Finite Group Databasebeta

← #24991439

Subgroups — #24991439

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#19144599C211yesmaximal, characteristic
2#19143330C211yesmaximal, characteristic
3#19135540C211yesmaximal, characteristic, complemented
4C4×#13063247C211yesmaximal, characteristic
5#19132496C211yesmaximal, characteristic, complemented
6#19132432C211yesmaximal, characteristic, complemented
7C43×#1493C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×C4×D172C2211yescharacteristic
10#14583227—21no—
11#14583186C411yescharacteristic, complemented
12#14583186C411yescharacteristic, complemented
13#14583101C411yescharacteristic, complemented
14#14583101C411yescharacteristic, complemented
15#14583049—21no—
16C4×#10621884—21no—
17C4×#10621884—21no—
18#14582976—21no—
19#14582969—22no—
20#14582964—21no—
21#14582952C2211yescharacteristic
22C2×#13063247—21no—
23#14582862—21no—
24C4×#10621877C2211yescharacteristic
25C4×C4⋊Dic43C2211yescharacteristic
26#14582662—21no—
27#14582658—21no—
28#14582658—21no—
29C43×#533C2211yescharacteristic
30C43×#423C2211yescharacteristic
31C2×C4×C8×C43C2211yescharacteristic
32C43×Q8⋊C8—22no—
33C22×D172D411yescharacteristic
34C22×C4×D43—21no—
35C2×#10621884—21no—
36C2×#10621884—21no—
37C2×#10621877D411yescharacteristic
38C2×#10621877D411yescharacteristic
39C2×#10621872—22no—
40M16×D43—42no—
41M16×D43—42no—
42C2×C8×D43—22no—
43C4×D172—21no—
44C4×D172—21no—
45C4×D172C2×C411yescharacteristic
46C4×D172C2×C411yescharacteristic
47C4×D172D411yescharacteristic
48C4×D172D411yescharacteristic
49C2×C4⋊Dic43—21no—
50C2×C4⋊Dic43D411yescharacteristic
51C2×(C2×D43)⋊C4—21no—
52C2×C4×Dic43—21no—
53#13063256—21no—
54#13063256—21no—
55C4⋊(C43⋊C8)C2×C411yescharacteristic
56C4⋊(C43⋊C8)C2×C411yescharacteristic
57#13063249—21no—
58#13063249—21no—
59#13063247—24no—
60#13063245—21no—
61#13063245—21no—
62C22⋊(C43⋊C8)—21no—
63(C2×D43)⋊C8—22no—
64(C2×D43)⋊C8—22no—
65#13063236—21no—
66C4×C43⋊C8—21no—
67C4×C43⋊C8—21no—
68C43⋊#95—21no—
69C2×M16×C43—21no—
70C22×C8×C43—21no—
71C4⋊Q8×C43C2×C411yescharacteristic
72C4⋊Q8×C43C2×C411yescharacteristic
73#125×C43—21no—
74C22⋊Q8×C43—21no—
75C22⋊Q8×C43—21no—
76C4×Q8×C43—21no—
77C4×Q8×C43—21no—
78#117×C43—21no—
79C2×C42×C43C2311yescharacteristic
80C4⋊C8×C43—21no—
81C4⋊C8×C43D412yes—
82C4×C8×C43—21no—
83C4×C8×C43—21no—
84C23×D43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—21no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C22×Dic43—21no—
91C22×Dic43—41no—
92C2×D172—21no—
93C2×D172—22no—
94C2×D172—41no—
95C2×D172C22⋊C411yescharacteristic
96C2×D172C22⋊C411yescharacteristic
97C2×C4×D43—21no—
98C2×C4×D43—21no—
99C2×C4×D43—21no—
100C2×C4×D43—21no—
101C2×C4×D43—41no—
102C2×C4×D43—41no—
103C2×C4×D43—41no—
104C2×C4×D43—41no—
105M16×C43—41no—
106M16×C43—41no—
107C2×C8×C43—22no—
108C2×C8×C43—22no—
109C2×C8×C43—41no—
110C2×C8×C43—41no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—41no—
116C4⋊C4×C43—41no—
117C22⋊C4×C43—41no—
118C42×C43—41no—
119C42×C43C22×C411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43C2×D411yescharacteristic
122C42×C43#4111yescharacteristic
