Finite Group Databasebeta

← #25097575

Subgroups — #25097575

Order 11008.

1550 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583367C211yesmaximal, characteristic
2C2×#14582942C211yesmaximal, characteristic, complemented
3C2×#14582901C211yesmaximal, characteristic
4C2×#14582898C211yesmaximal, characteristic
5C2×#14582798C211yesmaximal, characteristic, complemented
6#19134864C212yesmaximal, complemented
7#19134857C212yesmaximal, complemented
8#19134850C212yesmaximal, complemented
9#19134843C212yesmaximal, complemented
10#19134288C211yesmaximal, characteristic, complemented
11C43×#1736C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C22×#10621877C2211yescharacteristic
14#14583367—24no—
15#14583367—24no—
16C2×#13063290C2211yescharacteristic
17C2×#13063290C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×(C22⋊D43)⋊C4—21no—
21C2×(C22⋊D43)⋊C4—21no—
22C2×#13063282—21no—
23C22×C4⋊Dic43—21no—
24C22×C4⋊Dic43C2211yescharacteristic
25C22×C4×Dic43C2211yescharacteristic
26C2×C42×D43—21no—
27#14582942—24no—
28C2×#13063258C2212yes—
29C2×#13063256C2212yes—
30#14582901—24no—
31#14582898C418yescomplemented
32C2×#13063250C2212yes—
33C2×#13063248C2212yes—
34C2×#13063247C2212yes—
35C2×#13063245C2212yes—
36#14582798—21no—
37#14582798—21no—
38#14582798C2212yes—
39#14582798C2212yes—
40C2×C43⋊#95—21no—
41#14582653C2212yes—
42#14582653C2212yes—
43C22×M16×C43C2211yescharacteristic
44C2×#117×C43C2211yescharacteristic
45C22×C4⋊C4×C43C2211yescharacteristic
46C43×#340C2212yes—
47C43×#340C2212yes—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898C2×C414yes—
52C2×#10621898D414yes—
53C2×#10621898Q814yes—
54C22×Dic86C2311yescharacteristic
55C22×D172C2311yescharacteristic
56C22×C22⋊D43—21no—
57C23×Dic43—21no—
58C23×Dic43D411yescharacteristic
59C23×Dic43D411yescharacteristic
60C22×C4×D43—21no—
61C22×C4×D43—21no—
62C22×C4×D43—21no—
63C2×#10621877—22no—
64C2×#10621877—22no—
65C2×#10621877C2×C414yescomplemented
66C22×C43⋊C8C2312yes—
67#13063290—22no—
68#13063290—22no—
69#13063290—22no—
70#13063290—22no—
71#13063287—22no—
72#13063287—22no—
73#13063287—22no—
74#13063287—22no—
75(C22⋊D43)⋊C4—28no—
76(C22⋊D43)⋊C4—28no—
77#13063282—28no—
78C2×C4⋊Dic43—22no—
79C2×C4⋊Dic43—22no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—22no—
83C2×C4⋊Dic43—44no—
84C2×C4⋊Dic43C2312yes—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×C4×Dic43—22no—
90C2×C4×Dic43—22no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43D411yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97C42×D43—28no—
98#13063258—24no—
99#13063256—24no—
100#13063250—24no—
101#13063248C2×C418yescomplemented
102#13063247—24no—
103#13063245C2×C418yescomplemented
104C43⋊#95—22no—
105C43⋊#95—22no—
106C23×C4×C43—21no—
107C23×C4×C43C2311yescharacteristic
108C2×M16×C43—22no—
109C2×M16×C43—22no—
110C2×M16×C43—22no—
111C22×C8×C43C2312yes—
112#117×C43—22no—
113#117×C43D414yes—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—22no—
116C2×C4⋊C4×C43C2×C414yescomplemented
117C2×C4⋊C4×C43C2312yes—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C42×C43—21no—
122C24×C43C2×D411yescharacteristic
123C23×D43—21no—
124C22×C4×C43—24no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—22no—
128C22×C4×C43—42no—
129C22×C4×C43—42no—
130C22×C4×C43C22×C412yes—
131C22×C4×C43C2×D412yes—
132C22×C4×C43C2×D412yes—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×Q812yes—
135C22×C4×C43#4112yes—
136C22×C4×C43#4112yes—
