Finite Group Databasebeta

← #25063655

Subgroups — #25063655

Order 11008.

934 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148213C211yesmaximal, characteristic
2#19143724C211yesmaximal, characteristic, complemented
3#19143240C211yesmaximal, characteristic, complemented
4#19133059C212yesmaximal, complemented
5#19133050C211yesmaximal, characteristic, complemented
6#19133035C211yesmaximal, characteristic, complemented
7#19133022C212yesmaximal, complemented
8#19133002C212yesmaximal, complemented
9#19132988C212yesmaximal, complemented
10#19132975C211yesmaximal, characteristic, complemented
11C43×#1485C211yesmaximal, characteristic, complemented
12#14583624C411yescharacteristic
13#14583623C411yescharacteristic
14#14583620—21no—
15#14583583C412yes—
16#14583581—22no—
17#14583564C411yescharacteristic
18#14583559C412yes—
19#14583552C411yescharacteristic
20#14583551—21no—
21#14583453—21no—
22#14583436C2212yes—
23#14583427—22no—
24C4×#10621902—21no—
25C4×#10621898C2211yescharacteristic
26C4×#10621898C2211yescharacteristic
27C4×Q8×D43C2212yes—
28C8×Dic86—21no—
29#14582978—21no—
30#14582974—22no—
31#14582961—22no—
32#14582951C2212yes—
33#14582950C2212yes—
34#14582950C2212yes—
35#14582927—21no—
36#14582923C2211yescharacteristic
37#14582921C2212yes—
38#14582867—21no—
39C2×C4×C43⋊C8C2211yescharacteristic
40#14582631C2212yes—
41Q8⋊(C43⋊C8)C2212yes—
42Q8⋊(C43⋊C8)C2212yes—
43#14582629C2211yescharacteristic
44#14582629C2211yescharacteristic
45#14582628C2212yes—
46#14582626C2211yescharacteristic
47#14582626C2211yescharacteristic
48C43×#533C2211yescharacteristic
49C43×#431C2211yescharacteristic
50C4×M16×C43C2211yescharacteristic
51C43×Q8⋊C8C2212yes—
52C43×Q8⋊C8C2212yes—
53C2×#10621902—21no—
54C2×#10621898C2×C411yescharacteristic
55C2×#10621898D411yescharacteristic
56C2×Q8×D43C2×C412yes—
57C2×#10621877—21no—
58C2×#10621872—22no—
59C22×C43⋊C8—21no—
60#13063324—21no—
61#13063323—21no—
62#13063320—22no—
63#13063320—22no—
64#13063318—22no—
65#13063316C2×C412yes—
66#13063315—22no—
67#13063315—22no—
68#13063314C2×C412yes—
69#13063311—22no—
70#13063310—22no—
71#13063310—22no—
72#13063307—22no—
73#13063305—21no—
74#13063303—22no—
75#13063303—22no—
76#13063301—21no—
77#13063301C2×C412yes—
78#13063300C2×C412yes—
79#13063298—22no—
80Q8×Dic43—21no—
81Q8×Dic43C2×C412yes—
82C4×Dic86—22no—
83C4×Dic86C2×C411yescharacteristic
84C4×Dic86C2×C411yescharacteristic
85C4×Dic86D411yescharacteristic
86C4×Dic86C2311yescharacteristic
87#13063290—22no—
88#13063290C2×C412yes—
89C4×D172—22no—
90C4×D172C2×C411yescharacteristic
91C4×D172C2×C411yescharacteristic
92C4×D172D411yescharacteristic
93C4×D172C2311yescharacteristic
94#13063287—21no—
95#13063287—22no—
96C4×C22⋊D43—21no—
97C4×C22⋊D43—21no—
98C4×C22⋊D43C2×C412yes—
99C4×C22⋊D43D412yes—
100#13063284C2×C411yescharacteristic
101#13063284D411yescharacteristic
102#13063283—22no—
103#13063283—21no—
104#13063282—21no—
105#13063282—22no—
106#13063282D412yes—
107C4⋊C4×D43—22no—
108C4⋊C4×D43C2×C412yes—
109C42×D43—22no—
110C42×D43—21no—
111C42×D43C2312yes—
112C4⋊(C43⋊C8)—21no—
113C4⋊(C43⋊C8)C2312yes—
114Dic43⋊C8—22no—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117(C2×D43)⋊C8—22no—
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—22no—
120C4×C43⋊C8—21no—
