Finite Group Databasebeta

← #24991466

Subgroups — #24991466

Order 11008.

500 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144622C211yesmaximal, characteristic
2M16×Dic86C211yesmaximal, characteristic, complemented
3C4×#13063248C211yesmaximal, characteristic, complemented
4#19133046C211yesmaximal, characteristic
5#19132498C211yesmaximal, characteristic, complemented
6#19132433C211yesmaximal, characteristic, complemented
7C43×#1980C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9#14583215—21no—
10#14583181C411yescharacteristic, complemented
11#14583181C411yescharacteristic, complemented
12#14583096C411yescharacteristic, complemented
13#14583096C411yescharacteristic, complemented
14#14583037—21no—
15#14583029—21no—
16#14583027—22no—
17C8×Dic86—21no—
18C4×#10621883—21no—
19C4×#10621883—21no—
20#14582952C2211yescharacteristic
21#14582923C2211yescharacteristic
22#14582922—21no—
23C2×#13063248—21no—
24M16×Dic43—21no—
25C2×C4×C43⋊C8C2211yescharacteristic
26#14582661—21no—
27D4⋊(C43⋊C8)—22no—
28C43×#532C2211yescharacteristic
29C2×#104×C43—21no—
30C2×#104×C43—21no—
31C4×M16×C43C2211yescharacteristic
32C4×C4⋊C4×C43C2211yescharacteristic
33C22×Dic86D411yescharacteristic
34C2×#10621883—21no—
35C2×#10621883—21no—
36C2×#10621877—21no—
37C22×C43⋊C8—21no—
38C4×Dic86—21no—
39C4×Dic86—21no—
40C4×Dic86C2×C411yescharacteristic
41C4×Dic86C2×C411yescharacteristic
42C4×Dic86D411yescharacteristic
43C4×Dic86D411yescharacteristic
44C2×C4⋊Dic43D411yescharacteristic
45C2×Dic43⋊C4—21no—
46C2×C4×Dic43—21no—
47#13063256—21no—
48#13063256—21no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)C2×C411yescharacteristic
51C4⋊(C43⋊C8)C2×C411yescharacteristic
52C4⋊(C43⋊C8)D412yes—
53Dic43⋊C8—22no—
54Dic43⋊C8—22no—
55#13063248—24no—
56#13063248—21no—
57#13063248—21no—
58#13063246—21no—
59#13063246—21no—
60C22⋊(C43⋊C8)—21no—
61#13063235—22no—
62C4×C43⋊C8—21no—
63C4×C43⋊C8—21no—
64C4×C43⋊C8—21no—
65C8×Dic43—22no—
66C2×#41×C43—21no—
67C2×M16×C43D411yescharacteristic
68C2×M16×C43D411yescharacteristic
69C4⋊Q8×C43C2×C411yescharacteristic
70#127×C43C2×C411yescharacteristic
71#124×C43—21no—
72#121×C43—21no—
73#121×C43—21no—
74C4×D4×C43—21no—
75C4×D4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C42×C43—21no—
78C2×C42×C43C2311yescharacteristic
79#104×C43—42no—
80#104×C43—42no—
81#97×C43—21no—
82C4×C8×C43—21no—
83#95×C43—21no—
84#41×C43—41no—
85#41×C43—41no—
86#41×C43—41no—
87#41×C43—41no—
88C2×Q8×C43—21no—
89C2×D4×C43—21no—
90C2×D4×C43—21no—
91C2×D4×C43—21no—
92C2×D4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43#4111yescharacteristic
98C22×Dic43—21no—
99C22×Dic43—21no—
100C2×Dic86—22no—
101C2×Dic86—21no—
102C2×Dic86—41no—
103C2×Dic86C22⋊C411yescharacteristic
104C2×Dic86C22⋊C411yescharacteristic
105M16×C43—21no—
106M16×C43—21no—
107M16×C43—21no—
108M16×C43SD1612yescomplemented
109C2×C8×C43—21no—
110C2×C8×C43—21no—
111C4⋊C4×C43—22no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C42×C43—41no—
118C42×C43—41no—
119C42×C43C22×C411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43C2×D411yescharacteristic
122C42×C43#4111yescharacteristic
123#10621883—42no—
124#10621883—42no—
125C4⋊Dic43—21no—
126C4⋊Dic43C22⋊C411yescharacteristic
127C4⋊Dic43C22⋊C411yescharacteristic
128Dic43⋊C4—21no—
129Dic43⋊C4—21no—
130Dic43⋊C4—21no—
131Dic43⋊C4—21no—
132C4×Dic43—21no—
133C4×Dic43—21no—
134C4×Dic43—21no—