137C22×C4×C43C2411yescharacteristic
138C2×C22⋊D43—24no—
139C2×C22⋊D43—24no—
140C2×C22⋊D43—24no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—21no—
146C22×Dic43—22no—
147C22×Dic43—41no—
148C22×Dic43—41no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156#10621898—28no—
157#10621898—28no—
158#10621898—28no—
159#10621898C4⋊C4116yescomplemented
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172C22×C412yes—
164C2×D172C2×D412yes—
165C2×D172C2×Q812yes—
166C2×C4×D43—24no—
167C2×C4×D43—24no—
168C2×C4×D43—24no—
169C2×C4×D43—24no—
170C2×C4×D43—24no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C2×C4×D43—42no—
174C2×C4×D43—42no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86C22×C412yes—
179C2×Dic86C2×D412yes—
180C2×Dic86C2×Q812yes—
181M16×C43—44no—
182C2×C8×C43—22no—
183C2×C8×C43—22no—
184C2×C8×C43—22no—
185C4⋊C4×C43—24no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43C22×C414yes—
190C4⋊C4×C43C2×D412yes—
191C4⋊C4×C43C2×D412yes—
192C22⋊C4×C43—24no—
193C42×C43—24no—
194(C2×D43)⋊C4—24no—
195(C2×D43)⋊C4—24no—
196C4⋊Dic43—22no—
197C4⋊Dic43—22no—
198C4⋊Dic43—44no—
199C4⋊Dic43—42no—
200C4⋊Dic43—44no—
201Dic43⋊C4—24no—
202Dic43⋊C4—24no—
203C4×Dic43—24no—
204C4×Dic43—24no—
205C4×Dic43—22no—
206C4×Dic43—22no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211#10621877—28no—
212C2×C43⋊C8—22no—
213C2×C43⋊C8—22no—
214C2×C43⋊C8C22×C414yes—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43C4×D412yes—
220C23×C43#12012yes—
221C23×C43C22⋊Q812yes—
222C23×C43C22×D411yescharacteristic
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C2×C4×C43—24no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—48no—
234C2×C4×C43—42no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—42no—
240C2×C4×C43C2×C4⋊C414yes—
241C2×C4×C43C4×D412yes—
242C2×C4×C43C4×D414yes—
243C2×C4×C43#12012yes—
244C2×C4×C43C22⋊Q812yes—
245C2×C4×C43C22⋊Q814yes—
246C2×C4×C43#12314yes—
247C2×C4×C43C23×C411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C22×Q811yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C22⋊D43—216no—
254C2×Dic43—22no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—44no—
268C2×Dic43—44no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—84no—
273C2×Dic43AGL(1,ℤ/8)12yes—
274C2×Dic43#13712yes—
275D172—22no—
276D172—22no—
277D172—22no—
278D172C2×C4⋊C414yescomplemented
279C4×D43—216no—
280C4×D43—48no—
281C4×D43—48no—
282Dic86—22no—
283Dic86—22no—
284Dic86—22no—
285Dic86C2×C4⋊C414yescomplemented
286C8×C43—42no—
287C43⋊C8—24no—
288#20875—431nomaximal, Sylow
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—22no—
293C22×C43—22no—
294C22×C43—22no—
295C22×C43#38514yes—
296C22×C43C2×C4×D411yescharacteristic
297C22×C43C2×#12011yescharacteristic
298C22×C43C2×C22⋊Q811yescharacteristic
299C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C43C2×#13711yescharacteristic
301C22×C43#57511yescharacteristic
302C22×C43#57511yescharacteristic
303C2×D43—24no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—42no—
310C4×C43—44no—
311C4×C43—42no—
312C4×C43—42no—
313C4×C43#38514yes—
314C4×C43C22×C4⋊C411yescharacteristic
315C4×C43C2×C4×D411yescharacteristic
316C4×C43C2×C22⋊Q811yescharacteristic
317C4×C43C2×#12311yescharacteristic
318Dic43—22no—
319Dic43—22no—
320Dic43—24no—
321Dic43—41no—
322Dic43—41no—
323Dic43—82no—
324C2×C4×#41—431no—
325C2×#428—431no—
326C2×#417—431no—
327C2×#417—431no—
328C2×#389—431no—
329#1865—432no—
330#1864—432no—
331#1863—432no—
332#1862—432no—
