Finite Group Databasebeta

← #24991441

Subgroups — #24991441

Order 11008.

540 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144604C211yesmaximal, characteristic
2M16×D172C211yesmaximal, characteristic
3#19135539C211yesmaximal, characteristic, complemented
4C4×#13063247C211yesmaximal, characteristic
5#19133051C211yesmaximal, characteristic, complemented
6#19132497C211yesmaximal, characteristic, complemented
7C43×#1278C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9#14583456C2211yescharacteristic
10C2×C4×D172C2211yescharacteristic
11#14583230—21no—
12#14583190C411yescharacteristic, complemented
13#14583190C411yescharacteristic, complemented
14#14583105C411yescharacteristic, complemented
15#14583105C411yescharacteristic, complemented
16#14583052—21no—
17C4×#10621873—21no—
18C4×#10621873—21no—
19#14582978—21no—
20#14582972—22no—
21C8×D172—21no—
22#14582923C2211yescharacteristic
23C2×#13063247—21no—
24#14582862—21no—
25C4×C4⋊Dic43C2211yescharacteristic
26#14582662—21no—
27#14582660—21no—
28#14582660—21no—
29#14582631—22no—
30C43×#431C2211yescharacteristic
31C4×M16×C43C2211yescharacteristic
32C2×C4×C8×C43C2211yescharacteristic
33C22×D172D411yescharacteristic
34C22×C4×D43—21no—
35C2×#10621873—21no—
36C2×#10621873—21no—
37C2×#10621877—21no—
38C2×#10621872—22no—
39M16×D43—42no—
40M16×D43—42no—
41C2×C8×D43—22no—
42#13063325C2×C411yescharacteristic
43#13063325C2×C411yescharacteristic
44#13063317—21no—
45#13063304—21no—
46#13063304—21no—
47C4×Dic86—21no—
48C4×Dic86—21no—
49C4×D172—21no—
50C4×D172—21no—
51C4×D172C2×C411yescharacteristic
52C4×D172C2×C411yescharacteristic
53C4×D172D411yescharacteristic
54C4×D172D411yescharacteristic
55#13063284—21no—
56C2×C4⋊Dic43—21no—
57C2×C4⋊Dic43D411yescharacteristic
58C2×(C2×D43)⋊C4—21no—
59C2×C4×Dic43—21no—
60#13063257—21no—
61#13063257—21no—
62C4⋊(C43⋊C8)—21no—
63C4⋊(C43⋊C8)D412yes—
64#13063250—21no—
65#13063250—21no—
66#13063247—24no—
67#13063247—21no—
68#13063247—21no—
69(C2×D43)⋊C8—22no—
70(C2×D43)⋊C8—22no—
71C43⋊#95—21no—
72C2×M16×C43D411yescharacteristic
73C2×M16×C43D411yescharacteristic
74C22×C8×C43—21no—
75C2×C42×C43C2311yescharacteristic
76C4⋊C8×C43C2×C411yescharacteristic
77C4⋊C8×C43C2×C411yescharacteristic
78C22⋊C8×C43—21no—
79#97×C43—21no—
80C4×C8×C43—21no—
81C4×C8×C43—21no—
82C4×C8×C43—21no—
83C4×C8×C43—21no—
84C23×D43—21no—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43#4111yescharacteristic
88C22×Dic43—21no—
89C22×Dic43—41no—
90C2×D172—21no—
91C2×D172—22no—
92C2×D172—41no—
93C2×D172C22⋊C411yescharacteristic
94C2×D172C22⋊C411yescharacteristic
95C2×C4×D43—21no—
96C2×C4×D43—21no—
97C2×C4×D43—21no—
98C2×C4×D43—21no—
99C2×C4×D43—41no—
100C2×C4×D43—41no—
101C2×C4×D43—41no—
102C2×C4×D43—41no—
103C2×Dic86—21no—
104C2×Dic86—21no—
105M16×C43—21no—
106M16×C43—21no—
107M16×C43—21no—
108M16×C43SD1612yescomplemented
109C2×C8×C43—21no—
110C2×C8×C43—22no—
111C2×C8×C43—21no—
112C2×C8×C43—21no—
113C2×C8×C43—21no—
114C2×C8×C43—41no—
115C2×C8×C43—41no—
116C42×C43C22×C411yescharacteristic
117C42×C43C2×D411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43#4111yescharacteristic
120C22⋊Dic43—41no—
121(C2×D43)⋊C4—21no—
122(C2×D43)⋊C4—21no—
123(C2×D43)⋊C4—21no—
124(C2×D43)⋊C4—21no—
125C4⋊Dic43—21no—
126C4⋊Dic43—22no—
127C4⋊Dic43—21no—
128C4⋊Dic43—21no—
129C4⋊Dic43—21no—
130C4⋊Dic43—21no—
131C4⋊Dic43—41no—
132C4⋊Dic43C22⋊C411yescharacteristic
133C4⋊Dic43C22⋊C411yescharacteristic
134Dic43⋊C4—41no—
135Dic43⋊C4—41no—
136C4×Dic43—41no—
137C4×Dic43—41no—
138C4×Dic43—41no—
139#10621877—41no—
140#10621877—41no—
