Finite Group Databasebeta

← #25105650

Subgroups — #25105650

Order 11008.

1538 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
1C2×C22⋊Q8×D43C211yesmaximal, characteristic
2C2×#14582862C211yesmaximal, characteristic
3#380×D43C211yesmaximal, characteristic
4#19135029C211yesmaximal, characteristic, complemented
5#19135028C211yesmaximal, characteristic, complemented
6#19135026C211yesmaximal, characteristic, complemented
7#19134901C212yesmaximal, complemented
8#19134899C212yesmaximal, complemented
9#19134680C212yesmaximal, complemented
10#19134528C212yesmaximal, complemented
11C43×#1894C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C22×#10621877C2211yescharacteristic
15C2×#13063305C2211yescharacteristic
16C2×#13063304C2211yescharacteristic
17C2×#13063303—21no—
18C2×#13063302—21no—
19C2×#13063301C2211yescharacteristic
20C22⋊Q8×D43—24no—
21C22⋊Q8×D43C418yescomplemented
22C2×C4⋊C4×D43—21no—
23C2×C4⋊C4×D43C2211yescharacteristic
24C2×C4⋊C4×D43C2212yes—
25C2×C22⋊C4×D43—21no—
26C2×C22⋊C4×D43—21no—
27C2×#13063250C2212yescomplemented
28C2×#13063249C2212yescomplemented
29C2×#13063248C2212yescomplemented
30#14582862—24no—
31C2×(C2×D43)⋊C8C2212yes—
32C2×(C2×D43)⋊C8C2212yes—
33#14582759C2211yescharacteristic
34#14582758—21no—
35#14582757—21no—
36#14582756C2212yes—
37#95×D43—21no—
38#14582662C2212yescomplemented
39#14582661C2212yescomplemented
40#14582661C2212yescomplemented
41C22×M16×C43C2211yescharacteristic
42C2×C22⋊Q8×C43C2211yescharacteristic
43C2×#103×C43C2212yescomplemented
44C43×#380C2211yescharacteristic
45C43×#340C2212yescomplemented
46C24×D43D411yescharacteristic
47C22×Dic86—21no—
48C22×Dic86C2311yescharacteristic
49C2×Q8×D43—22no—
50C2×Q8×D43—42no—
51C2×Q8×D43—42no—
52C2×Q8×D43C2×C414yescomplemented
53C23×Dic43D411yescharacteristic
54C22×C4×D43—21no—
55C22×C4×D43—21no—
56C22×C4×D43—22no—
57C22×C4×D43—42no—
58C22×C4×D43—42no—
59C22×C4×D43C2×C414yes—
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43D414yes—
63C22×C4×D43C2311yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C2×#10621877—22no—
66C2×#10621877—42no—
67C22×C43⋊C8C2312yes—
68#13063305—22no—
69#13063305C2×C414yes—
70#13063304—22no—
71#13063304C2×C414yescomplemented
72#13063303—28no—
73#13063302—28no—
74#13063301—22no—
75#13063301C2×C414yes—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2312yes—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—22no—
83C4⋊C4×D43—28no—
84C4⋊C4×D43—22no—
85C4⋊C4×D43—42no—
86C4⋊C4×D43—42no—
87C4⋊C4×D43C2×C414yescomplemented
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—22no—
93C22⋊C4×D43—28no—
94C22⋊C4×D43—44no—
95#13063250—42no—
96#13063249—42no—
97#13063248—42no—
98(C2×D43)⋊C8—24no—
99(C2×D43)⋊C8—24no—
100C43⋊#95—21no—
101C43⋊#95—22no—
102C22×Q8×C43C2311yescharacteristic
103C23×C4×C43C2311yescharacteristic
104C2×M16×C43—22no—
105C2×M16×C43—42no—
106C22×C8×C43C2312yes—
107C22⋊Q8×C43—22no—
108C22⋊Q8×C43C2×C414yescomplemented
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2312yes—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114#103×C43—42no—
115#95×C43—21no—
116C24×C43C2×D411yescharacteristic
117C23×D43—22no—
118C23×D43—22no—
119C23×D43—24no—
120C23×D43—42no—
121C23×D43C22⋊C414yes—
122C23×D43C2×D411yescharacteristic
123C23×D43C2×D411yescharacteristic
124C2×Q8×C43—21no—
125C2×Q8×C43—22no—
126C2×Q8×C43—22no—
127C2×Q8×C43C22×C412yes—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—22no—
