Finite Group Databasebeta

← #25066675

Subgroups — #25066675

Order 11008.

596 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144673C211yesmaximal, characteristic
2#19143739C211yesmaximal, characteristic
3#19143674C211yesmaximal, characteristic, complemented
4#19133468C211yesmaximal, characteristic, complemented
5#19133445C211yesmaximal, characteristic, complemented
6#19133436C211yesmaximal, characteristic, complemented
7#19133411C211yesmaximal, characteristic, complemented
8#19133404C211yesmaximal, characteristic, complemented
9#19133401C211yesmaximal, characteristic, complemented
10SD16×C43⋊C8C211yesmaximal, characteristic, complemented
11#19133385C211yesmaximal, characteristic, complemented
12#19133022C211yesmaximal, characteristic, complemented
13#19133000C211yesmaximal, characteristic
14#19132896C211yesmaximal, characteristic, complemented
15C43×#1588C211yesmaximal, characteristic, complemented
16#14583431C2211yescharacteristic
17C4×Q8×D43C2211yescharacteristic
18#14583231C411yescharacteristic
19#14583211C411yescharacteristic
20#14583209C411yescharacteristic
21#14583208C411yescharacteristic
22#14583120C411yescharacteristic
23#14583119C411yescharacteristic
24#14583056C411yescharacteristic
25#14583036C411yescharacteristic
26#14583029C2211yescharacteristic
27Q8×C43⋊C8C2211yescharacteristic
28C8×Dic86—21no—
29C8×Dic86C2211yescharacteristic
30#14583023—21no—
31#14583023C2211yescharacteristic
32#14583023C2211yescharacteristic
33C4×Dic172C2211yescharacteristic
34C4×#10621885C2211yescharacteristic
35C4×#10621883C2211yescharacteristic
36#14582975—21no—
37#14582967—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582957—21no—
40#14582951—21no—
41#14582951C2211yescharacteristic
42#14582950—21no—
43#14582950C2211yescharacteristic
44#14582950C2211yescharacteristic
45#14582950C2211yescharacteristic
46#14582927—21no—
47#14582921C2211yescharacteristic
48#14582651C2211yescharacteristic
49#14582650C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582631C2211yescharacteristic
52#14582631C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54#14582629C2211yescharacteristic
55#14582629C2211yescharacteristic
56D4⋊(C43⋊C8)C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C8×Q8×C43C2211yescharacteristic
61C4×SD16×C43C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×Q8×D43C2×C411yescharacteristic
68C2×Dic172C2×C411yescharacteristic
69C2×#10621885C2×C411yescharacteristic
70C2×#10621883C2×C411yescharacteristic
71C2×#10621872—21no—
72C22×C43⋊C8—21no—
73#13063318—21no—
74#13063316C2×C411yescharacteristic
75#13063312C2×C411yescharacteristic
76#13063307—21no—
77#13063305C2×C411yescharacteristic
78#13063296C2×C411yescharacteristic
79Q8×Dic43C2×C411yescharacteristic
80C4×Dic86—21no—
81C4×Dic86C2311yescharacteristic
82C4×Dic86C2311yescharacteristic
83#13063290—21no—
84#13063290C2×C411yescharacteristic
85C4×C22⋊D43—21no—
86#13063284—21no—
87C4⋊C4×D43—21no—
88C4⋊C4×D43C2×C411yescharacteristic
89C42×D43—21no—
90C42×D43C2311yescharacteristic
91#13063259C2×C411yescharacteristic
92#13063258C2×C411yescharacteristic
93#13063256C2×C411yescharacteristic
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97Dic43⋊C8—21no—
98Dic43⋊C8—21no—
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8C2×C411yescharacteristic
104Dic43⋊C8C2×C411yescharacteristic
105Dic43⋊C8D411yescharacteristic
106Dic43⋊C8D411yescharacteristic
107#13063250C2×C411yescharacteristic
108#13063250C2×C411yescharacteristic
109#13063249C2×C411yescharacteristic
110#13063248C2×C411yescharacteristic
111#13063248C2×C411yescharacteristic
112#13063246C2×C411yescharacteristic
113C22⋊(C43⋊C8)—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8C2×C411yescharacteristic
117(C2×D43)⋊C8C2×C411yescharacteristic
118(C2×D43)⋊C8D411yescharacteristic
119(C2×D43)⋊C8D411yescharacteristic
120#13063235—21no—
121C4×C43⋊C8—21no—
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×SD16×C43C2×C411yescharacteristic
130C2×M16×C43—21no—
131C4×Q8×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#106×C43C2×C411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139C22⋊C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×D4×C43C22×C411yescharacteristic
