Finite Group Databasebeta

← #25152769

Subgroups — #25152769

Order 11008.

1338 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D43C211yesmaximal, characteristic
2C2×#14583248C212yesmaximal, complemented
3#19142946C211yesmaximal, characteristic
4#19135842C211yesmaximal, characteristic, complemented
5#19135841C211yesmaximal, characteristic, complemented
6#19135838C211yesmaximal, characteristic, complemented
7#19135395C212yesmaximal, complemented
8#19134528C212yesmaximal
9#19134528C212yesmaximal
10#19134352C211yesmaximal, characteristic
11C43×#2043C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2212yes—
13C2×#13063325C2211yescharacteristic
14C2×#13063324—21no—
15C2×#13063324—21no—
16C2×#13063324C2211yescharacteristic
17C2×#13063323C2212yes—
18C4⋊Q8×D43—28no—
19C2×#13063303—21no—
20C2×C4⋊C4×D43—21no—
21C2×C4⋊C4×D43—21no—
22C2×C42×D43C2211yescharacteristic
23#14583248—28no—
24C2×#13063250C2212yes—
25C2×#13063250C2212yes—
26C2×#13063249C2212yes—
27C2×#13063249C2212yes—
28C2×#13063248C2212yes—
29C2×#13063248C2212yes—
30C2×(C2×D43)⋊C8C2212yes—
31C2×C8×Dic43C2212yes—
32#14582803—21no—
33#14582797C2211yescharacteristic
34#14582794—21no—
35#14582768C2211yescharacteristic
36#14582758—21no—
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582654C2211yescharacteristic
40C2×C4⋊Q8×C43C2211yescharacteristic
41C2×#103×C43C2212yes—
42C2×#103×C43C2212yes—
43C43×#389C2211yescharacteristic
44C43×#336C2211yescharacteristic
45C22×Dic86—22no—
46C22×Dic86—21no—
47C22×Dic86C2312yes—
48C2×Q8×D43—24no—
49C2×Q8×D43—24no—
50C2×Q8×D43—24no—
51C2×Q8×D43—24no—
52C2×Q8×D43—42no—
53C2×Q8×D43—42no—
54C22×C4×D43—22no—
55C22×C4×D43D411yescharacteristic
56C22×C4×D43D411yescharacteristic
57C22×C4×D43C2311yescharacteristic
58C22×C43⋊C8C2312yes—
59#13063325—24no—
60#13063324—28no—
61#13063324—28no—
62#13063324—24no—
63#13063323—24no—
64#13063323D418yes—
65#13063303—44no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×Dic43⋊C4—22no—
71C2×Dic43⋊C4—22no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C4⋊C4×D43—28no—
77C4⋊C4×D43—28no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×C4×Dic43D411yescharacteristic
81C2×C4×Dic43D411yescharacteristic
82C2×C4×Dic43C2311yescharacteristic
83C42×D43—24no—
84#13063250—24no—
85#13063250—42no—
86#13063249—24no—
87#13063249—42no—
88#13063248—24no—
89#13063248—42no—
90(C2×D43)⋊C8—24no—
91C8×Dic43—24no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C22×Q8×C43C2312yes—
96C22×C8×C43C2312yes—
97C4⋊Q8×C43—24no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C42×C43C2311yescharacteristic
104#103×C43—24no—
105#103×C43—42no—
106#95×C43—21no—
107C23×D43C2×D411yescharacteristic
108C2×Q8×C43—22no—
109C2×Q8×C43—22no—
110C2×Q8×C43—22no—
111C2×Q8×C43—22no—
112C2×Q8×C43—22no—
113C2×Q8×C43C2×D414yes—
114C22×C4×C43—22no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2411yescharacteristic
120C22×Dic43—22no—
121C22×Dic43—21no—
