Finite Group Databasebeta

← #25062876

Subgroups — #25062876

Order 11008.

922 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583582C211yesmaximal, characteristic
2#19143682C212yesmaximal, complemented
3#19132963C212yesmaximal, complemented
4#19132962C212yesmaximal, complemented
5#19132949C212yesmaximal, complemented
6#19132934C211yesmaximal, characteristic
7#19132929C211yesmaximal, characteristic, complemented
8#19132926C211yesmaximal, characteristic, complemented
9#19132914C211yesmaximal, characteristic
10#19132906C211yesmaximal, characteristic, complemented
11C43×#1458C211yesmaximal, characteristic, complemented
12#14583582—22no—
13#14583582—22no—
14#14583582—22no—
15#14583582—22no—
16C2×#13063320C2211yescharacteristic
17C2×#13063319C2211yescharacteristic
18C2×#13063317C411yescharacteristic
19C2×#13063315C411yescharacteristic
20C2×#13063315C2211yescharacteristic
21C2×#13063309C411yescharacteristic
22C2×#13063308C411yescharacteristic
23C2×#13063303C411yescharacteristic
24C2×#13063302C411yescharacteristic
25C2×C4×Dic86C2211yescharacteristic
26C2×(C22⋊D43)⋊C4C2211yescharacteristic
27C2×#13063282C411yescharacteristic
28C2×#13063281C2211yescharacteristic
29C22×Dic43⋊C4C411yescharacteristic
30#14583029—22no—
31#14583028—22no—
32#14583028—22no—
33C8×Dic86—22no—
34#14582956C2212yes—
35#14582953C2212yes—
36#14582953C2212yes—
37#14582949C2212yes—
38#14582949C2212yes—
39#14582625C2212yes—
40#14582624C2212yes—
41#14582624C2212yes—
42#14582623C2211yescharacteristic
43#14582623C2211yescharacteristic
44#14582622C2212yes—
45#14582622C2212yes—
46C2×#117×C43C2211yescharacteristic
47C43×#431C2212yes—
48C43×#324C2212yes—
49C43×#323C2211yescharacteristic
50C43×#323C2211yescharacteristic
51C22×Dic86C2×C411yescharacteristic
52C22×C22⋊D43C2×C411yescharacteristic
53C23×Dic43C2×C411yescharacteristic
54C23×Dic43C2×C411yescharacteristic
55C22×C4×D43C2×C411yescharacteristic
56#13063320—22no—
57#13063320—22no—
58#13063319—22no—
59#13063319—22no—
60#13063317—22no—
61#13063317—22no—
62#13063315—22no—
63#13063315—22no—
64#13063315—22no—
65#13063315—22no—
66#13063309—22no—
67#13063309—22no—
68#13063308—22no—
69#13063308—22no—
70#13063303—22no—
71#13063303—22no—
72#13063302—22no—
73#13063302—22no—
74C4×Dic86D412yes—
75C4×Dic86D412yes—
76C4×Dic86D412yes—
77C4×Dic86D412yes—
78(C22⋊D43)⋊C4—22no—
79(C22⋊D43)⋊C4—22no—
80#13063282—21no—
81#13063282—21no—
82#13063282—21no—
83#13063282—21no—
84#13063281—22no—
85#13063281—22no—
86C2×C4⋊Dic43C2×C411yescharacteristic
87C2×C4⋊Dic43C2×C411yescharacteristic
88C2×C4⋊Dic43C2×C411yescharacteristic
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4C2×C411yescharacteristic
94C2×Dic43⋊C4C2×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⋊C4C2×C411yescharacteristic
103C2×Dic43⋊C4C2311yescharacteristic
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)⋊C4C2311yescharacteristic
110C2×C4×Dic43C2×C411yescharacteristic
111C2×C4×Dic43C2311yescharacteristic
112C2×C4×Dic43C2311yescharacteristic
113C4⋊(C43⋊C8)—22no—
114Dic43⋊C8—22no—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117Dic43⋊C8—22no—
118C22⋊(C43⋊C8)C2312yes—
119C22⋊(C43⋊C8)C2312yes—
