Finite Group Databasebeta

← #456×Dic43 #25102505

Subgroups — #456×Dic43 #25102505

Order 11008.

1358 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
12−1+4×Dic43C211yesmaximal, characteristic
2#137×Dic43C212yesmaximal, complemented
3C4⋊Q8×Dic43C211yesmaximal, characteristic, complemented
4#19134989C211yesmaximal, characteristic, complemented
5#19134966C212yesmaximal, complemented
6#19134823C212yesmaximal, complemented
7#19134812C211yesmaximal, characteristic, complemented
8#19134554C211yesmaximal, characteristic
9#104×Dic43C212yesmaximal, complemented
10#101×Dic43C211yesmaximal, characteristic, complemented
11C2×C43×#456C211yesmaximal, characteristic
12#14583382—22no—
13#14583382—22no—
14#14583382C2212yes—
15#14583377—22no—
16#14583377C2211yescharacteristic
17#41×Dic43—22no—
18#41×Dic43—22no—
19#41×Dic43C2212yes—
20C2×Q8×Dic43—22no—
21C2×Q8×Dic43C2211yescharacteristic
22C2×Q8×Dic43C2211yescharacteristic
23#14583006—22no—
24#14583000—22no—
25Q16×Dic43—22no—
26SD16×Dic43—22no—
27#14582941C2212yes—
28C2×#13063252C2212yes—
29#14582908C2212yes—
30#14582900C2212yes—
31C2×#13063244C2211yescharacteristic
32M16×Dic43C2212yes—
33#14582806C2211yescharacteristic
34#14582806C2211yescharacteristic
35#14582798—22no—
36#14582769C2211yescharacteristic
37C4⋊C4×Dic43—22no—
38C42×Dic43C2211yescharacteristic
39#14582667C2212yes—
40#14582660C2212yes—
41#14582659C2212yes—
42C2×2−1+4×C43C2211yescharacteristic
43C2×#137×C43C2212yes—
44C2×C4⋊Q8×C43C2211yescharacteristic
45C43×#456C418yescomplemented
46C2×#104×C43C2212yes—
47C2×#101×C43C2211yescharacteristic
48C2×#10621877C2312yes—
49Q8×Dic43—22no—
50Q8×Dic43—24no—
51Q8×Dic43—22no—
52Q8×Dic43—22no—
53Q8×Dic43—22no—
54Q8×Dic43—22no—
55Q8×Dic43—22no—
56Q8×Dic43—22no—
57Q8×Dic43—22no—
58Q8×Dic43—22no—
59Q8×Dic43D412yes—
60Q8×Dic43D412yes—
61D4×Dic43—22no—
62D4×Dic43—24no—
63D4×Dic43—22no—
64D4×Dic43—22no—
65D4×Dic43—22no—
66D4×Dic43—24no—
67D4×Dic43—22no—
68D4×Dic43D412yes—
69D4×Dic43D412yes—
70#13063284—24no—
71#13063284—24no—
72#13063284—22no—
73#13063284—22no—
74#13063284—22no—
75#13063284C2312yes—
76C2×C4⋊Dic43—24no—
77C2×C4⋊Dic43—22no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—22no—
80C2×C4⋊Dic43D412yes—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4×Dic43—24no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—22no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43D412yes—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063259—22no—
92#13063257—22no—
93#13063252—24no—
94#13063249—22no—
95#13063249—22no—
96#13063249—22no—
97#13063246—22no—
98#13063244—22no—
99#13063235—22no—
100C8×Dic43—22no—
101C43⋊#95—22no—
102C43⋊#95—22no—
1032−1+4×C43—24no—
1042−1+4×C43—22no—
1052−1+4×C43C2×C414yes—
106C2×#41×C43—22no—
107C2×#41×C43—22no—
108C2×#41×C43C2312yes—
109C22×Q8×C43—22no—
110C22×Q8×C43C2311yescharacteristic
111C22×Q8×C43C2311yescharacteristic
112#137×C43—24no—
113#137×C43C2×C418yescomplemented
114C2×Q16×C43—22no—
115C2×SD16×C43—22no—
116C2×M16×C43C2312yes—
117C4⋊Q8×C43—22no—
118C4⋊Q8×C43C2×C414yescomplemented
119C2×C4⋊C4×C43—22no—
