Finite Group Databasebeta

← #25106108

Subgroups — #25106108

Order 11008.

1066 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D43C211yesmaximal, characteristic
2C2×#14582954C211yesmaximal, characteristic
3#19137000C211yesmaximal, characteristic
4#19135565C211yesmaximal, characteristic, complemented
5#19135564C211yesmaximal, characteristic, complemented
6#19135563C211yesmaximal, characteristic, complemented
7#19135551C212yesmaximal, complemented
8#19135549C212yesmaximal, complemented
9#19134684C212yesmaximal
10#19134680C212yesmaximal
11C43×#1992C211yesmaximal, characteristic, complemented
12C2×#13063317C2211yescharacteristic
13C2×#13063316C2211yescharacteristic
14C2×#13063316C2211yescharacteristic
15C2×#13063315—21no—
16C2×#13063315—21no—
17#125×D43—24no—
18#125×D43C418yescomplemented
19C2×#13063283—21no—
20C2×C4⋊C4×D43—21no—
21C2×C4⋊C4×D43—21no—
22C2×C4⋊C4×D43C2211yescharacteristic
23C2×C4⋊C4×D43C2211yescharacteristic
24C2×C42×D43C2211yescharacteristic
25#14582954—24no—
26C2×Dic43⋊C8C2212yes—
27C2×(C2×D43)⋊C8C2212yes—
28C2×#13063236C2211yescharacteristic
29#14582769C2211yescharacteristic
30#14582764—21no—
31#14582756—21no—
32#14582756C2212yes—
33C4⋊C4×Dic43—21no—
34C4⋊C4×Dic43C2212yes—
35#14582662C2212yes—
36#14582662C2212yes—
37#14582661C2212yes—
38#14582661C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C2×#125×C43C2211yescharacteristic
42C2×#97×C43C2211yescharacteristic
43C43×#384C2211yescharacteristic
44C43×#340C2212yes—
45C43×#340C2212yes—
46C22×C4×D43—21no—
47C22×C4×D43—21no—
48C22×C4×D43D411yescharacteristic
49C22×C4×D43D411yescharacteristic
50C22×C4×D43C2311yescharacteristic
51C22×C43⋊C8C2312yes—
52#13063317—22no—
53#13063317C2×C414yes—
54#13063316—22no—
55#13063316—22no—
56#13063316C2×C414yes—
57#13063316C2×C414yes—
58#13063315—28no—
59#13063315—28no—
60#13063283—44no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43C2312yes—
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×Dic43⋊C4—21no—
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C4⋊C4×D43—28no—
75C4⋊C4×D43—28no—
76C4⋊C4×D43—22no—
77C4⋊C4×D43—22no—
78C4⋊C4×D43C2×C414yes—
79C4⋊C4×D43C2×C414yes—
80C2×(C2×D43)⋊C4—22no—
81C2×C4×Dic43—22no—
82C2×C4×Dic43D411yescharacteristic
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43C2311yescharacteristic
85C42×D43C2×C414yes—
86C42×D43D414yes—
87Dic43⋊C8—24no—
88(C2×D43)⋊C8—24no—
89#13063236—22no—
90C43⋊#95—22no—
91C43⋊#95—22no—
92C22×C8×C43C2312yes—
93#125×C43—22no—
94#125×C43C2×C414yes—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43C2312yes—
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C42×C43C2311yescharacteristic
103#97×C43—22no—
104C23×D43C2×D411yescharacteristic
105C22×C4×C43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—22no—
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2411yescharacteristic
