Finite Group Databasebeta

← #25102193

Subgroups — #25102193

Order 11008.

1532 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063290C211yesmaximal, characteristic, complemented
2C2×#14583037C211yesmaximal, characteristic
3C2×#14582990C212yesmaximal, complemented
4#121×Dic43C211yesmaximal, characteristic
5#19134947C212yesmaximal, complemented
6#19134864C212yesmaximal, complemented
7#19134788C211yesmaximal, characteristic, complemented
8#19134531C211yesmaximal, characteristic, complemented
9#19134414C212yesmaximal, complemented
10C22⋊C8×Dic43C211yesmaximal, characteristic, complemented
11C43×#1874C211yesmaximal, characteristic
12C23×Dic86C2211yescharacteristic
13C22×#10621883C2212yes—
14C2×#13063290—28no—
15C2×#13063290—21no—
16C2×#13063290—21no—
17C2×#13063290C2212yes—
18C2×#13063290C2212yes—
19C2×D4×Dic43—21no—
20C2×D4×Dic43C2211yescharacteristic
21C22×Dic43⋊C4—21no—
22C22×C4×Dic43—21no—
23C22×C4×Dic43C2211yescharacteristic
24#14583037C418yescomplemented
25#14582990—28no—
26C2×#13063256C2212yes—
27C2×#13063250C2212yes—
28C2×#13063250C2212yes—
29C2×#13063248C2212yes—
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×C8×Dic43C2212yes—
32#14582802C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582792—21no—
35#14582779—21no—
36#14582759C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C22⋊C4×Dic43—21no—
39#14582661C2212yes—
40#14582653C2212yes—
41C2×#121×C43C2211yescharacteristic
42C22×C4⋊C4×C43C2211yescharacteristic
43C2×#102×C43C2212yes—
44C2×C22⋊C8×C43C2211yescharacteristic
45C43×#340C2212yes—
46C22×Dic86—21no—
47C22×Dic86—22no—
48C22×Dic86—24no—
49C22×Dic86—24no—
50C22×Dic86C2×C414yescomplemented
51C22×Dic86C2312yes—
52C23×Dic43—21no—
53C23×Dic43—21no—
54C23×Dic43D411yescharacteristic
55C23×Dic43D411yescharacteristic
56C2×#10621883—24no—
57C2×#10621883—24no—
58C2×#10621883C2×C418yescomplemented
59C22×C43⋊C8C2312yes—
60#13063290—28no—
61#13063290—28no—
62#13063290—24no—
63#13063290—24no—
64#13063290—24no—
65#13063290D418yescomplemented
66D4×Dic43—24no—
67D4×Dic43—44no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×Dic43⋊C4—28no—
72C2×Dic43⋊C4—22no—
73C2×Dic43⋊C4—22no—
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C4×Dic43—28no—
79C2×C4×Dic43—22no—
80C2×C4×Dic43—22no—
81C2×C4×Dic43—24no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87#13063256—24no—
88#13063250—24no—
89#13063250—24no—
90#13063248C2×C418yescomplemented
91C22⋊(C43⋊C8)C2×C414yescomplemented
92C8×Dic43—24no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C22×D4×C43—21no—
97C22×D4×C43C2311yescharacteristic
98C23×C4×C43—21no—
99C23×C4×C43C2311yescharacteristic
100C22×C8×C43C2312yes—
101#121×C43—22no—
102#121×C43C2×C414yes—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—24no—
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2312yes—
107C2×C22⋊C4×C43—21no—
108#102×C43—24no—
109C22⋊C8×C43—22no—
110C24×C43—21no—
111C24×C43C2×D411yescharacteristic
112C2×D4×C43—21no—
113C2×D4×C43—24no—
114C2×D4×C43—22no—
115C2×D4×C43—22no—
116C2×D4×C43—42no—
117C2×D4×C43—42no—
118C2×D4×C43C22×C412yes—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—24no—
