Finite Group Databasebeta

← #25014200

Subgroups — #25014200

Order 11008.

688 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143056C211yesmaximal, characteristic, complemented
2#19136267C211yesmaximal, characteristic, complemented
3#19136245C211yesmaximal, characteristic, complemented
4#19134565C211yesmaximal, characteristic, complemented
5#19132724C211yesmaximal, characteristic, complemented
6#19132716C211yesmaximal, characteristic, complemented
7C43×#3008C211yesmaximal, characteristic
8#14583374—21no—
9#14582916—21no—
10#14582904—21no—
11#14582883C2211yescharacteristic
12#14582873—21no—
13#14582873C2211yescharacteristic
14#14582873C2211yescharacteristic
15#14582873C2211yescharacteristic
16C2×#13063240—22no—
17C2×#13063240—22no—
18#14582692—22no—
19#14582686—22no—
20C2×H(5,𝔽2)×C43C2211yescharacteristic
21C2×AGL(1,ℤ/8)×C43C411yescharacteristic, complemented
22C22×D8×C43C411yescharacteristic, complemented
23C43×#535C2211yescharacteristic
24C43×#449—21no—
25C43×#449—21no—
26C43×#447—21no—
27C43×#447—21no—
28C43×#418C411yescharacteristic, complemented
29C43×#416C411yescharacteristic, complemented
30C43×#408C2211yescharacteristic
31C2×#10621877—21no—
32D4×Dic43—42no—
33D4×Dic43—42no—
34#13063284—21no—
35#13063284—21no—
36#13063284—21no—
37C2×C22⋊Dic43—24no—
38#13063252—42no—
39#13063246—42no—
40#13063244—21no—
41#13063242—21no—
42#13063240—24no—
43#13063240—21no—
44#13063240—21no—
45#13063240—21no—
46#13063240—21no—
47#13063240D412yes—
48#13063240D412yes—
49H(5,𝔽2)×C43—42no—
50H(5,𝔽2)×C43—42no—
51C2×#41×C43—21no—
52C2×#41×C43C2×C411yescharacteristic
53C2×#41×C43D411yescharacteristic
54C2×#41×C43D411yescharacteristic
55C2×#41×C43C2311yescharacteristic
56C22×D4×C43—21no—
57C22×D4×C43—21no—
58C22×D4×C43—21no—
59C22×D4×C43C2×C411yescharacteristic
60C22×D4×C43C2×C411yescharacteristic, complemented
61C22×D4×C43D411yescharacteristic
62C22×D4×C43D411yescharacteristic
63AGL(1,ℤ/8)×C43—42no—
64C2×SD16×C43—21no—
65C2×D8×C43—21no—
66C2×D8×C43—21no—
67C2×D8×C43—21no—
68C2×D8×C43—42no—
69C2×M16×C43C2×C411yescharacteristic, complemented
70C22×C8×C43C2×C411yescharacteristic, complemented
71#127×C43—21no—
72#124×C43—21no—
73#121×C43—21no—
74#121×C43—21no—
75#120×C43—21no—
76#120×C43—21no—
77#117×C43C2×C411yescharacteristic, complemented
78#103×C43—21no—
79#102×C43—21no—
80#102×C43—21no—
81#102×C43—21no—
82C22⋊C8×C43—21no—
83C22⋊C8×C43—21no—
84C24×C43—21no—
85C24×C43—21no—
86C24×C43—21no—
87C24×C43—21no—
88#41×C43—22no—
89#41×C43—22no—
90#41×C43—41no—
91#41×C43—41no—
92#41×C43—41no—
93#41×C43—41no—
94#41×C43—41no—
95#41×C43—41no—
96#41×C43—44no—
97C2×Q8×C43C22⋊C411yescharacteristic
98C2×Q8×C43#4111yescharacteristic
99C2×D4×C43—22no—
100C2×D4×C43—22no—
101C2×D4×C43—21no—
102C2×D4×C43—21no—
103C2×D4×C43—21no—
104C2×D4×C43—21no—
105C2×D4×C43—21no—
106C2×D4×C43—21no—
