Finite Group Databasebeta

← #25253459

Subgroups — #25253459

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#19146282C211yesmaximal, characteristic, complemented
3#19136827C211yesmaximal, characteristic, complemented
4#19136798C211yesmaximal, characteristic, complemented
5#19136787C211yesmaximal, characteristic, complemented
6#19136753C211yesmaximal, characteristic, complemented
7#19136691C211yesmaximal, characteristic, complemented
8#19136681C211yesmaximal, characteristic, complemented
9#19136651C211yesmaximal, characteristic, complemented
10#19136520C211yesmaximal, characteristic, complemented
11#19136509C211yesmaximal, characteristic, complemented
12C4×D688C211yesmaximal, characteristic, complemented
13#19136303C211yesmaximal, characteristic, complemented
14C2×#14582701C211yesmaximal, characteristic, complemented
15D4×C16×C43C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C22×D344C2211yescharacteristic
18#14583595—21no—
19#14583545—21no—
20C2×#13063270C2211yescharacteristic, complemented
21C2×D688C2211yescharacteristic
22C2×D688C2211yescharacteristic
23#14583301C2211yescharacteristic, complemented
24#14583283C2211yescharacteristic
25#14583224—21no—
26#14583218—21no—
27#14583200—21no—
28#14583140C2211yescharacteristic
29#14583135C2211yescharacteristic
30#14583135C2211yescharacteristic
31#14583135C2211yescharacteristic, complemented
32#14583115—21no—
33#14583052—21no—
34#14583046—21no—
35C4×D344C2211yescharacteristic
36C4×D344C2211yescharacteristic, complemented
37#14582937C2211yescharacteristic, complemented
38C2×#13063259C2211yescharacteristic
39#14582727C2211yescharacteristic, complemented
40#14582725C2211yescharacteristic, complemented
41#14582725C2211yescharacteristic, complemented
42#14582704C2211yescharacteristic, complemented
43#14582704C2211yescharacteristic, complemented
44#14582704C2211yescharacteristic, complemented
45#14582701C2211yescharacteristic
46#14582701C2211yescharacteristic
47#14582701C2211yescharacteristic
48#14582701C2211yescharacteristic
49#14582701C2211yescharacteristic
50#14582701C2211yescharacteristic
51#14582701C2211yescharacteristic, complemented
52C22×C16×C43C2211yescharacteristic
53C22×C16×C43C2211yescharacteristic, complemented
54C8×D4×C43C2211yescharacteristic
55C43×C4⋊C16C2211yescharacteristic, complemented
56C43×C22⋊C16C2211yescharacteristic
57C43×C22⋊C16C2211yescharacteristic, complemented
58C4×C16×C43C2211yescharacteristic, complemented
59C2×#10621898—21no—
60C22×D172—21no—
61#13063347—22no—
62#13063347—41no—
63C2×Dic172C2311yescharacteristic
64C2×#10621873—21no—
65C2×#10621873—21no—
66C2×D344—22no—
67C2×D344—21no—
68C2×D344—41no—
69C2×D344C2311yescharacteristic
70C2×D344C2311yescharacteristic
71C2×D344C2311yescharacteristic
72#13063320—41no—
73#13063317—21no—
74#13063313—21no—
75#13063310—41no—
76#13063307—41no—
77#13063304—21no—
78#13063299—21no—
79#13063299—21no—
80#13063299—21no—
81#13063298—41no—
82#13063297—41no—
83#13063293—41no—
84C4×D172—21no—
85C4×D172—21no—
86(C22⋊D43)⋊C4—41no—
87#13063284—21no—
88C2×C4⋊Dic43—21no—
89C22⋊C4×D43—41no—
90#13063270—41no—
91D688—22no—
92D688—41no—
93#13063259—21no—
94#13063259C2311yescharacteristic
95#13063259C2311yescharacteristic
96#13063259C2311yescharacteristic
97#13063259C2311yescharacteristic
98#13063257—21no—
99#13063257—21no—
100#13063250—21no—
101#13063247—21no—
102#13063247—21no—
103#13063247—21no—
104#13063247—21no—
105#13063247—21no—
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C4×D4×C43D411yescharacteristic
109C2×C16×C43—41no—
110C2×C16×C43—41no—
111C2×C16×C43C2311yescharacteristic
112C2×C16×C43C2311yescharacteristic
113C2×C16×C43C2311yescharacteristic
114C2×C16×C43C2311yescharacteristic
115C4⋊C8×C43D411yescharacteristic
116C22⋊C8×C43D411yescharacteristic
117C22⋊C8×C43D411yescharacteristic
118C4×C8×C43C2311yescharacteristic
119C23×D43—41no—
