Finite Group Databasebeta

← #24992162

Subgroups — #24992162

Order 11008.

1062 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142877C211yesmaximal, characteristic
2C2×#14582634C212yesmaximal, complemented
3#19132818C211yesmaximal, characteristic, complemented
4#19132475C212yesmaximal, complemented
5C22×C22⋊C8×C43C211yesmaximal, characteristic, complemented
6C2×#13063299C411yescharacteristic, complemented
7C2×#13063299C411yescharacteristic, complemented
8C2×#13063299C2211yescharacteristic
9C2×#13063294—21no—
10C22×C22⋊Dic43—21no—
11#14582778—21no—
12#14582778—21no—
13#14582778—21no—
14#14582759C411yescharacteristic, complemented
15#14582759C411yescharacteristic, complemented
16#14582759C2211yescharacteristic
17C2×C43⋊#95—21no—
18C2×C43⋊#95C2212yes—
19#14582634—24no—
20C24×C4×C43C2211yescharacteristic
21C23×C8×C43—21no—
22C2×C22⋊C8×C43—21no—
23C2×C22⋊C8×C43—24no—
24C2×C22⋊C8×C43C2212yes—
25C22×D172C2×C411yescharacteristic
26C22×C22⋊D43—21no—
27C22×C22⋊D43—21no—
28C22×C22⋊D43—21no—
29C23×Dic43—22no—
30#13063299—22no—
31#13063299—22no—
32#13063299—42no—
33#13063299—42no—
34#13063294—42no—
35#13063294—42no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×C4⋊Dic43C2×C411yescharacteristic
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×C22⋊Dic43—24no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—42no—
44C2×C22⋊Dic43—42no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—22no—
52C43⋊#95—22no—
53C43⋊#95—42no—
54C25×C43D411yescharacteristic
55C23×C4×C43—22no—
56C23×C4×C43—22no—
57C23×C4×C43—42no—
58C23×C4×C43—42no—
59C23×C4×C43C2×C411yescharacteristic
60C23×C4×C43C2×C411yescharacteristic
61C23×C4×C43D411yescharacteristic
62C23×C4×C43D411yescharacteristic
63C23×C4×C43D411yescharacteristic
64C23×C4×C43C2311yescharacteristic
65C22×C8×C43—24no—
66C22×C8×C43—22no—
67C22×C8×C43—42no—
68C22×C8×C43—42no—
69C22⋊C8×C43—24no—
70C22⋊C8×C43—22no—
71C22⋊C8×C43D414yescomplemented
72C24×C43—22no—
73C24×C43—22no—
74C24×C43—22no—
75C24×C43—22no—
76C24×C43—41no—
77C24×C43—41no—
78C24×C43C22⋊C411yescharacteristic
79C24×C43C22⋊C411yescharacteristic
80C24×C43D812yes—
81C24×C43SD1612yes—
82C24×C43C2×D411yescharacteristic
83C23×D43—21no—
84C22×C4×C43—22no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—22no—
88C22×C4×C43—22no—
89C22×C4×C43—22no—
90C22×C4×C43—22no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—22no—
94C22×C4×C43—22no—
95C22×C4×C43—22no—
96C22×C4×C43—41no—
97C22×C4×C43—41no—
98C22×C4×C43—41no—
99C22×C4×C43—41no—
100C22×C4×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43—41no—
103C22×C4×C43—48no—
104C22×C4×C43—48no—
105C22×C4×C43C22⋊C411yescharacteristic
106C22×C4×C43C22⋊C411yescharacteristic
107C22×C4×C43C22×C411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D412yes—
110C22×C4×C43#4112yes—
111C2×C22⋊D43—42no—
112C2×C22⋊D43—42no—
113C2×C22⋊D43—42no—
114C2×C22⋊D43—42no—
115C2×C22⋊D43—42no—
116C2×C22⋊D43—42no—
117C2×C22⋊D43—42no—
