Finite Group Databasebeta

← #25097835

Subgroups — #25097835

Order 11008.

1934 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063301C211yesmaximal, characteristic
2C2×#117×D43C211yesmaximal, characteristic
3C2×#14582908C211yesmaximal, characteristic, complemented
4C2×#14582862C211yesmaximal, characteristic
5#19134904C214yesmaximal, complemented
6#19134899C214yesmaximal, complemented
7#19134316C211yesmaximal, characteristic, complemented
8#19134315C211yesmaximal, characteristic, complemented
9C2×C43×#419C211yesmaximal, characteristic, complemented
10C23×C4×D43C2211yescharacteristic
11C22×#10621877C2211yescharacteristic
12C2×#13063301—24no—
13C2×#13063301—21no—
14C2×#13063301—21no—
15C2×#13063301C418yescomplemented
16C2×#13063301C2212yes—
17C2×#13063301C2212yes—
18C2×#13063284C2211yescharacteristic
19C2×#13063283C2212yes—
20C2×#13063282—21no—
21C2×#13063281—21no—
22#117×D43—24no—
23#117×D43—24no—
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4—21no—
26C2×C4⋊C4×D43C2212yes—
27C22×(C2×D43)⋊C4—21no—
28C2×C22⋊C4×D43—21no—
29C2×C42×D43—21no—
30#14582908—24no—
31C2×#13063249C2214yescomplemented
32#14582862—24no—
33C2×(C2×D43)⋊C8C2212yes—
34C2×(C2×D43)⋊C8C2212yes—
35#14582662C2214yescomplemented
36#14582661C2214yescomplemented
37C23×Q8×C43C2211yescharacteristic
38C22×M16×C43C2211yescharacteristic
39C2×#117×C43C2211yescharacteristic
40C43×#419—24no—
41C2×#103×C43C2214yescomplemented
42C24×D43D411yescharacteristic
43C23×Dic43—21no—
44C23×Dic43D411yescharacteristic
45C22×C4×D43—22no—
46C22×C4×D43—22no—
47C22×C4×D43—22no—
48C22×C4×D43—22no—
49C22×C4×D43—22no—
50C22×C4×D43C2×C414yes—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D414yes—
54C22×C4×D43C2311yescharacteristic
55C22×C4×D43C2311yescharacteristic
56C2×#10621877—22no—
57C2×#10621877—22no—
58C2×#10621877—22no—
59C22×C43⋊C8C2312yes—
60#13063301—28no—
61#13063301—28no—
62#13063301—24no—
63#13063301—24no—
64#13063301C2×C418yes—
65#13063301C2×C418yescomplemented
66#13063284—22no—
67#13063284D414yes—
68#13063283—24no—
69#13063283—24no—
70#13063282—28no—
71#13063281—28no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—22no—
74C2×C4⋊Dic43C2×C414yescomplemented
75C2×C4⋊Dic43C2312yes—
76C2×C4⋊Dic43C2312yes—
77C2×Dic43⋊C4—28no—
78C2×Dic43⋊C4—22no—
79C2×Dic43⋊C4—22no—
80C2×Dic43⋊C4—22no—
81C4⋊C4×D43—24no—
82C4⋊C4×D43—24no—
83C2×C22⋊Dic43—21no—
84C2×(C2×D43)⋊C4—28no—
85C2×(C2×D43)⋊C4—22no—
86C2×(C2×D43)⋊C4—22no—
87C2×(C2×D43)⋊C4—22no—
88C22⋊C4×D43—28no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—22no—
91C42×D43—28no—
92#13063249—28no—
93(C2×D43)⋊C8—24no—
94(C2×D43)⋊C8—24no—
95C22×Q8×C43—22no—
96C22×Q8×C43—21no—
97C22×Q8×C43—22no—
98C22×Q8×C43—22no—
99C22×Q8×C43—22no—
100C22×Q8×C43—22no—
