Finite Group Databasebeta

← #25063281

Subgroups — #25063281

Order 11008.

920 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#19148028C211yesmaximal, characteristic
2#19143713C211yesmaximal, characteristic, complemented
3C8×#10621898C211yesmaximal, characteristic, complemented
4#19133066C212yesmaximal, complemented
5#19133059C212yesmaximal, complemented
6#19133054C212yesmaximal, complemented
7#19133048C212yesmaximal, complemented
8#19132990C211yesmaximal, characteristic, complemented
9#19132980C211yesmaximal, characteristic, complemented
10#19132978C211yesmaximal, characteristic, complemented
11C2×C43×Q8⋊C8C211yesmaximal, characteristic, complemented
12#14583530C411yescharacteristic
13#14583521—21no—
14#14583521C412yes—
15#14583507—21no—
16#14583507C412yes—
17#14583496—22no—
18#14583480C411yescharacteristic
19#14583473C411yescharacteristic
20#14583473C411yescharacteristic
21#14583453—21no—
22#14583453C2212yes—
23#14583436—21no—
24#14583436C2212yes—
25#14583433—22no—
26C4×#10621898C2211yescharacteristic
27C4×#10621898C2211yescharacteristic
28#14583026—21no—
29C8×Dic86—21no—
30#14582976—21no—
31#14582970—22no—
32C8×D172—21no—
33C8×C22⋊D43—22no—
34#14582955C2212yes—
35#14582952C2211yescharacteristic
36#14582952C2211yescharacteristic
37#14582950C2212yes—
38#14582921C2212yes—
39C4×C8×D43C2212yes—
40#14582631C2211yescharacteristic
41#14582631C2211yescharacteristic
42Q8⋊(C43⋊C8)C2212yes—
43Q8⋊(C43⋊C8)C2212yes—
44#14582629C2212yes—
45#14582628C2211yescharacteristic
46#14582628C2211yescharacteristic
47#14582626C2212yes—
48C2×C4×Q8×C43C2211yescharacteristic
49C2×C4⋊C8×C43C2211yescharacteristic
50C2×C4×C8×C43C2211yescharacteristic
51C43×Q8⋊C8C2212yes—
52C43×Q8⋊C8C2212yes—
53C2×#10621898C2×C411yescharacteristic
54C2×#10621898C2×C411yescharacteristic
55C2×#10621872—22no—
56C2×C8×D43—22no—
57#13063324—21no—
58#13063324C2×C412yes—
59#13063323—21no—
60#13063323C2×C412yes—
61#13063320—22no—
62#13063320—22no—
63#13063319—22no—
64#13063319—22no—
65#13063317—22no—
66#13063316—21no—
67#13063316C2×C412yes—
68#13063315—22no—
69#13063315—22no—
70#13063314—21no—
71#13063314C2×C412yes—
72#13063313—22no—
73#13063310—22no—
74#13063310—22no—
75#13063308—22no—
76#13063308—22no—
77#13063305—21no—
78#13063305C2×C412yes—
79#13063304—22no—
80#13063303—22no—
81#13063303—22no—
82#13063301—21no—
83#13063301—21no—
84#13063301C2×C412yes—
85#13063301C2×C412yes—
86#13063300—21no—
87#13063300C2×C412yes—
88#13063299—22no—
89C4×Dic86—22no—
90C4×Dic86C2×C411yescharacteristic
91C4×Dic86D411yescharacteristic
92C4×Dic86D411yescharacteristic
93C4×Dic86C2311yescharacteristic
94C4×D172—22no—
95C4×D172C2×C411yescharacteristic
96C4×D172D411yescharacteristic
97C4×D172D411yescharacteristic
98C4×D172C2311yescharacteristic
99C4×C22⋊D43—21no—
100C4×C22⋊D43—21no—
101C4×C22⋊D43D412yes—
102C4×C22⋊D43D412yes—
103#13063284C2×C411yescharacteristic
104#13063284C2×C411yescharacteristic
105#13063282—22no—
106#13063282—21no—
107#13063282—22no—
108#13063282C2×C412yes—
109C42×D43—21no—
110C42×D43C2312yes—
111C4⋊(C43⋊C8)—21no—
112C4⋊(C43⋊C8)C2311yescharacteristic
113C4⋊(C43⋊C8)C2311yescharacteristic
114Dic43⋊C8—22no—
115Dic43⋊C8—22no—