118C2×C22⋊D43—41no—
119C2×C22⋊D43—41no—
120C2×C22⋊D43—42no—
121C22×Dic43—24no—
122C22×Dic43—21no—
123C22×Dic43—21no—
124C22×Dic43—21no—
125C22×Dic43—42no—
126C22×Dic43—42no—
127C22×Dic43—42no—
128C22×Dic43—42no—
129C22×Dic43—42no—
130C22×Dic43—42no—
131C2×D172—22no—
132C2×D172—41no—
133C2×D172—41no—
134C2×C8×C43—24no—
135C2×C8×C43—48no—
136C2×C8×C43—42no—
137C2×C8×C43—42no—
138C22⋊Dic43—48no—
139C22⋊Dic43—42no—
140C22⋊Dic43—42no—
141C22⋊Dic43—41no—
142C22⋊Dic43—41no—
143(C2×D43)⋊C4—42no—
144(C2×D43)⋊C4—42no—
145(C2×D43)⋊C4—41no—
146(C2×D43)⋊C4—41no—
147C4⋊Dic43—22no—
148C4⋊Dic43—41no—
149C4⋊Dic43—41no—
150C23×C43—21no—
151C23×C43—21no—
152C23×C43—21no—
153C23×C43—21no—
154C23×C43—21no—
155C23×C43—21no—
156C23×C43—21no—
157C23×C43—21no—
158C23×C43—24no—
159C23×C43—24no—
160C23×C43—21no—
161C23×C43—21no—
162C23×C43—21no—
163C23×C43—21no—
164C23×C43—21no—
165C23×C43—21no—
166C23×C43—24no—
167C23×C43—24no—
168C23×C43—42no—
169C23×C43—42no—
170C23×C43—44no—
171C23×C43—44no—
172C23×C43—44no—
173C23×C43—44no—
174C23×C43#9912yes—
175C23×C43#10212yes—
176C23×C43#10212yes—
177C23×C43#10412yes—
178C23×C43C2×C22⋊C411yescharacteristic
179C23×C43#12112yes—
180C23×C43C2×D811yescharacteristic
181C23×C43C2×SD1611yescharacteristic
182C23×C43#13512yes—
183C22×D43—41no—
184C22×D43—41no—
185C22×D43—41no—
186C22×D43—41no—
187C22×D43—41no—
188C22×D43—41no—
189C22×D43—41no—
190C2×C4×C43—24no—
191C2×C4×C43—24no—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—42no—
202C2×C4×C43—42no—
203C2×C4×C43—44no—
204C2×C4×C43—44no—
205C2×C4×C43—44no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43#9912yes—
209C2×C4×C43C4×D412yes—
210C2×C4×C43#12011yescharacteristic
211C2×C4×C43#12311yescharacteristic
212C22⋊D43—84no—
213C22⋊D43—84no—
214C22⋊D43—82no—
215C22⋊D43—82no—
216C2×Dic43—44no—
217C2×Dic43—44no—
218C2×Dic43—44no—
219C2×Dic43—41no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—82no—
229C2×Dic43—82no—
230C2×Dic43—82no—
231C2×Dic43—82no—
232D172—82no—
233C8×C43—44no—
234#9113—431nomaximal, Sylow
235C22×C43—22no—
236C22×C43—22no—
237C22×C43—22no—
238C22×C43—22no—
239C22×C43—22no—
240C22×C43—21no—
241C22×C43—21no—
242C22×C43—22no—
243C22×C43—22no—
244C22×C43—22no—
245C22×C43—22no—
246C22×C43—22no—
247C22×C43—21no—
248C22×C43—21no—
249C22×C43—22no—
250C22×C43—22no—
251C22×C43—22no—
252C22×C43—48no—
253C22×C43—48no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43#32714yescomplemented
259C22×C43#38611yescharacteristic
260C22×C43C2×#9911yescharacteristic
261C22×C43C2×#9911yescharacteristic
262C22×C43C2×#10211yescharacteristic
263C22×C43#41611yescharacteristic
264C22×C43C2×#10411yescharacteristic
265C22×C43#42111yescharacteristic
266C22×C43#46512yes—
267C22×C43#46612yes—
268C2×D43—81no—
269C2×D43—81no—
270C2×D43—81no—
271C2×D43—81no—
272C2×D43—81no—
273C2×D43—81no—
274C2×D43—81no—
275C4×C43—21no—
276C4×C43—22no—
277C4×C43—22no—
278C4×C43—21no—
279C4×C43—41no—
280Dic43—84no—
281Dic43—81no—
