Finite Group Databasebeta

← #25063109

Subgroups — #25063109

Order 11008.

1032 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147892C211yesmaximal, characteristic
2C2×#14582951C211yesmaximal, characteristic, complemented
3#431×D43C211yesmaximal, characteristic, complemented
4#19133002C214yesmaximal, complemented
5#19132998C211yesmaximal, characteristic, complemented
6#19132995C211yesmaximal, characteristic, complemented
7#19132993C211yesmaximal, characteristic, complemented
8#19132976C214yesmaximal, complemented
9C43×#1481C211yesmaximal, characteristic, complemented
10#14583454C411yescharacteristic
11#14583454C411yescharacteristic
12#14583450C411yescharacteristic
13#14583450C411yescharacteristic
14#14583449C2211yescharacteristic
15#14583436—21no—
16#14583436C2212yes—
17#14583435—21no—
18#14583435C412yes—
19#14583434—21no—
20#14583434—21no—
21#14583412—21no—
22#14583412C412yes—
23#14583411—21no—
24C4×#10621902—21no—
25C4×#10621902C2212yes—
26#14583367—21no—
27C2×C42×D43C2211yescharacteristic
28#14582952C2211yescharacteristic
29#14582951—21no—
30#14582951—21no—
31#14582951—21no—
32#14582951C2212yes—
33#14582951C2212yes—
34#14582950C2212yes—
35#14582949—21no—
36C2×C4⋊(C43⋊C8)C2211yescharacteristic
37C4⋊C8×D43—21no—
38C2×(C2×D43)⋊C8—21no—
39C22⋊C8×D43—21no—
40C2×C8×Dic43—21no—
41C4×C8×D43C2212yes—
42Q8⋊(C43⋊C8)C2214yescomplemented
43#14582628C2214yescomplemented
44#14582626C2214yescomplemented
45C43×#533C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C2×C4⋊C8×C43C2211yescharacteristic
48C43×Q8⋊C8C2214yescomplemented
49C2×#10621902—21no—
50C2×#10621902C2×C412yes—
51C2×#10621898—21no—
52C22×C4×D43C2×C411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C22×C4×D43D411yescharacteristic
55C22×C43⋊C8—21no—
56C2×C8×D43—22no—
57#13063325C2×C411yescharacteristic
58#13063322C2×C411yescharacteristic
59#13063320—22no—
60#13063320—22no—
61#13063316—21no—
62#13063316C2×C412yes—
63#13063314—21no—
64#13063314C2×C412yes—
65#13063313—21no—
66#13063310—22no—
67#13063310—22no—
68#13063309—22no—
69#13063305—21no—
70#13063305—21no—
71#13063301—21no—
72#13063301C2×C412yes—
73#13063300—21no—
74#13063300—21no—
75#13063300—21no—
76#13063300C2×C412yes—
77#13063299—21no—
78#13063299C2×C412yes—
79#13063295—22no—
80Q8×Dic43—21no—
81Q8×Dic43C2×C412yes—
82#13063290—21no—
83#13063290—21no—
84C4×D172—22no—
85C4×D172—22no—
86C4×D172—21no—
87C4×D172C2312yes—
88#13063287—22no—
89#13063287—22no—
90#13063287—21no—
91#13063287—21no—
92#13063287—21no—
93#13063287C2×C412yes—
94(C22⋊D43)⋊C4—22no—
95(C22⋊D43)⋊C4—22no—
96#13063283—21no—
97#13063283—22no—
98#13063283—22no—
99#13063283C2×C412yes—
100#13063282—22no—
101C2×C4×Dic43C2×C411yescharacteristic
102C2×C4×Dic43D411yescharacteristic
103C2×C4×Dic43D411yescharacteristic
104C42×D43—22no—
105C42×D43C2×C411yescharacteristic
106C42×D43C2×C411yescharacteristic
107C42×D43D411yescharacteristic
108C42×D43D411yescharacteristic
109C42×D43D411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43C2311yescharacteristic
112C42×D43C2311yescharacteristic
113C4⋊(C43⋊C8)—21no—
114C4⋊(C43⋊C8)—21no—
115C4⋊(C43⋊C8)C2312yes—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121C4×C43⋊C8C2312yes—
122C8×Dic43—22no—
123C8×Dic43—22no—
124C8×Dic43—22no—
125C22×C8×C43—21no—
