Finite Group Databasebeta

← #25064644

Subgroups — #25064644

Order 11008.

974 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147892C211yesmaximal, characteristic
2#19143225C211yesmaximal, characteristic, complemented
3#432×D43C211yesmaximal, characteristic, complemented
4#19133233C211yesmaximal, characteristic, complemented
5#19133229C211yesmaximal, characteristic, complemented
6#19133229C211yesmaximal, characteristic, complemented
7#19133225C214yesmaximal, complemented
8#19133182C214yesmaximal, complemented
9C43×#1537C211yesmaximal, characteristic, complemented
10#14583454C411yescharacteristic
11#14583454C411yescharacteristic
12#14583450C411yescharacteristic
13#14583450C411yescharacteristic
14#14583449C2211yescharacteristic
15#14583436—21no—
16#14583436—21no—
17#14583435—21no—
18#14583435—21no—
19#14583434C2212yes—
20#14583434C2212yes—
21#14583412—21no—
22#14583412—21no—
23#14583411C412yes—
24C4×#10621902—21no—
25C4×#10621902—21no—
26#14583367C412yes—
27C2×C42×D43C2211yescharacteristic
28#14582956C2211yescharacteristic
29#14582956C2211yescharacteristic
30#14582955—21no—
31#14582954C2212yes—
32#14582954C2212yes—
33#14582953—21no—
34#14582951—21no—
35#14582949—21no—
36#14582921—21no—
37C4⋊C8×D43—21no—
38#14582861—21no—
39C22⋊C8×D43—21no—
40#14582851C2212yes—
41#97×D43C2212yes—
42#14582641C2214yescomplemented
43#14582638C2214yescomplemented
44#14582638C2214yescomplemented
45C43×#533C2211yescharacteristic
46C43×#432C2211yescharacteristic
47C43×#432C2211yescharacteristic
48C43×#330C2214yescomplemented
49C2×#10621902—21no—
50C2×#10621902—21no—
51C2×#10621898C2×C412yes—
52C22×C4×D43C2×C411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C22×C4×D43D411yescharacteristic
55C2×#10621872—22no—
56C2×C8×D43—22no—
57#13063325C2×C411yescharacteristic
58#13063322C2×C411yescharacteristic
59#13063320—22no—
60#13063320—22no—
61#13063316—21no—
62#13063316—21no—
63#13063314—21no—
64#13063314—21no—
65#13063313C2312yes—
66#13063310—22no—
67#13063310—22no—
68#13063309—22no—
69#13063305C2×C412yes—
70#13063305C2×C412yes—
71#13063301—21no—
72#13063301—21no—
73#13063300—21no—
74#13063300—21no—
75#13063300C2×C412yes—
76#13063300C2×C412yes—
77#13063299—21no—
78#13063299—21no—
79#13063295—22no—
80Q8×Dic43—21no—
81Q8×Dic43—21no—
82#13063290C2×C412yes—
83#13063290C2×C412yes—
84C4×D172—22no—
85C4×D172—22no—
86C4×D172—21no—
87C4×D172—21no—
88#13063287—22no—
89#13063287—22no—
90#13063287—21no—
91#13063287—21no—
92#13063287C2×C412yes—
93#13063287C2×C412yes—
94(C22⋊D43)⋊C4—22no—
95(C22⋊D43)⋊C4—22no—
96#13063283—21no—
97#13063283—21no—
98#13063283—22no—
99#13063283—22no—
100#13063282—22no—
101C2×C4×Dic43C2×C411yescharacteristic
102C2×C4×Dic43D411yescharacteristic
103C2×C4×Dic43D411yescharacteristic
104C42×D43—22no—
105C42×D43C2×C411yescharacteristic
106C42×D43C2×C411yescharacteristic
107C42×D43D411yescharacteristic
108C42×D43D411yescharacteristic
109C42×D43D411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43C2311yescharacteristic
112C42×D43C2311yescharacteristic
113C4⋊(C43⋊C8)—21no—
114C4⋊(C43⋊C8)—21no—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)—21no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121#13063236C2312yes—
122#13063236C2312yes—
123#13063235—22no—