111C22×Dic43—21no—
112C22×Dic43—21no—
113C22×Dic43—22no—
114C22×Dic43C2×D411yescharacteristic
115C22×Dic43C2×D411yescharacteristic
116C22×Dic43C2×D411yescharacteristic
117C2×C4×D43—22no—
118C2×C4×D43—22no—
119C2×C4×D43—24no—
120C2×C4×D43—24no—
121C2×C4×D43—22no—
122C2×C4×D43—22no—
123C2×C4×D43—41no—
124C2×C4×D43—41no—
125C2×C4×D43—42no—
126C2×C4×D43—42no—
127C2×C4×D43—42no—
128C2×C4×D43—42no—
129C2×C4×D43C22⋊C414yes—
130C2×C4×D43C22⋊C414yes—
131C2×C4×D43C22×C412yes—
132C2×C4×D43C2×D412yes—
133C2×C8×C43—22no—
134C2×C8×C43—22no—
135C2×C8×C43—22no—
136C4⋊C4×C43—24no—
137C4⋊C4×C43—24no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—24no—
141C4⋊C4×C43—42no—
142C4⋊C4×C43—42no—
143C4⋊C4×C43C22×C412yes—
144C4⋊C4×C43C22×C412yes—
145C42×C43C22×C412yes—
146C42×C43C2×D412yes—
147(C2×D43)⋊C4—44no—
148C4⋊Dic43—21no—
149C4⋊Dic43—21no—
150C4⋊Dic43—24no—
151C4⋊Dic43—24no—
152C4⋊Dic43—24no—
153C4⋊Dic43—42no—
154C4⋊Dic43—42no—
155C4⋊Dic43C22×C412yes—
156C4⋊Dic43C22×C412yes—
157Dic43⋊C4—24no—
158Dic43⋊C4—24no—
159Dic43⋊C4—24no—
160Dic43⋊C4—24no—
161Dic43⋊C4—24no—
162Dic43⋊C4—24no—
163C4×Dic43—44no—
164C4×Dic43C22⋊C414yes—
165C4×Dic43C22⋊C414yes—
166C4×Dic43C22×C412yes—
167C4×Dic43C2×D412yes—
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×D43C2×C22⋊C412yes—
177C22×D43AGL(1,ℤ/8)12yes—
178C22×D43#13712yes—
179C2×C4×C43—21no—
180C2×C4×C43—21no—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—22no—
184C2×C4×C43—22no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—42no—
190C2×C4×C43—42no—
191C2×C4×C43—42no—
192C2×C4×C43C2×C22⋊C412yes—
193C2×C4×C43C2×C22⋊C412yes—
194C2×C4×C43C23×C411yescharacteristic
195C2×C4×C43C22×D411yescharacteristic
196C2×C4×C432−1+412yes—
197C2×C4×C432−1+412yes—
198C2×Dic43—21no—
199C2×Dic43—21no—
200C2×Dic43—21no—
201C2×Dic43—21no—
202C2×Dic43—21no—
203C2×Dic43—21no—
204C2×Dic43—22no—
205C2×Dic43—22no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—42no—
211C2×Dic43—42no—
212C2×Dic43—42no—
213C2×Dic43C2×C22⋊C412yes—
214C2×Dic43C2×C22⋊C412yes—
215C2×Dic43C2×C22⋊C412yes—
216C4×D43—28no—
217C4×D43—24no—
218C4×D43—24no—
219C4×D43—44no—
220C4×D43—48no—
221C4×D43—48no—
222C8×C43—42no—
223C43⋊C8—42no—
224#21838—431nomaximal, Sylow
225C22×C43C22×C22⋊C411yescharacteristic
226C22×C43#53611yescharacteristic
227C22×C43#53611yescharacteristic
228C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
229C22×C43C2×#13711yescharacteristic
230C22×C43#57511yescharacteristic
231C22×C43#57511yescharacteristic
232C2×D43—22no—
233C2×D43—22no—
234C2×D43—22no—
235C2×D43—22no—
236C2×D43—22no—
237C2×D43—22no—
238C2×D43#41714yes—
239C4×C43—22no—
240C4×C43—22no—
241C4×C43—42no—
242C4×C43—42no—
243C4×C43—82no—
244C4×C43#51912yes—
245C4×C43#53612yes—
246Dic43—22no—
247Dic43—22no—
248Dic43—22no—
