Finite Group Databasebeta

← #25253457

Subgroups — #25253457

Order 11008.

580 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146998C211yesmaximal, characteristic, complemented
2#19136826C211yesmaximal, characteristic, complemented
3#19136795C211yesmaximal, characteristic, complemented
4#19136783C211yesmaximal, characteristic, complemented
5#19136752C211yesmaximal, characteristic, complemented
6#19136693C211yesmaximal, characteristic, complemented
7#19136679C211yesmaximal, characteristic, complemented
8#19136647C211yesmaximal, characteristic, complemented
9#19136518C211yesmaximal, characteristic, complemented
10#19136507C211yesmaximal, characteristic, complemented
11C4×#13063266C211yesmaximal, characteristic, complemented
12D4×C43⋊C16C211yesmaximal, characteristic, complemented
13#19136302C211yesmaximal, characteristic, complemented
14C2×#14582700C211yesmaximal, characteristic, complemented
15C43×#3280C211yesmaximal, characteristic, complemented
16#14583595—21no—
17C2×#13063268C2211yescharacteristic, complemented
18C2×#13063266C2211yescharacteristic
19C2×#13063266C2211yescharacteristic
20C22×C43⋊C16C2211yescharacteristic
21C22×C43⋊C16C2211yescharacteristic, complemented
22#14583301C2211yescharacteristic, complemented
23#14583224—21no—
24#14583218—21no—
25#14583200—21no—
26#14583135C2211yescharacteristic
27#14583135C2211yescharacteristic, complemented
28C4×D344C2211yescharacteristic, complemented
29#14582937C2211yescharacteristic, complemented
30C2×#13063259C2211yescharacteristic
31#14582726C2211yescharacteristic, complemented
32#14582724C2211yescharacteristic, complemented
33#14582724C2211yescharacteristic, complemented
34C4⋊(C43⋊C16)C2211yescharacteristic, complemented
35#14582703C2211yescharacteristic, complemented
36#14582703C2211yescharacteristic, complemented
37#14582703C2211yescharacteristic, complemented
38#14582700C2211yescharacteristic
39#14582700C2211yescharacteristic
40#14582700C2211yescharacteristic
41#14582700C2211yescharacteristic
42#14582700C2211yescharacteristic
43#14582700C2211yescharacteristic
44#14582699C2211yescharacteristic, complemented
45C22⋊(C43⋊C16)C2211yescharacteristic
46C22⋊(C43⋊C16)C2211yescharacteristic, complemented
47C4×C43⋊C16C2211yescharacteristic, complemented
48C2×#135×C43C2211yescharacteristic
49C22×D8×C43C2211yescharacteristic
50C43×#546—21no—
51C43×#495C2211yescharacteristic
52C43×#467C2211yescharacteristic
53C43×#466C2211yescharacteristic
54C43×#463—21no—
55C43×#450—21no—
56C43×#449—21no—
57C4×D8×C43C2211yescharacteristic
58C8×D4×C43C2211yescharacteristic
59C2×D344C2311yescharacteristic
60#13063320—41no—
61#13063317—21no—
62#13063307—41no—
63#13063299—21no—
64#13063299—21no—
65#13063297—41no—
66C4×D172—21no—
67(C22⋊D43)⋊C4—41no—
68#13063284—21no—
69C2×C4⋊Dic43—21no—
70#13063268—41no—
71#13063266—22no—
72#13063266—41no—
73C2×C43⋊C16—41no—
74C2×C43⋊C16—41no—
75C2×C43⋊C16C2311yescharacteristic
76C2×C43⋊C16C2311yescharacteristic
77C2×C43⋊C16C2311yescharacteristic
78C2×C43⋊C16C2311yescharacteristic
79#13063259—21no—
80#13063259C2311yescharacteristic
81#13063259C2311yescharacteristic
82#13063259C2311yescharacteristic
83#13063257—21no—
84#13063257—21no—
85#13063247—21no—
86#13063247—21no—
87#13063247—21no—
88C2×#41×C43—21no—
89C22×D4×C43—21no—
90#135×C43—22no—
91#135×C43—41no—
92C2×Q16×C43C2311yescharacteristic
93C2×SD16×C43—21no—
94C2×SD16×C43—21no—
95C2×D8×C43—22no—
96C2×D8×C43—21no—
97C2×D8×C43—41no—
98C2×D8×C43C2311yescharacteristic
99C2×D8×C43C2311yescharacteristic
100C22×C8×C43C2311yescharacteristic
101C22×C8×C43C2311yescharacteristic
102#124×C43—21no—
103#123×C43—41no—
104C22⋊Q8×C43—21no—
105#121×C43—21no—
106#121×C43—41no—
107#120×C43—41no—
108C4×D4×C43—21no—
109C4×D4×C43D411yescharacteristic
110C2×C22⋊C4×C43—41no—
111#107×C43C2311yescharacteristic
112C4⋊C8×C43D411yescharacteristic
113#103×C43—21no—
114#102×C43—21no—
115#102×C43—21no—
116C22⋊C8×C43D411yescharacteristic
117C22⋊C8×C43D411yescharacteristic
118C4×C8×C43C2311yescharacteristic