120C2×C42×C43C2311yescharacteristic
121#104×C43C2×C418yescomplemented
122#101×C43C2×C414yescomplemented
123#41×C43—28no—
124#41×C43—28no—
125#41×C43—28no—
126#41×C43—28no—
127#41×C43—22no—
128#41×C43—22no—
129#41×C43C22×C414yes—
130#41×C43#4114yes—
131C2×Q8×C43—22no—
132C2×Q8×C43—28no—
133C2×Q8×C43—28no—
134C2×Q8×C43—22no—
135C2×Q8×C43—22no—
136C2×Q8×C43—21no—
137C2×Q8×C43—22no—
138C2×Q8×C43—22no—
139C2×Q8×C43C22×C412yes—
140C2×Q8×C43C22×C412yes—
141C2×Q8×C43C2×D412yes—
142C2×Q8×C43#4112yes—
143C2×D4×C43—22no—
144C2×D4×C43—22no—
145C2×D4×C43C2×D412yes—
146C22×C4×C43—24no—
147C22×C4×C43—22no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43C2×D412yes—
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—24no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D412yes—
159C22×Dic43C2×D411yescharacteristic
160Q16×C43—28no—
161SD16×C43—28no—
162M16×C43—22no—
163M16×C43C22×C414yes—
164C2×C8×C43—22no—
165C4⋊C4×C43—28no—
166C42×C43—21no—
167C42×C43C22×C412yes—
168C22⋊Dic43—24no—
169C22⋊Dic43—22no—
170C22⋊Dic43—22no—
171C22⋊Dic43—22no—
172C4⋊Dic43—24no—
173C4⋊Dic43—22no—
174C4⋊Dic43—22no—
175C4⋊Dic43—22no—
176C4⋊Dic43—22no—
177C4⋊Dic43—24no—
178C4⋊Dic43—22no—
179C4⋊Dic43—22no—
180C4⋊Dic43—44no—
181C4⋊Dic43—42no—
182C4⋊Dic43C2×D412yes—
183C4⋊Dic43C2×D412yes—
184C4×Dic43—24no—
185C4×Dic43—24no—
186C4×Dic43—24no—
187C4×Dic43—22no—
188C4×Dic43—22no—
189C4×Dic43—22no—
190C4×Dic43—22no—
191C4×Dic43—22no—
192C4×Dic43—22no—
193C4×Dic43—42no—
194C4×Dic43—41no—
195C4×Dic43—41no—
196C4×Dic43C2×D412yes—
197C4×Dic43C2×D412yes—
198#10621877—22no—
199#10621877—22no—
200C2×C43⋊C8—22no—
201C23×C43—22no—
202C23×C43C22×D411yescharacteristic
203Q8×C43—28no—
204Q8×C43—24no—
205Q8×C43—22no—
206Q8×C43—24no—
207Q8×C43—24no—
208Q8×C43—42no—
209Q8×C43C4×D414yes—
210D4×C43—28no—
211D4×C43—24no—
212D4×C43—24no—
213D4×C43—22no—
214D4×C43C4×D414yes—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—216no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—24no—
223C2×C4×C43—24no—
224C2×C4×C43—22no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C4×D414yes—
228C2×C4×C43C23×C411yescharacteristic
229C2×C4×C43C22×D412yes—
230C2×C4×C43C2×#4112yes—
231C2×C4×C43C2×#4111yescharacteristic
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—22no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—44no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—41no—
244C2×Dic43—82no—
245C2×Dic43—84no—
246C2×Dic43#12011yescharacteristic
247C2×Dic43#12012yes—
248C2×Dic43#12011yescharacteristic
249C8×C43—24no—
250C43⋊C8—42no—
251C4×#456—431nomaximal, Sylow
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—24no—
255C22×C43—42no—
256C22×C43—42no—
257C22×C43C2×C4×D411yescharacteristic
258C22×C43C2×#12011yescharacteristic
259C22×C43#52511yescharacteristic
260C4×C43—24no—
261C4×C43—24no—
262C4×C43—24no—
263C4×C43—42no—
264C4×C43C2×C4×D412yes—
265C4×C43#52512yes—
266Dic43—21no—
267Dic43—22no—
268Dic43—42no—
269Dic43—42no—
270Dic43—42no—
271Dic43—42no—
272Dic43—81no—
273Dic43#45612yesdirect product factor
274C4×2−1+4—431no—
275C2×#456D4311yescharacteristic