101C22×Q8×C43C2×C414yescomplemented
102C22×Q8×C43C2312yes—
103C23×C4×C43—21no—
104C23×C4×C43C2311yescharacteristic
105C2×M16×C43—22no—
106C2×M16×C43—22no—
107C2×M16×C43—22no—
108C22×C8×C43C2312yes—
109#117×C43—22no—
110#117×C43D414yes—
111C2×C4⋊C4×C43C2312yes—
112C2×C22⋊C4×C43—21no—
113C2×C42×C43—21no—
114#103×C43—28no—
115C24×C43C2×D411yescharacteristic
116C23×D43—22no—
117C23×D43—22no—
118C23×D43—24no—
119C23×D43—42no—
120C23×D43C22⋊C414yes—
121C23×D43C2×D411yescharacteristic
122C23×D43C2×D411yescharacteristic
123C2×Q8×C43—24no—
124C2×Q8×C43—22no—
125C2×Q8×C43—28no—
126C2×Q8×C43—28no—
127C2×Q8×C43—22no—
128C2×Q8×C43—22no—
129C2×Q8×C43—22no—
130C2×Q8×C43—22no—
131C2×Q8×C43—42no—
132C2×Q8×C43—44no—
133C2×Q8×C43—44no—
134C2×Q8×C43—42no—
135C2×Q8×C43C22×C414yes—
136C22×C4×C43—24no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—42no—
140C22×C4×C43—42no—
141C22×C4×C43C22×C412yes—
142C22×C4×C43C2×D412yes—
143C22×C4×C43C2×D412yes—
144C22×C4×C43C2×D412yes—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4112yes—
147C22×C4×C43#4112yes—
148C22×C4×C43C2411yescharacteristic
149C22×Dic43—24no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—44no—
155C22×Dic43C22⋊C414yes—
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C2×C4×D43—28no—
159C2×C4×D43—28no—
160C2×C4×D43—22no—
161C2×C4×D43—22no—
162C2×C4×D43—28no—
163C2×C4×D43—28no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43—28no—
175C2×C4×D43—44no—
176C2×C4×D43—44no—
177C2×C4×D43C22⋊C414yes—
178C2×C4×D43C22⋊C414yes—
179C2×C4×D43C22×C412yes—
180C2×C4×D43C22×C412yes—
181C2×C4×D43C2×D412yes—
182C2×C4×D43C2×D412yes—
183M16×C43—44no—
184C2×C8×C43—22no—
185C2×C8×C43—22no—
186C2×C8×C43—22no—
187C4⋊C4×C43—22no—
188C4⋊C4×C43C2×D414yes—
189C22⋊C4×C43—24no—
190C42×C43—24no—
191C22⋊Dic43—24no—
192(C2×D43)⋊C4—28no—
193(C2×D43)⋊C4—28no—
194(C2×D43)⋊C4—28no—
195C4⋊Dic43—24no—
196C4⋊Dic43—22no—
197C4⋊Dic43—22no—
198C4⋊Dic43C22×C414yes—
199C4⋊Dic43C2×D414yes—
200Dic43⋊C4—28no—
201Dic43⋊C4—28no—
202Dic43⋊C4—28no—
203C4×Dic43—28no—
204C4×Dic43—24no—
205#10621877—44no—
206C2×C43⋊C8—22no—
207C2×C43⋊C8—22no—
208C2×C43⋊C8—22no—
209C23×C43—22no—
210C23×C43—22no—
211C23×C43C2×C22⋊C412yes—
212C23×C43#12012yes—
213C23×C43#12312yes—
214C23×C43C22×D411yescharacteristic
215C22×D43—21no—
216C22×D43—21no—
217C22×D43—22no—
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—22no—
221C22×D43—22no—
222C22×D43—28no—
223C22×D43—28no—
224C22×D43—44no—
225C22×D43—48no—
226C22×D43—48no—
227C22×D43C2×C22⋊C412yes—
228C22×D43C2×C22⋊C412yes—
229C22×D43#13714yes—
230Q8×C43—24no—
231Q8×C43—24no—
232Q8×C43—42no—
233Q8×C43—42no—
234Q8×C43—48no—
235C2×C4×C43—24no—
236C2×C4×C43—24no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—48no—
