Finite Group Databasebeta

← #25129892

Subgroups — #25129892

Order 11008.

1144 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583454C211yesmaximal, characteristic
2C2×#14583231C212yesmaximal
3#389×D43C211yesmaximal, characteristic
4#19135925C211yesmaximal, characteristic, complemented
5#19135842C211yesmaximal, characteristic, complemented
6#19135841C211yesmaximal, characteristic, complemented
7#19134901C212yesmaximal
8#19134864C212yesmaximal, complemented
9#19134860C212yesmaximal, complemented
10#19134662C211yesmaximal, characteristic
11C43×#2058C211yesmaximal, characteristic, complemented
12#14583454—28no—
13C2×#13063325C2211yescharacteristic
14C2×#13063316—21no—
15C2×#13063305C2212yes—
16C2×#13063301—21no—
17C2×Q8×Dic43—21no—
18C2×#13063290C2212yes—
19C2×#13063283—21no—
20C2×C4⋊C4×D43—21no—
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23C2×C42×D43C2211yescharacteristic
24#14583231—28no—
25C2×#13063256C2212yes—
26C2×#13063250C2212yes—
27C2×#13063250C2212yes—
28C2×#13063248C2212yes—
29C2×#13063248C2212yes—
30C2×(C2×D43)⋊C8C2212yes—
31#14582798C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582796—21no—
34#14582795C2211yescharacteristic
35#14582794—21no—
36#95×D43—21no—
37#14582661C2212yes—
38#14582654C2211yescharacteristic
39#14582653C2212yes—
40C2×C4⋊Q8×C43C2211yescharacteristic
41C2×#106×C43C2212yes—
42C43×#389C2211yescharacteristic
43C43×#340C2212yes—
44C43×#336C2211yescharacteristic
45C22×Dic86C2312yes—
46C22×C4×D43—21no—
47C22×C4×D43—21no—
48C22×C4×D43D411yescharacteristic
49C22×C4×D43D411yescharacteristic
50C22×C4×D43C2311yescharacteristic
51C22×C43⋊C8C2312yes—
52#13063325—24no—
53#13063316—28no—
54#13063305—24no—
55#13063305D418yes—
56#13063301—28no—
57Q8×Dic43—28no—
58#13063290—24no—
59#13063290—24no—
60#13063283—28no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—22no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43C2311yescharacteristic
66C2×C4⋊Dic43C2311yescharacteristic
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—22no—
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C4⋊C4×D43—22no—
73C4⋊C4×D43—22no—
74C4⋊C4×D43—24no—
75C4⋊C4×D43—44no—
76C2×(C2×D43)⋊C4—22no—
77C2×C4×Dic43—22no—
78C2×C4×Dic43D411yescharacteristic
79C2×C4×Dic43D411yescharacteristic
80C2×C4×Dic43C2311yescharacteristic
81C42×D43—24no—
82#13063256—24no—
83#13063250—24no—
84#13063250—24no—
85#13063248—24no—
86#13063248—24no—
87(C2×D43)⋊C8—24no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C22×Q8×C43—21no—
92C22×C8×C43C2312yes—
93C4⋊Q8×C43—24no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2312yes—
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C42×C43C2311yescharacteristic
100#106×C43—24no—
101#95×C43—21no—
102C23×D43C2×D411yescharacteristic
103C2×Q8×C43—24no—
104C2×Q8×C43—42no—
105C2×Q8×C43—42no—
106C22×C4×C43—21no—
107C22×C4×C43—22no—
108C22×C4×C43—21no—
