Finite Group Databasebeta

← #25101960

Subgroups — #25101960

Order 11008.

1162 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583498C211yesmaximal, characteristic
2#19137197C211yesmaximal, characteristic, complemented
3#19136950C211yesmaximal, characteristic, complemented
4#19135581C211yesmaximal, characteristic, complemented
5#19135431C211yesmaximal, characteristic
6#19135430C211yesmaximal, characteristic
7#19135052C214yesmaximal, complemented
8#19134382C214yesmaximal, complemented
9C43×#1996C211yesmaximal, characteristic, complemented
10#14583498—22no—
11#14583498—22no—
12#14583498—22no—
13#14583498—22no—
14C2×#13063320C412yescomplemented
15C2×#13063316C412yescomplemented
16C2×#13063310C412yescomplemented
17C2×#13063309C2212yes—
18C2×#13063301C412yescomplemented
19C2×#13063299C2211yescharacteristic
20C2×(C22⋊D43)⋊C4C2212yes—
21C2×#13063281C2212yes—
22C22×Dic43⋊C4C2211yescharacteristic
23C2×#13063239C2214yes—
24C2×#13063239C2214yes—
25#14582786—22no—
26#14582780—22no—
27#14582760C2212yes—
28#14582759C2211yescharacteristic
29C4×Dic43⋊C4—22no—
30#14582750—22no—
31C22⋊C4×Dic43C2212yes—
32C22⋊C4×Dic43C2212yes—
33C4×C22⋊Dic43C2211yescharacteristic
34#14582666C2214yes—
35C2×C22⋊Q8×C43C2211yescharacteristic
36C43×#380C2211yescharacteristic
37C4×C22⋊C4×C43C2211yescharacteristic
38C43×#342C2214yes—
39C22×D172C2×C411yescharacteristic
40C22×C22⋊D43C2312yes—
41C23×Dic43C2311yescharacteristic
42C23×Dic43C2311yescharacteristic
43C22×C4×D43C2×C412yes—
44#13063320—24no—
45#13063320—24no—
46#13063316—24no—
47#13063316—24no—
48#13063310—24no—
49#13063310—24no—
50#13063309—24no—
51#13063309—24no—
52#13063301—24no—
53#13063301—24no—
54#13063299—21no—
55#13063299—21no—
56#13063299—21no—
57#13063299—21no—
58(C22⋊D43)⋊C4—24no—
59(C22⋊D43)⋊C4—24no—
60#13063281—24no—
61#13063281—24no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43C2×C411yescharacteristic
64C2×C4⋊Dic43C2×C412yes—
65C2×C4⋊Dic43C2×C412yes—
66C2×Dic43⋊C4—22no—
67C2×Dic43⋊C4C2×C412yes—
68C2×Dic43⋊C4C2×C412yes—
69C2×Dic43⋊C4C2×C412yes—
70C2×Dic43⋊C4D412yes—
71C2×Dic43⋊C4D412yes—
72C2×Dic43⋊C4D412yes—
73C2×Dic43⋊C4D412yes—
74C2×C22⋊Dic43C2312yes—
75C2×C22⋊Dic43C2312yes—
76C2×(C2×D43)⋊C4C2×C412yes—
77C2×(C2×D43)⋊C4C2×C412yes—
78C2×(C2×D43)⋊C4C2×C412yes—
79C2×(C2×D43)⋊C4C2×C412yes—
80C2×C4×Dic43—22no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—22no—
83C2×C4×Dic43—22no—
84C2×C4×Dic43C2×C412yes—
85#13063239—28no—
86#13063239—28no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C43⋊#95—22no—
90C43⋊#95—24no—
91C43⋊#95—22no—
92C22×Q8×C43C2×C411yescharacteristic
93C23×C4×C43C2311yescharacteristic
94C22⋊Q8×C43—21no—
95C22⋊Q8×C43—21no—
96C22⋊Q8×C43—21no—
97C22⋊Q8×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43C2×C412yes—
100C2×C4⋊C4×C43C2×C411yescharacteristic
101C2×C22⋊C4×C43C2312yes—
102C2×C22⋊C4×C43C2312yes—
103C2×C22⋊C4×C43C2312yes—
104C2×C42×C43—21no—
105#95×C43—21no—
106#95×C43—21no—
107C24×C43C2411yescharacteristic
