Finite Group Databasebeta

← #25079365

Subgroups — #25079365

Order 11008.

844 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145047C211yesmaximal, characteristic, complemented
2#19144595C211yesmaximal, characteristic, complemented
3C2×#14583094C211yesmaximal, characteristic, complemented
4#19134074C212yesmaximal, complemented
5#19134060C212yesmaximal, complemented
6#19133950C212yesmaximal, complemented
7#19133936C212yesmaximal, complemented
8#19133347C211yesmaximal, characteristic, complemented
9#19133273C211yesmaximal, characteristic, complemented
10#19133264C211yesmaximal, characteristic, complemented
11D4×M16×C43C211yesmaximal, characteristic, complemented
12C2×#13063353—21no—
13C2×#13063353—21no—
14C22×#10621882—21no—
15#14583449C2211yescharacteristic
16C2×#13063322C2211yescharacteristic
17#14583288—22no—
18#14583276C2212yescomplemented
19#14583272C2212yescomplemented
20#14583212—21no—
21#14583179C2211yescharacteristic, complemented
22#14583179C2211yescharacteristic, complemented
23#14583094—21no—
24#14583094—21no—
25#14583094C2212yes—
26#14583094C2212yes—
27#14583094C2211yescharacteristic, complemented
28#14583094C2211yescharacteristic, complemented
29#14583033—21no—
30C4×#10621882—21no—
31C4×#10621882—21no—
32#14582952C2211yescharacteristic
33C2×C4⋊(C43⋊C8)C2211yescharacteristic
34C2×#13063245—21no—
35#14582652C2212yescomplemented
36#14582650C2212yescomplemented
37#14582646C2212yescomplemented
38#14582642C2212yescomplemented
39#14582642C2212yescomplemented
40#14582642C2212yescomplemented
41C22×M16×C43—21no—
42C2×C4×D4×C43C2211yescharacteristic
43C43×#436C2212yescomplemented
44C43×#435—22no—
45C8×D4×C43C2212yescomplemented
46C43×#423C2211yescharacteristic
47C43×#407—21no—
48C4×M16×C43C2211yescharacteristic
49C2×#10621898—21no—
50C22×D172—21no—
51C22×D172—21no—
52C22×D172—21no—
53#13063353—44no—
54#13063353—44no—
55C2×#10621873—22no—
56C2×#10621873—22no—
57C2×D344—22no—
58C2×D344—22no—
59C2×#10621882—22no—
60C2×#10621882—22no—
61C2×#10621882—21no—
62C2×#10621882—21no—
63C2×#10621882—44no—
64C22×C43⋊C8—21no—
65#13063325C2311yescharacteristic
66#13063322—21no—
67#13063322—21no—
68#13063322—21no—
69#13063322C2312yes—
70#13063322C2311yescharacteristic
71#13063313—21no—
72#13063299—21no—
73#13063299—21no—
74C4×D172—21no—
75C4×D172—21no—
76#13063258—21no—
77#13063258—21no—
78C4⋊(C43⋊C8)—21no—
79C4⋊(C43⋊C8)C2312yes—
80C4⋊(C43⋊C8)C2311yescharacteristic
81C4⋊(C43⋊C8)C2311yescharacteristic
82#13063246—21no—
83#13063246—21no—
84#13063245—22no—
85#13063245—22no—
86#13063245—21no—
87#13063245—21no—
88C22⋊(C43⋊C8)—21no—
89C4×C43⋊C8—21no—
90C22×D4×C43D411yescharacteristic
91C23×C4×C43—21no—
92C2×M16×C43—21no—
93C2×M16×C43—22no—
94C2×M16×C43—44no—
95C2×M16×C43D411yescharacteristic
96C2×M16×C43D411yescharacteristic
97C22×C8×C43—22no—
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100C4×D4×C43D411yescharacteristic
101C4×D4×C43D411yescharacteristic
102C4×D4×C43C2311yescharacteristic
103C4×D4×C43C2311yescharacteristic
104C2×C4⋊C4×C43D411yescharacteristic
105C2×C22⋊C4×C43—21no—
106C2×C42×C43C2311yescharacteristic
107C4⋊C8×C43—21no—
108C4⋊C8×C43C2312yes—
109C22⋊C8×C43—22no—
110C22⋊C8×C43—22no—
111#97×C43D412yes—
112C4×C8×C43C2312yes—
113C24×C43—21no—
114C23×D43—41no—
