Finite Group Databasebeta

← #25253444

Subgroups — #25253444

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146964C211yesmaximal, characteristic, complemented
2#19146282C211yesmaximal, characteristic
3#19136827C211yesmaximal, characteristic, complemented
4#19136793C211yesmaximal, characteristic, complemented
5#19136787C211yesmaximal, characteristic, complemented
6#19136753C211yesmaximal, characteristic, complemented
7#19136691C211yesmaximal, characteristic, complemented
8#19136686C211yesmaximal, characteristic, complemented
9#19136658C211yesmaximal, characteristic, complemented
10#19136537C211yesmaximal, characteristic, complemented
11#19136526C211yesmaximal, characteristic, complemented
12C4×#13063270C211yesmaximal, characteristic, complemented
13#19136303C211yesmaximal, characteristic, complemented
14C2×#14582701C211yesmaximal, characteristic, complemented
15D4×C16×C43C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C22×D344C2211yescharacteristic
18#14583589—21no—
19#14583545—21no—
20C2×Dic344C2211yescharacteristic, complemented
21C2×#13063270C2211yescharacteristic
22C2×#13063270C2211yescharacteristic
23#14583301C2211yescharacteristic, complemented
24#14583283C2211yescharacteristic
25#14583241—21no—
26#14583230—21no—
27#14583207—21no—
28#14583140C2211yescharacteristic
29#14583140C2211yescharacteristic
30#14583140C2211yescharacteristic, complemented
31#14583135C2211yescharacteristic
32#14583115—21no—
33#14583052—21no—
34#14583046—21no—
35C4×Dic172C2211yescharacteristic, complemented
36C4×D344C2211yescharacteristic
37#14582937C2211yescharacteristic, complemented
38C2×#13063259C2211yescharacteristic
39#14582727C2211yescharacteristic, complemented
40#14582727C2211yescharacteristic, complemented
41#14582725C2211yescharacteristic, complemented
42#14582704C2211yescharacteristic, complemented
43#14582704C2211yescharacteristic, complemented
44#14582704C2211yescharacteristic, complemented
45#14582704C2211yescharacteristic, complemented
46#14582701C2211yescharacteristic
47#14582701C2211yescharacteristic
48#14582701C2211yescharacteristic
49#14582701C2211yescharacteristic
50#14582701C2211yescharacteristic
51#14582701C2211yescharacteristic
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×Dic172C2311yescharacteristic
65C2×#10621873—21no—
66C2×#10621873—21no—
67C2×D344—22no—
68C2×D344—21no—
69C2×D344—41no—
70C2×D344C2311yescharacteristic
71C2×D344C2311yescharacteristic
72#13063318—41no—
73#13063317—21no—
74#13063315—41no—
75#13063313—21no—
76#13063310—41no—
77#13063306—41no—
78#13063304—21no—
79#13063304—21no—
80#13063304—21no—
81#13063299—21no—
82#13063298—41no—
83#13063293—41no—
84C4×Dic86—21no—
85C4×D172—21no—
86#13063284—21no—
87#13063281—41no—
88C2×C4⋊Dic43—21no—
89C22⋊C4×D43—41no—
90Dic344—41no—
91#13063270—22no—
92#13063270—41no—
93#13063259—21no—
94#13063259C2311yescharacteristic
95#13063259C2311yescharacteristic
96#13063259C2311yescharacteristic
97#13063259C2311yescharacteristic
98#13063257—21no—
