Finite Group Databasebeta

← #24992163

Subgroups — #24992163

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
2C2×#14582633C212yesmaximal, complemented
3#19132818C211yesmaximal, characteristic, complemented
4#19132473C212yesmaximal, complemented
5C43×#2847C211yesmaximal, characteristic
6C23×C43⋊C8—21no—
7C22×C22⋊Dic43—21no—
8C2×C22⋊(C43⋊C8)—24no—
9C2×C22⋊(C43⋊C8)—21no—
10C2×C22⋊(C43⋊C8)C2212yes—
11C2×C43⋊#95—21no—
12C2×C43⋊#95C2212yes—
13#14582633—24no—
14C24×C4×C43C2211yescharacteristic
15C2×#121×C43C411yescharacteristic, complemented
16C2×#121×C43C411yescharacteristic, complemented
17C2×#121×C43C2211yescharacteristic
18C2×#120×C43—21no—
19C43×#386—21no—
20C43×#386—21no—
21C43×#386—21no—
22C43×#380C411yescharacteristic, complemented
23C43×#380C411yescharacteristic, complemented
24C43×#380C2211yescharacteristic
25C23×Dic43—22no—
26C22×C43⋊C8—24no—
27C22×C43⋊C8—22no—
28C22×C43⋊C8—42no—
29C22×C43⋊C8—42no—
30C2×C22⋊Dic43—24no—
31C2×C22⋊Dic43—42no—
32C2×C22⋊Dic43—42no—
33C22⋊(C43⋊C8)—24no—
34C22⋊(C43⋊C8)—22no—
35C22⋊(C43⋊C8)D414yescomplemented
36C43⋊#95—22no—
37C43⋊#95—22no—
38C43⋊#95—42no—
39C25×C43D411yescharacteristic
40C22×D4×C43—21no—
41C22×D4×C43—21no—
42C22×D4×C43—21no—
43C22×D4×C43C2×C411yescharacteristic
44C23×C4×C43—22no—
45C23×C4×C43—22no—
46C23×C4×C43—42no—
47C23×C4×C43—42no—
48C23×C4×C43C2×C411yescharacteristic
49C23×C4×C43C2×C411yescharacteristic
50C23×C4×C43D411yescharacteristic
51C23×C4×C43D411yescharacteristic
52C23×C4×C43D411yescharacteristic
53C23×C4×C43C2311yescharacteristic
54#121×C43—22no—
55#121×C43—22no—
56#121×C43—42no—
57#121×C43—42no—
58#120×C43—42no—
59#120×C43—42no—
60C2×C4⋊C4×C43C2×C411yescharacteristic
61C2×C4⋊C4×C43C2×C411yescharacteristic
62C2×C4⋊C4×C43C2×C411yescharacteristic
63C2×C22⋊C4×C43—21no—
64C2×C22⋊C4×C43—21no—
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43—21no—
67C2×C22⋊C4×C43—21no—
68C2×C22⋊C4×C43—21no—
69#95×C43—21no—
70#95×C43—21no—
71#95×C43—21no—
72C24×C43—22no—
73C24×C43—22no—
74C24×C43—22no—
75C24×C43—22no—
76C24×C43—21no—
77C24×C43—41no—
78C24×C43—41no—
79C24×C43C22⋊C411yescharacteristic
80C24×C43C22⋊C411yescharacteristic
81C24×C43D812yes—
82C24×C43SD1612yes—
83C24×C43C2×D411yescharacteristic
84C2×D4×C43—22no—
85C2×D4×C43—42no—
86C2×D4×C43—42no—
87C2×D4×C43—42no—
88C2×D4×C43—42no—
89C2×D4×C43—42no—
90C2×D4×C43—42no—
91C2×D4×C43—42no—
92C2×D4×C43—41no—
93C2×D4×C43—41no—
94C2×D4×C43—42no—
95C2×D4×C43—41no—
96C2×D4×C43—41no—
97C22×C4×C43—22no—
98C22×C4×C43—21no—
99C22×C4×C43—21no—
100C22×C4×C43—22no—
101C22×C4×C43—22no—
102C22×C4×C43—22no—
103C22×C4×C43—22no—
104C22×C4×C43—21no—
105C22×C4×C43—21no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—21no—
109C22×C4×C43—21no—
110C22×C4×C43—21no—
111C22×C4×C43—22no—
112C22×C4×C43—41no—
113C22×C4×C43—41no—
114C22×C4×C43—41no—
115C22×C4×C43—41no—
116C22×C4×C43—41no—
117C22×C4×C43—41no—
118C22×C4×C43—41no—
119C22×C4×C43—48no—
120C22×C4×C43—48no—
121C22×C4×C43C22⋊C411yescharacteristic
122C22×C4×C43C22⋊C411yescharacteristic
123C22×C4×C43C22×C411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D412yes—
126C22×C4×C43#4112yes—
127C22×Dic43—24no—
128C22×Dic43—42no—
129C22×Dic43—42no—
130C22×Dic43—42no—
131C22×Dic43—42no—
132C22×Dic43—42no—
133C22×Dic43—42no—
134C4⋊C4×C43—22no—
135C4⋊C4×C43—41no—
136C4⋊C4×C43—41no—
137C22⋊C4×C43—42no—
138C22⋊C4×C43—42no—
139C22⋊C4×C43—41no—
140C22⋊C4×C43—41no—
141C22⋊C4×C43—42no—
142C22⋊C4×C43—42no—
