no—
371#431—432no—
372#407—431no—
373#407—431no—
374#407—432no—
375#407C2×D4311yescharacteristic
376#407C2×D4311yescharacteristic
377C2×C22⋊C8—432no—
378#324—432no—
379#324—432no—
380#324—432no—
381#324—432no—
382#324C2×D4312yes—
383#324C2×D4312yes—
384#323—432no—
385#323—432no—
386C43#1740611yescharacteristic, complemented, Sylow
387C22×Q8—431no—
388C22×D4—431no—
389C22×D4—431no—
390C22×D4—431no—
391C23×C4—431no—
392C23×C4—431no—
393C23×C4C4×D4311yescharacteristic
394C23×C4C4×D4311yescharacteristic
395C23×C4C22×D4311yescharacteristic
396C2×M16—21no—
397C2×M16—21no—
398C2×M16—862no—
399C2×M16—861no—
400C2×M16—861no—
401C22×C8—862no—
402#126—862no—
403#126—862no—
404#126—862no—
405#126—862no—
406#125—862no—
407#125—862no—
408#125—862no—
409#125—862no—
410#123—862no—
411#123—862no—
412#123—862no—
413#123—862no—
414#123—862no—
415#123—862no—
416#123—862no—
417#123—862no—
418C22⋊Q8—862no—
419C22⋊Q8—862no—
420C22⋊Q8—862no—
421C22⋊Q8—862no—
422C22⋊Q8—862no—
423C22⋊Q8—862no—
424#121—862no—
425#121—862no—
426C4×D4—432no—
427C4×D4—432no—
428C4×D4—432no—
429C4×D4—432no—
430C4×D4—861no—
431C4×D4—861no—
432C4×D4—861no—
433C4×D4—861no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—431no—
445C2×C4⋊C4—431no—
446C2×C4⋊C4—431no—
447C2×C4⋊C4—431no—
448C2×C4⋊C4C4×D4311yescharacteristic
449C2×C4⋊C4C4×D4311yescharacteristic
450C2×C4⋊C4C22×D4311yescharacteristic
451C2×C4⋊C4C22×D4311yescharacteristic
452C2×C22⋊C4—431no—
453C2×C22⋊C4—431no—
454C2×C22⋊C4—431no—
455C2×C22⋊C4—431no—
456C2×C22⋊C4—431no—
457C2×C22⋊C4—431no—
458C2×C22⋊C4—431no—
459C2×C22⋊C4—431no—
460C2×C22⋊C4—431no—
461C2×C22⋊C4—431no—
462C2×C42—431no—
463C2×C42—431no—
464C4⋊C8—862no—
465C4⋊C8—862no—
466C22⋊C8—21no—
467C22⋊C8—21no—
468C22⋊C8—432no—
469C22⋊C8—432no—
470C22⋊C8—862no—
471C22⋊C8—862no—
472C22⋊C8—861no—
473C22⋊C8—861no—
474C22⋊C8C22×D4312yes—
475C22⋊C8C22×D4312yes—
476#97—862no—
477C4×C8—862no—
478C24—431no—
479C24—431no—
480C24C2×C4×D4311yescharacteristic
481C2×Q8—862no—
482C2×Q8—3441no—
483C2×D4—432no—
484C2×D4—432no—
485C2×D4—862no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—3441no—
489C2×D4—1722no—
490C2×D4—1722no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—42no—
496C22×C4—81no—
497C22×C4—81no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—432no—
502C22×C4—432no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—3441no—
509C22×C4—3441no—
510C22×C4C2×C4×D4311yescharacteristic
511C22×C4C2×C4×D4311yescharacteristic
512C22×C4C2×C4×D4311yescharacteristic
513C22×C4C2×C4×D4311yescharacteristic
514C22×C4C2×C4×D4311yescharacteristic
515C22×C4D4×D4311yescharacteristic
516C22×C4D4×D4311yescharacteristic
517C22×C4D4×D4311yescharacteristic
518C22×C4D4×D4311yescharacteristic
519C22×C4C23×D4311yescharacteristic
520M16—81no—
521M16—81no—
522M16—3442no—
523M16—3441no—
524M16—3441no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—862no—
528C2×C8—862no—
529C2×C8—3442no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—432no—
539C4⋊C4—432no—
540C4⋊C4—862no—
541C4⋊C4—862no—
542C4⋊C4—862no—
543C4⋊C4—862no—
544C4⋊C4—862no—
545C4⋊C4—862no—
546C4⋊C4—862no—
547C4⋊C4—862no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C22⋊C4—432no—
551C22⋊C4—432no—
552C22⋊C4—432no—
553C22⋊C4—432no—
554C22⋊C4—862no—
555C22⋊C4—862no—
556C22⋊C4—862no—
557C22⋊C4—862no—
558C22⋊C4—862no—
559C22⋊C4—862no—
560C22⋊C4—861no—
561C22⋊C4—861no—
562C22⋊C4—861no—
563C22⋊C4—861no—
564C42—432no—
565C42—432no—
566C42—861no—
567C42—861no—
568C23—22no—
569C23—41no—
570C23—41no—
571C23—432no—
572C23—862no—
573C23—862no—
574C23—861no—
575C23—1721no—
576C23—1721no—
577C23—1721no—
578C23—1721no—
579C23C22⋊C4×D4311yescharacteristic
580C23C22⋊C4×D4311yescharacteristic
581C23C22×C4×D4311yescharacteristic
582Q8—3442no—
583D4—3442no—
584D4—1722no—
585D4—1722no—
586D4—1722no—
587D4—1722no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—81no—
605C2×C4—81no—
606C2×C4—432no—
607C2×C4—432no—
608C2×C4—432no—
609C2×C4—862no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—862no—
614C2×C4—3441no—
615C2×C4—3441no—
616C2×C4—1722no—
617C2×C4—1722no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4C22⋊C4×D4311yescharacteristic
623C2×C4C22⋊C4×D4311yescharacteristic
624C2×C4C2×D4×D4311yescharacteristic
625C2×C4C2×D4×D4311yescharacteristic
626C8—42no—
627C8—42no—
628C8—1722no—
629C8—1722no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—21no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—44no—
639C22—862no—
640C22—862no—
641C22—862no—
642C22—3442no—
643C22—3442no—
644C22—1721no—
645C22—1721no—
646C22—1721no—
647C22C2×C22⋊C4×D4311yescharacteristic
648C22#1458366512yes—
649C4—21no—
650C4—21no—
651C4—21no—
652C4—21no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—862no—
658C4—862no—
659C4—862no—
660C4—1721no—
661C4—1721no—
662C4—1721no—
663C2—22no—
664C2—41no—
665C2—41no—
666C2—3441no—
667C2—1722no—
668C2#1914303811yescharacteristic
669C2#1914305311yescharacteristic
670C2#1914307511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1463C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063299C4
cosocleC22×C4×C43C24
hypercenter#1463D43
hypocenterC43#17406
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. #19143634C2semidirect
3. #19143622C2semidirect
4. #19132963C2semidirect
5. #19132957C2semidirect
6. #19132949C2semidirect
7. #19132942C2semidirect
8. #19132931C2semidirect
9. #19132931C2semidirect
10. #19132925C2semidirect
11. C43×#1463C2semidirect
338. #1463D43semidirect
386. C43#17406semidirect

Maximal subgroups

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

subgroupindex
C2×#145834962
#191436342
#191436222
#191329632
#191329572
#191329492
#191329422
#191329312
#191329252
C43×#14632
#1740643