135C4×Dic43—21no—
136#10621877—41no—
137#10621877—41no—
138C2×C43⋊C8—22no—
139C2×C43⋊C8—21no—
140C2×C43⋊C8—21no—
141C2×C43⋊C8—22no—
142C2×C43⋊C8—41no—
143C2×C43⋊C8—41no—
144C23×C43—41no—
145C23×C43#12111yescharacteristic
146Q8×C43—41no—
147Q8×C43—41no—
148D4×C43—42no—
149D4×C43—41no—
150D4×C43—41no—
151D4×C43—41no—
152D4×C43—41no—
153D4×C43—81no—
154D4×C43—81no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—41no—
158C2×C4×C43—42no—
159C2×C4×C43—41no—
160C2×C4×C43—81no—
161C2×C4×C43—81no—
162C2×C4×C43—81no—
163C2×C4×C43—81no—
164C2×C4×C43C2×C22⋊C411yescharacteristic
165C2×C4×C43C4×D411yescharacteristic
166C2×C4×C43C4×D411yescharacteristic
167C2×C4×C43#12011yescharacteristic
168C2×C4×C43#12111yescharacteristic
169C2×C4×C43#12311yescharacteristic
170C2×C4×C43C2×SD1611yescharacteristic
171C2×C4×C43#13511yescharacteristic
172C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C43#13711yescharacteristic
174C2×Dic43—21no—
175C2×Dic43—21no—
176C2×Dic43—21no—
177C2×Dic43—21no—
178C2×Dic43—42no—
179C2×Dic43—81no—
180Dic86—21no—
181Dic86—21no—
182Dic86—21no—
183Dic86—42no—
184Dic86#10412yescomplemented
185C8×C43—22no—
186C8×C43—41no—
187C43⋊C8—42no—
188C43⋊C8—41no—
189C43⋊C8—41no—
190C43⋊C8—42no—
191#8992—431nomaximal, Sylow
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—81no—
195C22×C43—81no—
196C22×C43—81no—
197C22×C43#38611yescharacteristic
198C22×C43#46011yescharacteristic
199C22×C43#46411yescharacteristic
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—82no—
204C4×C43—81no—
205C4×C43C2×#10411yescharacteristic
206C4×C43#42111yescharacteristic
207C4×C43C4×SD1611yescharacteristic
208C4×C43#44011yescharacteristic
209C4×C43#44811yescharacteristic
210C4×C43#44911yescharacteristic
211Dic43—22no—
212Dic43—41no—
213Dic43—41no—
214Dic43—41no—
215#3103—431no—
216Q8×M16—431no—
217#1980D4311yescharacteristic
218C4×#103—431no—
219#1492—431no—
220#1303—431no—
221#1278—431no—
222C2×C43—21no—
223C2×C43—21no—
224C2×C43—161no—
225C2×C43#187111yescharacteristic
226C2×C43#188011yescharacteristic
227C2×C43#188111yescharacteristic
228#532C2×D4311yescharacteristic
229C2×C4×Q8—431no—
230#481—861no—
231#475—431no—
232#475—431no—
233#460—431no—
234#460—431no—
235#448—861no—
236#446—861no—
237#446—862no—
238C8×Q8—861no—
239C4×SD16—861no—
240C4×SD16—861no—
241#431—431no—
242#423—431no—
243#423—861no—
244C2×#104—21no—
245C2×#104—21no—
246C2×#103—861no—
247C4×M16—861no—
248C4×M16C2×D4311yescharacteristic
249C2×C4×C8—431no—
250C4×C4⋊C4C2×D4311yescharacteristic
251#340—861no—
252D4⋊C8—862no—
253C43#899211yescharacteristic, complemented, Sylow
254C2×#41—21no—
255C22×Q8—431no—
256C2×SD16—861no—
257C2×SD16—861no—
258C2×M16—861no—
259C2×M16C22⋊D4311yescharacteristic
260C2×M16C22⋊D4311yescharacteristic
261C22×C8—861no—
262C4⋊Q8C4×D4311yescharacteristic
263#127C4×D4311yescharacteristic
264#124—21no—
265#121—21no—
266#121—21no—
267C4×Q8—431no—
268C4×Q8—431no—
269C4×Q8—431no—
270C4×Q8—431no—
271C4×Q8—861no—
272C4×Q8—861no—
273C4×D4—21no—
274C4×D4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—431no—
277C2×C4⋊C4—861no—
278C2×C42—21no—
279C2×C42—861no—
280C2×C42C22×D4311yescharacteristic
281#106—861no—
282#106—861no—
283C4⋊C8—431no—
284C4⋊C8—431no—
285C4⋊C8—432no—
286C4⋊C8—862no—
287C4⋊C8—862no—
288C4⋊C8—861no—
289#104—42no—
290#104—42no—
291#103—861no—
292#103—861no—
293#103—864no—
294#102—861no—
