Finite Group Databasebeta

← #25064155

Subgroups — #25064155

Order 11008.

1046 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148622C211yesmaximal, characteristic
2#19143629C211yesmaximal, characteristic, complemented
3#19137233C211yesmaximal, characteristic, complemented
4#19133161C212yesmaximal, complemented
5#19133148C212yesmaximal, complemented
6#19133135C212yesmaximal, complemented
7#19133122C212yesmaximal, complemented
8#19133118C211yesmaximal, characteristic, complemented
9#19133103C211yesmaximal, characteristic, complemented
10#19133082C211yesmaximal, characteristic, complemented
11C43×#1502C211yesmaximal, characteristic, complemented
12#14583615C411yescharacteristic, complemented
13#14583610C411yescharacteristic, complemented
14#14583601—21no—
15#14583599C412yescomplemented
16#14583569C411yescharacteristic, complemented
17#14583544C412yescomplemented
18#14583537—22no—
19#14583534C411yescharacteristic, complemented
20#14583533—21no—
21#14583500—21no—
22#14583483—22no—
23#14583433C2211yescharacteristic
24#14583409C2212yes—
25#121×D43C2212yes—
26#14583371—21no—
27C2×C4×D172C2211yescharacteristic
28#14582978—21no—
29#14582969—22no—
30C8×D172—21no—
31#14582956C2211yescharacteristic, complemented
32#14582861C2212yescomplemented
33C22⋊C8×D43C2212yescomplemented
34#14582800—21no—
35#14582795—21no—
36#14582790—22no—
37#14582761C2212yescomplemented
38#14582758C2212yescomplemented
39#14582745C2211yescharacteristic, complemented
40#14582637C2211yescharacteristic, complemented
41#14582637C2211yescharacteristic, complemented
42#14582635C2212yescomplemented
43#14582634C2211yescharacteristic
44#14582634C2211yescharacteristic
45#14582633C2212yescomplemented
46#14582633C2212yescomplemented
47#14582632C2212yes—
48C43×#532C2211yescharacteristic
49C43×#431C2211yescharacteristic, complemented
50C4×C4⋊C4×C43C2211yescharacteristic, complemented
51C43×#327C2212yescomplemented
52C43×#327C2212yescomplemented
53C2×#10621900C2×C412yes—
54C22×D172D411yescharacteristic
55C2×D4×D43—22no—
56C2×D4×D43—21no—
57C2×D4×D43C2×C412yes—
58C22×C4×D43C2312yes—
59C2×#10621872—22no—
60C2×C8×D43—22no—
61#13063321—21no—
62#13063319—21no—
63#13063318—22no—
64#13063317C2×C411yescharacteristic
65#13063316—21no—
66#13063314—22no—
67#13063313C2×C411yescharacteristic
68#13063309—22no—
69#13063308—21no—
70#13063308—22no—
71#13063307—22no—
72#13063305C2×C412yes—
73#13063304C2311yescharacteristic
74#13063301—22no—
75#13063300—21no—
76#13063300C2×C412yes—
77#13063299—22no—
78#13063299C2311yescharacteristic
79#13063298—22no—
80#13063298—22no—
81#13063297—22no—
82#13063297—22no—
83#13063296—21no—
84#13063296C2×C412yes—
85#13063296C2×C412yes—
86#13063295—22no—
87#13063293—22no—
88#13063293—22no—
89C4×Dic86C2×C411yescharacteristic
90C4×D172C2×C411yescharacteristic
91C4×D172C2×C412yes—
92C4×D172C2×C411yescharacteristic
93C4×D172C2×C411yescharacteristic
94C4×D172D411yescharacteristic
95C4×D172D411yescharacteristic
96C4×D172D412yes—
97D4×Dic43—22no—
98D4×Dic43—21no—
99#13063287—21no—
