Finite Group Databasebeta

← #24992160

Subgroups — #24992160

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
1C22×C22⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
2#19142877C211yesmaximal, characteristic
3C2×#14582632C212yesmaximal, complemented
4#19132474C212yesmaximal, complemented
5C43×C22⋊#95C211yesmaximal, characteristic, complemented
6C23×C43⋊C8—21no—
7C2×#13063299C411yescharacteristic, complemented
8C2×#13063299C411yescharacteristic, complemented
9C2×#13063299C2211yescharacteristic
10C2×#13063294—21no—
11C2×C22⋊(C43⋊C8)—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—
29C22×C43⋊C8—24no—
30C22×C43⋊C8—22no—
31C22×C43⋊C8—42no—
32C22×C43⋊C8—42no—
33#13063299—22no—
34#13063299—22no—
35#13063299—42no—
36#13063299—42no—
37#13063294—42no—
38#13063294—42no—
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×C4⋊Dic43C2×C411yescharacteristic
41C2×C4⋊Dic43C2×C411yescharacteristic
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C22⋊(C43⋊C8)—24no—
49C22⋊(C43⋊C8)—22no—
50C22⋊(C43⋊C8)D414yescomplemented
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C25×C43D411yescharacteristic
55C23×C4×C43—22no—
56C23×C4×C43—22no—
57C23×C4×C43—22no—
58C23×C4×C43—42no—
59C23×C4×C43—42no—
60C23×C4×C43C2×C411yescharacteristic
61C23×C4×C43C2×C411yescharacteristic
62C23×C4×C43D411yescharacteristic
63C23×C4×C43D411yescharacteristic
64C23×C4×C43D411yescharacteristic
65C23×C4×C43C2311yescharacteristic
66C2×C22⋊C4×C43—24no—
67C2×C22⋊C4×C43—42no—
68C2×C22⋊C4×C43—42no—
69#95×C43—22no—
70#95×C43—22no—
71#95×C43—42no—
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—24no—
94C22×C4×C43—22no—
95C22×C4×C43—22no—
96C22×C4×C43—22no—
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—41no—
104C22×C4×C43—42no—
105C22×C4×C43—42no—
106C22×C4×C43—42no—
107C22×C4×C43—48no—
108C22×C4×C43—48no—
109C22×C4×C43—42no—
110C22×C4×C43—42no—
111C22×C4×C43—42no—
112C22×C4×C43C22⋊C411yescharacteristic
113C22×C4×C43C22⋊C411yescharacteristic
114C22×C4×C43C22×C411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D412yes—
117C22×C4×C43#4112yes—
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—
127C2×C22⋊D43—42no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C2×D172—22no—
132C2×D172—41no—
133C2×D172—41no—
134C22⋊C4×C43—48no—
135C22⋊Dic43—42no—
136C22⋊Dic43—42no—
137C22⋊Dic43—41no—
138C22⋊Dic43—41no—
139(C2×D43)⋊C4—42no—
140(C2×D43)⋊C4—42no—
141(C2×D43)⋊C4—41no—
142(C2×D43)⋊C4—41no—
143C4⋊Dic43—22no—
144C4⋊Dic43—41no—
145C4⋊Dic43—41no—
146C2×C43⋊C8—24no—
147C2×C43⋊C8—48no—
148C2×C43⋊C8—42no—
149C2×C43⋊C8—42no—
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—44no—
209C2×C4×C43—44no—
210C2×C4×C43—44no—
211C2×C4×C43—82no—
212C2×C4×C43—82no—
213C2×C4×C43—82no—
214C2×C4×C43—82no—
215C2×C4×C43#9912yes—
216C2×C4×C43C4×D412yes—
217C2×C4×C43#12011yescharacteristic
218C2×C4×C43#12311yescharacteristic
219C22⋊D43—84no—
220C22⋊D43—84no—
221C22⋊D43—82no—
222C22⋊D43—82no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232D172—82no—
233C43⋊C8—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—
280C4×C43—84no—
281Dic43—81no—
282Dic43—81no—
283Dic43—81no—
284C22×C22⋊C8—431no—
285#2847—431no—
286C2×#327—432no—
287C22⋊#95D4311yescharacteristic, complemented
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—861no—
303C2×#121—431no—
304C2×#121—431no—
305C2×#121—431no—
306C2×#120—861no—
307C22×C22⋊C4—21no—
308C2×C22⋊C8—432no—
309C2×C22⋊C8—864no—
310C2×C22⋊C8—861no—
311#386—861no—
312#386—861no—
313#386—861no—
314#380—431no—
315#380—431no—
316#380—431no—
317C2×#95—21no—
318C2×#95C2×D4312yes—
319#327—864no—
