Finite Group Databasebeta

← #25063270

Subgroups — #25063270

Order 11008.

984 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148017C211yesmaximal, characteristic
2#19143713C211yesmaximal, characteristic, complemented
3C8×#10621898C211yesmaximal, characteristic, complemented
4#19133062C212yesmaximal, complemented
5#19133057C212yesmaximal, complemented
6#19133052C212yesmaximal, complemented
7#19133044C212yesmaximal, complemented
8#19132986C211yesmaximal, characteristic, complemented
9#19132980C211yesmaximal, characteristic, complemented
10#19132978C211yesmaximal, characteristic, complemented
11C2×C43×D4⋊C8C211yesmaximal, characteristic, complemented
12#14583530C411yescharacteristic
13#14583514—21no—
14#14583514C412yes—
15#14583500—21no—
16#14583500C412yes—
17#14583487—22no—
18#14583480C411yescharacteristic
19#14583466C411yescharacteristic
20#14583466C411yescharacteristic
21#14583446—21no—
22#14583446C2212yes—
23#14583431—21no—
24#14583431C2212yes—
25#14583410—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#14582955C2212yescomplemented
35#14582952C2211yescharacteristic
36#14582952C2211yescharacteristic
37#14582950C2212yescomplemented
38#14582921C2212yescomplemented
39C4×C8×D43C2212yescomplemented
40#14582631C2211yescharacteristic, complemented
41#14582631C2211yescharacteristic, complemented
42#14582629C2212yescomplemented
43#14582628C2211yescharacteristic, complemented
44#14582628C2211yescharacteristic, complemented
45D4⋊(C43⋊C8)C2212yes—
46D4⋊(C43⋊C8)C2212yes—
47#14582626C2212yescomplemented
48C2×C4×D4×C43C2211yescharacteristic
49C2×C4⋊C8×C43C2211yescharacteristic
50C2×C4×C8×C43C2211yescharacteristic
51C43×D4⋊C8C2212yes—
52C43×D4⋊C8C2212yes—
53C2×#10621898—22no—
54C2×#10621898C2×C411yescharacteristic
55C2×#10621898C2×C411yescharacteristic
56C2×#10621872—22no—
57C2×C8×D43—22no—
58#13063324—21no—
59#13063324C2×C412yes—
60#13063321—21no—
61#13063321C2×C412yes—
62#13063318—22no—
63#13063318—22no—
64#13063316—21no—
65#13063316C2×C412yes—
66#13063312—21no—
67#13063312C2×C412yes—
68#13063311—22no—
69#13063311—22no—
70#13063308—22no—
71#13063308—22no—
72#13063307—22no—
73#13063307—22no—
74#13063305—21no—
75#13063305C2×C412yes—
76#13063304—22no—
77#13063304—22no—
78#13063300—21no—
79#13063300C2×C412yes—
80#13063299—22no—
81#13063299—22no—
82#13063298—22no—
83#13063298—22no—
84#13063296—21no—
85#13063296—21no—
86#13063296C2×C412yes—
87#13063296C2×C412yes—
88#13063294—22no—
89#13063294—22no—
90C4×Dic86C2×C411yescharacteristic
91C4×Dic86D411yescharacteristic
92C4×Dic86D411yescharacteristic
93C4×Dic86C2311yescharacteristic
94C4×D172C2×C411yescharacteristic
95C4×D172D411yescharacteristic
96C4×D172D411yescharacteristic
97C4×D172C2311yescharacteristic
98C4×C22⋊D43—21no—
99C4×C22⋊D43—21no—
100C4×C22⋊D43—22no—
101C4×C22⋊D43—22no—
102C4×C22⋊D43D412yes—
103C4×C22⋊D43D412yes—
104#13063284—22no—
105#13063284C2×C411yescharacteristic
106#13063284C2×C411yescharacteristic
107#13063282—21no—
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×D4×C43C2×C411yescharacteristic
125C23×C4×C43—21no—
126C22×C8×C43—21no—
127C22×C8×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43C2×C412yes—
131C4×D4×C43C2312yes—
132C2×C4⋊C4×C43C2×C411yescharacteristic
133C2×C22⋊C4×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2312yes—
137C4×C8×C43—21no—
138C4×C8×C43C2311yescharacteristic
139C4×C8×C43C2311yescharacteristic
