Finite Group Databasebeta

← #24988192

Subgroups — #24988192

Order 11008.

852 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583596C211yesmaximal, characteristic
2#19134695C211yesmaximal, characteristic, complemented
3#19134692C211yesmaximal, characteristic, complemented
4C4×#13063239C211yesmaximal, characteristic, complemented
5#19133111C211yesmaximal, characteristic, complemented
6#19132931C211yesmaximal, characteristic, complemented
7C43×#1507C211yesmaximal, characteristic, complemented
8#14583596—22no—
9#14583596—22no—
10#14583596—22no—
11#14583596—22no—
12C2×#13063318—21no—
13C2×#13063316C411yescharacteristic, complemented
14C2×#13063306—21no—
15C2×#13063296—21no—
16C2×#13063296C411yescharacteristic, complemented
17C2×D4×Dic43C411yescharacteristic, complemented
18C2×C4×C22⋊D43C2211yescharacteristic
19C2×(C22⋊D43)⋊C4—21no—
20C2×#13063284C2211yescharacteristic
21C2×C4⋊C4×D43C411yescharacteristic, complemented
22C2×#13063239—21no—
23#14582863C2211yescharacteristic
24C4×C22⋊Dic43C2211yescharacteristic
25#14582665—21no—
26#14582660—22no—
27#14582659—22no—
28#14582633—22no—
29#14582624—21no—
30#14582622—21no—
31C2×#121×C43C2211yescharacteristic
32C43×#407C2211yescharacteristic
33C4×C22⋊C4×C43C2211yescharacteristic
34C43×#327—22no—
35C22×C22⋊D43—21no—
36C22×C22⋊D43D411yescharacteristic
37C23×Dic43—21no—
38C22×C4×D43—21no—
39C22×C4×D43C2×C411yescharacteristic
40C2×#10621877—21no—
41#13063318—24no—
42#13063318—24no—
43#13063316—22no—
44#13063316—22no—
45#13063306—24no—
46#13063306—24no—
47#13063296—24no—
48#13063296—24no—
49#13063296—22no—
50#13063296—22no—
51D4×Dic43—22no—
52D4×Dic43—22no—
53C4×C22⋊D43—21no—
54C4×C22⋊D43—21no—
55C4×C22⋊D43—21no—
56C4×C22⋊D43—21no—
57(C22⋊D43)⋊C4—24no—
58(C22⋊D43)⋊C4—24no—
59#13063284—21no—
60#13063284—21no—
61#13063284D412yes—
62#13063284D412yes—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43C2×C411yescharacteristic
65C2×C4⋊Dic43C2×C411yescharacteristic
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4D411yescharacteristic
69C4⋊C4×D43—22no—
70C4⋊C4×D43—22no—
71C2×C22⋊Dic43—21no—
72C2×C22⋊Dic43—21no—
73C2×C22⋊Dic43—21no—
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43D411yescharacteristic
76C2×(C2×D43)⋊C4D411yescharacteristic
77C2×C4×Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43C2×C411yescharacteristic
80#13063239—24no—
81C22⋊(C43⋊C8)—21no—
82C22⋊(C43⋊C8)—21no—
83C43⋊#95—21no—
84C22×D4×C43—21no—
85C22×D4×C43C2×C411yescharacteristic
86C23×C4×C43C2311yescharacteristic
87C2×M16×C43—21no—
88#121×C43—21no—
89#121×C43—21no—
90#121×C43D412yes—
91#121×C43D412yes—
92C2×C4⋊C4×C43C2×C411yescharacteristic
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C42×C43—21no—
96C22⋊C8×C43—21no—
97C22⋊C8×C43—21no—
98#95×C43—21no—
99C24×C43—21no—
100C24×C43C2×D411yescharacteristic
101C23×D43C22⋊C411yescharacteristic
102C2×D4×C43—21no—
103C2×D4×C43—22no—
104C2×D4×C43—22no—