115C2×D4×C43—21no—
116C2×D4×C43—22no—
117C2×D4×C43—41no—
118C2×D4×C43C2×D411yescharacteristic
119C2×D4×C43C2×D411yescharacteristic
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—42no—
126C22×C4×C43—42no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43#4111yescharacteristic
130C2×C22⋊D43—41no—
131#10621898—42no—
132#10621898—42no—
133C2×D172—21no—
134C2×D172—22no—
135C2×D172—21no—
136C2×D172—22no—
137C2×D172—21no—
138C2×D172—22no—
139C2×D172—41no—
140C2×D172—41no—
141C2×D172—41no—
142C2×D172—42no—
143C2×D172—42no—
144C2×D172—42no—
145C2×D172—42no—
146C2×D172—82no—
147C2×C4×D43—41no—
148C2×Dic86—21no—
149M16×C43—22no—
150M16×C43—42no—
151M16×C43—44no—
152M16×C43D814yescomplemented
153C2×C8×C43—22no—
154C2×C8×C43—44no—
155C2×C8×C43C2×D412yes—
156C2×C8×C43C2×D412yes—
157C4⋊C4×C43—21no—
158C4⋊C4×C43C2×D411yescharacteristic
159C4⋊C4×C43C2×D411yescharacteristic
160C22⋊C4×C43—21no—
161C22⋊C4×C43—21no—
162C22⋊C4×C43—21no—
163C22⋊C4×C43—21no—
164C42×C43C2×D411yescharacteristic
165C42×C43C2×D411yescharacteristic
166C42×C43#4111yescharacteristic
167C42×C43C2411yescharacteristic
168#10621882—42no—
169#10621882—44no—
170#10621882—42no—
171#10621882—44no—
172(C2×D43)⋊C4—41no—
173(C2×D43)⋊C4—41no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C2×C43⋊C8—21no—
177C2×C43⋊C8—21no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—42no—
180D344—44no—
181D344—44no—
182#10621873—44no—
183#10621873—44no—
184C23×C43—21no—
185C23×C43—21no—
186C23×C43—42no—
187C23×C43—42no—
188C23×C43—81no—
189C23×C43#12111yescharacteristic
190C22×D43—41no—
191C22×D43—42no—
192C22×D43—82no—
193C22×D43—82no—
194C22×D43—82no—
195D4×C43—21no—
196D4×C43—21no—
197D4×C43—21no—
198D4×C43—42no—
199D4×C43AGL(1,ℤ/8)12yescomplemented
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—41no—
205C2×C4×C43—42no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43#12111yescharacteristic
213C2×C4×C43#12111yescharacteristic
214C2×C4×C43#12111yescharacteristic
215C2×C4×C43C2×D812yes—
216C2×C4×C43AGL(1,ℤ/8)12yes—
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C22⋊D43—82no—
221C2×Dic43—41no—
222D172—42no—
223D172—41no—
224D172—42no—
225D172—41no—
226D172—42no—
227D172—41no—
228D172—41no—
229D172—42no—
230D172—81no—
231D172—82no—
232D172—82no—
233D172—82no—
234D172—82no—
235C4×D43—82no—
236Dic86—41no—
237Dic86—41no—
238C8×C43—22no—
239C8×C43—42no—
240C8×C43C2×D814yescomplemented
241C43⋊C8—42no—
242C43⋊C8—41no—
243C43⋊C8—41no—
244#19162—431nomaximal, Sylow
245C22×C43—21no—
246C22×C43—21no—
247C22×C43—22no—
248C22×C43—41no—
249C22×C43—41no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43—41no—
253C22×C43—84no—
254C22×C43#45912yes—
255C22×C43C2×#12111yescharacteristic
256C2×D43—82no—
257C2×D43—81no—
258C2×D43—82no—
259C2×D43—81no—
260C2×D43—82no—
261C2×D43—81no—
262C2×D43—164no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43#45912yes—
269C4×C43C22×D811yescharacteristic
270C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
271C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
272C4×C43#57511yescharacteristic
273Dic43—81no—
274#3151—431no—
275#3100—431no—
276C2×#459—431no—
277D4×M16D4311yescharacteristic, complemented
278#1687—432no—
279#1685—432no—
280#1667—432no—
281#1665—432no—
