Finite Group Databasebeta

← #25069150

Subgroups — #25069150

Order 11008.

904 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148000C211yesmaximal, characteristic
2#19144725C212yesmaximal, complemented
3#19133602C212yesmaximal, complemented
4#19133585C212yesmaximal
5#19133568C212yesmaximal, complemented
6#19133551C212yesmaximal
7#19133145C212yesmaximal, complemented
8#19132929C211yesmaximal, characteristic
9C43×#2599C211yesmaximal, characteristic
10#14583530—21no—
11#14583530C2212yes—
12#14583527—22no—
13#14583527—22no—
14#14583525—21no—
15#14583525C2212yes—
16#14583456—21no—
17#14583456C2212yes—
18#14583452—24no—
19C2×#13063284—21no—
20#14583229C2214yes—
21#14583184—22no—
22#14583109—22no—
23#14583055C2214yes—
24#14583004—24no—
25#14582956C2212yes—
26#14582635C2214yes—
27#14582635C2214yes—
28#14582625C2212yes—
29#14582623C2212yes—
30C2×C4×Q8×C43C2211yescharacteristic
31C2×#117×C43C2211yescharacteristic
32C43×#398C2211yescharacteristic
33C43×#397C2211yescharacteristic
34C43×#395C2211yescharacteristic
35C43×#393C2211yescharacteristic
36C43×#388—21no—
37C43×#387—21no—
38C43×#387—21no—
39C43×#385—21no—
40C43×#383C2211yescharacteristic
41C2×#10621885—24no—
42#13063325—21no—
43#13063325—21no—
44#13063325D412yes—
45#13063325D412yes—
46#13063324—24no—
47#13063324—24no—
48#13063317—22no—
49#13063317—22no—
50#13063316—24no—
51#13063316—24no—
52#13063304—22no—
53#13063304—22no—
54#13063304—22no—
55#13063304C2314yes—
56#13063302—24no—
57#13063302—24no—
58#13063302—24no—
59#13063302—24no—
60C4×Dic86—22no—
61C4×Dic86—22no—
62C4×Dic86—22no—
63C4×Dic86D414yes—
64#13063284—22no—
65#13063284—22no—
66#13063284—22no—
67#13063284—22no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C22⋊Dic43—22no—
71C2×C4×Dic43—22no—
72#13063256—24no—
73C4⋊(C43⋊C8)—22no—
74#13063249—24no—
75#13063248—24no—
76C22⋊(C43⋊C8)C2314yes—
77#13063236—22no—
78C22×Q8×C43C2311yescharacteristic
79C23×C4×C43D411yescharacteristic
80C4×Q8×C43—22no—
81C4×Q8×C43—22no—
82#117×C43—22no—
83#117×C43—22no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43D411yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43D411yescharacteristic
93C2×C22⋊C4×C43C2311yescharacteristic
94C2×C42×C43—21no—
95C2×C42×C43D411yescharacteristic
96C2×C42×C43C2311yescharacteristic
97#95×C43—21no—
98#95×C43—21no—
99#95×C43—21no—
100#95×C43—21no—
101#95×C43—21no—
102#95×C43—21no—
103#95×C43C2311yescharacteristic
104#95×C43C2311yescharacteristic
105C24×C43C2×D411yescharacteristic
106C2×Q8×C43—22no—
107C2×Q8×C43—42no—
108C22×C4×C43—21no—
109C22×C4×C43—21no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2411yescharacteristic
122C22×Dic43—22no—
123C22×Dic43—22no—
124C2×Dic86—22no—
125C2×Dic86—22no—
126C2×Dic86—22no—
127C2×Dic86C2×D414yes—
128C4⋊C4×C43—22no—
129C4⋊C4×C43—22no—
130C4⋊C4×C43—22no—
131C4⋊C4×C43—42no—
132C4⋊C4×C43—41no—
133C4⋊C4×C43—41no—
134C4⋊C4×C43—42no—
135C22⋊C4×C43—22no—
136C22⋊C4×C43—22no—
137C22⋊C4×C43—42no—
138C22⋊C4×C43—42no—
139C42×C43—21no—
140C42×C43—21no—
141C42×C43—42no—
142C42×C43C2×D412yes—
143C42×C43C2×D412yes—
144C22⋊Dic43—24no—
145C22⋊Dic43—24no—
146#10621885—48no—
