Finite Group Databasebeta

← #25063464

Subgroups — #25063464

Order 11008.

980 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148162C211yesmaximal, characteristic
2#19143551C211yesmaximal, characteristic, complemented
3#19143260C211yesmaximal, characteristic, complemented
4#19133054C212yesmaximal, complemented
5#19133050C211yesmaximal, characteristic, complemented
6#19133028C212yesmaximal, complemented
7#19133021C211yesmaximal, characteristic, complemented
8#19133002C212yesmaximal, complemented
9#19132976C212yesmaximal, complemented
10C2×#14582626C211yesmaximal, characteristic, complemented
11C43×#1481C211yesmaximal, characteristic, complemented
12#14583623C411yescharacteristic
13#14583615C411yescharacteristic
14#14583610C411yescharacteristic
15#14583602—21no—
16#14583591C412yes—
17#14583587—21no—
18#14583576—22no—
19#14583552C411yescharacteristic
20#14583540C412yes—
21#14583436—22no—
22#14583436C2212yes—
23#14583411—21no—
24C4×#10621902C2212yes—
25C4×#10621898C2211yescharacteristic
26C2×C4×D172C2211yescharacteristic
27#117×D43—21no—
28#14583023—21no—
29#14582964—21no—
30(C22⋊D43)⋊C8—22no—
31#14582959—22no—
32#14582955C2212yescomplemented
33#14582951C2212yescomplemented
34#14582950C2212yescomplemented
35#14582923C2211yescharacteristic
36#14582865—21no—
37#14582854—21no—
38C2×C4×C43⋊C8C2211yescharacteristic
39C4×C8×D43C2212yescomplemented
40Q8⋊(C43⋊C8)C2212yescomplemented
41Q8⋊(C43⋊C8)C2212yescomplemented
42#14582628C2212yes—
43#14582628C2212yes—
44#14582626C2211yescharacteristic
45#14582626C2211yescharacteristic
46#14582626C2211yescharacteristic
47#14582626C2211yescharacteristic
48C43×#533C2211yescharacteristic
49C43×#431C2211yescharacteristic
50C2×C4⋊C8×C43C2211yescharacteristic
51C43×Q8⋊C8C2212yescomplemented
52C43×Q8⋊C8C2212yescomplemented
53C2×#10621902C2×C412yes—
54C2×#10621898D411yescharacteristic
55C22×D172C2×C411yescharacteristic
56C22×C4×D43—21no—
57C2×#10621877—21no—
58C22×C43⋊C8—21no—
59C2×C8×D43—22no—
60#13063320—22no—
61#13063320—22no—
62#13063320—22no—
63#13063316—22no—
64#13063316C2×C412yes—
65#13063314—22no—
66#13063314C2×C412yes—
67#13063310—22no—
68#13063310—22no—
69#13063310—22no—
70#13063309—22no—
71#13063305—21no—
72#13063305—21no—
73#13063301—22no—
74#13063301C2×C412yes—
75#13063300—21no—
76#13063300—21no—
77#13063300—22no—
78#13063300C2×C412yes—
79#13063295—22no—
80Q8×Dic43C2×C412yes—
81C4×Dic86C2×C411yescharacteristic
82C4×Dic86D411yescharacteristic
83C4×D172—22no—
84C4×D172—22no—
85C4×D172—21no—
86C4×D172—21no—
87C4×D172C2×C411yescharacteristic
88C4×D172C2×C411yescharacteristic
89C4×D172C2×C411yescharacteristic
90C4×D172D411yescharacteristic
91C4×D172C2311yescharacteristic
92C4×D172C2311yescharacteristic
93#13063287—22no—
94#13063287C2×C412yes—
95C4×C22⋊D43C2×C412yes—
96C4×C22⋊D43D412yes—
97#13063284D411yescharacteristic
98#13063283—21no—
99#13063283—21no—
100#13063283—22no—
101#13063283C2×C412yes—
102#13063282—22no—
103#13063282D412yes—
104#13063281—22no—
105C2×C4⋊Dic43C2×C411yescharacteristic
106C4⋊C4×D43—21no—
107C4⋊C4×D43—21no—
108C2×(C2×D43)⋊C4—21no—
109C22⋊C4×D43—22no—
110C42×D43—22no—
111C42×D43C2312yes—
112C4⋊(C43⋊C8)—21no—
113C4⋊(C43⋊C8)C2312yes—
114Dic43⋊C8—22no—
115(C2×D43)⋊C8—22no—
116(C2×D43)⋊C8—22no—
117(C2×D43)⋊C8—22no—
118#13063235—22no—
119C4×C43⋊C8—21no—
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C8×Dic43—22no—