123#10621884—42no—
124#10621884—42no—
125(C2×D43)⋊C4—21no—
126(C2×D43)⋊C4—21no—
127(C2×D43)⋊C4—21no—
128(C2×D43)⋊C4—21no—
129C4⋊Dic43—21no—
130C4⋊Dic43—22no—
131C4⋊Dic43—41no—
132C4⋊Dic43C22⋊C411yescharacteristic
133C4⋊Dic43C22⋊C411yescharacteristic
134C4×Dic43—41no—
135C4×Dic43—41no—
136#10621877—21no—
137#10621877—21no—
138#10621877—21no—
139#10621877SD1612yescomplemented
140C2×C43⋊C8—21no—
141C2×C43⋊C8—21no—
142C2×C43⋊C8—21no—
143C2×C43⋊C8—21no—
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—
153Q8×C43—42no—
154Q8×C43—41no—
155Q8×C43—41no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43C2×C22⋊C411yescharacteristic
162C2×C4×C43C4×D411yescharacteristic
163C2×C4×C43C4×D411yescharacteristic
164C2×C4×C43#12011yescharacteristic
165C2×C4×C43#12111yescharacteristic
166C2×C4×C43#12311yescharacteristic
167C2×C4×C43C2×SD1611yescharacteristic
168C2×C4×C43#13511yescharacteristic
169C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C43#13711yescharacteristic
171C2×Dic43—21no—
172C2×Dic43—21no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—42no—
176C2×Dic43—81no—
177C2×Dic43—81no—
178D172—21no—
179D172—21no—
180D172—21no—
181D172—42no—
182D172#10412yes—
183C4×D43—41no—
184C4×D43—41no—
185C4×D43—41no—
186C4×D43—41no—
187C4×D43—41no—
188C4×D43—41no—
189C4×D43—41no—
190C4×D43—41no—
191C8×C43—42no—
192C8×C43—42no—
193C43⋊C8—22no—
194C43⋊C8—41no—
195C43⋊C8—41no—
196C43⋊C8—41no—
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×C43—81no—
215C4×C43—81no—
216C4×C43C2×#10411yescharacteristic
217C4×C43#42111yescharacteristic
218C4×C43C4×SD1611yescharacteristic
219C4×C43#44011yescharacteristic
220C4×C43#45011yescharacteristic
221C4×C43#45211yescharacteristic
222Dic43—41no—
223Dic43—41no—
224Dic43—82no—
225#3101—431no—
226D4×M16—431no—
227#1986—431no—
228C4×#102—431no—
229#1493D4311yescharacteristic, complemented
230#1303—431no—
231#1278—431no—
232C2×C43—21no—
233C2×C43—21no—
234C2×C43#187111yescharacteristic
235C2×C43#187711yescharacteristic
236C2×C43#188111yescharacteristic
237D43—42no—
238D43—81no—
239C22×M16—861no—
240#533C2×D4311yescharacteristic
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#431—431no—
254#423C2×D4311yescharacteristic
255C2×#102—861no—
256#407—861no—
257C4×M16—431no—
258C2×C4×C8C2×D4311yescharacteristic
259C4×C4⋊C4—431no—
260#340—861no—
261#339—861no—
262#339—861no—
263Q8⋊C8—22no—
264C43#898911yescharacteristic, complemented, Sylow
265C22×D4—431no—
266C23×C4—861no—
267C2×SD16—861no—
268C2×SD16—861no—
269C2×M16—21no—
270C2×M16—431no—
271C2×M16—431no—
272C2×M16—862no—
273C2×M16—1722no—
274C2×M16—1722no—
275C22×C8—21no—
276C22×C8—862no—
277C4⋊Q8C4×D4311yescharacteristic
278C4⋊Q8C4×D4311yescharacteristic
279#125—21no—
280C22⋊Q8—21no—
281C22⋊Q8—21no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×D4—431no—
285C4×D4—431no—
286C4×D4—431no—
287C4×D4—431no—
288C4×D4—861no—
289C4×D4—861no—
290#117—21no—
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—21no—
299C4⋊C8—431no—
300C4⋊C8—431no—
301C4⋊C8C22⋊D4312yes—
302#103—861no—
303#103—861no—
304#102—861no—
305#102—861no—
306#102—864no—
