Finite Group Databasebeta

← #25068010

Subgroups — #25068010

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144615C211yesmaximal, characteristic
2#19143757C211yesmaximal, characteristic, complemented
3#19143724C211yesmaximal, characteristic, complemented
4#19133499C211yesmaximal, characteristic, complemented
5#19133481C211yesmaximal, characteristic, complemented
6#19133475C211yesmaximal, characteristic, complemented
7#19133475C211yesmaximal, characteristic, complemented
8#19133447C211yesmaximal, characteristic, complemented
9#19133426C211yesmaximal, characteristic, complemented
10#19133409C211yesmaximal, characteristic, complemented
11C8×Dic172C211yesmaximal, characteristic, complemented
12#19133370C211yesmaximal, characteristic, complemented
13#19133061C211yesmaximal, characteristic, complemented
14#19132983C211yesmaximal, characteristic, complemented
15C43×#1454C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17C4×#10621898C2211yescharacteristic
18#14583241C411yescharacteristic
19#14583224C411yescharacteristic
20#14583207C411yescharacteristic
21#14583200C411yescharacteristic
22#14583122C411yescharacteristic
23#14583115C411yescharacteristic
24#14583063C411yescharacteristic
25#14583046C411yescharacteristic
26#14583029C2211yescharacteristic
27C8×Dic86C2211yescharacteristic
28C8×Dic86C2211yescharacteristic
29C8×Dic86C2211yescharacteristic
30C4×Dic172C2211yescharacteristic
31C4×#10621873C2211yescharacteristic
32C4×#10621873C2211yescharacteristic
33C4×D344C2211yescharacteristic
34#14582978C2211yescharacteristic
35#14582978C2211yescharacteristic
36#14582978C2211yescharacteristic
37#14582974—21no—
38#14582974—21no—
39#14582967—21no—
40C8×D172C2211yescharacteristic
41(C22⋊D43)⋊C8—21no—
42#14582959—21no—
43#14582951—21no—
44#14582924—21no—
45#14582923C2211yescharacteristic
46#14582921—21no—
47C2×C4⋊(C43⋊C8)C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582652C2211yescharacteristic
50#14582652C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582631C2211yescharacteristic
54#14582631C2211yescharacteristic
55#14582631C2211yescharacteristic
56#14582628C2211yescharacteristic
57#14582628C2211yescharacteristic
58#14582628C2211yescharacteristic
59#14582628C2211yescharacteristic
60C43×#431C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×#322C2211yescharacteristic
64C43×#322C2211yescharacteristic
65C43×#322C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C2×#10621898C2×C411yescharacteristic
68C2×Dic172C2×C411yescharacteristic
69C2×#10621873C2×C411yescharacteristic
70C2×#10621873C2×C411yescharacteristic
71C2×D344C2×C411yescharacteristic
72C2×#10621877—21no—
73C2×#10621872—21no—
74C2×#10621872—21no—
75C2×#10621872—21no—
76C22×C43⋊C8—21no—
77C2×C8×D43—21no—
78#13063319—21no—
79#13063317C2×C411yescharacteristic
80#13063313C2×C411yescharacteristic
81#13063308—21no—
82#13063304C2×C411yescharacteristic
83#13063299C2×C411yescharacteristic
84C4×Dic86C2×C411yescharacteristic
85C4×Dic86C2311yescharacteristic
86C4×Dic86C2311yescharacteristic
87C4×D172C2×C411yescharacteristic
88C4×D172C2311yescharacteristic
89C4×D172C2311yescharacteristic
90C4×C22⋊D43—21no—
91C4×C22⋊D43—21no—
92C4×C22⋊D43—21no—
93#13063284C2×C411yescharacteristic
94#13063282—21no—
95#13063282—21no—
96C42×D43—21no—
97#13063259C2×C411yescharacteristic
98#13063259C2×C411yescharacteristic
99#13063257C2×C411yescharacteristic
100#13063257C2×C411yescharacteristic
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063250C2×C411yescharacteristic
112#13063250C2×C411yescharacteristic
113#13063250C2×C411yescharacteristic
114#13063250C2×C411yescharacteristic
115#13063247C2×C411yescharacteristic
116#13063247C2×C411yescharacteristic
117#13063247C2×C411yescharacteristic
118#13063247C2×C411yescharacteristic
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123#13063235—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—
148C2×C22⋊D43—21no—
149#10621898—22no—
150#10621898—41no—
151C2×D172C22×C411yescharacteristic
152C2×D172C22×C411yescharacteristic
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×Dic86C22×C411yescharacteristic
158C2×Dic86C22×C411yescharacteristic
