Finite Group Databasebeta

← #25063420

Subgroups — #25063420

Order 11008.

1112 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147892C211yesmaximal, characteristic
2#423×D43C211yesmaximal, characteristic, complemented
3C2×C4×#10621872C211yesmaximal, characteristic, complemented
4#19133050C211yesmaximal, characteristic, complemented
5#19133047C211yesmaximal, characteristic, complemented
6#19133045C211yesmaximal, characteristic, complemented
7#19133033C214yesmaximal, complemented
8#19133007C214yesmaximal, complemented
9C43×#1493C211yesmaximal, characteristic, complemented
10C22×#10621872—21no—
11C2×M16×D43—21no—
12#14583454C411yescharacteristic
13#14583454C411yescharacteristic
14#14583450C411yescharacteristic
15#14583450C411yescharacteristic
16#14583449C2211yescharacteristic
17#14583436—21no—
18#14583436C2212yes—
19#14583435—21no—
20#14583435C412yes—
21#14583434—21no—
22#14583434—21no—
23#14583412—21no—
24#14583412C412yes—
25#14583411—21no—
26C4×#10621902—21no—
27C4×#10621902C2212yes—
28#14583367—21no—
29C2×C42×D43C2211yescharacteristic
30#14582923C2211yescharacteristic
31#14582922—21no—
32#14582921—21no—
33#14582921C2212yes—
34C4⋊C8×D43—21no—
35C4⋊C8×D43C2212yes—
36C4×#10621872—21no—
37C4×#10621872—21no—
38C4×#10621872C2212yes—
39C4×#10621872C2212yes—
40C2×#13063235—21no—
41C2×C4×C43⋊C8C2211yescharacteristic
42Q8⋊(C43⋊C8)C2214yescomplemented
43#14582628C2214yescomplemented
44#14582626C2214yescomplemented
45C43×#533C2211yescharacteristic
46C43×#423C2211yescharacteristic
47C2×C4×C8×C43C2211yescharacteristic
48C43×Q8⋊C8C2214yescomplemented
49C2×#10621902—21no—
50C2×#10621902C2×C412yes—
51C2×#10621898—21no—
52C22×C4×D43C2×C411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C22×C4×D43D411yescharacteristic
55C2×#10621877—21no—
56C2×#10621872—28no—
57C2×#10621872—22no—
58C2×#10621872—22no—
59C2×#10621872—22no—
60M16×D43—44no—
61C22×C43⋊C8—21no—
62C2×C8×D43—22no—
63#13063325C2×C411yescharacteristic
64#13063322C2×C411yescharacteristic
65#13063320—22no—
66#13063320—22no—
67#13063316—21no—
68#13063316C2×C412yes—
69#13063314—21no—
70#13063314C2×C412yes—
71#13063313—21no—
72#13063310—22no—
73#13063310—22no—
74#13063309—22no—
75#13063305—21no—
76#13063305—21no—
77#13063301—21no—
78#13063301C2×C412yes—
79#13063300—21no—
80#13063300—21no—
81#13063300—21no—
82#13063300C2×C412yes—
83#13063299—21no—
84#13063299C2×C412yes—
85#13063295—22no—
86Q8×Dic43—21no—
87Q8×Dic43C2×C412yes—
88#13063290—21no—
89#13063290—21no—
90C4×D172—22no—
91C4×D172—22no—
92C4×D172—21no—
93C4×D172C2312yes—
94#13063287—22no—
95#13063287—22no—
96#13063287—21no—
97#13063287—21no—
98#13063287—21no—
99#13063287C2×C412yes—
100(C22⋊D43)⋊C4—22no—
101(C22⋊D43)⋊C4—22no—
102#13063283—21no—
103#13063283—22no—
104#13063283—22no—
105#13063283C2×C412yes—
106#13063282—22no—
107C2×C4×Dic43C2×C411yescharacteristic
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43D411yescharacteristic
110C42×D43—22no—
111C42×D43C2×C411yescharacteristic
112C42×D43C2×C411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43D411yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43C2311yescharacteristic
118C42×D43C2311yescharacteristic
119C4⋊(C43⋊C8)—21no—
120C4⋊(C43⋊C8)C2312yes—
121Dic43⋊C8—22no—
122Dic43⋊C8—22no—
123#13063235—22no—
124#13063235—22no—
125C4×C43⋊C8—21no—
126C4×C43⋊C8C2312yes—
127C2×M16×C43—21no—
128C22×C8×C43—21no—
129C4⋊Q8×C43C2×C411yescharacteristic
130C4⋊Q8×C43C2×C411yescharacteristic
131#125×C43—21no—
132C22⋊Q8×C43—21no—