141C2×C43⋊C8—22no—
142#10621873—42no—
143#10621873—42no—
144#10621872—44no—
145C8×D43—44no—
146C23×C43#12111yescharacteristic
147C22×D43—21no—
148C22×D43—21no—
149C22×D43—42no—
150C22×D43—41no—
151C22×D43—41no—
152C22×D43—81no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—41no—
156C2×C4×C43C2×C22⋊C411yescharacteristic
157C2×C4×C43C4×D411yescharacteristic
158C2×C4×C43C4×D411yescharacteristic
159C2×C4×C43#12011yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12311yescharacteristic
162C2×C4×C43C2×SD1611yescharacteristic
163C2×C4×C43#13511yescharacteristic
164C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C43#13711yescharacteristic
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—42no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—81no—
174C2×Dic43—81no—
175D172—21no—
176D172—21no—
177D172—21no—
178D172—42no—
179D172#10412yes—
180C4×D43—41no—
181C4×D43—41no—
182C4×D43—41no—
183C4×D43—41no—
184C4×D43—41no—
185C4×D43—41no—
186C4×D43—41no—
187C4×D43—41no—
188Dic86—42no—
189Dic86—41no—
190Dic86—41no—
191C8×C43—22no—
192C8×C43—42no—
193C8×C43—41no—
194C8×C43—41no—
195C8×C43—41no—
196C43⋊C8—42no—
197#8989—431nomaximal, Sylow
198C22×C43—21no—
199C22×C43—21no—
200C22×C43#38611yescharacteristic
201C22×C43#46111yescharacteristic
202C22×C43#46311yescharacteristic
203C2×D43—22no—
204C2×D43—41no—
205C2×D43—41no—
206C2×D43—41no—
207C2×D43—41no—
208C2×D43—41no—
209C2×D43—82no—
210C2×D43—82no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43C2×#10411yescharacteristic
215C4×C43#42111yescharacteristic
216C4×C43C4×SD1611yescharacteristic
217C4×C43#44011yescharacteristic
218C4×C43#45011yescharacteristic
219C4×C43#45211yescharacteristic
220Dic43—41no—
221Dic43—41no—
222Dic43—82no—
223Dic43—81no—
224Dic43—81no—
225#3101—431no—
226D4×M16—431no—
227#1986—431no—
228C4×#102—431no—
229#1493—431no—
230#1303—431no—
231#1278D4311yescharacteristic, complemented
232C2×C43—21no—
233C2×C43—21no—
234C2×C43#187111yescharacteristic
235C2×C43#187711yescharacteristic
236C2×C43#188111yescharacteristic
237D43—42no—
238D43—81no—
239C22×M16—861no—
240#533—431no—
241C2×C4×D4—431no—
242#483—861no—
243#476—431no—
244#476—431no—
245#461—431no—
246#461—431no—
247#450—861no—
248C4×SD16—861no—
249C4×SD16—861no—
250#436—861no—
251#435—862no—
252C8×D4—861no—
253#431C2×D4311yescharacteristic
254#423—431no—
255C2×#102—861no—
256#407—861no—
257C4×M16C2×D4311yescharacteristic
258C2×C4×C8C2×D4311yescharacteristic
259C4×C4⋊C4—431no—
260#340—861no—
261#339—861no—
262#339—861no—
263Q8⋊C8—862no—
264C43#898911yescharacteristic, complemented, Sylow
265C22×D4—431no—
266C23×C4—861no—
267C2×SD16—861no—
268C2×SD16—861no—
269C2×M16—862no—
270C2×M16—861no—
271C2×M16—1722no—
272C2×M16—1722no—
273C2×M16D17211yescharacteristic
274C2×M16D17211yescharacteristic
275C22×C8—21no—
276C22×C8—862no—
277C4⋊Q8—431no—
278C4⋊Q8—431no—
279#125—861no—
280C22⋊Q8—861no—
281C22⋊Q8—861no—
282C4×Q8—861no—
283C4×Q8—861no—
284C4×D4—431no—
285C4×D4—431no—
286C4×D4—431no—
287C4×D4—431no—
288C4×D4—861no—
289C4×D4—861no—
290#117—861no—
291C2×C4⋊C4—431no—
292C2×C4⋊C4—861no—
293C2×C22⋊C4—861no—
294C2×C42—861no—
295C2×C42C22×D4311yescharacteristic
296#106—861no—
297#106—861no—
298C4⋊C8—432no—
299C4⋊C8—861no—
300C4⋊C8C4×D4311yescharacteristic
301C4⋊C8C4×D4311yescharacteristic
302#103—861no—
303#103—861no—
304#102—861no—
305#102—861no—
306#102—864no—
307C22⋊C8—21no—
308C22⋊C8—862no—
309C22⋊C8—862no—
310#97—21no—
311C4×C8—21no—
312C4×C8—21no—
313C4×C8—21no—
314C4×C8—21no—
315#95—861no—
316C24—861no—
