Finite Group Databasebeta

← #25253452

Subgroups — #25253452

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#19146992C211yesmaximal, characteristic, complemented
2#19146283C211yesmaximal, characteristic, complemented
3#19136825C211yesmaximal, characteristic, complemented
4#19136799C211yesmaximal, characteristic, complemented
5#19136783C211yesmaximal, characteristic, complemented
6#19136755C211yesmaximal, characteristic, complemented
7#19136690C211yesmaximal, characteristic, complemented
8#19136648C211yesmaximal, characteristic, complemented
9#19136516C211yesmaximal, characteristic, complemented
10#19136505C211yesmaximal, characteristic, complemented
11#19136439C211yesmaximal, characteristic, complemented
12C16×C22⋊D43C211yesmaximal, characteristic, complemented
13#19136303C211yesmaximal, characteristic, complemented
14#357×D43C211yesmaximal, characteristic, complemented
15C43×#2215C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic
18#14583596—21no—
19#14583546—21no—
20C2×#13063269C2211yescharacteristic, complemented
21C2×#13063266C2211yescharacteristic
22C2×C16×D43C2211yescharacteristic
23#14583300C2211yescharacteristic, complemented
24#14583282C2211yescharacteristic
25#14583220—21no—
26#14583216—21no—
27#14583201—21no—
28#14583141C2211yescharacteristic
29#14583132C2211yescharacteristic
30#14583113—21no—
31#14583051—21no—
32#14583042—21no—
33D8×Dic43C2211yescharacteristic, complemented
34#14582981C2211yescharacteristic
35C8×C22⋊D43C2211yescharacteristic
36#14582937C2211yescharacteristic, complemented
37#107×D43C2211yescharacteristic
38#14582726C2211yescharacteristic, complemented
39#14582724C2211yescharacteristic, complemented
40Dic43⋊C16C2211yescharacteristic, complemented
41#14582704C2211yescharacteristic, complemented
42#14582704C2211yescharacteristic, complemented
43#14582702C2211yescharacteristic, complemented
44#14582701C2211yescharacteristic
45#14582701C2211yescharacteristic
46#14582700C2211yescharacteristic
47#14582700C2211yescharacteristic
48#14582699C2211yescharacteristic
49C22⋊(C43⋊C16)C2211yescharacteristic, complemented
50(C2×D43)⋊C16C2211yescharacteristic
51C16×Dic43C2211yescharacteristic, complemented
52C2×D16×C43C2211yescharacteristic
53C22×C16×C43C2211yescharacteristic, complemented
54C43×#466C2211yescharacteristic
55C43×#466C2211yescharacteristic, complemented
56C43×#366C2211yescharacteristic, complemented
57C43×#357C2211yescharacteristic
58C43×#357C2211yescharacteristic, complemented
59C2×#10621898—21no—
60C2×D4×D43—21no—
61#13063347—22no—
62#13063347—41no—
63C2×Dic172C2311yescharacteristic
64C2×#10621873—21no—
65C2×#10621883—21no—
66C2×D344C2311yescharacteristic
67C2×#10621882—21no—
68D8×D43—22no—
69D8×D43—41no—
70C2×C8×D43C2311yescharacteristic
71#13063318—41no—
72#13063316—21no—
73#13063312—21no—
74#13063307—41no—
75#13063306—41no—
76#13063305—21no—
77#13063296—21no—
78#13063296—41no—
79#13063296—41no—
80#13063293—41no—
81D4×Dic43—21no—
82#13063287—21no—
83C4×C22⋊D43D411yescharacteristic
84(C22⋊D43)⋊C4—41no—
85#13063284—21no—
86C4⋊C4×D43—21no—
87C22⋊C4×D43—41no—
88#13063269—41no—
89#13063266—22no—
90C2×C43⋊C16C2311yescharacteristic
91C2×C43⋊C16C2311yescharacteristic
92C16×D43—41no—
93#13063259C2311yescharacteristic
94#13063259C2311yescharacteristic
95#13063258—21no—
96#13063257—21no—
97#13063256—21no—
98Dic43⋊C8D411yescharacteristic
99#13063248—21no—
100#13063246—21no—
101#13063246—21no—
102#13063245—21no—
103C22⋊(C43⋊C8)D411yescharacteristic
104(C2×D43)⋊C8D411yescharacteristic
105C8×Dic43C2311yescharacteristic
106C2×D8×C43C2311yescharacteristic
107C2×D8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109#121×C43—21no—
110#121×C43—21no—
111D16×C43—41no—
112C2×C16×C43—41no—
113C2×C16×C43C2311yescharacteristic
114C2×C16×C43C2311yescharacteristic