100C4×C22⋊D43—21no—
101C4×C22⋊D43—22no—
102(C22⋊D43)⋊C4—22no—
103#13063283—21no—
104#13063283C2×C412yes—
105#13063282—21no—
106C2×C4⋊Dic43D411yescharacteristic
107C2×Dic43⋊C4—22no—
108C4⋊C4×D43C2×C412yes—
109C2×(C2×D43)⋊C4—22no—
110C2×(C2×D43)⋊C4—22no—
111C2×(C2×D43)⋊C4—22no—
112C2×(C2×D43)⋊C4D412yes—
113C22⋊C4×D43—22no—
114C2×C4×Dic43—21no—
115C4⋊(C43⋊C8)—21no—
116C22⋊(C43⋊C8)C2312yes—
117(C2×D43)⋊C8—22no—
118(C2×D43)⋊C8—22no—
119#13063236—21no—
120C43⋊#95—21no—
121C43⋊#95—22no—
122C43⋊#95C2311yescharacteristic
123C43⋊#95C2311yescharacteristic
124C2×#41×C43—21no—
125C4⋊Q8×C43C2×C411yescharacteristic
126#127×C43C2×C411yescharacteristic
127#124×C43—21no—
128#121×C43—21no—
129#121×C43C2312yes—
130C4×D4×C43—21no—
131C4×D4×C43C2×C412yes—
132C2×C4⋊C4×C43—21no—
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C22⋊C8×C43C2311yescharacteristic
137C22⋊C8×C43C2311yescharacteristic
138C4×C8×C43—21no—
139#95×C43C2312yes—
140C23×D43—22no—
141C23×D43C2×D412yes—
142#41×C43—81no—
143#41×C43—81no—
144C2×Q8×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—22no—
148C2×D4×C43C22×C412yes—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C2×C22⋊D43—22no—
155C2×C22⋊D43—21no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—22no—
158C2×C22⋊D43—22no—
159C22×Dic43—22no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43C2×D412yes—
163#10621900—82no—
164D4×D43—44no—
165D4×D43—82no—
166D4×D43—82no—
167D4×D43—82no—
168C2×D172—22no—
169C2×D172—42no—
170C2×D172C22⋊C411yescharacteristic
171C2×D172C22⋊C411yescharacteristic
172C2×D172C22⋊C412yes—
173C2×D172C22×C411yescharacteristic
174C2×C4×D43—21no—
175C2×C4×D43—22no—
176C2×C4×D43—82no—
177C2×C4×D43C22×C412yes—
178C2×C4×D43C22×C412yes—
179C2×C4×D43C2×D412yes—
180C2×C4×D43C2×D412yes—
181C2×Dic86C22×C411yescharacteristic
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—42no—
186C4⋊C4×C43C22×C412yes—
187C22⋊C4×C43—22no—
188C22⋊C4×C43—22no—
189C42×C43—81no—
190C42×C43C22×C411yescharacteristic
191C42×C43C22×C411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196C22⋊Dic43—21no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—21no—
199(C2×D43)⋊C4—21no—
200(C2×D43)⋊C4—21no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—22no—
203(C2×D43)⋊C4—22no—
204(C2×D43)⋊C4—82no—
205(C2×D43)⋊C4—82no—
206(C2×D43)⋊C4C22⋊C412yes—
207(C2×D43)⋊C4C22⋊C412yes—
208(C2×D43)⋊C4C22⋊C412yes—
209(C2×D43)⋊C4C22⋊C412yes—
210C4⋊Dic43—22no—
211C4⋊Dic43C22⋊C411yescharacteristic
212C4⋊Dic43C22⋊C411yescharacteristic
213C4⋊Dic43C22⋊C412yes—
214C4⋊Dic43C22×C411yescharacteristic
215C4⋊Dic43C22×C411yescharacteristic
216Dic43⋊C4—21no—
217Dic43⋊C4—21no—
218Dic43⋊C4—21no—
219Dic43⋊C4—21no—
220Dic43⋊C4—22no—
221Dic43⋊C4—82no—
222C4×Dic43—21no—
223C4×Dic43—22no—
224C4×Dic43—42no—
225C2×C43⋊C8—22no—
226#10621872—82no—
227C8×D43—82no—
228C23×C43—22no—
229C23×C43C22×D411yescharacteristic
230C22×D43—22no—
231C22×D43—22no—
232C22×D43—21no—
233C22×D43—42no—
234C22×D43—42no—
235C22×D43—44no—
236C22×D43—82no—
237C22×D43—82no—
238C22×D43C2×C22⋊C412yes—
