Finite Group Databasebeta

← #25062663

Subgroups — #25062663

Order 11008.

1450 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063307C211yesmaximal, characteristic
2#407×D43C212yesmaximal, complemented
3#19132940C218yesmaximal, complemented
4#19132924C212yesmaximal, complemented
5#19132922C211yesmaximal, characteristic, complemented
6C43×#1462C211yesmaximal, characteristic, complemented
7C23×C22⋊D43C411yescharacteristic
8C23×C4×D43C2211yescharacteristic
9C2×M16×D43—22no—
10C2×#13063307—22no—
11C2×#13063307—22no—
12C2×#13063307—22no—
13C2×#13063307—22no—
14C2×#13063307C414yes—
15C2×#13063307C2214yes—
16C22×C4⋊Dic43C411yescharacteristic
17C22×Dic43⋊C4C2211yescharacteristic
18C22×C22⋊Dic43C411yescharacteristic
19C22×(C2×D43)⋊C4C411yescharacteristic
20#14582863C2212yes—
21#14582862—22no—
22#14582861—22no—
23#14582861C2214yescomplemented
24C22⋊C8×D43—22no—
25C22⋊C8×D43C2214yescomplemented
26#14582624C2218yescomplemented
27#14582623C2214yescomplemented
28C22×C22⋊C4×C43C2211yescharacteristic
29C43×#407C2212yes—
30C43×#323C2214yescomplemented
31C24×D43C2×C411yescharacteristic
32C22×C22⋊D43—22no—
33C22×C22⋊D43—21no—
34C22×C22⋊D43—21no—
35C22×C22⋊D43—44no—
36C22×C22⋊D43C2×C414yes—
37C23×Dic43C2×C411yescharacteristic
38C23×Dic43C2×C411yescharacteristic
39C23×Dic43C2×C411yescharacteristic
40C22×C4×D43—44no—
41C22×C4×D43C2×C412yes—
42C22×C4×D43D412yes—
43C22×C4×D43D412yes—
44C22×C4×D43D412yes—
45C22×C4×D43D412yes—
46C22×C4×D43C2312yes—
47C2×#10621877—22no—
48C2×#10621872—24no—
49M16×D43—48no—
50C2×C8×D43—24no—
51#13063307—24no—
52#13063307—24no—
53#13063307—24no—
54#13063307—24no—
55#13063307—24no—
56#13063307—24no—
57#13063307—24no—
58#13063307—24no—
59C2×C4⋊Dic43—22no—
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43C2×C414yes—
63C2×Dic43⋊C4—22no—
64C2×Dic43⋊C4—22no—
65C2×Dic43⋊C4C2×C412yes—
66C2×Dic43⋊C4C2312yes—
67C2×C22⋊Dic43—22no—
68C2×C22⋊Dic43—21no—
69C2×C22⋊Dic43—21no—
70C2×C22⋊Dic43C2×C414yes—
71C2×(C2×D43)⋊C4—22no—
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4C2×C414yes—
75C22⋊(C43⋊C8)—22no—
76C22⋊(C43⋊C8)C2314yes—
77(C2×D43)⋊C8—24no—
78(C2×D43)⋊C8—24no—
79C25×C43C2×C411yescharacteristic
80C23×C4×C43C2×C411yescharacteristic
81C23×C4×C43C2311yescharacteristic
82C2×M16×C43—22no—
83C2×C22⋊C4×C43—22no—
84C2×C22⋊C4×C43—22no—
85C2×C22⋊C4×C43C2×C412yes—
86C2×C22⋊C4×C43C2312yes—
87C22⋊C8×C43—22no—
88C22⋊C8×C43C2314yes—
89C24×C43—21no—
90C24×C43—21no—
91C24×C43—42no—
92C24×C43—42no—
93C24×C43—42no—
94C24×C43C22×C411yescharacteristic
95C24×C43C22×C412yes—
96C23×D43—24no—
97C23×D43—42no—
98C23×D43—42no—
99C23×D43C22⋊C412yes—
100C23×D43C22⋊C411yescharacteristic
101C23×D43C22⋊C411yescharacteristic
102C23×D43C22×C412yes—
103C22×C4×C43—21no—
104C22×C4×C43—21no—
105C22×C4×C43—42no—
106C22×C4×C43—42no—
107C22×C4×C43C22×C412yes—
108C22×C4×C43C22×C411yescharacteristic
