Finite Group Databasebeta

← #25072762

Subgroups — #25072762

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
1#19144991C211yesmaximal, characteristic, complemented
2#19144717C211yesmaximal, characteristic, complemented
3#19144686C211yesmaximal, characteristic
4#19133767C214yesmaximal, complemented
5#19133705C214yesmaximal, complemented
6#19133312C211yesmaximal, characteristic, complemented
7#19133042C211yesmaximal, characteristic, complemented
8#19133038C211yesmaximal, characteristic, complemented
9C2×C43×#556C211yesmaximal, characteristic, complemented
10#14583449C2211yescharacteristic
11#14583261—22no—
12#14583251C2212yescomplemented
13#14583247C2212yescomplemented
14#14583217—21no—
15#14583212—21no—
16#14583194C2212yescomplemented
17#14583189C2212yes—
18#14583099C2212yescomplemented
19#14583094C2212yes—
20#14583038—21no—
21#14583033—21no—
22#14583009—22no—
23#14582997—22no—
24#14582956C2211yescharacteristic
25#14582956C2211yescharacteristic
26#14582898—22no—
27C4×#10621877C2211yescharacteristic
28#14582645C2214yescomplemented
29Q8⋊(C43⋊C8)C2214yescomplemented
30D4⋊(C43⋊C8)C2214yes—
31C43×#556—22no—
32C43×#556—22no—
33C43×#556—22no—
34C43×#556C2214yes—
35C2×C4⋊Q8×C43C2211yescharacteristic
36C2×#126×C43—22no—
37C2×#124×C43—21no—
38C2×C22⋊Q8×C43—21no—
39C2×C4×Q8×C43—21no—
40C2×C4×Q8×C43C2211yescharacteristic
41C2×C4×D4×C43C2211yescharacteristic
42C2×#117×C43—21no—
43C2×#10621898—21no—
44C2×#10621884—22no—
45C2×#10621882—22no—
46C2×#10621877—21no—
47#13063325C2311yescharacteristic
48#13063322C2311yescharacteristic
49#13063313—21no—
50#13063299—21no—
51#13063299—21no—
52C4×D172—21no—
53C4×D172—21no—
54#13063258—22no—
55#13063256—22no—
56C4⋊(C43⋊C8)C2312yes—
57C4⋊(C43⋊C8)C2312yes—
58#13063249—22no—
59#13063248—24no—
60#13063246—22no—
61#13063245—22no—
62#13063245—22no—
63#13063245—24no—
64C22⋊(C43⋊C8)—21no—
65C22⋊(C43⋊C8)—21no—
66#13063236—21no—
67#13063236—21no—
68#13063236—21no—
69C4×C43⋊C8C2312yes—
70C22×Q8×C43—21no—
71C22×Q8×C43D411yescharacteristic
72C22×D4×C43D411yescharacteristic
73C23×C4×C43—21no—
74C4⋊Q8×C43—21no—
75C4⋊Q8×C43—21no—
76C4⋊Q8×C43D412yes—
77C4⋊Q8×C43C2312yes—
78#126×C43—28no—
79#126×C43—28no—
80#124×C43—24no—
81#124×C43—24no—
82C22⋊Q8×C43—24no—
83C22⋊Q8×C43—24no—
84C4×Q8×C43—24no—
85C4×Q8×C43—24no—
86C4×Q8×C43—21no—
87C4×Q8×C43—21no—
88C4×Q8×C43D412yes—
89C4×Q8×C43C2312yes—
90C4×D4×C43—21no—
91C4×D4×C43—21no—
92C4×D4×C43D412yes—
93C4×D4×C43C2312yes—
94#117×C43—24no—
95#117×C43—24no—
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43D411yescharacteristic
100C2×C4⋊C4×C43D411yescharacteristic
101C2×C4⋊C4×C43D412yes—
102C2×C22⋊C4×C43—22no—
103C2×C22⋊C4×C43—22no—
104C2×C22⋊C4×C43—21no—
105C2×C42×C43—22no—
106C2×C42×C43—21no—
107C2×C42×C43C2311yescharacteristic
108C24×C43—21no—
109C2×Q8×C43—21no—
110C2×Q8×C43—22no—
111C2×Q8×C43—22no—
112C2×Q8×C43—42no—
113C2×Q8×C43—44no—
114C2×Q8×C43C2×D412yes—
115C2×D4×C43—21no—
116C2×D4×C43—42no—
117C2×D4×C43C2×D412yes—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—22no—
124C22×C4×C43—44no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C2×C22⋊D43—41no—
129#10621898—44no—
130C2×D172—21no—
131C2×D172—21no—
132C2×D172—21no—
133C2×C4×D43—41no—
134C2×Dic86—21no—
135C4⋊C4×C43—28no—
136C4⋊C4×C43—22no—
137C4⋊C4×C43—22no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—22no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43C2×D412yes—
144C4⋊C4×C43C2×D412yes—