320C43#911311yescharacteristic, complemented, Sylow
321C25C22⋊D4311yescharacteristic
322C22×D4—431no—
323C22×D4—861no—
324C22×D4—861no—
325C22×D4—861no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—42no—
330C23×C4—42no—
331C23×C4C4×D4311yescharacteristic
332C23×C4C4×D4311yescharacteristic
333C23×C4D17211yescharacteristic
334C23×C4D17211yescharacteristic
335C23×C4C22⋊D4311yescharacteristic
336C23×C4C22×D4311yescharacteristic
337C22×C8—864no—
338C22×C8—862no—
339C22×C8—1722no—
340C22×C8—1722no—
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—24no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—861no—
354C2×C22⋊C4—861no—
355C2×C22⋊C4—861no—
356C2×C22⋊C4—861no—
357C2×C22⋊C4—861no—
358C2×C22⋊C4—861no—
359C22⋊C8—434no—
360C22⋊C8—864no—
361C22⋊C8—862no—
362#95—22no—
363#95—22no—
364#95—42no—
365#95—861no—
366#95—861no—
367#95—861no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—41no—
373C24—41no—
374C24—861no—
375C24(C2×D43)⋊C411yescharacteristic
376C24(C2×D43)⋊C411yescharacteristic
377C24#1062188212yes—
378C24#1062188412yes—
379C24C2×C22⋊D4311yescharacteristic
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—24no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—48no—
414C22×C4—48no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—861no—
422C22×C4—861no—
423C22×C4—861no—
424C22×C4(C2×D43)⋊C411yescharacteristic
425C22×C4(C2×D43)⋊C411yescharacteristic
426C22×C4C2×C4×D4311yescharacteristic
427C22×C4C2×D17211yescharacteristic
428C22×C4D4×D4312yes—
429C22×C4#1062190012yes—
430C2×C8—864no—
431C2×C8—1728no—
432C2×C8—1722no—
433C2×C8—1722no—
434C4⋊C4—862no—
435C4⋊C4—1721no—
436C4⋊C4—1721no—
437C22⋊C4—48no—
438C22⋊C4—1722no—
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#1306324512yes—
479C23#1306324512yes—
480C23#1306325312yes—
481C23C2×(C2×D43)⋊C411yescharacteristic
482C23#1306329712yes—
483C23C2×#1062188211yescharacteristic
484C23C2×#1062188411yescharacteristic
485C23#1306334512yes—
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—44no—
510C2×C4—44no—
511C2×C4—44no—
512C2×C4—82no—
513C2×C4—82no—
514C2×C4—82no—
515C2×C4—82no—
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×C4(C22⋊D43)⋊C412yes—
527C2×C4#1306329511yescharacteristic
528C2×C4#1306330911yescharacteristic
529C8—1724no—
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#1458263214yescomplemented
561C22#1458277611yescharacteristic
562C22C2×#1306323911yescharacteristic
563C22C2×#1306323911yescharacteristic
564C22C2×#1306324511yescharacteristic
565C22#1458289311yescharacteristic
566C22C2×#1306325311yescharacteristic
567C22#1458291711yescharacteristic
568C22#1458313012yes—
569C22#1458313312yes—
570C4—21no—
571C4—22no—
572C4—21no—
573C4—22no—
574C4—41no—
575C4—84no—
576C4—3441no—
577C4—3441no—
578C4—3441no—
579C2—22no—
580C2—22no—
581C2—24no—
582C2—42no—
583C2—6881no—
584C2C2×#1458263211yescharacteristic
585C2#1913308411yescharacteristic
586C2#1913314911yescharacteristic
587C2#1913316211yescharacteristic
588C2#1913489511yescharacteristic
589C2#1913502111yescharacteristic
590C2#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#9113
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. C22×C22⋊(C43⋊C8)C2semidirect
3. C2×#14582632C2semidirect
4. #19132474C2semidirect
5. C43×C22⋊#95C2semidirect
7. C2×#13063299C4semidirect
8. C2×#13063299C4semidirect
17. #14582759C4semidirect
18. #14582759C4semidirect
50. C22⋊(C43⋊C8)D4semidirect
258. C22×C43#327semidirect
287. C22⋊#95D43semidirect
320. C43#9113semidirect
560. C22#14582632semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊(C43⋊C8)2
#191428772
C2×#145826322
#191324742
C43×C22⋊#952
#911343