133C22⋊Q8×C43C2×C412yes—
134C4×Q8×C43—21no—
135C4×Q8×C43C2312yes—
136#117×C43—21no—
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2312yes—
140C4×C8×C43—21no—
141C4×C8×C43C2312yes—
142C23×D43C22⋊C411yescharacteristic
143C2×Q8×C43—21no—
144C2×Q8×C43C22×C412yes—
145C22×C4×C43C22×C411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C2×C22⋊D43—22no—
149C22×Dic43C22⋊C411yescharacteristic
150C22×Dic43C22⋊C411yescharacteristic
151C22×Dic43C22⋊C411yescharacteristic
152#10621902—44no—
153#10621902—44no—
154#10621898—42no—
155#10621898—42no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—22no—
159C2×D172—22no—
160C2×D172C22×C412yes—
161C2×C4×D43—22no—
162C2×C4×D43—22no—
163C2×C4×D43—24no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—42no—
168C2×C4×D43C22⋊C411yescharacteristic
169C2×C4×D43C22⋊C411yescharacteristic
170C2×C4×D43C22⋊C411yescharacteristic
171C2×C4×D43C22⋊C411yescharacteristic
172C2×C4×D43C22⋊C411yescharacteristic
173C2×C4×D43C22⋊C411yescharacteristic
174C2×C4×D43C22×C411yescharacteristic
175C2×C4×D43C22×C411yescharacteristic
176C2×C4×D43C2×D411yescharacteristic
177C2×C4×D43C2×D411yescharacteristic
178C2×C4×D43C2×D411yescharacteristic
179C2×C4×D43C2×D411yescharacteristic
180C2×Dic86—21no—
181M16×C43—42no—
182C2×C8×C43—24no—
183C2×C8×C43—22no—
184C2×C8×C43—22no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—22no—
190C4⋊C4×C43C22×C412yes—
191C22⋊C4×C43—22no—
192C42×C43—22no—
193C42×C43C22×C411yescharacteristic
194C42×C43C2×D411yescharacteristic
195C42×C43C2×D411yescharacteristic
196C42×C43C2411yescharacteristic
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—22no—
203(C2×D43)⋊C4—22no—
204(C2×D43)⋊C4—22no—
205C4⋊Dic43—21no—
206C4⋊Dic43—22no—
207C4⋊Dic43—22no—
208C4⋊Dic43C22×C412yes—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211C4×Dic43—22no—
212C4×Dic43—22no—
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22×C411yescharacteristic
220C4×Dic43C22×C411yescharacteristic
221C4×Dic43C2×D411yescharacteristic
222C4×Dic43C2×D411yescharacteristic
223C4×Dic43C2×D411yescharacteristic
224C4×Dic43C2×D411yescharacteristic
225#10621877—42no—
226C2×C43⋊C8—24no—
227C2×C43⋊C8—22no—
228C2×C43⋊C8—22no—
229#10621872—28no—
230#10621872—28no—
231#10621872—44no—
232C8×D43—44no—
233C23×C43C2×C22⋊C411yescharacteristic
234C22×D43—22no—
235C22×D43—22no—
236C22×D43—22no—
237C22×D43—41no—
238C22×D43C2×C22⋊C411yescharacteristic
239C22×D43C2×C22⋊C411yescharacteristic
240Q8×C43—24no—
241Q8×C43—42no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43AGL(1,ℤ/8)12yes—
250C2×C4×C43#13712yes—
251C2×C4×C43C23×C411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C22⋊D43—44no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—41no—
259C2×Dic43C2×C22⋊C411yescharacteristic
260C2×Dic43C2×C22⋊C411yescharacteristic
261C2×Dic43C2×C22⋊C411yescharacteristic
262C2×Dic43C2×C22⋊C411yescharacteristic
263C2×Dic43C2×C22⋊C411yescharacteristic
264C2×Dic43C2×C22⋊C411yescharacteristic
265D172—24no—
266D172—44no—
267D172—44no—
268D172—42no—
269D172—42no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—21no—
274C4×D43—21no—
275C4×D43—21no—
276C4×D43—21no—
277C4×D43—22no—
278C4×D43—22no—
279C4×D43—22no—
280C4×D43—22no—
281C4×D43—41no—
282C4×D43—41no—
283C4×D43—44no—
284C4×D43—42no—
285C4×D43—42no—
286C4×D43—44no—
287C4×D43#10414yes—
288Dic86—42no—
289C8×C43—24no—
290C8×C43—42no—
291C43⋊C8—24no—
292C43⋊C8—42no—
293#17504—431nomaximal, Sylow
294C22×C43—21no—
295C22×C43—21no—
296C22×C43#41712yes—