116C22⋊(C43⋊C8)—21no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—22no—
120#13063235—22no—
121C4×C43⋊C8—21no—
122C4×C43⋊C8C2312yes—
123C8×Dic43—22no—
124C22×Q8×C43C2×C411yescharacteristic
125C22×C8×C43—21no—
126C22×C8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43C2×C412yes—
130C4×Q8×C43C2312yes—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43C2×C411yescharacteristic
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2312yes—
137C4×C8×C43—21no—
138C4×C8×C43C2311yescharacteristic
139C4×C8×C43C2311yescharacteristic
140C2×Q8×C43—21no—
141C2×Q8×C43—22no—
142C2×Q8×C43—22no—
143C2×Q8×C43C22×C412yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C2×C22⋊D43—21no—
150C2×C22⋊D43C22⋊C412yes—
151#10621898—22no—
152#10621898—22no—
153#10621898—22no—
154#10621898—22no—
155C2×D172—22no—
156C2×D172C22⋊C411yescharacteristic
157C2×D172C22×C411yescharacteristic
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43C22×C412yes—
162C2×C4×D43C2×D412yes—
163C2×C4×D43C2×D412yes—
164C2×Dic86—22no—
165C2×Dic86C22⋊C411yescharacteristic
166C2×Dic86C22×C411yescharacteristic
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—22no—
170C2×C8×C43—42no—
171C2×C8×C43—81no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43C22×C412yes—
176C42×C43—22no—
177C42×C43—22no—
178C42×C43C22×C411yescharacteristic
179C42×C43C2×D411yescharacteristic
180C42×C43C2×D411yescharacteristic
181C42×C43C2411yescharacteristic
182C22⋊Dic43—21no—
183C22⋊Dic43C22⋊C412yes—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—22no—
187(C2×D43)⋊C4—22no—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4C22⋊C412yes—
193(C2×D43)⋊C4C22⋊C412yes—
194C4⋊Dic43—22no—
195C4⋊Dic43—22no—
196C4⋊Dic43C22⋊C411yescharacteristic
197C4⋊Dic43C22⋊C411yescharacteristic
198C4⋊Dic43C22×C411yescharacteristic
199C4⋊Dic43C22×C411yescharacteristic
200Dic43⋊C4—21no—
201Dic43⋊C4—21no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4C22⋊C412yes—
209Dic43⋊C4C22⋊C412yes—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43C22×C412yes—
214C4×Dic43C2×D412yes—
215C4×Dic43C2×D412yes—
216C2×C43⋊C8—22no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219#10621872—82no—
220C8×D43—44no—
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—22no—
230C2×C4×C43—22no—
231C2×C4×C43—41no—
232C2×C4×C43—42no—
233C2×C4×C43—81no—
234C2×C4×C43C2×C22⋊C411yescharacteristic
235C2×C4×C43C2×C22⋊C411yescharacteristic
236C2×C4×C43C2×C22⋊C411yescharacteristic
237C2×C4×C43#13112yes—
238C2×C4×C43#13112yes—
239C2×C4×C43C23×C411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C22⋊D43—24no—
243C22⋊D43—42no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43C2×C22⋊C412yes—
248C2×Dic43C2×C22⋊C412yes—
249C2×Dic43C2×C22⋊C412yes—
250D172—21no—
251D172—21no—
252D172—22no—
253D172—82no—
254C4×D43—22no—
255C4×D43—22no—
256C4×D43—22no—
257C4×D43—22no—
258C4×D43—42no—
259C4×D43—41no—
260C4×D43—41no—
261C4×D43—42no—
262C4×D43—81no—
263Dic86—22no—
264Dic86—21no—
265Dic86—21no—
266Dic86—82no—
267C8×C43—22no—
268C8×C43—41no—
269C8×C43—42no—
270C43⋊C8—42no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273#17484—431nomaximal, Sylow
274C22×C43—21no—
275C22×C43—21no—
