Finite Group Databasebeta

← #25106332

Subgroups — #25106332

Order 11008.

1234 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583431C211yesmaximal, characteristic
2C2×#14582955C211yesmaximal, characteristic, complemented
3#384×D43C211yesmaximal, characteristic, complemented
4#19135562C212yesmaximal, complemented
5#19135410C212yesmaximal, complemented
6#19134909C212yesmaximal
7#19134901C212yesmaximal, complemented
8#19134601C211yesmaximal, characteristic, complemented
9#19134597C211yesmaximal, characteristic, complemented
10#19134595C211yesmaximal, characteristic, complemented
11C43×#1802C211yesmaximal, characteristic, complemented
12#14583431—24no—
13#14583431C418yescomplemented
14C2×#13063318—21no—
15C2×#13063316C2211yescharacteristic
16C2×#13063312C2211yescharacteristic
17C2×#13063307—21no—
18C2×#13063305C2211yescharacteristic
19C2×#13063296C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×C4×C22⋊D43—21no—
22C2×#13063284—21no—
23C2×C4⋊C4×D43—21no—
24C2×C4⋊C4×D43—21no—
25C2×C4⋊C4×D43C2212yes—
26C2×C42×D43C2211yescharacteristic
27#14582955—24no—
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063250C2212yes—
30C2×#13063248C2212yes—
31C2×#13063246C2212yes—
32C2×(C2×D43)⋊C8C2212yes—
33C2×#13063235C2212yes—
34#14582769C2211yescharacteristic
35#14582768—21no—
36#14582768—21no—
37#14582768C2212yes—
38#14582662C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C2×C4×D4×C43C2211yescharacteristic
42C2×C4⋊C8×C43C2211yescharacteristic
43C2×#102×C43C2212yes—
44C43×#384C2211yescharacteristic
45C43×#340C2212yes—
46C22×Dic86C2311yescharacteristic
47C22×C22⋊D43—21no—
48C22×C4×D43—22no—
49C22×C4×D43D411yescharacteristic
50C22×C4×D43D411yescharacteristic
51C22×C4×D43C2311yescharacteristic
52C22×C43⋊C8C2312yes—
53#13063318—28no—
54#13063316—22no—
55#13063316C2×C414yescomplemented
56#13063312—22no—
57#13063312C2×C414yescomplemented
58#13063307—28no—
59#13063305—22no—
60#13063305C2×C414yes—
61#13063296—22no—
62#13063296C2×C414yes—
63C4×Dic86—22no—
64C4×Dic86C2×C414yescomplemented
65C4×C22⋊D43—28no—
66#13063284—28no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2312yes—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—22no—
76C2×Dic43⋊C4—22no—
77C2×Dic43⋊C4—22no—
78C4⋊C4×D43—42no—
79C4⋊C4×D43—42no—
80C4⋊C4×D43—44no—
81C4⋊C4×D43—44no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43D411yescharacteristic
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90C42×D43C2×C414yes—
91C42×D43D414yes—
92C4⋊(C43⋊C8)—22no—
93#13063250—42no—
94#13063248—42no—
95#13063246—42no—
96(C2×D43)⋊C8—24no—
97#13063235—24no—
98C22×D4×C43C2311yescharacteristic
99C23×C4×C43—21no—
100C22×C8×C43C2312yes—
101C4×D4×C43—22no—
102C4×D4×C43C2×C414yescomplemented
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43C2312yes—
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C22⋊C4×C43—21no—
108C2×C42×C43C2311yescharacteristic
109C4⋊C8×C43—22no—
110#102×C43—42no—
111C24×C43—21no—
112C23×D43C2×D411yescharacteristic
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43C22×C412yes—
119C22×C4×C43—24no—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—42no—