276C4×#137—432no—
277C4×C4⋊Q8—431no—
278#1886—431no—
279#1882—432no—
280#1859—432no—
281#1857—431no—
282#1793—431no—
283C4×#104—432no—
284C4×#101—431no—
285C2×C43—21no—
286C2×C43—21no—
287C2×C43—44no—
288C2×C43C4×#12011yescharacteristic
289C2×C43C2×#45611yescharacteristic
290C2×C43#301811yescharacteristic
291C2×2−1+4C2×D4311yescharacteristic
292C2×#137C2×D4312yes—
293C2×C4⋊Q8C2×D4311yescharacteristic
294#520—432no—
295#520—862no—
296#520—862no—
297#519—431no—
298#519—862no—
299C4×#41—432no—
300C4×#41—862no—
301C4×#41—862no—
302C2×C4×Q8—431no—
303C2×C4×Q8—431no—
304C2×C4×Q8—862no—
305#456Dic4318yesdirect product factor
306#441—862no—
307#440—862no—
308C4×Q16—862no—
309C4×SD16—862no—
310#428—432no—
311C2×#104—432no—
312C2×#104C2×D4312yes—
313#419—432no—
314#417—432no—
315C2×#101—431no—
316C2×#101C2×D4311yescharacteristic
317C4×M16—432no—
318#391—431no—
319#391—431no—
320#389—862no—
321#384—431no—
322C4×C4⋊C4—862no—
323C43—431no—
324#343—432no—
325#339—432no—
326#339—432no—
327C43C4×#45611yescharacteristic, complemented, Sylow
3282−1+4—24no—
3292−1+4—22no—
3302−1+4C2×Dic4314yes—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41C22×D4312yes—
334C22×Q8—22no—
335C22×Q8C22×D4311yescharacteristic
336C22×Q8C22×D4311yescharacteristic
337#137—24no—
338#137C2×Dic4318yescomplemented
339C2×Q16—22no—
340C2×SD16—22no—
341C2×M16—432no—
342C2×M16C22×D4312yes—
343C4⋊Q8—22no—
344C4⋊Q8C2×Dic4314yescomplemented
345C4×Q8—432no—
346C4×Q8—432no—
347C4×Q8—862no—
348C4×Q8—862no—
349C4×Q8—862no—
350C4×Q8—862no—
351C4×Q8—862no—
352C4×Q8—862no—
353C4×Q8—862no—
354C4×Q8—864no—
355C4×Q8—862no—
356C4×Q8—862no—
357C4×D4—432no—
358C4×D4—432no—
359C4×D4—862no—
360C4×D4—862no—
361C4×D4—864no—
362C4×D4—862no—
363C4×D4—862no—
364C4×D4—864no—
365C4×D4—862no—
366#117—432no—
367#117—862no—
368#117—862no—
369#117—864no—
370#117—864no—
371#117—862no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—432no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—862no—
377C2×C4⋊C4—864no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—862no—
380C2×C42—431no—
381C2×C42—432no—
382C2×C42—431no—
383C2×C42—862no—
384C2×C42—861no—
385C2×C42—864no—
386C2×C42—861no—
387C2×C42—861no—
388C2×C42C22×D4311yescharacteristic
389#107—862no—
390#106—862no—
391#104—864no—
392#104C2×Dic4318yescomplemented
393#103—862no—
394#103—862no—
395#103—862no—
396#102—862no—
397#101—862no—
398#101C2×Dic4314yescomplemented
399#97—862no—
400C4×C8—862no—
401#95—862no—
402#95—862no—
403#41—28no—
404#41—28no—
405#41—28no—
406#41—28no—
407#41—22no—
408#41—22no—
409#41#1062190014yes—
410#41C22×Dic4314yes—
411C2×Q8—22no—
412C2×Q8—28no—
413C2×Q8—28no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—21no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8D4×D4312yes—
420C2×Q8#1062190012yes—
421C2×Q8C22×Dic4312yes—
422C2×Q8C22×Dic4312yes—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4D4×D4312yes—
426C22×C4—24no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—431no—
431C22×C4—431no—
432C22×C4—432no—
433C22×C4—862no—
434C22×C4—862no—
