Finite Group Databasebeta

← #24992182

Subgroups — #24992182

Order 11008.

1030 conjugacy classes of subgroups.

The subgroup lattice has 588 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
5C2×C43×#407C211yesmaximal, 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
21C22×M16×C43—21no—
22C43×#407—24no—
23C2×C22⋊C8×C43—21no—
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—44no—
35C2×C4⋊Dic43C2×C411yescharacteristic
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×C4⋊Dic43C2×C411yescharacteristic
38C2×C22⋊Dic43—24no—
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—42no—
43C2×C22⋊Dic43—42no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—22no—
51C43⋊#95—22no—
52C43⋊#95—42no—
53C25×C43D411yescharacteristic
54C23×C4×C43—22no—
55C23×C4×C43—22no—
56C23×C4×C43—42no—
57C23×C4×C43—42no—
58C23×C4×C43C2×C411yescharacteristic
59C23×C4×C43C2×C411yescharacteristic
60C23×C4×C43D411yescharacteristic
61C23×C4×C43D411yescharacteristic
62C23×C4×C43D411yescharacteristic
63C23×C4×C43C2311yescharacteristic
64C2×M16×C43—24no—
65C2×M16×C43—42no—
66C2×M16×C43—42no—
67C22×C8×C43—22no—
68C22⋊C8×C43—24no—
69C22⋊C8×C43—22no—
70C22⋊C8×C43D414yescomplemented
71C24×C43—22no—
72C24×C43—22no—
73C24×C43—21no—
74C24×C43—21no—
75C24×C43—22no—
76C24×C43—22no—
77C24×C43—41no—
78C24×C43—41no—
79C24×C43C22⋊C411yescharacteristic
80C24×C43C22⋊C411yescharacteristic
81C24×C43C2×D411yescharacteristic
82C23×D43—21no—
83C22×C4×C43—22no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—22no—
87C22×C4×C43—22no—
88C22×C4×C43—22no—
89C22×C4×C43—22no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—22no—
93C22×C4×C43—22no—
94C22×C4×C43—22no—
95C22×C4×C43—41no—
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—48no—
103C22×C4×C43—48no—
104C22×C4×C43C22⋊C411yescharacteristic
105C22×C4×C43C22⋊C411yescharacteristic
106C22×C4×C43C22×C411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D412yes—
109C22×C4×C43#4112yes—
110C2×C22⋊D43—42no—
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—
120C22×Dic43—24no—
121C22×Dic43—21no—
122C22×Dic43—21no—
123C22×Dic43—21no—
124C22×Dic43—42no—
125C22×Dic43—42no—
126C22×Dic43—42no—
127C22×Dic43—42no—
128C22×Dic43—42no—
129C22×Dic43—42no—
130C2×D172—22no—
131C2×D172—41no—
132C2×D172—41no—
133M16×C43—48no—
134C2×C8×C43—24no—
135C2×C8×C43—42no—
136C2×C8×C43—42no—
137C22⋊Dic43—48no—
138C22⋊Dic43—42no—
139C22⋊Dic43—42no—
140C22⋊Dic43—42no—
141(C2×D43)⋊C4—42no—
142(C2×D43)⋊C4—42no—
143(C2×D43)⋊C4—41no—
144(C2×D43)⋊C4—41no—
145C4⋊Dic43—22no—
146C4⋊Dic43—41no—
147C4⋊Dic43—41no—
148C23×C43—21no—
149C23×C43—21no—
150C23×C43—21no—
151C23×C43—21no—
152C23×C43—24no—
153C23×C43—24no—
154C23×C43—21no—
155C23×C43—21no—
156C23×C43—21no—
157C23×C43—21no—
158C23×C43—21no—
159C23×C43—21no—
160C23×C43—21no—
161C23×C43—21no—
162C23×C43—21no—
163C23×C43—21no—
164C23×C43—21no—
165C23×C43—21no—
166C23×C43—44no—
167C23×C43—44no—
168C23×C43—44no—
169C23×C43—44no—
170C23×C43—42no—
171C23×C43—42no—
172C23×C43—42no—
173C23×C43—42no—
174C23×C43#9912yes—
175C23×C43#10412yes—
176C23×C43C2×C22⋊C411yescharacteristic
177C23×C43#12112yes—
178C23×C43AGL(1,ℤ/8)11yescharacteristic
179C23×C43AGL(1,ℤ/8)12yes—
180C23×C43#13711yescharacteristic
181C22×D43—41no—
182C22×D43—41no—
183C22×D43—41no—
184C22×D43—41no—
185C22×D43—41no—
186C22×D43—41no—
187C22×D43—41no—
188C2×C4×C43—24no—
189C2×C4×C43—24no—
190C2×C4×C43—21no—
191C2×C4×C43—21no—
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—42no—
200C2×C4×C43—42no—
201C2×C4×C43—44no—
