Finite Group Databasebeta

← #25079429

Subgroups — #25079429

Order 11008.

696 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144989C211yesmaximal, characteristic, complemented
2#19144595C211yesmaximal, characteristic
3C2×#14583189C211yesmaximal, characteristic, complemented
4#19134170C212yesmaximal, complemented
5#19134128C212yesmaximal, complemented
6#19134046C212yesmaximal, complemented
7#19134004C212yesmaximal, complemented
8#19133347C211yesmaximal, characteristic, complemented
9#19133277C211yesmaximal, characteristic, complemented
10#19133273C211yesmaximal, characteristic, complemented
11D4×M16×C43C211yesmaximal, characteristic, complemented
12#14583449C2211yescharacteristic
13C2×#13063325C2211yescharacteristic
14#14583259—22no—
15#14583250C2212yescomplemented
16#14583246C2212yescomplemented
17#14583212—21no—
18#14583189—21no—
19#14583189—21no—
20#14583189C2212yes—
21#14583189C2212yes—
22#14583179C2211yescharacteristic
23#14583179C2211yescharacteristic
24#14583094C2211yescharacteristic
25#14583094C2211yescharacteristic
26#14583033—21no—
27C4×#10621882—21no—
28C4×#10621882—21no—
29#14582952C2211yescharacteristic
30C2×#13063256—21no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32#14582901—21no—
33#14582901—21no—
34C2×#13063246—21no—
35#14582652C2212yescomplemented
36#14582650C2212yescomplemented
37#14582647C2212yescomplemented
38#14582647C2212yescomplemented
39#14582646C2212yescomplemented
40#14582642C2212yescomplemented
41C22×M16×C43—21no—
42C2×C4×D4×C43C2211yescharacteristic
43C43×#436C2212yes—
44C43×#435—22no—
45C8×D4×C43C2212yes—
46C43×#423C2211yescharacteristic
47C43×#407—21no—
48C4×M16×C43C2211yescharacteristic
49C2×#10621898—21no—
50C22×Dic86—21no—
51C2×#10621882—21no—
52C2×#10621882—21no—
53C22×C43⋊C8—21no—
54#13063325—21no—
55#13063325—21no—
56#13063325—21no—
57#13063325C2311yescharacteristic
58#13063325C2312yes—
59#13063322C2311yescharacteristic
60#13063313—21no—
61#13063299—21no—
62#13063299—21no—
63C4×D172—21no—
64C4×D172—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67#13063258—21no—
68#13063258—21no—
69#13063256—22no—
70#13063256—22no—
71C4⋊(C43⋊C8)—21no—
72C4⋊(C43⋊C8)C2311yescharacteristic
73C4⋊(C43⋊C8)C2311yescharacteristic
74C4⋊(C43⋊C8)C2312yes—
75#13063250—22no—
76#13063250—22no—
77#13063247—22no—
78#13063247—22no—
79#13063246—22no—
80#13063246—22no—
81#13063246—21no—
82#13063246—21no—
83#13063245—21no—
84#13063245—21no—
85C22⋊(C43⋊C8)—21no—
86C4×C43⋊C8—21no—
87C22×D4×C43D411yescharacteristic
88C23×C4×C43—21no—
89C2×M16×C43—21no—
90C2×M16×C43—22no—
91C2×M16×C43—44no—
92C2×M16×C43D411yescharacteristic
93C2×M16×C43D411yescharacteristic
94C22×C8×C43—22no—
95C4×D4×C43—21no—
96C4×D4×C43—21no—
97C4×D4×C43D411yescharacteristic
98C4×D4×C43D411yescharacteristic
99C4×D4×C43C2311yescharacteristic
100C4×D4×C43C2311yescharacteristic
101C2×C4⋊C4×C43D411yescharacteristic
102C2×C22⋊C4×C43—21no—
103C2×C42×C43C2311yescharacteristic