120C2×D4×C43D811yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C2×C22⋊D43—41no—
124C2×C22⋊D43—41no—
125C2×C22⋊D43—41no—
126C2×C22⋊D43—41no—
127C22×Dic43—41no—
128#10621898—42no—
129#10621898—81no—
130C2×D172—21no—
131C2×D172—21no—
132C2×D172—21no—
133C2×D172—41no—
134C2×D172—42no—
135C2×D172—81no—
136C2×C4×D43—41no—
137C2×C4×D43—41no—
138C2×C4×D43—41no—
139C2×Dic86—21no—
140C2×C8×C43—21no—
141C2×C8×C43—21no—
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43C2×D411yescharacteristic
145C2×C8×C43C2×D411yescharacteristic
146C2×C8×C43C2×D411yescharacteristic
147C2×C8×C43C2411yescharacteristic
148C4⋊C4×C43D811yescharacteristic
149C22⋊C4×C43D811yescharacteristic
150C22⋊C4×C43D811yescharacteristic
151C42×C43C2×D411yescharacteristic
152C22⋊Dic43—41no—
153C22⋊Dic43—41no—
154(C2×D43)⋊C4—41no—
155(C2×D43)⋊C4—41no—
156(C2×D43)⋊C4—41no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4—41no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161C4⋊Dic43—21no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43—41no—
166Dic43⋊C4—41no—
167Dic43⋊C4—41no—
168Dic43⋊C4—41no—
169C4×Dic43—41no—
170Dic172—21no—
171Dic172—21no—
172D344—21no—
173D344—21no—
174D344—21no—
175D344—21no—
176D344—21no—
177D344—42no—
178D344#4112yes—
179#10621873—42no—
180#10621873—81no—
181C16×C43—21no—
182C16×C43—21no—
183C16×C43—21no—
184C16×C43—21no—
185C23×C43C2×D811yescharacteristic
186C23×C43C2×D811yescharacteristic
187C22×D43—41no—
188C22×D43—41no—
189C22×D43—41no—
190C22×D43—82no—
191C22×D43—82no—
192C22×D43—161no—
193D4×C43—22no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43C2×D811yescharacteristic
199C2×C4×C43C2×D811yescharacteristic
200C2×C4×C43C2×D811yescharacteristic
201C2×C4×C43C2×D811yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C22⋊D43—82no—
204C22⋊D43—82no—
205C22⋊D43—161no—
206C22⋊D43—161no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—161no—
213D172—22no—
214D172—41no—
215D172—41no—
216D172—41no—
217D172—41no—
218D172—41no—
219D172—82no—
220C4×D43—82no—
221C4×D43—161no—
222C4×D43—161no—
223Dic86—41no—
224Dic86—41no—
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#50812yes—
237C22×C43C22×D811yescharacteristic
238C2×D43—42no—
239C2×D43—81no—
240C2×D43—81no—
241C2×D43—81no—
242C2×D43—81no—
243C2×D43—81no—
244C2×D43—81no—
245C2×D43—81no—
246C2×D43—81no—
247C2×D43—164no—
248C4×C43—21no—
249C4×C43—21no—
250C4×C43—21no—
251C4×C43—21no—
252C4×C43#54611yescharacteristic
253C4×C43#57711yescharacteristic
254Dic43—81no—
255Dic43—81no—
256Dic43—81no—
257Dic43—81no—
258Dic43—81no—
259#3339—431no—
260#3280—431no—
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×C16D4311yescharacteristic, complemented
272#2138—431no—
273C2×#357—431no—
274C2×C43—22no—
275C2×C43—41no—
276C2×C43#329411yescharacteristic
277C2×C43C2×#50811yescharacteristic
278C2×C43#341511yescharacteristic
279D43—82no—
280D43—161no—
281D43—161no—
282C2×#135—431no—
283C22×D8—431no—
284#553—861no—
285#546—861no—
286C2×SD32—431no—
287C2×D16—431no—
288C2×D16—431no—
289C22×C16C2×D4311yescharacteristic
290C22×C16C2×D4311yescharacteristic, complemented
291#499—431no—
292#495—431no—
293#482—861no—
294#481—861no—
295#478—861no—
296#467—431no—
297#466—431no—
298#466—431no—
299#466—431no—
300#463—861no—
301#450—861no—
302#449—861no—
303C4×D8—431no—
304C4×D8—431no—
305C8×D4C2×D4311yescharacteristic
306#427—431no—
307C2×#107—431no—
308#367—431no—
309#366—431no—
310#366—431no—
311C4⋊C16C2×D4311yescharacteristic, complemented
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⋊C16C2×D4311yescharacteristic
323C22⋊C16C2×D4311yescharacteristic, complemented
324C4×C16C2×D4311yescharacteristic, complemented
325C43#3386411yescharacteristic, complemented, Sylow
326C2×#41—861no—
327C22×D4—861no—
328#135—862no—
329#135—1721no—
330C2×Q16—431no—
331C2×SD16—861no—
332C2×SD16—861no—
333C2×D8—431no—
334C2×D8—431no—
335C2×D8—431no—