115#107×C43C2311yescharacteristic
116#107×C43C2311yescharacteristic
117#102×C43—21no—
118#102×C43—21no—
119C23×D43—41no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—41no—
123C2×D4×C43—41no—
124C22×C4×C43C2×D411yescharacteristic
125C2×C22⋊D43—41no—
126C2×C22⋊D43—41no—
127C2×C22⋊D43—41no—
128C2×C22⋊D43D811yescharacteristic
129C22×Dic43—41no—
130D4×D43—42no—
131D4×D43—81no—
132#10621898—42no—
133#10621898—81no—
134C2×D172—21no—
135C2×C4×D43—41no—
136C2×C4×D43—41no—
137C2×C4×D43—41no—
138C2×C4×D43C2×D411yescharacteristic
139C2×Dic86—21no—
140D8×C43—21no—
141D8×C43—21no—
142D8×C43—21no—
143D8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43C2×D411yescharacteristic
147C2×C8×C43C2411yescharacteristic
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C22⋊C4×C43—41no—
151C22⋊C4×C43—41no—
152C22⋊Dic43—41no—
153C22⋊Dic43—41no—
154C22⋊Dic43—41no—
155C22⋊Dic43—41no—
156C22⋊Dic43—41no—
157C22⋊Dic43D811yescharacteristic
158#10621883—81no—
159#10621882—42no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—41no—
162(C2×D43)⋊C4D811yescharacteristic
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43—41no—
166C4⋊Dic43—41no—
167Dic43⋊C4—41no—
168Dic43⋊C4—41no—
169Dic43⋊C4D811yescharacteristic
170C4×Dic43—41no—
171C4×Dic43C2×D411yescharacteristic
172C2×C43⋊C8C2×D411yescharacteristic
173C2×C43⋊C8C2×D411yescharacteristic
174Dic172—21no—
175Dic172—21no—
176D344—21no—
177D344#4112yes—
178#10621873—42no—
179C8×D43—21no—
180C8×D43—21no—
181C16×C43—21no—
182C16×C43—21no—
183C43⋊C16—21no—
184C43⋊C16—21no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43C2×D811yescharacteristic
188C22×D43—41no—
189C22×D43—82no—
190C22×D43—82no—
191C22×D43—161no—
192C22×D43C2×D811yescharacteristic
193D4×C43—41no—
194D4×C43—41no—
195D4×C43—41no—
196D4×C43—41no—
197D4×C43—161no—
198D4×C43—161no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43C2×D811yescharacteristic
204C2×C4×C43C22×D411yescharacteristic
205C22⋊D43—22no—
206C22⋊D43—82no—
207C22⋊D43—82no—
208C22⋊D43—82no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—161no—
213C2×Dic43C2×D811yescharacteristic
214C2×Dic43C2×D811yescharacteristic
215C2×Dic43C2×D811yescharacteristic
216D172—22no—
217D172—41no—
218C4×D43—21no—
219C4×D43—21no—
220C4×D43—82no—
221C4×D43—161no—
222C4×D43—161no—
223Dic86—41no—
224Dic86—41no—
225C8×C43—21no—
226C8×C43C2×#4111yescharacteristic
227C8×C43H(5,𝔽2)11yescharacteristic
228C43⋊C8—21no—
229C43⋊C8—21no—
230#33864—431nomaximal, Sylow
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—81no—
235C22×C43—81no—
236C22×C43—81no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43—81no—
240C22×C43C22×D811yescharacteristic
241C2×D43—21no—
242C2×D43—21no—
243C2×D43—42no—
244C2×D43—81no—
245C2×D43—81no—
246C2×D43—164no—
247C2×D43#50812yes—
248C4×C43—21no—
249C4×C43—81no—
250C4×C43—81no—
251C4×C43#54611yescharacteristic
252C4×C43#57711yescharacteristic
253Dic43—21no—
254Dic43—21no—
255Dic43—21no—
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#2215D4311yescharacteristic, complemented
267#2210—431no—
268#2186—431no—
269#2184—431no—
270C4×D16—431no—
271D4×C16—431no—
272#2138—431no—
273C2×#357—431no—
274C2×C43—41no—
275C2×C43—161no—
276C2×C43—161no—
277C2×C43#329411yescharacteristic
278C2×C43C2×#50811yescharacteristic
279C2×C43#341511yescharacteristic
280D43—22no—
281D43—82no—
282C2×#135—431no—
283C22×D8—431no—
284#553—861no—
285#546—861no—
286C2×SD32—431no—
287C2×D16—431no—
288C2×D16C2×D4311yescharacteristic
289C22×C16—431no—
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#466C2×D4311yescharacteristic
299#466C2×D4311yescharacteristic, complemented
300#463—861no—
301#450—861no—
302#449—861no—
303C4×D8—431no—
304C4×D8—431no—
305C8×D4—431no—
306#427—431no—
307C2×#107—431no—
308#367—431no—
309#366—431no—
