Finite Group Databasebeta

← #24992180

Subgroups — #24992180

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
1C2×#14582863C211yesmaximal, characteristic, complemented
2#19142877C211yesmaximal, characteristic
3C2×#14582632C212yesmaximal, complemented
4#19132474C212yesmaximal, complemented
5C43×C22⋊#95C211yesmaximal, characteristic, complemented
6C22×#10621877—21no—
7C2×#13063299C411yescharacteristic, complemented
8C2×#13063299C411yescharacteristic, complemented
9C2×#13063299C2211yescharacteristic
10C2×#13063294—21no—
11#14582863—24no—
12C2×C22⋊(C43⋊C8)—21no—
13C2×C22⋊(C43⋊C8)C2212yes—
14#14582778—21no—
15#14582778—21no—
16#14582778—21no—
17#14582759C411yescharacteristic, complemented
18#14582759C411yescharacteristic, complemented
19#14582759C2211yescharacteristic
20#14582632—24no—
21C24×C4×C43C2211yescharacteristic
22C22×C22⋊C4×C43—21no—
23C2×#95×C43—21no—
24C2×#95×C43C2212yes—
25C22×D172C2×C411yescharacteristic
26C22×C22⋊D43—21no—
27C22×C22⋊D43—21no—
28C22×C22⋊D43—21no—
29C2×#10621877—24no—
30C2×#10621877—42no—
31C2×#10621877—42no—
32C22×C43⋊C8—22no—
33#13063299—22no—
34#13063299—22no—
35#13063299—42no—
36#13063299—42no—
37#13063294—44no—
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×C4⋊Dic43C2×C411yescharacteristic
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C22⋊(C43⋊C8)—24no—
48C22⋊(C43⋊C8)—22no—
49C22⋊(C43⋊C8)D414yescomplemented
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C25×C43D411yescharacteristic
54C23×C4×C43—22no—
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
65C2×C22⋊C4×C43—24no—
66C2×C22⋊C4×C43—42no—
67C2×C22⋊C4×C43—42no—
68#95×C43—22no—
69#95×C43—22no—
70#95×C43—42no—
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—24no—
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—42no—
104C22×C4×C43—42no—
105C22×C4×C43—42no—
106C22×C4×C43—48no—
107C22×C4×C43—48no—
108C22×C4×C43—42no—
109C22×C4×C43—42no—
110C22×C4×C43—42no—
111C22×C4×C43C22⋊C411yescharacteristic
112C22×C4×C43C22⋊C411yescharacteristic
113C22×C4×C43C22×C411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D412yes—
116C22×C4×C43#4112yes—
117C2×C22⋊D43—42no—
118C2×C22⋊D43—42no—
119C2×C22⋊D43—42no—
120C2×C22⋊D43—42no—
121C2×C22⋊D43—42no—
122C2×C22⋊D43—42no—
123C2×C22⋊D43—42no—
124C2×C22⋊D43—42no—
125C2×C22⋊D43—41no—
126C2×C22⋊D43—41no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C2×D172—22no—
131C2×D172—41no—
132C2×D172—41no—
133C22⋊C4×C43—48no—
134C22⋊Dic43—42no—
135C22⋊Dic43—42no—
136C22⋊Dic43—42no—
137(C2×D43)⋊C4—42no—
138(C2×D43)⋊C4—42no—
139(C2×D43)⋊C4—41no—
140(C2×D43)⋊C4—41no—
141C4⋊Dic43—22no—
142C4⋊Dic43—41no—
143C4⋊Dic43—41no—
144#10621877—48no—
145C2×C43⋊C8—24no—
146C2×C43⋊C8—42no—
147C2×C43⋊C8—42no—
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)12yes—
179C23×C43AGL(1,ℤ/8)11yescharacteristic
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—44no—
207C2×C4×C43—44no—
208C2×C4×C43—44no—
209C2×C4×C43—82no—
210C2×C4×C43—82no—
211C2×C4×C43—82no—
212C2×C4×C43—82no—
213C2×C4×C43#9912yes—
214C2×C4×C43C4×D412yes—
215C2×C4×C43#12011yescharacteristic
216C2×C4×C43#12311yescharacteristic
217C22⋊D43—84no—
218C22⋊D43—84no—
219C22⋊D43—82no—
220C22⋊D43—82no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230D172—82no—
231C43⋊C8—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—
278C4×C43—84no—
279Dic43—81no—
280Dic43—81no—
281Dic43—81no—
282C2×#407—431no—
283#2847—431no—
284C2×#327—432no—
285C22⋊#95D4311yescharacteristic, complemented
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—861no—
301C2×#121—431no—
302C2×#121—431no—
303C2×#121—431no—
304C2×#120—861no—
305C22×C22⋊C4—21no—
306#407—864no—
307C2×C22⋊C8—432no—
308C2×C22⋊C8—861no—