133C22×C4×C43C22×C412yes—
134C22×C4×C43C2×D412yes—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2411yescharacteristic
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—22no—
140C22×Dic43—42no—
141C22×Dic43C22⋊C414yes—
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144Q8×D43—48no—
145Q8×D43—44no—
146Q8×D43—44no—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×C4×D43—24no—
152C2×C4×D43—24no—
153C2×C4×D43—42no—
154C2×C4×D43—42no—
155C2×C4×D43—44no—
156C2×C4×D43—44no—
157C2×C4×D43—44no—
158C2×C4×D43—48no—
159C2×C4×D43—44no—
160C2×C4×D43—44no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43—44no—
164C2×C4×D43C22⋊C414yes—
165C2×C4×D43C22⋊C414yes—
166C2×C4×D43C22×C412yes—
167C2×C4×D43C22×C412yes—
168C2×C4×D43C2×D412yes—
169C2×C4×D43C2×D412yes—
170C2×Dic86—22no—
171C2×Dic86—22no—
172C2×Dic86—21no—
173C2×Dic86—24no—
174C2×Dic86—44no—
175C2×Dic86C22×C412yes—
176M16×C43—44no—
177C2×C8×C43—22no—
178C2×C8×C43—22no—
179C2×C8×C43—22no—
180C4⋊C4×C43—24no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43C22×C412yes—
185C22⋊C4×C43—24no—
186C22⋊C4×C43—42no—
187C22⋊Dic43—24no—
188C22⋊Dic43—42no—
189(C2×D43)⋊C4—24no—
190(C2×D43)⋊C4—24no—
191(C2×D43)⋊C4—44no—
192C4⋊Dic43—21no—
193C4⋊Dic43—24no—
194C4⋊Dic43—22no—
195C4⋊Dic43—22no—
196C4⋊Dic43C22×C412yes—
197Dic43⋊C4—24no—
198Dic43⋊C4—24no—
199Dic43⋊C4—24no—
200Dic43⋊C4—44no—
201#10621877—44no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—22no—
204C2×C43⋊C8—22no—
205C23×C43—22no—
206C23×C43—21no—
207C23×C43—22no—
208C23×C43—21no—
209C23×C43C2×C22⋊C412yes—
210C23×C43C22×D411yescharacteristic
211C22×D43—22no—
212C22×D43—22no—
213C22×D43—21no—
214C22×D43—22no—
215C22×D43—21no—
216C22×D43—28no—
217C22×D43—28no—
218C22×D43—44no—
219C22×D43—48no—
220C22×D43—48no—
221C22×D43C2×C22⋊C412yes—
222C22×D43C2×C22⋊C412yes—
223C22×D43AGL(1,ℤ/8)12yes—
224C22×D43#13712yes—
225C22×D43#13714yes—
226Q8×C43—24no—
227Q8×C43—41no—
228Q8×C43—41no—
229C2×C4×C43—22no—
230C2×C4×C43—24no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—42no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43C2×C22⋊C412yes—
242C2×C4×C43C23×C411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43H(5,𝔽2)12yes—
245C2×C4×C43H(5,𝔽2)12yes—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—44no—
251C2×Dic43—42no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43C2×C22⋊C412yes—
258C2×Dic43C2×C22⋊C412yes—
259C4×D43—24no—
260C4×D43—24no—
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—44no—
266C4×D43—44no—
267C4×D43—48no—
268C4×D43—48no—
269C4×D43—88no—
270Dic86—24no—
271Dic86—48no—
272Dic86—41no—
273Dic86—41no—
274C8×C43—42no—
275C43⋊C8—42no—
276#21765—431nomaximal, Sylow
277C22×C43—22no—
278C22×C43—22no—
279C22×C43—22no—
280C22×C43—42no—
281C22×C43—42no—
282C22×C43C22×C22⋊C411yescharacteristic
283C22×C43#53412yes—
284C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C43C2×#13712yes—
286C22×C43C2×#13711yescharacteristic
287C2×D43—22no—
288C2×D43—22no—
289C2×D43—22no—
290C2×D43—22no—
291C2×D43—24no—
292C2×D43—24no—
293C2×D43—24no—
294C2×D43—24no—
295C2×D43—416no—
296C2×D43#41714yes—
297C2×D43#41914yes—
298C4×C43—22no—
299C4×C43—42no—
300C4×C43—42no—
301C4×C43—82no—
302C4×C43#51812yes—
303C4×C43#53411yescharacteristic
304C4×C43#53411yescharacteristic
305Dic43—22no—
306Dic43—22no—
307Dic43—42no—
308Dic43—42no—
309Dic43—82no—