123C22×C4×C43—42no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C2×C22⋊D43—24no—
128C2×C22⋊D43—42no—
129C2×C22⋊D43—42no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—22no—
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C22×Dic43C2×D411yescharacteristic
136C2×C4×D43—22no—
137C2×C4×D43—22no—
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—44no—
145C2×C4×D43—44no—
146C2×C4×D43—44no—
147C2×C4×D43C22⋊C414yes—
148C2×C4×D43C22⋊C414yes—
149C2×C4×D43C22×C412yes—
150C2×C4×D43C2×D412yes—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86C22×C412yes—
157C2×C8×C43—22no—
158C2×C8×C43—22no—
159C2×C8×C43—22no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—22no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—42no—
164C4⋊C4×C43—42no—
165C4⋊C4×C43C22×C412yes—
166C22⋊C4×C43—24no—
167C42×C43C22×C412yes—
168C42×C43C2×D412yes—
169C22⋊Dic43—24no—
170C22⋊Dic43—24no—
171C22⋊Dic43—24no—
172(C2×D43)⋊C4—24no—
173C4⋊Dic43—21no—
174C4⋊Dic43—24no—
175C4⋊Dic43—24no—
176C4⋊Dic43—22no—
177C4⋊Dic43—22no—
178C4⋊Dic43—42no—
179C4⋊Dic43—42no—
180C4⋊Dic43C22×C412yes—
181Dic43⋊C4—24no—
182Dic43⋊C4—24no—
183Dic43⋊C4—44no—
184Dic43⋊C4—44no—
185Dic43⋊C4—44no—
186C4×Dic43—24no—
187C4×Dic43C22⋊C414yes—
188C4×Dic43C22⋊C414yes—
189C4×Dic43C22×C412yes—
190C4×Dic43C2×D412yes—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—22no—
194C23×C43—22no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43C22×D411yescharacteristic
202C22×D43—21no—
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43C2×C22⋊C412yes—
207C22×D43AGL(1,ℤ/8)12yes—
208C22×D43#13712yes—
209D4×C43—22no—
210D4×C43—22no—
211D4×C43—41no—
212D4×C43—41no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—48no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43C2×C22⋊C412yes—
223C2×C4×C43C2×C22⋊C412yes—
224C2×C4×C43AGL(1,ℤ/8)12yes—
225C2×C4×C43#13712yes—
226C2×C4×C43C23×C411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43H(5,𝔽2)11yescharacteristic
229C2×C4×C43H(5,𝔽2)11yescharacteristic
230C2×C4×C432−1+411yescharacteristic
231C2×C4×C432−1+411yescharacteristic
232C22⋊D43—48no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43C2×C22⋊C412yes—
249C2×Dic43C2×C22⋊C412yes—
250C2×Dic43C2×C22⋊C412yes—
251C4×D43—28no—
252C4×D43—22no—
253C4×D43—22no—
254C4×D43—22no—
255C4×D43—22no—
256C4×D43—28no—
257C4×D43—88no—
258Dic86—22no—
259Dic86—22no—
260Dic86—41no—
261Dic86—41no—
262C8×C43—42no—
263C43⋊C8—42no—
264#21867—431nomaximal, Sylow
265C22×C43—42no—
266C22×C43—42no—
267C22×C43—42no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43C22×C22⋊C411yescharacteristic
273C22×C43#53511yescharacteristic
274C22×C43#53611yescharacteristic
275C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
276C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C43C2×#13711yescharacteristic
278C22×C43C2×#13711yescharacteristic
279C2×D43—22no—
280C2×D43—22no—
281C2×D43—22no—
282C2×D43—22no—
283C2×D43—22no—
284C2×D43—22no—
285C2×D43#41714yes—
286C4×C43—22no—
287C4×C43—42no—
288C4×C43—82no—
289C4×C43#41714yes—
290C4×C43#52011yescharacteristic
291C4×C43#52011yescharacteristic
292C4×C43#53711yescharacteristic
293C4×C43#53711yescharacteristic
294Dic43—22no—
295Dic43—22no—
