Finite Group Databasebeta

← #25072761

Subgroups — #25072761

Order 11008.

940 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583619C211yesmaximal, characteristic, complemented
2#19144988C211yesmaximal, characteristic, complemented
3#19144713C211yesmaximal, characteristic, complemented
4#19133765C214yesmaximal, complemented
5#19133703C214yesmaximal, complemented
6#19133313C211yesmaximal, characteristic, complemented
7#19133041C211yesmaximal, characteristic, complemented
8#19133038C211yesmaximal, characteristic, complemented
9C43×#3109C211yesmaximal, characteristic
10#14583619—22no—
11#14583619—22no—
12#14583619—22no—
13#14583619C2214yes—
14C2×#13063325C2211yescharacteristic
15C2×#13063318—22no—
16C2×#13063312—21no—
17C2×#13063304—21no—
18C2×C4×Dic86C2211yescharacteristic
19C2×#13063290—21no—
20C2×#13063284—21no—
21#14583258—22no—
22#14583249C2212yescomplemented
23#14583245C2212yescomplemented
24#14583210—21no—
25#14583191C2212yescomplemented
26#14583096C2212yescomplemented
27#14583037—21no—
28#14582999—22no—
29#14582956C2211yescharacteristic
30#14582900—22no—
31C4×#10621877C2211yescharacteristic
32#14582646C2214yescomplemented
33#14582629C2214yescomplemented
34D4⋊(C43⋊C8)C2214yes—
35C43×#532C2211yescharacteristic
36C2×C4×D4×C43C2211yescharacteristic
37C43×#481—21no—
38C43×#476C2212yes—
39C43×#459C2212yes—
40C43×#447—21no—
41C43×#442—22no—
42C43×#432C2211yescharacteristic
43C22×Dic86—21no—
44C22×Dic86D411yescharacteristic
45C2×#10621883—22no—
46C2×#10621877—21no—
47#13063325—21no—
48#13063325—21no—
49#13063325D412yes—
50#13063325C2312yes—
51#13063318—28no—
52#13063318—28no—
53#13063312—24no—
54#13063312—24no—
55#13063304—24no—
56#13063304—24no—
57C4×Dic86—21no—
58C4×Dic86—21no—
59C4×Dic86D412yes—
60C4×Dic86C2312yes—
61#13063290—24no—
62#13063290—24no—
63#13063284—24no—
64#13063284—24no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43D411yescharacteristic
67C2×C4⋊Dic43D412yes—
68C2×Dic43⋊C4—22no—
69C2×Dic43⋊C4—21no—
70C2×C22⋊Dic43—22no—
71C2×C22⋊Dic43—22no—
72C2×C4×Dic43—22no—
73C2×C4×Dic43—21no—
74#13063258—22no—
75C4⋊(C43⋊C8)C2312yes—
76#13063249—24no—
77#13063248—22no—
78#13063246—22no—
79#13063246—24no—
80C22⋊(C43⋊C8)—21no—
81#13063236—21no—
82#13063236—21no—
83C4×C43⋊C8C2312yes—
84C2×#41×C43—21no—
85C22×D4×C43D411yescharacteristic
86C23×C4×C43—21no—
87C2×D8×C43—22no—
88C4⋊Q8×C43C2311yescharacteristic
89#127×C43C2311yescharacteristic
90#124×C43—21no—
91#121×C43—21no—
92#121×C43—21no—
93C4×D4×C43—21no—
94C4×D4×C43—21no—
95C4×D4×C43—21no—
96C4×D4×C43—21no—
97C4×D4×C43D412yes—
98C4×D4×C43C2312yes—
99C2×C4⋊C4×C43D411yescharacteristic
100C2×C22⋊C4×C43—21no—
101C2×C42×C43C2311yescharacteristic
102#106×C43—22no—
103C4⋊C8×C43C2312yes—
104#102×C43—22no—
105#102×C43—22no—
106C22⋊C8×C43—21no—
107#97×C43—21no—
108C24×C43—21no—
109#41×C43—44no—
110C2×Q8×C43—21no—
111C2×D4×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—42no—
116C2×D4×C43—41no—
117C2×D4×C43C2×D412yes—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—21no—
121C22×C4×C43—44no—
122C22×C4×C43—41no—
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—22no—
129C2×Dic86—22no—
130C2×Dic86—21no—
131C2×Dic86—22no—
132C2×Dic86—42no—
133C2×Dic86—44no—
134C2×Dic86C2×D412yes—
135D8×C43—44no—
136C2×C8×C43—22no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43C2×D412yes—
141C22⋊C4×C43—22no—
142C22⋊C4×C43—22no—
143C22⋊C4×C43—41no—
144C22⋊C4×C43—41no—
145C42×C43C2×D411yescharacteristic
146C42×C43C2×D411yescharacteristic