310C22×C22⋊Q8—431no—
311C2×#407—431no—
312C2×#380—431no—
313#1894—431no—
314#1894—431no—
315#1894—431no—
316#1894D4311yescharacteristic, complemented
317#1872—432no—
318#1872—432no—
319#1823—432no—
320#1787—432no—
321C2×C43—42no—
322C2×C43#230811yescharacteristic
323C2×C43C2×#41911yescharacteristic
324C2×C43C2×#41711yescharacteristic
325C2×C43#319312yes—
326C2×C43#319512yes—
327D43—24no—
328D43—24no—
329C23×Q8—431no—
330C24×C4—431no—
331C22×M16—431no—
332C22×M16C2×D4311yescharacteristic
333C2×C22⋊Q8—431no—
334C2×C22⋊Q8—431no—
335C2×C22⋊Q8—438no—
336C2×C22⋊Q8—431no—
337C2×C22⋊Q8—861no—
338C2×C22⋊Q8—861no—
339C2×C22⋊Q8—864no—
340C2×C22⋊Q8C2×D4311yescharacteristic
341C22×C4⋊C4—431no—
342C22×C4⋊C4—432no—
343C22×C4⋊C4—861no—
344C22×C22⋊C4—861no—
345C22×C22⋊C4—861no—
346C2×#103—432no—
347C2×#103—432no—
348C2×#103—432no—
349C2×#103C2×D4312yescomplemented
350#407—864no—
351C2×C22⋊C8—432no—
352C2×C22⋊C8—432no—
353#380—431no—
354#380—432no—
355#380—861no—
356#380—861no—
357#380C2×D4311yescharacteristic
358C2×#95—861no—
359#340—432no—
360#340—432no—
361#340—432no—
362#340C2×D4312yescomplemented
363C43#2176511yescharacteristic, complemented, Sylow
364C25—431no—
365C22×Q8—434no—
366C22×Q8—431no—
367C22×Q8—861no—
368C22×Q8—862no—
369C22×Q8—1722no—
370C22×Q8—1722no—
371C22×Q8C22×D4311yescharacteristic
372C23×C4—431no—
373C23×C4—431no—
374C23×C4—431no—
375C23×C4—434no—
376C23×C4—431no—
377C23×C4—431no—
378C23×C4—434no—
379C23×C4—861no—
380C23×C4—861no—
381C23×C4—862no—
382C23×C4—1722no—
383C23×C4—1722no—
384C23×C4C22×D4311yescharacteristic
385C2×M16—22no—
386C2×M16—42no—
387C2×M16—862no—
388C2×M16—1722no—
389C22×C8—432no—
390C22×C8C22×D4312yes—
391C22⋊Q8—22no—
392C22⋊Q8—434no—
393C22⋊Q8—434no—
394C22⋊Q8—434no—
395C22⋊Q8—868no—
396C22⋊Q8—868no—
397C22⋊Q8—862no—
398C22⋊Q8—862no—
399C22⋊Q8—862no—
400C22⋊Q8C4×D4314yescomplemented
401C2×C4⋊C4—21no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—434no—
404C2×C4⋊C4—432no—
405C2×C4⋊C4—862no—
406C2×C4⋊C4—868no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—862no—
412C2×C4⋊C4—1722no—
413C2×C4⋊C4—1722no—
414C2×C4⋊C4C22×D4312yes—
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—868no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—862no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—1724no—
425#103—42no—
426#103—1722no—
427#103—1722no—
428#103—1722no—
429C22⋊C8—864no—
430C22⋊C8—864no—
431#95—21no—
432#95—862no—
433#95—861no—
434C24—431no—
435C24—431no—
436C24—434no—
437C24—862no—
438C24—864no—
439C24—862no—
440C24—1722no—
441C24D4×D4311yescharacteristic
442C2×Q8—21no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—432no—
446C2×Q8—864no—
447C2×Q8—861no—
448C2×Q8—862no—
449C2×Q8—862no—
450C2×Q8—1724no—
451C2×Q8—1728no—
452C2×Q8—1724no—
453C2×Q8—1724no—
454C2×Q8C2×C4×D4312yes—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—434no—
463C22×C4—432no—
464C22×C4—432no—
465C22×C4—432no—
466C22×C4—432no—
467C22×C4—434no—
468C22×C4—434no—
469C22×C4—864no—
470C22×C4—864no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—862no—
478C22×C4—1728no—
479C22×C4—1724no—
480C22×C4—1724no—
481C22×C4—1722no—
482C22×C4—1722no—
483C22×C4—1724no—
484C22×C4—1724no—
485C22×C4—1724no—
486C22×C4—1722no—
487C22×C4—1722no—
488C22×C4—1724no—
489C22×C4—1722no—
490C22×C4C2×C4×D4312yes—
491C22×C4D4×D4311yescharacteristic
492C22×C4D4×D4312yes—