122C22×Dic43—21no—
123C22×Dic43C2×D411yescharacteristic
124C22×Dic43C2×D411yescharacteristic
125C22×Dic43C2×D411yescharacteristic
126Q8×D43—48no—
127Q8×D43—48no—
128Q8×D43—48no—
129Q8×D43—48no—
130C2×C4×D43—22no—
131C2×C4×D43—21no—
132C2×C4×D43—21no—
133C2×C4×D43—22no—
134C2×C4×D43—22no—
135C2×C4×D43—22no—
136C2×C4×D43—22no—
137C2×C4×D43—28no—
138C2×C4×D43—44no—
139C2×C4×D43—44no—
140C2×C4×D43SD1614yes—
141C2×C4×D43Q1614yes—
142C2×C4×D43#4114yes—
143C2×Dic86—22no—
144C2×Dic86—22no—
145C2×Dic86—22no—
146C2×Dic86—22no—
147C2×Dic86—28no—
148C2×Dic86—22no—
149C2×Dic86—44no—
150C2×Dic86—44no—
151C2×Dic86—42no—
152C2×Dic86—42no—
153C2×Dic86—42no—
154C2×Dic86C2×D414yes—
155C2×C8×C43—22no—
156C2×C8×C43—22no—
157C2×C8×C43—22no—
158C4⋊C4×C43—24no—
159C4⋊C4×C43—24no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—42no—
164C42×C43—22no—
165(C2×D43)⋊C4—42no—
166(C2×D43)⋊C4—42no—
167C4⋊Dic43—24no—
168C4⋊Dic43—24no—
169C4⋊Dic43—22no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172Dic43⋊C4—28no—
173Dic43⋊C4—28no—
174Dic43⋊C4—42no—
175Dic43⋊C4—42no—
176Dic43⋊C4—42no—
177Dic43⋊C4—42no—
178C4×Dic43—22no—
179C4×Dic43—22no—
180C4×Dic43C2×D414yes—
181C2×C43⋊C8—22no—
182C2×C43⋊C8—22no—
183C2×C43⋊C8—22no—
184C23×C43C22×D411yescharacteristic
185C22×D43—21no—
186C22×D43—21no—
187C22×D43—21no—
188C22×D43—21no—
189C22×D43#12412yes—
190C22×D43C2×SD1612yes—
191C22×D43C2×Q1612yes—
192Q8×C43—24no—
193Q8×C43—24no—
194Q8×C43—42no—
195Q8×C43—42no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—24no—
201C2×C4×C43—42no—
202C2×C4×C43—42no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43C2×SD1612yes—
210C2×C4×C43C2×Q1612yes—
211C2×C4×C43C22×D412yes—
212C2×C4×C43C2×#4112yes—
213C2×C4×C43H(5,𝔽2)11yescharacteristic
214C2×C4×C43H(5,𝔽2)11yescharacteristic
215C2×Dic43—21no—
216C2×Dic43—21no—
217C2×Dic43—24no—
218C2×Dic43—42no—
219C2×Dic43—42no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43#12012yes—
227C2×Dic43#12012yes—
228C2×Dic43#12412yes—
229C2×Dic43C2×SD1612yes—
230C2×Dic43C2×Q1612yes—
231C2×Dic43#13712yes—
232C2×Dic43#13712yes—
233C4×D43—24no—
234C4×D43—24no—
235C4×D43—28no—
236C4×D43—28no—
237C4×D43—416no—
238Dic86—24no—
239Dic86—24no—
240Dic86—416no—
241Dic86—42no—
242Dic86—42no—
243Dic86—84no—
244C8×C43—42no—
245C43⋊C8—42no—
246#25856—431nomaximal, Sylow
247C22×C43C2×#12011yescharacteristic
248C22×C43C2×#12411yescharacteristic
249C22×C43#53511yescharacteristic
250C22×C43C22×SD1611yescharacteristic
251C22×C43C22×Q1611yescharacteristic
252C22×C43C2×#13711yescharacteristic
253C22×C43C2×#13711yescharacteristic
254C2×D43—22no—
255C2×D43—22no—
256C2×D43—22no—
257C2×D43—22no—
258C2×D43—22no—
259C2×D43—22no—
260C2×D43#48714yescomplemented
261C4×C43—22no—
262C4×C43—22no—
263C4×C43—44no—
264C4×C43—81no—
265C4×C43—81no—
266C4×C43#54612yes—
267C4×C43#54612yes—
268Dic43—22no—
269Dic43—44no—
270Dic43—81no—
271Dic43—81no—
272Dic43#44814yes—
273Dic43#45114yes—