140C24×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—22no—
143C2×D4×C43—22no—
144C2×D4×C43C22×C412yes—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—21no—
148C22×C4×C43—81no—
149C22×C4×C43—81no—
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C2×C22⋊D43—22no—
154C2×C22⋊D43—22no—
155C2×C22⋊D43—21no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—22no—
158C2×C22⋊D43C22⋊C412yes—
159#10621898—22no—
160#10621898—22no—
161#10621898—22no—
162#10621898—22no—
163#10621898—82no—
164#10621898—82no—
165C2×D172—22no—
166C2×D172C22⋊C411yescharacteristic
167C2×D172C22×C411yescharacteristic
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43C22×C412yes—
172C2×C4×D43C2×D412yes—
173C2×C4×D43C2×D412yes—
174C2×Dic86—22no—
175C2×Dic86C22⋊C411yescharacteristic
176C2×Dic86C22×C411yescharacteristic
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—22no—
180C2×C8×C43—42no—
181C2×C8×C43—81no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43C22×C412yes—
184C22⋊C4×C43—22no—
185C22⋊C4×C43—22no—
186C42×C43C22×C411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2411yescharacteristic
190C22⋊Dic43—22no—
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—21no—
195C22⋊Dic43C22⋊C412yes—
196(C2×D43)⋊C4—21no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4C22⋊C412yes—
201(C2×D43)⋊C4C22⋊C412yes—
202C4⋊Dic43—22no—
203C4⋊Dic43—22no—
204C4⋊Dic43C22⋊C411yescharacteristic
205C4⋊Dic43C22⋊C411yescharacteristic
206C4⋊Dic43C22×C411yescharacteristic
207C4⋊Dic43C22×C411yescharacteristic
208Dic43⋊C4—21no—
209Dic43⋊C4—21no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4C22⋊C412yes—
213Dic43⋊C4C22⋊C412yes—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43C22×C412yes—
218C4×Dic43C2×D412yes—
219C4×Dic43C2×D412yes—
220C2×C43⋊C8—22no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223#10621872—82no—
224C8×D43—44no—
225C23×C43—22no—
226C23×C43—42no—
227C23×C43—81no—
228C23×C43—81no—
229C23×C43C2×C22⋊C411yescharacteristic
230C22×D43—21no—
231C22×D43C2×C22⋊C412yes—
232D4×C43—22no—
233D4×C43—22no—
234D4×C43—42no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—41no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—82no—
242C2×C4×C43—81no—
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43#13112yes—
247C2×C4×C43#13112yes—
248C2×C4×C43C23×C411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C22⋊D43—24no—
252C22⋊D43—42no—
253C22⋊D43—82no—
254C22⋊D43—82no—
255C22⋊D43—82no—
256C22⋊D43—82no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43C2×C22⋊C412yes—
261C2×Dic43C2×C22⋊C412yes—
262C2×Dic43C2×C22⋊C412yes—
263D172—21no—
264D172—21no—
265D172—22no—
266D172—82no—
267C4×D43—22no—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—42no—
272C4×D43—41no—
273C4×D43—41no—
274C4×D43—42no—
275C4×D43—81no—
276Dic86—22no—
277Dic86—21no—
278Dic86—21no—
279Dic86—82no—
280C8×C43—22no—
281C8×C43—41no—
282C8×C43—42no—
283C43⋊C8—42no—
284C43⋊C8—41no—
285C43⋊C8—41no—
286#17483—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—84no—
293C22×C43#40812yes—
294C22×C43C22×C22⋊C411yescharacteristic
295C2×D43—22no—
296C2×D43—22no—
297C2×D43—22no—
298C2×D43—41no—
299C2×D43—41no—
300C2×D43—41no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—42no—
305C4×C43#40812yes—
306C4×C43C2×#13111yescharacteristic
307C4×C43C2×#13111yescharacteristic
308C4×C43#57611yescharacteristic
309C4×C43#57711yescharacteristic
310Dic43—22no—
311Dic43—22no—