147C4⋊Dic43—22no—
148C4⋊Dic43—22no—
149C4⋊Dic43—22no—
150C4⋊Dic43—22no—
151C4⋊Dic43—22no—
152C4⋊Dic43—22no—
153C4⋊Dic43—22no—
154C4⋊Dic43C2×D414yes—
155Dic43⋊C4—24no—
156Dic43⋊C4—24no—
157Dic43⋊C4—24no—
158Dic43⋊C4—24no—
159C4×Dic43—24no—
160C4×Dic43—24no—
161C2×C43⋊C8—24no—
162C23×C43—21no—
163C23×C43—21no—
164C23×C43—41no—
165C23×C43—41no—
166C23×C43#13712yes—
167C23×C43C22×D411yescharacteristic
168Q8×C43—24no—
169Q8×C43—42no—
170C2×C4×C43—24no—
171C2×C4×C43—24no—
172C2×C4×C43—21no—
173C2×C4×C43—21no—
174C2×C4×C43—21no—
175C2×C4×C43—21no—
176C2×C4×C43—22no—
177C2×C4×C43—21no—
178C2×C4×C43—21no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43#12011yescharacteristic
195C2×C4×C43#12012yes—
196C2×C4×C43#12011yescharacteristic
197C2×C4×C43#13712yes—
198C2×C4×C43C22×D412yes—
199C2×Dic43—24no—
200C2×Dic43—24no—
201C2×Dic43—82no—
202C2×Dic43—82no—
203Dic86—44no—
204Dic86—82no—
205Dic86—82no—
206Dic86—82no—
207C43⋊C8—44no—
208#18155—431nomaximal, Sylow
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—22no—
212C22×C43—42no—
213C22×C43—41no—
214C22×C43—41no—
215C22×C43—81no—
216C22×C43C2×#12011yescharacteristic
217C22×C43C2×#13711yescharacteristic
218C22×C43C2×#13711yescharacteristic
219C4×C43—21no—
220C4×C43—21no—
221C4×C43—22no—
222C4×C43—22no—
223C4×C43—22no—
224C4×C43—41no—
225C4×C43—41no—
226C4×C43—42no—
227C4×C43—81no—
228C4×C43—81no—
229C4×C43—81no—
230Dic43—44no—
231Dic43—44no—
232#3458—431no—
233#3113—432no—
234#2599D4311yescharacteristic
235#1611—432no—
236#1608—432no—
237#1605—432no—
238#1602—432no—
239#1515—432no—
240#1464—431no—
241C2×C43—21no—
242C2×C43—21no—
243C2×C43—42no—
244C2×C43#300411yescharacteristic
245C2×C43#302211yescharacteristic
246C2×C43#302511yescharacteristic
247#544—432no—
248#544—862no—
249#544—862no—
250#544—861no—
251#543—432no—
252#543—861no—
253#533—432no—
254#533—864no—
255#533—861no—
256C2×C4×Q8C2×D4311yescharacteristic
257C2×#117—861no—
258C2×#117C2×D4311yescharacteristic
259#483—434no—
260#475—862no—
261#462—862no—
262#451—434no—
263#441—864no—
264#432—432no—
265#398C2×D4311yescharacteristic
266#397C2×D4311yescharacteristic
267#395C2×D4311yescharacteristic
268#393C2×D4311yescharacteristic
269#388—21no—
270#387—21no—
271#387—21no—
272#385—21no—
273#383C2×D4311yescharacteristic
274#328—434no—
275#328—434no—
276#324—432no—
277#323—432no—
278C43#1815511yescharacteristic, complemented, Sylow
279C22×Q8C22×D4311yescharacteristic
280C23×C4C22⋊D4311yescharacteristic
281C2×Q16—864no—
282C4⋊Q8—432no—
283C4⋊Q8—432no—
284C4⋊Q8—861no—
285C4⋊Q8—861no—
286C4⋊Q8—864no—
287C4⋊Q8—864no—
288#125—862no—
289#125—864no—
290#125—864no—
291#125—862no—
292C22⋊Q8—434no—
293C22⋊Q8—864no—
294C22⋊Q8—864no—
295C22⋊Q8—864no—
296C22⋊Q8—864no—
297C22⋊Q8—862no—
298C22⋊Q8—862no—
299C22⋊Q8—862no—
300C4×Q8—22no—
301C4×Q8—22no—
302C4×Q8—434no—
303C4×Q8—862no—
304C4×Q8—862no—
305C4×Q8—862no—
306#117—22no—
307#117—22no—
308#117—862no—
309#117—862no—
310#117—862no—
311#117—862no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—861no—
316C2×C4⋊C4—861no—
317C2×C4⋊C4C22⋊D4311yescharacteristic
318C2×C4⋊C4C22×D4311yescharacteristic
