Finite Group Databasebeta

← #25067322

Subgroups — #25067322

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145163C211yesmaximal, characteristic
2#19143573C211yesmaximal, characteristic, complemented
3#19143567C211yesmaximal, characteristic, complemented
4#19133447C211yesmaximal, characteristic, complemented
5#19133444C211yesmaximal, characteristic, complemented
6#19133441C211yesmaximal, characteristic, complemented
7#19133436C211yesmaximal, characteristic, complemented
8#19133431C211yesmaximal, characteristic, complemented
9#19133428C211yesmaximal, characteristic, complemented
10#19133425C211yesmaximal, characteristic, complemented
11#19133357C211yesmaximal, characteristic, complemented
12#19133052C211yesmaximal, characteristic, complemented
13#19133052C211yesmaximal, characteristic, complemented
14#322×D43C211yesmaximal, characteristic, complemented
15C43×#1581C211yesmaximal, characteristic, complemented
16#14583431C2211yescharacteristic
17#14583431C2211yescharacteristic
18#14583300C411yescharacteristic
19#14583282C411yescharacteristic
20#14583252C411yescharacteristic
21#14583252C411yescharacteristic
22#14583141C411yescharacteristic
23#14583132C411yescharacteristic
24#14583127C411yescharacteristic
25#14583127C411yescharacteristic
26#14583029C2211yescharacteristic
27#14583026C2211yescharacteristic
28C8×Dic86C2211yescharacteristic
29#14583023C2211yescharacteristic
30C4×Dic172C2211yescharacteristic
31C4×#10621883C2211yescharacteristic
32C4×#10621883C2211yescharacteristic
33#14582977C2211yescharacteristic
34#14582973—21no—
35#14582968—21no—
36D4×C43⋊C8C2211yescharacteristic
37C8×C22⋊D43—21no—
38(C22⋊D43)⋊C8—21no—
39#14582957—21no—
40#14582957—21no—
41#14582955C2211yescharacteristic
42#14582955C2211yescharacteristic
43#14582857—21no—
44#14582854—21no—
45C4×C8×D43C2211yescharacteristic
46C4×C8×D43C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582649C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582631C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582629C2211yescharacteristic
54#14582629C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic
56D4⋊(C43⋊C8)C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582621C2211yescharacteristic
59#14582620C2211yescharacteristic
60C4×D8×C43C2211yescharacteristic
61C43×#436C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×Dic172C2×C411yescharacteristic
68C2×#10621883C2×C411yescharacteristic
69C2×#10621883C2×C411yescharacteristic
70C2×#10621877—21no—
71C22×C43⋊C8—21no—
72C2×C8×D43—21no—
73C2×C8×D43C2×C411yescharacteristic
74C2×C8×D43C2×C411yescharacteristic
75C2×C8×D43D411yescharacteristic
76C2×C8×D43D411yescharacteristic
77#13063318—21no—
78#13063318—21no—
79#13063316C2×C411yescharacteristic
80#13063316C2×C411yescharacteristic
81#13063312C2×C411yescharacteristic
82#13063312C2×C411yescharacteristic
83#13063307—21no—
84#13063307—21no—
85#13063305C2×C411yescharacteristic
86#13063305C2×C411yescharacteristic
87#13063296C2×C411yescharacteristic
88#13063296C2×C411yescharacteristic
89C4×Dic86C2311yescharacteristic
90C4×Dic86C2311yescharacteristic
91C4×C22⋊D43—21no—
92C4×C22⋊D43—21no—
93#13063284—21no—
94#13063284—21no—
95C42×D43C2311yescharacteristic
96#13063259C2×C411yescharacteristic
97#13063256C2×C411yescharacteristic
98#13063256C2×C411yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105#13063250C2×C411yescharacteristic
106#13063250C2×C411yescharacteristic
107#13063248C2×C411yescharacteristic
108#13063248C2×C411yescharacteristic
109#13063246C2×C411yescharacteristic
110#13063246C2×C411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113(C2×D43)⋊C8—21no—
114(C2×D43)⋊C8—21no—
115#13063235—21no—
116#13063235—21no—
117#13063235—21no—
118#13063235—21no—
119C4×C43⋊C8C2311yescharacteristic
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C8×Dic43—21no—
123C8×Dic43—21no—
124C8×Dic43—21no—
125C8×Dic43C2×C411yescharacteristic
126C8×Dic43C2×C411yescharacteristic
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C2×D8×C43C2×C411yescharacteristic
130C2×M16×C43—21no—
131C22×C8×C43—21no—
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#107×C43C2×C411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#102×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×D4×C43C22×C411yescharacteristic
