Finite Group Databasebeta

← #25150260

Subgroups — #25150260

Order 11008.

1116 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583518C211yesmaximal, characteristic
2C2×#14583249C211yesmaximal, characteristic, complemented
3#19140362C211yesmaximal, characteristic, complemented
4#19135602C212yesmaximal, complemented
5#19135595C212yesmaximal
6#19135568C211yesmaximal, characteristic, complemented
7#19135407C211yesmaximal, characteristic, complemented
8#19134938C212yesmaximal, complemented
9#19134931C212yesmaximal, complemented
10#19134364C211yesmaximal, characteristic, complemented
11C2×C43×#497C211yesmaximal, characteristic, complemented
12#14583518—24no—
13#14583518—24no—
14C2×#13063325C2211yescharacteristic
15C2×#13063318—21no—
16C2×#13063311—21no—
17C2×#13063309—21no—
18C2×#13063302—21no—
19C2×#13063301C2211yescharacteristic
20C2×#13063301C2212yes—
21C2×#13063296C2211yescharacteristic
22C2×Q8×Dic43C2211yescharacteristic
23C2×D4×Dic43C2211yescharacteristic
24C2×#13063282C2211yescharacteristic
25#14583249—24no—
26C2×#13063249C2212yes—
27C2×#13063249C2212yes—
28C2×#13063249C2212yes—
29C2×#13063246C2212yes—
30C2×(C2×D43)⋊C8C2212yes—
31C2×C4×C43⋊C8C2211yescharacteristic
32#14582830—21no—
33#14582830—21no—
34#14582825—21no—
35#14582825—21no—
36#14582806C2212yes—
37#14582765C2211yescharacteristic
38#14582662C2212yes—
39#14582662C2212yes—
40#14582653C2212yes—
41C22×Q16×C43C2212yes—
42C22×SD16×C43C2212yes—
43C2×C4⋊Q8×C43C2211yescharacteristic
44C2×#124×C43C2211yescharacteristic
45C43×#497—24no—
46C2×#97×C43C2211yescharacteristic
47C22×Dic86—21no—
48C22×C22⋊D43—21no—
49C23×Dic43—21no—
50C22×C4×D43C2311yescharacteristic
51C22×C43⋊C8C2312yes—
52#13063325—22no—
53#13063325D414yes—
54#13063318—28no—
55#13063311—28no—
56#13063309—28no—
57#13063302—28no—
58#13063301—22no—
59#13063301—22no—
60#13063301—42no—
61#13063301—42no—
62#13063296—22no—
63#13063296—22no—
64Q8×Dic43—22no—
65Q8×Dic43—22no—
66D4×Dic43—22no—
67D4×Dic43—22no—
68#13063282—22no—
69#13063282—22no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2312yes—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—22no—
77C2×Dic43⋊C4D411yescharacteristic
78C2×Dic43⋊C4D411yescharacteristic
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—22no—
83C2×(C2×D43)⋊C4D411yescharacteristic
84C2×(C2×D43)⋊C4D411yescharacteristic
85C2×C4×Dic43—21no—
86C2×C4×Dic43C2311yescharacteristic
87#13063249—24no—
88#13063249—24no—
89#13063249—42no—
90#13063246—42no—
91(C2×D43)⋊C8—24no—
92C4×C43⋊C8—22no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—22no—
96C43⋊#95—22no—
97C22×Q8×C43C2312yes—
98C22×Q8×C43C2311yescharacteristic
99C22×D4×C43C2311yescharacteristic
100C2×Q16×C43—24no—
101C2×Q16×C43—24no—
102C2×Q16×C43—42no—
103C2×SD16×C43—24no—
104C2×SD16×C43—24no—
105C2×SD16×C43—42no—
106C22×C8×C43C2312yes—
107C4⋊Q8×C43—22no—
108C4⋊Q8×C43—22no—
109#124×C43—22no—
110#124×C43D414yes—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C42×C43C2311yescharacteristic
116#97×C43—22no—
117C24×C43—21no—
118C23×D43C2×D411yescharacteristic
119C2×Q8×C43—21no—
120C2×Q8×C43—22no—
121C2×Q8×C43—22no—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—22no—
125C2×Q8×C43—22no—
126C2×Q8×C43—22no—
127C2×Q8×C43—22no—
128C2×Q8×C43C2×D412yes—
129C2×D4×C43—21no—
130C2×D4×C43—22no—
131C2×D4×C43—22no—
132C2×D4×C43C2×D412yes—
133C22×C4×C43—21no—
134C22×C4×C43—22no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C2×C22⋊D43—24no—
139C2×C22⋊D43—82no—
140C22×Dic43—24no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—22no—
144C22×Dic43—82no—
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—22no—
151C2×C4×D43—22no—
152C2×Dic86—24no—
153C2×Dic86—82no—
154Q16×C43—48no—
155SD16×C43—48no—
156C2×C8×C43—22no—
157C2×C8×C43—22no—
158C2×C8×C43#4114yes—
159C4⋊C4×C43—42no—
