Finite Group Databasebeta

← #24991440

Subgroups — #24991440

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#19144603C211yesmaximal, characteristic
2D4×#10621877C211yesmaximal, characteristic
3#19135538C211yesmaximal, characteristic, complemented
4#19133051C211yesmaximal, characteristic, complemented
5#19132498C211yesmaximal, characteristic, complemented
6#19132432C211yesmaximal, characteristic, complemented
7C4×#102×C43C211yesmaximal, characteristic
8C22×#10621877—21no—
9#14583456C2211yescharacteristic
10#14583229—21no—
11#14583189C411yescharacteristic, complemented
12#14583189C411yescharacteristic, complemented
13#14583104C411yescharacteristic, complemented
14#14583104C411yescharacteristic, complemented
15#14583050—21no—
16C4×#10621883—21no—
17C4×#10621883—21no—
18#14582977—21no—
19#14582971—22no—
20D4×C43⋊C8—21no—
21#14582952C2211yescharacteristic
22#14582923C2211yescharacteristic
23#14582863—21no—
24C4×#10621877C2211yescharacteristic
25#14582659—21no—
26#14582659—21no—
27#14582631—22no—
28C2×C4×D4×C43C2211yescharacteristic
29C2×#102×C43—21no—
30C2×C4×C8×C43C2211yescharacteristic
31C4×C4⋊C4×C43C2211yescharacteristic
32C43×#340—21no—
33C2×#10621883—21no—
34C2×#10621883—21no—
35C2×#10621877—22no—
36C2×#10621877—21no—
37C2×#10621877—42no—
38C2×#10621877—42no—
39C2×#10621877D411yescharacteristic
40C2×#10621877D411yescharacteristic
41C22×C43⋊C8—22no—
42#13063325C2×C411yescharacteristic
43#13063325C2×C411yescharacteristic
44#13063317—21no—
45#13063304—21no—
46#13063304—21no—
47C4×Dic86—21no—
48C4×Dic86—21no—
49#13063284—21no—
50#13063256—21no—
51#13063256—21no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)C2×C411yescharacteristic
54C4⋊(C43⋊C8)C2×C411yescharacteristic
55C4⋊(C43⋊C8)D412yes—
56#13063248—21no—
57#13063248—21no—
58#13063246—21no—
59#13063246—21no—
60C22⋊(C43⋊C8)—22no—
61C22⋊(C43⋊C8)—22no—
62C22⋊(C43⋊C8)—21no—
63#13063236—21no—
64C4×C43⋊C8—21no—
65C4×C43⋊C8—21no—
66C22×D4×C43D411yescharacteristic
67C23×C4×C43—21no—
68C22×C8×C43—21no—
69C4×D4×C43—21no—
70C4×D4×C43—21no—
71C4×D4×C43C2×C411yescharacteristic
72C4×D4×C43C2×C411yescharacteristic
73C4×D4×C43D411yescharacteristic
74C4×D4×C43D411yescharacteristic
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43D411yescharacteristic
77C2×C22⋊C4×C43—21no—
78C2×C42×C43—21no—
79C2×C42×C43C2311yescharacteristic
80#102×C43—24no—
81C4×C8×C43—21no—
82C4×C8×C43—21no—
83#95×C43—21no—
84C24×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—22no—
87C2×D4×C43—41no—
88C2×D4×C43C22⋊C411yescharacteristic
89C2×D4×C43C22⋊C411yescharacteristic
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43—41no—
98C22×C4×C43—41no—
99C22×C4×C43—41no—
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43#4111yescharacteristic
103C2×Dic86—21no—
104C2×Dic86—21no—
105C2×C8×C43—22no—
106C2×C8×C43—41no—
107C2×C8×C43—41no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—22no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43C22⋊C411yescharacteristic
112C4⋊C4×C43C22⋊C411yescharacteristic
113C22⋊C4×C43—21no—
114C22⋊C4×C43—21no—
115C22⋊C4×C43—21no—
116C22⋊C4×C43—21no—
117C42×C43—41no—
118C42×C43—41no—
119C42×C43C22×C411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43C2×D411yescharacteristic
122C42×C43#4111yescharacteristic
123C22⋊Dic43—41no—
124#10621883—42no—