312Dic43—22no—
313Dic43—41no—
314Dic43—41no—
315Dic43—41no—
316#3460—431no—
317#2989—431no—
318C8×#41—431no—
319#1496—432no—
320#1495—432no—
321#1494—432no—
322#1492—432no—
323#1478—431no—
324#1477—431no—
325#1476—431no—
326C2×D4⋊C8D4311yescharacteristic, complemented
327C2×C43—22no—
328C2×C43—82no—
329C2×C43C2×#40811yescharacteristic
330C2×C43#289711yescharacteristic
331C2×C43#290111yescharacteristic
332D43—42no—
333D43—81no—
334#544—431no—
335#542—432no—
336#542—861no—
337#540—432no—
338#540—861no—
339#538—862no—
340#537—431no—
341#535—431no—
342#535—431no—
343#532—432no—
344#532—861no—
345#529—432no—
346#529—861no—
347#525—862no—
348C4×#41—431no—
349C4×#41—431no—
350C2×C4×D4C2×D4311yescharacteristic
351#446—861no—
352C8×Q8—861no—
353#436—861no—
354#435—862no—
355C8×D4—861no—
356C8×D4—862no—
357#432—432no—
358#431—431no—
359#431—432no—
360#431—431no—
361#423—432no—
362C2×C4⋊C8C2×D4311yescharacteristic
363C2×C4×C8—432no—
364C2×C4×C8C2×D4311yescharacteristic
365Q8⋊C8—432no—
366Q8⋊C8—431no—
367Q8⋊C8—431no—
368D4⋊C8—432no—
369D4⋊C8—432no—
370D4⋊C8—432no—
371D4⋊C8—431no—
372D4⋊C8—431no—
373D4⋊C8C2×D4312yes—
374D4⋊C8C2×D4312yes—
375C43#1748311yescharacteristic, complemented, Sylow
376C2×#41—431no—
377C2×#41—431no—
378C2×#41—862no—
379C22×D4C4×D4311yescharacteristic
380C23×C4—21no—
381C2×M16—862no—
382C22×C8—21no—
383C22×C8—21no—
384C22×C8—862no—
385C4⋊Q8—432no—
386C4⋊Q8—861no—
387#127—432no—
388#127—861no—
389#126—862no—
390#126—862no—
391#125—432no—
392#125—861no—
393#124—432no—
394#124—862no—
395#124—862no—
396#124—861no—
397#123—862no—
398#123—862no—
399#123—862no—
400#123—862no—
401C22⋊Q8—432no—
402C22⋊Q8—862no—
403C22⋊Q8—861no—
404C22⋊Q8—862no—
405#121—432no—
406#121—432no—
407#121—432no—
408#121—862no—
409#121—862no—
410#121—862no—
411#121—861no—
412#121—861no—
413#121—861no—
414#121—862no—
415#120—862no—
416#120—862no—
417C4×Q8—431no—
418C4×Q8—431no—
419C4×Q8—431no—
420C4×Q8—431no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—432no—
424C4×D4—432no—
425C4×D4—431no—
426C4×D4—431no—
427C4×D4—431no—
428C4×D4—431no—
429C4×D4—862no—
430C4×D4—862no—
431C4×D4—861no—
432C4×D4—861no—
433C4×D4C4×D4312yes—
434C4×D4C22×D4312yes—
435#117—431no—
436#117—432no—
437#117—431no—
438#117—862no—
439#117—861no—
440C2×C4⋊C4C4×D4311yescharacteristic
441C2×C22⋊C4—21no—
442C2×C42—432no—
443C2×C42—861no—
444C2×C42C22×D4311yescharacteristic
445C4⋊C8—21no—
446C4⋊C8—431no—
447C4⋊C8—431no—
448C4⋊C8—862no—
449C4⋊C8—862no—
450C4⋊C8—861no—
451C4⋊C8C22×D4312yes—
452C22⋊C8—862no—
453C22⋊C8—862no—
454C22⋊C8—861no—
455C22⋊C8—861no—
456#97—862no—
457C4×C8—21no—
458C4×C8—432no—
459C4×C8—862no—
460C4×C8—861no—
461C4×C8C22×D4311yescharacteristic
462C4×C8C22×D4311yescharacteristic
463C24—21no—
464#41—862no—
465#41—862no—
466#41—862no—
467#41—862no—
468#41—3442no—
469#41—3442no—
470C2×Q8—431no—
471C2×Q8—431no—
472C2×Q8—862no—
473C2×D4—21no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—432no—
477C2×D4—431no—
478C2×D4—431no—
479C2×D4—862no—
480C2×D4—862no—
481C2×D4—862no—
482C2×D4—862no—
483C2×D4—862no—
484C2×D4—861no—
485C2×D4C2×C4×D4312yes—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—81no—
490C22×C4—81no—
491C22×C4—432no—
492C22×C4—432no—
493C22×C4—432no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4C2×C4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499C22×C4D4×D4311yescharacteristic
