Finite Group Databasebeta

← #25066676

Subgroups — #25066676

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#19144677C211yesmaximal, characteristic
2#19143746C211yesmaximal, characteristic
3#19143675C211yesmaximal, characteristic, complemented
4#19133475C211yesmaximal, characteristic, complemented
5#19133468C211yesmaximal, characteristic, complemented
6#19133447C211yesmaximal, characteristic, complemented
7#19133440C211yesmaximal, characteristic, complemented
8#19133415C211yesmaximal, characteristic, complemented
9#19133409C211yesmaximal, characteristic, complemented
10C8×Dic172C211yesmaximal, characteristic, complemented
11C8×#10621873C211yesmaximal, characteristic, complemented
12#19133384C211yesmaximal, characteristic, complemented
13#19133025C211yesmaximal, characteristic, complemented
14#19133004C211yesmaximal, characteristic
15C43×#1454C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18#14583230C411yescharacteristic
19#14583213C411yescharacteristic
20#14583207C411yescharacteristic
21#14583207C411yescharacteristic
22#14583122C411yescharacteristic
23#14583122C411yescharacteristic
24#14583057C411yescharacteristic
25#14583040C411yescharacteristic
26#14583029C2211yescharacteristic
27C8×Dic86C2211yescharacteristic
28C8×Dic86C2211yescharacteristic
29C8×Dic86C2211yescharacteristic
30C8×Dic86C2211yescharacteristic
31C8×Dic86C2211yescharacteristic
32#14583023—21no—
33#14583023—21no—
34C4×Dic172C2211yescharacteristic
35C4×Dic172C2211yescharacteristic
36C4×#10621873C2211yescharacteristic
37C4×#10621873C2211yescharacteristic
38#14582978C2211yescharacteristic
39#14582974—21no—
40#14582973—21no—
41C8×D172C2211yescharacteristic
42#14582959—21no—
43#14582952C2211yescharacteristic
44#14582949—21no—
45#14582949—21no—
46#14582924—21no—
47#14582923C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582652C2211yescharacteristic
50#14582650C2211yescharacteristic
51#14582650C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582631C2211yescharacteristic
54#14582631C2211yescharacteristic
55#14582631C2211yescharacteristic
56#14582631C2211yescharacteristic
57#14582631C2211yescharacteristic
58#14582628C2211yescharacteristic
59#14582628C2211yescharacteristic
60C43×#431C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×#322C2211yescharacteristic
64C43×#322C2211yescharacteristic
65C43×#322C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C22×Dic86C2×C411yescharacteristic
68C2×Dic172C2×C411yescharacteristic
69C2×Dic172C2×C411yescharacteristic
70C2×#10621873C2×C411yescharacteristic
71C2×#10621873C2×C411yescharacteristic
72C2×#10621877—21no—
73C2×#10621872—21no—
74C2×C8×D43—21no—
75#13063319—21no—
76#13063317C2×C411yescharacteristic
77#13063313C2×C411yescharacteristic
78#13063308—21no—
79#13063304C2×C411yescharacteristic
80#13063299C2×C411yescharacteristic
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86C2×C411yescharacteristic
84C4×Dic86C2×C411yescharacteristic
85C4×Dic86C2311yescharacteristic
86C4×Dic86C2311yescharacteristic
87C4×Dic86C2311yescharacteristic
88C4×D172C2311yescharacteristic
89C4×C22⋊D43—21no—
90#13063282—21no—
91C2×C4⋊Dic43C2×C411yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×C4×Dic43—21no—
94#13063259C2×C411yescharacteristic
95#13063259C2×C411yescharacteristic
96#13063257C2×C411yescharacteristic
97#13063257C2×C411yescharacteristic
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109#13063250C2×C411yescharacteristic
110#13063250C2×C411yescharacteristic
111#13063250C2×C411yescharacteristic
112#13063250C2×C411yescharacteristic
113#13063250C2×C411yescharacteristic
114#13063250C2×C411yescharacteristic
115#13063247C2×C411yescharacteristic
116#13063247C2×C411yescharacteristic
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120#13063235—21no—
121C4×C43⋊C8—21no—
122C8×Dic43—21no—
123C8×Dic43—21no—
124C8×Dic43—21no—
125C8×Dic43—21no—
126C8×Dic43—21no—
127C2×C42×C43C2311yescharacteristic
128C4⋊C8×C43—21no—
129C4⋊C8×C43C2×C411yescharacteristic
130C4⋊C8×C43C2×C411yescharacteristic
131C4⋊C8×C43D411yescharacteristic
132C4⋊C8×C43D411yescharacteristic
133C22⋊C8×C43—21no—