276C22×C43#40812yes—
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#40812yes—
290C4×C43C2×#13111yescharacteristic
291C4×C43C2×#13111yescharacteristic
292C4×C43#57711yescharacteristic
293C4×C43#57811yescharacteristic
294Dic43—22no—
295Dic43—22no—
296Dic43—22no—
297Dic43—41no—
298Dic43—41no—
299Dic43—41no—
300#3461—431no—
301#2989—431no—
302C8×#41—431no—
303#1497—432no—
304#1495—432no—
305#1494—432no—
306#1493—432no—
307#1479—431no—
308#1477—431no—
309#1476—431no—
310C2×Q8⋊C8D4311yescharacteristic, complemented
311C2×C43—22no—
312C2×C43C2×#40811yescharacteristic
313C2×C43#289811yescharacteristic
314C2×C43#290111yescharacteristic
315D43—42no—
316D43—81no—
317#544—431no—
318#542—432no—
319#542—861no—
320#541—432no—
321#541—861no—
322#539—862no—
323#537—431no—
324#536—431no—
325#536—431no—
326#533—432no—
327#533—861no—
328#529—432no—
329#529—862no—
330#529—861no—
331C4×#41—431no—
332C4×#41—431no—
333C2×C4×Q8C2×D4311yescharacteristic
334#446—861no—
335C8×Q8—861no—
336#436—861no—
337#435—862no—
338C8×D4—861no—
339C8×D4—862no—
340#432—432no—
341#431—431no—
342#431—432no—
343#431—431no—
344#423—432no—
345C2×C4⋊C8C2×D4311yescharacteristic
346C2×C4×C8—432no—
347C2×C4×C8C2×D4311yescharacteristic
348Q8⋊C8—432no—
349Q8⋊C8—432no—
350Q8⋊C8—432no—
351Q8⋊C8—431no—
352Q8⋊C8—431no—
353Q8⋊C8C2×D4312yes—
354Q8⋊C8C2×D4312yes—
355D4⋊C8—432no—
356D4⋊C8—431no—
357D4⋊C8—431no—
358C43#1748411yescharacteristic, complemented, Sylow
359C2×#41—431no—
360C2×#41—431no—
361C22×Q8C4×D4311yescharacteristic
362C2×M16—862no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—862no—
366C4⋊Q8—432no—
367C4⋊Q8—432no—
368C4⋊Q8—861no—
369C4⋊Q8—861no—
370#126—862no—
371#126—862no—
372#126—862no—
373#126—862no—
374#125—432no—
375#125—862no—
376#125—862no—
377#125—861no—
378#125—862no—
379#124—432no—
380#124—862no—
381#124—861no—
382#123—862no—
383#123—862no—
384#123—862no—
385#123—862no—
386C22⋊Q8—432no—
387C22⋊Q8—432no—
388C22⋊Q8—432no—
389C22⋊Q8—862no—
390C22⋊Q8—862no—
391C22⋊Q8—862no—
392C22⋊Q8—861no—
393C22⋊Q8—861no—
394C22⋊Q8—861no—
395#121—432no—
396#121—861no—
397#121—862no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8—431no—
401C4×Q8—431no—
402C4×Q8—431no—
403C4×Q8—431no—
404C4×Q8—862no—
405C4×Q8C4×D4312yes—
406C4×Q8C22×D4312yes—
407C4×D4—432no—
408C4×D4—432no—
409C4×D4—431no—
410C4×D4—431no—
411C4×D4—431no—
412C4×D4—431no—
413C4×D4—862no—
414C4×D4—861no—
415C4×D4—861no—
416#117—431no—
417#117—432no—
418#117—431no—
419#117—862no—
420#117—862no—
421#117—861no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4C4×D4311yescharacteristic
424C2×C42—21no—
425C2×C42—432no—
426C2×C42—861no—
427C2×C42C22×D4311yescharacteristic
428C4⋊C8—21no—
429C4⋊C8—431no—
430C4⋊C8—431no—
431C4⋊C8—862no—
432C4⋊C8—862no—
433C4⋊C8—861no—
434C4⋊C8C22×D4312yes—
435C22⋊C8—862no—
436C22⋊C8—862no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439#97—862no—
440C4×C8—21no—
441C4×C8—432no—
442C4×C8—862no—
443C4×C8—861no—
444C4×C8C22×D4311yescharacteristic
445C4×C8C22×D4311yescharacteristic
446#41—862no—
447#41—862no—
448#41—862no—
449#41—862no—
450C2×Q8—21no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—431no—
454C2×Q8—431no—
455C2×Q8—862no—