500M16—3442no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—22no—
504C2×C8—42no—
505C2×C8—81no—
506C2×C8—862no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—1724no—
510C4⋊C4—21no—
511C4⋊C4—431no—
512C4⋊C4—431no—
513C4⋊C4—432no—
514C4⋊C4—432no—
515C4⋊C4—431no—
516C4⋊C4—431no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4C2×C4×D4312yes—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—432no—
527C22⋊C4—432no—
528C22⋊C4—432no—
529C22⋊C4—862no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—861no—
536C22⋊C4—861no—
537C22⋊C4—861no—
538C42—432no—
539C42—432no—
540C42—432no—
541C42—861no—
542C42—861no—
543C42—861no—
544C42C2×C4×D4311yescharacteristic
545C42D4×D4311yescharacteristic
546C42D4×D4311yescharacteristic
547C42C23×D4311yescharacteristic
548C23—22no—
549C23—42no—
550C23—81no—
551C23—81no—
552C23—432no—
553C23—861no—
554C23C22⋊C4×D4311yescharacteristic
555Q8—862no—
556Q8—861no—
557Q8—861no—
558Q8—3442no—
559D4—22no—
560D4—22no—
561D4—42no—
562D4—864no—
563D4—862no—
564D4—861no—
565D4—861no—
566D4—3442no—
567D4—3442no—
568D4—3442no—
569D4—3442no—
570D4—3442no—
571D4—1722no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—82no—
579C2×C4—81no—
580C2×C4—432no—
581C2×C4—432no—
582C2×C4—432no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—3441no—
591C2×C4—1722no—
592C2×C4—1722no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4C22⋊C4×D4311yescharacteristic
596C2×C4C22⋊C4×D4311yescharacteristic
597C2×C4C22⋊C4×D4311yescharacteristic
598C2×C4#1306333112yes—
599C2×C4#1306333312yes—
600C2×C4C22×C4×D4311yescharacteristic
601C2×C4C2×D4×D4311yescharacteristic
602C2×C4C2×D4×D4311yescharacteristic
603C8—22no—
604C8—41no—
605C8—42no—
606C8—1722no—
607C8—1721no—
608C8—1721no—
609C22—21no—
610C22—21no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—84no—
615C22—862no—
616C22—862no—
617C22—862no—
618C22—1721no—
619C22—1721no—
620C22—1721no—
621C22#1458286412yes—
622C22C2×C22⋊C4×D4311yescharacteristic
623C4—21no—
624C4—21no—
625C4—21no—
626C4—42no—
627C4—862no—
628C4—862no—
629C4—862no—
630C4—1721no—
631C4—1721no—
632C4—1721no—
633C4#1458286412yes—
634C4C2×#1306333111yescharacteristic
635C4C2×#1306333311yescharacteristic
636C4#1458370011yescharacteristic
637C4#1458370511yescharacteristic
638C2—22no—
639C2—82no—
640C2—3441no—
641C2—1722no—
642C2C2×#1458286411yescharacteristic
643C2#1914311611yescharacteristic
644C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC2×C43×D4⋊C8C2
socleC22×C43C22×C22⋊C4
prime radical#19148017C2
cosocleC42×C43C24
hypercenterC2×D4⋊C8D43
hypocenterC43#17483
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #19143713C2semidirect
3. C8×#10621898C2semidirect
4. #19133062C2semidirect
5. #19133057C2semidirect
6. #19133052C2semidirect
7. #19133044C2semidirect
8. #19132986C2semidirect
9. #19132980C2semidirect
10. #19132978C2semidirect
11. C2×C43×D4⋊C8C2semidirect
34. #14582955C22semidirect
37. #14582950C22semidirect
38. #14582921C22semidirect
39. C4×C8×D43C22semidirect
40. #14582631C22semidirect
41. #14582631C22semidirect
42. #14582629C22semidirect
43. #14582628C22semidirect
44. #14582628C22semidirect
47. #14582626C22semidirect
326. C2×D4⋊C8D43semidirect
375. C43#17483semidirect

Maximal subgroups

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

subgroupindex
#191480172
#191437132
C8×#106218982
#191330622
#191330572
#191330522
#191330442
#191329862
#191329802
#191329782
C2×C43×D4⋊C82
#1748343