296Dic43—22no—
297Dic43—42no—
298Dic43—42no—
299Dic43—82no—
300C2×#529—431no—
301C2×#432—431no—
302C2×#384—431no—
303#1992—432no—
304#1959—432no—
305#1874—432no—
306#1872—432no—
307#1803—431no—
308#1803—431no—
309#1802—431no—
310#1802D4311yescharacteristic, complemented
311C2×C43—82no—
312C2×C43#231111yescharacteristic
313C2×C43C2×#41711yescharacteristic
314C2×C43C2×#41711yescharacteristic
315C2×C43#321711yescharacteristic
316C2×C43#321811yescharacteristic
317C2×C43#323811yescharacteristic
318C2×C43#323911yescharacteristic
319D43—24no—
320#529—438no—
321#529—864no—
322C2×#126—861no—
323C2×#125—431no—
324C2×#124—431no—
325C2×#123—861no—
326C2×C22⋊Q8—431no—
327C2×#121—431no—
328C2×C4×Q8—431no—
329C2×C4×D4—861no—
330C2×C4×D4C2×D4311yescharacteristic
331C2×#117—861no—
332C22×C4⋊C4—432no—
333C22×C4⋊C4—861no—
334C22×C4⋊C4—861no—
335C22×C42—431no—
336#432—864no—
337C2×C4⋊C8—431no—
338C2×C4⋊C8C2×D4311yescharacteristic
339C2×#103—432no—
340C2×#103—432no—
341C2×#102—432no—
342C2×#102C2×D4312yes—
343C2×C22⋊C8—432no—
344C2×#97—432no—
345#384—432no—
346#384—431no—
347#384—861no—
348#384—861no—
349#384C2×D4311yescharacteristic
350#340—432no—
351#340—432no—
352#340—432no—
353#340C2×D4312yes—
354C43#2186711yescharacteristic, complemented, Sylow
355C22×Q8—431no—
356C22×D4—861no—
357C22×D4C22×D4311yescharacteristic
358C23×C4—21no—
359C23×C4—431no—
360C23×C4—431no—
361C23×C4—431no—
362C23×C4—862no—
363C22×C8—432no—
364C22×C8C22×D4312yes—
365#126—868no—
366#125—434no—
367#125—862no—
368#124—434no—
369#124—862no—
370#123—868no—
371C22⋊Q8—434no—
372C22⋊Q8—862no—
373#121—434no—
374#121—862no—
375C4×Q8—434no—
376C4×Q8—862no—
377C4×D4—22no—
378C4×D4—868no—
379C4×D4C4×D4314yescomplemented
380#117—868no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—432no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—862no—
390C2×C4⋊C4—862no—
391C2×C4⋊C4—862no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—1722no—
395C2×C4⋊C4—1722no—
396C2×C4⋊C4—1724no—
397C2×C4⋊C4—1724no—
398C2×C4⋊C4C22×D4312yes—
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—861no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C42—431no—
406C2×C42—431no—
407C2×C42—431no—
408C2×C42—434no—
409C2×C42—434no—
410C2×C42—861no—
411C2×C42C22×D4311yescharacteristic
412C4⋊C8—22no—
413C4⋊C8—862no—
414#103—1722no—
415#103—1722no—
416#102—42no—
417#102—1722no—
418C22⋊C8—864no—
419#97—864no—
420C24—21no—
421C24—431no—
422C2×Q8—432no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—864no—
434C2×D4—1722no—
435C2×D4—1722no—
436C2×D4C2×C4×D4312yes—
437C22×C4—21no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—434no—
446C22×C4—434no—
447C22×C4—432no—
448C22×C4—432no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—862no—
460C22×C4—1724no—
461C22×C4—1724no—
462C22×C4—1724no—
463C22×C4D4×D4311yescharacteristic
464C22×C4D4×D4311yescharacteristic
465C22×C4C23×D4311yescharacteristic
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—862no—
470C2×C8—862no—
471C2×C8—862no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—432no—
478C4⋊C4—864no—
479C4⋊C4—864no—
480C4⋊C4—864no—
481C4⋊C4—864no—
482C4⋊C4—861no—
483C4⋊C4—862no—
484C4⋊C4—862no—