336C2×D8—862no—
337C2×D8—861no—
338C2×D8—1721no—
339C22×C8C22×D4311yescharacteristic
340C22×C8C22×D4311yescharacteristic
341#126—1721no—
342#125—861no—
343#124—861no—
344#123—1721no—
345#123—1721no—
346C22⋊Q8—861no—
347#121—861no—
348#121—861no—
349#121—861no—
350#121—1721no—
351#121—1721no—
352#120—1721no—
353C4×D4—861no—
354C4×D4—861no—
355C4×D4—1721no—
356C4×D4D17211yescharacteristic
357#117—861no—
358C2×C4⋊C4—861no—
359C2×C22⋊C4—1721no—
360SD32—1721no—
361D16—862no—
362D16—1721no—
363C2×C16—41no—
364C2×C16—41no—
365C2×C16C22×D4311yescharacteristic
366C2×C16C22×D4311yescharacteristic
367C2×C16C22×D4311yescharacteristic
368C2×C16C22×D4311yescharacteristic
369#107—431no—
370#107—431no—
371#107—431no—
372#107—431no—
373#107—861no—
374#106—861no—
375#106—861no—
376C4⋊C8D17211yescharacteristic
377#103—861no—
378#102—861no—
379#102—861no—
380#102—861no—
381#102—861no—
382#102—861no—
383C22⋊C8D17211yescharacteristic
384C22⋊C8D17211yescharacteristic
385C4×C8C22×D4311yescharacteristic
386C24—1721no—
387#41—3441no—
388#41—1722no—
389C2×Q8—861no—
390C2×D4—861no—
391C2×D4—861no—
392C2×D4—861no—
393C2×D4—3441no—
394C2×D4—1722no—
395C2×D4—1721no—
396C2×D4—1721no—
397C2×D4—1721no—
398C2×D4—1721no—
399C2×D4—1721no—
400C2×D4D34411yescharacteristic
401C22×C4—1721no—
402C22×C4—1721no—
403C22×C4—1721no—
404C22×C4—1721no—
405C22×C4C2×D17211yescharacteristic
406C22×C4C2×D17211yescharacteristic
407Q16—861no—
408Q16—861no—
409SD16—3441no—
410SD16—1722no—
411D8—432no—
412D8—861no—
413D8—861no—
414D8—861no—
415D8—861no—
416D8—861no—
417D8—1722no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8C2×D17211yescharacteristic
423C2×C8C2×D17211yescharacteristic
424C2×C8C2×D17211yescharacteristic
425C2×C8C23×D4311yescharacteristic
426C4⋊C4—861no—
427C4⋊C4—861no—
428C4⋊C4—861no—
429C4⋊C4—861no—
430C4⋊C4—1721no—
431C4⋊C4—1721no—
432C4⋊C4—1721no—
433C4⋊C4—1721no—
434C4⋊C4D34411yescharacteristic
435C22⋊C4—1721no—
436C22⋊C4—1721no—
437C22⋊C4—1721no—
438C22⋊C4—1721no—
439C22⋊C4—1721no—
440C22⋊C4—1721no—
441C22⋊C4—1721no—
442C22⋊C4—1721no—
443C22⋊C4—1721no—
444C22⋊C4D34411yescharacteristic
445C22⋊C4D34411yescharacteristic
446C42—1721no—
447C42C2×D17211yescharacteristic
448C16—21no—
449C16—21no—
450C16—21no—
451C16—21no—
452C23—3442no—
453C23—3442no—
454C23—1721no—
455C23—1721no—
456C23—1721no—
457C23—6881no—
458C23C2×D34411yescharacteristic
459C23C2×D34411yescharacteristic
460Q8—1721no—
461Q8—1721no—
462D4—22no—
463D4—862no—
464D4—3442no—
465D4—3442no—
466D4—3442no—
467D4—1721no—
468D4—1721no—
469D4—1721no—
470D4—1721no—
471D4—1721no—
472D4—6881no—
473D4—6881no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—3442no—
479C2×C4—1721no—
480C2×C4—1721no—
481C2×C4—1721no—
482C2×C4—1721no—
483C2×C4—1721no—
484C2×C4—6881no—
485C2×C4—6881no—
486C2×C4—6881no—
487C2×C4C2×D34411yescharacteristic
488C2×C4C2×D34411yescharacteristic
489C2×C4C2×D34411yescharacteristic
490C2×C4C2×D34411yescharacteristic
491C2×C4C22×D17211yescharacteristic
492C8—21no—
493C8—21no—
494C8—21no—
495C8#41×D4311yescharacteristic
496C8#1306337011yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—3441no—
503C22—3441no—
504C22—3441no—
505C22—3441no—
506C22—3441no—
507C22—3441no—
508C22—3441no—
509C22—3441no—
510C22—1722no—
511C22—6884no—
512C22#1458333112yes—
513C22C22×D34411yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—3441no—
519C4—3441no—
520C4—3441no—
521C4—3441no—
522C4—3441no—
523C4#1458354411yescharacteristic
524C4#1458371111yescharacteristic
525C2—22no—
526C2—41no—
527C2—3442no—
528C2—6881no—
529C2—6881no—
530C2#1914640911yescharacteristic
531C2C2×#1458333111yescharacteristic
532C2#1914773611yescharacteristic
subgroupG/H
centerC22C22×D344
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingD4×C16×C43C2
socleC22×C43C22×D8
hypercenterD4×C16D43
hypocenterC43#33864
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×C16