107C2×D4×C43—22no—
108C2×D4×C43—22no—
109C2×D4×C43—21no—
110C2×D4×C43—21no—
111C2×D4×C43—44no—
112C2×D4×C43—44no—
113C2×D4×C43—41no—
114C2×D4×C43—41no—
115C2×D4×C43—44no—
116C2×D4×C43—41no—
117C2×D4×C43—41no—
118C2×D4×C43—41no—
119C2×D4×C43—41no—
120C2×D4×C43C22⋊C411yescharacteristic
121C2×D4×C43C22⋊C411yescharacteristic
122C2×D4×C43C22⋊C411yescharacteristic
123C2×D4×C43C2×D411yescharacteristic
124C2×D4×C43C2×D411yescharacteristic
125C2×D4×C43#4111yescharacteristic
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43C22×C411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×Dic43—44no—
133SD16×C43—42no—
134D8×C43—42no—
135D8×C43—42no—
136D8×C43—42no—
137M16×C43—41no—
138C2×C8×C43—21no—
139C2×C8×C43—21no—
140C2×C8×C43—41no—
141C4⋊C4×C43—21no—
142C22⋊C4×C43—21no—
143C22⋊C4×C43—41no—
144C22⋊C4×C43—41no—
145C42×C43—21no—
146C22⋊Dic43—22no—
147C22⋊Dic43—22no—
148C22⋊Dic43—44no—
149C22⋊Dic43—41no—
150C4⋊Dic43—41no—
151C4⋊Dic43—41no—
152C4⋊Dic43—41no—
153C4×Dic43—41no—
154C4×Dic43—41no—
155C4×Dic43—41no—
156#10621877—41no—
157#10621877—41no—
158C2×C43⋊C8—41no—
159C23×C43—24no—
160C23×C43—21no—
161C23×C43—21no—
162C23×C43—21no—
163C23×C43—42no—
164C23×C43—42no—
165C23×C43—41no—
166C23×C43—81no—
167C23×C43—161no—
168C23×C43—161no—
169C23×C43—161no—
170C23×C43—161no—
171C23×C43C4×D411yescharacteristic
172C23×C43#12011yescharacteristic
173C23×C43#12111yescharacteristic
174Q8×C43—21no—
175Q8×C43—21no—
176Q8×C43—41no—
177D4×C43—24no—
178D4×C43—21no—
179D4×C43—21no—
180D4×C43—21no—
181D4×C43—21no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—41no—
185D4×C43—42no—
186D4×C43—42no—
187D4×C43—42no—
188D4×C43—42no—
189D4×C43—42no—
190D4×C43—41no—
191D4×C43—41no—
192D4×C43—81no—
193D4×C43—161no—
194D4×C43—161no—
195D4×C43#9912yes—
196D4×C43#9912yes—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—41no—
208C2×C4×C43C2×C22⋊C411yescharacteristic
209C2×C4×C43C4×D411yescharacteristic
210C2×C4×C43#12111yescharacteristic
211C2×C4×C43#12311yescharacteristic
212C2×Dic43—42no—
213C2×Dic43—42no—
214C2×Dic43—81no—
215C2×Dic43—164no—
216C8×C43—41no—
217C8×C43—41no—
218C43⋊C8—81no—
219#13102—431nomaximal, Sylow
220C22×C43—21no—
221C22×C43—22no—
222C22×C43—22no—
223C22×C43—21no—
224C22×C43—21no—
225C22×C43—41no—
226C22×C43—41no—
227C22×C43—41no—
228C22×C43—41no—
229C22×C43—81no—
230C22×C43—81no—
231C22×C43—81no—
232C22×C43—81no—
233C22×C43—81no—
234C22×C43—84no—
235C22×C43—81no—
236C22×C43—162no—
237C22×C43—162no—
238C22×C43—162no—
239C22×C43#38611yescharacteristic
240C4×C43—21no—
241C4×C43—21no—
242C4×C43—21no—
243C4×C43—41no—
244C4×C43—81no—
245C4×C43C2×#9911yescharacteristic
246C4×C43C2×#9911yescharacteristic
247Dic43—82no—
248Dic43—82no—
249Dic43—161no—
250#3008D4311yescharacteristic
251#2883—431no—
252#2128—431no—
253#2122—431no—
254#1795—431no—