145C2×D4×C43C22×C411yescharacteristic
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C2×C22⋊D43—21no—
149C2×C22⋊D43—21no—
150C2×C4×D43C22×C411yescharacteristic
151C2×C4×D43C2×D411yescharacteristic
152C2×C4×D43#4111yescharacteristic
153C2×Dic86C22×C411yescharacteristic
154C2×Dic86C22×C411yescharacteristic
155D8×C43—41no—
156M16×C43—42no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—42no—
161C2×C8×C43C22×C411yescharacteristic
162C2×C8×C43C22×C411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C4⋊C4×C43C22×C411yescharacteristic
166C4⋊C4×C43C22×C411yescharacteristic
167C22⋊C4×C43—21no—
168C22⋊C4×C43—21no—
169C42×C43C2411yescharacteristic
170C22⋊Dic43—21no—
171C22⋊Dic43—21no—
172C22⋊Dic43—21no—
173C22⋊Dic43—21no—
174C22⋊Dic43—21no—
175C22⋊Dic43—21no—
176#10621883—41no—
177#10621883—41no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43C22×C411yescharacteristic
185C4⋊Dic43C22×C411yescharacteristic
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43C22×C411yescharacteristic
193C4×Dic43C2×D411yescharacteristic
194C4×Dic43#4111yescharacteristic
195#10621877—42no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—42no—
200C2×C43⋊C8C22×C411yescharacteristic
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204Dic172—41no—
205C8×D43—22no—
206C8×D43—22no—
207C8×D43—41no—
208C8×D43—41no—
209C8×D43—42no—
210C23×C43—21no—
211C23×C43—21no—
212C22×D43C4×D411yescharacteristic
213D4×C43—21no—
214D4×C43—21no—
215D4×C43—21no—
216D4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43C23×C411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C22⋊D43—42no—
227C22⋊D43—42no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43C4×D411yescharacteristic
233C2×Dic43C4×D411yescharacteristic
234C2×Dic43C4×D411yescharacteristic
235C4×D43—22no—
236C4×D43—21no—
237C4×D43—21no—
238C4×D43—21no—
239C4×D43—21no—
240Dic86—21no—
241Dic86—21no—
242Dic86—21no—
243Dic86—21no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—21no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43—41no—
250C8×C43#13512yes—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8#13512yes—
258#17978—431nomaximal, Sylow
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43C2×C4×D411yescharacteristic
266C2×D43—21no—
267C2×D43—21no—
268C2×D43#44412yes—
269C4×C43—21no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43#56811yescharacteristic
273C4×C43#56811yescharacteristic
274C4×C43C2×#13511yescharacteristic
275C4×C43C2×#13511yescharacteristic
276Dic43—21no—
277Dic43—21no—
278Dic43—21no—
279Dic43—41no—
280Dic43—41no—
281Dic43—41no—
282Dic43—41no—
283#3168—431no—
284#2966—431no—
285#2966—431no—
286#1584—431no—
287#1584—431no—
288#1583—431no—
289#1583—431no—
290#1582—431no—
291#1582—431no—
292#1581—431no—
293#1581D4311yescharacteristic, complemented
294#1568—431no—
295#1494—431no—
296#1494—431no—
297C2×#322—431no—
298C2×C43—81no—
299C2×C43—81no—
300C2×C43#293211yescharacteristic
301C2×C43C4×#13511yescharacteristic
302C2×C43C2×#44411yescharacteristic
303D43—22no—
304#529—431no—
305#529—431no—
306#499—431no—
307#495—431no—
308#488—431no—
309#488—431no—
310#467—431no—
311#466—431no—
312#465—431no—
313#465—431no—
314#446—431no—
315#446—431no—
316C8×Q8—431no—
317C8×Q8—431no—
318C4×Q16—431no—
319C4×SD16—431no—
320C4×SD16—431no—
321C4×D8C2×D4311yescharacteristic
322#436—431no—
323#436C2×D4311yescharacteristic
324#435—861no—
325#435—861no—
326C8×D4—431no—
327C8×D4—861no—
328C8×D4—861no—
329C8×D4C2×D4311yescharacteristic
330#433—861no—
331#433—861no—
332#432—431no—
333#432—431no—
334#405—861no—
335#405—861no—
336C2×C4×C8—431no—
337C2×C4×C8—431no—
338C2×C4×C8—431no—
339#335—431no—
340#335C2×D4311yescharacteristic
341#334—431no—
342#334—431no—
343Q8⋊C8—431no—
344Q8⋊C8—431no—
345Q8⋊C8—431no—
346Q8⋊C8—431no—
347D4⋊C8—431no—
348D4⋊C8—431no—
349D4⋊C8C2×D4311yescharacteristic
350D4⋊C8C2×D4311yescharacteristic
351#322—431no—
352#322—431no—
353#322—431no—
354#322C2×D4311yescharacteristic
355C43#1797811yescharacteristic, complemented, Sylow
356C2×Q16—431no—
357C2×SD16—431no—
358C2×SD16—431no—
359C2×D8C4×D4311yescharacteristic
360C2×M16—21no—
361C2×M16—861no—
362C22×C8—21no—
363C22×C8—431no—
364C22×C8—431no—
