Finite Group Databasebeta

← #25063580

Subgroups — #25063580

Order 11008.

1020 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148213C211yesmaximal, characteristic
2#19143725C211yesmaximal, characteristic, complemented
3C4×#13063331C211yesmaximal, characteristic, complemented
4#19133048C212yesmaximal, complemented
5#19133033C212yesmaximal, complemented
6#19133032C211yesmaximal, characteristic, complemented
7#19133016C211yesmaximal, characteristic, complemented
8#19133014C212yesmaximal, complemented
9#19132978C211yesmaximal, characteristic, complemented
10#19132976C212yesmaximal, complemented
11C43×#1493C211yesmaximal, characteristic, complemented
12C2×#13063331—21no—
13#14583624C411yescharacteristic
14#14583623C411yescharacteristic
15#14583620C412yes—
16#14583583—21no—
17#14583581—22no—
18#14583564C411yescharacteristic
19#14583559—21no—
20#14583552C411yescharacteristic
21#14583551C412yes—
22#14583453C2212yes—
23#14583436—21no—
24#14583427—22no—
25C4×#10621902C2212yes—
26C4×#10621898C2211yescharacteristic
27C4×#10621898C2211yescharacteristic
28C4×Q8×D43—21no—
29#14583023—21no—
30#14582976—21no—
31#14582975—22no—
32#14582952C2211yescharacteristic
33#14582951C2212yes—
34#14582921C2212yes—
35#14582854—21no—
36#14582853—22no—
37C4×#10621877C2211yescharacteristic
38C4×#10621872C2212yes—
39C4×C8×D43C2212yes—
40#14582631C2211yescharacteristic
41#14582631C2211yescharacteristic
42Q8⋊(C43⋊C8)C2212yes—
43Q8⋊(C43⋊C8)C2212yes—
44#14582629C2212yes—
45#14582628C2211yescharacteristic
46#14582628C2211yescharacteristic
47#14582626C2212yes—
48C43×#533C2211yescharacteristic
49C43×#423C2211yescharacteristic
50C2×C4×C8×C43C2211yescharacteristic
51C43×Q8⋊C8C2212yes—
52C43×Q8⋊C8C2212yes—
53C2×#10621902C2×C412yes—
54C2×#10621898C2×C411yescharacteristic
55C2×#10621898D411yescharacteristic
56C2×Q8×D43—21no—
57#13063331—28no—
58C2×#10621877—21no—
59C2×#10621872—22no—
60C2×#10621872—22no—
61C2×C8×D43—22no—
62#13063324C2×C412yes—
63#13063323C2×C412yes—
64#13063320—22no—
65#13063320—22no—
66#13063318—22no—
67#13063316—21no—
68#13063315—22no—
69#13063315—22no—
70#13063314—21no—
71#13063311—22no—
72#13063310—22no—
73#13063310—22no—
74#13063307—22no—
75#13063305C2×C412yes—
76#13063303—22no—
77#13063303—22no—
78#13063301—21no—
79#13063301C2×C412yes—
80#13063300—21no—
81#13063298—22no—
82Q8×Dic43—21no—
83Q8×Dic43C2×C412yes—
84C4×Dic86—22no—
85C4×Dic86C2×C411yescharacteristic
86C4×Dic86C2×C411yescharacteristic
87C4×Dic86D411yescharacteristic
88C4×Dic86C2311yescharacteristic
89#13063290—21no—
90#13063290—22no—
91C4×D172—22no—
92C4×D172C2×C411yescharacteristic
93C4×D172C2×C411yescharacteristic
94C4×D172D411yescharacteristic
95C4×D172C2311yescharacteristic
96#13063287—22no—
97#13063287C2×C412yes—
98C4×C22⋊D43—21no—
99C4×C22⋊D43—21no—
100C4×C22⋊D43C2×C412yes—
101C4×C22⋊D43D412yes—
102#13063284C2×C411yescharacteristic
103#13063284D411yescharacteristic
104#13063283—22no—
105#13063283C2×C412yes—
106#13063282—22no—
107#13063282—21no—
108#13063282D412yes—
109C4⋊C4×D43—21no—
110C4⋊C4×D43—22no—
111C42×D43—21no—
112C42×D43—22no—
113C42×D43C2312yes—
114C4⋊(C43⋊C8)C2311yescharacteristic
115C4⋊(C43⋊C8)C2311yescharacteristic
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—22no—