124C8×Dic43—22no—
125C4⋊Q8×C43C2×C411yescharacteristic
126C4⋊Q8×C43C2×C411yescharacteristic
127#125×C43C2312yes—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—21no—
130C4×Q8×C43—21no—
131C4×Q8×C43—21no—
132#117×C43C2×C412yes—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138#97×C43C2312yes—
139#97×C43C2312yes—
140C23×D43C22⋊C411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C2×C22⋊D43—22no—
147C22×Dic43C22⋊C411yescharacteristic
148C22×Dic43C22⋊C411yescharacteristic
149C22×Dic43C22⋊C411yescharacteristic
150#10621902—44no—
151#10621902—44no—
152#10621898—44no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—22no—
156C2×D172—22no—
157C2×D172C22×C412yes—
158C2×C4×D43—22no—
159C2×C4×D43—22no—
160C2×C4×D43—22no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43C22⋊C411yescharacteristic
165C2×C4×D43C22⋊C411yescharacteristic
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22⋊C411yescharacteristic
168C2×C4×D43C22⋊C411yescharacteristic
169C2×C4×D43C22⋊C411yescharacteristic
170C2×C4×D43C22×C411yescharacteristic
171C2×C4×D43C22×C411yescharacteristic
172C2×C4×D43C2×D411yescharacteristic
173C2×C4×D43C2×D411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×C4×D43C2×D411yescharacteristic
176C2×Dic86C22×C412yes—
177C2×C8×C43—22no—
178C2×C8×C43—22no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43C22×C412yes—
184C4⋊C4×C43C22×C412yes—
185C22⋊C4×C43—22no—
186C42×C43—22no—
187C42×C43C22×C411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43C2411yescharacteristic
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—22no—
202C4⋊Dic43—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205C4×Dic43—22no—
206C4×Dic43—22no—
207C4×Dic43C22⋊C411yescharacteristic
208C4×Dic43C22⋊C411yescharacteristic
209C4×Dic43C22⋊C411yescharacteristic
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22×C411yescharacteristic
214C4×Dic43C22×C411yescharacteristic
215C4×Dic43C2×D411yescharacteristic
216C4×Dic43C2×D411yescharacteristic
217C4×Dic43C2×D411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219C2×C43⋊C8—22no—
220C2×C43⋊C8—22no—
221#10621872—44no—
222C8×D43—44no—
223C23×C43C2×C22⋊C411yescharacteristic
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43C2×C22⋊C411yescharacteristic
229C22×D43C2×C22⋊C411yescharacteristic
230Q8×C43—42no—
231Q8×C43—42no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43C2×C22⋊C411yescharacteristic
238C2×C4×C43C2×C22⋊C411yescharacteristic
239C2×C4×C43C2×C22⋊C411yescharacteristic
240C2×C4×C43C23×C411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C22⋊D43—44no—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43C2×C22⋊C411yescharacteristic
249C2×Dic43C2×C22⋊C411yescharacteristic
250C2×Dic43C2×C22⋊C411yescharacteristic
251C2×Dic43C2×C22⋊C411yescharacteristic
252C2×Dic43C2×C22⋊C411yescharacteristic
253C2×Dic43C2×C22⋊C411yescharacteristic
254D172—42no—
255D172—42no—
256D172—42no—
257D172—44no—
258D172—44no—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—41no—
266C4×D43—41no—
267C4×D43—41no—
268C4×D43—41no—
269C4×D43—41no—
270C4×D43—41no—
271C4×D43—44no—
272C4×D43—44no—
273C4×D43—44no—
274Dic86—42no—
275C8×C43—42no—
276C8×C43—42no—
277C43⋊C8—42no—
278C43⋊C8—42no—
279#17662—431nomaximal, Sylow
