Finite Group Databasebeta

← #25072706

Subgroups — #25072706

Order 11008.

962 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583610C211yesmaximal, characteristic
2#19144721C211yesmaximal, characteristic, complemented
3#19144690C211yesmaximal, characteristic
4#19133806C214yesmaximal, complemented
5#19133799C214yesmaximal, complemented
6#19133321C211yesmaximal, characteristic, complemented
7#19133043C211yesmaximal, characteristic, complemented
8#19133039C211yesmaximal, characteristic
9C43×#3139C211yesmaximal, characteristic, complemented
10#14583610—22no—
11#14583610—22no—
12#14583610—22no—
13#14583610C2214yes—
14C2×#13063316—21no—
15C2×#13063305—21no—
16C2×#13063301—22no—
17C2×C4×Dic86C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063287—21no—
20C2×C4⋊C4×D43—21no—
21#14583232—21no—
22#14583227—21no—
23#14583181C2212yescomplemented
24#14583176C2212yes—
25#14583106C2212yescomplemented
26#14583101C2212yes—
27#14583054—21no—
28#14583049—21no—
29#14583004—22no—
30#14582997—22no—
31#14582956C2211yescharacteristic
32#14582956C2211yescharacteristic
33#14582648C2214yescomplemented
34#14582631C2214yescomplemented
35#14582628C2214yes—
36C43×#533C2211yescharacteristic
37C2×C4⋊Q8×C43C2211yescharacteristic
38C43×#491—22no—
39C43×#487C2212yescomplemented
40C43×#487C2212yescomplemented
41C43×#419—22no—
42C4×M16×C43C2211yescharacteristic
43C22×Dic86D411yescharacteristic
44C22×D172D411yescharacteristic
45C22×C4×D43—21no—
46C22×C4×D43—22no—
47C2×#10621885—22no—
48C2×#10621884—22no—
49#13063316—24no—
50#13063316—24no—
51#13063305—24no—
52#13063305—24no—
53#13063301—28no—
54#13063301—28no—
55C4×Dic86—21no—
56C4×Dic86—21no—
57C4×Dic86D412yes—
58C4×Dic86C2312yes—
59C4×D172—21no—
60C4×D172—21no—
61C4×D172D412yes—
62C4×D172C2312yes—
63#13063287—24no—
64#13063287—24no—
65C2×C4⋊Dic43—22no—
66C2×C4⋊Dic43D411yescharacteristic
67C2×C4⋊Dic43D411yescharacteristic
68C2×Dic43⋊C4—22no—
69C2×Dic43⋊C4—21no—
70C4⋊C4×D43—24no—
71C4⋊C4×D43—24no—
72C2×(C2×D43)⋊C4—22no—
73C2×(C2×D43)⋊C4—21no—
74C2×C4×Dic43—21no—
75#13063258—22no—
76#13063256—22no—
77C4⋊(C43⋊C8)C2312yes—
78C4⋊(C43⋊C8)C2312yes—
79#13063249—22no—
80#13063249—22no—
81#13063248—22no—
82#13063245—22no—
83C22⋊(C43⋊C8)—21no—
84C22⋊(C43⋊C8)—21no—
85#13063236—21no—
86#13063236—21no—
87C22×Q8×C43D412yes—
88C2×M16×C43—21no—
89C4⋊Q8×C43—21no—
90C4⋊Q8×C43—21no—
91C4⋊Q8×C43D412yes—
92C4⋊Q8×C43C2311yescharacteristic
93C4⋊Q8×C43C2311yescharacteristic
94C4⋊Q8×C43C2312yes—
95#125×C43—21no—
96C22⋊Q8×C43—21no—
97C22⋊Q8×C43—21no—
98C4×Q8×C43—21no—
99C4×Q8×C43—21no—
100#117×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C42×C43C2311yescharacteristic
104#103×C43—24no—
105#103×C43—24no—
106#97×C43—21no—
107C4×C8×C43C2312yes—
108C23×D43—21no—
109C2×Q8×C43—22no—
110C2×Q8×C43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—44no—
113C2×Q8×C43C2×D414yes—
114C22×C4×C43—22no—
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×Dic43—21no—
119C22×Dic43—21no—
120C22×Dic43—21no—
121C2×D172—21no—
122C2×D172—24no—
123C2×D172C2×D412yes—
124C2×C4×D43—22no—
125C2×C4×D43—22no—
126C2×C4×D43—28no—
127C2×C4×D43—44no—
128C2×C4×D43—84no—
129C2×Dic86—21no—
130C2×Dic86—42no—
131C2×Dic86C2×D412yes—
132M16×C43—42no—
133C2×C8×C43—22no—
134C4⋊C4×C43—22no—
135C4⋊C4×C43—22no—
136C4⋊C4×C43—22no—
137C4⋊C4×C43—22no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—41no—
143C4⋊C4×C43—41no—
144C22⋊C4×C43—41no—
145C42×C43—41no—