485C4⋊C4—1722no—
486C4⋊C4—1724no—
487C4⋊C4—1724no—
488C4⋊C4—1724no—
489C4⋊C4—1722no—
490C4⋊C4C2×C4×D4312yes—
491C22⋊C4—24no—
492C22⋊C4—864no—
493C22⋊C4—864no—
494C22⋊C4—864no—
495C22⋊C4—864no—
496C42—434no—
497C42—434no—
498C42—432no—
499C42—432no—
500C42—864no—
501C42C2×C4×D4312yes—
502C42D4×D4312yes—
503C23—22no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—432no—
511C23—432no—
512C23—432no—
513C23—861no—
514C23—861no—
515C23—861no—
516C23—861no—
517C23C2×D4×D4311yescharacteristic
518Q8—862no—
519Q8—862no—
520Q8—1721no—
521Q8—1721no—
522D4—22no—
523D4—22no—
524D4—41no—
525D4—41no—
526D4—1728no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—48no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—432no—
537C2×C4—432no—
538C2×C4—432no—
539C2×C4—868no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—862no—
547C2×C4—862no—
548C2×C4—868no—
549C2×C4—862no—
550C2×C4—862no—
551C2×C4—862no—
552C2×C4—862no—
553C2×C4—3448no—
554C2×C4—1722no—
555C2×C4—1722no—
556C2×C4—1722no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4C22⋊C4×D4312yes—
562C2×C4C22⋊C4×D4312yes—
563C2×C4#1306334912yes—
564C2×C4#1306335412yes—
565C2×C4C22×C4×D4311yescharacteristic
566C2×C4C2×D4×D4311yescharacteristic
567C2×C4#1306337011yescharacteristic
568C2×C4#1306337111yescharacteristic
569C2×C4#1306337211yescharacteristic
570C2×C4#1306337311yescharacteristic
571C8—42no—
572C8—1722no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—434no—
581C22—862no—
582C22—862no—
583C22—862no—
584C22—862no—
585C22—862no—
586C22—862no—
587C22C2×C22⋊C4×D4311yescharacteristic
588C22#1458346511yescharacteristic
589C22#1458347211yescharacteristic
590C22AGL(1,ℤ/8)×D4311yescharacteristic
591C22C2×#1306334911yescharacteristic
592C22#137×D4311yescharacteristic
593C22C2×#1306335411yescharacteristic
594C4—22no—
595C4—42no—
596C4—82no—
597C4—862no—
598C4—862no—
599C4—862no—
600C4—3442no—
601C4—1722no—
602C4—1722no—
603C4#1458289714yes—
604C4#1458337911yescharacteristic
605C4#1458338011yescharacteristic
606C4#1458347811yescharacteristic
607C4#1458347911yescharacteristic
608C2—82no—
609C2—864no—
610C2#1913718411yescharacteristic
611C2#417×D4311yescharacteristic
612C2C2×#1458289711yescharacteristic
613C2#1914561211yescharacteristic
614C2#1914562111yescharacteristic
615C2#1914581511yescharacteristic
616C2#1914582411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1802C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
cosocleC22×C4×C43C24
hypercenter#1802D43
hypocenterC43#21867
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#14582955C2semidirect
3. #384×D43C2semidirect
4. #19135562C2semidirect
5. #19135410C2semidirect
7. #19134901C2semidirect
8. #19134601C2semidirect
9. #19134597C2semidirect
10. #19134595C2semidirect
11. C43×#1802C2semidirect
13. #14583431C4semidirect
55. #13063316C2×C4semidirect
57. #13063312C2×C4semidirect
64. C4×Dic86C2×C4semidirect
102. C4×D4×C43C2×C4semidirect
310. #1802D43semidirect
354. C43#21867semidirect
379. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834312
C2×#145829552
#384×D432
#191355622
#191354102
#191349092
#191349012
#191346012
#191345972
#191345952
C43×#18022
#2186743