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C8×Dic43—22no—
124C2×M16×C43—21no—
125C4⋊Q8×C43C2×C411yescharacteristic
126C4⋊Q8×C43C2×C411yescharacteristic
127#125×C43—21no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43C2×C412yes—
130C4×Q8×C43—21no—
131C4×Q8×C43C2312yes—
132#117×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137#97×C43—21no—
138C4×C8×C43—21no—
139C4×C8×C43C2312yes—
140C2×Q8×C43—21no—
141C2×Q8×C43C22×C412yes—
142C22×C4×C43C22×C411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C2×C22⋊D43—21no—
146C2×C22⋊D43C22⋊C412yes—
147#10621902—44no—
148Q8×D43—24no—
149Q8×D43—42no—
150#10621898—22no—
151#10621898—41no—
152#10621898—42no—
153C2×D172—22no—
154C2×D172C22⋊C411yescharacteristic
155C2×D172C22×C411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—22no—
160C2×C4×D43—22no—
161C2×C4×D43C22×C412yes—
162C2×C4×D43C2×D412yes—
163C2×C4×D43C2×D412yes—
164C2×Dic86—22no—
165C2×Dic86C22⋊C411yescharacteristic
166C2×Dic86C22×C411yescharacteristic
167M16×C43—42no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—22no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43C22×C412yes—
177C22⋊C4×C43—22no—
178C42×C43—22no—
179C42×C43C22×C411yescharacteristic
180C42×C43C2×D411yescharacteristic
181C42×C43C2×D411yescharacteristic
182C42×C43C2411yescharacteristic
183C22⋊Dic43—21no—
184C22⋊Dic43C22⋊C412yes—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—22no—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4C22⋊C412yes—
192(C2×D43)⋊C4C22⋊C412yes—
193C4⋊Dic43—22no—
194C4⋊Dic43—22no—
195C4⋊Dic43C22⋊C411yescharacteristic
196C4⋊Dic43C22⋊C411yescharacteristic
197C4⋊Dic43C22×C411yescharacteristic
198C4⋊Dic43C22×C411yescharacteristic
199Dic43⋊C4—21no—
200Dic43⋊C4—21no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4C22⋊C412yes—
206Dic43⋊C4C22⋊C412yes—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—22no—
211C4×Dic43—22no—
212C4×Dic43C22×C412yes—
213C4×Dic43C2×D412yes—
214C4×Dic43C2×D412yes—
215#10621877—81no—
216C2×C43⋊C8—22no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—42no—
220#10621872—82no—
221C23×C43C2×C22⋊C411yescharacteristic
222C22×D43—21no—
223C22×D43C2×C22⋊C412yes—
224Q8×C43—22no—
225Q8×C43—22no—
226Q8×C43—42no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43C2×C22⋊C411yescharacteristic
235C2×C4×C43C2×C22⋊C411yescharacteristic
236C2×C4×C43C2×C22⋊C411yescharacteristic
237C2×C4×C43C23×C411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C22⋊D43—42no—
241C22⋊D43—42no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43C2×C22⋊C412yes—
246C2×Dic43C2×C22⋊C412yes—
247C2×Dic43C2×C22⋊C412yes—
248D172—21no—
249D172—21no—
250D172—22no—
251D172—44no—
252C4×D43—22no—
253C4×D43—22no—
254C4×D43—22no—
255C4×D43—22no—
256C4×D43—42no—
257C4×D43—42no—
258C4×D43—44no—
259C4×D43—44no—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43—42no—
263Dic86—21no—
264Dic86—22no—
265Dic86—44no—
266Dic86#13112yes—
267C8×C43—42no—
268C8×C43—41no—
269C8×C43—41no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272C43⋊C8—42no—
273#17525—431nomaximal, Sylow
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43C22×C22⋊C411yescharacteristic
278C2×D43—22no—
279C2×D43—22no—
