Finite Group Databasebeta

← #25068883

Subgroups — #25068883

Order 11008.

1012 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148000C211yesmaximal, characteristic, complemented
2#19144603C212yesmaximal, complemented
3#19133602C212yesmaximal, complemented
4#19133585C212yesmaximal, complemented
5#19133534C212yesmaximal, complemented
6#19133517C212yesmaximal
7#19133093C212yesmaximal, complemented
8#19132909C211yesmaximal, characteristic, complemented
9C43×#2392C211yesmaximal, 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#14583189—22no—
22#14583104—22no—
23#14583050C2214yes—
24C4×#10621883—24no—
25#14582952C2212yes—
26#14582635C2214yes—
27#14582635C2214yes—
28#14582625C2212yes—
29#14582623C2212yes—
30C2×C4×D4×C43—21no—
31C2×C4×D4×C43C2211yescharacteristic
32C2×#117×C43C2211yescharacteristic
33C43×#398C2211yescharacteristic
34C43×#397C2211yescharacteristic
35C43×#396—21no—
36C43×#394—21no—
37C43×#394C2211yescharacteristic
38C43×#392C2211yescharacteristic
39C4×C4⋊C4×C43C2211yescharacteristic
40C4×C22⋊C4×C43—21no—
41C2×#10621883—24no—
42#13063325—21no—
43#13063325—21no—
44#13063325D412yescomplemented
45#13063325D412yescomplemented
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×Dic86D414yescomplemented
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#13063248—24no—
75#13063246—24no—
76C22⋊(C43⋊C8)C2314yes—
77C4×C43⋊C8—22no—
78C22×D4×C43—21no—
79C22×D4×C43C2311yescharacteristic
80C23×C4×C43—21no—
81C23×C4×C43D411yescharacteristic
82C4×D4×C43—22no—
83C4×D4×C43—22no—
84C4×D4×C43—44no—
85#117×C43—22no—
86#117×C43—22no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43D411yescharacteristic
90C2×C4⋊C4×C43C2311yescharacteristic
91C2×C4⋊C4×C43C2311yescharacteristic
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43D411yescharacteristic
98C2×C22⋊C4×C43C2311yescharacteristic
99C2×C42×C43—21no—
100C2×C42×C43D411yescharacteristic
101C2×C42×C43C2311yescharacteristic
102#95×C43—21no—
103#95×C43—21no—
104#95×C43C2311yescharacteristic
105#95×C43C2311yescharacteristic
106C24×C43—21no—
107C24×C43C2×D411yescharacteristic
108C2×D4×C43—22no—
109C2×D4×C43—42no—
110C2×D4×C43—42no—
111C2×D4×C43—42no—
112C2×D4×C43—42no—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—22no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—41no—
120C22×C4×C43—41no—
121C22×C4×C43—42no—
122C22×C4×C43—42no—
123C22×C4×C43SD1614yescomplemented
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2411yescharacteristic
130C22×Dic43—22no—
131C22×Dic43—22no—
132C2×Dic86—22no—
133C2×Dic86—22no—
134C2×Dic86—22no—
135C2×Dic86C2×D414yes—
136C4⋊C4×C43—22no—
137C4⋊C4×C43—22no—
138C4⋊C4×C43—22no—
139C4⋊C4×C43—42no—
140C4⋊C4×C43—42no—
141C22⋊C4×C43—22no—
142C22⋊C4×C43—22no—
143C22⋊C4×C43—42no—
144C22⋊C4×C43—42no—
145C22⋊C4×C43—42no—
146C22⋊C4×C43—42no—
147C22⋊C4×C43—42no—
148C42×C43—21no—
149C42×C43—21no—
150C42×C43—42no—
151C42×C43C2×D412yes—
152C42×C43C2×D412yes—
153C22⋊Dic43—24no—
154C22⋊Dic43—24no—
155#10621883—48no—
156C4⋊Dic43—22no—
157C4⋊Dic43—22no—
158C4⋊Dic43—22no—
159C4⋊Dic43—22no—
160C4⋊Dic43—22no—
161C4⋊Dic43—22no—
162C4⋊Dic43—22no—
163C4⋊Dic43C2×D414yes—
164Dic43⋊C4—24no—
165Dic43⋊C4—24no—
166Dic43⋊C4—24no—
167Dic43⋊C4—24no—
168C4×Dic43—24no—
169C4×Dic43—24no—
170C2×C43⋊C8—24no—
171C23×C43—21no—
172C23×C43—21no—
173C23×C43—22no—
174C23×C43—41no—
175C23×C43—41no—