119C24×C43—41no—
120#41×C43—42no—
121#41×C43—81no—
122C2×Q8×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—41no—
126C2×D4×C43—41no—
127C2×D4×C43—41no—
128C2×D4×C43—42no—
129C2×D4×C43—81no—
130C2×D4×C43D811yescharacteristic
131C22×C4×C43—41no—
132C22×C4×C43—41no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C2×C22⋊D43—41no—
136C2×C22⋊D43—41no—
137C22×Dic43—41no—
138C2×D172—21no—
139C2×C4×D43—41no—
140Q16×C43—21no—
141Q16×C43—21no—
142SD16×C43—42no—
143SD16×C43—81no—
144D8×C43—21no—
145D8×C43—21no—
146D8×C43—21no—
147D8×C43—42no—
148D8×C43#4112yes—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43C2×D411yescharacteristic
154C2×C8×C43C2×D411yescharacteristic
155C2×C8×C43C2×D411yescharacteristic
156C2×C8×C43C2411yescharacteristic
157C4⋊C4×C43—21no—
158C4⋊C4×C43—41no—
159C4⋊C4×C43D811yescharacteristic
160C22⋊C4×C43—41no—
161C22⋊C4×C43—41no—
162C22⋊C4×C43—41no—
163C22⋊C4×C43—41no—
164C22⋊C4×C43—41no—
165C22⋊C4×C43D811yescharacteristic
166C22⋊C4×C43D811yescharacteristic
167C42×C43C2×D411yescharacteristic
168C22⋊Dic43—41no—
169(C2×D43)⋊C4—41no—
170(C2×D43)⋊C4—41no—
171(C2×D43)⋊C4—41no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—41no—
176Dic43⋊C4—41no—
177Dic43⋊C4—41no—
178C4×Dic43—41no—
179D344—21no—
180D344—21no—
181C43⋊C16—21no—
182C43⋊C16—21no—
183C43⋊C16—21no—
184C43⋊C16—21no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43—82no—
188C23×C43—82no—
189C23×C43—161no—
190C23×C43C2×D811yescharacteristic
191C23×C43C2×D811yescharacteristic
192C22×D43—41no—
193Q8×C43—41no—
194Q8×C43—41no—
195D4×C43—22no—
196D4×C43—22no—
197D4×C43—41no—
198D4×C43—41no—
199D4×C43—41no—
200D4×C43—82no—
201D4×C43—82no—
202D4×C43—161no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—82no—
210C2×C4×C43—161no—
211C2×C4×C43C2×D811yescharacteristic
212C2×C4×C43C2×D811yescharacteristic
213C2×C4×C43C2×D811yescharacteristic
214C2×C4×C43C2×D811yescharacteristic
215C2×C4×C43C22×D411yescharacteristic
216C22⋊D43—82no—
217C22⋊D43—161no—
218C2×Dic43—41no—
219C2×Dic43—41no—
220C2×Dic43—41no—
221C2×Dic43—161no—
222D172—41no—
223D172—41no—
224C4×D43—161no—
225C8×C43—21no—
226C8×C43—21no—
227C8×C43—21no—
228C8×C43C2×#4111yescharacteristic
229C8×C43H(5,𝔽2)11yescharacteristic
230#33864—431nomaximal, Sylow
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—42no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43—81no—
240C22×C43—81no—
241C22×C43—81no—
242C22×C43—164no—
243C22×C43#50812yes—
244C22×C43C22×D811yescharacteristic
245C2×D43—81no—
246C2×D43—81no—
247C2×D43—81no—
248C4×C43—21no—
249C4×C43—21no—
250C4×C43—21no—
251C4×C43—21no—
252C4×C43—81no—
253C4×C43—81no—
254C4×C43#54611yescharacteristic
255C4×C43#57711yescharacteristic
256Dic43—81no—
257Dic43—81no—
258Dic43—81no—
259#3339—431no—
260#3280D4311yescharacteristic, complemented
261#2242—431no—
262#2236—431no—
263#2234—431no—
264#2228—431no—
265#2217—431no—
266#2215—431no—
267#2210—431no—
268#2186—431no—
269#2184—431no—
270C4×D16—431no—
271D4×C16—431no—
272#2138—431no—
273C2×#357—431no—
274C2×C43—22no—
275C2×C43—41no—
276C2×C43—82no—
277C2×C43—161no—
278C2×C43#329411yescharacteristic
279C2×C43C2×#50811yescharacteristic
280C2×C43#341511yescharacteristic
281D43—161no—
282C2×#135C2×D4311yescharacteristic
283C22×D8C2×D4311yescharacteristic
284#553—861no—
285#546—21no—
286C2×SD32—431no—
287C2×D16—431no—
288C2×D16—431no—
289C22×C16—431no—
290C22×C16—431no—
291#499—431no—
292#495C2×D4311yescharacteristic
293#482—861no—
294#481—861no—
295#478—861no—
296#467C2×D4311yescharacteristic
297#466—431no—
298#466—431no—
299#466C2×D4311yescharacteristic
300#463—21no—
301#450—21no—
302#449—21no—
303C4×D8—431no—
304C4×D8C2×D4311yescharacteristic
305C8×D4C2×D4311yescharacteristic
306#427—431no—
307C2×#107—431no—
308#367—431no—
309#366—431no—
310#366—431no—
311C4⋊C16—431no—
312#358—431no—
313#358—431no—
314#358—431no—
315#357—431no—
316#357—431no—
317#357—431no—
318#357—431no—
319#357—431no—
320#357—431no—
321#357—431no—
322C22⋊C16—431no—