239C22×D43C2×C22⋊C412yes—
240Q8×C43—81no—
241D4×C43—42no—
242D4×C43—42no—
243D4×C43—42no—
244D4×C43—42no—
245D4×C43—81no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—41no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—82no—
255C2×C4×C43C2×C22⋊C411yescharacteristic
256C2×C4×C43C2×C22⋊C411yescharacteristic
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C23×C411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C22⋊D43—44no—
262C22⋊D43—41no—
263C22⋊D43—41no—
264C22⋊D43—82no—
265C22⋊D43—82no—
266C22⋊D43—82no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—42no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—82no—
278C2×Dic43C2×C22⋊C412yes—
279C2×Dic43C2×C22⋊C412yes—
280D172—22no—
281D172—22no—
282D172—42no—
283D172—41no—
284D172—82no—
285C4×D43—42no—
286C4×D43—42no—
287C4×D43—42no—
288C4×D43—42no—
289C4×D43—42no—
290C4×D43—82no—
291Dic86—41no—
292C8×C43—41no—
293C8×C43—41no—
294C43⋊C8—42no—
295#17599—431nomaximal, Sylow
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—42no—
301C22×C43C22×C22⋊C411yescharacteristic
302C22×C43#57611yescharacteristic
303C22×C43#57711yescharacteristic
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—22no—
308C2×D43—22no—
309C2×D43—22no—
310C2×D43—41no—
311C2×D43—41no—
312C2×D43—41no—
313C2×D43—82no—
314C2×D43—82no—
315C2×D43—164no—
316C4×C43—21no—
317C4×C43—21no—
318C4×C43—21no—
319C4×C43—21no—
320C4×C43—21no—
321C4×C43—42no—
322C4×C43—82no—
323C4×C43#42112yes—
324Dic43—22no—
325Dic43—22no—
326Dic43—41no—
327Dic43—41no—
328Dic43—41no—
329Dic43—81no—
330Dic43—81no—
331#3519—431no—
332#2974—431no—
333#2319—431no—
334#1519—432no—
335#1516—432no—
336#1513—432no—
337#1510—432no—
338#1509—431no—
339#1505—431no—
340#1502D4311yescharacteristic, complemented
341#1500—431no—
342C2×C43—21no—
343C2×C43—21no—
344C2×C43—82no—
345C2×C43#288311yescharacteristic
346C2×C43#289711yescharacteristic
347C2×C43C2×#42111yescharacteristic
348D43—42no—
349D43—42no—
350D43—81no—
351#555—431no—
352#554—431no—
353#553—432no—
354#553—861no—
355#550—431no—
356#546—432no—
357#546—862no—
358D42—431no—
359D42—861no—
360#540—861no—
361#538—862no—
362#532C2×D4311yescharacteristic
363#529—431no—
364#525—432no—
365C2×#121—432no—
366#518—861no—
367C2×C4×D4—431no—
368#436—861no—
369#435—862no—
370C8×D4—861no—
371#432—431no—
372#431C2×D4311yescharacteristic, complemented
373#407—432no—
374C2×C22⋊C8—432no—
375#390—861no—
376#389—861no—
377#388—862no—
378#381—432no—
379#380—432no—
380C4×C4⋊C4C2×D4311yescharacteristic, complemented
381#376—431no—
382#328—431no—
383#328—431no—
384#328—432no—
385#327—432no—
386#327—432no—
387#327—431no—
388#327—431no—
389#327—432no—
390#327C2×D4312yescomplemented
391#327C2×D4312yescomplemented
392C43#1759911yescharacteristic, complemented, Sylow
393C2×#41—21no—
394C2×#41—432no—
395C22×D4—432no—
396C22×D4—431no—
397C22×D4—861no—
398C22×D4—862no—
399C23×C4—432no—
400C2×M16—862no—
401C22×C8—862no—
402C4⋊Q8C4×D4311yescharacteristic
403#127—861no—
404#127C4×D4311yescharacteristic
405#126—862no—