333#1736D4311yescharacteristic, complemented
334#1728—431no—
335C2×C43—24no—
336C2×C43C2×#38511yescharacteristic
337C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
338C2×C43C4×#13711yescharacteristic
339C2×C43#300611yescharacteristic
340C2×C43#300711yescharacteristic
341C2×C43#307911yescharacteristic
342C2×C43#308011yescharacteristic
343D43—44no—
344C22×#41—431no—
345C22×M16—431no—
346C22×M16C2×D4311yescharacteristic
347C4×#41—864no—
348C4×#41—864no—
349C2×C4×Q8—431no—
350C2×C4×Q8—431no—
351C2×C4×D4—431no—
352C2×C4×D4—431no—
353C2×C4×D4—861no—
354C2×C4×D4—861no—
355C2×#117—861no—
356C2×#117C2×D4311yescharacteristic
357C22×C4⋊C4—431no—
358C22×C4⋊C4—861no—
359C22×C4⋊C4C2×D4311yescharacteristic
360C22×C42—431no—
361C22×C42—861no—
362#428—864no—
363C2×#107—432no—
364C2×#106—432no—
365#417—438no—
366#417—864no—
367C2×#103—432no—
368C2×#103—432no—
369C2×#102—432no—
370C2×#102—432no—
371#389—432no—
372#389—432no—
373#389—861no—
374#389—861no—
375C2×#95—861no—
376#340C2×D4312yes—
377#340C2×D4312yes—
378#336—432no—
379#336—432no—
380C43#2087511yescharacteristic, complemented, Sylow
381C2×#41—434no—
382C2×#41—434no—
383C2×#41—434no—
384C2×#41—862no—
385C2×#41—862no—
386C2×#41—862no—
387C22×Q8—431no—
388C22×D4—431no—
389C22×D4—861no—
390C23×C4—21no—
391C23×C4—431no—
392C23×C4—431no—
393C23×C4—861no—
394C23×C4—861no—
395C23×C4—861no—
396C23×C4—861no—
397C23×C4C22×D4311yescharacteristic
398C2×M16—22no—
399C2×M16—22no—
400C2×M16—22no—
401C2×M16—434no—
402C2×M16—862no—
403C2×M16—862no—
404C22×C8—432no—
405C22×C8C22×D4312yes—
406C4×Q8—862no—
407C4×Q8—862no—
408C4×Q8—862no—
409C4×Q8—862no—
410C4×D4—868no—
411C4×D4—868no—
412C4×D4—862no—
413C4×D4—862no—
414C4×D4—862no—
415C4×D4—862no—
416#117—22no—
417#117—868no—
418#117D17214yes—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—432no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—862no—
425C2×C4⋊C4—862no—
426C2×C4⋊C4—862no—
427C2×C4⋊C4—862no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—1724no—
430C2×C4⋊C4C4×D4314yescomplemented
431C2×C4⋊C4C22×D4312yes—
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C42—21no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—868no—
443C2×C42—861no—
444C2×C42—861no—
445C2×C42—862no—
446C2×C42—862no—
447#107—864no—
448#106—864no—
449#103—438no—
450#103—864no—
451#102—438no—
452#102—864no—
453#95—862no—
454#95—862no—
455C24—861no—
456C24D4×D4311yescharacteristic
457#41—4316no—
458#41—868no—
459#41—868no—
460#41—868no—
461C2×Q8—432no—
462C2×Q8—432no—
463C2×Q8—432no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×D4—432no—
468C2×D4—432no—
469C2×D4—432no—
470C2×D4—864no—
471C2×D4—864no—
472C2×D4—864no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—864no—
487C22×C4—864no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—861no—
491C22×C4—864no—
492C22×C4—864no—
493C22×C4—864no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—1722no—
498C22×C4—1722no—
499C22×C4—1722no—
500C22×C4—1722no—
501C22×C4—1721no—
502C22×C4—1721no—
503C22×C4—1722no—
504C22×C4—1722no—
505C22×C4—1722no—
506C22×C4C2×C4×D4312yes—
507C22×C4C2×D17212yes—
508C22×C4#1062189812yes—
509C22×C4D4×D4312yes—
510C22×C4D4×D4311yescharacteristic
511C22×C4#1062190012yes—
512C22×C4Q8×D4312yes—
513C22×C4C23×D4311yescharacteristic
514M16—44no—
515M16—868no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—434no—
520C2×C8—862no—
521C2×C8—862no—
522C4⋊C4—24no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—22no—