123C8×Dic43—22no—
124C22×C8×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×C43—21no—
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C22⋊C8×C43—21no—
139C4×C8×C43C2312yes—
140C23×D43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43C22×C412yes—
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C2×C22⋊D43C22⋊C412yes—
147C22×Dic43—21no—
148#10621902—24no—
149#10621902—42no—
150#10621898—22no—
151#10621898—22no—
152C2×D172—21no—
153C2×D172—22no—
154C2×D172—22no—
155C2×D172—22no—
156C2×D172—41no—
157C2×D172C22⋊C411yescharacteristic
158C2×D172C22×C411yescharacteristic
159C2×D172C22×C411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
168C2×C4×D43C22×C412yes—
169C2×C4×D43C2×D412yes—
170C2×C4×D43C2×D412yes—
171C2×Dic86C22⋊C411yescharacteristic
172C2×C8×C43—22no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—42no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43C22×C412yes—
182C22⋊C4×C43—22no—
183C42×C43—22no—
184C42×C43C22×C411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43C2411yescharacteristic
188C22⋊Dic43C22⋊C412yes—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4C22⋊C412yes—
200(C2×D43)⋊C4C22⋊C412yes—
201C4⋊Dic43—21no—
202C4⋊Dic43—22no—
203C4⋊Dic43—22no—
204C4⋊Dic43C22⋊C411yescharacteristic
205C4⋊Dic43C22⋊C411yescharacteristic
206C4⋊Dic43C22×C411yescharacteristic
207C4⋊Dic43C22×C411yescharacteristic
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4C22⋊C412yes—
211Dic43⋊C4C22⋊C412yes—
212C4×Dic43—22no—
213C4×Dic43—22no—
214C4×Dic43C22×C412yes—
215C4×Dic43C2×D412yes—
216C4×Dic43C2×D412yes—
217#10621877—42no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—22no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—42no—
222C8×D43—44no—
223C23×C43C2×C22⋊C411yescharacteristic
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—42no—
227C22×D43—42no—
228C22×D43—81no—
229C22×D43C2×C22⋊C412yes—
230Q8×C43—22no—
231Q8×C43—22no—
232Q8×C43—81no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—41no—
238C2×C4×C43C2×C22⋊C411yescharacteristic
239C2×C4×C43C2×C22⋊C411yescharacteristic
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43#13512yes—
242C2×C4×C43#13512yes—
243C2×C4×C43C23×C411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C22⋊D43—24no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—42no—
250C2×Dic43C2×C22⋊C412yes—
251C2×Dic43C2×C22⋊C412yes—
252C2×Dic43C2×C22⋊C412yes—
253D172—21no—
254D172—21no—
255D172—21no—
256D172—22no—
257D172—42no—
258D172—44no—
259D172—82no—
260D172#13112yes—
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—42no—
266C4×D43—44no—
267C4×D43—41no—
268C4×D43—41no—
269C4×D43—41no—
270C4×D43—41no—
271C4×D43—42no—
272C4×D43—42no—
273C4×D43—82no—
274Dic86—22no—
275C8×C43—42no—
276C8×C43—41no—
277C8×C43—41no—
278C43⋊C8—22no—
279C43⋊C8—41no—
280C43⋊C8—42no—
281#17508—431nomaximal, Sylow
282C22×C43—21no—
283C22×C43—21no—
284C22×C43#41612yes—
285C22×C43C22×C22⋊C411yescharacteristic
286C2×D43—22no—
287C2×D43—22no—
288C2×D43—22no—
289C2×D43—22no—
290C2×D43—41no—
291C2×D43—41no—
292C2×D43—41no—
293C2×D43—41no—
294C2×D43—41no—
295C2×D43—84no—
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—42no—
300C4×C43—42no—
301C4×C43#41612yes—
302C4×C43C2×#13111yescharacteristic
303C4×C43#56811yescharacteristic
304C4×C43C2×#13511yescharacteristic
305C4×C43C2×#13511yescharacteristic
