Finite Group Databasebeta

← #24992183

Subgroups — #24992183

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
2C2×#14582633C212yesmaximal, complemented
3#19132818C211yesmaximal, characteristic, complemented
4#19132473C212yesmaximal, complemented
5C43×#2847C211yesmaximal, characteristic
6C22×#10621877—21no—
7C22×C22⋊Dic43—21no—
8#14582863—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—
26C2×#10621877—24no—
27C2×#10621877—42no—
28C2×#10621877—42no—
29C22×C43⋊C8—22no—
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—44no—
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C4⋊C4×C43C2×C411yescharacteristic
61C2×C4⋊C4×C43C2×C411yescharacteristic
62C2×C22⋊C4×C43—21no—
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—
68#95×C43—21no—
69#95×C43—21no—
70#95×C43—21no—
71C24×C43—22no—
72C24×C43—22no—
73C24×C43—21no—
74C24×C43—21no—
75C24×C43—22no—
76C24×C43—22no—
77C24×C43—21no—
78C24×C43—41no—
79C24×C43—41no—
80C24×C43C22⋊C411yescharacteristic
81C24×C43C22⋊C411yescharacteristic
82C24×C43C2×D411yescharacteristic
83C2×D4×C43—22no—
84C2×D4×C43—42no—
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—41no—
95C2×D4×C43—41no—
96C22×C4×C43—22no—
97C22×C4×C43—21no—
98C22×C4×C43—21no—
99C22×C4×C43—22no—
100C22×C4×C43—22no—
101C22×C4×C43—22no—
102C22×C4×C43—22no—
103C22×C4×C43—21no—
104C22×C4×C43—21no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—21no—
108C22×C4×C43—21no—
109C22×C4×C43—21no—
110C22×C4×C43—22no—
111C22×C4×C43—41no—
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—48no—
119C22×C4×C43—48no—
120C22×C4×C43C22⋊C411yescharacteristic
121C22×C4×C43C22⋊C411yescharacteristic
122C22×C4×C43C22×C411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D412yes—
125C22×C4×C43#4112yes—
126C22×Dic43—24no—
127C22×Dic43—42no—
128C22×Dic43—42no—
129C22×Dic43—42no—
130C22×Dic43—42no—
131C22×Dic43—42no—
132C22×Dic43—42no—
133C4⋊C4×C43—22no—
134C4⋊C4×C43—41no—
135C4⋊C4×C43—41no—
136C22⋊C4×C43—42no—
137C22⋊C4×C43—42no—
138C22⋊C4×C43—42no—
139C22⋊C4×C43—42no—
140C22⋊C4×C43—41no—
141C22⋊C4×C43—41no—
142C22⋊C4×C43—42no—
143C22⋊Dic43—48no—
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—41no—
175C23×C43—41no—
176C23×C43—41no—
177C23×C43—41no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43#9912yes—
182C23×C43#10412yes—
183C23×C43C2×C22⋊C411yescharacteristic
184C23×C43#12112yes—
185C23×C43AGL(1,ℤ/8)11yescharacteristic
186C23×C43AGL(1,ℤ/8)12yes—
187C23×C43#13711yescharacteristic
188D4×C43—82no—
189D4×C43—84no—
190D4×C43—84no—
191D4×C43—82no—
192D4×C43—82no—
193C2×C4×C43—24no—
194C2×C4×C43—24no—
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—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—44no—
207C2×C4×C43—44no—
208C2×C4×C43—44no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
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#9912yes—
221C2×C4×C43C4×D412yes—
222C2×C4×C43#12011yescharacteristic
223C2×C4×C43#12311yescharacteristic
224C2×Dic43—44no—
225C2×Dic43—44no—
226C2×Dic43—44no—
227C2×Dic43—82no—
228C2×Dic43—82no—
229C2×Dic43—82no—
230C2×Dic43—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—81no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43#38611yescharacteristic
265C22×C43C2×#9911yescharacteristic
266C22×C43C2×#9911yescharacteristic
267C22×C43#41711yescharacteristic
268C22×C43#41811yescharacteristic
269C22×C43C2×#10411yescharacteristic
270C22×C43#42111yescharacteristic
271C22×C43#46812yes—
272C22×C43#46912yes—
273C4×C43—21no—
274C4×C43—22no—
275C4×C43—21no—
276C4×C43—22no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43—81no—
281Dic43—84no—
282C2×#407—431no—
283#2847D4311yescharacteristic
284C2×#327—432no—
285C22⋊#95—431no—
286#1294—432no—
287C2×C43—22no—
288C2×C43—22no—
289C2×C43—42no—
290C2×C43—42no—
291C2×C43—161no—
292C2×C43#150411yescharacteristic
293C2×C43#150711yescharacteristic
294C2×C43#151011yescharacteristic
295C2×C43#151311yescharacteristic
296C2×C43#187111yescharacteristic
297C2×C43#189511yescharacteristic
298C2×C43#189811yescharacteristic
299C24×C4C2×D4311yescharacteristic
300C22×M16—861no—
301C2×#121Dic4311yescharacteristic, complemented
302C2×#121Dic4311yescharacteristic, complemented
303C2×#121C2×D4311yescharacteristic