120#13063236—22no—
121#13063235—22no—
122#13063235—22no—
123C8×Dic43—22no—
124C8×Dic43—22no—
125C23×C4×C43C2×C411yescharacteristic
126#117×C43—22no—
127#117×C43—22no—
128C2×C4⋊C4×C43C2×C411yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43C2×C411yescharacteristic
131C2×C22⋊C4×C43C2311yescharacteristic
132C2×C42×C43C2×C411yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—22no—
135C22⋊C8×C43C2312yes—
136C22⋊C8×C43C2312yes—
137C4×C8×C43—22no—
138C24×C43C22×C411yescharacteristic
139C23×D43C22×C411yescharacteristic
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—22no—
143C22×C4×C43—41no—
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C22×C411yescharacteristic
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C2×C22⋊D43—22no—
151C2×C22⋊D43—22no—
152C2×C22⋊D43—41no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—22no—
158C22×Dic43—41no—
159C22×Dic43—42no—
160C22×Dic43C22×C411yescharacteristic
161C22×Dic43C22×C411yescharacteristic
162C22×Dic43C22×C411yescharacteristic
163C22×Dic43C22×C411yescharacteristic
164C22×Dic43C22×C411yescharacteristic
165C22×Dic43C22×C411yescharacteristic
166C22×Dic43C22×C411yescharacteristic
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—42no—
170C2×Dic86—42no—
171C2×Dic86C22⋊C412yes—
172C2×Dic86C22⋊C412yes—
173C2×C8×C43—22no—
174C2×C8×C43—22no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—22no—
177C22⋊C4×C43—22no—
178C22⋊C4×C43—22no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43C2×D412yes—
182C42×C43C2×D412yes—
183C22⋊Dic43—22no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—22no—
187(C2×D43)⋊C4—22no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—22no—
191C4⋊Dic43—22no—
192C4⋊Dic43—22no—
193C4⋊Dic43C22⋊C412yes—
194C4⋊Dic43C22⋊C412yes—
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—21no—
200Dic43⋊C4—21no—
201Dic43⋊C4—21no—
202Dic43⋊C4—21no—
203Dic43⋊C4—22no—
204Dic43⋊C4—21no—
205Dic43⋊C4—21no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4C22⋊C411yescharacteristic
209Dic43⋊C4C22⋊C411yescharacteristic
210Dic43⋊C4C22⋊C411yescharacteristic
211Dic43⋊C4C22⋊C411yescharacteristic
212Dic43⋊C4C22⋊C412yes—
213Dic43⋊C4C22⋊C412yes—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43C2×D412yes—
217C4×Dic43C2×D412yes—
218C4×Dic43C2×D412yes—
219C4×Dic43C2×D412yes—
220C2×C43⋊C8—22no—
221C2×C43⋊C8—22no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43#13112yes—
227C23×C43C23×C411yescharacteristic
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—41no—
232C22×D43—41no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C412yes—
249C2×C4×C43C22×D412yes—
250C22⋊D43—44no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—22no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—41no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43C2×C22⋊C411yescharacteristic
269C2×Dic43C2×C22⋊C411yescharacteristic
270C2×Dic43C2×C22⋊C412yes—
271C2×Dic43C2×C22⋊C411yescharacteristic
272C2×Dic43C2×C22⋊C412yes—
273C2×Dic43C2×C22⋊C411yescharacteristic
274C4×D43—42no—
275C4×D43—42no—
276Dic86—24no—
277Dic86—42no—
278C8×C43—42no—
279C8×C43—42no—
280C43⋊C8—42no—
281C43⋊C8—42no—