249Dic43—42no—
250Dic43—42no—
251Dic43—82no—
252C22×#125—431no—
253C2×#432—431no—
254#2285—431no—
255#1992—431no—
256#1992—431no—
257#1992—431no—
258#1992D4311yescharacteristic, complemented
259#1989—432no—
260#1989—432no—
261#1824—432no—
262#1823—432no—
263C2×C43#231011yescharacteristic
264C2×C43C2×#41711yescharacteristic
265C2×C43#289611yescharacteristic
266C2×C43#323411yescharacteristic
267C2×C43#323411yescharacteristic
268C2×C43#323611yescharacteristic
269C2×C43#323611yescharacteristic
270D43—24no—
271C2×#125—438no—
272C2×#125—431no—
273C2×#125—431no—
274C2×#125—431no—
275C2×#125—861no—
276C2×#125—861no—
277C2×#125—864no—
278C2×#125C2×D4311yescharacteristic
279C2×#117—861no—
280C22×C4⋊C4—431no—
281C22×C4⋊C4—431no—
282C22×C4⋊C4—861no—
283C22×C4⋊C4—861no—
284C22×C42—431no—
285#432—864no—
286C2×C4⋊C8—432no—
287C2×C22⋊C8—432no—
288C2×#97—431no—
289C2×#97C2×D4311yescharacteristic
290#384—431no—
291#384C2×D4311yescharacteristic
292#382—861no—
293#380—432no—
294#380—861no—
295C4×C4⋊C4—432no—
296C4×C4⋊C4—861no—
297#340—432no—
298#340—432no—
299#340—432no—
300#340—432no—
301#340—432no—
302#340—432no—
303#340C2×D4312yes—
304#340C2×D4312yes—
305C43#2183811yescharacteristic, complemented, Sylow
306C23×C4—431no—
307C23×C4—431no—
308C23×C4—431no—
309C23×C4—861no—
310C23×C4—861no—
311C22×C8—432no—
312C22×C8C22×D4312yes—
313#125—22no—
314#125—434no—
315#125—434no—
316#125—434no—
317#125—868no—
318#125—868no—
319#125—862no—
320#125—862no—
321#125—862no—
322#125C4×D4314yes—
323#117—1724no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—431no—
329C2×C4⋊C4—431no—
330C2×C4⋊C4—434no—
331C2×C4⋊C4—434no—
332C2×C4⋊C4—432no—
333C2×C4⋊C4—862no—
334C2×C4⋊C4—862no—
335C2×C4⋊C4—868no—
336C2×C4⋊C4—868no—
337C2×C4⋊C4—861no—
338C2×C4⋊C4—861no—
339C2×C4⋊C4—861no—
340C2×C4⋊C4—861no—
341C2×C4⋊C4—861no—
342C2×C4⋊C4—861no—
343C2×C4⋊C4—861no—
344C2×C4⋊C4—861no—
345C2×C4⋊C4—861no—
346C2×C4⋊C4—861no—
347C2×C4⋊C4C22×D4312yes—
348C2×C4⋊C4C22×D4311yescharacteristic
349C2×C4⋊C4C22×D4311yescharacteristic
350C2×C22⋊C4—862no—
351C2×C42—431no—
352C2×C42—431no—
353C2×C42—431no—
354C2×C42—434no—
355C2×C42—434no—
356C2×C42—862no—
357C2×C42C22×D4311yescharacteristic
358C4⋊C8—864no—
359C22⋊C8—864no—
360#97—22no—
361#97—862no—
362#95—862no—
363#95—862no—
364C24—431no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—431no—
369C22×C4—431no—
370C22×C4—431no—
371C22×C4—434no—
372C22×C4—432no—
373C22×C4—432no—
374C22×C4—434no—
375C22×C4—862no—
376C22×C4—862no—
377C22×C4—864no—
378C22×C4—864no—
379C22×C4—862no—
380C22×C4—862no—
381C22×C4—861no—
382C22×C4—861no—
383C22×C4—862no—
384C22×C4—1721no—
385C22×C4—1721no—
386C22×C4—1722no—
387C22×C4—1722no—
388C22×C4—1722no—
389C22×C4—1722no—
390C22×C4D4×D4311yescharacteristic
391C22×C4D4×D4311yescharacteristic
392C22×C4C23×D4311yescharacteristic
