Finite Group Databasebeta

← #25150265

Subgroups — #25150265

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×#14583520C211yesmaximal, characteristic
2C2×#14583291C211yesmaximal, characteristic, complemented
3C2×#14583249C211yesmaximal, characteristic, complemented
4#19135603C212yesmaximal, complemented
5#19135596C212yesmaximal
6#19135567C211yesmaximal, characteristic, complemented
7#19135404C211yesmaximal, characteristic, complemented
8#19134939C212yesmaximal, complemented
9#19134932C212yesmaximal, complemented
10#19134361C211yesmaximal, characteristic, complemented
11C43×#2621C211yesmaximal, characteristic, complemented
12C22×#10621885C2212yes—
13C22×#10621884C2212yes—
14#14583520—24no—
15#14583520—24no—
16C2×#13063325C2211yescharacteristic
17C2×#13063320—21no—
18C2×#13063313C2211yescharacteristic
19C2×#13063311—21no—
20C2×#13063307—21no—
21C2×#13063304C2211yescharacteristic
22C2×#13063303—21no—
23C2×#13063299C2211yescharacteristic
24C2×C4×Dic86C2211yescharacteristic
25C2×C4×D172C2211yescharacteristic
26#14583291—24no—
27#14583249—24no—
28C2×#13063249C2212yes—
29C2×#13063249C2212yes—
30C2×#13063248C2212yes—
31C2×#13063245C2212yes—
32C2×C22⋊(C43⋊C8)C2212yes—
33C2×#13063236C2211yescharacteristic
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582661C2212yes—
36#14582661C2212yes—
37#14582654C2212yes—
38C2×C4⋊Q8×C43C2211yescharacteristic
39C2×C22⋊Q8×C43C2212yes—
40C2×#117×C43C2211yescharacteristic
41C43×#398—21no—
42C43×#398—21no—
43C43×#397—21no—
44C43×#397—21no—
45C43×#391C2212yes—
46C43×#382C2211yescharacteristic
47C22×Dic86—21no—
48C22×Dic86C2311yescharacteristic
49C22×D172C2311yescharacteristic
50C22×C22⋊D43—21no—
51C22×C4×D43—21no—
52C2×#10621885—24no—
53C2×#10621885—24no—
54C2×#10621885—42no—
55C2×#10621884—24no—
56C2×#10621884—24no—
57C2×#10621884—42no—
58C22×C43⋊C8C2312yes—
59C22×C43⋊C8C2312yes—
60#13063325—22no—
61#13063325D414yes—
62#13063320—28no—
63#13063313—22no—
64#13063313D414yes—
65#13063311—28no—
66#13063307—28no—
67#13063304—22no—
68#13063304—22no—
69#13063303—28no—
70#13063299—22no—
71#13063299—22no—
72C4×Dic86—22no—
73C4×Dic86—22no—
74C4×D172—22no—
75C4×D172—22no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87#13063249—24no—
88#13063249—24no—
89#13063248—42no—
90#13063245—42no—
91C22⋊(C43⋊C8)—24no—
92#13063236—22no—
93C4×C43⋊C8—22no—
94C22×Q8×C43C2312yes—
95C23×C4×C43C2311yescharacteristic
96C4⋊Q8×C43—22no—
97C4⋊Q8×C43—22no—
98C22⋊Q8×C43—42no—
99C22⋊Q8×C43—42no—
100#117×C43—22no—
101#117×C43—22no—
102C2×C4⋊C4×C43—22no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43D411yescharacteristic
106C2×C4⋊C4×C43D411yescharacteristic
107C2×C4⋊C4×C43C2312yes—
108C2×C22⋊C4×C43—22no—
109C2×C22⋊C4×C43D411yescharacteristic
110C2×C22⋊C4×C43D411yescharacteristic
111C2×C42×C43C2311yescharacteristic
112C2×C42×C43C2311yescharacteristic
113#95×C43—21no—
114#95×C43—21no—
115#95×C43—22no—
116#95×C43—22no—
117C24×C43C2×D411yescharacteristic
118C23×D43—21no—
119C2×Q8×C43—22no—
120C2×Q8×C43—22no—
121C2×Q8×C43—22no—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—22no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2411yescharacteristic
137C2×C22⋊D43—24no—
138C2×C22⋊D43—82no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C2×D172—21no—
143C2×D172—22no—
144C2×D172—22no—
145C2×D172C2×D412yes—
146C2×C4×D43—24no—
147C2×C4×D43—82no—
148C2×Dic86—22no—
149C2×Dic86—22no—
150C2×Dic86—21no—
151C2×Dic86—24no—
152C2×Dic86—82no—
153C2×Dic86C2×D412yes—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—44no—
159C4⋊C4×C43—42no—
160C4⋊C4×C43—42no—
161C22⋊C4×C43—22no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—44no—
164C42×C43—21no—
165C42×C43—21no—
166C42×C43C2×D412yes—