202C2×C4×C43—44no—
203C2×C4×C43—44no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43#9912yes—
207C2×C4×C43C4×D412yes—
208C2×C4×C43#12011yescharacteristic
209C2×C4×C43#12311yescharacteristic
210C22⋊D43—84no—
211C22⋊D43—84no—
212C22⋊D43—82no—
213C22⋊D43—82no—
214C2×Dic43—44no—
215C2×Dic43—44no—
216C2×Dic43—44no—
217C2×Dic43—41no—
218C2×Dic43—41no—
219C2×Dic43—41no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—82no—
227C2×Dic43—82no—
228C2×Dic43—82no—
229C2×Dic43—82no—
230D172—82no—
231C8×C43—44no—
232#9117—431nomaximal, Sylow
233C22×C43—22no—
234C22×C43—22no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—22no—
238C22×C43—22no—
239C22×C43—21no—
240C22×C43—21no—
241C22×C43—22no—
242C22×C43—22no—
243C22×C43—22no—
244C22×C43—22no—
245C22×C43—22no—
246C22×C43—22no—
247C22×C43—48no—
248C22×C43—48no—
249C22×C43—41no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43—41no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43#38611yescharacteristic
258C22×C43C2×#9911yescharacteristic
259C22×C43C2×#9911yescharacteristic
260C22×C43#41711yescharacteristic
261C22×C43#41811yescharacteristic
262C22×C43C2×#10411yescharacteristic
263C22×C43#42111yescharacteristic
264C22×C43#46812yes—
265C22×C43#46912yes—
266C2×D43—81no—
267C2×D43—81no—
268C2×D43—81no—
269C2×D43—81no—
270C2×D43—81no—
271C2×D43—81no—
272C2×D43—81no—
273C4×C43—21no—
274C4×C43—22no—
275C4×C43—22no—
276C4×C43—21no—
277C4×C43—41no—
278Dic43—84no—
279Dic43—81no—
280Dic43—81no—
281Dic43—81no—
282C2×#407D4311yescharacteristic, complemented
283#2847—431no—
284C2×#327—432no—
285C22⋊#95—431no—
286#1294—432no—
287C2×C43—22no—
288C2×C43—22no—
289C2×C43—42no—
290C2×C43—42no—
291C2×C43#150411yescharacteristic
292C2×C43#150711yescharacteristic
293C2×C43#151011yescharacteristic
294C2×C43#151311yescharacteristic
295C2×C43#187111yescharacteristic
296C2×C43#189511yescharacteristic
297C2×C43#189811yescharacteristic
298D43—161no—
299C24×C4C2×D4311yescharacteristic
300C22×M16—21no—
301C2×#121—431no—
302C2×#121—431no—
303C2×#121—431no—
304C2×#120—861no—
305C22×C22⋊C4—861no—
306#407—24no—
307C2×C22⋊C8—21no—
308C2×C22⋊C8C2×D4312yes—
309#386—861no—
310#386—861no—
311#386—861no—
312#380—431no—
313#380—431no—
314#380—431no—
315C2×#95—432no—
316C2×#95—861no—
317#327—864no—
318C43#911711yescharacteristic, complemented, Sylow
319C25D17211yescharacteristic
320C22×D4—431no—
321C22×D4—861no—
322C22×D4—861no—
323C22×D4—861no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—42no—
327C23×C4—42no—
328C23×C4—862no—
329C23×C4C4×D4311yescharacteristic
330C23×C4C4×D4311yescharacteristic
331C23×C4D17211yescharacteristic
332C23×C4C22⋊D4311yescharacteristic
333C23×C4C22⋊D4311yescharacteristic
334C23×C4C22×D4311yescharacteristic
335C2×M16—24no—
336C2×M16—42no—
337C2×M16—42no—
338C22×C8—22no—
339#121—862no—
340#121—862no—
341#121—1722no—
342#121—1722no—
343#120—1724no—
344C2×C4⋊C4—431no—
345C2×C4⋊C4—431no—
346C2×C4⋊C4—431no—
347C2×C22⋊C4—864no—
348C2×C22⋊C4—861no—
349C2×C22⋊C4—861no—
350C2×C22⋊C4—861no—
351C2×C22⋊C4—861no—
352C2×C22⋊C4—861no—
353C2×C22⋊C4—861no—
354C2×C22⋊C4—1722no—
355C2×C22⋊C4—1722no—
356C22⋊C8—24no—
357C22⋊C8—22no—
358C22⋊C8C22⋊D4314yescomplemented
359#95—861no—
360#95—861no—
361#95—861no—
362#95—862no—
363#95—862no—
364#95—1722no—
365C24—22no—
366C24—22no—
367C24—21no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—41no—
372C24—41no—
373C24—861no—
374C24(C2×D43)⋊C411yescharacteristic
375C24(C2×D43)⋊C411yescharacteristic
376C24C2×D17211yescharacteristic
377C2×D4—862no—