122C22×C4×C43—21no—
123C22×C4×C43—22no—
124C22×C4×C43—42no—
125C22×C4×C43—42no—
126C22×C4×C43C22×C412yes—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43#4112yes—
129C22×C4×C43C2411yescharacteristic
130C22×Dic43—24no—
131C22×Dic43—24no—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—24no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—41no—
141C22×Dic43—42no—
142C22×Dic43—42no—
143C22×Dic43—42no—
144C22×Dic43SD1614yescomplemented
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C2×Dic86—24no—
150C2×Dic86—24no—
151C2×Dic86—216no—
152C2×Dic86—24no—
153C2×Dic86—22no—
154C2×Dic86—22no—
155C2×Dic86—22no—
156C2×Dic86—216no—
157C2×Dic86C22×C414yes—
158C2×Dic86C2×D414yes—
159C2×Dic86#4114yes—
160C2×C8×C43—22no—
161C2×C8×C43—22no—
162C2×C8×C43—22no—
163C4⋊C4×C43—24no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43C22×C412yes—
167C4⋊C4×C43C2×D414yes—
168C22⋊C4×C43—24no—
169C22⋊Dic43—42no—
170C22⋊Dic43—42no—
171C22⋊Dic43—42no—
172C22⋊Dic43—42no—
173#10621883—216no—
174C4⋊Dic43—22no—
175C4⋊Dic43—22no—
176C4⋊Dic43—42no—
177Dic43⋊C4—28no—
178Dic43⋊C4—28no—
179C4×Dic43—28no—
180C4×Dic43—22no—
181C4×Dic43—28no—
182C4×Dic43—22no—
183C4×Dic43—22no—
184C4×Dic43—42no—
185C4×Dic43C2×D414yes—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C2×C43⋊C8C22×C414yes—
189C23×C43—21no—
190C23×C43—21no—
191C23×C43—21no—
192C23×C43—21no—
193C23×C43—22no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43C4×D412yes—
201C23×C43C2×SD1612yes—
202C23×C43#13512yes—
203C23×C43C22×D411yescharacteristic
204D4×C43—24no—
205D4×C43—48no—
206D4×C43—42no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—24no—
210C2×C4×C43—24no—
211C2×C4×C43—22no—
212C2×C4×C43—24no—
213C2×C4×C43—48no—
214C2×C4×C43—41no—
215C2×C4×C43—42no—
216C2×C4×C43—41no—
217C2×C4×C43—42no—
218C2×C4×C43C4×D412yes—
219C2×C4×C43C23×C411yescharacteristic
220C2×C4×C43C22×D412yes—
221C2×C4×C43C2×#4112yes—
222C2×C4×C43C2×#4111yescharacteristic
223C2×Dic43—216no—
224C2×Dic43—24no—
225C2×Dic43—21no—
226C2×Dic43—24no—
227C2×Dic43—24no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—28no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—44no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—84no—
243C2×Dic43#12012yes—
244C2×Dic43#12012yes—
245C2×Dic43C2×SD1612yes—
246C2×Dic43C2×SD1612yes—
247C2×Dic43#13712yes—
248Dic86—216no—
249Dic86—24no—
250Dic86—24no—
251Dic86—24no—
252Dic86C4×D418yescomplemented
253C8×C43—42no—
254C43⋊C8—24no—
255C4×#448—431nomaximal, Sylow
256C22×C43—22no—
257C22×C43—22no—
258C22×C43—22no—
259C22×C43—22no—
260C22×C43—22no—
261C22×C43—22no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43C4×SD1614yescomplemented
270C22×C43C2×C4×D411yescharacteristic
271C22×C43C2×#12011yescharacteristic
272C22×C43#52511yescharacteristic
273C22×C43C22×SD1611yescharacteristic
274C22×C43C2×#13511yescharacteristic
275C22×C43C2×#13711yescharacteristic
276C22×C43#57511yescharacteristic
277C4×C43—22no—
278C4×C43—42no—
279C4×C43—44no—
280C4×C43C2×C4×D412yes—
281C4×C43#52512yes—
282Dic43—22no—
283Dic43—22no—
284Dic43—28no—
285Dic43—41no—
286Dic43—81no—
287Dic43—81no—