317C2×Q8—861no—
318C2×Q8—861no—
319C2×D4—431no—
320C2×D4—431no—
321C2×D4—862no—
322C2×D4—861no—
323C2×D4—1721no—
324C22×C4—861no—
325C22×C4—861no—
326C22×C4—861no—
327C22×C4—861no—
328C22×C4—861no—
329C22×C4—1721no—
330C22×C4—1721no—
331C22×C4—1721no—
332C22×C4—1721no—
333C22×C4—1721no—
334C22×C4C2×D17211yescharacteristic
335C22×C4D4×D4311yescharacteristic
336C22×C4#1062190211yescharacteristic
337SD16—1722no—
338SD16—1722no—
339M16—21no—
340M16—21no—
341M16—21no—
342M16—1724no—
343M16—1721no—
344M16—1721no—
345M16#1062187312yescomplemented
346C2×C8—21no—
347C2×C8—22no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—862no—
354C2×C8—1724no—
355C4⋊C4—431no—
356C4⋊C4—431no—
357C4⋊C4—862no—
358C4⋊C4—861no—
359C4⋊C4—861no—
360C4⋊C4—861no—
361C4⋊C4—861no—
362C4⋊C4—861no—
363C4⋊C4—1721no—
364C4⋊C4—1721no—
365C4⋊C4—1721no—
366C22⋊C4—861no—
367C22⋊C4—861no—
368C22⋊C4—861no—
369C22⋊C4—861no—
370C22⋊C4—1721no—
371C42—1721no—
372C42—1721no—
373C42—1721no—
374C42C2×C4×D4311yescharacteristic
375C42#1062189811yescharacteristic
376C42D4×D4311yescharacteristic
377C42D4×D4311yescharacteristic
378C23—861no—
379C23—861no—
380C23—3441no—
381C23—1722no—
382C23—1721no—
383C23—1721no—
384C23#1306330011yescharacteristic
385Q8—1722no—
386Q8—1721no—
387Q8—1721no—
388D4—432no—
389D4—861no—
390D4—861no—
391D4—861no—
392D4—1722no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—861no—
397C2×C4—861no—
398C2×C4—3441no—
399C2×C4—3441no—
400C2×C4—1722no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4—1721no—
404C2×C4—1721no—
405C2×C4—1721no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4—1721no—
409C2×C4—1721no—
410C2×C4—1721no—
411C2×C4—1721no—
412C2×C4—1721no—
413C2×C4C22⋊C4×D4311yescharacteristic
414C2×C4#1306328711yescharacteristic
415C2×C4C4×D17211yescharacteristic
416C2×C4#1306329511yescharacteristic
417C2×C4#1306329811yescharacteristic
418C2×C4#1306331011yescharacteristic
419C2×C4C2×#1062187311yescharacteristic
420C2×C4#1306334711yescharacteristic
421C2×C4#1306335311yescharacteristic
422C2×C4#1306335811yescharacteristic
423C8—22no—
424C8—42no—
425C8—41no—
426C8—41no—
427C8—41no—
428C8—1722no—
429C22—21no—
430C22—21no—
431C22—862no—
432C22—3442no—
433C22—3442no—
434C22—1721no—
435C22—1721no—
436C22—1721no—
437C22—1721no—
438C22—1721no—
439C22#1458277711yescharacteristic
440C22#1458310511yescharacteristic
441C22#1458311511yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—3442no—
446C4—3441no—
447C4—3441no—
448C4—1721no—
449C4—1721no—
450C4#104×D4311yescharacteristic
451C4#1458291411yescharacteristic
452C4C4×#1062187311yescharacteristic
453C4#1458300111yescharacteristic
454C4#1458305211yescharacteristic
455C4#1458306311yescharacteristic
456C2—21no—
457C2—21no—
458C2—3441no—
459C2—1722no—
460C2#1913489611yescharacteristic
461C2#1913492811yescharacteristic
462C2#1913495811yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1278C2
socleC22×C43#386
prime radicalC22×D172D4
cosocleC2×C42×C43C23
hypercenter#1278D43
hypocenterC43#8989
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
3. #19135539C2semidirect
5. #19133051C2semidirect
6. #19132497C2semidirect
7. C43×#1278C2semidirect
12. #14583190C4semidirect
13. #14583190C4semidirect
14. #14583105C4semidirect
15. #14583105C4semidirect
108. M16×C43SD16semidirect
231. #1278D43semidirect
264. C43#8989semidirect
345. M16#10621873semidirect

Maximal subgroups

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

subgroupindex
#191446042
M16×D1722
#191355392
C4×#130632472
#191330512
#191324972
C43×#12782
#898943