242C2×C4×C43C2×C22⋊C412yes—
243C2×C4×C43C4×D414yes—
244C2×C4×C43C4×D414yes—
245C2×C4×C43#12012yes—
246C2×C4×C43#12114yes—
247C2×C4×C43#12114yes—
248C2×C4×C43#12312yes—
249C2×C4×C43C23×C411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—28no—
260C2×Dic43—24no—
261C2×Dic43—24no—
262C2×Dic43—48no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—44no—
266C2×Dic43C2×C22⋊C412yes—
267C2×Dic43C2×C22⋊C412yes—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—28no—
277C4×D43—28no—
278C4×D43—416no—
279C8×C43—42no—
280C43⋊C8—42no—
281#20911—431nomaximal, Sylow
282C22×C43—24no—
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—24no—
286C22×C43#38614yes—
287C22×C43C22×C22⋊C411yescharacteristic
288C22×C43C2×#12011yescharacteristic
289C22×C43C2×#12311yescharacteristic
290C22×C43C2×#13712yes—
291C22×C43#57512yes—
292C2×D43—24no—
293C2×D43—22no—
294C2×D43—24no—
295C2×D43—22no—
296C2×D43—22no—
297C2×D43—22no—
298C2×D43—22no—
299C2×D43—416no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43#41914yescomplemented
303C4×C43—44no—
304C4×C43—44no—
305C4×C43#38614yes—
306C4×C43C2×C4×D411yescharacteristic
307C4×C43C2×C4×D411yescharacteristic
308C4×C43C2×#12111yescharacteristic
309C4×C43C2×#12111yescharacteristic
310Dic43—22no—
311Dic43—22no—
312Dic43—44no—
313Dic43—44no—
314C22×C22⋊Q8—431no—
315C22×#117—431no—
316C2×#419—431no—
317C2×#419D4311yescharacteristic, complemented
318C2×#407—431no—
319#1873—434no—
320#1872—434no—
321#1736—431no—
322#1736—431no—
323C2×C43—24no—
324C2×C43C2×#38611yescharacteristic
325C2×C43C2×#41911yescharacteristic
326C2×C43#289611yescharacteristic
327C2×C43#300712yes—
328C2×C43#309512yes—
329D43—24no—
330D43—42no—
331C23×Q8C2×D4311yescharacteristic
332C24×C4—431no—
333C22×M16—431no—
334C22×M16C2×D4311yescharacteristic
335C2×C22⋊Q8—432no—
336C2×C22⋊Q8—432no—
337C2×C22⋊Q8—438no—
338C2×C22⋊Q8—861no—
339C2×C22⋊Q8—864no—
340C2×C22⋊Q8—861no—
341C2×#117—431no—
342C2×#117—432no—
343C2×#117—861no—
344C2×#117—861no—
345C2×#117—864no—
346C2×#117—864no—
347C2×#117C2×D4311yescharacteristic
348C22×C4⋊C4—431no—
349C22×C4⋊C4—432no—
350C22×C4⋊C4—861no—
351C22×C22⋊C4—861no—
352C22×C22⋊C4—861no—
353C22×C42—861no—
354#419—24no—
355#419—864no—
356C2×#103—434no—
357C2×#103C2×D4314yescomplemented
358#407—864no—
359C2×C22⋊C8—432no—
360C2×C22⋊C8—432no—
361#340—434no—
362#340—434no—
363C43#2091111yescharacteristic, complemented, Sylow
364C25—431no—
365C22×Q8—22no—
366C22×Q8—21no—
367C22×Q8—22no—
368C22×Q8—22no—
369C22×Q8—22no—
370C22×Q8—22no—
371C22×Q8C4×D4314yescomplemented
372C22×Q8C22×D4312yes—
373C23×C4—21no—
374C23×C4—431no—
375C23×C4—434no—
376C23×C4—431no—
377C23×C4—434no—
378C23×C4—431no—
379C23×C4—431no—
380C23×C4—431no—
381C23×C4—862no—