280C2×D43—22no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—41no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—42no—
288C4×C43—42no—
289C4×C43#42112yes—
290C4×C43C2×#13111yescharacteristic
291C4×C43#56811yescharacteristic
292C4×C43#57711yescharacteristic
293C4×C43#57811yescharacteristic
294Dic43—22no—
295Dic43—22no—
296Dic43—22no—
297Dic43—22no—
298Dic43—41no—
299Dic43—41no—
300#3482—431no—
301#2991—431no—
302#2922—431no—
303#1495—432no—
304#1493—431no—
305#1489—431no—
306#1487—432no—
307#1485D4311yescharacteristic, complemented
308#1482—432no—
309#1479—432no—
310#1476—431no—
311C2×C43—41no—
312C2×C43#288011yescharacteristic
313C2×C43#289811yescharacteristic
314C2×C43C2×#42111yescharacteristic
315D43—42no—
316D43—81no—
317#557—431no—
318#556—431no—
319#556—861no—
320#552—432no—
321#552—862no—
322D4×Q8—431no—
323#548—432no—
324#547—431no—
325#547—861no—
326#533—861no—
327#533C2×D4311yescharacteristic
328#529—432no—
329#529—862no—
330C4×#41—431no—
331C4×#41—431no—
332C4×#41—861no—
333C2×C4×Q8—432no—
334C8×Q8—861no—
335#436—861no—
336#436—862no—
337#433—862no—
338#431—432no—
339#431—432no—
340#431—432no—
341#431C2×D4311yescharacteristic
342#424—861no—
343#423—431no—
344#423—432no—
345#408—861no—
346C4×M16C2×D4311yescharacteristic
347C2×C4×C8—431no—
348Q8⋊C8—432no—
349Q8⋊C8—432no—
350Q8⋊C8—431no—
351Q8⋊C8—431no—
352Q8⋊C8—432no—
353Q8⋊C8C2×D4312yes—
354Q8⋊C8C2×D4312yes—
355D4⋊C8—431no—
356D4⋊C8—431no—
357D4⋊C8—432no—
358C43#1752511yescharacteristic, complemented, Sylow
359C2×#41—431no—
360C2×#41—431no—
361C2×#41—861no—
362C22×Q8—432no—
363C2×M16—21no—
364C2×M16—862no—
365C2×M16—861no—
366C22×C8—861no—
367C4⋊Q8—861no—
368C4⋊Q8—861no—
369C4⋊Q8C4×D4311yescharacteristic
370C4⋊Q8C4×D4311yescharacteristic
371#126—862no—
372#126—862no—
373#126—862no—
374#125—21no—
375#125—432no—
376#125—862no—
377#125—862no—
378#124—432no—
379#124—862no—
380#123—862no—
381#123—862no—
382#123—862no—
383C22⋊Q8—21no—
384C22⋊Q8—432no—
385C22⋊Q8—862no—
386C22⋊Q8—862no—
387C22⋊Q8—861no—
388C22⋊Q8—861no—
389C22⋊Q8C4×D4312yes—
390#121—432no—
391#121—862no—
392C4×Q8—21no—
393C4×Q8—431no—
394C4×Q8—431no—
395C4×Q8—432no—
396C4×Q8—432no—
397C4×Q8—431no—
398C4×Q8—431no—
399C4×Q8—862no—
400C4×Q8—862no—
401C4×Q8—861no—
402C4×Q8C22×D4312yes—
403C4×D4—432no—
404C4×D4—432no—
405C4×D4—431no—
406C4×D4—431no—
407C4×D4—431no—
408C4×D4—431no—
409C4×D4—862no—
410C4×D4—862no—
411C4×D4—861no—
412C4×D4—861no—
413C4×D4—861no—
414#117—21no—
415#117—431no—
416#117—432no—
417#117—431no—
418#117—862no—
419#117—862no—
420#117—861no—
421#117—861no—
422C2×C4⋊C4—432no—
423C2×C4⋊C4—862no—
424C2×C42—432no—
425C2×C42—862no—
426C2×C42—861no—
427C2×C42C22×D4311yescharacteristic
428C4⋊C8—432no—
429C4⋊C8—862no—
430C4⋊C8—862no—
431C4⋊C8—862no—
432C4⋊C8—861no—
433C4⋊C8C22×D4311yescharacteristic
434C4⋊C8C22×D4311yescharacteristic
435C22⋊C8—21no—
436C22⋊C8—862no—
437C22⋊C8—862no—
438C22⋊C8—862no—
439#97—21no—
440C4×C8—21no—
441C4×C8—431no—
442C4×C8—431no—
443C4×C8—862no—
444C4×C8—861no—
445C4×C8C22×D4312yes—
446#41—862no—
447#41—1721no—
448#41—1722no—
449#41—1724no—
450C2×Q8—21no—
451C2×Q8—431no—
452C2×Q8—431no—
453C2×Q8—862no—
454C2×Q8—864no—
455C2×Q8—1722no—
456C2×Q8C2×C4×D4312yes—
457C2×D4—432no—
458C2×D4—431no—
459C2×D4—431no—
460C2×D4—862no—
461C2×D4—861no—