323C22⋊C16—431no—
324C4×C16—431no—
325C43#3386411yescharacteristic, complemented, Sylow
326C2×#41—21no—
327C22×D4—21no—
328#135—22no—
329#135—41no—
330C2×Q16C22×D4311yescharacteristic
331C2×SD16—21no—
332C2×SD16—21no—
333C2×D8—22no—
334C2×D8—21no—
335C2×D8—41no—
336C2×D8—431no—
337C2×D8C22×D4311yescharacteristic
338C2×D8C22×D4311yescharacteristic
339C22×C8C22×D4311yescharacteristic
340C22×C8C22×D4311yescharacteristic
341#126—1721no—
342#125—861no—
343#124—21no—
344#123—41no—
345#123—1721no—
346C22⋊Q8—21no—
347#121—21no—
348#121—41no—
349#121—861no—
350#121—861no—
351#121—1721no—
352#120—41no—
353C4×D4—21no—
354C4×D4—861no—
355C4×D4—1721no—
356C4×D4C22⋊D4311yescharacteristic
357#117—861no—
358C2×C4⋊C4—861no—
359C2×C22⋊C4—41no—
360SD32—1721no—
361D16—862no—
362D16—1721no—
363C2×C16—431no—
364C2×C16—431no—
365C2×C16—431no—
366C2×C16—431no—
367C2×C16—1721no—
368C2×C16—1721no—
369#107—431no—
370#107—431no—
371#107—431no—
372#107—861no—
373#107C22×D4311yescharacteristic
374#106—861no—
375#106—861no—
376C4⋊C8C22⋊D4311yescharacteristic
377#103—21no—
378#102—21no—
379#102—21no—
380#102—861no—
381#102—861no—
382#102—861no—
383C22⋊C8C22⋊D4311yescharacteristic
384C22⋊C8C22⋊D4311yescharacteristic
385C4×C8C22×D4311yescharacteristic
386C24—41no—
387#41—42no—
388#41—81no—
389C2×Q8—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—42no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—81no—
397C2×D4—861no—
398C2×D4—1721no—
399C2×D4—1721no—
400C2×D4#1062188211yescharacteristic
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—1721no—
404C22×C4—1721no—
405C22×C4C2×C22⋊D4311yescharacteristic
406C22×C4C2×C22⋊D4311yescharacteristic
407Q16—21no—
408Q16—21no—
409SD16—42no—
410SD16—81no—
411D8—21no—
412D8—21no—
413D8—21no—
414D8—42no—
415D8—861no—
416D8—861no—
417D8#1062190012yes—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8C2×C22⋊D4311yescharacteristic
423C2×C8C2×C22⋊D4311yescharacteristic
424C2×C8C2×C22⋊D4311yescharacteristic
425C2×C8C23×D4311yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—861no—
429C4⋊C4—861no—
430C4⋊C4—861no—
431C4⋊C4—1721no—
432C4⋊C4—1721no—
433C4⋊C4—1721no—
434C4⋊C4#1062188211yescharacteristic
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—1721no—
441C22⋊C4—1721no—
442C22⋊C4—1721no—
443C22⋊C4—1721no—
444C22⋊C4#1062188211yescharacteristic
445C22⋊C4#1062188211yescharacteristic
446C42—1721no—
447C42C2×C22⋊D4311yescharacteristic
448C16—861no—
449C16—861no—
450C16—861no—
451C16—861no—
452C23—41no—
453C23—41no—
454C23—82no—
455C23—82no—
456C23—161no—
457C23—1721no—
458C23C2×#1062188211yescharacteristic
459C23C2×#1062188211yescharacteristic
460Q8—41no—
461Q8—41no—
462D4—22no—
463D4—22no—
464D4—41no—
465D4—41no—
466D4—41no—
467D4—82no—
468D4—82no—
469D4—161no—
470D4—3442no—
471D4—1721no—
472D4—1721no—
473D4—6881no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—82no—
481C2×C4—161no—
482C2×C4—1721no—
483C2×C4—1721no—
484C2×C4—1721no—
485C2×C4—6881no—
486C2×C4—6881no—
487C2×C4C2×#1062188211yescharacteristic
488C2×C4C2×#1062188211yescharacteristic
489C2×C4C2×#1062188211yescharacteristic
490C2×C4C2×#1062188211yescharacteristic
491C2×C4C22×C22⋊D4311yescharacteristic
492C8—21no—
493C8—21no—
494C8—21no—
495C8C2×#1062190011yescharacteristic
496C8#1306337011yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—42no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—164no—
509C22—3441no—
510C22—3441no—
511C22—3441no—
512C22#1458332912yes—
513C22C22×#1062188211yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—81no—
519C4—81no—
520C4—3441no—
521C4—3441no—
522C4—3441no—
523C4#1458354311yescharacteristic
524C4#1458371011yescharacteristic
525C2—22no—
526C2—41no—
527C2—82no—
528C2—161no—
529C2—6881no—
530C2#1914640811yescharacteristic
531C2C2×#1458332911yescharacteristic
532C2#1914773411yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3280C2
socleC22×C43C22×D8
hypercenter#3280D43
hypocenterC43#33864
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3280