406#126—861no—
407#125—431no—
408#125—861no—
409#124—21no—
410#124—431no—
411#124—862no—
412#123—862no—
413#123—862no—
414#123—862no—
415#123—861no—
416C22⋊Q8—431no—
417C22⋊Q8—432no—
418C22⋊Q8—862no—
419#121—21no—
420#121—432no—
421#121—432no—
422#121—431no—
423#121—432no—
424#121—862no—
425#121—862no—
426#121—862no—
427#121—862no—
428#121—861no—
429#121—861no—
430#121—862no—
431#121C22×D4312yes—
432#120—862no—
433#120—862no—
434#120—862no—
435C4×Q8—431no—
436C4×D4—21no—
437C4×D4—431no—
438C4×D4—432no—
439C4×D4—431no—
440C4×D4—431no—
441C4×D4—431no—
442C4×D4—432no—
443C4×D4—431no—
444C4×D4—862no—
445C4×D4—862no—
446C4×D4—861no—
447C4×D4—861no—
448C4×D4—862no—
449C4×D4—861no—
450C4×D4C4×D4312yes—
451#117—432no—
452#117—861no—
453#117—861no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—431no—
456C2×C4⋊C4—432no—
457C2×C4⋊C4—862no—
458C2×C22⋊C4—432no—
459C2×C22⋊C4—862no—
460C2×C22⋊C4—862no—
461C2×C22⋊C4—862no—
462C2×C22⋊C4—862no—
463C2×C42—21no—
464C2×C42—861no—
465C2×C42C22×D4311yescharacteristic
466C4⋊C8—21no—
467C4⋊C8—861no—
468C22⋊C8—432no—
469C22⋊C8—862no—
470C22⋊C8—862no—
471C22⋊C8C22×D4311yescharacteristic
472C22⋊C8C22×D4311yescharacteristic
473#97—861no—
474C4×C8—21no—
475#95—431no—
476#95—431no—
477#95—862no—
478#95—861no—
479#95C22×D4312yes—
480C24—432no—
481C24—862no—
482#41—81no—
483#41—81no—
484#41—3442no—
485C2×Q8—21no—
486C2×Q8—431no—
487C2×D4—22no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—431no—
491C2×D4—431no—
492C2×D4—432no—
493C2×D4—431no—
494C2×D4—862no—
495C2×D4—862no—
496C2×D4—862no—
497C2×D4—862no—
498C2×D4—862no—
499C2×D4—861no—
500C2×D4—3442no—
501C2×D4—3442no—
502C2×D4—3442no—
503C2×D4—1722no—
504C2×D4—1724no—
505C2×D4C2×C4×D4312yes—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—432no—
509C22×C4—432no—
510C22×C4—432no—
511C22×C4—432no—
512C22×C4—432no—
513C22×C4—862no—
514C22×C4—862no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—3442no—
519C22×C4D4×D4311yescharacteristic
520C22×C4D4×D4311yescharacteristic
521C22×C4C23×D4311yescharacteristic
522M16—3442no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—862no—
526C2×C8—3442no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—431no—
530C4⋊C4—431no—
531C4⋊C4—432no—
532C4⋊C4—431no—
533C4⋊C4—431no—
534C4⋊C4—862no—
535C4⋊C4—862no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—3442no—
541C4⋊C4C2×C4×D4312yes—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—432no—
545C22⋊C4—432no—
546C22⋊C4—432no—
547C22⋊C4—432no—
548C22⋊C4—862no—
549C22⋊C4—862no—
550C22⋊C4—862no—
551C22⋊C4—862no—
552C22⋊C4—862no—
553C22⋊C4—861no—
554C22⋊C4—861no—
555C22⋊C4—861no—
556C22⋊C4—861no—
557C22⋊C4—861no—
558C22⋊C4—3442no—
559C22⋊C4—3442no—
560C42—81no—
561C42—862no—
562C42—861no—
563C42—1722no—
564C42C2×C4×D4311yescharacteristic
565C42C2×C4×D4311yescharacteristic
566C42D4×D4311yescharacteristic
567C42D4×D4311yescharacteristic
568C23—22no—
569C23—432no—
570C23—432no—
571C23—862no—
572C23—862no—
573C23—861no—
574C23—3442no—
575C23—3442no—
576C23—1722no—