288Dic43#44814yescomplemented
289C22×C4×Q8—431no—
290C2×#448—431no—
291C2×C4×SD16—432no—
292C4×#121—431no—
293#1880—432no—
294#1874D4311yescharacteristic
295#1865—432no—
296#1853—431no—
297#1787—431no—
298C4×#103—432no—
299C4×C22⋊C8—431no—
300C2×C43—24no—
301C2×C43—82no—
302C2×C43C4×#12011yescharacteristic
303C2×C43C2×C4×SD1611yescharacteristic
304C2×C43C4×#13711yescharacteristic
305C2×C43C2×#44811yescharacteristic
306C2×C43#300211yescharacteristic
307C2×C43#310311yescharacteristic
308C2×C43#310811yescharacteristic
309C23×Q8—431no—
310C22×SD16—432no—
311C2×#121C2×D4311yescharacteristic
312C2×C4×Q8—432no—
313C2×C4×Q8—432no—
314C2×C4×Q8—861no—
315C2×C4×Q8—861no—
316C2×C4×Q8—868no—
317C2×C4×D4—431no—
318C2×C4×D4—861no—
319C22×C4⋊C4—861no—
320C22×C4⋊C4C2×D4311yescharacteristic
321C22×C42—431no—
322C22×C42—861no—
323#448—438no—
324C4×SD16—868no—
325C2×#106—432no—
326C2×#103—432no—
327C2×#103—432no—
328C2×#103—432no—
329C2×#102C2×D4312yes—
330C2×C22⋊C8—431no—
331C2×C22⋊C8C2×D4311yescharacteristic
332C2×C4×C8—432no—
333#390—431no—
334#389—431no—
335#388—861no—
336#386—861no—
337#380—431no—
338C4×C4⋊C4—431no—
339C4×C22⋊C4—861no—
340#340—432no—
341#340C2×D4312yes—
342#336—432no—
343C43C4×#44811yescharacteristic, complemented, Sylow
344C22×Q8—434no—
345C22×Q8—432no—
346C22×Q8—864no—
347C22×Q8—864no—
348C22×Q8—861no—
349C22×Q8—862no—
350C22×D4—21no—
351C22×D4C22×D4311yescharacteristic
352C23×C4—21no—
353C23×C4—431no—
354C23×C4—431no—
355C23×C4—861no—
356C23×C4—861no—
357C23×C4C22×D4311yescharacteristic
358C2×SD16—438no—
359C2×SD16—864no—
360C2×SD16—864no—
361C22×C8—432no—
362C22×C8C22×D4312yes—
363#121—22no—
364#121C4×D4314yes—
365C4×Q8—438no—
366C4×Q8—864no—
367C4×Q8—864no—
368C4×Q8—868no—
369C4×Q8—868no—
370C4×Q8—864no—
371C4×D4—864no—
372C4×D4—1724no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—862no—
378C2×C4⋊C4—862no—
379C2×C4⋊C4—868no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4C22×D4311yescharacteristic
382C2×C4⋊C4C22×D4312yes—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C42—431no—
389C2×C42—431no—
390C2×C42—431no—
391C2×C42—431no—
392C2×C42—864no—
393C2×C42—862no—
394C2×C42—862no—
395C2×C42—868no—
396C2×C42—861no—
397#106—864no—
398#103—438no—
399#103—864no—
400#103—864no—
401#102—24no—
402C22⋊C8—22no—
403C22⋊C8—434no—
404C4×C8—864no—
405#95—861no—
406#95—861no—
407#95—861no—
408C24—21no—
409C24D4×D4311yescharacteristic
410C2×Q8—434no—
411C2×Q8—434no—
412C2×Q8—434no—
413C2×Q8—8616no—
414C2×Q8—864no—
415C2×Q8—864no—
416C2×Q8—8616no—
417C2×Q8—864no—
418C2×Q8—862no—
419C2×Q8—862no—
420C2×Q8—862no—
421C2×D4—24no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4C2×C4×D4312yes—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—431no—
436C22×C4—434no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—864no—
444C22×C4—864no—
445C22×C4—864no—
446C22×C4—862no—
447C22×C4—862no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—1722no—
451C22×C4—1722no—
452C22×C4—1722no—
453C22×C4—1721no—
454C22×C4C2×C4×D4312yes—
455C22×C4D4×D4311yescharacteristic
456C22×C4#1062190012yes—
457C22×C4C23×D4311yescharacteristic