Complements

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

NH ≅ G/Ntype
1. #19146998C2semidirect
2. #19136826C2semidirect
3. #19136795C2semidirect
4. #19136783C2semidirect
5. #19136752C2semidirect
6. #19136693C2semidirect
7. #19136679C2semidirect
8. #19136647C2semidirect
9. #19136518C2semidirect
10. #19136507C2semidirect
11. C4×#13063266C2semidirect
12. D4×C43⋊C16C2semidirect
13. #19136302C2semidirect
14. C2×#14582700C2semidirect
15. C43×#3280C2semidirect
17. C2×#13063268C22semidirect
21. C22×C43⋊C16C22semidirect
22. #14583301C22semidirect
27. #14583135C22semidirect
28. C4×D344C22semidirect
29. #14582937C22semidirect
31. #14582726C22semidirect
32. #14582724C22semidirect
33. #14582724C22semidirect
34. C4⋊(C43⋊C16)C22semidirect
35. #14582703C22semidirect
36. #14582703C22semidirect
37. #14582703C22semidirect
44. #14582699C22semidirect
46. C22⋊(C43⋊C16)C22semidirect
47. C4×C43⋊C16C22semidirect
260. #3280D43semidirect
325. C43#33864semidirect

Maximal subgroups

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

subgroupindex
#191469982
#191368262
#191367952
#191367832
#191367522
#191366932
#191366792
#191366472
#191365182
#191365072
C4×#130632662
D4×C43⋊C162
#191363022
C2×#145827002
C43×#32802
#3386443