Finite Group Databasebeta

← #25067965

Subgroups — #25067965

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144627C211yesmaximal, characteristic
2#19143682C211yesmaximal, characteristic, complemented
3#19143661C211yesmaximal, characteristic
4#19133499C211yesmaximal, characteristic, complemented
5#19133487C211yesmaximal, characteristic, complemented
6#19133475C211yesmaximal, characteristic, complemented
7#19133454C211yesmaximal, characteristic, complemented
8#19133440C211yesmaximal, characteristic, complemented
9#19133433C211yesmaximal, characteristic, complemented
10#19133409C211yesmaximal, characteristic, complemented
11C8×#10621873C211yesmaximal, characteristic, complemented
12#19133375C211yesmaximal, characteristic, complemented
13#19133065C211yesmaximal, characteristic
14#19132991C211yesmaximal, characteristic, complemented
15C43×#1454C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18#14583218C411yescharacteristic
19#14583218C411yescharacteristic
20#14583185C411yescharacteristic
21#14583185C411yescharacteristic
22#14583100C411yescharacteristic
23#14583100C411yescharacteristic
24#14583040C411yescharacteristic
25#14583040C411yescharacteristic
26#14583029C2211yescharacteristic
27#14583029C2211yescharacteristic
28#14583028—21no—
29#14583028—21no—
30C8×Dic86C2211yescharacteristic
31C8×Dic86C2211yescharacteristic
32C4×#10621873C2211yescharacteristic
33C4×#10621873C2211yescharacteristic
34C4×#10621873C2211yescharacteristic
35C4×#10621873C2211yescharacteristic
36#14582978C2211yescharacteristic
37#14582978C2211yescharacteristic
38#14582976—21no—
39C8×D172C2211yescharacteristic
40C8×D172C2211yescharacteristic
41#14582964—21no—
42#14582956C2211yescharacteristic
43#14582953—21no—
44#14582952C2211yescharacteristic
45#14582949—21no—
46#14582864—21no—
47#14582864—21no—
48#14582652C2211yescharacteristic
49#14582652C2211yescharacteristic
50#14582650C2211yescharacteristic
51#14582650C2211yescharacteristic
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×#10621898—21no—
68C22×Dic86C2×C411yescharacteristic
69C2×#10621873C2×C411yescharacteristic
70C2×#10621873C2×C411yescharacteristic
71C2×#10621873C2×C411yescharacteristic
72C2×#10621873C2×C411yescharacteristic
73C2×#10621872—21no—
74C2×#10621872—21no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77#13063325C2×C411yescharacteristic
78#13063322C2×C411yescharacteristic
79#13063313—21no—
80#13063299—21no—
81#13063299C2×C411yescharacteristic
82#13063299C2×C411yescharacteristic
83C4×Dic86—21no—
84C4×Dic86—21no—
85C4×Dic86C2×C411yescharacteristic
86C4×Dic86C2×C411yescharacteristic
87C4×Dic86C2311yescharacteristic
88C4×Dic86C2311yescharacteristic
89C4×D172—21no—
90C4×D172C2311yescharacteristic
91C4×D172C2311yescharacteristic
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×C4×Dic43—21no—
95#13063257C2×C411yescharacteristic
96#13063257C2×C411yescharacteristic
97#13063257C2×C411yescharacteristic
98#13063257C2×C411yescharacteristic
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—
107#13063250C2×C411yescharacteristic
108#13063250C2×C411yescharacteristic
109#13063250C2×C411yescharacteristic
110#13063250C2×C411yescharacteristic
111#13063247C2×C411yescharacteristic
112#13063247C2×C411yescharacteristic
113#13063247C2×C411yescharacteristic
114#13063247C2×C411yescharacteristic
115C22⋊(C43⋊C8)—21no—
116C22⋊(C43⋊C8)—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063236—21no—
122#13063235—21no—
123#13063235—21no—
124C4×C43⋊C8—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—
149C22×Dic43—21no—
150C22×Dic43—21no—
151#10621898—81no—
152#10621898—81no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172C22×C411yescharacteristic
156C2×D172C22×C411yescharacteristic
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×Dic86—22no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—41no—