109C22×C4×C43C2×D412yes—
110C22×C4×C43C2×D412yes—
111C22×C4×C43C2411yescharacteristic
112C2×C22⋊D43—24no—
113C2×C22⋊D43—24no—
114C2×C22⋊D43—48no—
115C2×C22⋊D43—44no—
116C2×C22⋊D43—48no—
117C2×C22⋊D43—44no—
118C22×Dic43—21no—
119C22×Dic43—21no—
120C22×Dic43—21no—
121C22×Dic43—21no—
122C22×Dic43—42no—
123C22×Dic43—42no—
124C22×Dic43—42no—
125C22×Dic43C22⋊C412yes—
126C22×Dic43C22⋊C411yescharacteristic
127C22×Dic43C22⋊C411yescharacteristic
128C22×Dic43C22×C412yes—
129C22×Dic43C22×C412yes—
130C22×Dic43C22×C412yes—
131C2×C4×D43—28no—
132C2×C4×D43—44no—
133C2×C4×D43—44no—
134C2×C4×D43—44no—
135C2×C4×D43—44no—
136C2×C4×D43—44no—
137C2×C4×D43C22⋊C412yes—
138C2×C4×D43C22⋊C412yes—
139C2×C4×D43C22⋊C412yes—
140C2×C4×D43C22⋊C412yes—
141C2×C4×D43C2×D412yes—
142C2×C4×D43C2×D412yes—
143C2×C4×D43C2×D412yes—
144C2×C4×D43C2×D412yes—
145M16×C43—44no—
146C2×C8×C43—24no—
147C22⋊C4×C43—24no—
148C22⋊C4×C43—24no—
149C22⋊Dic43—24no—
150C22⋊Dic43—24no—
151(C2×D43)⋊C4—24no—
152(C2×D43)⋊C4—24no—
153C4⋊Dic43—24no—
154C4⋊Dic43—24no—
155Dic43⋊C4—24no—
156Dic43⋊C4—24no—
157#10621877—44no—
158C2×C43⋊C8—24no—
159#10621872—48no—
160C8×D43—48no—
161C23×C43—22no—
162C23×C43—22no—
163C23×C43—22no—
164C23×C43—22no—
165C23×C43—24no—
166C23×C43—42no—
167C23×C43—42no—
168C23×C43—42no—
169C23×C43—42no—
170C23×C43—42no—
171C23×C43—42no—
172C23×C43—42no—
173C23×C43—42no—
174C23×C43—88no—
175C23×C43C2×C22⋊C411yescharacteristic
176C23×C43C2×C22⋊C411yescharacteristic
177C23×C43C23×C411yescharacteristic
178C22×D43—24no—
179C22×D43—22no—
180C22×D43—24no—
181C22×D43—24no—
182C22×D43—24no—
183C22×D43—41no—
184C22×D43—42no—
185C22×D43—41no—
186C22×D43—41no—
187C22×D43—41no—
188C22×D43—42no—
189C22×D43—416no—
190C22×D43#9914yes—
191C22×D43C2×C22⋊C412yes—
192C22×D43C2×C22⋊C412yes—
193C2×C4×C43—24no—
194C2×C4×C43—22no—
195C2×C4×C43—41no—
196C2×C4×C43—42no—
197C2×C4×C43—41no—
198C2×C4×C43—42no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43C2×C22⋊C412yes—
202C2×C4×C43C22×D412yes—
203C22⋊D43—48no—
204C22⋊D43—48no—
205C2×Dic43—24no—
206C2×Dic43—22no—
207C2×Dic43—22no—
208C2×Dic43—24no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—42no—
212C2×Dic43—42no—
213C2×Dic43—42no—
214C2×Dic43—42no—
215C2×Dic43—42no—
216C2×Dic43—42no—
217C2×Dic43C2×C22⋊C412yes—
218C2×Dic43C2×C22⋊C412yes—
219C4×D43—24no—
220C4×D43—24no—
221C4×D43—24no—
222C4×D43—24no—
223C4×D43—42no—
224C4×D43—42no—
225C4×D43—42no—
226C4×D43—42no—
227C8×C43—44no—
228C43⋊C8—44no—
229#17392—431nomaximal, Sylow
230C22×C43—28no—
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—42no—
238C22×C43—42no—
239C22×C43—42no—
240C22×C43—84no—
241C22×C43—84no—
242C22×C43—84no—
243C22×C43C2×#9912yes—
244C22×C43#41312yes—
245C22×C43C22×C22⋊C411yescharacteristic
246C22×C43#56812yes—
247C2×D43—22no—
248C2×D43—22no—
249C2×D43—22no—
250C2×D43—22no—
251C2×D43—22no—
252C2×D43—44no—