126C4⋊Q8×C43C2×C411yescharacteristic
127C4⋊Q8×C43C2×C411yescharacteristic
128#125×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43C2×C412yes—
131C4×Q8×C43—21no—
132C4×Q8×C43C2312yes—
133#117×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2312yes—
138C22⋊C8×C43—21no—
139C4×C8×C43C2312yes—
140C23×D43C22⋊C411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43C22×C412yes—
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C2×C22⋊D43—22no—
147C22×Dic43C22⋊C411yescharacteristic
148C22×Dic43C22⋊C411yescharacteristic
149C22×Dic43C22⋊C411yescharacteristic
150#10621902—28no—
151#10621902—44no—
152#10621898—42no—
153#10621898—42no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—22no—
157C2×D172—22no—
158C2×D172C22×C412yes—
159C2×C4×D43—22no—
160C2×C4×D43—22no—
161C2×C4×D43—24no—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—22no—
165C2×C4×D43—42no—
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22⋊C411yescharacteristic
168C2×C4×D43C22⋊C411yescharacteristic
169C2×C4×D43C22⋊C411yescharacteristic
170C2×C4×D43C22⋊C411yescharacteristic
171C2×C4×D43C22⋊C411yescharacteristic
172C2×C4×D43C22×C411yescharacteristic
173C2×C4×D43C22×C411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×C4×D43C2×D411yescharacteristic
176C2×C4×D43C2×D411yescharacteristic
177C2×C4×D43C2×D411yescharacteristic
178C2×Dic86—21no—
179C2×C8×C43—22no—
180C2×C8×C43—22no—
181C2×C8×C43—42no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—22no—
186C4⋊C4×C43—22no—
187C4⋊C4×C43C22×C412yes—
188C22⋊C4×C43—22no—
189C42×C43—22no—
190C42×C43C22×C411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43C2411yescharacteristic
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)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—22no—
202C4⋊Dic43—21no—
203C4⋊Dic43—22no—
204C4⋊Dic43—22no—
205C4⋊Dic43C22×C412yes—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22×C411yescharacteristic
217C4×Dic43C22×C411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219C4×Dic43C2×D411yescharacteristic
220C4×Dic43C2×D411yescharacteristic
221C4×Dic43C2×D411yescharacteristic
222C2×C43⋊C8—22no—
223C2×C43⋊C8—22no—
224C2×C43⋊C8—42no—
225C8×D43—44no—
226C23×C43C2×C22⋊C411yescharacteristic
227C22×D43—22no—
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—41no—
231C22×D43C2×C22⋊C411yescharacteristic
232C22×D43C2×C22⋊C411yescharacteristic
233Q8×C43—24no—
234Q8×C43—42no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—41no—
239C2×C4×C43C2×C22⋊C411yescharacteristic
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43#13512yes—
243C2×C4×C43#13512yes—
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C22⋊D43—44no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43C2×C22⋊C411yescharacteristic
253C2×Dic43C2×C22⋊C411yescharacteristic
254C2×Dic43C2×C22⋊C411yescharacteristic
255C2×Dic43C2×C22⋊C411yescharacteristic
256C2×Dic43C2×C22⋊C411yescharacteristic
257C2×Dic43C2×C22⋊C411yescharacteristic
258D172—24no—
259D172—42no—
260D172—44no—
261D172—44no—
262D172—42no—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—21no—
266C4×D43—21no—
267C4×D43—21no—
268C4×D43—21no—
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—41no—
275C4×D43—41no—
276C4×D43—42no—
277C4×D43—42no—
278C4×D43—44no—
279C4×D43—44no—
280C4×D43#13114yes—