146C22×C4×C43—21no—
147C2×C22⋊D43—21no—
148Q8×D43—22no—
149Q8×D43—22no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43C22×C411yescharacteristic
153C2×C4×D43C2×D411yescharacteristic
154C2×C4×D43#4111yescharacteristic
155C2×Dic86—21no—
156C2×Dic86C22×C411yescharacteristic
157C2×Dic86C22×C411yescharacteristic
158SD16×C43—22no—
159M16×C43—81no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C22×C411yescharacteristic
164C2×C8×C43C22×C411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43—21no—
168C4⋊C4×C43C22×C411yescharacteristic
169C4⋊C4×C43C22×C411yescharacteristic
170C22⋊C4×C43—21no—
171C42×C43—21no—
172C42×C43C2411yescharacteristic
173C22⋊Dic43—21no—
174C22⋊Dic43—21no—
175C22⋊Dic43—21no—
176#10621885—22no—
177#10621883—22no—
178(C2×D43)⋊C4—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43C22×C411yescharacteristic
183C4⋊Dic43C22×C411yescharacteristic
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43C22×C411yescharacteristic
194C4×Dic43C2×D411yescharacteristic
195C4×Dic43#4111yescharacteristic
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—81no—
200C2×C43⋊C8C22×C411yescharacteristic
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204Dic172—22no—
205#10621872—81no—
206C23×C43—21no—
207C22×D43C4×D411yescharacteristic
208Q8×C43—21no—
209Q8×C43#13112yes—
210D4×C43—21no—
211D4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43C23×C411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C22⋊D43—81no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43C4×D411yescharacteristic
226C2×Dic43C4×D411yescharacteristic
227C2×Dic43C4×D411yescharacteristic
228C4×D43—24no—
229C4×D43—21no—
230C4×D43—21no—
231C4×D43—21no—
232C4×D43—21no—
233C4×D43—41no—
234C4×D43—81no—
235Dic86—24no—
236Dic86—21no—
237Dic86—21no—
238Dic86—21no—
239Dic86#13112yes—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254#17919—431nomaximal, Sylow
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43C2×C4×D411yescharacteristic
259C2×D43—21no—
260C2×D43—21no—
261C2×D43—21no—
262C4×C43—22no—
263C4×C43—21no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43C2×#13111yescharacteristic
267C4×C43C2×#13111yescharacteristic
268C4×C43#57711yescharacteristic
269C4×C43#57811yescharacteristic
270Dic43—21no—
271Dic43—22no—
272Dic43—21no—
273Dic43—21no—
274Dic43—41no—
275Dic43—41no—
276Dic43—41no—
277#3108—431no—
278#2993—431no—
279#2982—431no—
280#1588D4311yescharacteristic, complemented
281#1587—431no—
282#1584—431no—
283#1583—431no—
284#1579—431no—
285SD16⋊C8—431no—
286C8×Q16—431no—
287C8×SD16—431no—
288#1574—431no—
289#1487—431no—
290#1482—431no—
291#1454—431no—
292C2×C43—81no—
293C2×C43#292911yescharacteristic
294C2×C43#294711yescharacteristic
295C2×C43#295711yescharacteristic
296D43—41no—
297#529—431no—
298C2×C4×Q8—431no—
299#483—431no—
300#480—431no—
301#479—431no—
302#479—431no—
303#464—431no—
304#464—431no—
305#451—431no—
306#448—431no—
307#446—431no—
308C8×Q8—431no—
309C8×Q8—431no—
310C8×Q8—431no—
311C8×Q8—431no—
312C8×Q8—861no—
313C8×Q8—861no—
314C8×Q8C2×D4311yescharacteristic
315C4×Q16—431no—
316C4×Q16—431no—
317C4×SD16—431no—
318C4×SD16C2×D4311yescharacteristic
319#436—861no—
320#436C2×D4311yescharacteristic
321#435—861no—
322C8×D4—431no—
323#433—861no—
324#431—431no—
325#431—431no—
326#431—431no—
327#431—431no—
328#431—861no—
329#431—861no—
330#424—861no—
331#423—431no—
332#335—431no—
333#335C2×D4311yescharacteristic
334#334—431no—
335#334—431no—
336Q8⋊C8—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341Q8⋊C8C2×D4311yescharacteristic
342D4⋊C8—431no—
343D4⋊C8C2×D4311yescharacteristic
344#322—431no—
345#322—431no—
346#322C2×D4311yescharacteristic
347C82—431no—
348C43#1791911yescharacteristic, complemented, Sylow
349C22×Q8—431no—
350C2×Q16—431no—
351C2×Q16—431no—
352C2×SD16—431no—
353C2×SD16C4×D4311yescharacteristic
354C2×M16—21no—
355C2×M16—861no—
356C22×C8—861no—
357#126—861no—
358#125—431no—
359#124—431no—
360#123—861no—
361C22⋊Q8—431no—
362#121—431no—
363C4×Q8—431no—
364C4×Q8—431no—
365C4×Q8—431no—
366C4×Q8—431no—
367C4×Q8—861no—
368C4×Q8—861no—
369C4×Q8C22×D4311yescharacteristic
370C4×D4—861no—