119#13063236—21no—
120#13063235—22no—
121C4×C43⋊C8—21no—
122C4×C43⋊C8C2312yes—
123C8×Dic43—22no—
124C8×Dic43—22no—
125C2×M16×C43—21no—
126C22×C8×C43—21no—
127C4⋊Q8×C43C2×C411yescharacteristic
128C4⋊Q8×C43C2×C411yescharacteristic
129#125×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43C2×C412yes—
132C4×Q8×C43—21no—
133C4×Q8×C43C2312yes—
134#117×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2312yes—
138C4×C8×C43—21no—
139C4×C8×C43C2311yescharacteristic
140C4×C8×C43C2311yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43C22×C412yes—
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C2×C22⋊D43—21no—
147C2×C22⋊D43C22⋊C412yes—
148#10621902—24no—
149#10621902—42no—
150Q8×D43—44no—
151#10621898—22no—
152#10621898—24no—
153#10621898—41no—
154C2×D172—22no—
155C2×D172C22⋊C411yescharacteristic
156C2×D172C22×C411yescharacteristic
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—22no—
161C2×C4×D43—22no—
162C2×C4×D43C22×C412yes—
163C2×C4×D43C2×D412yes—
164C2×C4×D43C2×D412yes—
165C2×Dic86—22no—
166C2×Dic86C22⋊C411yescharacteristic
167C2×Dic86C22×C411yescharacteristic
168M16×C43—81no—
169C2×C8×C43—24no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—22no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43C22×C412yes—
179C22⋊C4×C43—22no—
180C42×C43—22no—
181C42×C43C22×C411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43C2×D411yescharacteristic
184C42×C43C2411yescharacteristic
185C22⋊Dic43—21no—
186C22⋊Dic43C22⋊C412yes—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4C22⋊C412yes—
194(C2×D43)⋊C4C22⋊C412yes—
195C4⋊Dic43—22no—
196C4⋊Dic43—22no—
197C4⋊Dic43C22⋊C411yescharacteristic
198C4⋊Dic43C22⋊C411yescharacteristic
199C4⋊Dic43C22×C411yescharacteristic
200C4⋊Dic43C22×C411yescharacteristic
201Dic43⋊C4—21no—
202Dic43⋊C4—21no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4C22⋊C412yes—
208Dic43⋊C4C22⋊C412yes—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—22no—
213C4×Dic43—22no—
214C4×Dic43C22×C412yes—
215C4×Dic43C2×D412yes—
216C4×Dic43C2×D412yes—
217#10621877—24no—
218C2×C43⋊C8—22no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221#10621872—28no—
222#10621872—82no—
223C8×D43—28no—
224C23×C43C2×C22⋊C411yescharacteristic
225C22×D43—21no—
226C22×D43C2×C22⋊C412yes—
227Q8×C43—22no—
228Q8×C43—22no—
229Q8×C43—42no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
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—24no—
244C22⋊D43—42no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43C2×C22⋊C412yes—
249C2×Dic43C2×C22⋊C412yes—
250C2×Dic43C2×C22⋊C412yes—
251D172—21no—
252D172—22no—
253D172—44no—
254D172#13112yescomplemented
255C4×D43—22no—
256C4×D43—22no—
257C4×D43—22no—
258C4×D43—22no—
259C4×D43—24no—
260C4×D43—44no—
261C4×D43—42no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—42no—
265C4×D43—44no—
266Dic86—21no—
267Dic86—21no—
268Dic86—44no—
269Dic86#10414yes—
270C8×C43—22no—
271C8×C43—22no—
272C8×C43—42no—
273C43⋊C8—24no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276#17518—431nomaximal, Sylow
277C22×C43—21no—
278C22×C43—21no—
279C22×C43—21no—
280C22×C43C22×C22⋊C411yescharacteristic
281C2×D43—22no—
282C2×D43—22no—
283C2×D43—22no—
284C2×D43—22no—
285C2×D43—41no—
286C2×D43—41no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—42no—