365C22×C8—431no—
366C22×C8—431no—
367C22×C8—861no—
368C22×C8—861no—
369#126—861no—
370#126—861no—
371#125—431no—
372#125—431no—
373#124—431no—
374#124—431no—
375#123—861no—
376#123—861no—
377C22⋊Q8—431no—
378C22⋊Q8—431no—
379#121—431no—
380#121—431no—
381C4×Q8—431no—
382C4×Q8—431no—
383C4×D4—861no—
384C4×D4—861no—
385C4×D4C22×D4311yescharacteristic
386C4×D4C22×D4311yescharacteristic
387#117—861no—
388#117—861no—
389C2×C42—431no—
390#107—431no—
391#107C4×D4311yescharacteristic
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⋊C8C22×D4311yescharacteristic
401C4⋊C8C22×D4311yescharacteristic
402#103—431no—
403#103—431no—
404#103—431no—
405#103—431no—
406#102—431no—
407#102—431no—
408#102C4×D4311yescharacteristic
409#102C4×D4311yescharacteristic
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—861no—
413C22⋊C8—861no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416#97—861no—
417#97—861no—
418#97—861no—
419#97—861no—
420C4×C8—431no—
421C4×C8—431no—
422C4×C8—431no—
423C4×C8—431no—
424C4×C8—431no—
425C4×C8—431no—
426C4×C8—431no—
427C4×C8—861no—
428C4×C8—861no—
429C4×C8—861no—
430C4×C8C22×D4311yescharacteristic
431C4×C8C22×D4311yescharacteristic
432C4×C8C22×D4311yescharacteristic
433C2×Q8—431no—
434C2×Q8—431no—
435C2×D4—861no—
436C2×D4—861no—
437C2×D4C2×C4×D4311yescharacteristic
438C2×D4C2×C4×D4311yescharacteristic
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—431no—
444Q16—1721no—
445SD16—1721no—
446SD16—1721no—
447D8—41no—
448M16—42no—
449M16—1722no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—862no—
459C2×C8—862no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—1721no—
464C2×C8—1721no—
465C2×C8—1722no—
466C2×C8—1722no—
467C2×C8C2×C4×D4311yescharacteristic
468C2×C8C2×C4×D4311yescharacteristic
469C2×C8D4×D4311yescharacteristic
470C2×C8D4×D4311yescharacteristic
471C4⋊C4—431no—
472C4⋊C4—431no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4C2×C4×D4311yescharacteristic
482C4⋊C4C2×C4×D4311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—861no—
486C22⋊C4—861no—
487C22⋊C4—861no—
488C22⋊C4—861no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C22⋊C4—861no—
492C22⋊C4—861no—
493C42—431no—
494C42—431no—
495C42—431no—
496C42—861no—
497C42—861no—
498C42C23×D4311yescharacteristic
499C23—21no—
500C23—21no—
501C23—431no—
502Q8—861no—
503Q8—861no—
504Q8—861no—
505Q8—861no—
506D4—21no—
507D4—21no—
508D4—21no—
509D4—21no—
510D4—1722no—
511D4—1722no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—431no—
519C2×C4—431no—
520C2×C4—431no—
521C2×C4—862no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4C22×C4×D4311yescharacteristic
531C2×C4C2×D4×D4311yescharacteristic
532C2×C4#41×D4311yescharacteristic
533C8—21no—
534C8—21no—
535C8—21no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—432no—
540C8—861no—
541C8—861no—
542C8—861no—
543C8—1721no—
544C8—1721no—
545C8—1721no—
546C8#1306334412yes—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—432no—
554C22—861no—
555C22—861no—
556C22C4×D4×D4311yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—861no—
561C4—861no—
562C4—861no—
563C4—1721no—
564C4—1721no—
565C4—1721no—
566C4—1721no—
567C4#1458366411yescharacteristic
568C4#1458366511yescharacteristic
569C4#135×D4311yescharacteristic
570C4C2×#1306334411yescharacteristic
571C2—81no—
572C2—81no—
573C2—862no—
574C2#1914330911yescharacteristic
575C2C4×#1306334411yescharacteristic
576C2#444×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1581C2
socleC22×C43C2×C4×D4
prime radical#14583132C4
cosocleC42×C43C24
hypercenter#1581D43
hypocenterC43#17978
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
2. #19143573C2semidirect
3. #19143567C2semidirect
4. #19133447C2semidirect
5. #19133444C2semidirect
6. #19133441C2semidirect
7. #19133436C2semidirect
8. #19133431C2semidirect
9. #19133428C2semidirect
10. #19133425C2semidirect
11. #19133357C2semidirect
12. #19133052C2semidirect
13. #19133052C2semidirect
14. #322×D43C2semidirect
15. C43×#1581C2semidirect
293. #1581D43semidirect
355. C43#17978semidirect

Maximal subgroups

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

subgroupindex
#191451632
#191435732
#191435672
#191334472
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