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—21no—
283C22×C43C22×C22⋊C411yescharacteristic
284C2×D43—21no—
285C2×D43—21no—
286C2×D43—21no—
287C2×D43—21no—
288C2×D43—21no—
289C2×D43—44no—
290C2×D43—42no—
291C2×D43—42no—
292C2×D43—42no—
293C2×D43#42112yes—
294C4×C43—21no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—42no—
300C4×C43—42no—
301C4×C43#41312yes—
302Dic43—21no—
303Dic43—21no—
304Dic43—21no—
305Dic43—21no—
306Dic43—21no—
307Dic43—42no—
308Dic43#42112yes—
309#3444—431no—
310#2920—431no—
311C2×#432—431no—
312#1537—431no—
313#1537D4311yescharacteristic, complemented
314#1536—431no—
315#1536—431no—
316#1535—434no—
317#1524—434no—
318C2×C43—41no—
319C2×C43C2×#41311yescharacteristic
320C2×C43C2×#42111yescharacteristic
321C2×C43C2×#42111yescharacteristic
322D43—22no—
323D43—41no—
324D43—82no—
325#533—431no—
326#533—431no—
327#533C2×D4311yescharacteristic
328#532—431no—
329#532—431no—
330#532—431no—
331#529—432no—
332#529—432no—
333#529—861no—
334#529—861no—
335#529—861no—
336#529—861no—
337#525—432no—
338#525—861no—
339#525—861no—
340C4×#41—432no—
341C4×#41—861no—
342C4×#41—861no—
343C22×C42—431no—
344#432—431no—
345#432—431no—
346#432—432no—
347#432—432no—
348#432—861no—
349#432—861no—
350#432C2×D4311yescharacteristic
351#432C2×D4311yescharacteristic
352#431—861no—
353#431—861no—
354#423—861no—
355C2×C4⋊C8—861no—
356#407—861no—
357C2×C22⋊C8—861no—
358C4×M16—432no—
359C2×#97—432no—
360#330—434no—
361#330C2×D4314yescomplemented
362#329—434no—
363#329—434no—
364C43#1766211yescharacteristic, complemented, Sylow
365C2×#41—432no—
366C2×#41—861no—
367C2×#41—861no—
368C23×C4—431no—
369C23×C4—431no—
370C23×C4—431no—
371C2×M16—862no—
372C22×C8—862no—
373C4⋊Q8—431no—
374C4⋊Q8C4×D4311yescharacteristic
375C4⋊Q8C4×D4311yescharacteristic
376#127—431no—
377#126—862no—
378#126—862no—
379#125—861no—
380#125—861no—
381#125C22×D4312yes—
382#124—432no—
383#124—861no—
384#124—861no—
385#123—862no—
386#123—862no—
387#123—862no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390C22⋊Q8—432no—
391C22⋊Q8—432no—
392C22⋊Q8—861no—
393C22⋊Q8—861no—
394#121—432no—
395#121—432no—
396#121—861no—
397#121—861no—
398#121—861no—
399#121—861no—
400#120—862no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—432no—
404C4×Q8—432no—
405C4×Q8—861no—
406C4×Q8—861no—
407C4×D4—432no—
408C4×D4—432no—
409C4×D4—862no—
410C4×D4—862no—
411C4×D4—861no—
412C4×D4—861no—
413C4×D4—862no—
414C4×D4—862no—
415C4×D4—862no—
416C4×D4—862no—
417C4×D4—861no—
418C4×D4—861no—
419#117—862no—
420#117—862no—
421#117—862no—
422#117—861no—
423#117—861no—
424#117C4×D4312yes—
425C2×C42—431no—
426C2×C42—431no—
427C2×C42—431no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—431no—
431C2×C42—431no—
432C2×C42—431no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—862no—
437C2×C42C22×D4311yescharacteristic
438C4⋊C8—21no—
439C4⋊C8—21no—
440C4⋊C8—862no—
441C4⋊C8—862no—
442C4⋊C8—861no—
443C4⋊C8—861no—
444C22⋊C8—21no—
445C22⋊C8—21no—
446C22⋊C8—862no—
447C22⋊C8—862no—
448C22⋊C8—861no—
449C22⋊C8—861no—
450#97—432no—
451#97—432no—
452#97—862no—
453#97C22×D4312yes—
454#97C22×D4312yes—
455C4×C8—862no—
456C24—431no—
457#41—1724no—
458#41—1724no—
459#41—1724no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—432no—