99#13063257—21no—
100#13063250—21no—
101#13063250—21no—
102#13063250—21no—
103#13063250—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—
125C22×Dic43—41no—
126#10621898—42no—
127#10621898—81no—
128C2×D172—21no—
129C2×D172—21no—
130C2×D172—41no—
131C2×D172—42no—
132C2×D172—81no—
133C2×C4×D43—41no—
134C2×C4×D43—41no—
135C2×Dic86—21no—
136C2×Dic86—21no—
137C2×C8×C43—21no—
138C2×C8×C43—21no—
139C2×C8×C43—21no—
140C2×C8×C43—21no—
141C2×C8×C43C2×D411yescharacteristic
142C2×C8×C43C2×D411yescharacteristic
143C2×C8×C43C2×D411yescharacteristic
144C2×C8×C43C2411yescharacteristic
145C4⋊C4×C43D811yescharacteristic
146C22⋊C4×C43D811yescharacteristic
147C22⋊C4×C43D811yescharacteristic
148C42×C43C2×D411yescharacteristic
149C22⋊Dic43—41no—
150C22⋊Dic43—41no—
151C22⋊Dic43—41no—
152C22⋊Dic43—41no—
153(C2×D43)⋊C4—41no—
154(C2×D43)⋊C4—41no—
155(C2×D43)⋊C4—41no—
156(C2×D43)⋊C4—41no—
157C4⋊Dic43—21no—
158C4⋊Dic43—21no—
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⋊C4—41no—
168C4×Dic43—41no—
169C4×Dic43—41no—
170Dic172—21no—
171Dic172—21no—
172Dic172—21no—
173Dic172—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—82no—
190C22×D43—82no—
191C22×D43—161no—
192D4×C43—22no—
193C2×C4×C43—21no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43C2×D811yescharacteristic
198C2×C4×C43C2×D811yescharacteristic
199C2×C4×C43C2×D811yescharacteristic
200C2×C4×C43C2×D811yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C22⋊D43—82no—
203C22⋊D43—161no—
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—82no—
211D172—22no—
212D172—41no—
213D172—41no—
214D172—41no—
215D172—82no—
216C4×D43—82no—
217C4×D43—161no—
218Dic86—41no—
219Dic86—41no—
220Dic86—41no—
221Dic86—41no—
222C8×C43—21no—
223C8×C43—21no—
224C8×C43—21no—
225C8×C43C2×#4111yescharacteristic
226C8×C43H(5,𝔽2)11yescharacteristic
227#33863—431nomaximal, Sylow
228C22×C43—21no—
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—21no—
233C22×C43#50812yes—
234C22×C43C22×D811yescharacteristic
235C2×D43—42no—
236C2×D43—81no—
237C2×D43—81no—
238C2×D43—81no—
239C2×D43—81no—
240C2×D43—81no—
241C2×D43—164no—
242C4×C43—21no—
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—21no—
246C4×C43#54611yescharacteristic
247C4×C43#57711yescharacteristic
248Dic43—81no—
249Dic43—81no—
250Dic43—81no—
251Dic43—81no—
252Dic43—81no—
253Dic43—81no—
254#3336—431no—
255#3280—431no—
256#2242—431no—
257#2235—431no—
258#2234—431no—
259#2228—431no—
260#2217—431no—
261#2216—431no—
262#2211—431no—
263#2189—431no—
264#2187—431no—
265C4×SD32—431no—
266D4×C16D4311yescharacteristic, complemented
267#2138—431no—
268C2×#357—431no—
269C2×C43—22no—
270C2×C43—41no—
271C2×C43#329411yescharacteristic
272C2×C43C2×#50811yescharacteristic
273C2×C43#341611yescharacteristic
274D43—82no—
275D43—161no—
276C2×#135—431no—
277C22×D8—431no—
278#552—861no—
279#546—861no—
280C2×Q32—431no—
281C2×SD32—431no—
282C2×SD32—431no—
283C22×C16C2×D4311yescharacteristic
284C22×C16C2×D4311yescharacteristic, complemented