577C23—1722no—
578C23—1724no—
579C23C2×D4×D4311yescharacteristic
580Q8—81no—
581Q8—1721no—
582D4—42no—
583D4—42no—
584D4—42no—
585D4—42no—
586D4—81no—
587D4—862no—
588D4—862no—
589D4—3442no—
590D4—3442no—
591D4—3442no—
592D4—3442no—
593D4—1722no—
594D4—1721no—
595D4—1724no—
596D4—1721no—
597D4—1721no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—82no—
607C2×C4—432no—
608C2×C4—432no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—3442no—
613C2×C4—3442no—
614C2×C4—1722no—
615C2×C4—1722no—
616C2×C4—1722no—
617C2×C4—1722no—
618C2×C4—1722no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1722no—
626C2×C4C22⋊C4×D4311yescharacteristic
627C2×C4C22⋊C4×D4311yescharacteristic
628C2×C4C22⋊C4×D4311yescharacteristic
629C2×C4C22⋊C4×D4311yescharacteristic
630C2×C4C22×C4×D4311yescharacteristic
631C2×C4C2×D4×D4311yescharacteristic
632C8—41no—
633C8—41no—
634C8—1722no—
635C22—21no—
636C22—21no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—862no—
641C22—862no—
642C22—862no—
643C22—862no—
644C22—862no—
645C22—862no—
646C22—3442no—
647C22—3442no—
648C22—1721no—
649C22—1721no—
650C22—1721no—
651C22—6884no—
652C22C2×C22⋊C4×D4311yescharacteristic
653C22#1458370011yescharacteristic
654C22#1458370511yescharacteristic
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—42no—
661C4—82no—
662C4—862no—
663C4—862no—
664C4—3441no—
665C4—3441no—
666C4—1721no—
667C4—1721no—
668C4—1721no—
669C4#1458291412yes—
670C2—21no—
671C2—21no—
672C2—82no—
673C2—3441no—
674C2—1722no—
675C2—1722no—
676C2#1914305411yescharacteristic
677C2#1914311611yescharacteristic
678C2C2×#1458291411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1502C2
socleC22×C43C22×C22⋊C4
prime radical#19148622C2
cosocleC22×C4×C43C24
hypercenter#1502D43
hypocenterC43#17599
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
2. #19143629C2semidirect
3. #19137233C2semidirect
4. #19133161C2semidirect
5. #19133148C2semidirect
6. #19133135C2semidirect
7. #19133122C2semidirect
8. #19133118C2semidirect
9. #19133103C2semidirect
10. #19133082C2semidirect
11. C43×#1502C2semidirect
12. #14583615C4semidirect
13. #14583610C4semidirect
15. #14583599C4semidirect
16. #14583569C4semidirect
17. #14583544C4semidirect
19. #14583534C4semidirect
31. #14582956C22semidirect
32. #14582861C22semidirect
33. C22⋊C8×D43C22semidirect
37. #14582761C22semidirect
38. #14582758C22semidirect
39. #14582745C22semidirect
40. #14582637C22semidirect
41. #14582637C22semidirect
42. #14582635C22semidirect
45. #14582633C22semidirect
46. #14582633C22semidirect
49. C43×#431C22semidirect
50. C4×C4⋊C4×C43C22semidirect
51. C43×#327C22semidirect
52. C43×#327C22semidirect
340. #1502D43semidirect
372. #431C2×D43semidirect
380. C4×C4⋊C4C2×D43semidirect
390. #327C2×D43semidirect
391. #327C2×D43semidirect
392. C43#17599semidirect

Maximal subgroups

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

subgroupindex
#191486222
#191436292
#191372332
#191331612
#191331482
#191331352
#191331222
#191331182
#191331032
#191330822
C43×#15022
#1759943