105C2×D4×C43—42no—
106C2×D4×C43—82no—
107C2×D4×C43C22⋊C412yes—
108C22×C4×C43—21no—
109C22×C4×C43—42no—
110C22×C4×C43—41no—
111C22×C4×C43C22×C411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C2×C22⋊D43—24no—
118C2×C22⋊D43—21no—
119C2×C22⋊D43—21no—
120C2×C22⋊D43—22no—
121C2×C22⋊D43—41no—
122C2×C22⋊D43—42no—
123C2×C22⋊D43—42no—
124C22×Dic43—24no—
125C22×Dic43—21no—
126C22×Dic43—21no—
127C22×Dic43—41no—
128C22×Dic43—82no—
129C22×Dic43C22⋊C411yescharacteristic
130C22×Dic43C22⋊C411yescharacteristic
131C22×Dic43C22⋊C411yescharacteristic
132C2×C4×D43—21no—
133C2×C4×D43—21no—
134C2×C4×D43—24no—
135C2×C4×D43—42no—
136C2×C4×D43—82no—
137M16×C43—42no—
138C2×C8×C43—41no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43C22⋊C412yes—
141C22⋊C4×C43—22no—
142C22⋊C4×C43—22no—
143C22⋊C4×C43—22no—
144C22⋊C4×C43—41no—
145C42×C43—42no—
146C22⋊Dic43—24no—
147C22⋊Dic43—24no—
148C22⋊Dic43—22no—
149C22⋊Dic43—22no—
150C22⋊Dic43—22no—
151C22⋊Dic43—21no—
152C22⋊Dic43—21no—
153C22⋊Dic43—41no—
154(C2×D43)⋊C4—21no—
155(C2×D43)⋊C4—21no—
156C4⋊Dic43—24no—
157C4⋊Dic43—21no—
158C4⋊Dic43—21no—
159C4⋊Dic43C22⋊C412yes—
160C4⋊Dic43C22⋊C412yes—
161Dic43⋊C4—24no—
162Dic43⋊C4—24no—
163Dic43⋊C4—21no—
164Dic43⋊C4—21no—
165C4×Dic43—21no—
166C4×Dic43—21no—
167C4×Dic43—22no—
168C4×Dic43—22no—
169C4×Dic43—42no—
170#10621877—42no—
171C2×C43⋊C8—41no—
172C23×C43—21no—
173C23×C43—21no—
174C23×C43—22no—
175C23×C43—41no—
176C23×C43—41no—
177C23×C43—42no—
178C23×C43—42no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43C2×C22⋊C411yescharacteristic
182C23×C43#12011yescharacteristic
183C23×C43#12011yescharacteristic
184C22×D43—21no—
185C22×D43—21no—
186C22×D43—41no—
187C22×D43—41no—
188C22×D43#10412yes—
189D4×C43—42no—
190D4×C43—42no—
191D4×C43—82no—
192D4×C43—82no—
193C2×C4×C43—22no—
194C2×C4×C43—22no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—42no—
201C2×C4×C43—42no—
202C2×C4×C43—81no—
203C2×C4×C43—81no—
204C2×C4×C43C2×C22⋊C411yescharacteristic
205C2×C4×C43C2×C22⋊C411yescharacteristic
206C2×C4×C43#12011yescharacteristic
207C2×C4×C43#12011yescharacteristic
208C22⋊D43—42no—
209C22⋊D43—42no—
210C22⋊D43—48no—
211C2×Dic43—21no—
212C2×Dic43—21no—
213C2×Dic43—22no—
214C2×Dic43—22no—
215C2×Dic43—21no—
216C2×Dic43—21no—
217C2×Dic43—21no—
218C2×Dic43—42no—
219C2×Dic43—41no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—42no—
224C2×Dic43—84no—
225C2×Dic43—81no—
226C2×Dic43—81no—
227C4×D43—42no—
228C4×D43—42no—
229C4×D43—84no—
230C8×C43—81no—
231C43⋊C8—81no—
232#8362—431nomaximal, Sylow
233C22×C43—21no—
234C22×C43—21no—
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×C43—42no—
244C22×C43—81no—
245C22×C43—81no—
246C22×C43—82no—
247C22×C43—82no—
248C22×C43#37911yescharacteristic
249C22×C43C2×#10411yescharacteristic
250C22×C43#42111yescharacteristic
251C2×D43—22no—
252C2×D43—42no—
253C2×D43—41no—
254C2×D43—41no—
255C2×D43—42no—
256C4×C43—21no—