285#499—431no—
286#495—431no—
287#485—861no—
288#483—861no—
289#479—861no—
290#467—431no—
291#467—431no—
292#467—431no—
293#466—431no—
294#463—861no—
295#450—861no—
296#449—861no—
297C4×Q16—431no—
298C4×D8—431no—
299C8×D4C2×D4311yescharacteristic
300#427—431no—
301C2×#107—431no—
302#367—431no—
303#367—431no—
304#366—431no—
305C4⋊C16C2×D4311yescharacteristic, complemented
306#358—431no—
307#358—431no—
308#358—431no—
309#358—431no—
310#357—431no—
311#357—431no—
312#357—431no—
313#357—431no—
314#357—431no—
315#357—431no—
316C22⋊C16C2×D4311yescharacteristic
317C22⋊C16C2×D4311yescharacteristic, complemented
318C4×C16C2×D4311yescharacteristic, complemented
319C43#3386311yescharacteristic, complemented, Sylow
320C2×#41—861no—
321C22×D4—861no—
322#135—862no—
323#135—1721no—
324C2×Q16—431no—
325C2×Q16—431no—
326C2×SD16—861no—
327C2×SD16—861no—
328C2×D8—431no—
329C2×D8—431no—
330C2×D8—862no—
331C2×D8—861no—
332C2×D8—1721no—
333C22×C8C22×D4311yescharacteristic
334C22×C8C22×D4311yescharacteristic
335#126—1721no—
336#125—861no—
337#125—1721no—
338#124—861no—
339#123—1721no—
340#123—1721no—
341C22⋊Q8—861no—
342C22⋊Q8—861no—
343C22⋊Q8—861no—
344#121—861no—
345#121—1721no—
346#120—1721no—
347C4×Q8—861no—
348C4×D4—861no—
349C4×D4D17211yescharacteristic
350#117—861no—
351#117—1721no—
352C2×C4⋊C4—861no—
353C2×C22⋊C4—1721no—
354Q32—1721no—
355SD32—862no—
356SD32—1721no—
357C2×C16—41no—
358C2×C16—41no—
359C2×C16C22×D4311yescharacteristic
360C2×C16C22×D4311yescharacteristic
361C2×C16C22×D4311yescharacteristic
362C2×C16C22×D4311yescharacteristic
363#107—431no—
364#107—431no—
365#107—431no—
366#107—431no—
367#107—861no—
368#106—861no—
369#106—861no—
370C4⋊C8D17211yescharacteristic
371#103—861no—
372#103—861no—
373#103—861no—
374#103—861no—
375#102—861no—
376#102—861no—
377C22⋊C8D17211yescharacteristic
378C22⋊C8D17211yescharacteristic
379C4×C8C22×D4311yescharacteristic
380C24—1721no—
381#41—3441no—
382#41—1722no—
383C2×Q8—861no—
384C2×Q8—861no—
385C2×D4—861no—
386C2×D4—861no—
387C2×D4—3441no—
388C2×D4—1722no—
389C2×D4—1721no—
390C2×D4—1721no—
391C2×D4—1721no—
392C2×D4D34411yescharacteristic
393C22×C4—1721no—
394C22×C4—1721no—
395C22×C4—1721no—
396C22×C4C2×D17211yescharacteristic
397C22×C4C2×D17211yescharacteristic
398Q16—861no—
399Q16—861no—
400Q16—861no—
401Q16—861no—
402SD16—3441no—
403SD16—1722no—
404D8—432no—
405D8—861no—
406D8—861no—
407D8—861no—
408D8—1722no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8C2×D17211yescharacteristic
414C2×C8C2×D17211yescharacteristic
415C2×C8C2×D17211yescharacteristic
416C2×C8C23×D4311yescharacteristic
417C4⋊C4—861no—
418C4⋊C4—861no—
419C4⋊C4—861no—
420C4⋊C4—861no—
421C4⋊C4—1721no—
422C4⋊C4—1721no—
423C4⋊C4—1721no—
424C4⋊C4—1721no—
425C4⋊C4—1721no—
426C4⋊C4—1721no—
427C4⋊C4—1721no—
428C4⋊C4D34411yescharacteristic
429C22⋊C4—1721no—
430C22⋊C4—1721no—
431C22⋊C4—1721no—
432C22⋊C4—1721no—
433C22⋊C4—1721no—
434C22⋊C4—1721no—
435C22⋊C4—1721no—
436C22⋊C4—1721no—
437C22⋊C4D34411yescharacteristic
