Finite Group Databasebeta

← #25064872

Subgroups — #25064872

Order 11008.

872 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148419C211yesmaximal, characteristic
2#19143613C211yesmaximal, characteristic
3#19143612C211yesmaximal, characteristic
4#19133232C211yesmaximal, characteristic, complemented
5#19133231C212yesmaximal, complemented
6#19133197C211yesmaximal, characteristic, complemented
7#19133195C212yesmaximal, complemented
8#19133195C212yesmaximal, complemented
9#19133189C211yesmaximal, characteristic, complemented
10#19133188C212yesmaximal, complemented
11C43×#1528C211yesmaximal, characteristic, complemented
12#14583626—21no—
13#14583626—21no—
14#14583605—21no—
15#14583605—21no—
16#14583604—22no—
17#14583604—22no—
18#14583530C411yescharacteristic
19#14583530C411yescharacteristic
20#14583529C412yes—
21#14583529C412yes—
22#14583456C2211yescharacteristic
23#14583455C2212yes—
24#125×D43C2212yes—
25#14583380C411yescharacteristic
26#14583380C411yescharacteristic
27C4×#10621898C2211yescharacteristic
28C8×Dic86—21no—
29#14583023—21no—
30#14582978—21no—
31#14582976—21no—
32#14582975—22no—
33#14582974—22no—
34#14582956C2211yescharacteristic
35#14582954C2212yes—
36#14582954C2212yes—
37C4×#10621877C2211yescharacteristic
38#14582851C2212yes—
39#14582851C2212yes—
40#14582641C2212yes—
41#14582641C2212yes—
42#14582640C2211yescharacteristic
43#14582640C2212yes—
44#14582640C2211yescharacteristic
45#14582640C2211yescharacteristic
46#14582640C2211yescharacteristic
47#14582640C2212yes—
48C2×#125×C43C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C4×M16×C43C2211yescharacteristic
51C43×#330C2212yes—
52C43×#330C2212yes—
53C2×#10621898C2×C411yescharacteristic
54C2×#10621877—21no—
55C2×#10621872—22no—
56C2×#10621872—22no—
57#13063325C2×C411yescharacteristic
58#13063325C2×C411yescharacteristic
59#13063324—21no—
60#13063324—21no—
61#13063324—22no—
62#13063324—22no—
63#13063324C2×C412yes—
64#13063324C2×C412yes—
65#13063317C2311yescharacteristic
66#13063317C2311yescharacteristic
67#13063316—21no—
68#13063316—21no—
69#13063316C2×C412yes—
70#13063316C2×C412yes—
71#13063315—22no—
72#13063315—22no—
73#13063315—22no—
74#13063315—22no—
75#13063305—22no—
76#13063305—22no—
77#13063304—21no—
78#13063304—21no—
79#13063304—22no—
80#13063304—22no—
81#13063303—22no—
82#13063303—22no—
83#13063303—22no—
84#13063303—22no—
85C4×Dic86—21no—
86C4×Dic86—21no—
87C4×Dic86D411yescharacteristic
88C4×Dic86D411yescharacteristic
89#13063290—21no—
90#13063290—21no—
91#13063290—22no—
92#13063290—22no—
93C4×D172D411yescharacteristic
94C4×D172D411yescharacteristic
95#13063287—21no—
96#13063287—21no—
97C4×C22⋊D43—22no—
98C4×C22⋊D43—22no—
99C4×C22⋊D43D412yes—
100C4×C22⋊D43D412yes—
101#13063284C2×C411yescharacteristic
102#13063284C2×C411yescharacteristic
103#13063284C2×C411yescharacteristic
104#13063283C2×C412yes—
105#13063283C2×C412yes—
106#13063282C2×C412yes—
107C4⋊C4×D43—22no—
108C4⋊C4×D43—22no—
109C4⋊C4×D43C2×C412yes—
110C4⋊C4×D43C2×C412yes—
111C42×D43C2312yes—
112C4⋊(C43⋊C8)—21no—