163C2×Dic86C22×C411yescharacteristic
164C2×Dic86C22×C411yescharacteristic
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43C22×C411yescharacteristic
168C2×C8×C43C22×C411yescharacteristic
169C2×C8×C43C22×C411yescharacteristic
170C2×C8×C43C22×C411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C42×C43C22×C411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43#4111yescharacteristic
178C42×C43C2411yescharacteristic
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43C22×C411yescharacteristic
186C4⋊Dic43C22×C411yescharacteristic
187C4⋊Dic43C22×C411yescharacteristic
188C4⋊Dic43C22×C411yescharacteristic
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201#10621873—22no—
202#10621873—22no—
203#10621873—41no—
204#10621873—41no—
205#10621872—81no—
206#10621872—81no—
207C8×D43—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—81no—
224C22⋊D43—81no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—42no—
232C2×Dic43—42no—
233D172—21no—
234D172—21no—
235D172—21no—
236D172—21no—
237D172—42no—
238D172—81no—
239C4×D43—41no—
240C4×D43—41no—
241C4×D43—41no—
242C4×D43—41no—
243Dic86—21no—
244Dic86—21no—
245Dic86—21no—
246Dic86—42no—
247Dic86—81no—
248Dic86#13112yes—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—41no—
258C8×C43—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263#18030—431nomaximal, Sylow
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—21no—
267C22×C43C2×C4×D411yescharacteristic
268C2×D43—41no—
269C2×D43—41no—
270C2×D43—41no—
271C2×D43—41no—
272C2×D43—41no—
273C2×D43—41no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43C2×#13111yescharacteristic
279C4×C43#56811yescharacteristic
280C4×C43#57711yescharacteristic
281C4×C43#57711yescharacteristic
282Dic43—22no—
283Dic43—41no—
284Dic43—41no—
285Dic43—41no—
286Dic43—41no—
287Dic43—41no—
288#3103—431no—
289#2984—431no—
290#2979—431no—
291#1592—431no—
292#1590—431no—
293#1588—431no—
294#1585—431no—
295#1583—431no—
296#1582—431no—
297SD16⋊C8—431no—
298C8×SD16—431no—
299#1572—431no—
300#1496—431no—
301#1479—431no—
302#1454D4311yescharacteristic, complemented
303C2×C43—41no—
304C2×C43#293311yescharacteristic
305C2×C43#294911yescharacteristic
306C2×C43#295511yescharacteristic
307D43—81no—
308D43—81no—
309#532—431no—
310C2×C4×Q8—431no—
311#481—431no—
312#481—431no—
313#475—431no—
314#475—431no—
315#460—431no—
316#460—431no—
317#448—431no—
318#448—431no—
319#446—431no—
320#446—431no—
321#446—861no—
322#446—861no—
323C8×Q8—431no—
324C8×Q8—431no—
325C4×SD16—431no—
326C4×SD16—431no—
327C4×SD16—431no—
328C4×SD16—431no—
329#436—431no—
330#436—431no—
331#436—861no—
332C8×D4—431no—
333C8×D4—431no—
334C8×D4—861no—
335#432—431no—
336#432—861no—
337#431—431no—
338#431—861no—
339#431C2×D4311yescharacteristic
340#431C2×D4311yescharacteristic
341#431C2×D4311yescharacteristic
342#408—861no—
343#408—861no—
344#335—431no—
345#335—431no—
346#334—431no—
347#334—431no—
348Q8⋊C8—431no—
349Q8⋊C8—431no—
350Q8⋊C8—431no—
351Q8⋊C8—431no—
352D4⋊C8—431no—
353D4⋊C8—431no—
354D4⋊C8—431no—
355D4⋊C8—431no—
356#322C2×D4311yescharacteristic
357#322C2×D4311yescharacteristic
358#322C2×D4311yescharacteristic
359C82C2×D4311yescharacteristic
360C43#1803011yescharacteristic, complemented, Sylow
361C2×#41—861no—
362C22×Q8—431no—
363C2×SD16—431no—
364C2×SD16—431no—
365C2×SD16—431no—
366C2×SD16—431no—
367C2×M16—861no—
368C2×M16—861no—
369C22×C8—861no—
370C22×C8—861no—
371C4⋊Q8—431no—
372#127—431no—
373#124—861no—
374#121—431no—
375#121—431no—
376#121—861no—
377C4×Q8—431no—
378C4×Q8—431no—
379C4×Q8—431no—
380C4×Q8—431no—
381C4×Q8—861no—
382C4×Q8—861no—
383C4×D4—431no—
384C4×D4—431no—
385C4×D4—861no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—861no—
388C2×C42—861no—
389C2×C42C22×D4311yescharacteristic
390#106—431no—
