Finite Group Databasebeta

← #25106423

Subgroups — #25106423

Order 11008.

1098 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
1C2×#14583498C211yesmaximal, characteristic
2#19137212C211yesmaximal, characteristic, complemented
3#19137195C211yesmaximal, characteristic, complemented
4#19135581C211yesmaximal, characteristic, complemented
5#19135431C211yesmaximal, characteristic
6#19135430C211yesmaximal, characteristic
7#19135052C214yesmaximal, complemented
8#19134582C214yesmaximal, 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#14582796—22no—
26#14582794—22no—
27#14582783—22no—
28#14582781—22no—
29#14582760C2212yes—
30#14582759C2211yescharacteristic
31#14582757C2212yes—
32#14582757C2212yes—
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—44no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43C2×C411yescharacteristic
63C2×C4⋊Dic43C2×C412yes—
64C2×C4⋊Dic43C2×C412yes—
65C2×Dic43⋊C4—22no—
66C2×Dic43⋊C4—22no—
67C2×Dic43⋊C4—22no—
68C2×Dic43⋊C4C2×C412yes—
69C2×Dic43⋊C4C2×C412yes—
70C2×Dic43⋊C4C2×C412yes—
71C2×Dic43⋊C4D412yes—
72C2×Dic43⋊C4D412yes—
73C2×Dic43⋊C4D412yes—
74C2×Dic43⋊C4D412yes—
75C2×C22⋊Dic43C2312yes—
76C2×C22⋊Dic43C2312yes—
77C2×(C2×D43)⋊C4C2×C412yes—
78C2×(C2×D43)⋊C4C2×C412yes—
79C2×(C2×D43)⋊C4C2×C412yes—
80C2×(C2×D43)⋊C4C2×C412yes—
81C2×C4×Dic43—22no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43C2×C412yes—
84#13063239—44no—
85#13063239—44no—
86C43⋊#95—21no—
87C43⋊#95—21no—
88C43⋊#95—22no—
89C43⋊#95—22no—
90C43⋊#95—24no—
91C22×Q8×C43C2×C411yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C22⋊Q8×C43—21no—
94C22⋊Q8×C43—21no—
95C22⋊Q8×C43—21no—
96C22⋊Q8×C43—21no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43C2×C412yes—
99C2×C4⋊C4×C43C2×C411yescharacteristic
100C2×C22⋊C4×C43C2312yes—
101C2×C22⋊C4×C43C2312yes—
102C2×C22⋊C4×C43C2312yes—
103C2×C42×C43—21no—
104#95×C43—21no—
105#95×C43—21no—
106C24×C43C2411yescharacteristic
107C23×D43C22×C412yes—
108C2×Q8×C43—21no—
109C2×Q8×C43—21no—
110C2×Q8×C43—81no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—81no—
114C22×C4×C43C22×C412yes—
115C22×C4×C43C22×C412yes—
116C22×C4×C43C22×C411yescharacteristic
117C22×C4×C43C22×C411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C2×C22⋊D43—22no—
123C2×C22⋊D43—22no—
124C2×C22⋊D43—24no—
125C2×C22⋊D43—24no—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—81no—
131C22×Dic43C22×C412yes—
132C22×Dic43C22×C412yes—
133C22×Dic43C22×C412yes—
134C22×Dic43C2×D412yes—
135C22×Dic43C2×D412yes—
136C22×Dic43C2×D412yes—
137C22×Dic43C2×D412yes—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—81no—
141C2×C4×D43—24no—
142C2×C4×D43—82no—
143C4⋊C4×C43—22no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—81no—
148C22⋊C4×C43—22no—
149C22⋊C4×C43—22no—
150C22⋊C4×C43—22no—
151C22⋊C4×C43—24no—
152C22⋊C4×C43—22no—
153C42×C43—81no—
154C22⋊Dic43—22no—
155C22⋊Dic43—24no—
156C22⋊Dic43—22no—
157(C2×D43)⋊C4—22no—
158(C2×D43)⋊C4—22no—
159(C2×D43)⋊C4—24no—
160(C2×D43)⋊C4—24no—
161(C2×D43)⋊C4—24no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43—24no—
165C4⋊Dic43—24no—
166C4⋊Dic43—81no—
167Dic43⋊C4—24no—
168Dic43⋊C4—44no—
169Dic43⋊C4—82no—
170Dic43⋊C4—82no—
171Dic43⋊C4C22⋊C414yes—
172Dic43⋊C4C22⋊C414yes—
173Dic43⋊C4C22⋊C414yes—
174Dic43⋊C4C22⋊C414yes—
175C4×Dic43—24no—
176C4×Dic43—44no—
177C4×Dic43—81no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43C23×C411yescharacteristic
181C23×C43C22×D411yescharacteristic
182C23×C43C22×D411yescharacteristic
183C23×C43H(5,𝔽2)12yes—
184C23×C432−1+412yes—
