Finite Group Databasebeta

← #25251924

Subgroups — #25251924

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145128C211yesmaximal, characteristic, complemented
2#19145075C211yesmaximal, characteristic
3#19136836C211yesmaximal, characteristic, complemented
4#19136835C211yesmaximal, characteristic, complemented
5#19136834C211yesmaximal, characteristic, complemented
6#19136830C211yesmaximal, characteristic, complemented
7#19136827C211yesmaximal, characteristic, complemented
8#19136825C211yesmaximal, characteristic, complemented
9#19136817C211yesmaximal, characteristic, complemented
10#19136309C211yesmaximal, characteristic, complemented
11#19136304C211yesmaximal, characteristic, complemented
12#19136299C211yesmaximal, characteristic, complemented
13#357×D43C211yesmaximal, characteristic, complemented
14#19136190C211yesmaximal, characteristic, complemented
15C43×#2240C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17C2×#13063344C2211yescharacteristic
18C2×D8×D43C2211yescharacteristic
19#14583526—21no—
20#14583462—21no—
21C2×#13063264C2211yescharacteristic
22C2×C16×D43C2211yescharacteristic
23#14583307—21no—
24#14583305—21no—
25#14583303C2211yescharacteristic, complemented
26#14583301C2211yescharacteristic, complemented
27#14583300C2211yescharacteristic, complemented
28#14583287—21no—
29#14583286—21no—
30#14583283C2211yescharacteristic
31#14583282C2211yescharacteristic
32#14583274C2211yescharacteristic
33#14582940—21no—
34#14582936C2211yescharacteristic
35#107×D43C2211yescharacteristic
36#14582853C2211yescharacteristic
37#14582704C2211yescharacteristic, complemented
38#14582704C2211yescharacteristic, complemented
39#14582702C2211yescharacteristic, complemented
40#14582702C2211yescharacteristic, complemented
41#14582701C2211yescharacteristic
42#14582701C2211yescharacteristic
43#14582700C2211yescharacteristic
44#14582700C2211yescharacteristic
45#14582700C2211yescharacteristic, complemented
46#14582700C2211yescharacteristic, complemented
47#14582699C2211yescharacteristic
48#14582699C2211yescharacteristic
49#14582675C2211yescharacteristic, complemented
50#14582674C2211yescharacteristic, complemented
51C16×Dic43C2211yescharacteristic, complemented
52C43×#500C2211yescharacteristic, complemented
53C43×#493C2211yescharacteristic
54C43×#357C2211yescharacteristic
55C43×#357C2211yescharacteristic
56C43×#357C2211yescharacteristic, complemented
57C43×#357C2211yescharacteristic, complemented
58C4×C16×C43C2211yescharacteristic, complemented
59C2×#10621900—21no—
60C2×D4×D43—21no—
61#13063349—44no—
62#13063344—22no—
63#13063344—22no—
64C2×Dic172C2311yescharacteristic
65C2×#10621873—21no—
66C2×#10621883—21no—
67C2×#10621883—21no—
68C2×D344C2311yescharacteristic
69C2×#10621882—21no—
70C2×#10621882—21no—
71D8×D43—22no—
72D8×D43—22no—
73C2×#10621872D411yescharacteristic
74C2×C8×D43C2311yescharacteristic
75#13063324—21no—
76#13063323—41no—
77#13063321—21no—
78#13063317—21no—
79#13063316—21no—
80#13063315—41no—
81#13063313—21no—
82#13063312—21no—
83#13063303—41no—
84#13063301—41no—
85#13063297—41no—
86#13063297—41no—
87#13063293—41no—
88#13063293—41no—
89#13063283—21no—
90#13063282D411yescharacteristic
91C4⋊C4×D43—21no—
92#13063264—22no—
93C2×C43⋊C16C2311yescharacteristic
94C2×C43⋊C16C2311yescharacteristic
95C16×D43—22no—
96#13063259C2311yescharacteristic
97#13063259C2311yescharacteristic
98#13063258—21no—
99#13063258—21no—
100#13063257—21no—
101#13063256—21no—
102#13063256—21no—
103#13063236D411yescharacteristic
104#13063235D411yescharacteristic
105C8×Dic43C2311yescharacteristic
106C2×D8×C43—21no—
107C2×D8×C43C2311yescharacteristic
108C2×D8×C43C2311yescharacteristic
109C4⋊Q8×C43—21no—
110#127×C43—21no—
111C2×C16×C43C2311yescharacteristic
112C2×C16×C43C2311yescharacteristic
113#107×C43—21no—
114#107×C43C2311yescharacteristic
115#107×C43C2311yescharacteristic
116C4×C8×C43C2311yescharacteristic
117C23×D43—41no—
118C2×Q8×C43—41no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—41no—