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—42no—
260C4×C43—82no—
261C4×C43#41012yes—
262Dic43—42no—
263Dic43—41no—
264Dic43—41no—
265Dic43—41no—
266Dic43—42no—
267Dic43—82no—
268C2×#553—431no—
269#1826—431no—
270#1826—431no—
271C4×#99—431no—
272#1507—431no—
273#1507D4311yescharacteristic, complemented
274#1465—431no—
275C2×C43—21no—
276C2×C43—21no—
277C2×C43—41no—
278C2×C43—41no—
279C2×C43—82no—
280C2×C43#178211yescharacteristic
281C2×C43#178911yescharacteristic
282C2×C43#179511yescharacteristic
283D43—42no—
284#553—862no—
285#553—862no—
286#553—862no—
287#553—862no—
288C2×#126—861no—
289C2×#125—431no—
290C2×#123—861no—
291C2×#121—431no—
292C2×#121—861no—
293C2×#121C2×D4311yescharacteristic
294C2×C4×D4—431no—
295C2×C4×D4—431no—
296C2×C4×D4—861no—
297C2×#117—431no—
298C22×C4⋊C4—431no—
299C2×#99—861no—
300#407—431no—
301#407C2×D4311yescharacteristic
302C4×C22⋊C4—431no—
303C4×C22⋊C4C2×D4311yescharacteristic
304#342—861no—
305#339—862no—
306#339—862no—
307#327—22no—
308#327—862no—
309#324—861no—
310#323—861no—
311C43#836211yescharacteristic, complemented, Sylow
312C22×D4—21no—
313C22×D4—431no—
314C22×D4—861no—
315C22×D4C4×D4311yescharacteristic
316C23×C4—431no—
317C23×C4—861no—
318C23×C4—861no—
319C23×C4C22×D4311yescharacteristic
320C2×M16—21no—
321C2×M16—861no—
322#126—864no—
323#126—864no—
324#125—862no—
325#125—862no—
326#123—864no—
327#123—864no—
328#121—21no—
329#121—21no—
330#121—862no—
331#121—864no—
332#121—864no—
333#121—862no—
334#121D17212yes—
335#121C22⋊D4312yes—
336C4×D4—864no—
337C4×D4—864no—
338C4×D4—862no—
339C4×D4—862no—
340C4×D4—861no—
341C4×D4—861no—
342C4×D4—861no—
343C4×D4—861no—
344#117—432no—
345#117—432no—
346#117—861no—
347#117—861no—
348C2×C4⋊C4—431no—
349C2×C4⋊C4—431no—
350C2×C4⋊C4—431no—
351C2×C4⋊C4—862no—
352C2×C4⋊C4—861no—
353C2×C4⋊C4—861no—
354C2×C4⋊C4—861no—
355C2×C4⋊C4—862no—
356C2×C4⋊C4C4×D4311yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—431no—
360C2×C22⋊C4—431no—
361C2×C22⋊C4—861no—
362C2×C22⋊C4—861no—
363C2×C22⋊C4—861no—
364C2×C22⋊C4—861no—
365C2×C42—21no—
366C2×C42—431no—
367C2×C42—861no—
368C2×C42—861no—
369#99—864no—
370C22⋊C8—21no—
371C22⋊C8—21no—
372C22⋊C8—861no—
373C22⋊C8—861no—
374#95—21no—
375#95—861no—
376C24—21no—
377C24—431no—
378C24D4×D4311yescharacteristic
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—42no—
383C2×D4—82no—
384C2×D4—862no—
385C2×D4—864no—
386C2×D4—861no—
387C2×D4—861no—
388C2×D4—1721no—
389C2×D4—1722no—
390C2×D4—1722no—
391C2×D4(C2×D43)⋊C412yes—
392C22×C4—21no—
393C22×C4—42no—
394C22×C4—41no—
395C22×C4—431no—
396C22×C4—431no—
397C22×C4—431no—
398C22×C4—864no—
399C22×C4—864no—
400C22×C4—861no—
401C22×C4—861no—
402C22×C4—861no—
403C22×C4—861no—
404C22×C4—3442no—
405C22×C4—3442no—
406C22×C4—1722no—
407C22×C4—1721no—
408C22×C4C2×C4×D4311yescharacteristic
409C22×C4C2×D17211yescharacteristic
410C22×C4D4×D4311yescharacteristic
411C22×C4D4×D4311yescharacteristic