526C4⋊C4—864no—
527C4⋊C4—864no—
528C4⋊C4—862no—
529C4⋊C4—862no—
530C4⋊C4—1724no—
531C4⋊C4—1724no—
532C4⋊C4—1722no—
533C4⋊C4C2×C4×D4314yes—
534C4⋊C4C2×D17212yes—
535C4⋊C4C2×D17212yes—
536C22⋊C4—24no—
537C22⋊C4—864no—
538C22⋊C4—864no—
539C42—24no—
540C42—864no—
541C42—864no—
542C42—862no—
543C42—862no—
544C42—861no—
545C42—861no—
546C42—861no—
547C42—861no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—862no—
553C23—862no—
554C23—862no—
555C23—1721no—
556C23—1721no—
557C23—1721no—
558C23—1721no—
559C23(C22⋊D43)⋊C412yes—
560C23#1306329512yes—
561C23#1306330312yes—
562C23C2×D4×D4311yescharacteristic
563Q8—434no—
564Q8—862no—
565Q8—862no—
566Q8—862no—
567D4—434no—
568D4—8616no—
569D4—862no—
570D4—862no—
571D4—862no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—48no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—432no—
583C2×C4—432no—
584C2×C4—862no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—8616no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—3444no—
599C2×C4—1728no—
600C2×C4—1728no—
601C2×C4—1724no—
602C2×C4—1724no—
603C2×C4—1722no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4C4⋊C4×D4314yes—
607C2×C4(C22⋊D43)⋊C412yes—
608C2×C4C4×D17214yes—
609C2×C4#1306329512yes—
610C2×C4#1306330312yes—
611C2×C4#1306330514yes—
612C2×C4#1306330714yes—
613C2×C4C22×C4×D4311yescharacteristic
614C2×C4C2×D4×D4311yescharacteristic
615C2×C4C22×D17211yescharacteristic
616C2×C4C2×Q8×D4311yescharacteristic
617C2×C4C2×#1062190011yescharacteristic
618C2×C4C2×#1062189811yescharacteristic
619C8—42no—
620C8—864no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—22no—
627C22—864no—
628C22—1722no—
629C22—1722no—
630C22—1722no—
631C22—1722no—
632C22—1722no—
633C22—1722no—
634C22#1458277314yes—
635C22C2×(C22⋊D43)⋊C411yescharacteristic
636C22C2×#1306329511yescharacteristic
637C22C2×#1306330311yescharacteristic
638C22AGL(1,ℤ/8)×D4311yescharacteristic
639C22#137×D4311yescharacteristic
640C22#1458369511yescharacteristic
641C22#1458369811yescharacteristic
642C4—42no—
643C4—42no—
644C4—44no—
645C4—862no—
646C4—862no—
647C4—864no—
648C4—3442no—
649C4—1721no—
650C4—1721no—
651C4#1458277314yes—
652C4C2×C4⋊C4×D4311yescharacteristic
653C4C2×C4×D17211yescharacteristic
654C4C2×#1306330511yescharacteristic
655C4C2×#1306330711yescharacteristic
656C2—24no—
657C2—1724no—
658C2C2×#1458277311yescharacteristic
659C2#1914339911yescharacteristic
660C2#1914341011yescharacteristic
661C2#1914384811yescharacteristic
662C2#1914385611yescharacteristic
663C2#1914440811yescharacteristic
664C2#1914441611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1736C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1736D43
hypocenterC43#20875
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C2×#14582942C2semidirect
5. C2×#14582798C2semidirect
6. #19134864C2semidirect
7. #19134857C2semidirect
8. #19134850C2semidirect
9. #19134843C2semidirect
10. #19134288C2semidirect
11. C43×#1736C2semidirect
31. #14582898C4semidirect
65. C2×#10621877C2×C4semidirect
101. #13063248C2×C4semidirect
103. #13063245C2×C4semidirect
116. C2×C4⋊C4×C43C2×C4semidirect
159. #10621898C4⋊C4semidirect
278. D172C2×C4⋊C4semidirect
285. Dic86C2×C4⋊C4semidirect
333. #1736D43semidirect
380. C43#20875semidirect
430. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833672
C2×#145829422
C2×#145829012
C2×#145828982
C2×#145827982
#191348642
#191348572
#191348502
#191348432
#191342882
C43×#17362
#2087543