146C42×C43C2×D411yescharacteristic
147C42×C43C2×D411yescharacteristic
148C42×C43C2×D411yescharacteristic
149C42×C43C2411yescharacteristic
150#10621885—44no—
151#10621884—44no—
152(C2×D43)⋊C4—28no—
153(C2×D43)⋊C4—22no—
154(C2×D43)⋊C4—22no—
155C4⋊Dic43—28no—
156C4⋊Dic43—21no—
157C4⋊Dic43—21no—
158C4⋊Dic43C2×D412yes—
159C4⋊Dic43C2×D412yes—
160Dic43⋊C4—28no—
161Dic43⋊C4—22no—
162Dic43⋊C4—22no—
163C4×Dic43—22no—
164C4×Dic43—22no—
165C2×C43⋊C8—22no—
166C2×C43⋊C8—22no—
167C23×C43#12011yescharacteristic
168C22×D43—24no—
169C22×D43—22no—
170C22×D43—42no—
171C22×D43—42no—
172Q8×C43—44no—
173Q8×C43—42no—
174Q8×C43—42no—
175Q8×C43—82no—
176C2×C4×C43—22no—
177C2×C4×C43—22no—
178C2×C4×C43—22no—
179C2×C4×C43—24no—
180C2×C4×C43—44no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43#12011yescharacteristic
184C2×C4×C43#12011yescharacteristic
185C2×C4×C43#12011yescharacteristic
186C2×C4×C43C22×D411yescharacteristic
187C2×C4×C43C22×D411yescharacteristic
188C2×C4×C43C22×D411yescharacteristic
189C2×Dic43—22no—
190C2×Dic43—22no—
191C2×Dic43—22no—
192C2×Dic43—42no—
193C2×Dic43—42no—
194C2×Dic43—42no—
195D172—24no—
196D172—22no—
197D172#13714yes—
198C4×D43—44no—
199C4×D43—44no—
200C4×D43—88no—
201Dic86—22no—
202Dic86—22no—
203Dic86—42no—
204C8×C43—42no—
205C43⋊C8—42no—
206C43⋊C8—42no—
207#18530—431nomaximal, Sylow
208C22×C43—21no—
209C22×C43—21no—
210C22×C43#45512yes—
211C22×C43C2×#12011yescharacteristic
212C2×D43—24no—
213C2×D43—48no—
214C2×D43—42no—
215C2×D43—42no—
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—21no—
219C4×C43—21no—
220C4×C43—44no—
221C4×C43—81no—
222C4×C43—81no—
223C4×C43C2×#13712yes—
224C4×C43#57512yes—
225Dic43—42no—
226Dic43—42no—
227Dic43—42no—
228C2×#554—431no—
229#3139D4311yescharacteristic, complemented
230#3113—431no—
231#3110—431no—
232#1644—434no—
233#1643—434no—
234#1558—431no—
235#1491—431no—
236#1490—431no—
237C2×C43—22no—
238C2×C43#300411yescharacteristic
239C2×C43#300511yescharacteristic
240C2×C43C2×#45511yescharacteristic
241D43—44no—
242#554—434no—
243#554—862no—
244#554—862no—
245#554—862no—
246#533C2×D4311yescharacteristic
247C2×C4⋊Q8C2×D4311yescharacteristic
248C2×#125—861no—
249C2×C22⋊Q8—861no—
250C2×C22⋊Q8—862no—
251C2×C4×Q8—431no—
252C2×C4×D4—431no—
253C2×C4×D4—861no—
254C22×C4⋊C4—861no—
255#491—22no—
256#487C2×D4312yescomplemented
257#487C2×D4312yescomplemented
258#484—861no—
259#483—861no—
260#475—432no—
261#474—432no—
262#462—432no—
263#461—432no—
264#451—861no—
265#450—861no—
266#441—862no—
267#440—862no—
268#432—431no—
269#432—431no—
270#419—22no—
271C4×M16C2×D4311yescharacteristic
272#333—434no—
273Q8⋊C8—434no—
274D4⋊C8—434no—
275C43#1853011yescharacteristic, complemented, Sylow
276C22×Q8—431no—
277C22×Q8C22⋊D4312yes—
278C22×D4—431no—
279C23×C4—862no—
280C23×C4—861no—
281C2×Q16—862no—
282C2×SD16—862no—
283C2×M16—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8C22⋊D4312yes—
287C4⋊Q8C22×D4311yescharacteristic
288C4⋊Q8C22×D4311yescharacteristic
289C4⋊Q8C22×D4312yes—
290#125—21no—
291#125—864no—
292#125—864no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—864no—
296C22⋊Q8—864no—
297C22⋊Q8—868no—
298C22⋊Q8—868no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8—432no—
302C4×Q8—432no—
303C4×Q8—861no—
304C4×Q8—861no—
305C4×D4—432no—
306C4×D4—432no—
307C4×D4—864no—
308C4×D4—864no—
309C4×D4—861no—
310C4×D4—861no—
311#117—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—431no—