145C4⋊C4×C43C2×D414yes—
146C22⋊C4×C43—28no—
147C22⋊C4×C43—28no—
148C22⋊C4×C43—22no—
149C22⋊C4×C43—22no—
150C42×C43—28no—
151C42×C43—22no—
152C42×C43—22no—
153C42×C43C2×D411yescharacteristic
154C42×C43C2×D411yescharacteristic
155C42×C43C2×D411yescharacteristic
156C42×C43C2411yescharacteristic
157#10621884—44no—
158#10621882—44no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161C4⋊Dic43—21no—
162C4⋊Dic43—21no—
163#10621877—42no—
164C2×C43⋊C8—22no—
165C2×C43⋊C8—22no—
166C2×C43⋊C8—22no—
167C23×C43—22no—
168C23×C43—42no—
169C23×C43—42no—
170C23×C43—42no—
171C23×C43#12011yescharacteristic
172C22×D43—41no—
173Q8×C43—22no—
174Q8×C43—22no—
175Q8×C43—42no—
176Q8×C43—44no—
177Q8×C43—44no—
178D4×C43—22no—
179D4×C43—22no—
180D4×C43—42no—
181C2×C4×C43—22no—
182C2×C4×C43—22no—
183C2×C4×C43—22no—
184C2×C4×C43—22no—
185C2×C4×C43—22no—
186C2×C4×C43—22no—
187C2×C4×C43—24no—
188C2×C4×C43—44no—
189C2×C4×C43—42no—
190C2×C4×C43—42no—
191C2×C4×C43—44no—
192C2×C4×C43—42no—
193C2×C4×C43—44no—
194C2×C4×C43#12011yescharacteristic
195C2×C4×C43#12011yescharacteristic
196C2×C4×C43#12011yescharacteristic
197C2×C4×C43C22×D411yescharacteristic
198C2×C4×C43C22×D411yescharacteristic
199C2×C4×C43C22×D411yescharacteristic
200C22⋊D43—82no—
201C2×Dic43—41no—
202D172—42no—
203D172—42no—
204D172—42no—
205C4×D43—82no—
206Dic86—42no—
207C43⋊C8—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#45412yes—
218C22×C43C2×#12011yescharacteristic
219C2×D43—81no—
220C2×D43—81no—
221C2×D43—81no—
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—42no—
227C4×C43—42no—
228C4×C43—44no—
229C4×C43—42no—
230C4×C43#57512yes—
231C4×C43#57512yes—
232Dic43—81no—
233C2×#556D4311yescharacteristic, complemented
234#3141—431no—
235#3112—431no—
236#3109—431no—
237#1638—434no—
238#1628—434no—
239#1556—431no—
240#1491—431no—
241#1490—431no—
242C2×C43—22no—
243C2×C43—82no—
244C2×C43#300511yescharacteristic
245C2×C43#300511yescharacteristic
246C2×C43C2×#45411yescharacteristic
247D43—161no—
248#556—22no—
249#556—22no—
250#556—22no—
251#556C2×D4314yes—
252#532—431no—
253C2×C4⋊Q8C2×D4311yescharacteristic
254C2×#126—22no—
255C2×#124—21no—
256C2×C22⋊Q8—21no—
257C2×C4×Q8—21no—
258C2×C4×Q8C2×D4311yescharacteristic
259C2×C4×D4C2×D4311yescharacteristic
260C2×#117—21no—
261#489—862no—
262#487—432no—
263#486—432no—
264#481—861no—
265#480—861no—
266#477—432no—
267#476—432no—
268#460—432no—
269#459—432no—
270#448—861no—
271#447—861no—
272#442—862no—
273#440—862no—
274#432—431no—
275#432—431no—
276#417—862no—
277C4×M16—431no—
278#332—434no—
279Q8⋊C8—434no—
280D4⋊C8—434no—
281C43#1853611yescharacteristic, complemented, Sylow
282C2×#41—861no—
283C22×Q8—21no—
284C22×Q8C22⋊D4311yescharacteristic
285C22×D4C22⋊D4311yescharacteristic
286C23×C4—21no—
287C2×SD16—862no—
288C2×D8—862no—
289C2×M16—861no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—431no—
293C4⋊Q8C22⋊D4312yes—
294C4⋊Q8C22×D4312yes—
295#127—431no—
296#126—28no—
297#126—28no—
298#124—24no—
299#124—24no—
300#124—861no—
301C22⋊Q8—24no—
302C22⋊Q8—24no—
303#121—861no—
304#121—861no—
305C4×Q8—24no—
306C4×Q8—24no—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×Q8C22⋊D4312yes—
310C4×Q8C22×D4312yes—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—861no—
314C4×D4—861no—
315C4×D4C22⋊D4312yes—
316C4×D4C22×D4312yes—
317#117—24no—
318#117—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4C22⋊D4311yescharacteristic