113Dic43⋊C8—22no—
114Dic43⋊C8—22no—
115C22⋊(C43⋊C8)—21no—
116(C2×D43)⋊C8—22no—
117(C2×D43)⋊C8—22no—
118#13063236C2311yescharacteristic
119#13063236C2312yes—
120#13063236C2311yescharacteristic
121C4×C43⋊C8—21no—
122C8×Dic43—22no—
123C8×Dic43—22no—
124C2×M16×C43—21no—
125#125×C43—21no—
126#125×C43—21no—
127#125×C43C2×C412yes—
128#125×C43C2312yes—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43C2×C411yescharacteristic
132C2×C4⋊C4×C43C2×C411yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136#97×C43C2311yescharacteristic
137#97×C43C2312yes—
138#97×C43C2311yescharacteristic
139C4×C8×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C22×C411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C2×C22⋊D43C22⋊C412yes—
146#10621898—24no—
147C2×D172C22⋊C411yescharacteristic
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43C22×C412yes—
151C2×C4×D43C2×D412yes—
152C2×C4×D43C2×D412yes—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—22no—
156C2×Dic86—22no—
157C2×Dic86C22⋊C411yescharacteristic
158M16×C43—42no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—22no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43C22×C412yes—
169C4⋊C4×C43C22×C412yes—
170C42×C43C22×C411yescharacteristic
171C42×C43C2×D411yescharacteristic
172C42×C43C2×D411yescharacteristic
173C42×C43C2411yescharacteristic
174C22⋊Dic43—21no—
175C22⋊Dic43—21no—
176C22⋊Dic43C22⋊C412yes—
177(C2×D43)⋊C4—22no—
178(C2×D43)⋊C4—22no—
179(C2×D43)⋊C4C22⋊C412yes—
180(C2×D43)⋊C4C22⋊C412yes—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—22no—
184C4⋊Dic43—22no—
185C4⋊Dic43C22⋊C411yescharacteristic
186C4⋊Dic43C22⋊C411yescharacteristic
187C4⋊Dic43C22×C411yescharacteristic
188C4⋊Dic43C22×C411yescharacteristic
189C4⋊Dic43C22×C411yescharacteristic
190C4⋊Dic43C22×C411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—22no—
196Dic43⋊C4—22no—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4C22⋊C412yes—
202Dic43⋊C4C22⋊C412yes—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—22no—
206C4×Dic43—22no—
207C4×Dic43C22×C412yes—
208C4×Dic43C2×D412yes—
209C4×Dic43C2×D412yes—
210#10621877—42no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—22no—
213C2×C43⋊C8—21no—
214#10621872—44no—
215#10621872—44no—
216C23×C43C2×C22⋊C411yescharacteristic
217C22×D43C2×C22⋊C412yes—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—81no—
224C2×C4×C43—81no—
225C2×C4×C43C2×C22⋊C411yescharacteristic
226C2×C4×C43C2×C22⋊C411yescharacteristic
227C2×C4×C43C2×C22⋊C411yescharacteristic
228C2×C4×C43C23×C411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C22⋊D43—24no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43C2×C22⋊C412yes—
237C2×Dic43C2×C22⋊C412yes—
238C2×Dic43C2×C22⋊C412yes—
239D172—22no—
240C4×D43—24no—
241C4×D43—42no—
242C4×D43—42no—
243C4×D43—82no—
244C4×D43—82no—
245Dic86—82no—
246Dic86—82no—
247Dic86—81no—
248Dic86—81no—
249Dic86#10114yes—
250C8×C43—22no—
251C8×C43—42no—
252C8×C43—41no—
253C43⋊C8—22no—
254C43⋊C8—42no—
255C43⋊C8—41no—