282#17423—431nomaximal, Sylow
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—22no—
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43C22×C22⋊C411yescharacteristic
291C22×C43C2×#13111yescharacteristic
292C22×C43#56811yescharacteristic
293C2×D43—41no—
294C2×D43—41no—
295C2×D43—41no—
296C2×D43—81no—
297C2×D43—81no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—22no—
301C4×C43—22no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—41no—
305Dic43—21no—
306Dic43—21no—
307Dic43—22no—
308Dic43—22no—
309Dic43—21no—
310Dic43—41no—
311Dic43—41no—
312Dic43—41no—
313Dic43#41312yes—
314C2×#552—431no—
315#2984—432no—
316#1473—432no—
317#1473—432no—
318#1470—432no—
319#1466—431no—
320#1464—431no—
321#1464—431no—
322#1460—431no—
323#1458—431no—
324#1458D4311yescharacteristic, complemented
325C2×C43—21no—
326C2×C43—21no—
327C2×C43—42no—
328C2×C43#288011yescharacteristic
329C2×C43#288411yescharacteristic
330C2×C43C2×#41311yescharacteristic
331D43—81no—
332#552—862no—
333#552—862no—
334#552—862no—
335#552—862no—
336C2×#126—431no—
337C2×#126—431no—
338C2×#125—431no—
339C2×#125—431no—
340C2×#125—431no—
341C2×#123—431no—
342C2×#123—431no—
343C2×C22⋊Q8—431no—
344C2×C22⋊Q8—431no—
345C2×C4×Q8—431no—
346C2×C4×D4—431no—
347C2×#117—431no—
348C2×#117—431no—
349C2×#117C2×D4311yescharacteristic
350C22×C4⋊C4—431no—
351#446—862no—
352#446—862no—
353#446—862no—
354C8×Q8—862no—
355#432—432no—
356#432—432no—
357#432—432no—
358#431—432no—
359#431—432no—
360#431C2×D4312yes—
361#324—432no—
362#324—432no—
363#324—432no—
364#324C2×D4312yes—
365#323—431no—
366#323—431no—
367#323—432no—
368#323—432no—
369#323C2×D4311yescharacteristic
370#323C2×D4311yescharacteristic
371C43#1742311yescharacteristic, complemented, Sylow
372C22×Q8—431no—
373C22×D4—431no—
374C23×C4—431no—
375C23×C4—431no—
376C23×C4—431no—
377C23×C4C4×D4311yescharacteristic
378#126—862no—
379#126—862no—
380#126—862no—
381#126—862no—
382#125—862no—
383#125—862no—
384#125—862no—
385#125—862no—
386#125—862no—
387#125—862no—
388#123—862no—
389#123—862no—
390#123—862no—
391#123—862no—
392C22⋊Q8—862no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395C22⋊Q8—862no—
396C4×Q8—432no—
397C4×Q8—432no—
398C4×Q8—432no—
399C4×Q8—432no—
400C4×D4—862no—
401C4×D4—862no—
402#117—22no—
403#117—22no—
404#117—861no—
405#117—861no—
406#117—861no—
407#117—861no—
408#117—862no—
409#117—862no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4C4×D4311yescharacteristic
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C22⋊C4—431no—
431C2×C22⋊C4—431no—
432C2×C22⋊C4—431no—
433C2×C22⋊C4—431no—
434C2×C22⋊C4—431no—
435C2×C22⋊C4—431no—
436C2×C22⋊C4C4×D4311yescharacteristic
437C2×C22⋊C4C22×D4311yescharacteristic
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42C4×D4311yescharacteristic
442C2×C42C22×D4311yescharacteristic
443C4⋊C8—22no—
444C4⋊C8—862no—
445C4⋊C8—862no—
446C4⋊C8—862no—
447C4⋊C8—862no—
448C4⋊C8—862no—
449C22⋊C8—432no—
450C22⋊C8—432no—
451C22⋊C8C22×D4312yes—
452C22⋊C8C22×D4312yes—
453#97—862no—
454#97—862no—
455#97—862no—
456C4×C8—22no—
457C4×C8—862no—
458C4×C8—862no—
459C24—431no—
460C24C2×C4×D4311yescharacteristic
461C2×Q8—432no—