297C22×C43C22×C22⋊C411yescharacteristic
298C2×D43—21no—
299C2×D43—21no—
300C2×D43—21no—
301C2×D43—21no—
302C2×D43—21no—
303C2×D43—44no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43C2×#10412yes—
308C4×C43—21no—
309C4×C43—21no—
310C4×C43—42no—
311C4×C43—42no—
312C4×C43#41712yes—
313C4×C43C2×#10412yes—
314C4×C43#56812yes—
315C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
316C4×C43C2×#13711yescharacteristic
317Dic43—21no—
318Dic43—21no—
319Dic43—21no—
320Dic43—21no—
321Dic43—21no—
322Dic43—42no—
323Dic43C2×#10412yes—
324#3444—431no—
325C2×#423—431no—
326C2×C4×M16—431no—
327#1493—431no—
328#1493D4311yescharacteristic, complemented
329#1492—431no—
330#1492—431no—
331#1489—434no—
332#1483—434no—
333C2×C43—22no—
334C2×C43#287911yescharacteristic
335C2×C43C2×#41711yescharacteristic
336C2×C43C22×#10411yescharacteristic
337D43—22no—
338D43—41no—
339D43—82no—
340C22×M16—861no—
341C22×M16—861no—
342#533—431no—
343#533—431no—
344#533C2×D4311yescharacteristic
345#532—431no—
346#532—431no—
347#532—431no—
348#529—432no—
349#529—432no—
350#529—861no—
351#529—861no—
352#529—861no—
353#529—861no—
354#525—432no—
355#525—861no—
356#525—861no—
357C4×#41—432no—
358C4×#41—861no—
359C4×#41—861no—
360C22×C42—431no—
361#423—431no—
362#423—432no—
363#423—861no—
364#423—861no—
365#423C2×D4311yescharacteristic
366C2×C4⋊C8—432no—
367C2×C4⋊C8—861no—
368C4×M16—432no—
369C4×M16—432no—
370C4×M16—861no—
371C4×M16—861no—
372C2×#97—861no—
373C2×C4×C8—431no—
374C2×C4×C8C2×D4311yescharacteristic
375Q8⋊C8—434no—
376Q8⋊C8C2×D4314yescomplemented
377D4⋊C8—434no—
378D4⋊C8—434no—
379C43#1750411yescharacteristic, complemented, Sylow
380C2×#41—432no—
381C2×#41—861no—
382C2×#41—861no—
383C23×C4—431no—
384C23×C4—431no—
385C23×C4—431no—
386C2×M16—21no—
387C2×M16—862no—
388C2×M16—862no—
389C2×M16—868no—
390C2×M16—862no—
391C2×M16—861no—
392C2×M16—1724no—
393C22×C8—21no—
394C22×C8—862no—
395C22×C8—861no—
396C4⋊Q8—431no—
397C4⋊Q8C4×D4311yescharacteristic
398C4⋊Q8C4×D4311yescharacteristic
399#127—431no—
400#126—862no—
401#126—862no—
402#125—21no—
403#125—432no—
404#125—861no—
405#124—432no—
406#124—861no—
407#124—861no—
408#123—862no—
409#123—862no—
410#123—862no—
411C22⋊Q8—21no—
412C22⋊Q8—432no—
413C22⋊Q8—861no—
414C22⋊Q8—861no—
415C22⋊Q8—861no—
416C22⋊Q8C4×D4312yes—
417#121—432no—
418#121—432no—
419#121—861no—
420#121—861no—
421#121—861no—
422#121—861no—
423#120—862no—
424C4×Q8—21no—
425C4×Q8—432no—
426C4×Q8—861no—
427C4×Q8—861no—
428C4×Q8—861no—
429C4×Q8C22×D4312yes—
430C4×D4—432no—
431C4×D4—432no—
432C4×D4—862no—
433C4×D4—862no—
434C4×D4—861no—
435C4×D4—861no—
436C4×D4—861no—
437C4×D4—862no—
438C4×D4—862no—
439C4×D4—862no—
440C4×D4—862no—
441C4×D4—861no—
442#117—21no—
443#117—432no—
444#117—862no—
445#117—862no—
446#117—862no—
447#117—861no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—431no—
451C2×C42—431no—
452C2×C42—431no—
453C2×C42—431no—
454C2×C42—431no—
455C2×C42—431no—
456C2×C42—431no—
457C2×C42—431no—
458C2×C42—431no—
459C2×C42—862no—
460C2×C42C22×D4311yescharacteristic
461C4⋊C8—21no—
462C4⋊C8—432no—
463C4⋊C8—862no—
464C4⋊C8—862no—
465C4⋊C8—861no—
466C4⋊C8C22×D4312yes—
467#97—862no—
468#97—862no—
469C4×C8—21no—
470C4×C8—432no—
471C4×C8—861no—
472C4×C8C22×D4312yes—
473C24—431no—
474#41—1724no—
475#41—1724no—
476#41—1722no—
477#41—1722no—
478C2×Q8—21no—
479C2×Q8—861no—
480C2×Q8C2×C4×D4312yes—
481C2×D4—432no—
482C2×D4—862no—
483C2×D4—862no—
484C2×D4—862no—
485C2×D4—861no—
486C2×D4—861no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—864no—