304C2×#120—21no—
305C22×C22⋊C4—861no—
306#407—864no—
307C2×C22⋊C8—432no—
308C2×C22⋊C8—861no—
309#386—21no—
310#386—21no—
311#386—21no—
312#380Dic4311yescharacteristic, complemented
313#380Dic4311yescharacteristic, complemented
314#380C2×D4311yescharacteristic
315C2×#95—432no—
316C2×#95—861no—
317#327—864no—
318C43#911711yescharacteristic, complemented, Sylow
319C25C22⋊D4311yescharacteristic
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4C2×Dic4311yescharacteristic
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—42no—
327C23×C4—42no—
328C23×C4—862no—
329C23×C4C2×Dic4311yescharacteristic
330C23×C4C2×Dic4311yescharacteristic
331C23×C4C22⋊D4311yescharacteristic
332C23×C4C22⋊D4311yescharacteristic
333C23×C4C22⋊D4311yescharacteristic
334C23×C4C22×D4311yescharacteristic
335C2×M16—864no—
336C2×M16—1722no—
337C2×M16—1722no—
338C22×C8—862no—
339#121—22no—
340#121—22no—
341#121—42no—
342#121—42no—
343#120—44no—
344C2×C4⋊C4C2×Dic4311yescharacteristic
345C2×C4⋊C4C2×Dic4311yescharacteristic
346C2×C4⋊C4C2×Dic4311yescharacteristic
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—864no—
354C2×C22⋊C4—1722no—
355C2×C22⋊C4—1722no—
356C22⋊C8—434no—
357C22⋊C8—864no—
358C22⋊C8—862no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—862no—
363#95—862no—
364#95—1722no—
365C24—22no—
366C24—22no—
367C24—21no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—21no—
372C24—41no—
373C24—41no—
374C24C22⋊Dic4311yescharacteristic
375C24C22⋊Dic4311yescharacteristic
376C24C2×C22⋊D4311yescharacteristic
377C2×D4—22no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—41no—
388C2×D4—42no—
389C2×D4—41no—
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—21no—
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—1722no—
416C22×C4—1722no—
417C22×C4—1722no—
418C22×C4—1722no—
419C22×C4—1722no—
420C22×C4—1722no—
421C22×C4C22⋊Dic4311yescharacteristic
422C22×C4C22⋊Dic4311yescharacteristic
423C22×C4D4×D4312yes—
424C22×C4#1062190012yes—
425C22×C4C22×Dic4311yescharacteristic
426C22×C4C2×C22⋊D4311yescharacteristic
427M16—1728no—
428C2×C8—864no—
429C2×C8—1722no—
430C2×C8—1722no—
431C4⋊C4—22no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C22⋊C4—42no—
435C22⋊C4—42no—
436C22⋊C4—42no—
437C22⋊C4—42no—
438C22⋊C4—42no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—1728no—
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—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23#1306324012yes—
476C23#1306325212yes—
477C23C2×C22⋊Dic4311yescharacteristic
478C23#1306329712yes—
479C23#1306335011yescharacteristic
480C23#1306335112yes—
481C23#1306335511yescharacteristic
482D4—82no—
483D4—84no—
484D4—84no—
485D4—82no—
486D4—82no—
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—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—3442no—
515C2×C4—3442no—
516C2×C4—3442no—
517C2×C4—3442no—
518C2×C4—1724no—
519C2×C4—1724no—
520C2×C4—1724no—
521C2×C4#1306324012yes—
522C2×C4D4×Dic4312yes—
523C2×C4#1306329311yescharacteristic
524C2×C4#1306330611yescharacteristic
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—81no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22#1458277911yescharacteristic
558C22C2×#1306324011yescharacteristic
559C22C2×#1306324011yescharacteristic
560C22#1458290011yescharacteristic
561C22#1458290411yescharacteristic
562C22C2×#1306325211yescharacteristic
563C22#1458291611yescharacteristic
564C22#1458314312yes—
565C22#1458315012yes—
566C4—21no—
567C4—22no—
568C4—21no—
569C4—22no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—3444no—
575C2—22no—
576C2—22no—
577C2—42no—
578C2—42no—
579C2—161no—
580C2#1913309911yescharacteristic
581C2#1913311111yescharacteristic
582C2#1913312411yescharacteristic
583C2#1913313811yescharacteristic
584C2#1913489811yescharacteristic
585C2#1913503411yescharacteristic
586C2#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#9117
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. C2×#14582863C2semidirect
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
301. C2×#121Dic43semidirect
302. C2×#121Dic43semidirect
312. #380Dic43semidirect
313. #380Dic43semidirect
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
C2×#145826332
#191328182
#191324732
C43×#28472
#911743