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—862no—
397C2×C8—862no—
398C2×C8—862no—
399C4⋊C4—24no—
400C4⋊C4—24no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—24no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—432no—
407C4⋊C4—432no—
408C4⋊C4—864no—
409C4⋊C4—864no—
410C4⋊C4—864no—
411C4⋊C4—864no—
412C4⋊C4—864no—
413C4⋊C4—864no—
414C4⋊C4—864no—
415C4⋊C4—864no—
416C4⋊C4—861no—
417C4⋊C4—861no—
418C4⋊C4—864no—
419C4⋊C4—1722no—
420C4⋊C4—1722no—
421C4⋊C4C2×C4×D4312yes—
422C4⋊C4C2×C4×D4312yes—
423C22⋊C4—1724no—
424C42—434no—
425C42—434no—
426C42—432no—
427C42—432no—
428C42—1724no—
429C42C2×C4×D4312yes—
430C42D4×D4312yes—
431C23—432no—
432C23—432no—
433C23—432no—
434C23—861no—
435C23—861no—
436C23—861no—
437C23—861no—
438C23C2×D4×D4311yescharacteristic
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—432no—
453C2×C4—432no—
454C2×C4—432no—
455C2×C4—868no—
456C2×C4—861no—
457C2×C4—861no—
458C2×C4—861no—
459C2×C4—861no—
460C2×C4—861no—
461C2×C4—861no—
462C2×C4—864no—
463C2×C4—864no—
464C2×C4—862no—
465C2×C4—862no—
466C2×C4—1724no—
467C2×C4—1728no—
468C2×C4—1728no—
469C2×C4—1722no—
470C2×C4—1722no—
471C2×C4—1722no—
472C2×C4—1721no—
473C2×C4—1721no—
474C2×C4—1721no—
475C2×C4—1721no—
476C2×C4C22⋊C4×D4312yes—
477C2×C4C22⋊C4×D4312yes—
478C2×C4C22×C4×D4311yescharacteristic
479C2×C4C2×D4×D4311yescharacteristic
480C2×C4#1306337212yes—
481C2×C4#1306337312yes—
482C8—42no—
483C8—1722no—
484C22—434no—
485C22—862no—
486C22—862no—
487C22—862no—
488C22—862no—
489C22—862no—
490C22—862no—
491C22C2×C22⋊C4×D4311yescharacteristic
492C22#1458346911yescharacteristic
493C22#1458347411yescharacteristic
494C22AGL(1,ℤ/8)×D4311yescharacteristic
495C22#137×D4311yescharacteristic
496C22#1458369511yescharacteristic
497C22#1458369811yescharacteristic
498C4—22no—
499C4—22no—
500C4—42no—
501C4—42no—
502C4—82no—
503C4—862no—
504C4—862no—
505C4—862no—
506C4—3442no—
507C4—1722no—
508C4—1722no—
509C4#1458337512yes—
510C4#1458347212yes—
511C2—864no—
512C2#1913717811yescharacteristic
513C2#417×D4311yescharacteristic
514C2#1914311111yescharacteristic
515C2#1914578011yescharacteristic
516C2#1914578611yescharacteristic
517C2#1914579611yescharacteristic
518C2#1914580211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1992C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1992D43
hypocenterC43#21838
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
4. #19135565C2semidirect
5. #19135564C2semidirect
6. #19135563C2semidirect
7. #19135551C2semidirect
8. #19135549C2semidirect
11. C43×#1992C2semidirect
18. #125×D43C4semidirect
258. #1992D43semidirect
305. C43#21838semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D432
C2×#145829542
#191370002
#191355652
#191355642
#191355632
#191355512
#191355492
#191346842
#191346802
C43×#19922
#2183843