291C4×C43—42no—
292C4×C43C2×#10412yes—
293C4×C43C2×#13111yescharacteristic
294C4×C43#56811yescharacteristic
295C4×C43#57711yescharacteristic
296C4×C43#57811yescharacteristic
297Dic43—22no—
298Dic43—22no—
299Dic43—41no—
300Dic43—41no—
301Dic43—41no—
302Dic43C2×#10414yes—
303#3482—431no—
304#2991—431no—
305C4×#131—431no—
306#1493—432no—
307#1493D4311yescharacteristic, complemented
308#1489—431no—
309#1489—432no—
310#1485—432no—
311#1485—431no—
312#1476—431no—
313#1476—432no—
314C2×C43—41no—
315C2×C43#288011yescharacteristic
316C2×C43#289811yescharacteristic
317C2×C43C22×#10411yescharacteristic
318D43—42no—
319D43—42no—
320C2×#131—861no—
321#557—431no—
322#556—431no—
323#556—432no—
324#552—861no—
325#552—862no—
326D4×Q8—431no—
327#548—861no—
328#547—431no—
329#547—432no—
330#533—432no—
331#533C2×D4311yescharacteristic
332#529—862no—
333#529—861no—
334C4×#41—431no—
335C4×#41—432no—
336C4×#41—431no—
337C2×C4×Q8—861no—
338C8×Q8—861no—
339#436—861no—
340#436—862no—
341#431—431no—
342#431—432no—
343#423—432no—
344#423C2×D4311yescharacteristic
345#405—862no—
346#405—861no—
347C4×M16—431no—
348C4×M16—432no—
349C2×C4×C8—432no—
350C2×C4×C8C2×D4311yescharacteristic
351Q8⋊C8—432no—
352Q8⋊C8—432no—
353Q8⋊C8—432no—
354Q8⋊C8—431no—
355Q8⋊C8—431no—
356Q8⋊C8C2×D4312yes—
357Q8⋊C8C2×D4312yes—
358D4⋊C8—432no—
359D4⋊C8—431no—
360D4⋊C8—431no—
361C43#1751811yescharacteristic, complemented, Sylow
362C2×#41—431no—
363C2×#41—432no—
364C2×#41—431no—
365C22×Q8—861no—
366#131—868no—
367C2×M16—21no—
368C2×M16—862no—
369C2×M16—862no—
370C2×M16—861no—
371C22×C8—21no—
372C22×C8—862no—
373C4⋊Q8—432no—
374C4⋊Q8—432no—
375C4⋊Q8C4×D4311yescharacteristic
376C4⋊Q8C4×D4311yescharacteristic
377#126—862no—
378#126—862no—
379#126—862no—
380#125—21no—
381#125—862no—
382#125—862no—
383#125—861no—
384#124—862no—
385#124—861no—
386#123—862no—
387#123—862no—
388#123—862no—
389C22⋊Q8—21no—
390C22⋊Q8—432no—
391C22⋊Q8—432no—
392C22⋊Q8—862no—
393C22⋊Q8—862no—
394C22⋊Q8—861no—
395C22⋊Q8C4×D4312yes—
396#121—862no—
397#121—861no—
398C4×Q8—21no—
399C4×Q8—431no—
400C4×Q8—431no—
401C4×Q8—432no—
402C4×Q8—431no—
403C4×Q8—431no—
404C4×Q8—862no—
405C4×Q8—862no—
406C4×Q8—861no—
407C4×Q8—861no—
408C4×Q8C22×D4312yes—
409C4×D4—432no—
410C4×D4—432no—
411C4×D4—432no—
412C4×D4—431no—
413C4×D4—431no—
414C4×D4—431no—
415C4×D4—431no—
416C4×D4—862no—
417C4×D4—862no—
418C4×D4—861no—
419C4×D4—861no—
420#117—21no—
421#117—431no—
422#117—432no—
423#117—431no—
424#117—432no—
425#117—862no—
426#117—862no—
427#117—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—862no—
430C2×C42—432no—
431C2×C42—862no—
432C2×C42—861no—
433C2×C42C22×D4311yescharacteristic
434C4⋊C8—21no—
435C4⋊C8—431no—
436C4⋊C8—431no—
437C4⋊C8—862no—
438C4⋊C8C22×D4312yes—
439C22⋊C8—862no—
440C22⋊C8—861no—
441#97—862no—
442#97—861no—
443C4×C8—21no—
444C4×C8—432no—
445C4×C8—862no—
446C4×C8—862no—
447C4×C8—861no—
448C4×C8C22×D4311yescharacteristic
449C4×C8C22×D4311yescharacteristic
450#41—864no—
451#41—862no—
452#41—864no—
453#41—1721no—
454#41—1722no—
455C2×Q8—21no—
456C2×Q8—431no—
457C2×Q8—431no—
458C2×Q8—862no—
459C2×Q8—1724no—
460C2×Q8C2×C4×D4312yes—
461C2×D4—432no—
462C2×D4—431no—
463C2×D4—431no—
464C2×D4—862no—