462C2×Q8—432no—
463C2×Q8—1722no—
464C2×D4—862no—
465C2×D4—862no—
466C2×D4—1721no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—862no—
485C22×C4—1722no—
486C22×C4—1721no—
487C22×C4—1722no—
488C22×C4C2×C4×D4311yescharacteristic
489C22×C4C2×C4×D4311yescharacteristic
490C22×C4C2×C4×D4311yescharacteristic
491C22×C4C2×C4×D4311yescharacteristic
492C22×C4C2×C4×D4311yescharacteristic
493C22×C4C23×D4311yescharacteristic
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—862no—
497C2×C8—862no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—431no—
501C4⋊C4—431no—
502C4⋊C4—431no—
503C4⋊C4—431no—
504C4⋊C4—432no—
505C4⋊C4—432no—
506C4⋊C4—432no—
507C4⋊C4—432no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—862no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—861no—
526C22⋊C4—861no—
527C22⋊C4—862no—
528C22⋊C4—862no—
529C22⋊C4—861no—
530C22⋊C4—861no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C42—21no—
534C42—21no—
535C42—432no—
536C42—432no—
537C42—432no—
538C42—432no—
539C42—861no—
540C42—861no—
541C42D4×D4312yes—
542C42D4×D4312yes—
543C23—21no—
544C23—21no—
545C23—41no—
546C23—41no—
547C23—861no—
548C23—861no—
549C23—861no—
550C23—1721no—
551C23—1721no—
552C23#1306333112yes—
553C23C22×C4×D4311yescharacteristic
554Q8—864no—
555Q8—1722no—
556D4—1724no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—431no—
571C2×C4—431no—
572C2×C4—431no—
573C2×C4—432no—
574C2×C4—432no—
575C2×C4—431no—
576C2×C4—862no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4—1722no—
589C2×C4—1721no—
590C2×C4—1722no—
591C2×C4—1722no—
592C2×C4—1722no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4C22⋊C4×D4311yescharacteristic
596C2×C4C22⋊C4×D4311yescharacteristic
597C2×C4C22⋊C4×D4312yes—
598C2×C4C2×D4×D4312yes—
599C8—42no—
600C8—42no—
601C8—1722no—
602C8—1722no—
603C22—21no—
604C22—21no—
605C22—22no—
606C22—42no—
607C22—42no—
608C22—41no—
609C22—41no—
610C22—3441no—
611C22—3441no—
612C22—1721no—
613C22—1721no—
614C22—1721no—
615C22C2×C22⋊C4×D4311yescharacteristic
616C22C2×#1306333111yescharacteristic
617C22#1458366511yescharacteristic
618C4—21no—
619C4—21no—
620C4—22no—
621C4—22no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—432no—
626C4—861no—
627C4—861no—
628C4—862no—
629C4—861no—
630C4—862no—
631C4—1721no—
632C4—1721no—
633C4—1721no—
634C2—21no—
635C2—21no—
636C2—42no—
637C2—3441no—
638C2#1914304111yescharacteristic
639C2#1914305711yescharacteristic
640C2#413×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1458C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C2×C4
cosocleC22×C4×C43C24
hypercenter#1458D43
hypocenterC43#17423
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #19143682C2semidirect
3. #19132963C2semidirect
4. #19132962C2semidirect
5. #19132949C2semidirect
7. #19132929C2semidirect
8. #19132926C2semidirect
10. #19132906C2semidirect
11. C43×#1458C2semidirect
324. #1458D43semidirect
371. C43#17423semidirect

Maximal subgroups

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

subgroupindex
C2×#145835822
#191436822
#191329632
#191329622
#191329492
#191329342
#191329292
#191329262
#191329142
#191329062
C43×#14582
#1742343