160C4⋊C4×C43—42no—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—24no—
163C42×C43C2×D412yes—
164C42×C43C2×D412yes—
165C22⋊Dic43—24no—
166C22⋊Dic43—24no—
167(C2×D43)⋊C4—24no—
168(C2×D43)⋊C4—22no—
169(C2×D43)⋊C4—22no—
170(C2×D43)⋊C4—44no—
171C4⋊Dic43—24no—
172C4⋊Dic43—24no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—22no—
176C4⋊Dic43—22no—
177C4⋊Dic43C2×D412yes—
178C4⋊Dic43C2×D412yes—
179Dic43⋊C4—24no—
180Dic43⋊C4—22no—
181Dic43⋊C4—22no—
182Dic43⋊C4—44no—
183C4×Dic43—24no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—22no—
189C23×C43—22no—
190C23×C43—41no—
191C23×C43—41no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43C22×D411yescharacteristic
195C22×D43—21no—
196C22×D43—21no—
197C22×D43—21no—
198C22×D43—22no—
199C22×D43—22no—
200Q8×C43—24no—
201Q8×C43—42no—
202Q8×C43—42no—
203Q8×C43—42no—
204Q8×C43—42no—
205Q8×C43—42no—
206D4×C43—24no—
207D4×C43—42no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43#12012yes—
217C2×C4×C43#12012yes—
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C2×#4112yes—
221C2×C4×C43H(5,𝔽2)12yes—
222C22⋊D43—84no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—22no—
226C2×Dic43—21no—
227C2×Dic43—22no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—84no—
238C4×D43—42no—
239C4×D43—42no—
240Dic86—84no—
241C8×C43—24no—
242C43⋊C8—42no—
243#25613—431nomaximal, Sylow
244C22×C43—42no—
245C22×C43—42no—
246C22×C43—42no—
247C22×C43—82no—
248C22×C43—82no—
249C22×C43C2×#12011yescharacteristic
250C22×C43#53211yescharacteristic
251C22×C43#53511yescharacteristic
252C22×C43#57712yes—
253C22×C43#57812yes—
254C2×D43—42no—
255C2×D43—41no—
256C2×D43—42no—
257C2×D43—41no—
258C2×D43—41no—
259C4×C43—22no—
260C4×C43—22no—
261C4×C43—42no—
262C4×C43—82no—
263C4×C43#54612yes—
264C4×C43#55012yes—
265Dic43—41no—
266Dic43—42no—
267Dic43—42no—
268Dic43—41no—
269Dic43—41no—
270Dic43—82no—
271C2×#542—431no—
272C2×#497D4311yescharacteristic, complemented
273C2×#487—431no—
274#2621—431no—
275#2001—432no—
276#2000—432no—
277#1993—431no—
278#1958—431no—
279#1878—432no—
280#1877—432no—
281#1750—431no—
282C2×C43—82no—
283C2×C43#243111yescharacteristic
284C2×C43#300911yescharacteristic
285C2×C43#301111yescharacteristic
286C2×C43#317812yes—
287C2×C43#322512yes—
288D43—81no—
289C22×Q16C2×D4312yes—
290C22×SD16C2×D4312yes—
291#542—864no—
292#542—864no—
293C2×C4⋊Q8—431no—
294C2×C4⋊Q8C2×D4311yescharacteristic
295C2×#126—861no—
296C2×#124—861no—
297C2×#124C2×D4311yescharacteristic
298C2×#123—861no—
299C2×C22⋊Q8—431no—
300C2×C22⋊Q8—432no—
301C2×C22⋊Q8—861no—
302C2×#121—431no—
303C2×C4×Q8—431no—
304C2×C4×D4—431no—
305C2×#117—431no—
306#497—24no—
307#487—864no—
308C2×#103—432no—
309C2×#103—432no—
310C2×#103—432no—
311C2×#102—432no—
312C2×C22⋊C8—432no—
313C2×#97C2×D4311yescharacteristic
314C2×C4×C8—431no—
315#398—861no—
316#398—861no—
317#397—861no—
318#397—861no—
319#391—432no—
320#382—431no—
321#340—432no—
322#340—432no—
323#336—432no—
324C43#2561311yescharacteristic, complemented, Sylow
325C22×Q8—861no—
326C22×Q8C22×D4312yes—
327C22×Q8C22×D4311yescharacteristic
328C22×D4—861no—
329C22×D4C22×D4311yescharacteristic
330C23×C4—431no—
331C23×C4—861no—
332C2×Q16—24no—
333C2×Q16—24no—
334C2×Q16—42no—
335C2×SD16—24no—
336C2×SD16—24no—
337C2×SD16—42no—
338C22×C8—432no—
339C22×C8C22×D4312yes—
340C4⋊Q8—22no—
341C4⋊Q8—22no—
342C4⋊Q8—434no—
343C4⋊Q8—862no—
344#126—868no—
345#124—22no—
346#124—868no—
347#124C22⋊D4314yes—
348#123—868no—
349C22⋊Q8—868no—
350C22⋊Q8—862no—
351C22⋊Q8—862no—
352C22⋊Q8—1722no—
353C22⋊Q8—1722no—
354#121—862no—
355#121—862no—
356C4×Q8—862no—
357C4×Q8—862no—
358C4×D4—862no—
359C4×D4—862no—
360#117—862no—
361#117—862no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—431no—
365C2×C4⋊C4—431no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—431no—