122C2×D4×C43—41no—
123C2×C22⋊D43—41no—
124C2×C22⋊D43—41no—
125C2×C22⋊D43—41no—
126C2×C22⋊D43—41no—
127C22×Dic43—41no—
128#10621900—42no—
129#10621900—42no—
130D4×D43—42no—
131D4×D43—42no—
132C2×D172—21no—
133C2×C4×D43—41no—
134C2×C4×D43C2×D411yescharacteristic
135C2×Dic86—21no—
136C2×Dic86—41no—
137D8×C43—21no—
138D8×C43—21no—
139D8×C43—21no—
140D8×C43—21no—
141D8×C43—42no—
142C2×C8×C43C2×D411yescharacteristic
143C2×C8×C43C2411yescharacteristic
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—41no—
147C42×C43C2×D411yescharacteristic
148C22⋊Dic43—41no—
149C22⋊Dic43—41no—
150#10621883—42no—
151#10621883—42no—
152#10621882—42no—
153#10621882—42no—
154(C2×D43)⋊C4—41no—
155(C2×D43)⋊C4—41no—
156(C2×D43)⋊C4—41no—
157(C2×D43)⋊C4D811yescharacteristic
158(C2×D43)⋊C4D811yescharacteristic
159C4⋊Dic43—21no—
160C4⋊Dic43—21no—
161C4⋊Dic43—41no—
162Dic43⋊C4—41no—
163Dic43⋊C4—41no—
164Dic43⋊C4—41no—
165Dic43⋊C4—41no—
166Dic43⋊C4—41no—
167Dic43⋊C4D811yescharacteristic
168Dic43⋊C4D811yescharacteristic
169C4×Dic43—41no—
170C4×Dic43C2×D411yescharacteristic
171C2×C43⋊C8C2×D411yescharacteristic
172C2×C43⋊C8C2×D411yescharacteristic
173Dic172—21no—
174Dic172—21no—
175D344—21no—
176D344—21no—
177#10621873—42no—
178#10621872SD1614yes—
179C8×D43#4112yes—
180C8×D43#4112yes—
181C16×C43—21no—
182C16×C43—21no—
183C43⋊C16—21no—
184C43⋊C16—21no—
185C23×C43—41no—
186C23×C43—41no—
187C22×D43—41no—
188C22×D43—82no—
189C22×D43—161no—
190C22×D43—161no—
191C22×D43C2×D811yescharacteristic
192Q8×C43—161no—
193D4×C43—41no—
194D4×C43—41no—
195D4×C43—41no—
196D4×C43—41no—
197D4×C43—161no—
198D4×C43—161no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43C2×D811yescharacteristic
202C2×C4×C43C2×D811yescharacteristic
203C2×C4×C43C22×D411yescharacteristic
204C22⋊D43—82no—
205C22⋊D43—82no—
206C22⋊D43—161no—
207C22⋊D43—161no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—82no—
212C2×Dic43C2×D811yescharacteristic
213C2×Dic43C2×D811yescharacteristic
214C2×Dic43C2×D811yescharacteristic
215D172—41no—
216D172—41no—
217C4×D43—161no—
218C4×D43#12412yes—
219C4×D43C2×SD1612yes—
220Dic86—41no—
221Dic86—41no—
222Dic86—161no—
223C8×C43C2×SD1612yes—
224C8×C43C2×#4111yescharacteristic
225C8×C43C2×#4111yescharacteristic
226C43⋊C8#12412yes—
227C43⋊C8C2×SD1612yes—
228#33702—431nomaximal, Sylow
229C22×C43—81no—
230C22×C43—81no—
231C22×C43—81no—
232C22×C43—81no—
233C22×C43—81no—
234C22×C43—81no—
235C22×C43C22×D811yescharacteristic
236C2×D43—21no—
237C2×D43—21no—
238C2×D43—81no—
239C2×D43—81no—
240C2×D43—81no—
241C2×D43—164no—
242C2×D43#48612yes—
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—81no—
246C4×C43—81no—
247C4×C43C2×#12411yescharacteristic
248C4×C43C22×SD1611yescharacteristic
249Dic43—21no—
250Dic43—21no—
251Dic43—81no—
252Dic43—81no—
253Dic43—81no—
254Dic43#48612yes—
255#3164—431no—
256#3155—431no—
257#2244—431no—
258#2244—431no—
259#2243—431no—
260#2243—431no—
261#2242—431no—
262#2242—431no—
263#2240—431no—
264#2240D4311yescharacteristic, complemented
265#2140—431no—
266#2139—431no—
267#2138—431no—
268C2×#357—431no—
269#2108—431no—
270C2×C43—161no—
271C2×C43—161no—
272C2×C43C2×#48611yescharacteristic
273C2×C43#341511yescharacteristic
274C2×C43#341611yescharacteristic
275D43—22no—
276D43—161no—
277C2×AGL(1,ℤ/8)—861no—
278C2×#135—431no—
279C22×D8—431no—
280#544—861no—
281#535—861no—
282C2×M32—431no—
283C22×C16—431no—
284#501—861no—
285#501—861no—
286#500—431no—
287#500C2×D4311yescharacteristic, complemented
288#499—431no—
289#499—431no—
290#496—861no—
291#496—861no—
292#495—431no—
293#495—431no—
294#493—431no—
295#493C2×D4311yescharacteristic
296#428—861no—
297#427—431no—
298C2×#107—431no—
299#405—431no—
300#358—431no—
301#358—431no—
302#358—431no—
303#358—431no—
304#357—431no—
305#357—431no—
306#357—431no—
307#357—431no—
308#357—431no—
309#357—431no—
310#357—431no—
311#357—431no—
312#357C2×D4311yescharacteristic
313#357C2×D4311yescharacteristic