465C2×D4—861no—
466C22×C4—432no—
467C22×C4—432no—
468C22×C4—432no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4C2×C4×D4311yescharacteristic
475C22×C4D4×D4311yescharacteristic
476C22×C4D4×D4311yescharacteristic
477M16—81no—
478M16—868no—
479M16—864no—
480M16—3442no—
481C2×C8—24no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—22no—
485C2×C8—868no—
486C2×C8—862no—
487C2×C8—861no—
488C2×C8—861no—
489C4⋊C4—21no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—432no—
495C4⋊C4—431no—
496C4⋊C4—432no—
497C4⋊C4—431no—
498C4⋊C4—431no—
499C4⋊C4—431no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4C2×C4×D4312yes—
509C22⋊C4—22no—
510C22⋊C4—432no—
511C22⋊C4—432no—
512C22⋊C4—432no—
513C22⋊C4—862no—
514C22⋊C4—862no—
515C22⋊C4—862no—
516C22⋊C4—862no—
517C22⋊C4—861no—
518C22⋊C4—861no—
519C22⋊C4—861no—
520C42—22no—
521C42—432no—
522C42—432no—
523C42—432no—
524C42—862no—
525C42—862no—
526C42—861no—
527C42—861no—
528C42—861no—
529C42C2×C4×D4311yescharacteristic
530C42D4×D4311yescharacteristic
531C42D4×D4311yescharacteristic
532C42C23×D4311yescharacteristic
533C23—432no—
534C23—861no—
535C23C22⋊C4×D4311yescharacteristic
536Q8—22no—
537Q8—22no—
538Q8—42no—
539Q8—434no—
540Q8—861no—
541Q8—861no—
542Q8—1724no—
543D4—432no—
544D4—864no—
545D4—861no—
546D4—862no—
547D4—1724no—
548D4—1722no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—432no—
557C2×C4—432no—
558C2×C4—432no—
559C2×C4—864no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—1722no—
568C2×C4—1724no—
569C2×C4—1724no—
570C2×C4—1722no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4C22⋊C4×D4311yescharacteristic
574C2×C4C22⋊C4×D4311yescharacteristic
575C2×C4C22⋊C4×D4311yescharacteristic
576C2×C4C22×C4×D4311yescharacteristic
577C2×C4C2×D4×D4311yescharacteristic
578C2×C4C2×D4×D4311yescharacteristic
579C8—22no—
580C8—22no—
581C8—42no—
582C8—864no—
583C8—1721no—
584C8—1721no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—862no—
589C22—862no—
590C22—862no—
591C22—862no—
592C22—1721no—
593C22—1721no—
594C22C2×C22⋊C4×D4311yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—42no—
599C4—42no—
600C4—434no—
601C4—862no—
602C4—862no—
603C4—1721no—
604C4—1721no—
605C4—1721no—
606C4#104×D4312yes—
607C4#131×D4311yescharacteristic
608C4#1458366411yescharacteristic
609C4#1458370511yescharacteristic
610C4#1458371211yescharacteristic
611C2—41no—
612C2—1722no—
613C2—1722no—
614C2#1914304311yescharacteristic
615C2#1914312311yescharacteristic
616C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1493C2
socleC22×C43C22×C22⋊C4
prime radical#19148213C2
cosocleC42×C43C24
hypercenter#1493D43
hypocenterC43#17518
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. #19143725C2semidirect
3. C4×#13063331C2semidirect
4. #19133048C2semidirect
5. #19133033C2semidirect
6. #19133032C2semidirect
7. #19133016C2semidirect
8. #19133014C2semidirect
9. #19132978C2semidirect
10. #19132976C2semidirect
11. C43×#1493C2semidirect
254. D172#131semidirect
307. #1493D43semidirect
361. C43#17518semidirect

Maximal subgroups

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

subgroupindex
#191482132
#191437252
C4×#130633312
#191330482
#191330332
#191330322
#191330162
#191330142
#191329782
#191329762
C43×#14932
#1751843