108C23×D43C22×C412yes—
109C2×Q8×C43—21no—
110C2×Q8×C43—21no—
111C2×Q8×C43—81no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—81no—
115C22×C4×C43C22×C412yes—
116C22×C4×C43C22×C412yes—
117C22×C4×C43C22×C411yescharacteristic
118C22×C4×C43C22×C411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C2×C22⋊D43—22no—
124C2×C22⋊D43—22no—
125C2×C22⋊D43—24no—
126C2×C22⋊D43—24no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—81no—
132C22×Dic43C22×C412yes—
133C22×Dic43C22×C412yes—
134C22×Dic43C22×C412yes—
135C22×Dic43C2×D412yes—
136C22×Dic43C2×D412yes—
137C22×Dic43C2×D412yes—
138C22×Dic43C2×D412yes—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—81no—
142C2×C4×D43—24no—
143C2×C4×D43—82no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—81no—
149C22⋊C4×C43—22no—
150C22⋊C4×C43—22no—
151C22⋊C4×C43—22no—
152C22⋊C4×C43—24no—
153C22⋊C4×C43#4114yes—
154C42×C43—81no—
155C22⋊Dic43—22no—
156C22⋊Dic43—24no—
157C22⋊Dic43#4114yes—
158(C2×D43)⋊C4—22no—
159(C2×D43)⋊C4—22no—
160(C2×D43)⋊C4—24no—
161(C2×D43)⋊C4—24no—
162(C2×D43)⋊C4—24no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43—24no—
166C4⋊Dic43—24no—
167C4⋊Dic43—81no—
168Dic43⋊C4—28no—
169Dic43⋊C4—24no—
170Dic43⋊C4C22⋊C414yes—
171Dic43⋊C4C22⋊C414yes—
172Dic43⋊C4C22⋊C414yes—
173Dic43⋊C4C22⋊C414yes—
174C4×Dic43—28no—
175C4×Dic43—24no—
176C4×Dic43—82no—
177C4×Dic43—82no—
178C4×Dic43—81no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43C23×C411yescharacteristic
182C23×C43C22×D411yescharacteristic
183C23×C43C22×D411yescharacteristic
184C23×C43C2×#4112yes—
185C23×C43C2×#4112yes—
186C22×D43—22no—
187C22×D43—24no—
188C22×D43—42no—
189C22×D43—42no—
190Q8×C43—81no—
191Q8×C43—81no—
192C2×C4×C43—22no—
193C2×C4×C43—22no—
194C2×C4×C43—24no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—42no—
202C2×C4×C43—42no—
203C2×C4×C43—42no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43C2×C22⋊C411yescharacteristic
209C2×C4×C43C2×C22⋊C411yescharacteristic
210C2×C4×C43C2×C22⋊C411yescharacteristic
211C2×C4×C43C2×C22⋊C411yescharacteristic
212C22⋊D43—44no—
213C22⋊D43—42no—
214C22⋊D43—42no—
215C2×Dic43—24no—
216C2×Dic43—22no—
217C2×Dic43—22no—
218C2×Dic43—22no—
219C2×Dic43—22no—
220C2×Dic43—22no—
221C2×Dic43—24no—
222C2×Dic43—24no—
223C2×Dic43—42no—
224C2×Dic43—42no—
225C2×Dic43—42no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C2×Dic43—42no—
229C2×Dic43—42no—
230C2×Dic43—42no—
231C2×Dic43C2×C22⋊C414yes—
232C2×Dic43C2×C22⋊C414yes—
233D172—81no—
234D172—81no—
235C4×D43—84no—
236#21423—431nomaximal, Sylow
237C22×C43—21no—
238C22×C43—21no—
239C22×C43—21no—
240C22×C43—21no—
241C22×C43—21no—
242C22×C43—21no—
243C22×C43—42no—
244C22×C43—42no—
245C22×C43C22×C22⋊C411yescharacteristic
246C22×C43C4×#4112yes—
247C22×C43#52512yes—
248C22×C43#53211yescharacteristic
249C22×C43#53211yescharacteristic
250C2×D43—42no—
251C2×D43—42no—
252C2×D43—42no—
253C2×D43—84no—
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—21no—