412C22×C4D4×D4311yescharacteristic
413C22×C4C2×C22⋊D4311yescharacteristic
414M16—42no—
415M16—1722no—
416C2×C8—41no—
417C2×C8—1721no—
418C4⋊C4—21no—
419C4⋊C4—432no—
420C4⋊C4—432no—
421C4⋊C4—864no—
422C4⋊C4—864no—
423C4⋊C4—864no—
424C4⋊C4—861no—
425C4⋊C4—861no—
426C4⋊C4—861no—
427C4⋊C4—861no—
428C4⋊C4(C2×D43)⋊C412yes—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—41no—
433C22⋊C4—864no—
434C22⋊C4—864no—
435C22⋊C4—861no—
436C22⋊C4—862no—
437C22⋊C4—861no—
438C22⋊C4—862no—
439C22⋊C4—861no—
440C22⋊C4—861no—
441C22⋊C4—862no—
442C22⋊C4—1721no—
443C42—42no—
444C42—861no—
445C42—861no—
446C42—862no—
447C42—862no—
448C42—1722no—
449C23—21no—
450C23—21no—
451C23—22no—
452C23—41no—
453C23—41no—
454C23—42no—
455C23—42no—
456C23—41no—
457C23—41no—
458C23—432no—
459C23—861no—
460C23—861no—
461C23—1721no—
462C23—1721no—
463C23C22⋊C4×D4311yescharacteristic
464C23#1306329311yescharacteristic
465C23#1306329511yescharacteristic
466D4—42no—
467D4—42no—
468D4—82no—
469D4—82no—
470D4—1722no—
471D4—1722no—
472D4—1728no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—81no—
483C2×C4—81no—
484C2×C4—861no—
485C2×C4—861no—
486C2×C4—862no—
487C2×C4—862no—
488C2×C4—861no—
489C2×C4—861no—
490C2×C4—861no—
491C2×C4—3444no—
492C2×C4—3441no—
493C2×C4—3441no—
494C2×C4—3444no—
495C2×C4—1722no—
496C2×C4—1722no—
497C2×C4—1722no—
498C2×C4—1721no—
499C2×C4—1721no—
500C2×C4—1722no—
501C2×C4—1721no—
502C2×C4—1721no—
503C2×C4C22⋊C4×D4311yescharacteristic
504C2×C4C2×(C2×D43)⋊C411yescharacteristic
505C2×C4#1306329311yescharacteristic
506C2×C4#1306329511yescharacteristic
507C8—81no—
508C8—3441no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—81no—
521C22—81no—
522C22—82no—
523C22—82no—
524C22—862no—
525C22—1722no—
526C22—1722no—
527C22—1721no—
528C22—1721no—
529C22#1458275411yescharacteristic
530C22#104×D4311yescharacteristic
531C22#1458291411yescharacteristic
532C4—21no—
533C4—21no—
534C4—21no—
535C4—42no—
536C4—82no—
537C4—3442no—
538C4—1721no—
539C4—1721no—
540C4—1722no—
541C4—1722no—
542C4—1721no—
543C4#1458287112yes—
544C2—21no—
545C2—21no—
546C2—41no—
547C2—41no—
548C2—82no—
549C2—1722no—
550C2#1913451111yescharacteristic
551C2#1913453711yescharacteristic
552C2#1913456211yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1507C2
socleC22×C43#379
prime radicalC2×#14583596C2
cosocleC23×C4×C43C23
hypercenter#1507D43
hypocenterC43#8362
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #19134695C2semidirect
3. #19134692C2semidirect
4. C4×#13063239C2semidirect
5. #19133111C2semidirect
6. #19132931C2semidirect
7. C43×#1507C2semidirect
13. C2×#13063316C4semidirect
16. C2×#13063296C4semidirect
17. C2×D4×Dic43C4semidirect
21. C2×C4⋊C4×D43C4semidirect
273. #1507D43semidirect
311. C43#8362semidirect

Maximal subgroups

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

subgroupindex
C2×#145835962
#191346952
#191346922
C4×#130632392
#191331112
#191329312
C43×#15072
#836243