368C2×C4⋊C4—432no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—862no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—431no—
376C2×C22⋊C4—431no—
377C2×C22⋊C4—861no—
378C2×C22⋊C4—861no—
379C2×C22⋊C4—861no—
380C2×C22⋊C4—862no—
381C2×C42—431no—
382C2×C42—861no—
383C2×C42C22×D4311yescharacteristic
384#103—864no—
385#103—864no—
386#103—1722no—
387#102—1722no—
388C22⋊C8—864no—
389#97—22no—
390C4×C8—862no—
391#95—862no—
392#95—862no—
393#95—861no—
394#95—861no—
395C24—21no—
396C24—431no—
397C2×Q8—21no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—864no—
407C2×Q8—3442no—
408C2×Q8C2×C22⋊D4312yes—
409C2×D4—21no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—864no—
413C2×D4—3442no—
414C2×D4C2×C22⋊D4312yes—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—431no—
418C22×C4—431no—
419C22×C4—431no—
420C22×C4—864no—
421C22×C4—861no—
422C22×C4—861no—
423C22×C4—861no—
424C22×C4—861no—
425C22×C4—862no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—3442no—
429C22×C4D4×D4311yescharacteristic
430C22×C4D4×D4311yescharacteristic
431C22×C4C23×D4311yescharacteristic
432Q16—48no—
433SD16—48no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—862no—
437C2×C8—862no—
438C2×C8—862no—
439C2×C8#1062190014yes—
440C4⋊C4—42no—
441C4⋊C4—42no—
442C4⋊C4—432no—
443C4⋊C4—432no—
444C4⋊C4—864no—
445C4⋊C4—864no—
446C4⋊C4—862no—
447C4⋊C4—862no—
448C4⋊C4—864no—
449C4⋊C4—861no—
450C4⋊C4—861no—
451C4⋊C4—862no—
452C4⋊C4—862no—
453C4⋊C4—1724no—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—864no—
457C22⋊C4—864no—
458C22⋊C4—864no—
459C22⋊C4—862no—
460C22⋊C4—862no—
461C22⋊C4—1724no—
462C42—864no—
463C42—861no—
464C42—861no—
465C42D4×D4312yes—
466C42C2×C22⋊D4312yes—
467C23—22no—
468C23—41no—
469C23—42no—
470C23—42no—
471C23—41no—
472C23—861no—
473C23—861no—
474C23—862no—
475C23—862no—
476C23—861no—
477C23C2×D4×D4311yescharacteristic
478Q8—24no—
479Q8—42no—
480Q8—42no—
481Q8—42no—
482Q8—42no—
483Q8—42no—
484Q8—3444no—
485D4—24no—
486D4—42no—
487D4—3444no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—861no—
497C2×C4—862no—
498C2×C4—861no—
499C2×C4—862no—
500C2×C4—861no—
501C2×C4—861no—
502C2×C4—862no—
503C2×C4—862no—
504C2×C4—861no—
505C2×C4—3444no—
506C2×C4—1722no—
507C2×C4—1722no—
508C2×C4—1722no—
509C2×C4—1722no—
510C2×C4—1722no—
511C2×C4—1722no—
512C2×C4—1722no—
513C2×C4#1306329312yes—
514C2×C4#1306329312yes—
515C2×C4C2×D4×D4311yescharacteristic
516C2×C4C22×C22⋊D4311yescharacteristic
517C2×C4C2×#1062190012yes—
518C2×C4#1306337012yes—
519C8—24no—
520C8—1722no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—82no—
525C22—82no—
526C22—1722no—
527C22—1721no—
528C22—1721no—
529C22—1721no—
530C22—1722no—
531C22C2×#1306329311yescharacteristic
532C22#1458344711yescharacteristic
533C22#1458346211yescharacteristic
534C22#1458370812yes—
535C22#1458371512yes—
536C4—22no—
537C4—22no—
538C4—42no—
539C4—82no—
540C4—3442no—
541C4—1721no—
542C4—1721no—
543C4—1722no—
544C4—1722no—
545C4—1721no—
546C4#1458354312yes—
547C4#1458356912yes—
548C2—82no—
549C2—3441no—
550C2#1913821111yescharacteristic
551C2#1914387111yescharacteristic
552C2#1914388911yescharacteristic
553C2#1914526012yes—
554C2#1914569912yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#497C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenterC2×#497D43
hypocenterC43#25613
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
2. C2×#14583249C2semidirect
3. #19140362C2semidirect
4. #19135602C2semidirect
6. #19135568C2semidirect
7. #19135407C2semidirect
8. #19134938C2semidirect
9. #19134931C2semidirect
10. #19134364C2semidirect
11. C2×C43×#497C2semidirect
272. C2×#497D43semidirect
324. C43#25613semidirect

Maximal subgroups

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

subgroupindex
C2×#145835182
C2×#145832492
#191403622
#191356022
#191355952
#191355682
#191354072
#191349382
#191349312
#191343642
C2×C43×#4972
#2561343