310#366C2×D4311yescharacteristic, complemented
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#357C2×D4311yescharacteristic
321#357C2×D4311yescharacteristic, complemented
322C22⋊C16—431no—
323C22⋊C16—431no—
324C4×C16—431no—
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—861no—
335C2×D8—862no—
336C2×D8—1721no—
337C2×D8C22×D4311yescharacteristic
338C2×D8C22×D4311yescharacteristic
339C22×C8—431no—
340C22×C8C22×D4311yescharacteristic
341#126—1721no—
342#125—861no—
343#124—861no—
344#123—1721no—
345#123—1721no—
346C22⋊Q8—861no—
347#121—21no—
348#121—21no—
349#121—861no—
350#121—1721no—
351#121—1721no—
352#120—1721no—
353C4×D4—431no—
354C4×D4—861no—
355C4×D4—861no—
356C4×D4—1721no—
357#117—861no—
358C2×C4⋊C4—861no—
359C2×C22⋊C4—1721no—
360SD32—1721no—
361D16—41no—
362D16—862no—
363C2×C16—41no—
364C2×C16—431no—
365C2×C16—431no—
366C2×C16—1721no—
367C2×C16C22×D4311yescharacteristic
368C2×C16C22×D4311yescharacteristic
369#107—431no—
370#107—431no—
371#107—861no—
372#107C22×D4311yescharacteristic
373#107C22×D4311yescharacteristic
374#106—861no—
375#106—861no—
376C4⋊C8—431no—
377#103—861no—
378#102—21no—
379#102—21no—
380#102—861no—
381#102—861no—
382#102—861no—
383C22⋊C8—431no—
384C22⋊C8—431no—
385C4×C8—431no—
386C24—1721no—
387#41—3441no—
388#41—1722no—
389C2×Q8—861no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—431no—
395C2×D4—861no—
396C2×D4—3441no—
397C2×D4—1721no—
398C2×D4—1722no—
399C2×D4—1721no—
400C2×D4—1721no—
401C22×C4—431no—
402C22×C4—1721no—
403C22×C4—1721no—
404C22×C4—1721no—
405C22×C4—1721no—
406C22×C4D4×D4311yescharacteristic
407Q16—861no—
408Q16—861no—
409SD16—3441no—
410SD16—1722no—
411D8—21no—
412D8—21no—
413D8—21no—
414D8—21no—
415D8—432no—
416D8—861no—
417D8—1722no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—431no—
421C2×C8—431no—
422C2×C8—861no—
423C2×C8—861no—
424C2×C8D4×D4311yescharacteristic
425C2×C8C23×D4311yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—431no—
429C4⋊C4—861no—
430C4⋊C4—861no—
431C4⋊C4—1721no—
432C4⋊C4—1721no—
433C4⋊C4—1721no—
434C4⋊C4—1721no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—431no—
438C22⋊C4—431no—
439C22⋊C4—1721no—
440C22⋊C4—1721no—
441C22⋊C4—1721no—
442C22⋊C4—1721no—
443C22⋊C4—1721no—
444C22⋊C4—1721no—
445C22⋊C4—1721no—
446C42—431no—
447C42—1721no—
448C16—21no—
449C16—21no—
450C16—861no—
451C16—861no—
452C23—41no—
453C23—41no—
454C23—431no—
455C23—3442no—
456C23—3442no—
457C23—1721no—
458C23—6881no—
459C23D8×D4311yescharacteristic
460Q8—1721no—
461Q8—1721no—
462D4—41no—
463D4—41no—
464D4—41no—
465D4—41no—
466D4—161no—
467D4—161no—
468D4—862no—
469D4—862no—
470D4—3442no—
471D4—3442no—
472D4—3442no—
473D4—1721no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—431no—
479C2×C4—431no—
480C2×C4—431no—
481C2×C4—861no—
482C2×C4—861no—
483C2×C4—3442no—
484C2×C4—1721no—
485C2×C4—1721no—
486C2×C4—1721no—
487C2×C4—6881no—
488C2×C4—6881no—
489C2×C4—6881no—
490C2×C4D8×D4311yescharacteristic
491C2×C4C2×D4×D4311yescharacteristic
492C8—21no—
493C8—861no—
494C8—861no—
495C8#41×D4311yescharacteristic
496C8#1306337011yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—432no—
507C22—861no—
508C22—861no—
509C22—3441no—
510C22—3441no—
511C22—1722no—
512C22—6884no—
513C22C2×D8×D4311yescharacteristic
514C4—21no—
515C4—81no—
516C4—81no—
517C4—861no—
518C4—861no—
519C4—861no—
520C4—3441no—
521C4—3441no—
522C4—3441no—
523C4#1458353811yescharacteristic
524C4#1458370611yescharacteristic
525C2—41no—
526C2—161no—
527C2—161no—
528C2—862no—
529C2—3442no—
530C2#1914640311yescharacteristic
531C2#508×D4311yescharacteristic
532C2#1914773211yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2215C2
socleC22×C43C22×D8
hypercenter#2215D43
hypocenterC43#33864
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2215