382C23×C4—862no—
383C23×C4—862no—
384C23×C4—862no—
385C23×C4—862no—
386C23×C4—861no—
387C23×C4C22×D4311yescharacteristic
388C2×M16—22no—
389C2×M16—22no—
390C2×M16—22no—
391C2×M16—862no—
392C2×M16—862no—
393C2×M16—862no—
394C22×C8—432no—
395C22×C8C22×D4312yes—
396C22⋊Q8—438no—
397C22⋊Q8—438no—
398C22⋊Q8—868no—
399C22⋊Q8—868no—
400C22⋊Q8—864no—
401C22⋊Q8—864no—
402#117—22no—
403#117—434no—
404#117—868no—
405#117—868no—
406#117—864no—
407#117—862no—
408#117—864no—
409#117C22⋊D4314yes—
410C2×C4⋊C4—434no—
411C2×C4⋊C4—432no—
412C2×C4⋊C4—432no—
413C2×C4⋊C4—864no—
414C2×C4⋊C4—862no—
415C2×C4⋊C4—868no—
416C2×C4⋊C4—862no—
417C2×C4⋊C4—862no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—862no—
420C2×C4⋊C4—864no—
421C2×C4⋊C4C22×D4312yes—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—868no—
424C2×C22⋊C4—862no—
425C2×C22⋊C4—868no—
426C2×C22⋊C4—862no—
427C2×C22⋊C4—862no—
428C2×C22⋊C4—861no—
429C2×C42—21no—
430C2×C42—868no—
431C2×C42—862no—
432C2×C42—861no—
433#103—28no—
434#103—868no—
435C22⋊C8—864no—
436C22⋊C8—864no—
437C24—431no—
438C24—431no—
439C24—434no—
440C24—864no—
441C24—862no—
442C24—862no—
443C24—1722no—
444C24D4×D4311yescharacteristic
445C2×Q8—24no—
446C2×Q8—22no—
447C2×Q8—28no—
448C2×Q8—28no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—42no—
454C2×Q8—44no—
455C2×Q8—44no—
456C2×Q8—42no—
457C2×Q8C2×C4×D4314yes—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—434no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—434no—
467C22×C4—434no—
468C22×C4—432no—
469C22×C4—432no—
470C22×C4—432no—
471C22×C4—432no—
472C22×C4—868no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—868no—
476C22×C4—868no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—868no—
480C22×C4—868no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—864no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—1724no—
495C22×C4—1724no—
496C22×C4—1724no—
497C22×C4C2×C4×D4312yes—
498C22×C4#1062189812yes—
499C22×C4D4×D4311yescharacteristic
500C22×C4D4×D4312yes—
501C22×C4D4×D4312yes—
502C22×C4#1062190012yes—
503C22×C4C2×C22⋊D4312yes—
504C22×C4C23×D4311yescharacteristic
505M16—44no—
506M16—1724no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—862no—
511C2×C8—862no—
512C2×C8—862no—
513C4⋊C4—22no—
514C4⋊C4—434no—
515C4⋊C4—434no—
516C4⋊C4—868no—
517C4⋊C4—868no—
518C4⋊C4—868no—
519C4⋊C4—864no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4C2×C22⋊D4314yes—
523C22⋊C4—24no—
524C22⋊C4—868no—
525C22⋊C4—868no—
526C22⋊C4—868no—
527C22⋊C4—864no—
528C42—24no—
529C42—868no—
530C42—864no—
531C23—22no—
532C23—22no—
533C23—432no—
534C23—434no—
535C23—432no—
536C23—868no—
537C23—861no—
538C23—861no—
539C23—862no—
540C23—861no—
541C23—861no—
542C23—862no—
543C23—862no—