438C22⋊C4D34411yescharacteristic
439C42—1721no—
440C42—1721no—
441C42C2×D17211yescharacteristic
442C16—21no—
443C16—21no—
444C16—21no—
445C16—21no—
446C23—3442no—
447C23—3442no—
448C23—1721no—
449C23—1721no—
450C23—6881no—
451C23C2×D34411yescharacteristic
452C23C2×D34411yescharacteristic
453Q8—1721no—
454Q8—1721no—
455Q8—1721no—
456Q8—1721no—
457D4—22no—
458D4—862no—
459D4—3442no—
460D4—3442no—
461D4—1721no—
462D4—1721no—
463D4—1721no—
464D4—6881no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—3442no—
470C2×C4—3442no—
471C2×C4—1721no—
472C2×C4—1721no—
473C2×C4—1721no—
474C2×C4—1721no—
475C2×C4—1721no—
476C2×C4—1721no—
477C2×C4—6881no—
478C2×C4C2×D34411yescharacteristic
479C2×C4C2×D34411yescharacteristic
480C2×C4C2×D34411yescharacteristic
481C2×C4C2×D34411yescharacteristic
482C2×C4C22×D17211yescharacteristic
483C8—21no—
484C8—21no—
485C8—21no—
486C8#41×D4311yescharacteristic
487C8#1306337011yescharacteristic
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—3441no—
494C22—3441no—
495C22—3441no—
496C22—3441no—
497C22—3441no—
498C22—1722no—
499C22—6884no—
500C22#1458333112yes—
501C22C22×D34411yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—3441no—
507C4—3441no—
508C4—3441no—
509C4—3441no—
510C4—3441no—
511C4—3441no—
512C4#1458354411yescharacteristic
513C4#1458371111yescharacteristic
514C2—22no—
515C2—41no—
516C2—3442no—
517C2—6881no—
518C2#1914640911yescharacteristic
519C2C2×#1458333111yescharacteristic
520C2#1914774311yescharacteristic
subgroupG/H
centerC22C22×D344
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingD4×C16×C43C2
socleC22×C43C22×D8
prime radical#19146282C2
hypercenterD4×C16D43
hypocenterC43#33863
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. #19146964C2semidirect
3. #19136827C2semidirect
4. #19136793C2semidirect
5. #19136787C2semidirect
6. #19136753C2semidirect
7. #19136691C2semidirect
8. #19136686C2semidirect
9. #19136658C2semidirect
10. #19136537C2semidirect
11. #19136526C2semidirect
12. C4×#13063270C2semidirect
13. #19136303C2semidirect
14. C2×#14582701C2semidirect
15. D4×C16×C43C2semidirect
20. C2×Dic344C22semidirect
23. #14583301C22semidirect
30. #14583140C22semidirect
35. C4×Dic172C22semidirect
37. #14582937C22semidirect
39. #14582727C22semidirect
40. #14582727C22semidirect
41. #14582725C22semidirect
42. #14582704C22semidirect
43. #14582704C22semidirect
44. #14582704C22semidirect
45. #14582704C22semidirect
53. C22×C16×C43C22semidirect
55. C43×C4⋊C16C22semidirect
57. C43×C22⋊C16C22semidirect
58. C4×C16×C43C22semidirect
266. D4×C16D43semidirect
284. C22×C16C2×D43semidirect
305. C4⋊C16C2×D43semidirect
317. C22⋊C16C2×D43semidirect
318. C4×C16C2×D43semidirect
319. C43#33863semidirect

Maximal subgroups

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

subgroupindex
#191469642
#191462822
#191368272
#191367932
#191367872
#191367532
#191366912
#191366862
#191366582
#191365372
#191365262
C4×#130632702
#191363032
C2×#145827012
D4×C16×C432
#3386343