Finite Group Databasebeta

← #25082111

Subgroups — #25082111

Order 11008.

594 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145756C211yesmaximal, characteristic, complemented
2#19144758C211yesmaximal, characteristic
3#19144667C211yesmaximal, characteristic
4#19143703C211yesmaximal, characteristic
5#19134054C211yesmaximal, characteristic, complemented
6#19134047C211yesmaximal, characteristic, complemented
7#19134026C211yesmaximal, characteristic, complemented
8#19134019C211yesmaximal, characteristic, complemented
9#19133990C211yesmaximal, characteristic, complemented
10#19133985C211yesmaximal, characteristic, complemented
11#19133978C211yesmaximal, characteristic, complemented
12#19133971C211yesmaximal, characteristic, complemented
13#19133296C211yesmaximal, characteristic, complemented
14#19133250C211yesmaximal, characteristic, complemented
15C43×#1572C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583456C2211yescharacteristic
18C4×#10621898C2211yescharacteristic
19#14583304C2211yescharacteristic
20#14583297C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583250C2211yescharacteristic
23#14583241—21no—
24#14583241—21no—
25#14583241—21no—
26#14583241—21no—
27#14583207—21no—
28#14583207—21no—
29#14583195C2211yescharacteristic
30#14583190C2211yescharacteristic
31#14583185C2211yescharacteristic
32#14583180C2211yescharacteristic
33#14583110C2211yescharacteristic
34#14583110C2211yescharacteristic
35#14583105C2211yescharacteristic
36#14583105C2211yescharacteristic
37#14583063—21no—
38#14583063—21no—
39C8×Dic86C2211yescharacteristic
40C8×Dic86C2211yescharacteristic
41#14583007—21no—
42#14583001—21no—
43C4×Dic172—21no—
44C4×#10621873—21no—
45C8×D172C2211yescharacteristic
46C8×D172C2211yescharacteristic
47(C22⋊D43)⋊C8—21no—
48(C22⋊D43)⋊C8—21no—
49#14582951—21no—
50C2×C4⋊(C43⋊C8)C2211yescharacteristic
51C4⋊C8×D43—21no—
52#14582647C2211yescharacteristic
53#14582647C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#432C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68C2×Dic172—21no—
69C2×Dic172—21no—
70C2×#10621873—21no—
71C2×#10621873—21no—
72C22×C43⋊C8—21no—
73C2×C8×D43—21no—
74C2×C8×D43—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063317—21no—
80#13063317—21no—
81#13063304—21no—
82#13063304—21no—
83#13063304—21no—
84#13063304—21no—
85C4×Dic86—21no—
86C4×Dic86—21no—
87C4×Dic86—21no—
88C4×Dic86—21no—
89C4×Dic86D411yescharacteristic
90C4×Dic86C2311yescharacteristic
91C4×D172D411yescharacteristic
92C4×D172C2311yescharacteristic
93C4×C22⋊D43—21no—
94C4×C22⋊D43—21no—
95#13063284—21no—
96#13063284—21no—
97#13063284D411yescharacteristic
98#13063282—21no—
99C42×D43—21no—
100#13063259—21no—
101#13063259—21no—
102#13063259—21no—
103#13063259—21no—
104#13063257—21no—
105#13063257—21no—
106#13063257—21no—
107#13063257—21no—
108C4⋊(C43⋊C8)—21no—
109C4⋊(C43⋊C8)C2311yescharacteristic
110C4⋊(C43⋊C8)C2311yescharacteristic
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113#13063250—21no—
114#13063250—21no—
115#13063250—21no—
116#13063250—21no—
117#13063250—21no—
118#13063250—21no—
119#13063250—21no—
120#13063250—21no—
121#13063250—21no—
122#13063250—21no—
123#13063247—21no—
124#13063247—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43D411yescharacteristic
131C4⋊C8×C43D411yescharacteristic
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C2×C22⋊D43—21no—
148#10621898—22no—
149#10621898—22no—
150C2×D172C2×D411yescharacteristic
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86C2×D411yescharacteristic
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C42×C43C2×D411yescharacteristic