544C23—868no—
545C23—1724no—
546C23—1728no—
547C23—1728no—
548C23C22⋊C4×D4312yes—
549C23#1306329312yes—
550C23#1306330712yes—
551C23C2×D4×D4311yescharacteristic
552Q8—24no—
553Q8—24no—
554Q8—42no—
555Q8—42no—
556Q8—48no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—48no—
564C2×C4—432no—
565C2×C4—432no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—868no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—868no—
580C2×C4—868no—
581C2×C4—864no—
582C2×C4—864no—
583C2×C4—17216no—
584C2×C4—1728no—
585C2×C4—1722no—
586C2×C4—1722no—
587C2×C4—1724no—
588C2×C4C22⋊C4×D4312yes—
589C2×C4(C22⋊D43)⋊C414yes—
590C2×C4C4×C22⋊D4314yes—
591C2×C4#1306329312yes—
592C2×C4#1306329614yes—
593C2×C4#1306329814yes—
594C2×C4#1306330712yes—
595C2×C4C22×C4×D4311yescharacteristic
596C2×C4C2×D4×D4311yescharacteristic
597C2×C4C2×D4×D4311yescharacteristic
598C2×C4C22×C22⋊D4311yescharacteristic
599C2×C4C2×#1062190011yescharacteristic
600C2×C4C2×#1062189811yescharacteristic
601C8—42no—
602C8—1722no—
603C22—24no—
604C22—24no—
605C22—22no—
606C22—22no—
607C22—434no—
608C22—864no—
609C22—864no—
610C22—862no—
611C22—862no—
612C22—862no—
613C22—862no—
614C22—862no—
615C22—17216no—
616C22—1722no—
617C22—1722no—
618C22#1458277514yes—
619C22C2×C22⋊C4×D4311yescharacteristic
620C22C2×#1306329311yescharacteristic
621C22C2×#1306330711yescharacteristic
622C22#137×D4312yes—
623C22#1458369812yes—
624C4—44no—
625C4—44no—
626C4—862no—
627C4—862no—
628C4—1724no—
629C4—1724no—
630C4#1458277514yes—
631C4C2×(C22⋊D43)⋊C411yescharacteristic
632C4C2×C4×C22⋊D4311yescharacteristic
633C4C2×#1306329611yescharacteristic
634C4C2×#1306329811yescharacteristic
635C2—24no—
636C2—864no—
637C2—1722no—
638C2C2×#1458277511yescharacteristic
639C2#419×D4311yescharacteristic
640C2#1914311311yescharacteristic
641C2#1914385112yes—
642C2#1914454112yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#419C2
socleC23×C43C22×D4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenterC2×#419D43
hypocenterC43#20911
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
3. C2×#14582908C2semidirect
5. #19134904C2semidirect
6. #19134899C2semidirect
7. #19134316C2semidirect
8. #19134315C2semidirect
9. C2×C43×#419C2semidirect
15. C2×#13063301C4semidirect
31. C2×#13063249C22semidirect
35. #14582662C22semidirect
36. #14582661C22semidirect
41. C2×#103×C43C22semidirect
65. #13063301C2×C4semidirect
74. C2×C4⋊Dic43C2×C4semidirect
101. C22×Q8×C43C2×C4semidirect
302. C2×D43#419semidirect
317. C2×#419D43semidirect
357. C2×#103C2×D43semidirect
363. C43#20911semidirect
371. C22×Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633012
C2×#117×D432
C2×#145829082
C2×#145828622
#191349042
#191348992
#191343162
#191343152
C2×C43×#4192
#2091143