306Dic43—22no—
307Dic43—22no—
308Dic43—22no—
309Dic43—41no—
310Dic43—41no—
311#3475—431no—
312C8×#41—431no—
313#2925—431no—
314#1494—432no—
315#1493—431no—
316#1488—432no—
317#1486—431no—
318#1482—432no—
319#1481D4311yescharacteristic, complemented
320#1476—432no—
321C2×D4⋊C8—431no—
322C2×C43—22no—
323C2×C43#288011yescharacteristic
324C2×C43C2×#41611yescharacteristic
325C2×C43#290111yescharacteristic
326D43—42no—
327D43—42no—
328D43—81no—
329#556—431no—
330#555—431no—
331#554—431no—
332#553—861no—
333#552—432no—
334#552—861no—
335#551—862no—
336#547—431no—
337#546—432no—
338#533C2×D4311yescharacteristic
339#529—432no—
340#529—862no—
341#525—861no—
342C4×#41—431no—
343C4×#41—432no—
344C2×C4×D4—431no—
345C2×#117—861no—
346C8×Q8—861no—
347C8×D4—862no—
348C8×D4—861no—
349#433—862no—
350#432—432no—
351#431—432no—
352#431—432no—
353#431C2×D4311yescharacteristic
354#423—431no—
355C2×C4⋊C8C2×D4311yescharacteristic
356#408—861no—
357#405—861no—
358C2×C4×C8—431no—
359C2×C4×C8—432no—
360Q8⋊C8—432no—
361Q8⋊C8—432no—
362Q8⋊C8C2×D4312yescomplemented
363Q8⋊C8C2×D4312yescomplemented
364D4⋊C8—431no—
365D4⋊C8—431no—
366D4⋊C8—431no—
367D4⋊C8—431no—
368D4⋊C8—432no—
369D4⋊C8—432no—
370C43#1750811yescharacteristic, complemented, Sylow
371C2×#41—431no—
372C2×#41—432no—
373C22×D4—431no—
374C23×C4—861no—
375C2×M16—861no—
376C22×C8—21no—
377C22×C8—862no—
378C22×C8—861no—
379C4⋊Q8C4×D4311yescharacteristic
380C4⋊Q8C4×D4311yescharacteristic
381#126—862no—
382#126—862no—
383#126—862no—
384#125—21no—
385#125—432no—
386#125—862no—
387#124—432no—
388#124—862no—
389#123—862no—
390#123—862no—
391#123—862no—
392#123—862no—
393C22⋊Q8—21no—
394C22⋊Q8—432no—
395C22⋊Q8—861no—
396C22⋊Q8—861no—
397C22⋊Q8—862no—
398C22⋊Q8C4×D4312yes—
399#121—432no—
400#121—862no—
401#121—861no—
402#121—861no—
403#120—862no—
404C4×Q8—21no—
405C4×Q8—431no—
406C4×Q8—431no—
407C4×Q8—432no—
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—431no—
417C4×D4—431no—
418C4×D4—862no—
419C4×D4—862no—
420C4×D4—862no—
421C4×D4—861no—
422C4×D4—861no—
423#117—21no—
424#117—431no—
425#117—432no—
426#117—432no—
427#117—862no—
428#117—862no—
429#117—862no—
430#117—861no—
431#117—861no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C22⋊C4—862no—
436C2×C22⋊C4—861no—
437C2×C42—432no—
438C2×C42—862no—
439C2×C42C22×D4311yescharacteristic
440C4⋊C8—21no—
441C4⋊C8—21no—
442C4⋊C8—432no—
443C4⋊C8—862no—
444C4⋊C8—861no—
445C4⋊C8C22×D4311yescharacteristic
446C4⋊C8C22×D4311yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—862no—
449C22⋊C8—862no—
450C22⋊C8—862no—
451#97—862no—
452C4×C8—431no—
453C4×C8—431no—
454C4×C8—862no—
455C4×C8—862no—
456C4×C8—861no—
457C4×C8C22×D4312yes—
458C24—861no—
459#41—862no—
460#41—862no—
461#41—864no—
462#41—1722no—
463C2×Q8—21no—
464C2×Q8—431no—
465C2×Q8C2×C4×D4312yes—
466C2×D4—432no—
467C2×D4—431no—
468C2×D4—431no—
469C2×D4—431no—
470C2×D4—862no—
471C2×D4—862no—
472C2×D4—862no—
473C2×D4—861no—
474C2×D4—1721no—
475C22×C4—432no—
476C22×C4—432no—
477C22×C4—432no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—1722no—
486C22×C4—1722no—
487C22×C4C2×C4×D4311yescharacteristic
488C22×C4D4×D4311yescharacteristic
489C22×C4D4×D4311yescharacteristic
490M16—1722no—
491C2×C8—22no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—42no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—862no—