185C22×D43—22no—
186C22×D43—24no—
187C22×D43—42no—
188C22×D43—42no—
189Q8×C43—81no—
190Q8×C43—81no—
191C2×C4×C43—22no—
192C2×C4×C43—22no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
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×C43C2×C22⋊C411yescharacteristic
208C2×C4×C43C2×C22⋊C411yescharacteristic
209C2×C4×C43C2×C22⋊C411yescharacteristic
210C2×C4×C43C2×C22⋊C411yescharacteristic
211C22⋊D43—42no—
212C22⋊D43—42no—
213C22⋊D43—44no—
214C2×Dic43—24no—
215C2×Dic43—22no—
216C2×Dic43—22no—
217C2×Dic43—24no—
218C2×Dic43—22no—
219C2×Dic43—24no—
220C2×Dic43—42no—
221C2×Dic43—42no—
222C2×Dic43—42no—
223C2×Dic43—42no—
224C2×Dic43—42no—
225C2×Dic43—42no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C2×Dic43—42no—
229C2×Dic43C2×C22⋊C414yes—
230C2×Dic43C2×C22⋊C414yes—
231D172—81no—
232D172—81no—
233C4×D43—84no—
234#21877—431nomaximal, Sylow
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—21no—
239C22×C43—21no—
240C22×C43—21no—
241C22×C43—42no—
242C22×C43—42no—
243C22×C43C22×C22⋊C411yescharacteristic
244C22×C43#52012yes—
245C22×C43#53511yescharacteristic
246C22×C43#53611yescharacteristic
247C22×C43#53712yes—
248C2×D43—42no—
249C2×D43—42no—
250C2×D43—42no—
251C2×D43—84no—
252C4×C43—21no—
253C4×C43—21no—
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—42no—
257C4×C43—42no—
258C4×C43—82no—
259C4×C43—82no—
260Dic43—24no—
261Dic43—24no—
262Dic43—42no—
263Dic43—82no—
264Dic43—82no—
265C2×#539—431no—
266#2316—431no—
267#2313—431no—
268#1996—431no—
269#1996D4311yescharacteristic, complemented
270#1964—431no—
271#1964—431no—
272#1899—434no—
273#1799—434no—
274C2×C43—21no—
275C2×C43—22no—
276C2×C43—22no—
277C2×C43—21no—
278C2×C43#231111yescharacteristic
279C2×C43#288311yescharacteristic
280C2×C43#288411yescharacteristic
281D43—82no—
282#539—862no—
283#539—862no—
284#539—862no—
285#539—862no—
286C2×#126—432no—
287C2×#125—432no—
288C2×#123—432no—
289C2×#123—432no—
290C2×C22⋊Q8—432no—
291C2×C22⋊Q8C2×D4311yescharacteristic
292C2×#121—431no—
293C2×C4×D4—432no—
294C2×#117—432no—
295C22×C4⋊C4—431no—
296C2×#99—434no—
297C2×#99—434no—
298#389—862no—
299#389—862no—
300#387—862no—
301#387—862no—
302#381—432no—
303#380—431no—
304#380—432no—
305#380—432no—
306#380C2×D4311yescharacteristic
307C4×C22⋊C4—431no—
308C4×C22⋊C4C2×D4311yescharacteristic
309#342—434no—
310#342C2×D4314yes—
311C43#2187711yescharacteristic, complemented, Sylow
312C22×Q8C4×D4311yescharacteristic
313C22×D4—432no—
314C22×D4—431no—
315C23×C4—431no—
316C23×C4—431no—
317C23×C4—432no—
318C23×C4C22×D4311yescharacteristic
319#126—864no—
320#126—864no—
321#125—864no—
322#125—864no—
323#123—864no—
324#123—864no—
325#123—864no—
326#123—864no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—864no—
332C22⋊Q8—864no—
333#121—861no—
334#121—861no—
335#121—861no—
336#121—861no—
337C4×D4—864no—
338C4×D4—864no—
339#117—1724no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—432no—
342C2×C4⋊C4—432no—
343C2×C4⋊C4—432no—
344C2×C4⋊C4—432no—
345C2×C4⋊C4—432no—
346C2×C4⋊C4—432no—
347C2×C4⋊C4—432no—
348C2×C4⋊C4—431no—
349C2×C4⋊C4—432no—
350C2×C4⋊C4—432no—
351C2×C4⋊C4—862no—
352C2×C4⋊C4—862no—
353C2×C4⋊C4—861no—
354C2×C4⋊C4—862no—
355C2×C4⋊C4C4×D4312yes—
356C2×C4⋊C4C4×D4311yescharacteristic
357C2×C22⋊C4—432no—
358C2×C22⋊C4—432no—
359C2×C22⋊C4—432no—
360C2×C22⋊C4—432no—
361C2×C22⋊C4—432no—
362C2×C22⋊C4—432no—
363C2×C22⋊C4C22×D4312yes—
364C2×C22⋊C4C22×D4312yes—
365C2×C22⋊C4C22×D4312yes—
366C2×C42—21no—
367C2×C42—432no—
368C2×C42—861no—
369C2×C42—862no—
370#99—1724no—