253C2×D43—48no—
254C2×D43—48no—
255C2×D43—44no—
256C2×D43C2×#9914yes—
257C4×C43—22no—
258C4×C43—22no—
259C4×C43—42no—
260Dic43—22no—
261Dic43—22no—
262Dic43—42no—
263Dic43—42no—
264C22×#123—431no—
265C2×#407—432no—
266#1468—438no—
267#1463—432no—
268#1462—431no—
269#1462D4311yescharacteristic, complemented
270C2×C43—22no—
271C2×C43—22no—
272C2×C43—22no—
273C2×C43—82no—
274C2×C43#287911yescharacteristic
275C2×C43C22×#9911yescharacteristic
276C2×C43C2×#41311yescharacteristic
277D43—24no—
278D43—42no—
279C23×D4—431no—
280C24×C4—431no—
281C22×M16—862no—
282C2×#123—434no—
283C2×#123—434no—
284C2×#123—862no—
285C2×#123—862no—
286C2×#123—862no—
287C2×#123—862no—
288C22×C4⋊C4—431no—
289C22×C4⋊C4—431no—
290C22×C22⋊C4—431no—
291C22×C22⋊C4—431no—
292C22×C22⋊C4C2×D4311yescharacteristic
293#407—432no—
294#407—434no—
295#407—862no—
296#407—862no—
297#407C2×D4312yes—
298C2×C22⋊C8—434no—
299C2×C22⋊C8—862no—
300#324—438no—
301#323—434no—
302#323C2×D4314yescomplemented
303C43#1739211yescharacteristic, complemented, Sylow
304C25—431no—
305C25C4×D4311yescharacteristic
306C22×D4—434no—
307C22×D4—861no—
308C22×D4—862no—
309C22×D4—861no—
310C22×D4—1724no—
311C23×C4—431no—
312C23×C4—432no—
313C23×C4—432no—
314C23×C4—432no—
315C23×C4—432no—
316C23×C4—432no—
317C23×C4—432no—
318C23×C4—431no—
319C23×C4—431no—
320C23×C4—1724no—
321C23×C4C4×D4311yescharacteristic
322C23×C4C22×D4311yescharacteristic
323C2×M16—22no—
324C2×M16—864no—
325C2×M16—862no—
326C2×M16—1728no—
327C22×C8—864no—
328#123—864no—
329#123—864no—
330#123—864no—
331#123—864no—
332#123—864no—
333#123—864no—
334#123—864no—
335#123—864no—
336C2×C4⋊C4—432no—
337C2×C4⋊C4—434no—
338C2×C4⋊C4—432no—
339C2×C4⋊C4—862no—
340C2×C4⋊C4—861no—
341C2×C4⋊C4—861no—
342C2×C4⋊C4—862no—
343C2×C4⋊C4—862no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—434no—
347C2×C22⋊C4—434no—
348C2×C22⋊C4—861no—
349C2×C22⋊C4—862no—
350C2×C22⋊C4—861no—
351C2×C22⋊C4—862no—
352C2×C22⋊C4—861no—
353C2×C22⋊C4—861no—
354C2×C22⋊C4C4×D4312yes—
355C2×C22⋊C4C22×D4312yes—
356C22⋊C8—22no—
357C22⋊C8—434no—
358C22⋊C8—864no—
359C22⋊C8—864no—
360C22⋊C8—862no—
361C22⋊C8C22×D4314yes—
362C24—21no—
363C24—21no—
364C24—42no—
365C24—42no—
366C24—42no—
367C24—431no—
368C24—432no—
369C24—432no—
370C24—431no—
371C24—864no—
372C24—1722no—
373C24—1722no—
374C24C2×C4×D4311yescharacteristic
375C24C2×C4×D4312yes—
376C2×D4—864no—
377C2×D4—864no—
378C2×D4—1724no—
379C2×D4—1728no—
380C2×D4—1724no—
381C2×D4—1728no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—432no—
387C22×C4—431no—
388C22×C4—431no—
389C22×C4—432no—
390C22×C4—432no—
391C22×C4—432no—
392C22×C4—432no—
393C22×C4—432no—
394C22×C4—432no—
395C22×C4—432no—
396C22×C4—432no—
397C22×C4—432no—
398C22×C4—432no—
399C22×C4—432no—
400C22×C4—868no—
401C22×C4—861no—
402C22×C4—861no—
403C22×C4—861no—
404C22×C4—861no—
405C22×C4—1724no—