282Dic43—81no—
283Dic43—81no—
284C22×C22⋊C8D4311yescharacteristic, complemented
285#2847—431no—
286C2×#327—432no—
287C22⋊#95—431no—
288#1294—432no—
289C2×C43—22no—
290C2×C43—24no—
291C2×C43—22no—
292C2×C43—42no—
293C2×C43C2×#32711yescharacteristic
294C2×C43#150111yescharacteristic
295C2×C43#151611yescharacteristic
296C2×C43#151911yescharacteristic
297C2×C43#187111yescharacteristic
298C2×C43#189311yescharacteristic
299C2×C43#189811yescharacteristic
300D43—161no—
301C24×C4C2×D4311yescharacteristic
302C23×C8—21no—
303C2×#121—431no—
304C2×#121—431no—
305C2×#121—431no—
306C2×#120—861no—
307C22×C22⋊C4—861no—
308C2×C22⋊C8—21no—
309C2×C22⋊C8—24no—
310C2×C22⋊C8C2×D4312yes—
311#386—861no—
312#386—861no—
313#386—861no—
314#380—431no—
315#380—431no—
316#380—431no—
317C2×#95—432no—
318C2×#95—861no—
319#327—864no—
320C43#911311yescharacteristic, complemented, Sylow
321C25D17211yescharacteristic
322C22×D4—431no—
323C22×D4—861no—
324C22×D4—861no—
325C22×D4—861no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—42no—
329C23×C4—42no—
330C23×C4—862no—
331C23×C4C4×D4311yescharacteristic
332C23×C4C4×D4311yescharacteristic
333C23×C4D17211yescharacteristic
334C23×C4C22⋊D4311yescharacteristic
335C23×C4C22⋊D4311yescharacteristic
336C23×C4C22×D4311yescharacteristic
337C22×C8—24no—
338C22×C8—22no—
339C22×C8—42no—
340C22×C8—42no—
341#121—862no—
342#121—862no—
343#121—1722no—
344#121—1722no—
345#120—1722no—
346#120—1722no—
347C2×C4⋊C4—431no—
348C2×C4⋊C4—431no—
349C2×C4⋊C4—431no—
350C2×C22⋊C4—864no—
351C2×C22⋊C4—861no—
352C2×C22⋊C4—861no—
353C2×C22⋊C4—861no—
354C2×C22⋊C4—861no—
355C2×C22⋊C4—861no—
356C2×C22⋊C4—861no—
357C2×C22⋊C4—1722no—
358C2×C22⋊C4—1722no—
359C22⋊C8—24no—
360C22⋊C8—22no—
361C22⋊C8C22⋊D4314yescomplemented
362#95—861no—
363#95—861no—
364#95—861no—
365#95—862no—
366#95—862no—
367#95—1722no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—41no—
373C24—41no—
374C24—861no—
375C24#1062187312yes—
376C24D34412yes—
377C24(C2×D43)⋊C411yescharacteristic
378C24(C2×D43)⋊C411yescharacteristic
379C24C2×D17211yescharacteristic
380C2×D4—862no—
381C2×D4—1721no—
382C2×D4—1721no—
383C2×D4—1722no—
384C2×D4—1722no—
385C2×D4—1722no—
386C2×D4—1722no—
387C2×D4—1722no—
388C2×D4—1722no—
389C2×D4—1722no—
390C2×D4—1721no—
391C2×D4—1721no—
392C2×D4—1722no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—48no—
413C22×C4—48no—
414C22×C4—864no—
415C22×C4—861no—
416C22×C4—861no—
417C22×C4—861no—
418C22×C4—1722no—
419C22×C4—1722no—
420C22×C4—1722no—
421C22×C4—1722no—
422C22×C4—1722no—
423C22×C4—1722no—
424C22×C4(C2×D43)⋊C411yescharacteristic
425C22×C4(C2×D43)⋊C411yescharacteristic
426C22×C4C2×C4×D4311yescharacteristic
427C22×C4#1062189812yes—
428C22×C4C2×C22⋊D4311yescharacteristic
429C22×C4C2×C22⋊D4312yes—
430C2×C8—24no—
431C2×C8—48no—
432C2×C8—42no—
433C2×C8—42no—
434C4⋊C4—862no—
435C4⋊C4—1721no—
436C4⋊C4—1721no—
437C22⋊C4—1722no—
438C22⋊C4—1728no—
439C22⋊C4—1722no—
440C22⋊C4—1722no—
441C22⋊C4—1721no—