315C2×C4⋊C4—431no—
316C2×C4⋊C4—864no—
317C2×C4⋊C4—864no—
318C2×C4⋊C4—862no—
319C2×C4⋊C4—862no—
320C2×C4⋊C4—861no—
321C2×C22⋊C4—862no—
322C2×C22⋊C4—861no—
323C2×C42—861no—
324C2×C42C22×D4311yescharacteristic
325#107—862no—
326#106—862no—
327C4⋊C8—432no—
328C4⋊C8—432no—
329#103—24no—
330#103—24no—
331#103—862no—
332#103—862no—
333#103—862no—
334#102—862no—
335C22⋊C8—861no—
336C22⋊C8—861no—
337#97—21no—
338#97—861no—
339#97—861no—
340C4×C8C22×D4312yes—
341C24—861no—
342C2×Q8—22no—
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—44no—
346C2×Q8—432no—
347C2×Q8—861no—
348C2×Q8—1722no—
349C2×Q8C2×C22⋊D4314yes—
350C2×D4—432no—
351C2×D4—864no—
352C2×D4—861no—
353C22×C4—22no—
354C22×C4—868no—
355C22×C4—861no—
356C22×C4—861no—
357C22×C4—861no—
358C22×C4—862no—
359C22×C4—862no—
360C22×C4—3444no—
361C22×C4—1724no—
362C22×C4D4×D4311yescharacteristic
363C22×C4D4×D4311yescharacteristic
364C22×C4C2×C22⋊D4311yescharacteristic
365Q16—1724no—
366SD16—1724no—
367M16—42no—
368C2×C8—22no—
369C2×C8—862no—
370C2×C8—862no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—432no—
382C4⋊C4—432no—
383C4⋊C4—868no—
384C4⋊C4—868no—
385C4⋊C4—861no—
386C4⋊C4—861no—
387C4⋊C4—862no—
388C4⋊C4—862no—
389C22⋊C4—41no—
390C22⋊C4—868no—
391C22⋊C4—862no—
392C22⋊C4—862no—
393C42—41no—
394C42—862no—
395C42—862no—
396C42D4×D4311yescharacteristic
397C42D4×D4311yescharacteristic
398C42C2×C22⋊D4311yescharacteristic
399C42C23×D4311yescharacteristic
400C23—864no—
401C23—862no—
402C23—1722no—
403C23—1722no—
404C23#1306329311yescharacteristic
405Q8—44no—
406Q8—42no—
407Q8—42no—
408Q8—82no—
409Q8—862no—
410Q8—862no—
411Q8—1722no—
412D4—434no—
413D4—864no—
414D4—862no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—44no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—862no—
423C2×C4—862no—
424C2×C4—862no—
425C2×C4—3448no—
426C2×C4—1724no—
427C2×C4—1722no—
428C2×C4—1722no—
429C2×C4—1722no—
430C2×C4—1724no—
431C2×C4#1306329311yescharacteristic
432C2×C4#1306329311yescharacteristic
433C2×C4#1306329311yescharacteristic
434C2×C4C2×D4×D4311yescharacteristic
435C2×C4C2×D4×D4311yescharacteristic
436C2×C4C22×C22⋊D4311yescharacteristic
437C8—42no—
438C8—1722no—
439C8—1722no—
440C22—21no—
441C22—21no—
442C22—864no—
443C22—1728no—
444C22—1722no—
445C22—1722no—
446C22#1458307612yes—
447C22C2×#1306329311yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—44no—
453C4—81no—
454C4—81no—
455C4—1722no—
456C4—1722no—
457C4—1722no—
458C4#137×D4312yes—
459C4#1458369812yes—
460C2—22no—
461C2—1724no—
462C2#1914382711yescharacteristic
463C2#1914383611yescharacteristic
464C2C2×#1458307611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3139C2
socleC22×C43C2×#120
prime radicalC22×D172D4
hypercenter#3139D43
hypocenterC43#18530
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
2. #19144721C2semidirect
4. #19133806C2semidirect
5. #19133799C2semidirect
6. #19133321C2semidirect
7. #19133043C2semidirect
9. C43×#3139C2semidirect
23. #14583181C22semidirect
25. #14583106C22semidirect
33. #14582648C22semidirect
34. #14582631C22semidirect
39. C43×#487C22semidirect
40. C43×#487C22semidirect
229. #3139D43semidirect
256. #487C2×D43semidirect
257. #487C2×D43semidirect
275. C43#18530semidirect

Maximal subgroups

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

subgroupindex
C2×#145836102
#191447212
#191446902
#191338062
#191337992
#191333212
#191330432
#191330392
C43×#31392
#1853043