176C23×C43—41no—
177C23×C43—41no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43—41no—
182C23×C43C2×SD1612yes—
183C23×C43C22×D411yescharacteristic
184D4×C43—24no—
185D4×C43—42no—
186D4×C43—48no—
187C2×C4×C43—21no—
188C2×C4×C43—21no—
189C2×C4×C43—24no—
190C2×C4×C43—24no—
191C2×C4×C43—22no—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—82no—
207C2×C4×C43—82no—
208C2×C4×C43#12012yes—
209C2×C4×C43#12011yescharacteristic
210C2×C4×C43#12011yescharacteristic
211C2×C4×C43C2×SD1612yes—
212C2×C4×C43C2×SD1612yes—
213C2×C4×C43#13712yes—
214C2×C4×C43C22×D412yes—
215C2×Dic43—24no—
216C2×Dic43—24no—
217C2×Dic43—82no—
218C2×Dic43—82no—
219Dic86—44no—
220Dic86—82no—
221Dic86—82no—
222Dic86—82no—
223C43⋊C8—44no—
224#18124—431nomaximal, Sylow
225C22×C43—21no—
226C22×C43—21no—
227C22×C43—22no—
228C22×C43—42no—
229C22×C43—42no—
230C22×C43—42no—
231C22×C43—41no—
232C22×C43—41no—
233C22×C43—42no—
234C22×C43—81no—
235C22×C43—81no—
236C22×C43—81no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43C2×#12011yescharacteristic
240C22×C43C22×SD1611yescharacteristic
241C22×C43C2×#13711yescharacteristic
242C4×C43—22no—
243C4×C43—22no—
244C4×C43—22no—
245C4×C43—42no—
246C4×C43—41no—
247C4×C43—41no—
248C4×C43—81no—
249C4×C43—81no—
250C4×C43#44812yes—
251C4×C43#44812yes—
252Dic43—44no—
253Dic43—44no—
254#3458—431no—
255#3101—432no—
256#2392D4311yescharacteristic
257#1611—432no—
258#1608—432no—
259#1599—432no—
260#1596—432no—
261#1503—432no—
262#1458—431no—
263C2×C43—21no—
264C2×C43—21no—
265C2×C43—42no—
266C2×C43—82no—
267C2×C43C2×#44811yescharacteristic
268C2×C43#301811yescharacteristic
269C2×C43#302511yescharacteristic
270#544—432no—
271#544—862no—
272#544—862no—
273#544—861no—
274#543—432no—
275#543—861no—
276#533—432no—
277#533—864no—
278#533—861no—
279C2×C4×D4—21no—
280C2×C4×D4C2×D4311yescharacteristic
281C2×#117—861no—
282C2×#117C2×D4311yescharacteristic
283#483—434no—
284#476—862no—
285#461—862no—
286#450—434no—
287C4×SD16—864no—
288#431—432no—
289#398C2×D4311yescharacteristic
290#397C2×D4311yescharacteristic
291#396—21no—
292#394—21no—
293#394C2×D4311yescharacteristic
294#392C2×D4311yescharacteristic
295C4×C4⋊C4C2×D4311yescharacteristic
296C4×C22⋊C4—21no—
297#328—434no—
298#328—434no—
299#324—432no—
300#323—432no—
301C43#1812411yescharacteristic, complemented, Sylow
302C22×D4—21no—
303C22×D4C22×D4311yescharacteristic
304C23×C4—21no—
305C23×C4C22⋊D4311yescharacteristic
306C2×SD16—864no—
307C4⋊Q8—432no—
308C4⋊Q8—432no—
309C4⋊Q8—861no—
310C4⋊Q8—861no—
311C4⋊Q8—864no—
312C4⋊Q8—864no—
313#125—862no—
314#125—864no—
315#125—864no—
316#125—862no—
317C22⋊Q8—434no—
318C22⋊Q8—864no—
319C22⋊Q8—864no—
320C22⋊Q8—864no—
321C22⋊Q8—864no—
322C22⋊Q8—862no—
323C22⋊Q8—862no—
324C22⋊Q8—862no—
325C4×Q8—434no—
326C4×Q8—862no—
327C4×Q8—862no—
328C4×Q8—862no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—44no—
332#117—22no—
333#117—22no—
334#117—862no—
335#117—862no—
336#117—862no—
337#117—862no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—861no—
341C2×C4⋊C4—861no—
342C2×C4⋊C4C22⋊D4311yescharacteristic
343C2×C4⋊C4C22×D4311yescharacteristic
344C2×C4⋊C4C22×D4311yescharacteristic
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—862no—
351C2×C22⋊C4C22⋊D4311yescharacteristic
352C2×C22⋊C4C22×D4311yescharacteristic
353C2×C42—21no—
354C2×C42—862no—
355C2×C42C22⋊D4311yescharacteristic