104C4⋊C8×C43—21no—
105C4⋊C8×C43C2312yes—
106C22⋊C8×C43—22no—
107C22⋊C8×C43—22no—
108#97×C43D412yes—
109C4×C8×C43C2312yes—
110C24×C43—21no—
111C2×D4×C43—21no—
112C2×D4×C43—22no—
113C2×D4×C43—41no—
114C2×D4×C43C2×D411yescharacteristic
115C2×D4×C43C2×D411yescharacteristic
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—42no—
122C22×C4×C43—42no—
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43#4111yescharacteristic
126C2×C22⋊D43—41no—
127C22×Dic43—41no—
128#10621898—42no—
129#10621898—42no—
130C2×D172—21no—
131C2×D172—21no—
132C2×D172—21no—
133C2×C4×D43—41no—
134C2×Dic86—21no—
135C2×Dic86—22no—
136C2×Dic86—41no—
137C2×Dic86—82no—
138M16×C43—22no—
139M16×C43—22no—
140M16×C43—44no—
141M16×C43—42no—
142C2×C8×C43—22no—
143C2×C8×C43—44no—
144C2×C8×C43C2×D412yes—
145C2×C8×C43C2×D412yes—
146C4⋊C4×C43—21no—
147C4⋊C4×C43C2×D411yescharacteristic
148C4⋊C4×C43C2×D411yescharacteristic
149C22⋊C4×C43—21no—
150C22⋊C4×C43—21no—
151C22⋊C4×C43—21no—
152C22⋊C4×C43—21no—
153C42×C43C2×D411yescharacteristic
154C42×C43C2×D411yescharacteristic
155C42×C43#4111yescharacteristic
156C42×C43C2411yescharacteristic
157#10621882—42no—
158#10621882—42no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161C4⋊Dic43—22no—
162C4⋊Dic43—21no—
163C4⋊Dic43—22no—
164C4⋊Dic43—21no—
165C4⋊Dic43—41no—
166C4⋊Dic43—41no—
167C2×C43⋊C8—21no—
168C2×C43⋊C8—21no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—42no—
171C23×C43—21no—
172C23×C43—21no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43—81no—
176C23×C43#12111yescharacteristic
177C22×D43—41no—
178D4×C43—21no—
179D4×C43—21no—
180D4×C43—21no—
181D4×C43—42no—
182D4×C43#13712yes—
183C2×C4×C43—21no—
184C2×C4×C43—21no—
185C2×C4×C43—21no—
186C2×C4×C43—21no—
187C2×C4×C43—41no—
188C2×C4×C43—42no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—42no—
194C2×C4×C43—42no—
195C2×C4×C43#12111yescharacteristic
196C2×C4×C43#12111yescharacteristic
197C2×C4×C43#12111yescharacteristic
198C2×C4×C43#13512yes—
199C2×C4×C43AGL(1,ℤ/8)12yes—
200C2×C4×C43C22×D411yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C2×#4111yescharacteristic
203C22⋊D43—82no—
204C2×Dic43—42no—
205C2×Dic43—41no—
206C2×Dic43—82no—
207D172—41no—
208D172—41no—
209D172—41no—
210D172—41no—
211D172—81no—
212C4×D43—82no—
213Dic86—41no—
214Dic86—41no—
215Dic86—82no—
216Dic86—82no—
217C8×C43—22no—
218C8×C43—22no—
219C8×C43—42no—
220C43⋊C8—41no—
221C43⋊C8—42no—
222C43⋊C8—41no—
223#19168—431nomaximal, Sylow
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—22no—
227C22×C43—41no—
228C22×C43—41no—
229C22×C43—41no—
230C22×C43—41no—
231C22×C43—41no—
232C22×C43—84no—
233C22×C43#46312yes—
234C22×C43C2×#12111yescharacteristic
235C2×D43—81no—
236C2×D43—81no—
237C2×D43—81no—
238C4×C43—21no—
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—41no—
242C4×C43—41no—
243C4×C43#46312yes—
244C4×C43C2×#13511yescharacteristic
245C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