319C2×C4⋊C4C22×D4311yescharacteristic
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—862no—
323C2×C22⋊C4C22⋊D4311yescharacteristic
324C2×C22⋊C4C22×D4311yescharacteristic
325C2×C42—21no—
326C2×C42—862no—
327C2×C42C22⋊D4311yescharacteristic
328C2×C42C22×D4311yescharacteristic
329#106—864no—
330C4⋊C8—862no—
331#103—864no—
332#103—864no—
333C22⋊C8—434no—
334#97—862no—
335#95—21no—
336#95—21no—
337#95—21no—
338#95—21no—
339#95—21no—
340#95—21no—
341#95C22×D4311yescharacteristic
342#95C22×D4311yescharacteristic
343C24C2×C22⋊D4311yescharacteristic
344C2×Q8—22no—
345C2×Q8—42no—
346C2×Q8—434no—
347C2×Q8—862no—
348C2×Q8—862no—
349C2×Q8—862no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—862no—
359C22×C4—862no—
360C22×C4C2×C22⋊D4311yescharacteristic
361C22×C4C2×C22⋊D4311yescharacteristic
362C22×C4C2×C22⋊D4311yescharacteristic
363C22×C4C2×C22⋊D4311yescharacteristic
364C22×C4C2×C22⋊D4311yescharacteristic
365C22×C4C23×D4311yescharacteristic
366Q16—1728no—
367C2×C8—864no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—42no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—42no—
375C4⋊C4—434no—
376C4⋊C4—862no—
377C4⋊C4—862no—
378C4⋊C4—864no—
379C4⋊C4—864no—
380C4⋊C4—862no—
381C4⋊C4—862no—
382C4⋊C4—862no—
383C4⋊C4—862no—
384C4⋊C4—864no—
385C4⋊C4—862no—
386C4⋊C4—864no—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—42no—
390C22⋊C4—42no—
391C22⋊C4—864no—
392C22⋊C4—864no—
393C42—21no—
394C42—21no—
395C42—42no—
396C42—864no—
397C42—864no—
398C42D4×D4312yes—
399C42D4×D4312yes—
400C23—21no—
401C23—21no—
402C23—41no—
403C23—41no—
404C23#1306335512yes—
405C23C22×C22⋊D4311yescharacteristic
406Q8—24no—
407Q8—42no—
408Q8—3442no—
409Q8—3442no—
410Q8—3442no—
411Q8—1724no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—864no—
437C2×C4—864no—
438C2×C4—3442no—
439C2×C4—3442no—
440C2×C4#1306329311yescharacteristic
441C2×C4#1306329311yescharacteristic
442C2×C4#1306329312yes—
443C2×C4#1306335512yes—
444C2×C4C2×D4×D4312yes—
445C8—1724no—
446C22—21no—
447C22—21no—
448C22—22no—
449C22—42no—
450C22—41no—
451C22—41no—
452C22—81no—
453C22C2×#1306329311yescharacteristic
454C22C2×#1306335511yescharacteristic
455C22C2×#1306335511yescharacteristic
456C4—22no—
457C4—22no—
458C4—21no—
459C4—21no—
460C4—22no—
461C4—41no—
462C4—42no—
463C4—41no—
464C4—81no—
465C4—81no—
466C4—81no—
467C4—1724no—
468C4—1724no—
469C2—21no—
470C2—21no—
471C2—42no—
472C2#1914382811yescharacteristic
473C2#1914397311yescharacteristic
474C2#1914398611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2599C2
socleC22×C43C2×#120
prime radicalC24×C43C2×D4
hypercenter#2599D43
hypocenterC43#18155
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2599

Complements

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

NH ≅ G/Ntype
2. #19144725C2semidirect
3. #19133602C2semidirect
5. #19133568C2semidirect
7. #19133145C2semidirect
278. C43#18155semidirect

Maximal subgroups

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

subgroupindex
#191480002
#191447252
#191336022
#191335852
#191335682
#191335512
#191331452
#191329292
C43×#25992
#1815543