147C42×C43C2×D411yescharacteristic
148C42×C43C2411yescharacteristic
149C22⋊Dic43—28no—
150C22⋊Dic43—28no—
151#10621883—44no—
152C4⋊Dic43—22no—
153C4⋊Dic43—21no—
154C4⋊Dic43—22no—
155C4⋊Dic43—22no—
156C4⋊Dic43C2×D414yes—
157C4⋊Dic43C2×D412yes—
158Dic43⋊C4—28no—
159Dic43⋊C4—22no—
160Dic43⋊C4—22no—
161C4×Dic43—28no—
162C4×Dic43—22no—
163C4×Dic43—22no—
164#10621877—42no—
165C2×C43⋊C8—22no—
166C2×C43⋊C8—22no—
167C23×C43—22no—
168C23×C43—42no—
169C23×C43—42no—
170C23×C43—42no—
171C23×C43—41no—
172C23×C43#12011yescharacteristic
173Q8×C43—42no—
174D4×C43—22no—
175D4×C43—22no—
176D4×C43—42no—
177D4×C43—42no—
178D4×C43—42no—
179D4×C43—42no—
180D4×C43—82no—
181C2×C4×C43—22no—
182C2×C4×C43—22no—
183C2×C4×C43—22no—
184C2×C4×C43—22no—
185C2×C4×C43—44no—
186C2×C4×C43—42no—
187C2×C4×C43—44no—
188C2×C4×C43—41no—
189C2×C4×C43—82no—
190C2×C4×C43#12011yescharacteristic
191C2×C4×C43#12011yescharacteristic
192C2×C4×C43#12011yescharacteristic
193C2×C4×C43C22×D411yescharacteristic
194C2×C4×C43C22×D411yescharacteristic
195C2×C4×C43C22×D411yescharacteristic
196C2×Dic43—22no—
197C2×Dic43—22no—
198C2×Dic43—24no—
199C2×Dic43—42no—
200C2×Dic43—44no—
201C2×Dic43—42no—
202Dic86—22no—
203Dic86—22no—
204Dic86—42no—
205Dic86—44no—
206Dic86—44no—
207C8×C43—42no—
208C43⋊C8—42no—
209C43⋊C8—42no—
210#18536—431nomaximal, Sylow
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—42no—
214C22×C43—42no—
215C22×C43—42no—
216C22×C43—84no—
217C22×C43—81no—
218C22×C43—81no—
219C22×C43—81no—
220C22×C43#45412yes—
221C22×C43C2×#12011yescharacteristic
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—42no—
227C4×C43—81no—
228C4×C43#57512yes—
229C4×C43#57512yes—
230Dic43—42no—
231Dic43—44no—
232Dic43—42no—
233C2×#556—431no—
234#3141—431no—
235#3112—431no—
236#3109D4311yescharacteristic
237#1638—434no—
238#1628—434no—
239#1556—431no—
240#1491—431no—
241#1490—431no—
242C2×C43—22no—
243C2×C43—82no—
244C2×C43—161no—
245C2×C43#300511yescharacteristic
246C2×C43#300511yescharacteristic
247C2×C43C2×#45411yescharacteristic
248#556—434no—
249#556—862no—
250#556—862no—
251#556—862no—
252#532C2×D4311yescharacteristic
253C2×C4⋊Q8—431no—
254C2×#126—862no—
255C2×#124—861no—
256C2×C22⋊Q8—861no—
257C2×C4×Q8—431no—
258C2×C4×Q8—861no—
259C2×C4×D4C2×D4311yescharacteristic
260C2×#117—861no—
261#489—862no—
262#487—432no—
263#486—432no—
264#481—21no—
265#480—861no—
266#477—432no—
267#476C2×D4312yes—
268#460—432no—
269#459C2×D4312yes—
270#448—861no—
271#447—21no—
272#442—22no—
273#440—862no—
274#432—431no—
275#432C2×D4311yescharacteristic
276#417—862no—
277C4×M16—431no—
278#332—434no—
279Q8⋊C8—434no—
280D4⋊C8—434no—
281C43#1853611yescharacteristic, complemented, Sylow
282C2×#41—21no—
283C22×Q8—431no—
284C22×Q8—861no—
285C22×D4C22⋊D4311yescharacteristic
286C23×C4—21no—
287C2×SD16—862no—
288C2×D8—22no—
289C2×M16—861no—
290C4⋊Q8—432no—
291C4⋊Q8—432no—
292C4⋊Q8—861no—
293C4⋊Q8—861no—
294C4⋊Q8C22×D4311yescharacteristic
295#127C22×D4311yescharacteristic
296#126—868no—
297#126—868no—
298#124—21no—
299#124—864no—
300#124—864no—
301C22⋊Q8—864no—
302C22⋊Q8—864no—
303#121—21no—
304#121—21no—
305C4×Q8—432no—
306C4×Q8—432no—
307C4×Q8—864no—
308C4×Q8—864no—
309C4×Q8—861no—
310C4×Q8—861no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4C22⋊D4312yes—
316C4×D4C22×D4312yes—
317#117—864no—
318#117—864no—
319C2×C4⋊C4—431no—
320C2×C4⋊C4—432no—
321C2×C4⋊C4—862no—
322C2×C4⋊C4—861no—
323C2×C4⋊C4—861no—
324C2×C4⋊C4C22⋊D4311yescharacteristic