309#386—861no—
310#386—861no—
311#386—861no—
312#380—431no—
313#380—431no—
314#380—431no—
315C2×#95—21no—
316C2×#95C2×D4312yes—
317#327—864no—
318C43#911711yescharacteristic, complemented, Sylow
319C25C22⋊D4311yescharacteristic
320C22×D4—431no—
321C22×D4—861no—
322C22×D4—861no—
323C22×D4—861no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—42no—
328C23×C4—42no—
329C23×C4C4×D4311yescharacteristic
330C23×C4C4×D4311yescharacteristic
331C23×C4D17211yescharacteristic
332C23×C4D17211yescharacteristic
333C23×C4C22⋊D4311yescharacteristic
334C23×C4C22×D4311yescharacteristic
335C2×M16—864no—
336C2×M16—1722no—
337C2×M16—1722no—
338C22×C8—862no—
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—24no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—861no—
351C2×C22⋊C4—861no—
352C2×C22⋊C4—861no—
353C2×C22⋊C4—861no—
354C2×C22⋊C4—861no—
355C2×C22⋊C4—861no—
356C22⋊C8—434no—
357C22⋊C8—864no—
358C22⋊C8—862no—
359#95—22no—
360#95—22no—
361#95—42no—
362#95—861no—
363#95—861no—
364#95—861no—
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×C22⋊D4311yescharacteristic
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—24no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—48no—
411C22×C4—48no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—861no—
419C22×C4—861no—
420C22×C4—861no—
421C22×C4(C2×D43)⋊C411yescharacteristic
422C22×C4(C2×D43)⋊C411yescharacteristic
423C22×C4C2×C4×D4311yescharacteristic
424C22×C4C2×D17211yescharacteristic
425C22×C4D4×D4312yes—
426C22×C4#1062190012yes—
427M16—1728no—
428C2×C8—864no—
429C2×C8—1722no—
430C2×C8—1722no—
431C4⋊C4—862no—
432C4⋊C4—1721no—
433C4⋊C4—1721no—
434C22⋊C4—48no—
435C22⋊C4—1722no—
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#1306325312yes—
477C23C2×(C2×D43)⋊C411yescharacteristic
478C23#1306329712yes—
479C23#1306335012yes—
480C23#1306335111yescharacteristic
481C23#1306335611yescharacteristic
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—44no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—82no—
509C2×C4—82no—
510C2×C4—82no—
511C2×C4—82no—
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×C4(C22⋊D43)⋊C412yes—
523C2×C4#1306329511yescharacteristic
524C2×C4#1306330911yescharacteristic
525C8—1724no—
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#1458277611yescharacteristic
558C22C2×#1306323911yescharacteristic
559C22C2×#1306323911yescharacteristic
560C22#1458289811yescharacteristic
561C22#1458290311yescharacteristic
562C22C2×#1306325311yescharacteristic
563C22#1458291711yescharacteristic
564C22#1458314712yes—
565C22#1458315012yes—
566C4—21no—
567C4—22no—
568C4—21no—
569C4—22no—
570C4—41no—
571C4—84no—
572C4—3441no—
573C4—3441no—
574C4—3441no—
575C2—22no—
576C2—22no—
577C2—42no—
578C2—42no—
579C2—6881no—
580C2#1913309711yescharacteristic
581C2#1913311011yescharacteristic
582C2#1913312311yescharacteristic
583C2#1913313611yescharacteristic
584C2#1913489511yescharacteristic
585C2#1913503111yescharacteristic
586C2#1913504611yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×C22⋊#95C2
socleC23×C43C2×C22⋊C4
prime radical#19142877C2
cosocleC23×C4×C43C23
hypercenterC22⋊#95D43
hypocenterC43#9117
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#14582863C2semidirect
3. C2×#14582632C2semidirect
4. #19132474C2semidirect
5. C43×C22⋊#95C2semidirect
7. C2×#13063299C4semidirect
8. C2×#13063299C4semidirect
17. #14582759C4semidirect
18. #14582759C4semidirect
49. C22⋊(C43⋊C8)D4semidirect
285. C22⋊#95D43semidirect
318. C43#9117semidirect

Maximal subgroups

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

subgroupindex
C2×#145828632
#191428772
C2×#145826322
#191324742
C43×C22⋊#952
#911743