Finite Group Databasebeta

← #25067959

Subgroups — #25067959

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#19143685C211yesmaximal, characteristic, complemented
3#19143661C211yesmaximal, characteristic
4#19133496C211yesmaximal, characteristic, complemented
5#19133484C211yesmaximal, characteristic, complemented
6#19133472C211yesmaximal, characteristic, complemented
7#19133451C211yesmaximal, characteristic, complemented
8#19133437C211yesmaximal, characteristic, complemented
9#19133430C211yesmaximal, characteristic, complemented
10#19133406C211yesmaximal, characteristic, complemented
11#19133394C211yesmaximal, characteristic, complemented
12#19133063C211yesmaximal, characteristic
13#19132989C211yesmaximal, characteristic, complemented
14#19132895C211yesmaximal, characteristic, complemented
15C43×#1572C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18#14583218C411yescharacteristic
19#14583218C411yescharacteristic
20#14583185C411yescharacteristic
21#14583185C411yescharacteristic
22#14583100C411yescharacteristic
23#14583100C411yescharacteristic
24#14583040C411yescharacteristic
25#14583040C411yescharacteristic
26#14583027—21no—
27#14583027—21no—
28#14583026C2211yescharacteristic
29#14583026C2211yescharacteristic
30#14583023C2211yescharacteristic
31#14583023C2211yescharacteristic
32C4×#10621873C2211yescharacteristic
33C4×#10621873C2211yescharacteristic
34C4×#10621873C2211yescharacteristic
35C4×#10621873C2211yescharacteristic
36#14582978—21no—
37#14582976C2211yescharacteristic
38#14582976C2211yescharacteristic
39C8×D172—21no—
40#14582964C2211yescharacteristic
41#14582964C2211yescharacteristic
42#14582953—21no—
43#14582952C2211yescharacteristic
44#14582952C2211yescharacteristic
45#14582949—21no—
46#14582864—21no—
47#14582864—21no—
48#14582629C2211yescharacteristic
49#14582629C2211yescharacteristic
50#14582629C2211yescharacteristic
51#14582629C2211yescharacteristic
52#14582626C2211yescharacteristic
53#14582626C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582626C2211yescharacteristic
56#14582621C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#432C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
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)—21no—
100C4⋊(C43⋊C8)D411yescharacteristic
101C4⋊(C43⋊C8)D411yescharacteristic
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106#13063250C2×C411yescharacteristic
107#13063250C2×C411yescharacteristic
108#13063250C2×C411yescharacteristic
109#13063250C2×C411yescharacteristic
110#13063247C2×C411yescharacteristic
111#13063247C2×C411yescharacteristic
112#13063247C2×C411yescharacteristic
113#13063247C2×C411yescharacteristic
114C22⋊(C43⋊C8)—21no—
115C22⋊(C43⋊C8)D411yescharacteristic
116C22⋊(C43⋊C8)D411yescharacteristic
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063235—21no—
122#13063235—21no—
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43C2×C411yescharacteristic
131C4⋊C8×C43C2×C411yescharacteristic
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43C2×C411yescharacteristic
139C22⋊C8×C43C2×C411yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
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×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C22×C411yescharacteristic
170C2×C8×C43C22×C411yescharacteristic
171C2×C8×C43C22×C411yescharacteristic
172C2×C8×C43C22×C411yescharacteristic
173C42×C43C22×C411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43#4111yescharacteristic
176C42×C43C2411yescharacteristic
177(C2×D43)⋊C4—21no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43C22×C411yescharacteristic
184C4⋊Dic43C22×C411yescharacteristic
185C4⋊Dic43C22×C411yescharacteristic
186C4⋊Dic43C22×C411yescharacteristic
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8C2×D411yescharacteristic
198C2×C43⋊C8C2×D411yescharacteristic
199C2×C43⋊C8C2×D411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
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—41no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43—41no—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—21no—
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#1572D4311yescharacteristic, complemented
300#1496—431no—
301#1479—431no—
302#1454—431no—
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—861no—
336#432C2×D4311yescharacteristic
337#431—431no—
338#431—431no—
339#431—861no—
340#431C2×D4311yescharacteristic
341#431C2×D4311yescharacteristic
342#408—861no—
343#408—861no—
344#335C2×D4311yescharacteristic
345#335C2×D4311yescharacteristic
346#334C2×D4311yescharacteristic
347#334C2×D4311yescharacteristic
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#322—431no—
357#322—431no—
358#322—431no—
359C82—431no—
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—431no—
395C4⋊C8—431no—
396C4⋊C8—861no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8C4×D4311yescharacteristic
402C4⋊C8C4×D4311yescharacteristic
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
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—21no—
417C22⋊C8—431no—
418C22⋊C8—431no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424C22⋊C8C4×D4311yescharacteristic
425C22⋊C8C4×D4311yescharacteristic
426#97—21no—
427#97—861no—
428#97—861no—
429C4×C8—21no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—431no—
433C4×C8—431no—
434C4×C8—861no—
435C4×C8—861no—
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×C4D4×D4311yescharacteristic
458C22×C4#1062190211yescharacteristic
459SD16—862no—
460SD16—862no—
461SD16—1721no—
462SD16—1721no—
463M16—3441no—
464M16—3441no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—431no—
470C2×C8—431no—
471C2×C8—431no—
472C2×C8—431no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—3441no—
476C2×C8—3441no—
477C2×C8C2×C4×D4311yescharacteristic
478C2×C8C2×C4×D4311yescharacteristic
479C2×C8C2×C4×D4311yescharacteristic
480C2×C8C2×C4×D4311yescharacteristic
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
500C42D4×D4311yescharacteristic
501C42#1062190211yescharacteristic
502C42C23×D4311yescharacteristic
503C23—861no—
504C23—861no—
505C23#1306328711yescharacteristic
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×C4#1306328711yescharacteristic
538C2×C4#1306328711yescharacteristic
539C2×C4#1306328711yescharacteristic
540C2×C4C22×C4×D4311yescharacteristic
541C2×C4C2×D4×D4311yescharacteristic
542C2×C4C2×#1062190211yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—861no—
552C8—861no—
553C8—861no—
554C8—861no—
555C8—1721no—
556C8—1721no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—1721no—
561C22—1721no—
562C22—1721no—
563C22—1721no—
564C22—1721no—
565C22—1721no—
566C22C2×#1306328711yescharacteristic
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#1458370611yescharacteristic
580C4#1458370611yescharacteristic
581C2—41no—
582C2—3441no—
583C2—3441no—
584C2#1914331911yescharacteristic
585C2#1914345311yescharacteristic
586C2#1914349711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1572C2
socleC22×C43C2×C4×D4
prime radical#14583449C22
cosocleC42×C43C24
hypercenter#1572D43
hypocenterC43#18030
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
2. #19143685C2semidirect
4. #19133496C2semidirect
5. #19133484C2semidirect
6. #19133472C2semidirect
7. #19133451C2semidirect
8. #19133437C2semidirect
9. #19133430C2semidirect
10. #19133406C2semidirect
11. #19133394C2semidirect
13. #19132989C2semidirect
14. #19132895C2semidirect
15. C43×#1572C2semidirect
299. #1572D43semidirect
360. C43#18030semidirect

Maximal subgroups

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

subgroupindex
#191446272
#191436852
#191436612
#191334962
#191334842
#191334722
#191334512
#191334372
#191334302
#191334062
#191333942
#191330632
#191329892
#191328952
C43×#15722
#1803043