Complements

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

NH ≅ G/Ntype
1. #19146998C2semidirect
2. #19146282C2semidirect
3. #19136827C2semidirect
4. #19136798C2semidirect
5. #19136787C2semidirect
6. #19136753C2semidirect
7. #19136691C2semidirect
8. #19136681C2semidirect
9. #19136651C2semidirect
10. #19136520C2semidirect
11. #19136509C2semidirect
12. C4×D688C2semidirect
13. #19136303C2semidirect
14. C2×#14582701C2semidirect
15. D4×C16×C43C2semidirect
20. C2×#13063270C22semidirect
23. #14583301C22semidirect
31. #14583135C22semidirect
36. C4×D344C22semidirect
37. #14582937C22semidirect
39. #14582727C22semidirect
40. #14582725C22semidirect
41. #14582725C22semidirect
42. #14582704C22semidirect
43. #14582704C22semidirect
44. #14582704C22semidirect
51. #14582701C22semidirect
53. C22×C16×C43C22semidirect
55. C43×C4⋊C16C22semidirect
57. C43×C22⋊C16C22semidirect
58. C4×C16×C43C22semidirect
271. D4×C16D43semidirect
290. C22×C16C2×D43semidirect
311. C4⋊C16C2×D43semidirect
323. C22⋊C16C2×D43semidirect
324. C4×C16C2×D43semidirect
325. C43#33864semidirect

Maximal subgroups

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

subgroupindex
#191469982
#191462822
#191368272
#191367982
#191367872
#191367532
#191366912
#191366812
#191366512
#191365202
#191365092
C4×D6882
#191363032
C2×#145827012
D4×C16×C432
#3386443