462C22×C4—432no—
463C22×C4—432no—
464C22×C4—432no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4C2×C4×D4311yescharacteristic
471C22×C4D4×D4311yescharacteristic
472C22×C4D4×D4311yescharacteristic
473M16—42no—
474M16—3442no—
475M16—3441no—
476C2×C8—22no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—862no—
482C2×C8—1722no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—431no—
489C4⋊C4—432no—
490C4⋊C4—431no—
491C4⋊C4—432no—
492C4⋊C4—431no—
493C4⋊C4—431no—
494C4⋊C4—862no—
495C4⋊C4—862no—
496C4⋊C4—862no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4C2×C4×D4312yes—
503C22⋊C4—22no—
504C22⋊C4—432no—
505C22⋊C4—432no—
506C22⋊C4—432no—
507C22⋊C4—862no—
508C22⋊C4—862no—
509C22⋊C4—862no—
510C22⋊C4—862no—
511C22⋊C4—861no—
512C22⋊C4—861no—
513C22⋊C4—861no—
514C42—22no—
515C42—432no—
516C42—432no—
517C42—432no—
518C42—862no—
519C42—862no—
520C42—861no—
521C42—861no—
522C42—861no—
523C42C2×C4×D4311yescharacteristic
524C42D4×D4311yescharacteristic
525C42D4×D4311yescharacteristic
526C42C23×D4311yescharacteristic
527C23—432no—
528C23—861no—
529C23C22⋊C4×D4311yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—42no—
533Q8—432no—
534Q8—861no—
535Q8—862no—
536Q8—1724no—
537D4—861no—
538D4—861no—
539D4—862no—
540D4—1724no—
541D4—1722no—
542D4—1722no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—432no—
551C2×C4—432no—
552C2×C4—432no—
553C2×C4—861no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1724no—
563C2×C4—1724no—
564C2×C4—1722no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4C22⋊C4×D4311yescharacteristic
568C2×C4C22⋊C4×D4311yescharacteristic
569C2×C4C22⋊C4×D4311yescharacteristic
570C2×C4C22×C4×D4311yescharacteristic
571C2×C4C2×D4×D4311yescharacteristic
572C2×C4C2×D4×D4311yescharacteristic
573C8—42no—
574C8—41no—
575C8—41no—
576C8—1721no—
577C8—1721no—
578C8—1722no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—862no—
583C22—862no—
584C22—862no—
585C22—1721no—
586C22—1721no—
587C22—1721no—
588C22C2×C22⋊C4×D4311yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—42no—
593C4—42no—
594C4—862no—
595C4—862no—
596C4—862no—
597C4—862no—
598C4—1721no—
599C4—1721no—
600C4#1458291412yes—
601C4#131×D4311yescharacteristic
602C4#1458366411yescharacteristic
603C4#1458370811yescharacteristic
604C4#1458371511yescharacteristic
605C2—41no—
606C2—3441no—
607C2—1722no—
608C2#1914304311yescharacteristic
609C2#1914312711yescharacteristic
610C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1485C2
socleC22×C43C22×C22⋊C4
prime radical#19148213C2
cosocleC42×C43C24
hypercenter#1485D43
hypocenterC43#17525
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1485

Complements

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

NH ≅ G/Ntype
2. #19143724C2semidirect
3. #19143240C2semidirect
4. #19133059C2semidirect
5. #19133050C2semidirect
6. #19133035C2semidirect
7. #19133022C2semidirect
8. #19133002C2semidirect
9. #19132988C2semidirect
10. #19132975C2semidirect
11. C43×#1485C2semidirect
307. #1485D43semidirect
358. C43#17525semidirect

Maximal subgroups

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

subgroupindex
#191482132
#191437242
#191432402
#191330592
#191330502
#191330352
#191330222
#191330022
#191329882
#191329752
C43×#14852
#1752543