456C2×Q8C2×C4×D4312yes—
457C2×D4—432no—
458C2×D4—431no—
459C2×D4—431no—
460C2×D4—862no—
461C2×D4—861no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—432no—
465C22×C4—432no—
466C22×C4—432no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4C2×C4×D4311yescharacteristic
471C22×C4D4×D4311yescharacteristic
472C22×C4D4×D4311yescharacteristic
473M16—3442no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—22no—
477C2×C8—42no—
478C2×C8—81no—
479C2×C8—862no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—1724no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—22no—
486C4⋊C4—432no—
487C4⋊C4—431no—
488C4⋊C4—431no—
489C4⋊C4—432no—
490C4⋊C4—431no—
491C4⋊C4—431no—
492C4⋊C4—862no—
493C4⋊C4—862no—
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—432no—
504C22⋊C4—432no—
505C22⋊C4—432no—
506C22⋊C4—862no—
507C22⋊C4—862no—
508C22⋊C4—862no—
509C22⋊C4—862no—
510C22⋊C4—862no—
511C22⋊C4—862no—
512C22⋊C4—861no—
513C22⋊C4—861no—
514C22⋊C4—861no—
515C42—22no—
516C42—22no—
517C42—432no—
518C42—432no—
519C42—432no—
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—862no—
534Q8—861no—
535Q8—861no—
536Q8—3442no—
537D4—864no—
538D4—862no—
539D4—861no—
540D4—861no—
541D4—3442no—
542D4—1722no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—81no—
550C2×C4—432no—
551C2×C4—432no—
552C2×C4—432no—
553C2×C4—862no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—3441no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4C22⋊C4×D4311yescharacteristic
566C2×C4C22⋊C4×D4311yescharacteristic
567C2×C4C22⋊C4×D4311yescharacteristic
568C2×C4#1306333112yes—
569C2×C4#1306333312yes—
570C2×C4C22×C4×D4311yescharacteristic
571C2×C4C2×D4×D4311yescharacteristic
572C2×C4C2×D4×D4311yescharacteristic
573C8—22no—
574C8—41no—
575C8—42no—
576C8—1722no—
577C8—1721no—
578C8—1721no—
579C22—21no—
580C22—21no—
581C22—862no—
582C22—862no—
583C22—862no—
584C22—1721no—
585C22—1721no—
586C22—1721no—
587C22#1458286412yes—
588C22C2×C22⋊C4×D4311yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—42no—
593C4—42no—
594C4—862no—
595C4—862no—
596C4—862no—
597C4—1721no—
598C4—1721no—
599C4—1721no—
600C4#1458286412yes—
601C4C2×#1306333111yescharacteristic
602C4C2×#1306333311yescharacteristic
603C4#1458370511yescharacteristic
604C4#1458371211yescharacteristic
605C2—22no—
606C2—3441no—
607C2—1722no—
608C2C2×#1458286411yescharacteristic
609C2#1914312311yescharacteristic
610C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC2×C43×Q8⋊C8C2
socleC22×C43C22×C22⋊C4
prime radical#14583480C4
cosocleC42×C43C24
hypercenterC2×Q8⋊C8D43
hypocenterC43#17484
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #19143713C2semidirect
3. C8×#10621898C2semidirect
4. #19133066C2semidirect
5. #19133059C2semidirect
6. #19133054C2semidirect
7. #19133048C2semidirect
8. #19132990C2semidirect
9. #19132980C2semidirect
10. #19132978C2semidirect
11. C2×C43×Q8⋊C8C2semidirect
310. C2×Q8⋊C8D43semidirect
358. C43#17484semidirect

Maximal subgroups

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

subgroupindex
#191480282
#191437132
C8×#106218982
#191330662
#191330592
#191330542
#191330482
#191329902
#191329802
#191329782
C2×C43×Q8⋊C82
#1748443