282#1565—431no—
283#1547—431no—
284#1545—431no—
285C2×C43—22no—
286C2×C43—42no—
287C2×C43—81no—
288C2×C43C2×#45911yescharacteristic
289C2×C43#305511yescharacteristic
290C2×C43#306811yescharacteristic
291D43—161no—
292D43—162no—
293C2×AGL(1,ℤ/8)—861no—
294C2×AGL(1,ℤ/8)—861no—
295C22×D8—861no—
296C22×M16—21no—
297#532—431no—
298C2×#127—431no—
299C2×C4×D4C2×D4311yescharacteristic
300#496—862no—
301#493—432no—
302#492—432no—
303#480—861no—
304#474—431no—
305#474—431no—
306#459—431no—
307#459—431no—
308#459—432no—
309#459—432no—
310#459—861no—
311#459—861no—
312#447—861no—
313C4×D8—861no—
314C4×D8—861no—
315#436C2×D4312yescomplemented
316#435—22no—
317C8×D4C2×D4312yescomplemented
318#431—431no—
319#423C2×D4311yescharacteristic
320C2×C4⋊C8—431no—
321C2×#102—861no—
322#407—21no—
323C4×M16C2×D4311yescharacteristic
324#335—432no—
325#334—432no—
326#332—432no—
327#331—432no—
328#331—432no—
329#331—432no—
330C43#1916211yescharacteristic, complemented, Sylow
331C2×#41—861no—
332C22×D4—861no—
333C22×D4—861no—
334C22×D4—861no—
335C22×D4D17211yescharacteristic
336C23×C4—21no—
337AGL(1,ℤ/8)—1724no—
338AGL(1,ℤ/8)—1724no—
339C2×SD16—862no—
340C2×SD16—862no—
341C2×D8—862no—
342C2×D8—862no—
343C2×D8—861no—
344C2×D8—861no—
345C2×D8—862no—
346C2×D8—862no—
347C2×D8—1724no—
348C2×M16—21no—
349C2×M16—22no—
350C2×M16—44no—
351C2×M16C22⋊D4311yescharacteristic
352C2×M16C22⋊D4311yescharacteristic
353C22×C8—22no—
354C22×C8—861no—
355C4⋊Q8—431no—
356#127—432no—
357#127—431no—
358#127—861no—
359#127—861no—
360#127—861no—
361#124—861no—
362#121—861no—
363#121—861no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—861no—
367C4×D4—861no—
368C4×D4D17211yescharacteristic
369C4×D4D17211yescharacteristic
370C4×D4C22×D4311yescharacteristic
371C4×D4C22×D4311yescharacteristic
372C2×C4⋊C4D17211yescharacteristic
373C2×C22⋊C4—21no—
374C2×C42C22×D4311yescharacteristic
375#107—861no—
376#107—861no—
377C4⋊C8—21no—
378C4⋊C8—431no—
379C4⋊C8—431no—
380C4⋊C8—432no—
381C4⋊C8—861no—
382C4⋊C8C22×D4312yes—
383#102—861no—
384#102—861no—
385#102—862no—
386#102—862no—
387#102—861no—
388#102—861no—
389C22⋊C8—22no—
390C22⋊C8—22no—
391C22⋊C8—861no—
392#97C22⋊D4312yes—
393C4×C8—861no—
394C4×C8C22×D4312yes—
395C24—21no—
396C24—1721no—
397#41—1722no—
398#41—1722no—
399C2×Q8—861no—
400C2×D4—22no—
401C2×D4—21no—
402C2×D4—41no—
403C2×D4—861no—
404C2×D4—862no—
405C2×D4—861no—
406C2×D4—862no—
407C2×D4—861no—
408C2×D4—862no—
409C2×D4—3442no—
410C2×D4—1722no—
411C2×D4—1722no—
412C2×D4—1721no—
413C2×D4—1721no—
414C2×D4—1721no—
415C2×D4—1721no—
416C2×D4—1722no—
417C2×D4—1722no—
418C2×D4C2×D17211yescharacteristic
419C2×D4C2×D17211yescharacteristic
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—1721no—
428C22×C4C2×D17211yescharacteristic
429C22×C4#1062189811yescharacteristic
430C22×C4C2×C22⋊D4311yescharacteristic
431SD16—1724no—
432SD16—1724no—
433D8—1724no—
434D8—1724no—
435D8—1722no—
436D8—1724no—
437D8—1722no—
438D8—1724no—
439M16—22no—
440M16—42no—
441M16—44no—
442M16#1062188214yescomplemented
443C2×C8—22no—
444C2×C8—44no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—862no—
448C2×C8—1722no—
449C2×C8C2×C22⋊D4312yes—
450C2×C8C2×C22⋊D4312yes—
451C4⋊C4—21no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4C2×D17211yescharacteristic