371#99—1724no—
372#95—21no—
373#95—21no—
374#95—862no—
375#95—862no—
376#95—864no—
377#95—861no—
378#95—861no—
379C24—432no—
380C24C23×D4311yescharacteristic
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—81no—
384C2×D4—862no—
385C2×D4—862no—
386C2×D4—864no—
387C2×D4—864no—
388C2×D4—861no—
389C2×D4—861no—
390C2×D4—3441no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—81no—
394C22×C4—432no—
395C22×C4—432no—
396C22×C4—432no—
397C22×C4—432no—
398C22×C4—432no—
399C22×C4—432no—
400C22×C4—432no—
401C22×C4—864no—
402C22×C4—862no—
403C22×C4—862no—
404C22×C4—862no—
405C22×C4—862no—
406C22×C4—3442no—
407C22×C4—3441no—
408C22×C4C2×C4×D4312yes—
409C22×C4C2×C4×D4312yes—
410C22×C4C2×C4×D4311yescharacteristic
411C22×C4C2×C4×D4311yescharacteristic
412C22×C4D4×D4311yescharacteristic
413C22×C4D4×D4311yescharacteristic
414C22×C4D4×D4311yescharacteristic
415C22×C4D4×D4311yescharacteristic
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—81no—
421C4⋊C4—434no—
422C4⋊C4—434no—
423C4⋊C4—434no—
424C4⋊C4—434no—
425C4⋊C4—864no—
426C4⋊C4—864no—
427C4⋊C4—864no—
428C4⋊C4—861no—
429C4⋊C4—861no—
430C4⋊C4—3442no—
431C4⋊C4—3442no—
432C4⋊C4—3441no—
433C4⋊C4—1724no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—24no—
438C22⋊C4—22no—
439C22⋊C4—864no—
440C22⋊C4—864no—
441C22⋊C4—864no—
442C22⋊C4—862no—
443C22⋊C4—862no—
444C22⋊C4—862no—
445C22⋊C4—864no—
446C22⋊C4—862no—
447C42—81no—
448C42—864no—
449C42—3441no—
450C42—1724no—
451C23—41no—
452C23—41no—
453C23—864no—
454C23—862no—
455C23—1722no—
456C23—1722no—
457C23C22×C4×D4311yescharacteristic
458C23C2×D4×D4311yescharacteristic
459C23C2×D4×D4311yescharacteristic
460C23#1306337112yes—
461C23#1306337312yes—
462Q8—81no—
463Q8—81no—
464D4—3441no—
465D4—3441no—
466D4—1722no—
467D4—1722no—
468D4—1724no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—434no—
486C2×C4—434no—
487C2×C4—864no—
488C2×C4—862no—
489C2×C4—862no—
490C2×C4—864no—
491C2×C4—862no—
492C2×C4—864no—
493C2×C4—3444no—
494C2×C4—1722no—
495C2×C4—1722no—
496C2×C4—1722no—
497C2×C4—1722no—
498C2×C4—1722no—
499C2×C4—1722no—
500C2×C4—1722no—
501C2×C4—1722no—
502C2×C4—1722no—
503C2×C4C22⋊C4×D4311yescharacteristic
504C2×C4C22⋊C4×D4311yescharacteristic
505C2×C4C22⋊C4×D4311yescharacteristic
506C2×C4C22⋊C4×D4311yescharacteristic
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—42no—
514C22—42no—
515C22—3444no—
516C22—1722no—
517C22—1722no—
518C22—1722no—
519C22C2×C22⋊C4×D4311yescharacteristic
520C22#1458338112yes—
521C22#1458346711yescharacteristic
522C22#1458347411yescharacteristic
523C22#1458347912yes—
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—42no—
529C4—42no—
530C4—82no—
531C4—82no—
532C4—864no—
533C4—864no—
534C4—3442no—
535C4—3442no—
536C4—1722no—
537C2—21no—
538C2—22no—
539C2—22no—
540C2—21no—
541C2—3442no—
542C2#1913718611yescharacteristic
543C2#1914305311yescharacteristic
544C2#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#21877
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. #19137212C2semidirect
3. #19137195C2semidirect
4. #19135581C2semidirect
7. #19135052C2semidirect
8. #19134582C2semidirect
9. C43×#1996C2semidirect
14. C2×#13063320C4semidirect
15. C2×#13063316C4semidirect
16. C2×#13063310C4semidirect
18. C2×#13063301C4semidirect
269. #1996D43semidirect
311. C43#21877semidirect

Maximal subgroups

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

subgroupindex
C2×#145834982
#191372122
#191371952
#191355812
#191354312
#191354302
#191350522
#191345822
C43×#19962
#2187743