442C22⋊C4—1721no—
443C22⋊C4—1722no—
444C22⋊C4—1721no—
445C22⋊C4—1721no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—24no—
457C23—24no—
458C23—24no—
459C23—24no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—42no—
465C23—42no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—1721no—
471C23—1721no—
472C23—1721no—
473C23—1721no—
474C23—1721no—
475C23—1721no—
476C23—1721no—
477C23#1306323912yes—
478C23#1306324712yes—
479C23#1306324712yes—
480C23#1306325112yes—
481C23C2×(C2×D43)⋊C411yescharacteristic
482C23#1306329912yes—
483C23C2×D34411yescharacteristic
484C23C2×#1062187311yescharacteristic
485C23#1306334712yes—
486D4—3442no—
487D4—3444no—
488D4—3442no—
489D4—3442no—
490D4—3444no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—3442no—
510C2×C4—3442no—
511C2×C4—3442no—
512C2×C4—3442no—
513C2×C4—1724no—
514C2×C4—1724no—
515C2×C4—1724no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4#1306323912yes—
526C2×C4C4×C22⋊D4312yes—
527C2×C4#1306329411yescharacteristic
528C2×C4#1306330811yescharacteristic
529C8—44no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—21no—
534C22—21no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—21no—
542C22—22no—
543C22—21no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—48no—
548C22—48no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—3441no—
554C22—3441no—
555C22—3441no—
556C22—3441no—
557C22—3441no—
558C22—3441no—
559C22—3441no—
560C22#1458263414yescomplemented
561C22#1458277811yescharacteristic
562C22C2×#1306323911yescharacteristic
563C22C2×#1306323911yescharacteristic
564C22C2×#1306324711yescharacteristic
565C22#1458289611yescharacteristic
566C22C2×#1306325111yescharacteristic
567C22#1458291511yescharacteristic
568C22#1458312812yes—
569C22#1458313512yes—
570C4—21no—
571C4—22no—
572C4—21no—
573C4—22no—
574C4—41no—
575C4—3444no—
576C4—3441no—
577C4—3441no—
578C4—3441no—
579C2—22no—
580C2—22no—
581C2—24no—
582C2—42no—
583C2—6881no—
584C2C2×#1458263411yescharacteristic
585C2#1913308711yescharacteristic
586C2#1913315211yescharacteristic
587C2#1913316411yescharacteristic
588C2#1913489711yescharacteristic
589C2#1913502311yescharacteristic
590C2#1913504811yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC22×C22⋊C8×C43C2
socleC23×C43C2×C22⋊C4
prime radical#19142877C2
cosocleC23×C4×C43C23
hypercenterC22×C22⋊C8D43
hypocenterC43#9113
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#14582634C2semidirect
3. #19132818C2semidirect
4. #19132475C2semidirect
5. C22×C22⋊C8×C43C2semidirect
6. C2×#13063299C4semidirect
7. C2×#13063299C4semidirect
14. #14582759C4semidirect
15. #14582759C4semidirect
71. C22⋊C8×C43D4semidirect
258. C22×C43#327semidirect
284. C22×C22⋊C8D43semidirect
320. C43#9113semidirect
361. C22⋊C8C22⋊D43semidirect
560. C22#14582634semidirect

Maximal subgroups

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

subgroupindex
#191428772
C2×#145826342
#191328182
#191324752
C22×C22⋊C8×C432
#911343