Complements

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

NH ≅ G/Ntype
1. #19146992C2semidirect
2. #19146283C2semidirect
3. #19136825C2semidirect
4. #19136799C2semidirect
5. #19136783C2semidirect
6. #19136755C2semidirect
7. #19136690C2semidirect
8. #19136648C2semidirect
9. #19136516C2semidirect
10. #19136505C2semidirect
11. #19136439C2semidirect
12. C16×C22⋊D43C2semidirect
13. #19136303C2semidirect
14. #357×D43C2semidirect
15. C43×#2215C2semidirect
20. C2×#13063269C22semidirect
23. #14583300C22semidirect
33. D8×Dic43C22semidirect
36. #14582937C22semidirect
38. #14582726C22semidirect
39. #14582724C22semidirect
40. Dic43⋊C16C22semidirect
41. #14582704C22semidirect
42. #14582704C22semidirect
43. #14582702C22semidirect
49. C22⋊(C43⋊C16)C22semidirect
51. C16×Dic43C22semidirect
53. C22×C16×C43C22semidirect
55. C43×#466C22semidirect
56. C43×#366C22semidirect
58. C43×#357C22semidirect
266. #2215D43semidirect
290. C22×C16C2×D43semidirect
299. #466C2×D43semidirect
310. #366C2×D43semidirect
321. #357C2×D43semidirect
325. C43#33864semidirect

Maximal subgroups

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

subgroupindex
#191469922
#191462832
#191368252
#191367992
#191367832
#191367552
#191366902
#191366482
#191365162
#191365052
#191364392
C16×C22⋊D432
#191363032
#357×D432
C43×#22152
#3386443