258C4×C43—44no—
259C4×C43—42no—
260C4×C43—42no—
261C4×C43—82no—
262Dic43—24no—
263Dic43—24no—
264Dic43—44no—
265Dic43—42no—
266Dic43—82no—
267C2×#539—431no—
268#2313—431no—
269#2274—431no—
270#1996—431no—
271#1996D4311yescharacteristic, complemented
272#1964—431no—
273#1964—431no—
274#1899—434no—
275C4×#99—434no—
276C2×C43—22no—
277C2×C43—21no—
278C2×C43—21no—
279C2×C43—22no—
280C2×C43#229711yescharacteristic
281C2×C43#288311yescharacteristic
282C2×C43#288411yescharacteristic
283D43—82no—
284#539—862no—
285#539—862no—
286#539—862no—
287#539—862no—
288C2×#126—432no—
289C2×#125—432no—
290C2×#123—432no—
291C2×#123—432no—
292C2×C22⋊Q8—432no—
293C2×C22⋊Q8C2×D4311yescharacteristic
294C2×#121—431no—
295C2×C4×D4—432no—
296C2×#117—432no—
297C22×C4⋊C4—431no—
298C2×#99—434no—
299C2×#99—434no—
300#387—862no—
301#387—862no—
302#381—432no—
303#380—431no—
304#380C2×D4311yescharacteristic
305C4×C4⋊C4—862no—
306C4×C4⋊C4—862no—
307C4×C22⋊C4—431no—
308C4×C22⋊C4—432no—
309C4×C22⋊C4—432no—
310C4×C22⋊C4C2×D4311yescharacteristic
311#342—434no—
312#342C2×D4314yes—
313C43#2142311yescharacteristic, complemented, Sylow
314C22×Q8C4×D4311yescharacteristic
315C22×D4—432no—
316C22×D4—431no—
317C23×C4—431no—
318C23×C4—431no—
319C23×C4—432no—
320C23×C4C22×D4311yescharacteristic
321#126—864no—
322#126—864no—
323#125—864no—
324#125—864no—
325#123—864no—
326#123—864no—
327#123—864no—
328#123—864no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—864no—
334C22⋊Q8—864no—
335#121—861no—
336#121—861no—
337#121—861no—
338#121—861no—
339C4×D4—864no—
340C4×D4—864no—
341#117—864no—
342#117—864no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—432no—
345C2×C4⋊C4—432no—
346C2×C4⋊C4—432no—
347C2×C4⋊C4—432no—
348C2×C4⋊C4—432no—
349C2×C4⋊C4—432no—
350C2×C4⋊C4—432no—
351C2×C4⋊C4—431no—
352C2×C4⋊C4—432no—
353C2×C4⋊C4—432no—
354C2×C4⋊C4—862no—
355C2×C4⋊C4—861no—
356C2×C4⋊C4C4×D4312yes—
357C2×C4⋊C4C4×D4311yescharacteristic
358C2×C22⋊C4—432no—
359C2×C22⋊C4—432no—
360C2×C22⋊C4—432no—
361C2×C22⋊C4—432no—
362C2×C22⋊C4—432no—
363C2×C22⋊C4—432no—
364C2×C22⋊C4C22×D4312yes—
365C2×C22⋊C4C22×D4312yes—
366C2×C22⋊C4C22×D4312yes—
367C2×C42—21no—
368C2×C42—432no—
369C2×C42—862no—
370C2×C42—862no—
371C2×C42—862no—
372C2×C42—861no—
373#99—868no—
374#99—868no—
375#95—21no—
376#95—21no—
377#95—862no—
378#95—862no—
379#95—864no—
380#95—861no—
381#95—861no—
382C24—432no—
383C24C23×D4311yescharacteristic
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—81no—
387C2×D4—862no—
388C2×D4—862no—
389C2×D4—864no—
390C2×D4—864no—
391C2×D4—861no—
392C2×D4—861no—
393C2×D4—3441no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—81no—
397C22×C4—432no—
398C22×C4—432no—
399C22×C4—432no—
400C22×C4—432no—
401C22×C4—432no—
402C22×C4—432no—
403C22×C4—432no—
404C22×C4—864no—
405C22×C4—862no—
406C22×C4—862no—
407C22×C4—862no—
408C22×C4—862no—
409C22×C4—3442no—
410C22×C4—3441no—
411C22×C4C2×C4×D4312yes—
412C22×C4C2×C4×D4312yes—