281Dic86—42no—
282C8×C43—42no—
283C8×C43—42no—
284C43⋊C8—42no—
285C43⋊C8—42no—
286#17458—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43#41612yes—
290C22×C43C22×C22⋊C411yescharacteristic
291C2×D43—21no—
292C2×D43—21no—
293C2×D43—21no—
294C2×D43—21no—
295C2×D43—21no—
296C2×D43—44no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43#40812yes—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—42no—
305C4×C43—42no—
306C4×C43#41612yes—
307C4×C43C2×#13112yes—
308C4×C43C2×#13511yescharacteristic
309C4×C43C2×#13511yescharacteristic
310Dic43—21no—
311Dic43—21no—
312Dic43—21no—
313Dic43—21no—
314Dic43—42no—
315Dic43#40812yes—
316Dic43#42112yes—
317#3444—431no—
318C2×#431—431no—
319C2×#431—431no—
320#1482—434no—
321#1481—431no—
322#1481D4311yescharacteristic, complemented
323#1480—431no—
324#1480—431no—
325#1476—434no—
326C2×C43—22no—
327C2×C43C2×#40811yescharacteristic
328C2×C43C2×#41611yescharacteristic
329C2×C43C2×#42111yescharacteristic
330D43—22no—
331D43—41no—
332D43—82no—
333#533—431no—
334#533—431no—
335#533C2×D4311yescharacteristic
336#532—431no—
337#532—431no—
338#532—431no—
339#529—432no—
340#529—432no—
341#529—861no—
342#529—861no—
343#529—861no—
344#529—861no—
345#525—432no—
346#525—861no—
347#525—861no—
348C4×#41—432no—
349C4×#41—861no—
350C4×#41—861no—
351C22×C42—431no—
352#431—431no—
353#431—432no—
354#431—432no—
355#431—432no—
356#431—861no—
357#431—861no—
358#431—861no—
359#431—861no—
360#431C2×D4311yescharacteristic
361C2×C4⋊C8—431no—
362C2×C4⋊C8—861no—
363C2×C4⋊C8C2×D4311yescharacteristic
364C2×C22⋊C8—861no—
365C2×C22⋊C8—861no—
366C2×C4×C8—432no—
367C2×C4×C8—861no—
368Q8⋊C8—434no—
369Q8⋊C8C2×D4314yescomplemented
370D4⋊C8—434no—
371D4⋊C8—434no—
372C43#1745811yescharacteristic, complemented, Sylow
373C2×#41—432no—
374C2×#41—861no—
375C2×#41—861no—
376C23×C4—431no—
377C23×C4—431no—
378C23×C4—431no—
379C22×C8—21no—
380C22×C8—862no—
381C22×C8—861no—
382C4⋊Q8—431no—
383C4⋊Q8C4×D4311yescharacteristic
384C4⋊Q8C4×D4311yescharacteristic
385#127—431no—
386#126—862no—
387#126—862no—
388#125—21no—
389#125—432no—
390#125—861no—
391#124—432no—
392#124—861no—
393#124—861no—
394#123—862no—
395#123—862no—
396#123—862no—
397C22⋊Q8—21no—
398C22⋊Q8—432no—
399C22⋊Q8—861no—
400C22⋊Q8—861no—
401C22⋊Q8—861no—
402C22⋊Q8C4×D4312yes—
403#121—432no—
404#121—432no—
405#121—861no—
406#121—861no—
407#121—861no—
408#121—861no—
409#120—862no—
410C4×Q8—21no—
411C4×Q8—432no—
412C4×Q8—861no—
413C4×Q8—861no—
414C4×Q8—861no—
415C4×Q8C22×D4312yes—
416C4×D4—432no—
417C4×D4—432no—
418C4×D4—862no—
419C4×D4—862no—
420C4×D4—861no—
421C4×D4—861no—
422C4×D4—861no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—861no—
428#117—21no—
429#117—432no—
430#117—862no—
431#117—862no—
432#117—862no—
433#117—861no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—862no—
446C2×C42C22×D4311yescharacteristic
447C4⋊C8—21no—
448C4⋊C8—21no—
449C4⋊C8—432no—
450C4⋊C8—862no—
451C4⋊C8—861no—
452C4⋊C8—861no—
453C4⋊C8C22×D4312yes—
454C22⋊C8—21no—
455C22⋊C8—862no—
456C22⋊C8—862no—
457C22⋊C8—862no—
458C22⋊C8—861no—
459C4×C8—432no—
460C4×C8—862no—
461C4×C8—862no—
462C4×C8—862no—
463C4×C8C22×D4312yes—
464C24—431no—
465#41—868no—
466#41—1724no—
467#41—1722no—
468#41—1722no—
469C2×Q8—21no—
470C2×Q8—861no—
471C2×Q8C2×C4×D4312yes—