167C42×C43C2×D412yes—
168C22⋊Dic43—24no—
169#10621885—48no—
170#10621884—48no—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—24no—
173(C2×D43)⋊C4—24no—
174(C2×D43)⋊C4—24no—
175C4⋊Dic43—24no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43C2×D412yes—
179C4⋊Dic43C2×D412yes—
180Dic43⋊C4—24no—
181Dic43⋊C4—24no—
182C4×Dic43—24no—
183C2×C43⋊C8—22no—
184C2×C43⋊C8—22no—
185C2×C43⋊C8—22no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C2×C43⋊C8#4114yes—
189C23×C43—21no—
190C23×C43—21no—
191C23×C43—21no—
192C23×C43—22no—
193C23×C43—22no—
194C23×C43C22×D411yescharacteristic
195C22×D43—22no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—42no—
199C22×D43—42no—
200Q8×C43—42no—
201Q8×C43—42no—
202Q8×C43—42no—
203Q8×C43—42no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43#12012yes—
222C2×C4×C43#12012yes—
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4112yes—
226C2×C4×C43H(5,𝔽2)12yes—
227C22⋊D43—84no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235D172—24no—
236D172—42no—
237C4×D43—84no—
238Dic86—24no—
239Dic86—42no—
240Dic86—84no—
241C43⋊C8—24no—
242C43⋊C8—42no—
243#25613—431nomaximal, Sylow
244C22×C43—42no—
245C22×C43—41no—
246C22×C43—42no—
247C22×C43—41no—
248C22×C43—41no—
249C22×C43C2×#12011yescharacteristic
250C22×C43#53211yescharacteristic
251C22×C43#53511yescharacteristic
252C22×C43#57712yes—
253C22×C43#57812yes—
254C2×D43—42no—
255C2×D43—42no—
256C2×D43—42no—
257C2×D43—82no—
258C2×D43—82no—
259C4×C43—22no—
260C4×C43—22no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—82no—
265C4×C43—82no—
266C4×C43#54612yes—
267C4×C43#55012yes—
268Dic43—42no—
269Dic43—42no—
270Dic43—42no—
271C2×#542—431no—
272C2×#497—431no—
273C2×#487—431no—
274#2621D4311yescharacteristic, complemented
275#2001—432no—
276#2000—432no—
277#1993—431no—
278#1958—431no—
279#1878—432no—
280#1877—432no—
281#1750—431no—
282C2×C43—81no—
283C2×C43#243111yescharacteristic
284C2×C43#300911yescharacteristic
285C2×C43#301111yescharacteristic
286C2×C43#317812yes—
287C2×C43#322512yes—
288D43—82no—
289C22×Q16—432no—
290C22×SD16—432no—
291#542—864no—
292#542—864no—
293C2×C4⋊Q8—431no—
294C2×C4⋊Q8C2×D4311yescharacteristic
295C2×#126—861no—
296C2×#124—431no—
297C2×#124—861no—
298C2×#123—861no—
299C2×C22⋊Q8—431no—
300C2×C22⋊Q8—861no—
301C2×C22⋊Q8C2×D4312yes—
302C2×#121—431no—
303C2×C4×Q8—431no—
304C2×C4×D4—431no—
305C2×#117C2×D4311yescharacteristic
306#497—864no—
307#487—864no—
308C2×#103—432no—
309C2×#103—432no—
310C2×#103—432no—
311C2×#102—432no—
312C2×C22⋊C8—432no—
313C2×#97—431no—
314C2×C4×C8—431no—
315#398—21no—
316#398—21no—
317#397—21no—
318#397—21no—
319#391C2×D4312yes—
320#382C2×D4311yescharacteristic
321#340—432no—
322#340—432no—
323#336—432no—
324C43#2561311yescharacteristic, complemented, Sylow
325C22×Q8—431no—
326C22×Q8—861no—
327C22×Q8C22×D4312yes—
328C22×D4—431no—
329C22×D4—861no—
330C23×C4—861no—
331C23×C4C22×D4311yescharacteristic
332C2×Q16—864no—
333C2×Q16—864no—
334C2×Q16—1722no—
335C2×SD16—864no—
336C2×SD16—864no—
337C2×SD16—1722no—
338C22×C8—432no—
339C22×C8—432no—
340C4⋊Q8—22no—
341C4⋊Q8—22no—
342C4⋊Q8—434no—
343C4⋊Q8—862no—
344#126—868no—
345#124—434no—
346#124—868no—
347#124—862no—
348#123—868no—
349C22⋊Q8—42no—
350C22⋊Q8—42no—
351C22⋊Q8—868no—
352C22⋊Q8—862no—
353C22⋊Q8—862no—
354#121—862no—
355#121—862no—
356C4×Q8—862no—
357C4×Q8—862no—
358C4×D4—862no—
359C4×D4—862no—
360#117—22no—
361#117—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—431no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4C22⋊D4311yescharacteristic
371C2×C4⋊C4C22⋊D4311yescharacteristic
372C2×C4⋊C4C22×D4312yes—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—861no—
375C2×C22⋊C4—861no—