498C2×C8—1724no—
499C2×C8—1722no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—431no—
506C4⋊C4—431no—
507C4⋊C4—432no—
508C4⋊C4—432no—
509C4⋊C4—431no—
510C4⋊C4—431no—
511C4⋊C4—862no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4—862no—
515C4⋊C4—861no—
516C4⋊C4C2×C4×D4312yes—
517C22⋊C4—22no—
518C22⋊C4—432no—
519C22⋊C4—432no—
520C22⋊C4—432no—
521C22⋊C4—862no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—861no—
528C22⋊C4—861no—
529C22⋊C4—861no—
530C22⋊C4—861no—
531C42—22no—
532C42—432no—
533C42—432no—
534C42—432no—
535C42—862no—
536C42—862no—
537C42C2×C4×D4311yescharacteristic
538C42D4×D4311yescharacteristic
539C42D4×D4311yescharacteristic
540C42C23×D4311yescharacteristic
541C23—432no—
542C23—861no—
543C23—861no—
544C23—3441no—
545C23—1722no—
546C23—1722no—
547C23C22⋊C4×D4311yescharacteristic
548Q8—22no—
549Q8—22no—
550Q8—81no—
551Q8—862no—
552D4—432no—
553D4—864no—
554D4—861no—
555D4—862no—
556D4—861no—
557D4—861no—
558D4—3442no—
559D4—1722no—
560D4—1724no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—432no—
567C2×C4—432no—
568C2×C4—432no—
569C2×C4—862no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—3442no—
576C2×C4—1722no—
577C2×C4—1724no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4—1722no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4C22⋊C4×D4311yescharacteristic
586C2×C4C22⋊C4×D4311yescharacteristic
587C2×C4C22⋊C4×D4311yescharacteristic
588C2×C4#1306334612yes—
589C2×C4#1306334812yes—
590C2×C4C22×C4×D4311yescharacteristic
591C2×C4C2×D4×D4311yescharacteristic
592C2×C4C2×D4×D4311yescharacteristic
593C8—42no—
594C8—41no—
595C8—41no—
596C8—862no—
597C8—1721no—
598C8—1722no—
599C22—21no—
600C22—21no—
601C22—862no—
602C22—862no—
603C22—862no—
604C22—862no—
605C22—3444no—
606C22—1721no—
607C22—1721no—
608C22—1721no—
609C22—1721no—
610C22—1721no—
611C22#1458289412yes—
612C22C2×C22⋊C4×D4311yescharacteristic
613C4—21no—
614C4—21no—
615C4—21no—
616C4—42no—
617C4—42no—
618C4—862no—
619C4—862no—
620C4—862no—
621C4—1721no—
622C4—1721no—
623C4#1458289412yes—
624C4#131×D4311yescharacteristic
625C4#1458366411yescharacteristic
626C4C2×#1306334611yescharacteristic
627C4C2×#1306334811yescharacteristic
628C2—22no—
629C2—3441no—
630C2—1722no—
631C2—1722no—
632C2#1914304311yescharacteristic
633C2C2×#1458289411yescharacteristic
634C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1481C2
socleC22×C43C22×C22⋊C4
prime radical#19148162C2
cosocleC42×C43C24
hypercenter#1481D43
hypocenterC43#17508
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
2. #19143551C2semidirect
3. #19143260C2semidirect
4. #19133054C2semidirect
5. #19133050C2semidirect
6. #19133028C2semidirect
7. #19133021C2semidirect
8. #19133002C2semidirect
9. #19132976C2semidirect
10. C2×#14582626C2semidirect
11. C43×#1481C2semidirect
32. #14582955C22semidirect
33. #14582951C22semidirect
34. #14582950C22semidirect
39. C4×C8×D43C22semidirect
40. Q8⋊(C43⋊C8)C22semidirect
41. Q8⋊(C43⋊C8)C22semidirect
51. C43×Q8⋊C8C22semidirect
52. C43×Q8⋊C8C22semidirect
319. #1481D43semidirect
362. Q8⋊C8C2×D43semidirect
363. Q8⋊C8C2×D43semidirect
370. C43#17508semidirect

Maximal subgroups

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

subgroupindex
#191481622
#191435512
#191432602
#191330542
#191330502
#191330282
#191330212
#191330022
#191329762
C2×#145826262
C43×#14812
#1750843