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2411yescharacteristic
112C22×Dic43—21no—
113C22×Dic43—22no—
114C22×Dic43—21no—
115C22×Dic43C2×D411yescharacteristic
116C22×Dic43C2×D411yescharacteristic
117C22×Dic43C2×D411yescharacteristic
118C2×C4×D43—21no—
119C2×C4×D43—21no—
120C2×C4×D43—22no—
121C2×C4×D43—24no—
122C2×C4×D43—22no—
123C2×C4×D43—22no—
124C2×C4×D43—22no—
125C2×C4×D43—22no—
126C2×C4×D43—41no—
127C2×C4×D43—42no—
128C2×C4×D43—42no—
129C2×C4×D43—42no—
130C2×C4×D43—42no—
131C2×C4×D43—42no—
132C2×C4×D43SD1614yes—
133C2×C4×D43C2×D414yes—
134C2×Dic86—22no—
135C2×Dic86—22no—
136C2×Dic86—22no—
137C2×Dic86—22no—
138C2×Dic86—22no—
139C2×Dic86C2×D414yes—
140C2×C8×C43—22no—
141C2×C8×C43—22no—
142C2×C8×C43—22no—
143C4⋊C4×C43—24no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—42no—
148C4⋊C4×C43C2×D414yes—
149C4⋊C4×C43#4112yes—
150C42×C43—22no—
151(C2×D43)⋊C4—28no—
152C4⋊Dic43—24no—
153C4⋊Dic43—24no—
154C4⋊Dic43—21no—
155C4⋊Dic43—28no—
156C4⋊Dic43—22no—
157C4⋊Dic43—42no—
158C4⋊Dic43#4112yes—
159Dic43⋊C4—24no—
160Dic43⋊C4—28no—
161Dic43⋊C4—42no—
162Dic43⋊C4—42no—
163Dic43⋊C4—42no—
164C4×Dic43—28no—
165C4×Dic43—22no—
166C4×Dic43—22no—
167C4×Dic43—22no—
168C2×C43⋊C8—22no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—22no—
171C23×C43C22×D411yescharacteristic
172C22×D43—21no—
173C22×D43—21no—
174C22×D43—21no—
175C22×D43—21no—
176C22×D43#12012yes—
177C22×D43C2×SD1612yes—
178C22×D43#13712yes—
179Q8×C43—48no—
180C2×C4×C43—21no—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—21no—
184C2×C4×C43—24no—
185C2×C4×C43—22no—
186C2×C4×C43—41no—
187C2×C4×C43—42no—
188C2×C4×C43—41no—
189C2×C4×C43—42no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43C2×SD1612yes—
194C2×C4×C43#13712yes—
195C2×C4×C43C22×D412yes—
196C2×C4×C43C2×#4111yescharacteristic
197C2×C4×C43C2×#4111yescharacteristic
198C2×C4×C432−1+412yes—
199C2×Dic43—21no—
200C2×Dic43—21no—
201C2×Dic43—21no—
202C2×Dic43—21no—
203C2×Dic43—21no—
204C2×Dic43—24no—
205C2×Dic43—22no—
206C2×Dic43—21no—
207C2×Dic43—21no—
208C2×Dic43—42no—
209C2×Dic43—42no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—41no—
214C2×Dic43—41no—
215C2×Dic43#12012yes—
216C2×Dic43C2×SD1612yes—
217C4×D43—28no—
218C4×D43—24no—
219C4×D43—24no—
220C4×D43—44no—
221C4×D43—48no—
222C4×D43—84no—
223Dic86—24no—
224Dic86—24no—
225Dic86—42no—
226Dic86—42no—
227C8×C43—42no—
228C43⋊C8—42no—
229#24063—431nomaximal, Sylow
230C22×C43C2×#12011yescharacteristic
231C22×C43#52511yescharacteristic
232C22×C43#53611yescharacteristic
233C22×C43C22×SD1611yescharacteristic
234C22×C43C2×#13711yescharacteristic
235C22×C43C2×#13711yescharacteristic
236C22×C43#57511yescharacteristic
237C2×D43—22no—
238C2×D43—22no—
239C2×D43—22no—
240C2×D43—22no—
241C2×D43—22no—
242C2×D43—22no—
243C2×D43#44814yes—
244C4×C43—22no—
245C4×C43—22no—
246C4×C43—42no—
247C4×C43—44no—
248C4×C43—81no—
249C4×C43#54712yes—
250C4×C43#54712yes—
251Dic43—22no—