143C22⋊C4×C43—41no—
144C22⋊C4×C43—41no—
145C22⋊Dic43—48no—
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—41no—
175C23×C43—41no—
176C23×C43—41no—
177C23×C43—41no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43#9912yes—
182C23×C43#10212yes—
183C23×C43#10212yes—
184C23×C43#10412yes—
185C23×C43C2×C22⋊C411yescharacteristic
186C23×C43#12112yes—
187C23×C43C2×D811yescharacteristic
188C23×C43C2×SD1611yescharacteristic
189C23×C43#13512yes—
190D4×C43—82no—
191D4×C43—84no—
192D4×C43—84no—
193D4×C43—82no—
194D4×C43—82no—
195C2×C4×C43—24no—
196C2×C4×C43—24no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—44no—
209C2×C4×C43—44no—
210C2×C4×C43—44no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43#9912yes—
223C2×C4×C43C4×D412yes—
224C2×C4×C43#12011yescharacteristic
225C2×C4×C43#12311yescharacteristic
226C2×Dic43—44no—
227C2×Dic43—44no—
228C2×Dic43—44no—
229C2×Dic43—82no—
230C2×Dic43—82no—
231C2×Dic43—82no—
232C2×Dic43—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—81no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43#32714yescomplemented
266C22×C43#38611yescharacteristic
267C22×C43C2×#9911yescharacteristic
268C22×C43C2×#9911yescharacteristic
269C22×C43C2×#10211yescharacteristic
270C22×C43#41611yescharacteristic
271C22×C43C2×#10411yescharacteristic
272C22×C43#42111yescharacteristic
273C22×C43#46512yes—
274C22×C43#46612yes—
275C4×C43—21no—
276C4×C43—22no—
277C4×C43—21no—
278C4×C43—22no—
279C4×C43—41no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43—81no—
283Dic43—84no—
284C22×C22⋊C8—431no—
285#2847D4311yescharacteristic
286C2×#327—432no—
287C22⋊#95—431no—
288#1294—432no—
289C2×C43—22no—
290C2×C43—24no—
291C2×C43—22no—
292C2×C43—42no—
293C2×C43—161no—
294C2×C43C2×#32711yescharacteristic
295C2×C43#150111yescharacteristic
296C2×C43#151611yescharacteristic
297C2×C43#151911yescharacteristic
298C2×C43#187111yescharacteristic
299C2×C43#189311yescharacteristic
300C2×C43#189811yescharacteristic
301C24×C4C2×D4311yescharacteristic
302C23×C8—861no—
303C2×#121Dic4311yescharacteristic, complemented
304C2×#121Dic4311yescharacteristic, complemented
305C2×#121C2×D4311yescharacteristic
306C2×#120—21no—
307C22×C22⋊C4—861no—
308C2×C22⋊C8—432no—
309C2×C22⋊C8—864no—
310C2×C22⋊C8—861no—
311#386—21no—
312#386—21no—
313#386—21no—
314#380Dic4311yescharacteristic, complemented
315#380Dic4311yescharacteristic, complemented
316#380C2×D4311yescharacteristic
317C2×#95—432no—
318C2×#95—861no—
319#327—864no—
320C43#911311yescharacteristic, complemented, Sylow
321C25C22⋊D4311yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4C2×Dic4311yescharacteristic
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—42no—
329C23×C4—42no—
330C23×C4—862no—
331C23×C4C2×Dic4311yescharacteristic
332C23×C4C2×Dic4311yescharacteristic
333C23×C4C22⋊D4311yescharacteristic
334C23×C4C22⋊D4311yescharacteristic
335C23×C4C22⋊D4311yescharacteristic
336C23×C4C22×D4311yescharacteristic
337C22×C8—864no—
338C22×C8—862no—
339C22×C8—1722no—
340C22×C8—1722no—
341#121—22no—
342#121—22no—
343#121—42no—
344#121—42no—
345#120—42no—
346#120—42no—
347C2×C4⋊C4C2×Dic4311yescharacteristic
348C2×C4⋊C4C2×Dic4311yescharacteristic
349C2×C4⋊C4C2×Dic4311yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—864no—
357C2×C22⋊C4—1722no—
358C2×C22⋊C4—1722no—
359C22⋊C8—434no—
360C22⋊C8—864no—
361C22⋊C8—862no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—862no—
366#95—862no—