255#1395—431no—
256#1391—431no—
257C2×C43—21no—
258C2×C43—41no—
259C2×C43—41no—
260C2×C43—41no—
261C2×C43—42no—
262C2×C43—42no—
263C2×C43—81no—
264C2×C43—161no—
265C2×C43#189811yescharacteristic
266C2×H(5,𝔽2)C2×D4311yescharacteristic
267C2×AGL(1,ℤ/8)Dic4311yescharacteristic, complemented
268C22×D8Dic4311yescharacteristic, complemented
269#535C2×D4311yescharacteristic
270#518—861no—
271#449—21no—
272#449—21no—
273#447—21no—
274#447—21no—
275#421—861no—
276#418—861no—
277#418Dic4311yescharacteristic, complemented
278#416Dic4311yescharacteristic, complemented
279#413—431no—
280#410—431no—
281#410—431no—
282#410—431no—
283#410—861no—
284C2×#99—862no—
285C2×#99—862no—
286#408C2×D4311yescharacteristic
287#353—862no—
288AΣL(1,𝔽16)—862no—
289C43#1310211yescharacteristic, complemented, Sylow
290H(5,𝔽2)—42no—
291H(5,𝔽2)—42no—
292C2×#41—21no—
293C2×#41C2×Dic4311yescharacteristic
294C2×#41C22⋊D4311yescharacteristic
295C2×#41C22⋊D4311yescharacteristic
296C2×#41C22×D4311yescharacteristic
297C22×D4—21no—
298C22×D4—21no—
299C22×D4—21no—
300C22×D4C2×Dic4311yescharacteristic
301C22×D4C2×Dic4311yescharacteristic, complemented
302C22×D4C22⋊D4311yescharacteristic
303C22×D4C22⋊D4311yescharacteristic
304AGL(1,ℤ/8)—42no—
305C2×SD16—21no—
306C2×D8—21no—
307C2×D8—21no—
308C2×D8—21no—
309C2×D8—42no—
310C2×M16—861no—
311C2×M16C2×Dic4311yescharacteristic, complemented
312C22×C8C2×Dic4311yescharacteristic, complemented
313#127—21no—
314#124—21no—
315#121—21no—
316#121—21no—
317#120—21no—
318#120—21no—
319C4×D4—1722no—
320C4×D4—1722no—
321#117—861no—
322#117—861no—
323#117—861no—
324#117C2×Dic4311yescharacteristic, complemented
325C2×C22⋊C4—864no—
326#104—1722no—
327#103—21no—
328#102—21no—
329#102—21no—
330#102—21no—
331#102—1722no—
332#101—861no—
333#100—861no—
334#99—432no—
335#99—432no—
336#99—864no—
337#99—861no—
338#99—861no—
339#99—861no—
340#99—861no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C24—21no—
344C24—21no—
345C24—21no—
346C24—21no—
347#41—22no—
348#41—22no—
349#41—41no—
350#41—41no—
351#41—41no—
352#41—41no—
353#41—41no—
354#41—41no—
355#41—44no—
356C2×Q8C22⋊Dic4311yescharacteristic
357C2×Q8#1062190011yescharacteristic
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—44no—
375C2×D4—44no—
376C2×D4—44no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4C22⋊Dic4311yescharacteristic
380C2×D4C22⋊Dic4311yescharacteristic
381C2×D4C22⋊Dic4311yescharacteristic
382C2×D4D4×D4311yescharacteristic
383C2×D4D4×D4311yescharacteristic
384C2×D4#1062190011yescharacteristic
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—1724no—
389C22×C4C22×Dic4311yescharacteristic
390C22×C4C2×C22⋊D4311yescharacteristic
391C22×C4C2×C22⋊D4311yescharacteristic
392SD16—42no—
393D8—42no—
394D8—42no—
395D8—42no—
396M16—41no—
397M16—1721no—