252Dic43—22no—
253Dic43—42no—
254Dic43—44no—
255Dic43—41no—
256Dic43—81no—
257C2×#533—431no—
258C2×#483—432no—
259C2×#389—431no—
260#2058—431no—
261#2058D4311yescharacteristic, complemented
262#2043—431no—
263#2043—431no—
264#1872—432no—
265#1865—432no—
266#1865—432no—
267#1817—431no—
268C2×C43#240611yescharacteristic
269C2×C43C2×#44811yescharacteristic
270C2×C43#300711yescharacteristic
271C2×C43#310111yescharacteristic
272C2×C43#311311yescharacteristic
273C2×C43#322911yescharacteristic
274C2×C43#323611yescharacteristic
275D43—24no—
276#533—868no—
277C2×C4⋊Q8—431no—
278C2×C4⋊Q8C2×D4311yescharacteristic
279C2×#125—861no—
280C2×C22⋊Q8—432no—
281C2×C22⋊Q8—861no—
282C2×C4×Q8—432no—
283C2×C4×Q8—861no—
284C2×#117—861no—
285C22×C4⋊C4—431no—
286C22×C4⋊C4—431no—
287C22×C4⋊C4—861no—
288C22×C42—431no—
289#483—868no—
290C2×#106—432no—
291C2×#106C2×D4312yes—
292C2×#103—432no—
293C2×#103—432no—
294C2×#103—432no—
295C2×#103—432no—
296C2×C22⋊C8—432no—
297#389—431no—
298#389—431no—
299#389—431no—
300#389—861no—
301#389—861no—
302#389C2×D4311yescharacteristic
303C2×#95—861no—
304#340—432no—
305#340C2×D4312yes—
306#336—432no—
307#336—431no—
308#336C2×D4311yescharacteristic
309C43#2406311yescharacteristic, complemented, Sylow
310C22×Q8—21no—
311C22×Q8—432no—
312C23×C4—431no—
313C23×C4—431no—
314C23×C4—431no—
315C23×C4—861no—
316C23×C4—861no—
317C22×C8—432no—
318C22×C8C22×D4312yes—
319C4⋊Q8—24no—
320C4⋊Q8—864no—
321#125—868no—
322C22⋊Q8—438no—
323C22⋊Q8—864no—
324C22⋊Q8—868no—
325C4×Q8—864no—
326C4×Q8—868no—
327C4×Q8—864no—
328#117—868no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—431no—
332C2×C4⋊C4—431no—
333C2×C4⋊C4—862no—
334C2×C4⋊C4—864no—
335C2×C4⋊C4—861no—
336C2×C4⋊C4—862no—
337C2×C4⋊C4—862no—
338C2×C4⋊C4—861no—
339C2×C4⋊C4—861no—
340C2×C4⋊C4—862no—
341C2×C4⋊C4—861no—
342C2×C4⋊C4—861no—
343C2×C4⋊C4—861no—
344C2×C4⋊C4—861no—
345C2×C4⋊C4—1724no—
346C2×C4⋊C4C22×D4311yescharacteristic
347C2×C4⋊C4C22×D4312yes—
348C2×C4⋊C4C22×D4311yescharacteristic
349C2×C22⋊C4—862no—
350C2×C42—431no—
351C2×C42—431no—
352C2×C42—431no—
353C2×C42—864no—
354C2×C42—862no—
355C2×C42C22×D4311yescharacteristic
356#106—24no—
357#106—864no—
358#103—864no—
359#103—864no—
360#103—864no—
361#103—864no—
362C22⋊C8—864no—
363#95—21no—
364#95—861no—
365#95—861no—
366#95—861no—
367C24—431no—
368C2×Q8—24no—
369C2×Q8—42no—
370C2×Q8—42no—
371C2×Q8—434no—
372C2×Q8—862no—
373C2×Q8—862no—
374C2×Q8—862no—
375C2×Q8—862no—
376C2×Q8—862no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—431no—
381C22×C4—431no—
382C22×C4—434no—
383C22×C4—434no—
384C22×C4—431no—
385C22×C4—862no—
386C22×C4—862no—
387C22×C4—862no—
388C22×C4—864no—
389C22×C4—861no—
390C22×C4—861no—
391C22×C4—862no—
392C22×C4—861no—
393C22×C4—862no—
394C22×C4—862no—
395C22×C4—861no—
396C22×C4—1721no—
397C22×C4—1722no—
398C22×C4—1722no—
399C22×C4—1722no—
400C22×C4—1722no—
401C22×C4—1722no—
402C22×C4D4×D4311yescharacteristic