325C2×C22⋊C4—21no—
326C2×C22⋊C4—862no—
327C2×C22⋊C4—862no—
328C2×C42—862no—
329C2×C42—861no—
330C2×C42C22×D4311yescharacteristic
331#107—862no—
332#106—22no—
333C4⋊C8—432no—
334C4⋊C8C22×D4312yes—
335#103—862no—
336#103—864no—
337#102—22no—
338#102—22no—
339#102—864no—
340#102—862no—
341C22⋊C8—21no—
342C22⋊C8—861no—
343#97—21no—
344#97—861no—
345#97—861no—
346C4×C8—432no—
347C24—21no—
348#41—44no—
349C2×Q8—21no—
350C2×Q8—432no—
351C2×Q8—861no—
352C2×Q8—862no—
353C2×Q8—862no—
354C2×Q8—1722no—
355C2×Q8—1724no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—42no—
361C2×D4—41no—
362C2×D4C2×C22⋊D4312yes—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—44no—
367C22×C4—41no—
368C22×C4—861no—
369C22×C4—862no—
370C22×C4—861no—
371C22×C4D4×D4311yescharacteristic
372C22×C4D4×D4311yescharacteristic
373C22×C4C2×C22⋊D4311yescharacteristic
374SD16—1724no—
375D8—44no—
376M16—1722no—
377C2×C8—22no—
378C2×C8—862no—
379C2×C8—862no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—434no—
384C4⋊C4—432no—
385C4⋊C4—868no—
386C4⋊C4—861no—
387C4⋊C4—862no—
388C4⋊C4—862no—
389C4⋊C4—862no—
390C4⋊C4—862no—
391C4⋊C4—862no—
392C4⋊C4C2×C22⋊D4312yes—
393C22⋊C4—22no—
394C22⋊C4—22no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—868no—
398C22⋊C4—868no—
399C42—868no—
400C42—862no—
401C42—862no—
402C42D4×D4311yescharacteristic
403C42D4×D4311yescharacteristic
404C42C2×C22⋊D4311yescharacteristic
405C42C23×D4311yescharacteristic
406C23—22no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—41no—
411C23#1306329311yescharacteristic
412Q8—42no—
413Q8—862no—
414Q8—862no—
415Q8—1722no—
416Q8—1724no—
417Q8—1724no—
418D4—22no—
419D4—22no—
420D4—42no—
421D4—42no—
422D4—42no—
423D4—42no—
424D4—82no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—41no—
433C2×C4—82no—
434C2×C4—862no—
435C2×C4—864no—
436C2×C4—862no—
437C2×C4—1722no—
438C2×C4—1724no—
439C2×C4—1722no—
440C2×C4#1306329311yescharacteristic
441C2×C4#1306329311yescharacteristic
442C2×C4#1306329311yescharacteristic
443C2×C4C2×D4×D4311yescharacteristic
444C2×C4C2×D4×D4311yescharacteristic
445C2×C4C22×C22⋊D4311yescharacteristic
446C8—42no—
447C8—1722no—
448C8—1722no—
449C22—21no—
450C22—21no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—84no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22#1458307012yes—
459C22C2×#1306329311yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—42no—
465C4—81no—
466C4—1722no—
467C4—1724no—
468C4—1722no—
469C4#1458369512yes—
470C4#1458369712yes—
471C2—22no—
472C2—82no—
473C2—161no—
474C2#1914383411yescharacteristic
475C2#1914383511yescharacteristic
476C2C2×#1458307011yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3109C2
socleC22×C43C2×#120
hypercenter#3109D43
hypocenterC43#18536
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3109

Complements

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

NH ≅ G/Ntype
1. C2×#14583619C2semidirect
2. #19144988C2semidirect
3. #19144713C2semidirect
4. #19133765C2semidirect
5. #19133703C2semidirect
6. #19133313C2semidirect
7. #19133041C2semidirect
8. #19133038C2semidirect
22. #14583249C22semidirect
23. #14583245C22semidirect
25. #14583191C22semidirect
26. #14583096C22semidirect
32. #14582646C22semidirect
33. #14582629C22semidirect
281. C43#18536semidirect

Maximal subgroups

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

subgroupindex
C2×#145836192
#191449882
#191447132
#191337652
#191337032
#191333132
#191330412
#191330382
C43×#31092
#1853643