323C2×C4⋊C4C22⋊D4311yescharacteristic
324C2×C4⋊C4C22⋊D4312yes—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—21no—
328C2×C42—22no—
329C2×C42—21no—
330C2×C42C22×D4311yescharacteristic
331#107—862no—
332#106—862no—
333C4⋊C8—432no—
334C4⋊C8—432no—
335#103—862no—
336#103—864no—
337#102—862no—
338#102—864no—
339#102—862no—
340#102—862no—
341C22⋊C8—861no—
342C22⋊C8—861no—
343#97—861no—
344#97—861no—
345#97—861no—
346C4×C8—432no—
347C24—21no—
348#41—1724no—
349C2×Q8—21no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—42no—
353C2×Q8—44no—
354C2×Q8—861no—
355C2×Q8C2×C22⋊D4312yes—
356C2×D4—21no—
357C2×D4—42no—
358C2×D4—861no—
359C2×D4—861no—
360C2×D4—861no—
361C2×D4—1721no—
362C2×D4C2×C22⋊D4312yes—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—44no—
370C22×C4—1721no—
371C22×C4C2×C22⋊D4311yescharacteristic
372C22×C4C2×C22⋊D4311yescharacteristic
373C22×C4C2×C22⋊D4311yescharacteristic
374SD16—1724no—
375D8—1724no—
376M16—1722no—
377C2×C8—862no—
378C2×C8—862no—
379C2×C8—862no—
380C4⋊C4—28no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—861no—
389C4⋊C4—861no—
390C4⋊C4C2×C22⋊D4314yes—
391C4⋊C4C2×C22⋊D4312yes—
392C4⋊C4C2×C22⋊D4312yes—
393C22⋊C4—28no—
394C22⋊C4—28no—
395C22⋊C4—22no—
396C22⋊C4—22no—
397C22⋊C4—1721no—
398C22⋊C4—1721no—
399C42—28no—
400C42—22no—
401C42—22no—
402C42C2×C22⋊D4311yescharacteristic
403C42C2×C22⋊D4311yescharacteristic
404C42C2×C22⋊D4311yescharacteristic
405C42C23×D4311yescharacteristic
406C23—22no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—1721no—
411C23#1306329411yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—42no—
415Q8—44no—
416Q8—44no—
417Q8—1722no—
418D4—22no—
419D4—22no—
420D4—42no—
421D4—3442no—
422D4—1722no—
423D4—1722no—
424D4—1722no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—44no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—3442no—
439C2×C4—1721no—
440C2×C4#1306329411yescharacteristic
441C2×C4#1306329411yescharacteristic
442C2×C4#1306329411yescharacteristic
443C2×C4C22×C22⋊D4311yescharacteristic
444C2×C4C22×C22⋊D4311yescharacteristic
445C2×C4C22×C22⋊D4311yescharacteristic
446C8—1722no—
447C8—1722no—
448C8—1722no—
449C22—21no—
450C22—21no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—84no—
455C22—3441no—
456C22—3441no—
457C22—3441no—
458C22#1458307212yes—
459C22C2×#1306329411yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—42no—
465C4—42no—
466C4—44no—
467C4—42no—
468C4—3441no—
469C4#1458369712yes—
470C4#1458369712yes—
471C2—22no—
472C2—82no—
473C2—6881no—
474C2#1914383711yescharacteristic
475C2#1914383711yescharacteristic
476C2C2×#1458307211yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#556C2
socleC22×C43C2×#120
prime radical#19144686C2
hypercenterC2×#556D43
hypocenterC43#18536
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #19144991C2semidirect
2. #19144717C2semidirect
4. #19133767C2semidirect
5. #19133705C2semidirect
6. #19133312C2semidirect
7. #19133042C2semidirect
8. #19133038C2semidirect
9. C2×C43×#556C2semidirect
12. #14583251C22semidirect
13. #14583247C22semidirect
16. #14583194C22semidirect
18. #14583099C22semidirect
28. #14582645C22semidirect
29. Q8⋊(C43⋊C8)C22semidirect
233. C2×#556D43semidirect
281. C43#18536semidirect

Maximal subgroups

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

subgroupindex
#191449912
#191447172
#191446862
#191337672
#191337052
#191333122
#191330422
#191330382
C2×C43×#5562
#1853643