125#10621883—42no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128C4⋊Dic43—21no—
129C4⋊Dic43—21no—
130Dic43⋊C4—41no—
131Dic43⋊C4—41no—
132C4×Dic43—41no—
133#10621877—21no—
134#10621877—21no—
135#10621877—21no—
136#10621877—44no—
137#10621877—41no—
138#10621877—41no—
139#10621877SD1612yescomplemented
140C2×C43⋊C8—21no—
141C2×C43⋊C8—21no—
142C2×C43⋊C8—21no—
143C2×C43⋊C8—21no—
144C2×C43⋊C8—22no—
145C2×C43⋊C8—44no—
146C23×C43—21no—
147C23×C43—21no—
148C23×C43—42no—
149C23×C43—41no—
150C23×C43—41no—
151C23×C43—81no—
152C23×C43#12111yescharacteristic
153D4×C43—21no—
154D4×C43—21no—
155D4×C43—21no—
156D4×C43—42no—
157D4×C43#10412yes—
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—42no—
174C2×C4×C43—81no—
175C2×C4×C43—81no—
176C2×C4×C43C2×C22⋊C411yescharacteristic
177C2×C4×C43C4×D411yescharacteristic
178C2×C4×C43C4×D411yescharacteristic
179C2×C4×C43#12011yescharacteristic
180C2×C4×C43#12111yescharacteristic
181C2×C4×C43#12311yescharacteristic
182C2×C4×C43C2×SD1611yescharacteristic
183C2×C4×C43#13511yescharacteristic
184C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C43#13711yescharacteristic
186C2×Dic43—41no—
187C2×Dic43—41no—
188Dic86—42no—
189Dic86—41no—
190Dic86—41no—
191C8×C43—42no—
192C43⋊C8—22no—
193C43⋊C8—41no—
194C43⋊C8—41no—
195C43⋊C8—42no—
196C43⋊C8—41no—
197#8989—431nomaximal, Sylow
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—22no—
201C22×C43—41no—
202C22×C43—41no—
203C22×C43—41no—
204C22×C43—41no—
205C22×C43—41no—
206C22×C43—82no—
207C22×C43—82no—
208C22×C43#38611yescharacteristic
209C22×C43#46111yescharacteristic
210C22×C43#46311yescharacteristic
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—41no—
215C4×C43—41no—
216C4×C43—82no—
217C4×C43C2×#10411yescharacteristic
218C4×C43#42111yescharacteristic
219C4×C43C4×SD1611yescharacteristic
220C4×C43#44011yescharacteristic
221C4×C43#45011yescharacteristic
222C4×C43#45211yescharacteristic
223Dic43—81no—
224Dic43—81no—
225#3101—431no—
226D4×M16—431no—
227#1986—431no—
228C4×#102D4311yescharacteristic
229#1493—431no—
230#1303—431no—
231#1278—431no—
232C2×C43—21no—
233C2×C43—21no—
234C2×C43—42no—
235C2×C43—81no—
236C2×C43#187111yescharacteristic
237C2×C43#187711yescharacteristic
238C2×C43#188111yescharacteristic
239C22×M16—861no—
240#533—431no—
241C2×C4×D4C2×D4311yescharacteristic
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#431—431no—
254#423—431no—
255C2×#102—21no—
256#407—861no—
257C4×M16—431no—
258C2×C4×C8C2×D4311yescharacteristic
259C4×C4⋊C4C2×D4311yescharacteristic
260#340—21no—
261#339—861no—
262#339—861no—
263Q8⋊C8—862no—
264C43#898911yescharacteristic, complemented, Sylow
265C22×D4C22⋊D4311yescharacteristic
266C23×C4—21no—
267C2×SD16—861no—
268C2×SD16—861no—
269C2×M16—431no—
270C2×M16—431no—
271C2×M16—862no—
272C2×M16—861no—
273C2×M16—1722no—
274C2×M16—1722no—
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—21no—
285C4×D4—21no—
286C4×D4C4×D4311yescharacteristic
287C4×D4C4×D4311yescharacteristic
288C4×D4D17211yescharacteristic
289C4×D4D17211yescharacteristic
290#117—861no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4C22⋊D4311yescharacteristic
293C2×C22⋊C4—21no—
294C2×C42—21no—
295C2×C42C22×D4311yescharacteristic
296#106—861no—
297#106—861no—
298C4⋊C8—431no—
299C4⋊C8—431no—
300C4⋊C8—432no—
301C4⋊C8—861no—
302#103—861no—
303#103—861no—
304#102—24no—
305#102—861no—
306#102—861no—