134C22⋊C8×C43C2×C411yescharacteristic
135C22⋊C8×C43C2×C411yescharacteristic
136C22⋊C8×C43D411yescharacteristic
137C22⋊C8×C43D411yescharacteristic
138C4×C8×C43C2311yescharacteristic
139C4×C8×C43C2311yescharacteristic
140C4×C8×C43C2311yescharacteristic
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C2×C22⋊D43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C2×D172C22×C411yescharacteristic
151C2×C4×D43—21no—
152C2×Dic86—21no—
153C2×Dic86—22no—
154C2×Dic86—22no—
155C2×Dic86C22×C411yescharacteristic
156C2×Dic86C22×C411yescharacteristic
157C2×Dic86C22×C411yescharacteristic
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43C22×C411yescharacteristic
161C2×C8×C43C22×C411yescharacteristic
162C2×C8×C43C22×C411yescharacteristic
163C2×C8×C43C22×C411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C42×C43C22×C411yescharacteristic
169C42×C43C2×D411yescharacteristic
170C42×C43#4111yescharacteristic
171C42×C43C2411yescharacteristic
172C22⋊Dic43—21no—
173(C2×D43)⋊C4—21no—
174(C2×D43)⋊C4—21no—
175(C2×D43)⋊C4—21no—
176(C2×D43)⋊C4—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43C22×C411yescharacteristic
179C4⋊Dic43C22×C411yescharacteristic
180C4⋊Dic43C22×C411yescharacteristic
181C4⋊Dic43C22×C411yescharacteristic
182Dic43⋊C4—21no—
183Dic43⋊C4—21no—
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195#10621877—81no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200Dic172—22no—
201Dic172—22no—
202#10621873—22no—
203#10621873—22no—
204#10621872—81no—
205C8×D43—81no—
206C23×C43C4×D411yescharacteristic
207C22×D43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—41no—
213C2×C4×C43C4×D411yescharacteristic
214C2×C4×C43C4×D411yescharacteristic
215C2×C4×C43C4×D411yescharacteristic
216C2×C4×C43C23×C411yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C22⋊D43—81no—
220C2×Dic43—24no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—81no—
229D172—21no—
230D172—21no—
231C4×D43—41no—
232C4×D43—41no—
233Dic86—24no—
234Dic86—21no—
235Dic86—21no—
236Dic86—21no—
237Dic86—21no—
238Dic86#13112yes—
239Dic86#13112yes—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—41no—
249C8×C43—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254#17919—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43C2×C4×D411yescharacteristic
259C2×D43—41no—
260C2×D43—41no—
261C2×D43—41no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43C2×#13111yescharacteristic
267C4×C43C2×#13111yescharacteristic
268C4×C43#57711yescharacteristic
269C4×C43#57811yescharacteristic
270Dic43—22no—
271Dic43—22no—
272Dic43—41no—
273Dic43—41no—
274Dic43—41no—
275Dic43—41no—
276Dic43—41no—
277#3108—431no—
278#2993—431no—
279#2982—431no—
280#1588—431no—
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#1454D4311yescharacteristic, complemented
292C2×C43—41no—
293C2×C43#292911yescharacteristic
294C2×C43#294711yescharacteristic
295C2×C43#295711yescharacteristic
296D43—81no—
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—431no—
313C8×Q8—861no—
314C8×Q8—861no—
315C4×Q16—431no—
316C4×Q16—431no—
317C4×SD16—431no—
318C4×SD16—431no—
319#436—431no—
320#436—861no—
321#435—861no—
322C8×D4—431no—
323#433—861no—
324#431—431no—
325#431—861no—
326#431—861no—
327#431C2×D4311yescharacteristic
328#431C2×D4311yescharacteristic
329#431C2×D4311yescharacteristic
330#424—861no—
331#423—431no—
332#335—431no—
333#335—431no—
334#334—431no—
335#334—431no—
336Q8⋊C8—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341Q8⋊C8—431no—
342D4⋊C8—431no—
343D4⋊C8—431no—
344#322C2×D4311yescharacteristic
345#322C2×D4311yescharacteristic
346#322C2×D4311yescharacteristic
347C82C2×D4311yescharacteristic
348C43#1791911yescharacteristic, complemented, Sylow
349C22×Q8—431no—
350C2×Q16—431no—
351C2×Q16—431no—
352C2×SD16—431no—
353C2×SD16—431no—
354C2×M16—861no—
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—431no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×D4—431no—
371C4×D4—861no—
372#117—861no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—861no—
375C2×C42—861no—
376C2×C42C22×D4311yescharacteristic
377#107—431no—
378#107—431no—
379#106—431no—
380#106—431no—