503C22×C4—862no—
504C22×C4—862no—
505C22×C4—862no—
506C22×C4—862no—
507C22×C4—862no—
508C22×C4—1722no—
509C22×C4C2×C4×D4311yescharacteristic
510C22×C4D4×D4311yescharacteristic
511C22×C4D4×D4311yescharacteristic
512M16—42no—
513M16—868no—
514M16—868no—
515M16—1724no—
516M16—1722no—
517C2×C8—24no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—864no—
521C2×C8—862no—
522C2×C8—862no—
523C2×C8—1724no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—432no—
530C4⋊C4—862no—
531C4⋊C4—862no—
532C4⋊C4—862no—
533C4⋊C4—862no—
534C4⋊C4—861no—
535C4⋊C4C2×C4×D4312yes—
536C22⋊C4—22no—
537C22⋊C4—862no—
538C22⋊C4—862no—
539C22⋊C4—862no—
540C22⋊C4—862no—
541C22⋊C4—862no—
542C22⋊C4—862no—
543C22⋊C4—862no—
544C22⋊C4—862no—
545C42—22no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—431no—
550C42—431no—
551C42—431no—
552C42—431no—
553C42—431no—
554C42—431no—
555C42—431no—
556C42—431no—
557C42—431no—
558C42—862no—
559C42—862no—
560C42C2×C4×D4311yescharacteristic
561C42D4×D4311yescharacteristic
562C42D4×D4311yescharacteristic
563C42C23×D4311yescharacteristic
564C23—431no—
565C23—431no—
566C23—862no—
567C23—862no—
568C23—862no—
569C23—1721no—
570C23C22⋊C4×D4311yescharacteristic
571Q8—24no—
572Q8—42no—
573Q8—1722no—
574D4—864no—
575D4—1724no—
576D4—1724no—
577D4—1724no—
578D4—1722no—
579D4—1722no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—431no—
585C2×C4—434no—
586C2×C4—431no—
587C2×C4—431no—
588C2×C4—431no—
589C2×C4—431no—
590C2×C4—431no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—862no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1724no—
608C2×C4—1724no—
609C2×C4—1721no—
610C2×C4—1722no—
611C2×C4—1722no—
612C2×C4C22⋊C4×D4311yescharacteristic
613C2×C4C22⋊C4×D4311yescharacteristic
614C2×C4C22⋊C4×D4311yescharacteristic
615C2×C4#1306335212yes—
616C2×C4#1306335712yes—
617C2×C4C22×C4×D4311yescharacteristic
618C2×C4C2×D4×D4311yescharacteristic
619C2×C4C2×D4×D4311yescharacteristic
620C8—24no—
621C8—42no—
622C8—864no—
623C8—1722no—
624C22—21no—
625C22—21no—
626C22—432no—
627C22—861no—
628C22—861no—
629C22—861no—
630C22—861no—
631C22—861no—
632C22—1724no—
633C22—1722no—
634C22—1722no—
635C22—1722no—
636C22#1458289912yes—
637C22C2×C22⋊C4×D4311yescharacteristic
638C4—21no—
639C4—21no—
640C4—42no—
641C4—42no—
642C4—432no—
643C4—861no—
644C4—861no—
645C4—861no—
646C4—861no—
647C4—861no—
648C4—1722no—
649C4#1458289912yes—
650C4#104×D4312yes—
651C4#1458366412yes—
652C4C2×#1306335211yescharacteristic
653C4C2×#1306335711yescharacteristic
654C2—22no—
655C2—862no—
656C2—3442no—
657C2—1721no—
658C2#1914303711yescharacteristic
659C2C2×#1458289911yescharacteristic
660C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1493C2
socleC22×C43C22×C22⋊C4
prime radical#19147892C2
cosocleC42×C43C24
hypercenter#1493D43
hypocenterC43#17504
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
2. #423×D43C2semidirect
3. C2×C4×#10621872C2semidirect
4. #19133050C2semidirect
5. #19133047C2semidirect
6. #19133045C2semidirect
7. #19133033C2semidirect
8. #19133007C2semidirect
9. C43×#1493C2semidirect
42. Q8⋊(C43⋊C8)C22semidirect
43. #14582628C22semidirect
44. #14582626C22semidirect
48. C43×Q8⋊C8C22semidirect
328. #1493D43semidirect
376. Q8⋊C8C2×D43semidirect
379. C43#17504semidirect

Maximal subgroups

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

subgroupindex
#191478922
#423×D432
C2×C4×#106218722
#191330502
#191330472
#191330452
#191330332
#191330072
C43×#14932
#1750443