314#357C2×D4311yescharacteristic, complemented
315#357C2×D4311yescharacteristic, complemented
316#346—431no—
317#346—431no—
318C4×C16—431no—
319C4×C16C2×D4311yescharacteristic, complemented
320C43#3370211yescharacteristic, complemented, Sylow
321C2×#41—861no—
322C22×D4—861no—
323AGL(1,ℤ/8)—1724no—
324#135—862no—
325#135—862no—
326C2×Q16—431no—
327C2×SD16—861no—
328C2×SD16—861no—
329C2×SD16—861no—
330C2×D8—21no—
331C2×D8—431no—
332C2×D8—862no—
333C2×D8—862no—
334C2×D8—861no—
335C2×D8—861no—
336C2×D8C22×D4311yescharacteristic
337C2×D8C22×D4311yescharacteristic
338C2×M16—431no—
339C22×C8—431no—
340C4⋊Q8—21no—
341C4⋊Q8—861no—
342C4⋊Q8—1721no—
343#127—21no—
344#127—861no—
345#125—861no—
346#125—861no—
347#125—1721no—
348#124—861no—
349#124—861no—
350C22⋊Q8—1721no—
351C22⋊Q8—1721no—
352#121—1721no—
353#121—1721no—
354#120—1721no—
355#120—1721no—
356#117—431no—
357#117—861no—
358C2×C4⋊C4—861no—
359M32—862no—
360C2×C16—431no—
361C2×C16—431no—
362C2×C16—862no—
363C2×C16C22×D4311yescharacteristic
364C2×C16C22×D4311yescharacteristic
365#107—21no—
366#107—431no—
367#107—431no—
368#107—861no—
369#107—861no—
370#107C22×D4311yescharacteristic
371#107C22×D4311yescharacteristic
372#106—861no—
373#106—861no—
374#106—861no—
375#97—431no—
376#97—431no—
377C4×C8—431no—
378C4×C8C22×D4311yescharacteristic
379C24—1721no—
380#41—1722no—
381#41—1722no—
382C2×Q8—41no—
383C2×Q8—861no—
384C2×Q8—1721no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—861no—
390C2×D4—1722no—
391C2×D4—1722no—
392C2×D4—1721no—
393C2×D4—1721no—
394C2×D4—1721no—
395C2×D4—1721no—
396C22×C4—431no—
397C22×C4—1721no—
398C22×C4—1721no—
399Q16—861no—
400Q16—861no—
401SD16—1722no—
402SD16—1722no—
403SD16—1722no—
404D8—21no—
405D8—21no—
406D8—21no—
407D8—21no—
408D8—42no—
409D8—861no—
410D8—861no—
411D8—1722no—
412D8—1722no—
413M16—434no—
414C2×C8—431no—
415C2×C8—431no—
416C2×C8—432no—
417C2×C8—432no—
418C2×C8D4×D4311yescharacteristic
419C2×C8C23×D4311yescharacteristic
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—41no—
423C4⋊C4—431no—
424C4⋊C4—431no—
425C4⋊C4—861no—
426C4⋊C4—861no—
427C4⋊C4—1721no—
428C4⋊C4—1721no—
429C4⋊C4—1721no—
430C4⋊C4—1721no—
431C4⋊C4—1721no—
432C4⋊C4—1721no—
433C22⋊C4—431no—
434C22⋊C4—431no—
435C22⋊C4—1721no—
436C22⋊C4—1721no—
437C22⋊C4—1721no—
438C22⋊C4—1721no—
439C22⋊C4—1721no—
440C42—431no—
441C42—1721no—
442C42D4×D4311yescharacteristic
443C16—21no—
444C16—21no—
445C16—861no—
446C16—861no—
447C23—41no—
448C23—41no—
449C23—431no—
450C23—3442no—
451C23—1721no—
452C23—6881no—
453C23—6881no—
454Q8—161no—
455Q8—1721no—
456Q8—1721no—
457Q8—6881no—
458D4—41no—
459D4—41no—
460D4—41no—
461D4—41no—
462D4—161no—
463D4—161no—
464D4—3442no—
465D4—3442no—
466D4—1721no—
467D4—1721no—
468D4—6881no—
469D4—6881no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—431no—
473C2×C4—432no—
474C2×C4—432no—
475C2×C4—431no—
476C2×C4—431no—
477C2×C4—3442no—
478C2×C4—1721no—
479C2×C4—1721no—
480C2×C4—1721no—
481C2×C4—6881no—
482C2×C4D8×D4311yescharacteristic
483C2×C4D8×D4311yescharacteristic
484C2×C4C2×D4×D4311yescharacteristic
485C8—432no—
486C8—432no—
487C8SD16×D4312yes—
488C8#41×D4311yescharacteristic
489C8#41×D4311yescharacteristic
490C22—81no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—81no—
496C22—432no—
497C22—861no—
498C22—861no—
499C22—3441no—
500C22—3441no—
501C22—3441no—
502C22—6884no—
503C22C2×D8×D4311yescharacteristic
504C4—21no—
505C4—21no—
506C4—81no—
507C4—81no—
508C4—432no—
509C4—861no—
510C4—861no—
511C4—3441no—
512C4—3441no—
513C4—3441no—
514C4#124×D4311yescharacteristic
515C4C2×SD16×D4311yescharacteristic
516C2—161no—
517C2—161no—
518C2—862no—
519C2—6881no—
520C2#486×D4311yescharacteristic
521C2#1914773211yescharacteristic
522C2#1914773711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2240C2
socleC22×C43C22×D8
prime radical#19145075C2
hypercenter#2240D43
hypocenterC43#33702
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2240