256#17692—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43C22×C22⋊C411yescharacteristic
261C2×D43—22no—
262C2×D43—22no—
263C2×D43—22no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—42no—
270C4×C43—42no—
271C4×C43C2×#10112yes—
272Dic43—22no—
273Dic43—22no—
274Dic43—41no—
275Dic43—41no—
276Dic43—41no—
277Dic43—41no—
278Dic43C2×#10114yes—
279#3504—431no—
280#2971—431no—
281#2971—431no—
282#1537—431no—
283#1537—432no—
284#1528—432no—
285#1528—432no—
286#1528—431no—
287#1528D4311yescharacteristic, complemented
288#1526—431no—
289#1526—432no—
290C2×C43—41no—
291C2×C43C22×#10111yescharacteristic
292C2×C43#290111yescharacteristic
293C2×C43#290111yescharacteristic
294D43—42no—
295#557—861no—
296#557—861no—
297#554—862no—
298#554—862no—
299#554—861no—
300#554—861no—
301#544—432no—
302#544—432no—
303#544—431no—
304#544—431no—
305#533—432no—
306#533—431no—
307C2×#125—432no—
308C2×#125C2×D4311yescharacteristic
309#520—431no—
310#520—431no—
311C4×#41—431no—
312C8×Q8—861no—
313C8×Q8—861no—
314#436—861no—
315#436—862no—
316#436—861no—
317#436—862no—
318#432—431no—
319#432—432no—
320#432—432no—
321#432C2×D4311yescharacteristic
322C4×M16—431no—
323C4×M16—432no—
324C4×M16—432no—
325C4×M16C2×D4311yescharacteristic
326#330—432no—
327#330—432no—
328#330—432no—
329#330—431no—
330#330—432no—
331#330—431no—
332#330—431no—
333#330—431no—
334#330C2×D4312yes—
335#330C2×D4312yes—
336C43#1769211yescharacteristic, complemented, Sylow
337C2×#41—431no—
338C2×M16—21no—
339C2×M16—862no—
340C2×M16—862no—
341C2×M16—861no—
342C4⋊Q8—432no—
343C4⋊Q8—432no—
344C4⋊Q8—431no—
345C4⋊Q8—431no—
346C4⋊Q8—862no—
347C4⋊Q8—862no—
348C4⋊Q8—861no—
349C4⋊Q8—861no—
350#125—21no—
351#125—21no—
352#125—432no—
353#125—432no—
354#125—431no—
355#125—431no—
356#125—862no—
357#125—862no—
358#125—862no—
359#125—862no—
360#125—861no—
361#125—861no—
362#125C4×D4312yes—
363#125C22×D4312yes—
364C22⋊Q8—862no—
365C22⋊Q8—862no—
366C22⋊Q8—862no—
367C22⋊Q8—862no—
368C22⋊Q8—862no—
369C22⋊Q8—862no—
370C22⋊Q8—862no—
371C22⋊Q8—862no—
372C22⋊Q8—861no—
373C22⋊Q8—861no—
374C4×Q8—431no—
375C4×Q8—431no—
376C4×Q8—862no—
377C4×Q8—862no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×Q8—861no—
381C4×Q8—861no—
382C4×D4—432no—
383C4×D4—432no—
384C4×D4—431no—
385C4×D4—431no—
386C4×D4—861no—
387C4×D4—861no—
388C4×D4—862no—
389C4×D4—862no—
390#117—431no—
391#117—432no—
392#117—431no—
393#117—431no—
394#117—432no—
395#117—432no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—432no—
399C2×C4⋊C4—432no—
400C2×C4⋊C4—862no—
401C2×C4⋊C4—862no—
402C2×C4⋊C4C4×D4311yescharacteristic
403C2×C4⋊C4C4×D4311yescharacteristic
404C2×C42—432no—
405C2×C42C22×D4311yescharacteristic
406C4⋊C8—21no—
407C4⋊C8—862no—
408C4⋊C8—862no—
409C4⋊C8—861no—
410C22⋊C8—21no—
411C22⋊C8—862no—
412C22⋊C8—862no—
413C22⋊C8—861no—
414#97—431no—
415#97—432no—
416#97—431no—
417#97C22×D4311yescharacteristic
418#97C22×D4312yes—
419#97C22×D4311yescharacteristic
420C4×C8—21no—
421C4×C8—862no—
422C4×C8—862no—
423C4×C8—861no—
424#41—864no—
425C2×Q8—431no—
426C2×Q8—862no—