398M16—1721no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—41no—
402C2×C8—1721no—
403C4⋊C4—21no—
404C4⋊C4—1721no—
405C4⋊C4—1721no—
406C4⋊C4—1721no—
407C22⋊C4—21no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—862no—
411C22⋊C4—862no—
412C22⋊C4—1721no—
413C22⋊C4—1724no—
414C42—21no—
415C42—1721no—
416C42—1721no—
417C42—1721no—
418C23—24no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—42no—
423C23—42no—
424C23—41no—
425C23—81no—
426C23—161no—
427C23—161no—
428C23—161no—
429C23—161no—
430C23D4×Dic4311yescharacteristic
431C23#1306329311yescharacteristic
432C23#1306329711yescharacteristic
433Q8—21no—
434Q8—21no—
435Q8—41no—
436D4—24no—
437D4—21no—
438D4—21no—
439D4—21no—
440D4—21no—
441D4—41no—
442D4—41no—
443D4—41no—
444D4—42no—
445D4—42no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—41no—
450D4—41no—
451D4—81no—
452D4—161no—
453D4—161no—
454D4#1306324012yes—
455D4#1306324012yes—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—3441no—
468C2×C4—1722no—
469C2×C4—1722no—
470C2×C4—6884no—
471C2×C4C2×C22⋊Dic4311yescharacteristic
472C2×C4D4×Dic4311yescharacteristic
473C2×C4#1306329711yescharacteristic
474C2×C4#1306330611yescharacteristic
475C8—41no—
476C8—41no—
477C8—3441no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—22no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—84no—
493C22—81no—
494C22—162no—
495C22—162no—
496C22—162no—
497C22#1458277911yescharacteristic
498C4—21no—
499C4—21no—
500C4—21no—
501C4—41no—
502C4—81no—
503C4—3442no—
504C4—3442no—
505C4—6881no—
506C4C2×#1306324011yescharacteristic
507C4C2×#1306324011yescharacteristic
508C2—21no—
509C2—41no—
510C2—41no—
511C2—41no—
512C2—42no—
513C2—42no—
514C2—81no—
515C2—161no—
516C2#1913504911yescharacteristic
subgroupG/H
centerC2#19135049
commutatorC22×C4×C43C22×C4
FrattiniC2×#41C22×D43
Fitting, prime radicalC43×#3008C2
socleC2×C43#1898
cosocleC2×#41×C43C23
hypercenter#3008D43
hypocenterC43#13102
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×H(5,𝔽2) ◁ #3008

Complements

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

NH ≅ G/Ntype
1. #19143056C2semidirect
2. #19136267C2semidirect
3. #19136245C2semidirect
4. #19134565C2semidirect
5. #19132724C2semidirect
6. #19132716C2semidirect
21. C2×AGL(1,ℤ/8)×C43C4semidirect
22. C22×D8×C43C4semidirect
28. C43×#418C4semidirect
29. C43×#416C4semidirect
60. C22×D4×C43C2×C4semidirect
69. C2×M16×C43C2×C4semidirect
70. C22×C8×C43C2×C4semidirect
77. #117×C43C2×C4semidirect
267. C2×AGL(1,ℤ/8)Dic43semidirect
268. C22×D8Dic43semidirect
277. #418Dic43semidirect
278. #416Dic43semidirect
289. C43#13102semidirect
301. C22×D4C2×Dic43semidirect
311. C2×M16C2×Dic43semidirect
312. C22×C8C2×Dic43semidirect
324. #117C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191430562
#191362672
#191362452
#191345652
#191327242
#191327162
C43×#30082
#1310243