493C22×C4C23×D4311yescharacteristic
494M16—44no—
495M16—1724no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—862no—
500C2×C8—862no—
501C2×C8—862no—
502C4⋊C4—24no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—432no—
507C4⋊C4—864no—
508C4⋊C4—864no—
509C4⋊C4—864no—
510C4⋊C4—864no—
511C4⋊C4—861no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4—1724no—
515C4⋊C4C2×C4×D4312yes—
516C22⋊C4—24no—
517C22⋊C4—42no—
518C22⋊C4—864no—
519C22⋊C4—864no—
520C22⋊C4—864no—
521C22⋊C4—1724no—
522C22⋊C4—1722no—
523C23—21no—
524C23—22no—
525C23—21no—
526C23—22no—
527C23—432no—
528C23—432no—
529C23—432no—
530C23—434no—
531C23—432no—
532C23—868no—
533C23—868no—
534C23—861no—
535C23—862no—
536C23—861no—
537C23—862no—
538C23—862no—
539C23—1724no—
540C23—1728no—
541C23—1728no—
542C23C22⋊C4×D4312yes—
543C23C2×D4×D4311yescharacteristic
544Q8—24no—
545Q8—41no—
546Q8—41no—
547Q8—864no—
548Q8—1728no—
549Q8—1721no—
550Q8—1721no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—432no—
564C2×C4—432no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—864no—
568C2×C4—864no—
569C2×C4—862no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—3448no—
576C2×C4—1724no—
577C2×C4—1724no—
578C2×C4—1728no—
579C2×C4—1728no—
580C2×C4—1724no—
581C2×C4—1722no—
582C2×C4—1722no—
583C2×C4—1722no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1722no—
587C2×C4C22⋊C4×D4312yes—
588C2×C4C22×C4×D4311yescharacteristic
589C2×C4C2×D4×D4311yescharacteristic
590C2×C4#1306337012yes—
591C2×C4#1306337112yes—
592C8—42no—
593C8—1722no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—42no—
598C22—42no—
599C22—434no—
600C22—434no—
601C22—862no—
602C22—862no—
603C22—864no—
604C22—864no—
605C22—862no—
606C22—862no—
607C22—864no—
608C22—864no—
609C22—17216no—
610C22C2×C22⋊C4×D4311yescharacteristic
611C22#1458345712yes—
612C22AGL(1,ℤ/8)×D4311yescharacteristic
613C22#137×D4312yes—
614C22#137×D4311yescharacteristic
615C4—22no—
616C4—42no—
617C4—42no—
618C4—82no—
619C4—862no—
620C4—862no—
621C4—3442no—
622C4—1722no—
623C4—1722no—
624C4#1458337112yes—
625C4#1458345911yescharacteristic
626C4#1458346011yescharacteristic
627C2—42no—
628C2—864no—
629C2—864no—
630C2#1913716911yescharacteristic
631C2#419×D4311yescharacteristic
632C2#417×D4311yescharacteristic
633C2#1914539612yes—
634C2#1914541512yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1894C2
socleC23×C43C22×D4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenter#1894D43
hypocenterC43#21765
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
4. #19135029C2semidirect
5. #19135028C2semidirect
6. #19135026C2semidirect
7. #19134901C2semidirect
8. #19134899C2semidirect
9. #19134680C2semidirect
10. #19134528C2semidirect
11. C43×#1894C2semidirect
21. C22⋊Q8×D43C4semidirect
27. C2×#13063250C22semidirect
28. C2×#13063249C22semidirect
29. C2×#13063248C22semidirect
38. #14582662C22semidirect
39. #14582661C22semidirect
40. #14582661C22semidirect
43. C2×#103×C43C22semidirect
45. C43×#340C22semidirect
52. C2×Q8×D43C2×C4semidirect
71. #13063304C2×C4semidirect
87. C4⋊C4×D43C2×C4semidirect
108. C22⋊Q8×C43C2×C4semidirect
316. #1894D43semidirect
349. C2×#103C2×D43semidirect
362. #340C2×D43semidirect
363. C43#21765semidirect
400. C22⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D432
C2×#145828622
#380×D432
#191350292
#191350282
#191350262
#191349012
#191348992
#191346802
#191345282
C43×#18942
#2176543