Complements

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

NH ≅ G/Ntype
1. #19145128C2semidirect
3. #19136836C2semidirect
4. #19136835C2semidirect
5. #19136834C2semidirect
6. #19136830C2semidirect
7. #19136827C2semidirect
8. #19136825C2semidirect
9. #19136817C2semidirect
10. #19136309C2semidirect
11. #19136304C2semidirect
12. #19136299C2semidirect
13. #357×D43C2semidirect
14. #19136190C2semidirect
15. C43×#2240C2semidirect
25. #14583303C22semidirect
26. #14583301C22semidirect
27. #14583300C22semidirect
37. #14582704C22semidirect
38. #14582704C22semidirect
39. #14582702C22semidirect
40. #14582702C22semidirect
45. #14582700C22semidirect
46. #14582700C22semidirect
49. #14582675C22semidirect
50. #14582674C22semidirect
51. C16×Dic43C22semidirect
52. C43×#500C22semidirect
56. C43×#357C22semidirect
57. C43×#357C22semidirect
58. C4×C16×C43C22semidirect
264. #2240D43semidirect
287. #500C2×D43semidirect
314. #357C2×D43semidirect
315. #357C2×D43semidirect
319. C4×C16C2×D43semidirect
320. C43#33702semidirect

Maximal subgroups

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

subgroupindex
#191451282
#191450752
#191368362
#191368352
#191368342
#191368302
#191368272
#191368252
#191368172
#191363092
#191363042
#191362992
#357×D432
#191361902
C43×#22402
#3370243