274C22×C4⋊Q8—431no—
275C2×#487—432no—
276#2857—431no—
277#2043—431no—
278#2043—431no—
279#2043—431no—
280#2043D4311yescharacteristic, complemented
281#1956—432no—
282#1787—432no—
283#1787—432no—
284C4×C22⋊C8—431no—
285C2×C43#243511yescharacteristic
286C2×C43C2×#44811yescharacteristic
287C2×C43C2×#45111yescharacteristic
288C2×C43C2×#48711yescharacteristic
289C2×C43#313911yescharacteristic
290C2×C43#320611yescharacteristic
291C2×C43#320911yescharacteristic
292D43—24no—
293C23×Q8—432no—
294C2×C4⋊Q8—431no—
295C2×C4⋊Q8—432no—
296C2×C4⋊Q8—431no—
297C2×C4⋊Q8—861no—
298C2×C4⋊Q8—861no—
299C2×C4⋊Q8—868no—
300C2×C4⋊Q8C2×D4311yescharacteristic
301C2×C22⋊Q8—861no—
302C22×C4⋊C4—861no—
303C22×C4⋊C4—861no—
304C22×C42—431no—
305#487—868no—
306C2×#103—432no—
307C2×#103—432no—
308C2×#103—432no—
309C2×#103—432no—
310C2×#103—432no—
311C2×#103—432no—
312C2×#103C2×D4312yes—
313C2×#103C2×D4312yes—
314C2×C22⋊C8—432no—
315C2×C4×C8—432no—
316#391—861no—
317#389—431no—
318#389—861no—
319#389C2×D4311yescharacteristic
320#384—431no—
321#380—431no—
322#380—431no—
323#380—861no—
324#336—431no—
325#336C2×D4311yescharacteristic
326C43#2585611yescharacteristic, complemented, Sylow
327C22×Q8—432no—
328C22×Q8—862no—
329C22×Q8—861no—
330C22×Q8—864no—
331C22×Q8—864no—
332C22×Q8—864no—
333C22×Q8—864no—
334C22×Q8—1722no—
335C22×Q8—1722no—
336C22×Q8C22×D4312yes—
337C23×C4—431no—
338C23×C4—431no—
339C23×C4—431no—
340C23×C4—862no—
341C22×C8—432no—
342C22×C8C22×D4312yes—
343C4⋊Q8—24no—
344C4⋊Q8—438no—
345C4⋊Q8—864no—
346C4⋊Q8—864no—
347C4⋊Q8—864no—
348C4⋊Q8—868no—
349C4⋊Q8—868no—
350C22⋊Q8—1724no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—431no—
355C2×C4⋊C4—431no—
356C2×C4⋊C4—868no—
357C2×C4⋊C4—868no—
358C2×C4⋊C4—862no—
359C2×C4⋊C4—862no—
360C2×C4⋊C4—861no—
361C2×C4⋊C4—861no—
362C2×C4⋊C4—861no—
363C2×C4⋊C4—861no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4—861no—
366C2×C4⋊C4C22×D4311yescharacteristic
367C2×C4⋊C4C22×D4311yescharacteristic
368C2×C22⋊C4—861no—
369C2×C22⋊C4—861no—
370C2×C42—431no—
371C2×C42—431no—
372C2×C42—431no—
373C2×C42—864no—
374C2×C42C22×D4311yescharacteristic
375#103—24no—
376#103—42no—
377#103—864no—
378#103—864no—
379#103—864no—
380#103—1722no—
381#103—1722no—
382#103—1722no—
383C22⋊C8—864no—
384C4×C8—864no—
385#95—21no—
386#95—861no—
387#95—861no—
388#95—861no—
389C24—431no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—434no—
396C2×Q8—868no—
397C2×Q8—862no—
398C2×Q8—862no—
399C2×Q8—862no—
400C2×Q8—862no—
401C2×Q8—862no—
402C2×Q8—1722no—
403C2×Q8—1722no—
404C2×Q8—1722no—
405C2×Q8—1724no—
406C2×Q8—1724no—
407C2×Q8—1728no—
408C2×Q8—1728no—
409C2×Q8—1728no—
410C2×Q8—1728no—
411C2×Q8D4×D4314yes—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—431no—
416C22×C4—431no—
417C22×C4—431no—
418C22×C4—434no—
419C22×C4—434no—
420C22×C4—434no—
421C22×C4—862no—
422C22×C4—862no—
423C22×C4—862no—
424C22×C4—862no—
425C22×C4—868no—