391#106—431no—
392#106—431no—
393#106—431no—
394C4⋊C8—21no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
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⋊C8—861no—
421C22⋊C8—861no—
422C22⋊C8C4×D4311yescharacteristic
423C22⋊C8C4×D4311yescharacteristic
424C22⋊C8D17211yescharacteristic
425C22⋊C8D17211yescharacteristic
426#97—861no—
427#97—861no—
428#97—861no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8—861no—
432C4×C8C22×D4311yescharacteristic
433C4×C8C22×D4311yescharacteristic
434C4×C8C22×D4311yescharacteristic
435C4×C8C22×D4311yescharacteristic
436C4×C8C22×D4311yescharacteristic
437C4×C8C22×D4311yescharacteristic
438#41—3441no—
439#41—3441no—
440C2×Q8—431no—
441C2×Q8—431no—
442C2×Q8—862no—
443C2×Q8—861no—
444C2×Q8—861no—
445C2×Q8—1721no—
446C2×D4—431no—
447C2×D4—431no—
448C2×D4—861no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4C2×C4×D4311yescharacteristic
457C22×C4C2×D17211yescharacteristic
458C22×C4#1062189811yescharacteristic
459SD16—862no—
460SD16—862no—
461SD16—1721no—
462SD16—1721no—
463M16—3441no—
464M16—3441no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—3441no—
472C2×C8—3441no—
473C2×C8C2×C4×D4311yescharacteristic
474C2×C8C2×C4×D4311yescharacteristic
475C2×C8C2×C4×D4311yescharacteristic
476C2×C8C2×C4×D4311yescharacteristic
477C2×C8C2×D17211yescharacteristic
478C2×C8C2×D17211yescharacteristic
479C2×C8C2×D17211yescharacteristic
480C2×C8C2×D17211yescharacteristic
481C4⋊C4—431no—
482C4⋊C4—431no—
483C4⋊C4—431no—
484C4⋊C4—431no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C22⋊C4—861no—
492C22⋊C4—861no—
493C22⋊C4—861no—
494C22⋊C4—861no—
495C42—861no—
496C42—861no—
497C42—861no—
498C42—861no—
499C42C2×C4×D4311yescharacteristic
500C42C2×D17211yescharacteristic
501C42#1062189811yescharacteristic
502C42C23×D4311yescharacteristic
503C23—861no—
504C23—861no—
505C23C4×D17211yescharacteristic
506Q8—432no—
507Q8—861no—
508Q8—861no—
509Q8—861no—
510Q8—3441no—
511Q8—1722no—
512D4—861no—
513D4—861no—
514D4—861no—
515D4—861no—
516D4—3441no—
517D4—3441no—
518D4—3441no—
519D4—1722no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4C4×D17211yescharacteristic
538C2×C4C4×D17211yescharacteristic
539C2×C4C4×D17211yescharacteristic
540C2×C4C22×C4×D4311yescharacteristic
541C2×C4C22×D17211yescharacteristic
542C2×C4C2×#1062189811yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—1721no—
554C8—1721no—
555C8—1721no—
556C8—1721no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—1721no—
561C22—1721no—
562C22—1721no—
563C22—1721no—
564C22—1721no—
565C22—1721no—
566C22C2×C4×D17211yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—862no—
572C4—1721no—
573C4—1721no—
574C4—1721no—
575C4—1721no—
576C4—1721no—
577C4#131×D4311yescharacteristic
578C4#1458366411yescharacteristic
579C4#1458371111yescharacteristic
580C4#1458371111yescharacteristic
581C2—41no—
582C2—3441no—
583C2—3441no—
584C2#1914332311yescharacteristic
585C2#1914345611yescharacteristic
586C2#1914349911yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1454C2
socleC22×C43C2×C4×D4
prime radical#14583449C22
cosocleC42×C43C24
hypercenter#1454D43
hypocenterC43#18030
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. #19143682C2semidirect
4. #19133499C2semidirect
5. #19133487C2semidirect
6. #19133475C2semidirect
7. #19133454C2semidirect
8. #19133440C2semidirect
9. #19133433C2semidirect
10. #19133409C2semidirect
11. C8×#10621873C2semidirect
12. #19133375C2semidirect
14. #19132991C2semidirect
15. C43×#1454C2semidirect
302. #1454D43semidirect
360. C43#18030semidirect

Maximal subgroups

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

subgroupindex
#191446272
#191436822
#191436612
#191334992
#191334872
#191334752
#191334542
#191334402
#191334332
#191334092
C8×#106218732
#191333752
#191330652
#191329912
C43×#14542
#1803043