376C2×C22⋊C4—861no—
377C2×C22⋊C4—861no—
378C2×C22⋊C4—861no—
379C2×C22⋊C4C22⋊D4311yescharacteristic
380C2×C22⋊C4C22⋊D4311yescharacteristic
381C2×C42—861no—
382C2×C42C22×D4311yescharacteristic
383C2×C42C22×D4311yescharacteristic
384#103—864no—
385#103—864no—
386#103—1722no—
387#102—1722no—
388C22⋊C8—864no—
389#97—862no—
390C4×C8—862no—
391#95—21no—
392#95—21no—
393#95—22no—
394#95—22no—
395C24—861no—
396C24C2×C22⋊D4311yescharacteristic
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—432no—
404C2×Q8—864no—
405C2×Q8—861no—
406C2×Q8—862no—
407C2×Q8—862no—
408C2×Q8—3442no—
409C2×D4—432no—
410C2×D4—864no—
411C2×D4—861no—
412C2×D4—862no—
413C2×D4—862no—
414C2×D4—3442no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—864no—
422C22×C4—861no—
423C22×C4—861no—
424C22×C4—861no—
425C22×C4—3442no—
426C22×C4C2×C22⋊D4311yescharacteristic
427C22×C4C2×C22⋊D4311yescharacteristic
428C22×C4C2×C22⋊D4311yescharacteristic
429C22×C4C2×C22⋊D4311yescharacteristic
430C22×C4C2×C22⋊D4311yescharacteristic
431C22×C4C23×D4311yescharacteristic
432Q16—1728no—
433SD16—1728no—
434C2×C8—434no—
435C2×C8—862no—
436C2×C8—862no—
437C2×C8—862no—
438C2×C8—862no—
439C2×C8—862no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—44no—
445C4⋊C4—42no—
446C4⋊C4—42no—
447C4⋊C4—432no—
448C4⋊C4—432no—
449C4⋊C4—864no—
450C4⋊C4—864no—
451C4⋊C4—864no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—44no—
457C22⋊C4—864no—
458C22⋊C4—864no—
459C22⋊C4—864no—
460C22⋊C4—864no—
461C22⋊C4—864no—
462C42—21no—
463C42—21no—
464C42—864no—
465C42D4×D4312yes—
466C42D4×D4312yes—
467C23—21no—
468C23—21no—
469C23—22no—
470C23—22no—
471C23—21no—
472C23—862no—
473C23—1721no—
474C23—1722no—
475C23—1722no—
476C23—1721no—
477C23C22×C22⋊D4311yescharacteristic
478Q8—42no—
479Q8—42no—
480Q8—42no—
481Q8—42no—
482Q8—864no—
483Q8—3444no—
484Q8—1722no—
485D4—864no—
486D4—3444no—
487D4—1722no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—862no—
506C2×C4—862no—
507C2×C4—862no—
508C2×C4—3444no—
509C2×C4—1721no—
510C2×C4—1722no—
511C2×C4—1722no—
512C2×C4—1721no—
513C2×C4#1306329312yes—
514C2×C4#1306329312yes—
515C2×C4C2×D4×D4311yescharacteristic
516C2×C4C2×D4×D4311yescharacteristic
517C2×C4#41×D4312yes—
518C2×C4#1306337012yes—
519C8—864no—
520C8—1722no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—42no—
526C22—3442no—
527C22—3442no—
528C22—1722no—
529C22—1722no—
530C22—1722no—
531C22C2×#1306329311yescharacteristic
532C22#1458344511yescharacteristic
533C22#1458346611yescharacteristic
534C22#1458370712yes—
535C22#1458371412yes—
536C4—22no—
537C4—22no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—82no—
542C4—82no—
543C4—1722no—
544C4—1722no—
545C4—1722no—
546C4#1458354612yes—
547C4#1458356712yes—
548C2—81no—
549C2—3442no—
550C2#1913821511yescharacteristic
551C2#1914387011yescharacteristic
552C2#1914388811yescharacteristic
553C2#1914526512yes—
554C2#1914570412yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2621C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#2621D43
hypocenterC43#25613
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2621

Complements

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

NH ≅ G/Ntype
2. C2×#14583291C2semidirect
3. C2×#14583249C2semidirect
4. #19135603C2semidirect
6. #19135567C2semidirect
7. #19135404C2semidirect
8. #19134939C2semidirect
9. #19134932C2semidirect
10. #19134361C2semidirect
11. C43×#2621C2semidirect
274. #2621D43semidirect
324. C43#25613semidirect

Maximal subgroups

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

subgroupindex
C2×#145835202
C2×#145832912
C2×#145832492
#191356032
#191355962
#191355672
#191354042
#191349392
#191349322
#191343612
C43×#26212
#2561343