458SD16—8616no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—434no—
463C2×C8—862no—
464C2×C8—862no—
465C4⋊C4—24no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—868no—
469C4⋊C4—868no—
470C4⋊C4—862no—
471C4⋊C4—862no—
472C4⋊C4—1722no—
473C4⋊C4C2×C4×D4312yes—
474C4⋊C4D4×D4314yes—
475C22⋊C4—24no—
476C22⋊C4—1722no—
477C22⋊C4—1722no—
478C22⋊C4—1722no—
479C22⋊C4—1722no—
480C42—434no—
481C42—862no—
482C42—862no—
483C42—868no—
484C42—868no—
485C42—862no—
486C42—1722no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—22no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23(C22⋊D43)⋊C412yes—
499C23SD16×D4312yes—
500C23#1306334412yes—
501C23C2×D4×D4311yescharacteristic
502Q8—438no—
503Q8—8616no—
504Q8—864no—
505Q8—864no—
506Q8—864no—
507D4—24no—
508D4—48no—
509D4—42no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—48no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—432no—
522C2×C4—432no—
523C2×C4—432no—
524C2×C4—432no—
525C2×C4—432no—
526C2×C4—868no—
527C2×C4—8616no—
528C2×C4—864no—
529C2×C4—861no—
530C2×C4—864no—
531C2×C4—864no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—3444no—
539C2×C4—1724no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4(C22⋊D43)⋊C412yes—
547C2×C4C22×C4×D4311yescharacteristic
548C2×C4C2×D4×D4312yes—
549C2×C4#41×D4312yes—
550C2×C4C2×#1062190011yescharacteristic
551C8—42no—
552C8—864no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22#1458299014yescomplemented
567C22C2×(C22⋊D43)⋊C411yescharacteristic
568C22#120×D4311yescharacteristic
569C22#1458340711yescharacteristic
570C22C2×SD16×D4311yescharacteristic
571C22C2×#1306334411yescharacteristic
572C22#137×D4311yescharacteristic
573C22#1458369511yescharacteristic
574C4—22no—
575C4—44no—
576C4—42no—
577C4—434no—
578C4—868no—
579C4—862no—
580C4—862no—
581C4—3441no—
582C4—3441no—
583C4—1721no—
584C4C4×D4×D4312yes—
585C4#1458340912yes—
586C2—24no—
587C2—82no—
588C2#1913710011yescharacteristic
589C2C2×#1458299011yescharacteristic
590C2#1914341911yescharacteristic
591C2#448×D4311yescharacteristic
592C2#1914380811yescharacteristic
593C2#1914462311yescharacteristic
594C2#1914467211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1874C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
cosocleC22×C4×C43C24
hypercenter#1874D43
hypocenterC43C4×#448
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C22×#13063290C2semidirect
3. C2×#14582990C2semidirect
5. #19134947C2semidirect
6. #19134864C2semidirect
7. #19134788C2semidirect
8. #19134531C2semidirect
9. #19134414C2semidirect
10. C22⋊C8×Dic43C2semidirect
24. #14583037C4semidirect
50. C22×Dic86C2×C4semidirect
58. C2×#10621883C2×C4semidirect
65. #13063290D4semidirect
90. #13063248C2×C4semidirect
91. C22⋊(C43⋊C8)C2×C4semidirect
144. C22×Dic43SD16semidirect
252. Dic86C4×D4semidirect
269. C22×C43C4×SD16semidirect
288. Dic43#448semidirect
343. C43C4×#448semidirect
566. C22#14582990semidirect

Maximal subgroups

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

subgroupindex
C22×#130632902
C2×#145830372
C2×#145829902
#121×Dic432
#191349472
#191348642
#191347882
#191345312
#191344142
C22⋊C8×Dic432
C43×#18742
C4×#44843