246C4×C43C2×#13711yescharacteristic
247C4×C43#57511yescharacteristic
248Dic43—81no—
249Dic43—82no—
250#3141—431no—
251#3100—431no—
252C2×#476—431no—
253D4×M16D4311yescharacteristic, complemented
254#1703—432no—
255#1697—432no—
256#1683—432no—
257#1677—432no—
258#1565—431no—
259#1548—431no—
260#1547—431no—
261C2×C43—22no—
262C2×C43—42no—
263C2×C43—81no—
264C2×C43C2×#46311yescharacteristic
265C2×C43#305611yescharacteristic
266C2×C43#306811yescharacteristic
267D43—161no—
268C22×M16—21no—
269#532—431no—
270C2×C4⋊Q8—431no—
271C2×C4×D4C2×D4311yescharacteristic
272#489—862no—
273#487—432no—
274#486—432no—
275#480—861no—
276#476—432no—
277#476—432no—
278#476—861no—
279#476—861no—
280#474—431no—
281#474—431no—
282#459—431no—
283#459—431no—
284#447—861no—
285C4×D8—861no—
286C4×D8—861no—
287#436C2×D4312yes—
288#435—22no—
289C8×D4C2×D4312yes—
290#431—431no—
291C2×#106—861no—
292#423C2×D4311yescharacteristic
293C2×C4⋊C8—431no—
294#417—861no—
295#417—861no—
296C2×#102—861no—
297#407—21no—
298C4×M16C2×D4311yescharacteristic
299#335—432no—
300#334—432no—
301#333—432no—
302#333—432no—
303#332—432no—
304#331—432no—
305C43#1916811yescharacteristic, complemented, Sylow
306C2×#41—861no—
307C22×Q8—861no—
308C22×D4D17211yescharacteristic
309C23×C4—21no—
310C2×D8—861no—
311C2×D8—861no—
312C2×M16—21no—
313C2×M16—22no—
314C2×M16—44no—
315C2×M16C22⋊D4311yescharacteristic
316C2×M16C22⋊D4311yescharacteristic
317C22×C8—22no—
318C22×C8—861no—
319C4⋊Q8—432no—
320C4⋊Q8—431no—
321C4⋊Q8—861no—
322C4⋊Q8—861no—
323C4⋊Q8—861no—
324#127—431no—
325#124—861no—
326#121—861no—
327#121—861no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—861no—
331C4×D4—861no—
332C4×D4D17211yescharacteristic
333C4×D4D17211yescharacteristic
334C4×D4C22×D4311yescharacteristic
335C4×D4C22×D4311yescharacteristic
336C2×C4⋊C4—861no—
337C2×C4⋊C4—861no—
338C2×C4⋊C4D17211yescharacteristic
339C2×C22⋊C4—21no—
340C2×C42C22×D4311yescharacteristic
341#107—861no—
342#107—861no—
343#106—862no—
344#106—862no—
345C4⋊C8—21no—
346C4⋊C8—432no—
347C4⋊C8—431no—
348C4⋊C8—431no—
349C4⋊C8—861no—
350C4⋊C8C22×D4312yes—
351#103—862no—
352#103—862no—
353#102—862no—
354#102—862no—
355#102—861no—
356#102—861no—
357#102—862no—
358#102—862no—
359#102—861no—
360#102—861no—
361C22⋊C8—22no—
362C22⋊C8—22no—
363C22⋊C8—861no—
364#97C22⋊D4312yes—
365C4×C8—861no—
366C4×C8C22×D4312yes—
367C24—21no—
368#41—1722no—
369#41—1722no—
370C2×Q8—861no—
371C2×Q8—862no—
372C2×Q8—3442no—
373C2×Q8—1721no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—41no—
377C2×D4—861no—
378C2×D4—861no—
379C2×D4—861no—
380C2×D4—1721no—
381C2×D4C2×D17211yescharacteristic
382C2×D4C2×D17211yescharacteristic
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—1721no—
391C22×C4—1721no—
392C22×C4C2×D17211yescharacteristic
393C22×C4#1062189811yescharacteristic
394C22×C4C2×C22⋊D4311yescharacteristic
395D8—1722no—
396D8—1722no—
397M16—22no—
398M16—22no—
399M16—44no—