307C22⋊C8—862no—
308C22⋊C8—862no—
309C22⋊C8—861no—
310#97—861no—
311C4×C8—21no—
312C4×C8—21no—
313C4×C8—861no—
314C4×C8—861no—
315#95—21no—
316C24—21no—
317C2×Q8—861no—
318C2×Q8—861no—
319C2×D4—22no—
320C2×D4—21no—
321C2×D4—41no—
322C2×D4(C2×D43)⋊C411yescharacteristic
323C2×D4(C2×D43)⋊C411yescharacteristic
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4D4×D4311yescharacteristic
335C22×C4#1062190011yescharacteristic
336C22×C4C2×C22⋊D4311yescharacteristic
337SD16—1722no—
338SD16—1722no—
339M16—432no—
340M16—861no—
341M16—861no—
342M16—861no—
343M16—1724no—
344M16—1721no—
345M16—1721no—
346C2×C8—22no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—861no—
350C2×C8—861no—
351C2×C8—861no—
352C2×C8—861no—
353C2×C8—862no—
354C2×C8—1724no—
355C4⋊C4—21no—
356C4⋊C4—22no—
357C4⋊C4—41no—
358C4⋊C4—861no—
359C4⋊C4—861no—
360C4⋊C4—861no—
361C4⋊C4—861no—
362C4⋊C4—1721no—
363C4⋊C4—1721no—
364C4⋊C4(C2×D43)⋊C411yescharacteristic
365C4⋊C4(C2×D43)⋊C411yescharacteristic
366C22⋊C4—21no—
367C22⋊C4—21no—
368C22⋊C4—21no—
369C22⋊C4—21no—
370C22⋊C4—1721no—
371C42—41no—
372C42—41no—
373C42—1721no—
374C42C2×C4×D4311yescharacteristic
375C42C2×D17211yescharacteristic
376C42D4×D4311yescharacteristic
377C42#1062190011yescharacteristic
378C23—21no—
379C23—21no—
380C23—42no—
381C23—41no—
382C23—41no—
383C23—81no—
384C23#1306329711yescharacteristic
385Q8—1722no—
386Q8—1721no—
387Q8—1721no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—42no—
392D4#1306325312yes—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—1721no—
412C2×C4—1721no—
413C2×C4C2×(C2×D43)⋊C411yescharacteristic
414C2×C4(C22⋊D43)⋊C411yescharacteristic
415C2×C4(C22⋊D43)⋊C411yescharacteristic
416C2×C4#1306329511yescharacteristic
417C2×C4#1306329711yescharacteristic
418C2×C4#1306330911yescharacteristic
419C2×C4SD16×D4311yescharacteristic
420C2×C4#1306334411yescharacteristic
421C2×C4#1306334911yescharacteristic
422C2×C4#1306335411yescharacteristic
423C8—42no—
424C8—862no—
425C8—1722no—
426C8—1721no—
427C8—1721no—
428C8—1721no—
429C22—21no—
430C22—21no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—82no—
438C22—82no—
439C22#1458277611yescharacteristic
440C22#1458310211yescharacteristic
441C22#1458311211yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—41no—
446C4—41no—
447C4—82no—
448C4—3441no—
449C4—3441no—
450C4C2×#1306325311yescharacteristic
451C4#1458291711yescharacteristic
452C4#1458299011yescharacteristic
453C4#1458299611yescharacteristic
454C4#1458305111yescharacteristic
455C4#1458306211yescharacteristic
456C2—21no—
457C2—21no—
458C2—42no—
459C2—81no—
460C2#1913489511yescharacteristic
461C2#1913492711yescharacteristic
462C2#1913495511yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC4×#102×C43C2
socleC22×C43#386
prime radicalC22×D4×C43D4
cosocleC2×C42×C43C23
hypercenterC4×#102D43
hypocenterC43#8989
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
3. #19135538C2semidirect
4. #19133051C2semidirect
5. #19132498C2semidirect
6. #19132432C2semidirect
11. #14583189C4semidirect
12. #14583189C4semidirect
13. #14583104C4semidirect
14. #14583104C4semidirect
139. #10621877SD16semidirect
264. C43#8989semidirect

Maximal subgroups

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

subgroupindex
#191446032
D4×#106218772
#191355382
#191330512
#191324982
#191324322
C4×#102×C432
#898943