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43C22×C411yescharacteristic
162C2×C8×C43C22×C411yescharacteristic
163C2×C8×C43C22×C411yescharacteristic
164C2×C8×C43C22×C411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C42×C43C22×C411yescharacteristic
170C42×C43C2×D411yescharacteristic
171C42×C43#4111yescharacteristic
172C42×C43C2411yescharacteristic
173C22⋊Dic43—21no—
174C22⋊Dic43—21no—
175(C2×D43)⋊C4—21no—
176(C2×D43)⋊C4—21no—
177(C2×D43)⋊C4—21no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181C4⋊Dic43C22×C411yescharacteristic
182C4⋊Dic43C22×C411yescharacteristic
183C4⋊Dic43C22×C411yescharacteristic
184C4⋊Dic43C22×C411yescharacteristic
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—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—
200C2×C43⋊C8—81no—
201Dic172—22no—
202D344—41no—
203#10621873—22no—
204#10621873—41no—
205#10621872—81no—
206#10621872—81no—
207#10621872—81no—
208C8×D43—81no—
209C23×C43C4×D411yescharacteristic
210C22×D43—21no—
211C22×D43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—41no—
217C2×C4×C43C4×D411yescharacteristic
218C2×C4×C43C4×D411yescharacteristic
219C2×C4×C43C4×D411yescharacteristic
220C2×C4×C43C23×C411yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C22⋊D43—42no—
224C22⋊D43—42no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231D172—21no—
232D172—21no—
233D172—21no—
234D172—21no—
235C4×D43—42no—
236C4×D43—42no—
237C4×D43—41no—
238C4×D43—41no—
239C4×D43—41no—
240C4×D43—41no—
241Dic86—21no—
242Dic86—21no—
243Dic86—21no—
244Dic86#13112yes—
245C8×C43—21no—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—41no—
254C8×C43—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259#18033—431nomaximal, Sylow
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43C2×C4×D411yescharacteristic
264C2×D43—41no—
265C2×D43—41no—
266C2×D43—41no—
267C2×D43—41no—
268C2×D43—41no—
269C2×D43—41no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43C2×#13111yescharacteristic
275C4×C43#56811yescharacteristic
276C4×C43#57611yescharacteristic
277C4×C43#57811yescharacteristic
278Dic43—22no—
279Dic43—41no—
280Dic43—41no—
281Dic43—41no—
282Dic43—41no—
283Dic43—41no—
284#3102—431no—
285#2994—431no—
286#2991—431no—
287#1592—431no—
288#1589—431no—
289#1588—431no—
290#1588—431no—
291#1584—431no—
292#1581—431no—
293SD16⋊C8—431no—
294C8×Q16—431no—
295#1571—431no—
296#1495—431no—
297#1477—431no—
298#1454D4311yescharacteristic, complemented
299C2×C43—41no—
300C2×C43#293311yescharacteristic
301C2×C43#295111yescharacteristic
302C2×C43#295511yescharacteristic
303D43—81no—
304D43—81no—
305#529—431no—
306C4×#41—431no—
307#485—431no—
308#482—431no—
309#479—431no—
310#478—431no—
311#464—431no—
312#463—431no—
313#452—431no—
314#449—431no—
315#446—431no—
316C8×Q8—431no—
317C8×Q8—431no—
318C8×Q8—431no—
319C4×Q16—431no—
320C4×SD16—431no—
321C4×SD16—431no—
322C4×D8—431no—
323#436—431no—
324#436—431no—
325#436—431no—
326#436—861no—
327#436—861no—
328#435—861no—
329C8×D4—431no—
330C8×D4—861no—
331#433—861no—
332#431—861no—
333#431C2×D4311yescharacteristic
334#431C2×D4311yescharacteristic
335#431C2×D4311yescharacteristic
336#424—861no—
337#423—431no—
338#423—861no—
339C2×C4⋊C8—431no—
340#335—431no—
341#335—431no—
342#335—431no—
343#335—431no—
344Q8⋊C8—431no—
345Q8⋊C8—431no—
346Q8⋊C8—431no—
347Q8⋊C8—431no—
348D4⋊C8—431no—
349D4⋊C8—431no—
350D4⋊C8—431no—
351D4⋊C8—431no—
352#322C2×D4311yescharacteristic
353#322C2×D4311yescharacteristic
354#322C2×D4311yescharacteristic
355C82C2×D4311yescharacteristic
356C43#1803311yescharacteristic, complemented, Sylow
357C2×#41—431no—
358C2×Q16—431no—
359C2×SD16—431no—
360C2×SD16—431no—
361C2×D8—431no—
362C2×M16—861no—
363C2×M16—861no—
364C2×M16—861no—
365C2×M16—861no—
366C22×C8—861no—
367C22×C8—861no—
368#126—861no—
369#125—431no—
370#124—431no—
371#123—861no—
372C22⋊Q8—431no—
373#121—431no—
374C4×Q8—431no—
375C4×Q8—431no—
376C4×Q8—431no—
377C4×D4—431no—
378C4×D4—431no—
379C4×D4—431no—
380C4×D4—861no—
381C4×D4—861no—
382C4×D4—861no—
383#117—431no—
384#117—861no—
385#117—861no—
386C2×C42—861no—
387C2×C42C22×D4311yescharacteristic
388#107—431no—
389#107—431no—
390#106—431no—