435C22×C4—864no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4D4×D4312yes—
439C22×C4C23×D4311yescharacteristic
440Q16—28no—
441SD16—28no—
442M16—22no—
443M16—862no—
444M16—862no—
445M16C22×Dic4314yes—
446C2×C8—22no—
447C2×C8—862no—
448C4⋊C4—28no—
449C4⋊C4—432no—
450C4⋊C4—432no—
451C4⋊C4—864no—
452C4⋊C4—862no—
453C4⋊C4—862no—
454C4⋊C4—864no—
455C4⋊C4—862no—
456C4⋊C4—862no—
457C4⋊C4—862no—
458C4⋊C4—862no—
459C4⋊C4—1724no—
460C4⋊C4—1722no—
461C22⋊C4—862no—
462C22⋊C4—862no—
463C22⋊C4—864no—
464C22⋊C4—862no—
465C42—21no—
466C42—432no—
467C42—432no—
468C42—862no—
469C42—862no—
470C42—862no—
471C42—862no—
472C42—864no—
473C42—864no—
474C42—864no—
475C42—862no—
476C42—862no—
477C42—1722no—
478C42—1721no—
479C42—1721no—
480C42C22×Dic4312yes—
481C23—22no—
482C23C2×D4×D4311yescharacteristic
483Q8—28no—
484Q8—24no—
485Q8—22no—
486Q8—24no—
487Q8—24no—
488Q8—42no—
489Q8D4×Dic4314yes—
490D4—28no—
491D4—24no—
492D4—24no—
493D4—22no—
494D4D4×Dic4314yes—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—216no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—431no—
508C2×C4—431no—
509C2×C4—432no—
510C2×C4—862no—
511C2×C4—862no—
512C2×C4—862no—
513C2×C4—862no—
514C2×C4—862no—
515C2×C4—3442no—
516C2×C4—3444no—
517C2×C4—1724no—
518C2×C4—1721no—
519C2×C4—1722no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1722no—
524C2×C4D4×Dic4314yes—
525C2×C4C23×Dic4311yescharacteristic
526C2×C4C2×D4×D4312yes—
527C2×C4C2×#1062190012yes—
528C2×C4C2×#1062190011yescharacteristic
529C8—24no—
530C8—1722no—
531C22—21no—
532C22—21no—
533C22—24no—
534C22—42no—
535C22—42no—
536C22C2×D4×Dic4311yescharacteristic
537C22#120×D4311yescharacteristic
538C22#1458340511yescharacteristic
539C4—24no—
540C4—24no—
541C4—24no—
542C4—42no—
543C4—432no—
544C4—862no—
545C4—861no—
546C4—3441no—
547C4—1722no—
548C4—1722no—
549C4—1722no—
550C4—1722no—
551C4C2×D4×Dic4312yes—
552C4#1458340512yes—
553C2—21no—
554C2—21no—
555C2—44no—
556C2#120×Dic4311yescharacteristic
557C2#456×D4311yescharacteristic
558C2#1914394711yescharacteristic
subgroupG/H
centerC22#120×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#456C2
socleC22×C43C2×#120
prime radicalC2×2−1+4×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#456D43
hypocenterC43C4×#456
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#456

Complements

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

NH ≅ G/Ntype
2. #137×Dic43C2semidirect
3. C4⋊Q8×Dic43C2semidirect
4. #19134989C2semidirect
5. #19134966C2semidirect
6. #19134823C2semidirect
7. #19134812C2semidirect
9. #104×Dic43C2semidirect
10. #101×Dic43C2semidirect
45. C43×#456C4semidirect
113. #137×C43C2×C4semidirect
118. C4⋊Q8×C43C2×C4semidirect
121. #104×C43C2×C4semidirect
122. #101×C43C2×C4semidirect
273. Dic43#456direct (N × H)
305. #456Dic43direct (N × H)
327. C43C4×#456semidirect
338. #137C2×Dic43semidirect
344. C4⋊Q8C2×Dic43semidirect
392. #104C2×Dic43semidirect
398. #101C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
2−1+4×Dic432
#137×Dic432
C4⋊Q8×Dic432
#191349892
#191349662
#191348232
#191348122
#191345542
#104×Dic432
#101×Dic432
C2×C43×#4562
C4×#45643