371C4×D4C22×D4311yescharacteristic
372#117—861no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—861no—
375C2×C42—431no—
376C2×C42—861no—
377#107—431no—
378#107—431no—
379#106—431no—
380#106C4×D4311yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—431no—
383C4⋊C8—431no—
384C4⋊C8—431no—
385C4⋊C8—431no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—861no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8C22×D4311yescharacteristic
396C4⋊C8C22×D4311yescharacteristic
397#103—431no—
398#103—431no—
399#103—431no—
400#103—431no—
401#103—431no—
402#103C4×D4311yescharacteristic
403#102—431no—
404#102C4×D4311yescharacteristic
405C22⋊C8—21no—
406C22⋊C8—431no—
407C22⋊C8—431no—
408C22⋊C8—431no—
409C22⋊C8—431no—
410C22⋊C8—861no—
411C22⋊C8—861no—
412C22⋊C8—861no—
413#97—861no—
414C4×C8—21no—
415C4×C8—431no—
416C4×C8—431no—
417C4×C8—431no—
418C4×C8—861no—
419C4×C8—861no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8C22×D4311yescharacteristic
424C4×C8C22×D4311yescharacteristic
425C4×C8C22×D4311yescharacteristic
426C2×Q8—431no—
427C2×Q8—431no—
428C2×Q8—861no—
429C2×Q8—862no—
430C2×Q8—862no—
431C2×Q8C2×C4×D4311yescharacteristic
432C2×D4—861no—
433C2×D4C2×C4×D4311yescharacteristic
434C22×C4—21no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—861no—
439C22×C4—861no—
440Q16—862no—
441Q16—862no—
442SD16—22no—
443SD16—862no—
444M16—81no—
445M16—3441no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—431no—
450C2×C8—431no—
451C2×C8—431no—
452C2×C8—431no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—3441no—
457C2×C8C2×C4×D4311yescharacteristic
458C2×C8C2×C4×D4311yescharacteristic
459C2×C8D4×D4311yescharacteristic
460C2×C8D4×D4311yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—431no—
463C4⋊C4—431no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4C2×C4×D4311yescharacteristic
473C4⋊C4C2×C4×D4311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—861no—
476C22⋊C4—861no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C42—21no—
480C42—431no—
481C42—431no—
482C42—431no—
483C42—861no—
484C42—861no—
485C42—861no—
486C42—861no—
487C42C23×D4311yescharacteristic
488C23—21no—
489C23—431no—
490Q8—21no—
491Q8—432no—
492Q8—864no—
493Q8—861no—
494Q8—861no—
495Q8—861no—
496Q8#1306333312yes—
497D4—21no—
498D4—21no—
499D4—3441no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—431no—
506C2×C4—431no—
507C2×C4—431no—
508C2×C4—864no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—3441no—
518C2×C4—1721no—
519C2×C4C22×C4×D4311yescharacteristic
520C2×C4C2×D4×D4311yescharacteristic
521C2×C4#41×D4311yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—861no—
530C8—861no—
531C8—861no—
532C8—861no—
533C8—1721no—
534C8—1721no—
535C8—1721no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—861no—
540C22—861no—
541C22—861no—
542C22C4×D4×D4311yescharacteristic
543C4—21no—
544C4—22no—
545C4—41no—
546C4—41no—
547C4—861no—
548C4—861no—
549C4—861no—
550C4—862no—
551C4—1721no—
552C4—1721no—
553C4—1721no—
554C4#131×D4311yescharacteristic
555C4C2×#1306333311yescharacteristic
556C4#1458370911yescharacteristic
557C4#1458371511yescharacteristic
558C2—81no—
559C2—1721no—
560C2#1914328611yescharacteristic
561C2#1914343511yescharacteristic
562C2#1914350711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1588C2
socleC22×C43C2×C4×D4
prime radical#13063296C2×C4
cosocleC42×C43C24
hypercenter#1588D43
hypocenterC43#17919
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1588

Complements

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

NH ≅ G/Ntype
3. #19143674C2semidirect
4. #19133468C2semidirect
5. #19133445C2semidirect
6. #19133436C2semidirect
7. #19133411C2semidirect
8. #19133404C2semidirect
9. #19133401C2semidirect
10. SD16×C43⋊C8C2semidirect
11. #19133385C2semidirect
12. #19133022C2semidirect
14. #19132896C2semidirect
15. C43×#1588C2semidirect
280. #1588D43semidirect
348. C43#17919semidirect

Maximal subgroups

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

subgroupindex
#191446732
#191437392
#191436742
#191334682
#191334452
#191334362
#191334112
#191334042
#191334012
SD16×C43⋊C82
#191333852
#191330222
#191330002
#191328962
C43×#15882
#1791943