367#95—1722no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—21no—
373C24—41no—
374C24—41no—
375C24#1062188212yes—
376C24#1062188312yes—
377C24C22⋊Dic4311yescharacteristic
378C24C22⋊Dic4311yescharacteristic
379C24C2×C22⋊D4311yescharacteristic
380C2×D4—22no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—42no—
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—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—48no—
416C22×C4—48no—
417C22×C4—864no—
418C22×C4—1722no—
419C22×C4—1722no—
420C22×C4—1722no—
421C22×C4—1722no—
422C22×C4—1722no—
423C22×C4—1722no—
424C22×C4C22⋊Dic4311yescharacteristic
425C22×C4C22⋊Dic4311yescharacteristic
426C22×C4D4×D4312yes—
427C22×C4#1062190012yes—
428C22×C4C22×Dic4311yescharacteristic
429C22×C4C2×C22⋊D4311yescharacteristic
430C2×C8—864no—
431C2×C8—1728no—
432C2×C8—1722no—
433C2×C8—1722no—
434C4⋊C4—22no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C22⋊C4—42no—
438C22⋊C4—42no—
439C22⋊C4—42no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—42no—
443C22⋊C4—41no—
444C22⋊C4—41no—
445C22⋊C4—1728no—
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—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23#1306324012yes—
478C23#1306324612yes—
479C23#1306324612yes—
480C23#1306325212yes—
481C23C2×C22⋊Dic4311yescharacteristic
482C23#1306329712yes—
483C23C2×#1062188211yescharacteristic
484C23C2×#1062188311yescharacteristic
485C23#1306334512yes—
486D4—82no—
487D4—84no—
488D4—82no—
489D4—82no—
490D4—84no—
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—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—3442no—
519C2×C4—3442no—
520C2×C4—3442no—
521C2×C4—3442no—
522C2×C4—1724no—
523C2×C4—1724no—
524C2×C4—1724no—
525C2×C4#1306324012yes—
526C2×C4D4×Dic4312yes—
527C2×C4#1306329311yescharacteristic
528C2×C4#1306330611yescharacteristic
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—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22#1458263314yescomplemented
561C22#1458277911yescharacteristic
562C22C2×#1306324011yescharacteristic
563C22C2×#1306324011yescharacteristic
564C22C2×#1306324611yescharacteristic
565C22#1458289511yescharacteristic
566C22C2×#1306325211yescharacteristic
567C22#1458291611yescharacteristic
568C22#1458312612yes—
569C22#1458313312yes—
570C4—21no—
571C4—22no—
572C4—21no—
573C4—22no—
574C4—41no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—3444no—
579C2—22no—
580C2—22no—
581C2—24no—
582C2—42no—
583C2—161no—
584C2C2×#1458263311yescharacteristic
585C2#1913308611yescharacteristic
586C2#1913315111yescharacteristic
587C2#1913316311yescharacteristic
588C2#1913489811yescharacteristic
589C2#1913502411yescharacteristic
590C2#1913504911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
Fitting, prime radicalC43×#2847C2
socleC23×C43C2×C22⋊C4
cosocleC23×C4×C43C23
hypercenter#2847D43
hypocenterC43#9113
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊(C43⋊C8)C2semidirect
2. C2×#14582633C2semidirect
3. #19132818C2semidirect
4. #19132473C2semidirect
15. C2×#121×C43C4semidirect
16. C2×#121×C43C4semidirect
22. C43×#380C4semidirect
23. C43×#380C4semidirect
35. C22⋊(C43⋊C8)D4semidirect
265. C22×C43#327semidirect
303. C2×#121Dic43semidirect
304. C2×#121Dic43semidirect
314. #380Dic43semidirect
315. #380Dic43semidirect
320. C43#9113semidirect
560. C22#14582633semidirect

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
C2×#145826332
#191328182
#191324732
C43×#28472
#911343