426C22×C4—862no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—862no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—1724no—
433C22×C4—1724no—
434C22×C4D4×D4311yescharacteristic
435C22×C4D4×D4311yescharacteristic
436C22×C4C23×D4311yescharacteristic
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—862no—
441C2×C8—862no—
442C2×C8—862no—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—42no—
449C4⋊C4—868no—
450C4⋊C4—868no—
451C4⋊C4—864no—
452C4⋊C4—864no—
453C4⋊C4—862no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—1722no—
457C4⋊C4—1722no—
458C4⋊C4—1722no—
459C4⋊C4—1722no—
460C22⋊C4—1722no—
461C22⋊C4—1722no—
462C42—22no—
463C42—434no—
464C42—862no—
465C42—862no—
466C23—432no—
467C23—432no—
468C23—432no—
469C23—861no—
470C23—861no—
471C23—861no—
472C23—861no—
473C23C2×D4×D4311yescharacteristic
474Q8—24no—
475Q8—24no—
476Q8—42no—
477Q8—42no—
478Q8—864no—
479Q8—864no—
480Q8—3444no—
481Q8—17216no—
482Q8—1722no—
483Q8—1722no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—24no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—432no—
498C2×C4—432no—
499C2×C4—432no—
500C2×C4—432no—
501C2×C4—432no—
502C2×C4—432no—
503C2×C4—432no—
504C2×C4—868no—
505C2×C4—868no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—864no—
509C2×C4—864no—
510C2×C4—864no—
511C2×C4—17216no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4—1722no—
519C2×C4—1722no—
520C2×C4SD16×D4312yes—
521C2×C4Q16×D4312yes—
522C2×C4C2×D4×D4312yes—
523C2×C4#41×D4312yes—
524C2×C4#1306337011yescharacteristic
525C2×C4#1306337111yescharacteristic
526C8—42no—
527C8—1722no—
528C22—434no—
529C22—862no—
530C22—862no—
531C22—862no—
532C22—862no—
533C22—862no—
534C22—862no—
535C22#120×D4311yescharacteristic
536C22#124×D4311yescharacteristic
537C22#1458346511yescharacteristic
538C22C2×SD16×D4311yescharacteristic
539C22C2×Q16×D4311yescharacteristic
540C22#137×D4311yescharacteristic
541C22#137×D4311yescharacteristic
542C4—22no—
543C4—22no—
544C4—44no—
545C4—81no—
546C4—81no—
547C4—434no—
548C4—434no—
549C4—862no—
550C4—3441no—
551C4—3441no—
552C4—1724no—
553C4#1458353812yes—
554C4#1458354112yes—
555C2—864no—
556C2#1913824111yescharacteristic
557C2#448×D4311yescharacteristic
558C2#451×D4311yescharacteristic
559C2#487×D4311yescharacteristic
560C2#1914497411yescharacteristic
561C2#1914551911yescharacteristic
562C2#1914554211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2043C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2043D43
hypocenterC43#25856
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
2. C2×#14583248C2semidirect
4. #19135842C2semidirect
5. #19135841C2semidirect
6. #19135838C2semidirect
7. #19135395C2semidirect
11. C43×#2043C2semidirect
260. C2×D43#487semidirect
280. #2043D43semidirect
326. C43#25856semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D432
C2×#145832482
#191429462
#191358422
#191358412
#191358382
#191353952
#191345282
#191343522
C43×#20432
#2585643