406C22×C4—1724no—
407C22×C4—1724no—
408C22×C4—1724no—
409C22×C4—1724no—
410C22×C4—1722no—
411C22×C4—1722no—
412C22×C4—1722no—
413C22×C4C2×C4×D4312yes—
414C22×C4C2×C4×D4311yescharacteristic
415C22×C4D4×D4312yes—
416C22×C4D4×D4312yes—
417C22×C4C23×D4311yescharacteristic
418M16—44no—
419M16—1728no—
420M16—1724no—
421C2×C8—24no—
422C2×C8—864no—
423C2×C8—1728no—
424C4⋊C4—864no—
425C4⋊C4—864no—
426C4⋊C4—864no—
427C4⋊C4—864no—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—864no—
431C22⋊C4—864no—
432C22⋊C4—864no—
433C22⋊C4—864no—
434C23—22no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—24no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—88no—
448C23—432no—
449C23—434no—
450C23—432no—
451C23—864no—
452C23—864no—
453C23—862no—
454C23—864no—
455C23—864no—
456C23—1721no—
457C23—1722no—
458C23—1721no—
459C23—1721no—
460C23—1721no—
461C23—1722no—
462C23—17216no—
463C23C22⋊C4×D4311yescharacteristic
464C23C22⋊C4×D4311yescharacteristic
465C23C22×C4×D4311yescharacteristic
466D4—1728no—
467D4—1728no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—432no—
477C2×C4—432no—
478C2×C4—864no—
479C2×C4—864no—
480C2×C4—864no—
481C2×C4—864no—
482C2×C4—864no—
483C2×C4—862no—
484C2×C4—862no—
485C2×C4—864no—
486C2×C4—1722no—
487C2×C4—1722no—
488C2×C4—1722no—
489C2×C4—1722no—
490C2×C4—1721no—
491C2×C4—1721no—
492C2×C4—1722no—
493C2×C4—1722no—
494C2×C4—1722no—
495C2×C4—1722no—
496C2×C4—1722no—
497C2×C4—1722no—
498C2×C4C22⋊C4×D4312yes—
499C2×C4C2×D4×D4312yes—
500C8—44no—
501C8—1724no—
502C22—28no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—84no—
513C22—84no—
514C22—84no—
515C22—434no—
516C22—862no—
517C22—862no—
518C22—862no—
519C22—862no—
520C22—862no—
521C22—1724no—
522C22—1728no—
523C22—1728no—
524C22—1724no—
525C22#99×D4312yes—
526C22#1458288012yes—
527C22C2×C22⋊C4×D4311yescharacteristic
528C22#1458366512yes—
529C4—22no—
530C4—22no—
531C4—42no—
532C4—862no—
533C4—862no—
534C4—1722no—
535C4—1722no—
536C2—22no—
537C2—22no—
538C2—22no—
539C2—82no—
540C2—864no—
541C2—1722no—
542C2#1914303811yescharacteristic
543C2C2×#99×D4311yescharacteristic
544C2C2×#1458288011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1462C2
socleC22×C43C22×C22⋊C4
prime radicalC23×C22⋊D43C4
cosocleC22×C4×C43C24
hypercenter#1462D43
hypocenterC43#17392
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
2. #407×D43C2semidirect
3. #19132940C2semidirect
4. #19132924C2semidirect
5. #19132922C2semidirect
6. C43×#1462C2semidirect
23. #14582861C22semidirect
25. C22⋊C8×D43C22semidirect
26. #14582624C22semidirect
27. #14582623C22semidirect
30. C43×#323C22semidirect
269. #1462D43semidirect
302. #323C2×D43semidirect
303. C43#17392semidirect

Maximal subgroups

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

subgroupindex
C22×#130633072
#407×D432
#191329402
#191329242
#191329222
C43×#14622
#1739243