378C2×D4—1721no—
379C2×D4—1721no—
380C2×D4—1722no—
381C2×D4—1722no—
382C2×D4—1722no—
383C2×D4—1722no—
384C2×D4—1722no—
385C2×D4—1722no—
386C2×D4—1722no—
387C2×D4—1722no—
388C2×D4—1721no—
389C2×D4—1721no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—48no—
410C22×C4—48no—
411C22×C4—864no—
412C22×C4—861no—
413C22×C4—861no—
414C22×C4—861no—
415C22×C4—1722no—
416C22×C4—1722no—
417C22×C4—1722no—
418C22×C4—1722no—
419C22×C4—1722no—
420C22×C4—1722no—
421C22×C4(C2×D43)⋊C411yescharacteristic
422C22×C4(C2×D43)⋊C411yescharacteristic
423C22×C4C2×C4×D4311yescharacteristic
424C22×C4#1062189812yes—
425C22×C4C2×C22⋊D4311yescharacteristic
426C22×C4C2×C22⋊D4312yes—
427M16—48no—
428C2×C8—24no—
429C2×C8—42no—
430C2×C8—42no—
431C4⋊C4—862no—
432C4⋊C4—1721no—
433C4⋊C4—1721no—
434C22⋊C4—1722no—
435C22⋊C4—1728no—
436C22⋊C4—1722no—
437C22⋊C4—1722no—
438C22⋊C4—1722no—
439C22⋊C4—1722no—
440C22⋊C4—1721no—
441C22⋊C4—1721no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—21no—
446C23—24no—
447C23—24no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—44no—
461C23—44no—
462C23—44no—
463C23—44no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—1721no—
469C23—1721no—
470C23—1721no—
471C23—1721no—
472C23—1721no—
473C23—1721no—
474C23—1721no—
475C23#1306323912yes—
476C23#1306325112yes—
477C23C2×(C2×D43)⋊C411yescharacteristic
478C23#1306329912yes—
479C23#1306335312yes—
480C23#1306335311yescharacteristic
481C23#1306335811yescharacteristic
482D4—3442no—
483D4—3444no—
484D4—3444no—
485D4—3442no—
486D4—3442no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—3442no—
506C2×C4—3442no—
507C2×C4—3442no—
508C2×C4—3442no—
509C2×C4—1724no—
510C2×C4—1724no—
511C2×C4—1724no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4#1306323912yes—
522C2×C4C4×C22⋊D4312yes—
523C2×C4#1306329411yescharacteristic
524C2×C4#1306330811yescharacteristic
525C8—44no—
526C22—22no—
527C22—21no—
528C22—21no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—21no—
533C22—21no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—48no—
541C22—48no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—3441no—
551C22—3441no—
552C22—3441no—
553C22—3441no—
554C22—3441no—
555C22—3441no—
556C22—3441no—
557C22#1458277811yescharacteristic
558C22C2×#1306323911yescharacteristic
559C22C2×#1306323911yescharacteristic
560C22#1458290111yescharacteristic
561C22#1458290511yescharacteristic
562C22C2×#1306325111yescharacteristic
563C22#1458291511yescharacteristic
564C22#1458314512yes—
565C22#1458315212yes—
566C4—21no—
567C4—22no—
568C4—21no—
569C4—22no—
570C4—41no—
571C4—3444no—
572C4—3441no—
573C4—3441no—
574C4—3441no—
575C2—22no—
576C2—22no—
577C2—42no—
578C2—42no—
579C2—6881no—
580C2#1913310011yescharacteristic
581C2#1913311211yescharacteristic
582C2#1913312511yescharacteristic
583C2#1913313911yescharacteristic
584C2#1913489711yescharacteristic
585C2#1913503311yescharacteristic
586C2#1913504811yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#407C2
socleC23×C43C2×C22⋊C4
prime radical#19142877C2
cosocleC23×C4×C43C23
hypercenterC2×#407D43
hypocenterC43#9117
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#14582634C2semidirect
3. #19132818C2semidirect
4. #19132475C2semidirect
5. C2×C43×#407C2semidirect
6. C2×#13063299C4semidirect
7. C2×#13063299C4semidirect
14. #14582759C4semidirect
15. #14582759C4semidirect
70. C22⋊C8×C43D4semidirect
282. C2×#407D43semidirect
318. C43#9117semidirect
358. C22⋊C8C22⋊D43semidirect

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
C2×C43×#4072
#911743