427C2×Q8—862no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×D4—432no—
431C2×D4—431no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—432no—
435C22×C4—432no—
436C22×C4—432no—
437C22×C4—862no—
438C22×C4—862no—
439C22×C4C2×C4×D4311yescharacteristic
440C22×C4D4×D4311yescharacteristic
441C22×C4D4×D4311yescharacteristic
442M16—42no—
443M16—1724no—
444M16—1724no—
445M16—1722no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—22no—
449C2×C8—861no—
450C2×C8—862no—
451C2×C8—861no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—432no—
459C4⋊C4—432no—
460C4⋊C4—431no—
461C4⋊C4—431no—
462C4⋊C4—431no—
463C4⋊C4—431no—
464C4⋊C4—431no—
465C4⋊C4—431no—
466C4⋊C4—862no—
467C4⋊C4—862no—
468C4⋊C4—862no—
469C4⋊C4—862no—
470C4⋊C4—862no—
471C4⋊C4—862no—
472C4⋊C4—862no—
473C4⋊C4—862no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4C2×C4×D4312yes—
481C4⋊C4C2×C4×D4312yes—
482C22⋊C4—432no—
483C22⋊C4—432no—
484C22⋊C4—432no—
485C22⋊C4—862no—
486C22⋊C4—862no—
487C22⋊C4—861no—
488C22⋊C4—861no—
489C42—432no—
490C42—432no—
491C42—432no—
492C42—862no—
493C42—862no—
494C42—861no—
495C42—861no—
496C42C2×C4×D4311yescharacteristic
497C42D4×D4311yescharacteristic
498C42D4×D4311yescharacteristic
499C42C23×D4311yescharacteristic
500C23—432no—
501C23C22⋊C4×D4311yescharacteristic
502Q8—434no—
503Q8—3441no—
504Q8—3441no—
505Q8—3442no—
506Q8—3442no—
507D4—864no—
508D4—862no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—81no—
515C2×C4—81no—
516C2×C4—432no—
517C2×C4—432no—
518C2×C4—432no—
519C2×C4—864no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—3442no—
525C2×C4—3442no—
526C2×C4—1722no—
527C2×C4—1722no—
528C2×C4C22⋊C4×D4311yescharacteristic
529C2×C4C22⋊C4×D4311yescharacteristic
530C2×C4C22⋊C4×D4311yescharacteristic
531C2×C4C22×C4×D4311yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4C2×D4×D4311yescharacteristic
534C8—22no—
535C8—41no—
536C8—42no—
537C8—862no—
538C8—1722no—
539C8—1721no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—862no—
544C22—862no—
545C22—862no—
546C22C2×C22⋊C4×D4311yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—42no—
553C4—42no—
554C4—434no—
555C4—862no—
556C4—862no—
557C4—1721no—
558C4—1721no—
559C4—1721no—
560C4—1721no—
561C4#101×D4312yes—
562C2—41no—
563C2—1722no—
564C2C2×#101×D4311yescharacteristic
565C2#1914313911yescharacteristic
566C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1528C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#10621898C2×C4
cosocleC42×C43C24
hypercenter#1528D43
hypocenterC43#17692
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
4. #19133232C2semidirect
5. #19133231C2semidirect
6. #19133197C2semidirect
7. #19133195C2semidirect
8. #19133195C2semidirect
9. #19133189C2semidirect
10. #19133188C2semidirect
11. C43×#1528C2semidirect
287. #1528D43semidirect
336. C43#17692semidirect

Maximal subgroups

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

subgroupindex
#191484192
#191436132
#191436122
#191332322
#191332312
#191331972
#191331952
#191331892
#191331882
C43×#15282
#1769243