413C22×C4C2×C4×D4311yescharacteristic
414C22×C4C2×C4×D4311yescharacteristic
415C22×C4D4×D4311yescharacteristic
416C22×C4D4×D4311yescharacteristic
417C22×C4D4×D4311yescharacteristic
418C22×C4D4×D4311yescharacteristic
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—81no—
424C4⋊C4—434no—
425C4⋊C4—434no—
426C4⋊C4—434no—
427C4⋊C4—434no—
428C4⋊C4—864no—
429C4⋊C4—864no—
430C4⋊C4—864no—
431C4⋊C4—868no—
432C4⋊C4—861no—
433C4⋊C4—861no—
434C4⋊C4—3441no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—24no—
439C22⋊C4—434no—
440C22⋊C4—864no—
441C22⋊C4—864no—
442C22⋊C4—864no—
443C22⋊C4—862no—
444C22⋊C4—862no—
445C22⋊C4—862no—
446C22⋊C4—864no—
447C22⋊C4#1062190214yes—
448C42—81no—
449C42—864no—
450C42—868no—
451C42—3441no—
452C42—3442no—
453C42—3442no—
454C23—41no—
455C23—41no—
456C23—864no—
457C23—862no—
458C23—1722no—
459C23—1722no—
460C23C22×C4×D4311yescharacteristic
461C23C2×D4×D4311yescharacteristic
462C23C2×D4×D4311yescharacteristic
463C23#41×D4312yes—
464C23C2×#1062190212yes—
465Q8—81no—
466Q8—81no—
467D4—3441no—
468D4—3441no—
469D4—1724no—
470D4—1722no—
471D4—1722no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—434no—
489C2×C4—434no—
490C2×C4—864no—
491C2×C4—862no—
492C2×C4—862no—
493C2×C4—862no—
494C2×C4—862no—
495C2×C4—862no—
496C2×C4—864no—
497C2×C4—864no—
498C2×C4—3444no—
499C2×C4—1722no—
500C2×C4—1722no—
501C2×C4—1722no—
502C2×C4—1722no—
503C2×C4—1722no—
504C2×C4—1722no—
505C2×C4—1722no—
506C2×C4—1722no—
507C2×C4C22⋊C4×D4311yescharacteristic
508C2×C4C22⋊C4×D4311yescharacteristic
509C2×C4C22⋊C4×D4311yescharacteristic
510C2×C4C22⋊C4×D4311yescharacteristic
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—42no—
518C22—42no—
519C22—3444no—
520C22—1722no—
521C22—1722no—
522C22—1722no—
523C22C2×C22⋊C4×D4311yescharacteristic
524C22C4×#1062190212yes—
525C22#1458341212yes—
526C22#1458344811yescharacteristic
527C22#1458345011yescharacteristic
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—44no—
533C4—42no—
534C4—42no—
535C4—82no—
536C4—864no—
537C4—864no—
538C4—3442no—
539C4—1724no—
540C4—1722no—
541C2—22no—
542C2—21no—
543C2—21no—
544C2—22no—
545C2—3442no—
546C2#1913708411yescharacteristic
547C2#1914305311yescharacteristic
548C2#1914305711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1996C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063299C22
cosocleC24×C43C24
hypercenter#1996D43
hypocenterC43#21423
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. #19137197C2semidirect
3. #19136950C2semidirect
4. #19135581C2semidirect
7. #19135052C2semidirect
8. #19134382C2semidirect
9. C43×#1996C2semidirect
14. C2×#13063320C4semidirect
15. C2×#13063316C4semidirect
16. C2×#13063310C4semidirect
18. C2×#13063301C4semidirect
271. #1996D43semidirect
313. C43#21423semidirect

Maximal subgroups

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

subgroupindex
C2×#145834982
#191371972
#191369502
#191355812
#191354312
#191354302
#191350522
#191343822
C43×#19962
#2142343