295#102—861no—
296C22⋊C8—861no—
297#97—21no—
298#97—862no—
299C4×C8—21no—
300C4×C8—862no—
301C4×C8—861no—
302C4×C8—861no—
303C4×C8—861no—
304#95—21no—
305#41—41no—
306#41—41no—
307#41—41no—
308#41—41no—
309C2×Q8—21no—
310C2×Q8—431no—
311C2×Q8—431no—
312C2×Q8—862no—
313C2×Q8—861no—
314C2×Q8—1721no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—861no—
322C22×C4—861no—
323C22×C4D4×D4311yescharacteristic
324C22×C4#1062190011yescharacteristic
325C22×C4C2×C22⋊D4311yescharacteristic
326SD16—1722no—
327SD16—1722no—
328M16—21no—
329M16—21no—
330M16—21no—
331M16—1721no—
332M16—1721no—
333M16#1062188312yescomplemented
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—862no—
337C2×C8—861no—
338C2×C8—861no—
339C2×C8—862no—
340C2×C8—1721no—
341C2×C8—1721no—
342C4⋊C4—22no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—41no—
346C4⋊C4—431no—
347C4⋊C4—431no—
348C4⋊C4—861no—
349C4⋊C4—861no—
350C4⋊C4—861no—
351C4⋊C4—861no—
352C4⋊C4—861no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C42—41no—
356C42—41no—
357C42—861no—
358C42—861no—
359C42—861no—
360C42—861no—
361C42C2×C4×D4311yescharacteristic
362C42#1062189811yescharacteristic
363C42D4×D4311yescharacteristic
364C42D4×D4311yescharacteristic
365C23—41no—
366C23#1306329611yescharacteristic
367Q8—41no—
368Q8—41no—
369Q8—432no—
370Q8—861no—
371Q8—861no—
372Q8—861no—
373Q8—1722no—
374D4—42no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—81no—
380D4—81no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—861no—
391C2×C4—861no—
392C2×C4—861no—
393C2×C4—861no—
394C2×C4—3441no—
395C2×C4—1722no—
396C2×C4C22⋊C4×D4311yescharacteristic
397C2×C4(C22⋊D43)⋊C411yescharacteristic
398C2×C4C4×C22⋊D4311yescharacteristic
399C2×C4#1306329311yescharacteristic
400C2×C4#1306329811yescharacteristic
401C2×C4#1306330711yescharacteristic
402C2×C4C2×#1062188311yescharacteristic
403C2×C4#1306334511yescharacteristic
404C2×C4#1306335111yescharacteristic
405C2×C4#1306335511yescharacteristic
406C8—22no—
407C8—41no—
408C8—1722no—
409C8—1722no—
410C8—1721no—
411C8—1721no—
412C22—21no—
413C22—21no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22#1458277511yescharacteristic
418C22#1458309611yescharacteristic
419C22#1458311811yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—82no—
424C4—81no—
425C4—862no—
426C4—1721no—
427C4—1721no—
428C4—1721no—
429C4#104×D4311yescharacteristic
430C4#1458291411yescharacteristic
431C4C4×#1062188311yescharacteristic
432C4#1458299911yescharacteristic
433C4#1458303711yescharacteristic
434C4#1458304211yescharacteristic
435C2—21no—
436C2—21no—
437C2—161no—
438C2#1913489411yescharacteristic
439C2#1913495311yescharacteristic
440C2#1913495411yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1980C2
socleC22×C43#386
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#1980D43
hypocenterC43#8992
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
2. M16×Dic86C2semidirect
3. C4×#13063248C2semidirect
5. #19132498C2semidirect
6. #19132433C2semidirect
10. #14583181C4semidirect
11. #14583181C4semidirect
12. #14583096C4semidirect
13. #14583096C4semidirect
108. M16×C43SD16semidirect
184. Dic86#104semidirect
253. C43#8992semidirect
333. M16#10621883semidirect

Maximal subgroups

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

subgroupindex
#191446222
M16×Dic862
C4×#130632482
#191330462
#191324982
#191324332
C43×#19802
#899243