391#106—431no—
392C4⋊C8—21no—
393C4⋊C8—431no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8C4×D4311yescharacteristic
404C4⋊C8C4×D4311yescharacteristic
405C4⋊C8D17211yescharacteristic
406C4⋊C8D17211yescharacteristic
407#103—431no—
408#103—431no—
409#103—431no—
410#103—431no—
411#102—431no—
412#102—431no—
413#102—431no—
414#102—431no—
415C22⋊C8—21no—
416C22⋊C8—861no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419C22⋊C8—861no—
420C22⋊C8C4×D4311yescharacteristic
421C22⋊C8C4×D4311yescharacteristic
422C22⋊C8D17211yescharacteristic
423C22⋊C8D17211yescharacteristic
424#97—861no—
425C4×C8—861no—
426C4×C8—861no—
427C4×C8—861no—
428C4×C8C22×D4311yescharacteristic
429C4×C8C22×D4311yescharacteristic
430C4×C8C22×D4311yescharacteristic
431C4×C8C22×D4311yescharacteristic
432C4×C8C22×D4311yescharacteristic
433C4×C8C22×D4311yescharacteristic
434#41—862no—
435#41—1721no—
436C2×Q8—431no—
437C2×Q8—431no—
438C2×D4—431no—
439C2×D4—431no—
440C2×D4—861no—
441C2×D4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4C2×C4×D4311yescharacteristic
447C22×C4C2×D17211yescharacteristic
448C22×C4#1062189811yescharacteristic
449Q16—862no—
450SD16—862no—
451SD16—1721no—
452D8—1721no—
453M16—3441no—
454M16—3441no—
455M16—3441no—
456M16—3441no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—3441no—
464C2×C8—3441no—
465C2×C8C2×C4×D4311yescharacteristic
466C2×C8C2×C4×D4311yescharacteristic
467C2×C8C2×C4×D4311yescharacteristic
468C2×C8C2×C4×D4311yescharacteristic
469C2×C8C2×D17211yescharacteristic
470C2×C8C2×D17211yescharacteristic
471C2×C8C2×D17211yescharacteristic
472C2×C8C2×D17211yescharacteristic
473C4⋊C4—431no—
474C4⋊C4—431no—
475C4⋊C4—431no—
476C4⋊C4—431no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—861no—
485C22⋊C4—861no—
486C22⋊C4—861no—
487C22⋊C4—861no—
488C22⋊C4—861no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C42—861no—
492C42—861no—
493C42—861no—
494C42—861no—
495C42C2×C4×D4311yescharacteristic
496C42C2×D17211yescharacteristic
497C42#1062189811yescharacteristic
498C42C23×D4311yescharacteristic
499C23—861no—
500C23—861no—
501C23C4×D17211yescharacteristic
502Q8—432no—
503Q8—861no—
504Q8—861no—
505Q8—861no—
506D4—861no—
507D4—861no—
508D4—861no—
509D4—861no—
510D4—1722no—
511D4—1722no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—1722no—
524C2×C4—1722no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4C4×D17211yescharacteristic
530C2×C4C4×D17211yescharacteristic
531C2×C4C4×D17211yescharacteristic
532C2×C4C22×C4×D4311yescharacteristic
533C2×C4C22×D17211yescharacteristic
534C2×C4C2×#1062189811yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—41no—
544C8—41no—
545C8—1721no—
546C8—1721no—
547C8—1721no—
548C8—1721no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—1721no—
553C22—1721no—
554C22—1721no—
555C22—1721no—
556C22—1721no—
557C22—1721no—
558C22C2×C4×D17211yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—862no—
564C4—1721no—
565C4—1721no—
566C4—1721no—
567C4—1721no—
568C4—1721no—
569C4#131×D4311yescharacteristic
570C4#1458366411yescharacteristic
571C4#1458370411yescharacteristic
572C4#1458371611yescharacteristic
573C2—41no—
574C2—3441no—
575C2—3441no—
576C2#1914332311yescharacteristic
577C2#1914347211yescharacteristic
578C2#1914349911yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1454C2
socleC22×C43C2×C4×D4
prime radical#14583046C4
cosocleC42×C43C24
hypercenter#1454D43
hypocenterC43#18033
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
2. #19143757C2semidirect
3. #19143724C2semidirect
4. #19133499C2semidirect
5. #19133481C2semidirect
6. #19133475C2semidirect
7. #19133475C2semidirect
8. #19133447C2semidirect
9. #19133426C2semidirect
10. #19133409C2semidirect
11. C8×Dic172C2semidirect
12. #19133370C2semidirect
13. #19133061C2semidirect
14. #19132983C2semidirect
15. C43×#1454C2semidirect
298. #1454D43semidirect
356. C43#18033semidirect

Maximal subgroups

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

subgroupindex
#191446152
#191437572
#191437242
#191334992
#191334812
#191334752
#191334472
#191334262
#191334092
C8×Dic1722
#191333702
#191330612
#191329832
C43×#14542
#1803343