463C2×D4—432no—
464C2×D4—862no—
465C2×D4—862no—
466C2×D4—862no—
467C2×D4—861no—
468C2×D4—861no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—1722no—
488C22×C4—1722no—
489C22×C4—1722no—
490C22×C4C2×C4×D4311yescharacteristic
491C22×C4D4×D4311yescharacteristic
492C22×C4D4×D4311yescharacteristic
493M16—1724no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—862no—
497C2×C8—862no—
498C2×C8—1724no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4C2×C4×D4312yes—
510C4⋊C4C2×C4×D4312yes—
511C22⋊C4—22no—
512C22⋊C4—862no—
513C22⋊C4—862no—
514C22⋊C4—862no—
515C22⋊C4—862no—
516C22⋊C4—862no—
517C22⋊C4—862no—
518C22⋊C4—862no—
519C22⋊C4—862no—
520C42—22no—
521C42—431no—
522C42—431no—
523C42—431no—
524C42—431no—
525C42—431no—
526C42—431no—
527C42—431no—
528C42—431no—
529C42—431no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—862no—
534C42—862no—
535C42C2×C4×D4311yescharacteristic
536C42D4×D4311yescharacteristic
537C42D4×D4311yescharacteristic
538C42C23×D4311yescharacteristic
539C23—431no—
540C23—431no—
541C23—862no—
542C23—862no—
543C23—1721no—
544C23—1721no—
545C23C22⋊C4×D4311yescharacteristic
546Q8—42no—
547Q8—42no—
548Q8—1722no—
549D4—1722no—
550D4—1722no—
551D4—1722no—
552D4—1724no—
553D4—1724no—
554D4—1724no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—431no—
561C2×C4—431no—
562C2×C4—431no—
563C2×C4—431no—
564C2×C4—431no—
565C2×C4—431no—
566C2×C4—862no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1724no—
581C2×C4—1724no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1724no—
585C2×C4C22⋊C4×D4311yescharacteristic
586C2×C4C22⋊C4×D4311yescharacteristic
587C2×C4C22⋊C4×D4311yescharacteristic
588C2×C4C22×C4×D4311yescharacteristic
589C2×C4C2×D4×D4311yescharacteristic
590C2×C4C2×D4×D4311yescharacteristic
591C8—42no—
592C8—42no—
593C8—1722no—
594C8—1722no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—432no—
599C22—861no—
600C22—861no—
601C22—861no—
602C22—861no—
603C22—861no—
604C22—1724no—
605C22—1722no—
606C22—1722no—
607C22—1722no—
608C22C2×C22⋊C4×D4311yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—21no—
614C4—42no—
615C4—42no—
616C4—432no—
617C4—861no—
618C4—861no—
619C4—861no—
620C4—861no—
621C4—861no—
622C4—1722no—
623C4#1458288212yes—
624C2—41no—
625C2—862no—
626C2—3442no—
627C2—1721no—
628C2C2×#1458288211yescharacteristic
629C2#421×D4311yescharacteristic
630C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1537C2
socleC22×C43C22×C22⋊C4
prime radical#19147892C2
cosocleC42×C43C24
hypercenter#1537D43
hypocenterC43#17662
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1537

Complements

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

NH ≅ G/Ntype
2. #19143225C2semidirect
3. #432×D43C2semidirect
4. #19133233C2semidirect
5. #19133229C2semidirect
6. #19133229C2semidirect
7. #19133225C2semidirect
8. #19133182C2semidirect
9. C43×#1537C2semidirect
42. #14582641C22semidirect
43. #14582638C22semidirect
44. #14582638C22semidirect
48. C43×#330C22semidirect
313. #1537D43semidirect
361. #330C2×D43semidirect
364. C43#17662semidirect

Maximal subgroups

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

subgroupindex
#191478922
#191432252
#432×D432
#191332332
#191332292
#191332252
#191331822
C43×#15372
#1766243