403C22×C4D4×D4311yescharacteristic
404C22×C4C23×D4311yescharacteristic
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—862no—
409C2×C8—862no—
410C2×C8—862no—
411C4⋊C4—24no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—42no—
416C4⋊C4—432no—
417C4⋊C4—868no—
418C4⋊C4—864no—
419C4⋊C4—864no—
420C4⋊C4—868no—
421C4⋊C4—864no—
422C4⋊C4—861no—
423C4⋊C4—862no—
424C4⋊C4—1722no—
425C4⋊C4—1722no—
426C4⋊C4—1722no—
427C4⋊C4—1722no—
428C4⋊C4D4×D4314yes—
429C4⋊C4#1062190212yes—
430C22⋊C4—868no—
431C42—22no—
432C42—862no—
433C42—862no—
434C42—868no—
435C42—862no—
436C23—432no—
437C23—432no—
438C23—432no—
439C23—861no—
440C23—861no—
441C23—861no—
442C23—861no—
443C23C2×D4×D4311yescharacteristic
444Q8—48no—
445Q8—864no—
446Q8—864no—
447Q8—1722no—
448Q8—1722no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—432no—
463C2×C4—432no—
464C2×C4—868no—
465C2×C4—861no—
466C2×C4—861no—
467C2×C4—861no—
468C2×C4—861no—
469C2×C4—864no—
470C2×C4—864no—
471C2×C4—861no—
472C2×C4—864no—
473C2×C4—862no—
474C2×C4—861no—
475C2×C4—861no—
476C2×C4—3444no—
477C2×C4—1724no—
478C2×C4—1728no—
479C2×C4—1721no—
480C2×C4—1721no—
481C2×C4—1721no—
482C2×C4—1722no—
483C2×C4—1721no—
484C2×C4—1721no—
485C2×C4—1722no—
486C2×C4SD16×D4312yes—
487C2×C4#1306335412yes—
488C2×C4C2×D4×D4312yes—
489C2×C4#41×D4311yescharacteristic
490C2×C4C2×#1062190211yescharacteristic
491C2×C4#1306337312yes—
492C8—42no—
493C8—1722no—
494C22—434no—
495C22—862no—
496C22—862no—
497C22—862no—
498C22—862no—
499C22—862no—
500C22—862no—
501C22#120×D4311yescharacteristic
502C22#1458341211yescharacteristic
503C22#1458347411yescharacteristic
504C22C2×SD16×D4311yescharacteristic
505C22#137×D4311yescharacteristic
506C22C2×#1306335411yescharacteristic
507C22#1458369511yescharacteristic
508C4—22no—
509C4—22no—
510C4—42no—
511C4—44no—
512C4—81no—
513C4—862no—
514C4—862no—
515C4—3441no—
516C4—1724no—
517C4—1722no—
518C4—1721no—
519C4#1458355112yes—
520C4#1458355212yes—
521C2—864no—
522C2#1913793111yescharacteristic
523C2#448×D4311yescharacteristic
524C2#1914385011yescharacteristic
525C2#1914460511yescharacteristic
526C2#1914472711yescharacteristic
527C2#1914574011yescharacteristic
528C2#1914580211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2058C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2058D43
hypocenterC43#24063
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2058

Complements

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

NH ≅ G/Ntype
4. #19135925C2semidirect
5. #19135842C2semidirect
6. #19135841C2semidirect
8. #19134864C2semidirect
9. #19134860C2semidirect
11. C43×#2058C2semidirect
261. #2058D43semidirect
309. C43#24063semidirect

Maximal subgroups

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

subgroupindex
C2×#145834542
C2×#145832312
#389×D432
#191359252
#191358422
#191358412
#191349012
#191348642
#191348602
#191346622
C43×#20582
#2406343