455C4⋊C4C2×D17211yescharacteristic
456C22⋊C4—21no—
457C22⋊C4—21no—
458C22⋊C4—21no—
459C22⋊C4—21no—
460C22⋊C4—1721no—
461C22⋊C4—1721no—
462C42C2×D17211yescharacteristic
463C42#1062189811yescharacteristic
464C42C2×C22⋊D4311yescharacteristic
465C42C23×D4311yescharacteristic
466C23—21no—
467C23—21no—
468C23—42no—
469C23—42no—
470C23—81no—
471C23—3442no—
472C23—3442no—
473C23—3442no—
474C23—1721no—
475C23—1722no—
476C23#1306329911yescharacteristic
477Q8—1721no—
478Q8—1721no—
479D4—21no—
480D4—21no—
481D4—21no—
482D4—42no—
483D4—3442no—
484D4—3441no—
485D4—3442no—
486D4—3442no—
487D4—3442no—
488D4—3442no—
489D4—1721no—
490D4—1722no—
491D4—1721no—
492D4—1722no—
493D4—1722no—
494D4—1721no—
495D4—1721no—
496D4—1722no—
497D4#1306335312yescomplemented
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—3442no—
511C2×C4—1721no—
512C2×C4#1306329911yescharacteristic
513C2×C4#1306329911yescharacteristic
514C2×C4#1306329911yescharacteristic
515C2×C4C2×#1062188212yes—
516C2×C4#1306335012yes—
517C2×C4C22×C22⋊D4311yescharacteristic
518C2×C4C22×D17211yescharacteristic
519C2×C4C2×#1062189811yescharacteristic
520C8—22no—
521C8—42no—
522C8—1722no—
523C8—1721no—
524C8—1721no—
525C8C2×#1062188214yescomplemented
526C22—21no—
527C22—21no—
528C22—22no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—84no—
535C22—3442no—
536C22—3441no—
537C22—3441no—
538C22—3442no—
539C22—3442no—
540C22—3441no—
541C22—6884no—
542C22#1458309412yes—
543C22C2×#1306329911yescharacteristic
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—3441no—
550C4#1458309412yes—
551C4C22×#1062188211yescharacteristic
552C4C2×#1306335011yescharacteristic
553C4C2×#1306335311yescharacteristic
554C4#1458369911yescharacteristic
555C2—22no—
556C2—42no—
557C2—81no—
558C2—6882no—
559C2—6881no—
560C2C2×#1458309411yescharacteristic
561C2#1914421411yescharacteristic
562C2#1914432311yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingD4×M16×C43C2
socleC22×C43C2×#121
hypercenterD4×M16D43
hypocenterC43#19162
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
1. #19145047C2semidirect
2. #19144595C2semidirect
3. C2×#14583094C2semidirect
4. #19134074C2semidirect
5. #19134060C2semidirect
6. #19133950C2semidirect
7. #19133936C2semidirect
8. #19133347C2semidirect
9. #19133273C2semidirect
10. #19133264C2semidirect
11. D4×M16×C43C2semidirect
18. #14583276C22semidirect
19. #14583272C22semidirect
21. #14583179C22semidirect
22. #14583179C22semidirect
27. #14583094C22semidirect
28. #14583094C22semidirect
35. #14582652C22semidirect
36. #14582650C22semidirect
37. #14582646C22semidirect
38. #14582642C22semidirect
39. #14582642C22semidirect
40. #14582642C22semidirect
43. C43×#436C22semidirect
45. C8×D4×C43C22semidirect
152. M16×C43D8semidirect
199. D4×C43AGL(1,ℤ/8)semidirect
240. C8×C43C2×D8semidirect
277. D4×M16D43semidirect
315. #436C2×D43semidirect
317. C8×D4C2×D43semidirect
330. C43#19162semidirect
442. M16#10621882semidirect
497. D4#13063353semidirect
525. C8C2×#10621882semidirect

Maximal subgroups

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

subgroupindex
#191450472
#191445952
C2×#145830942
#191340742
#191340602
#191339502
#191339362
#191333472
#191332732
#191332642
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