381C4⋊C8—21no—
382C4⋊C8—431no—
383C4⋊C8—431no—
384C4⋊C8—431no—
385C4⋊C8—431no—
386C4⋊C8—861no—
387C4⋊C8—861no—
388C4⋊C8—861no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8C4×D4311yescharacteristic
394C4⋊C8C4×D4311yescharacteristic
395C4⋊C8D17211yescharacteristic
396C4⋊C8D17211yescharacteristic
397#103—431no—
398#103—431no—
399#103—431no—
400#103—431no—
401#103—431no—
402#103—431no—
403#102—431no—
404#102—431no—
405C22⋊C8—21no—
406C22⋊C8—861no—
407C22⋊C8—861no—
408C22⋊C8—861no—
409C22⋊C8C4×D4311yescharacteristic
410C22⋊C8C4×D4311yescharacteristic
411C22⋊C8D17211yescharacteristic
412C22⋊C8D17211yescharacteristic
413#97—861no—
414C4×C8—861no—
415C4×C8—861no—
416C4×C8—861no—
417C4×C8—861no—
418C4×C8—861no—
419C4×C8—861no—
420C4×C8C22×D4311yescharacteristic
421C4×C8C22×D4311yescharacteristic
422C4×C8C22×D4311yescharacteristic
423C4×C8C22×D4311yescharacteristic
424C4×C8C22×D4311yescharacteristic
425C4×C8C22×D4311yescharacteristic
426C2×Q8—431no—
427C2×Q8—431no—
428C2×Q8—431no—
429C2×Q8—862no—
430C2×Q8—862no—
431C2×Q8—861no—
432C2×D4—431no—
433C2×D4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4C2×C4×D4311yescharacteristic
438C22×C4C2×D17211yescharacteristic
439C22×C4#1062189811yescharacteristic
440Q16—862no—
441Q16—862no—
442SD16—862no—
443SD16—862no—
444M16—3441no—
445M16—3441no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—3441no—
453C2×C8C2×C4×D4311yescharacteristic
454C2×C8C2×C4×D4311yescharacteristic
455C2×C8C2×C4×D4311yescharacteristic
456C2×C8C2×C4×D4311yescharacteristic
457C2×C8C2×D17211yescharacteristic
458C2×C8C2×D17211yescharacteristic
459C2×C8C2×D17211yescharacteristic
460C2×C8C2×D17211yescharacteristic
461C4⋊C4—431no—
462C4⋊C4—431no—
463C4⋊C4—431no—
464C4⋊C4—431no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C22⋊C4—861no—
475C22⋊C4—861no—
476C22⋊C4—861no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C42—861no—
480C42—861no—
481C42—861no—
482C42—861no—
483C42—861no—
484C42C2×C4×D4311yescharacteristic
485C42C2×D17211yescharacteristic
486C42#1062189811yescharacteristic
487C42C23×D4311yescharacteristic
488C23—861no—
489C23C4×D17211yescharacteristic
490Q8—432no—
491Q8—432no—
492Q8—864no—
493Q8—861no—
494Q8—861no—
495Q8—861no—
496Q8—861no—
497D4—861no—
498D4—861no—
499D4—3441no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—864no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—3441no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4C4×D17211yescharacteristic
517C2×C4C4×D17211yescharacteristic
518C2×C4C4×D17211yescharacteristic
519C2×C4C22×C4×D4311yescharacteristic
520C2×C4C22×D17211yescharacteristic
521C2×C4C2×#1062189811yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—41no—
531C8—41no—
532C8—1721no—
533C8—1721no—
534C8—1721no—
535C8—1721no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—1721no—
540C22—1721no—
541C22—1721no—
542C22C2×C4×D17211yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—862no—
548C4—862no—
549C4—1721no—
550C4—1721no—
551C4—1721no—
552C4—1721no—
553C4—1721no—
554C4#131×D4311yescharacteristic
555C4#131×D4311yescharacteristic
556C4#1458371111yescharacteristic
557C4#1458371611yescharacteristic
558C2—41no—
559C2—3441no—
560C2#1914329111yescharacteristic
561C2#1914344011yescharacteristic
562C2#1914351311yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1454C2
socleC22×C43C2×C4×D4
prime radical#13063299C2×C4
cosocleC42×C43C24
hypercenter#1454D43
hypocenterC43#17919
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
3. #19143675C2semidirect
4. #19133475C2semidirect
5. #19133468C2semidirect
6. #19133447C2semidirect
7. #19133440C2semidirect
8. #19133415C2semidirect
9. #19133409C2semidirect
10. C8×Dic172C2semidirect
11. C8×#10621873C2semidirect
12. #19133384C2semidirect
13. #19133025C2semidirect
15. C43×#1454C2semidirect
291. #1454D43semidirect
348. C43#17919semidirect

Maximal subgroups

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

subgroupindex
#191446772
#191437462
#191436752
#191334752
#191334682
#191334472
#191334402
#191334152
#191334092
C8×Dic1722
C8×#106218732
#191333842
#191330252
#191330042
C43×#14542
#1791943