168C42×C43C2×D411yescharacteristic
169C42×C43#4111yescharacteristic
170C42×C43C2411yescharacteristic
171C22⋊Dic43—21no—
172C22⋊Dic43—41no—
173C22⋊Dic43—41no—
174(C2×D43)⋊C4—21no—
175(C2×D43)⋊C4—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43C2×D411yescharacteristic
185C4⋊Dic43C2×D411yescharacteristic
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—41no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—41no—
196C4×Dic43—41no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—81no—
200Dic172—42no—
201Dic172—42no—
202#10621873—42no—
203#10621873—42no—
204C8×D43—81no—
205C8×D43—81no—
206C23×C43#12111yescharacteristic
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×C43#12111yescharacteristic
214C2×C4×C43#12111yescharacteristic
215C2×C4×C43#12111yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C22⋊D43—24no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227D172—21no—
228D172#13512yes—
229C4×D43—24no—
230C4×D43—41no—
231C4×D43—41no—
232C4×D43—81no—
233Dic86—21no—
234Dic86—41no—
235Dic86—41no—
236Dic86—41no—
237Dic86—41no—
238Dic86—41no—
239Dic86—41no—
240Dic86—81no—
241Dic86#13512yes—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252#19418—431nomaximal, Sylow
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43C2×#12111yescharacteristic
257C2×D43—22no—
258C2×D43—41no—
259C2×D43—41no—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43C2×#13511yescharacteristic
265C4×C43C2×#13511yescharacteristic
266C4×C43#57711yescharacteristic
267C4×C43#57811yescharacteristic
268Dic43—22no—
269Dic43—41no—
270Dic43—41no—
271Dic43—81no—
272Dic43—81no—
273Dic43—81no—
274Dic43—81no—
275#3231—431no—
276#3116—431no—
277#3107—431no—
278#2988—431no—
279#1684—431no—
280#1683—431no—
281#1680—431no—
282#1679—431no—
283#1674—431no—
284#1673—431no—
285#1672—431no—
286#1671—431no—
287#1572D4311yescharacteristic, complemented
288#1552—431no—
289#1542—431no—
290C2×C43—41no—
291C2×C43#304611yescharacteristic
292C2×C43#305011yescharacteristic
293C2×C43#306911yescharacteristic
294D43—42no—
295#533—431no—
296#533—431no—
297C4×#41—431no—
298#500—431no—
299#498—431no—
300#487—431no—
301#487—431no—
302#485—861no—
303#485—861no—
304#485—861no—
305#485—861no—
306#479—861no—
307#479—861no—
308#477—431no—
309#476—431no—
310#475—431no—
311#474—431no—
312#462—431no—
313#462—431no—
314#461—431no—
315#461—431no—
316#452—861no—
317#452—861no—
318C8×Q8—431no—
319C8×Q8—431no—
320#441—861no—
321#440—861no—
322C4×Q16—861no—
323C4×SD16—861no—
324C8×D4—431no—
325C8×D4—431no—
326C8×D4—861no—
327C8×D4—861no—
328#432C2×D4311yescharacteristic
329#431—861no—
330#431C2×D4311yescharacteristic
331#431C2×D4311yescharacteristic
332C2×C4⋊C8—431no—
333C2×C4⋊C8—861no—
334#335C2×D4311yescharacteristic
335#335C2×D4311yescharacteristic
336#334C2×D4311yescharacteristic
337#334C2×D4311yescharacteristic
338#333—431no—
339#333—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346C43#1941811yescharacteristic, complemented, Sylow
347C2×#41—431no—
348C2×Q16—861no—
349C2×Q16—861no—
350C2×SD16—861no—
351C2×SD16—861no—
352C22×C8—861no—
353C22×C8—861no—
354C22×C8—861no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
358C4⋊Q8—431no—
359#125—861no—
360#125—861no—
361C22⋊Q8—861no—
362C22⋊Q8—861no—
363C22⋊Q8—861no—
364C22⋊Q8—861no—
365C4×Q8—431no—
366C4×Q8—431no—
367C4×Q8—861no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×Q8—861no—
371C4×D4—431no—
372C4×D4—431no—
373C4×D4—861no—
374C4×D4—861no—
375#117—431no—
376#117—861no—
377#117—861no—
378#117—861no—
379C2×C42—861no—
380C2×C42C22×D4311yescharacteristic
381#107—861no—
382#107—861no—
383#107—861no—