472C2×D4—432no—
473C2×D4—862no—
474C2×D4—862no—
475C2×D4—862no—
476C2×D4—861no—
477C2×D4—861no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—864no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—1722no—
500C22×C4C2×C4×D4311yescharacteristic
501C22×C4D4×D4311yescharacteristic
502C22×C4D4×D4311yescharacteristic
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—42no—
506C2×C8—862no—
507C2×C8—862no—
508C2×C8—1724no—
509C2×C8—1722no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—432no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—861no—
521C4⋊C4C2×C4×D4312yes—
522C22⋊C4—22no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C22⋊C4—862no—
529C22⋊C4—862no—
530C22⋊C4—862no—
531C42—22no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—862no—
545C42—862no—
546C42C2×C4×D4311yescharacteristic
547C42D4×D4311yescharacteristic
548C42D4×D4311yescharacteristic
549C42C23×D4311yescharacteristic
550C23—431no—
551C23—431no—
552C23—862no—
553C23—862no—
554C23—862no—
555C23—1721no—
556C23C22⋊C4×D4311yescharacteristic
557Q8—24no—
558Q8—42no—
559Q8—1722no—
560D4—864no—
561D4—1722no—
562D4—1724no—
563D4—1724no—
564D4—1724no—
565D4—1722no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—431no—
571C2×C4—431no—
572C2×C4—434no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—431no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—862no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1724no—
595C2×C4—1724no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4C22⋊C4×D4311yescharacteristic
599C2×C4C22⋊C4×D4311yescharacteristic
600C2×C4C22⋊C4×D4311yescharacteristic
601C2×C4#1306334612yes—
602C2×C4#1306334812yes—
603C2×C4C22×C4×D4311yescharacteristic
604C2×C4C2×D4×D4311yescharacteristic
605C2×C4C2×D4×D4311yescharacteristic
606C8—42no—
607C8—42no—
608C8—1722no—
609C8—1722no—
610C22—21no—
611C22—21no—
612C22—432no—
613C22—861no—
614C22—861no—
615C22—861no—
616C22—861no—
617C22—861no—
618C22—1724no—
619C22—1722no—
620C22—1722no—
621C22—1722no—
622C22#1458289412yes—
623C22C2×C22⋊C4×D4311yescharacteristic
624C4—21no—
625C4—21no—
626C4—21no—
627C4—42no—
628C4—42no—
629C4—432no—
630C4—432no—
631C4—861no—
632C4—861no—
633C4—861no—
634C4—861no—
635C4—1722no—
636C4#1458289412yes—
637C4#131×D4312yes—
638C4C2×#1306334611yescharacteristic
639C4C2×#1306334811yescharacteristic
640C2—22no—
641C2—862no—
642C2—3442no—
643C2—1721no—
644C2#408×D4311yescharacteristic
645C2C2×#1458289411yescharacteristic
646C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1481C2
socleC22×C43C22×C22⋊C4
prime radical#19147892C2
cosocleC42×C43C24
hypercenter#1481D43
hypocenterC43#17458
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. C2×#14582951C2semidirect
3. #431×D43C2semidirect
4. #19133002C2semidirect
5. #19132998C2semidirect
6. #19132995C2semidirect
7. #19132993C2semidirect
8. #19132976C2semidirect
9. C43×#1481C2semidirect
42. Q8⋊(C43⋊C8)C22semidirect
43. #14582628C22semidirect
44. #14582626C22semidirect
48. C43×Q8⋊C8C22semidirect
322. #1481D43semidirect
369. Q8⋊C8C2×D43semidirect
372. C43#17458semidirect

Maximal subgroups

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

subgroupindex
#191478922
C2×#145829512
#431×D432
#191330022
#191329982
#191329952
#191329932
#191329762
C43×#14812
#1745843