400M16—42no—
401C2×C8—22no—
402C2×C8—44no—
403C2×C8—861no—
404C2×C8—861no—
405C2×C8—862no—
406C2×C8—1722no—
407C2×C8C2×C22⋊D4312yes—
408C2×C8C2×C22⋊D4312yes—
409C4⋊C4—21no—
410C4⋊C4—862no—
411C4⋊C4—862no—
412C4⋊C4—861no—
413C4⋊C4—861no—
414C4⋊C4—1721no—
415C4⋊C4—1721no—
416C4⋊C4C2×D17211yescharacteristic
417C4⋊C4C2×D17211yescharacteristic
418C22⋊C4—21no—
419C22⋊C4—21no—
420C22⋊C4—21no—
421C22⋊C4—21no—
422C22⋊C4—1721no—
423C22⋊C4—1721no—
424C42C2×D17211yescharacteristic
425C42#1062189811yescharacteristic
426C42C2×C22⋊D4311yescharacteristic
427C42C23×D4311yescharacteristic
428C23—21no—
429C23—21no—
430C23—42no—
431C23—42no—
432C23—81no—
433C23—1721no—
434C23#1306329911yescharacteristic
435Q8—3442no—
436Q8—3442no—
437Q8—1721no—
438Q8—1721no—
439D4—21no—
440D4—21no—
441D4—21no—
442D4—42no—
443D4—3441no—
444D4—3442no—
445D4—1721no—
446D4—1721no—
447D4—1721no—
448D4—1721no—
449D4#1306335812yes—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—3442no—
463C2×C4—3442no—
464C2×C4—1721no—
465C2×C4—1722no—
466C2×C4#1306329911yescharacteristic
467C2×C4#1306329911yescharacteristic
468C2×C4#1306329911yescharacteristic
469C2×C4#1306334512yes—
470C2×C4#1306335112yes—
471C2×C4C22×C22⋊D4311yescharacteristic
472C2×C4C22×D17211yescharacteristic
473C2×C4C2×#1062189811yescharacteristic
474C8—22no—
475C8—22no—
476C8—42no—
477C8—1721no—
478C8—1722no—
479C8—1721no—
480C22—21no—
481C22—21no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—84no—
489C22—3441no—
490C22—3441no—
491C22—3441no—
492C22#1458311412yes—
493C22C2×#1306329911yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—41no—
498C4—41no—
499C4—3441no—
500C4—3442no—
501C4#1458311412yes—
502C4C2×#1306334511yescharacteristic
503C4C2×#1306335111yescharacteristic
504C4C2×#1306335811yescharacteristic
505C4#1458369911yescharacteristic
506C2—22no—
507C2—42no—
508C2—81no—
509C2—6881no—
510C2C2×#1458311411yescharacteristic
511C2#1914422511yescharacteristic
512C2#1914432311yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingD4×M16×C43C2
socleC22×C43C2×#121
prime radical#19144595C2
hypercenterD4×M16D43
hypocenterC43#19168
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. #19144989C2semidirect
3. C2×#14583189C2semidirect
4. #19134170C2semidirect
5. #19134128C2semidirect
6. #19134046C2semidirect
7. #19134004C2semidirect
8. #19133347C2semidirect
9. #19133277C2semidirect
10. #19133273C2semidirect
11. D4×M16×C43C2semidirect
15. #14583250C22semidirect
16. #14583246C22semidirect
35. #14582652C22semidirect
36. #14582650C22semidirect
37. #14582647C22semidirect
38. #14582647C22semidirect
39. #14582646C22semidirect
40. #14582642C22semidirect
253. D4×M16D43semidirect
305. C43#19168semidirect

Maximal subgroups

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

subgroupindex
#191449892
#191445952
C2×#145831892
#191341702
#191341282
#191340462
#191340042
#191333472
#191332772
#191332732
D4×M16×C432
#1916843