384#107—861no—
385#106—861no—
386#106—861no—
387#106—861no—
388#106—861no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8D17211yescharacteristic
395C4⋊C8D17211yescharacteristic
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398C4⋊C8C22×D4311yescharacteristic
399C4⋊C8C22×D4311yescharacteristic
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#102—861no—
411#102—861no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416C22⋊C8D17211yescharacteristic
417C22⋊C8D17211yescharacteristic
418#97—21no—
419C4×C8—21no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8C22×D4311yescharacteristic
423C4×C8C22×D4311yescharacteristic
424#41—862no—
425#41—862no—
426C2×Q8—431no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×D4—431no—
432C2×D4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4C2×D17211yescharacteristic
437C22×C4D4×D4311yescharacteristic
438C22×C4#1062190211yescharacteristic
439Q16—1722no—
440Q16—1722no—
441SD16—1722no—
442SD16—1722no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—3441no—
450C2×C8—3441no—
451C2×C8—3441no—
452C2×C8C2×D17211yescharacteristic
453C2×C8C2×D17211yescharacteristic
454C2×C8C2×D17211yescharacteristic
455C2×C8C2×D17211yescharacteristic
456C4⋊C4—431no—
457C4⋊C4—431no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—1721no—
469C4⋊C4—1721no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C22⋊C4—861no—
473C22⋊C4—861no—
474C22⋊C4—861no—
475C22⋊C4—1721no—
476C22⋊C4—1721no—
477C42—861no—
478C42—861no—
479C42—861no—
480C42—1721no—
481C42—1721no—
482C42C2×D17211yescharacteristic
483C42D4×D4311yescharacteristic
484C42#1062190211yescharacteristic
485C42C23×D4311yescharacteristic
486C23—861no—
487C23#1306330011yescharacteristic
488Q8—432no—
489Q8—861no—
490Q8—3441no—
491Q8—1721no—
492Q8—1721no—
493Q8—1721no—
494Q8—1721no—
495Q8—1721no—
496Q8—1721no—
497D4—432no—
498D4—864no—
499D4—861no—
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—3441no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4#1306330011yescharacteristic
517C2×C4#1306330011yescharacteristic
518C2×C4#1306330011yescharacteristic
519C2×C4C2×D4×D4311yescharacteristic
520C2×C4C22×D17211yescharacteristic
521C2×C4C2×#1062190211yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—1721no—
531C8—1721no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—862no—
536C22—1721no—
537C22—1721no—
538C22C2×#1306330011yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—862no—
544C4—3441no—
545C4—3441no—
546C4—3441no—
547C4—3441no—
548C4—1721no—
549C4—1721no—
550C4#135×D4311yescharacteristic
551C4#135×D4311yescharacteristic
552C4#1458371111yescharacteristic
553C4#1458371611yescharacteristic
554C2—41no—
555C2—1722no—
556C2#1914414711yescharacteristic
557C2#1914417711yescharacteristic
558C2#1914433311yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1572C2
socleC22×C43C2×#121
prime radicalC2×#10621898D4
hypercenter#1572D43
hypocenterC43#19418
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
1. #19145756C2semidirect
5. #19134054C2semidirect
6. #19134047C2semidirect
7. #19134026C2semidirect
8. #19134019C2semidirect
9. #19133990C2semidirect
10. #19133985C2semidirect
11. #19133978C2semidirect
12. #19133971C2semidirect
13. #19133296C2semidirect
14. #19133250C2semidirect
15. C43×#1572C2semidirect
287. #1572D43semidirect
346. C43#19418semidirect

Maximal subgroups

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

subgroupindex
#191457562
#191447582
#191446672
#191437032
#191340542
#191340472
#191340262
#191340192
#191339902
#191339852
#191339782
#191339712
#191332962
#191332502
C43×#15722
#1941843