356C2×C42C22×D4311yescharacteristic
357#106—864no—
358C4⋊C8—862no—
359#103—864no—
360#102—864no—
361C22⋊C8—434no—
362C4×C8—862no—
363#95—21no—
364#95—21no—
365#95C22×D4311yescharacteristic
366#95C22×D4311yescharacteristic
367C24—21no—
368C24C2×C22⋊D4311yescharacteristic
369C2×Q8—434no—
370C2×Q8—862no—
371C2×Q8—862no—
372C2×Q8—862no—
373C2×D4—22no—
374C2×D4—42no—
375C2×D4—42no—
376C2×D4—42no—
377C2×D4—42no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—862no—
389C22×C4—862no—
390C22×C4#1062188314yescomplemented
391C22×C4C2×C22⋊D4311yescharacteristic
392C22×C4C2×C22⋊D4311yescharacteristic
393C22×C4C2×C22⋊D4311yescharacteristic
394C22×C4C2×C22⋊D4311yescharacteristic
395C22×C4C2×C22⋊D4311yescharacteristic
396C22×C4C23×D4311yescharacteristic
397SD16—1728no—
398C2×C8—864no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—42no—
403C4⋊C4—42no—
404C4⋊C4—434no—
405C4⋊C4—862no—
406C4⋊C4—862no—
407C4⋊C4—864no—
408C4⋊C4—864no—
409C4⋊C4—862no—
410C4⋊C4—862no—
411C4⋊C4—862no—
412C4⋊C4—862no—
413C4⋊C4—864no—
414C4⋊C4—862no—
415C4⋊C4—864no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—42no—
419C22⋊C4—42no—
420C22⋊C4—42no—
421C22⋊C4—42no—
422C22⋊C4—42no—
423C22⋊C4—864no—
424C22⋊C4—864no—
425C42—21no—
426C42—21no—
427C42—42no—
428C42—864no—
429C42—864no—
430C42D4×D4312yes—
431C42D4×D4312yes—
432C23—21no—
433C23—21no—
434C23—22no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23C2×#1062188312yes—
444C23C22×C22⋊D4311yescharacteristic
445Q8—3442no—
446Q8—3442no—
447Q8—3442no—
448Q8—1724no—
449D4—24no—
450D4—42no—
451D4—48no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—82no—
472C2×C4—82no—
473C2×C4—864no—
474C2×C4—864no—
475C2×C4—3442no—
476C2×C4—3442no—
477C2×C4#1306329312yes—
478C2×C4#1306329311yescharacteristic
479C2×C4#1306329311yescharacteristic
480C2×C4C2×#1062188312yes—
481C2×C4C2×#1062188312yes—
482C2×C4#1306335512yes—
483C2×C4C2×D4×D4312yes—
484C8—1724no—
485C22—21no—
486C22—21no—
487C22—22no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—41no—
492C22—41no—
493C22—42no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22C2×#1306329311yescharacteristic
500C22C22×#1062188311yescharacteristic
501C22C2×#1306335511yescharacteristic
502C4—22no—
503C4—22no—
504C4—22no—
505C4—42no—
506C4—41no—
507C4—41no—
508C4—81no—
509C4—81no—
510C4—1724no—
511C4—1724no—
512C4#1458303712yes—
513C4#1458303712yes—
514C2—21no—
515C2—21no—
516C2—42no—
517C2—82no—
518C2C2×#1458303711yescharacteristic
519C2#1914394311yescharacteristic
520C2#1914398611yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2392C2
socleC22×C43C2×#120
prime radicalC43×#392C22
hypercenter#2392D43
hypocenterC43#18124
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2392

Complements

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

NH ≅ G/Ntype
1. #19148000C2semidirect
2. #19144603C2semidirect
3. #19133602C2semidirect
4. #19133585C2semidirect
5. #19133534C2semidirect
7. #19133093C2semidirect
8. #19132909C2semidirect
44. #13063325D4semidirect
45. #13063325D4semidirect
63. C4×Dic86D4semidirect
123. C22×C4×C43SD16semidirect
301. C43#18124semidirect
390. C22×C4#10621883semidirect

Maximal subgroups

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

subgroupindex
#191480002
#191446032
#191336022
#191335852
#191335342
#191335172
#191330932
#191329092
C43×#23922
#1812443