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—861no—
316C24—861no—
317C2×Q8—21no—
318C2×Q8—21no—
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×C4#1062189811yescharacteristic
335C22×C4D4×D4311yescharacteristic
336C22×C4D4×D4311yescharacteristic
337SD16—1722no—
338SD16—1722no—
339M16—41no—
340M16—41no—
341M16—432no—
342M16—861no—
343M16—861no—
344M16—861no—
345M16—1724no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—861no—
351C2×C8—861no—
352C2×C8—861no—
353C2×C8—861no—
354C2×C8—1724no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—431no—
362C4⋊C4—431no—
363C4⋊C4—862no—
364C4⋊C4—861no—
365C4⋊C4—1721no—
366C22⋊C4—41no—
367C22⋊C4—861no—
368C22⋊C4—861no—
369C22⋊C4—861no—
370C22⋊C4—861no—
371C42—41no—
372C42—1721no—
373C42—1721no—
374C42C2×C4×D4311yescharacteristic
375C42D4×D4311yescharacteristic
376C42#1062190011yescharacteristic
377C42C2×C22⋊D4311yescharacteristic
378C23—861no—
379C23—861no—
380C23—3441no—
381C23—1722no—
382C23—1721no—
383C23—1721no—
384C23#1306329811yescharacteristic
385Q8—42no—
386Q8—41no—
387Q8—41no—
388D4—432no—
389D4—861no—
390D4—861no—
391D4—861no—
392D4—1722no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—861no—
399C2×C4—861no—
400C2×C4—3441no—
401C2×C4—3441no—
402C2×C4—1722no—
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(C22⋊D43)⋊C411yescharacteristic
415C2×C4C4×C22⋊D4311yescharacteristic
416C2×C4#1306329311yescharacteristic
417C2×C4#1306329611yescharacteristic
418C2×C4#1306330711yescharacteristic
419C2×C4SD16×D4311yescharacteristic
420C2×C4#1306334811yescharacteristic
421C2×C4#1306335211yescharacteristic
422C2×C4#1306335711yescharacteristic
423C8—42no—
424C8—42no—
425C8—862no—
426C8—1721no—
427C8—1721no—
428C8—1721no—
429C22—21no—
430C22—21no—
431C22—862no—
432C22—3442no—
433C22—3442no—
434C22—1721no—
435C22—1721no—
436C22—1721no—
437C22—1721no—
438C22—1721no—
439C22#1458277511yescharacteristic
440C22#1458310311yescharacteristic
441C22#1458311711yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—81no—
446C4—81no—
447C4—3442no—
448C4—1721no—
449C4—1721no—
450C4#104×D4311yescharacteristic
451C4#1458291411yescharacteristic
452C4#1458298411yescharacteristic
453C4#1458300211yescharacteristic
454C4#1458304811yescharacteristic
455C4#1458306011yescharacteristic
456C2—21no—
457C2—21no—
458C2—3441no—
459C2—1722no—
460C2#1913489411yescharacteristic
461C2#1913492611yescharacteristic
462C2#1913496011yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1493C2
socleC22×C43#386
prime radicalC22×D172D4
cosocleC2×C42×C43C23
hypercenter#1493D43
hypocenterC43#8989
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
3. #19135540C2semidirect
5. #19132496C2semidirect
6. #19132432C2semidirect
7. C43×#1493C2semidirect
11. #14583186C4semidirect
12. #14583186C4semidirect
13. #14583101C4semidirect
14. #14583101C4semidirect
139. #10621877SD16semidirect
229. #1493D43semidirect
264. C43#8989semidirect

Maximal subgroups

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

subgroupindex
#191445992
#191433302
#191355402
C4×#130632472
#191324962
#191324322
C43×#14932
#898943