Finite Group Databasebeta

← #24988279

Subgroups — #24988279

Order 11008.

1034 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D43C211yesmaximal, characteristic
2#19134580C211yesmaximal, characteristic
3#19134530C211yesmaximal, characteristic, complemented
4#19133168C211yesmaximal, characteristic, complemented
5#19133166C211yesmaximal, characteristic, complemented
6#19132911C211yesmaximal, characteristic
7C43×#1787C211yesmaximal, characteristic, complemented
8C22×Q8×D43C411yescharacteristic, complemented
9Q8×C22⋊D43—22no—
10Q8×C22⋊D43—22no—
11Q8×C22⋊D43—22no—
12Q8×C22⋊D43—22no—
13C2×#13063323—21no—
14C2×#13063323C411yescharacteristic, complemented
15C2×#13063304—21no—
16C2×#13063304C2211yescharacteristic
17C2×#13063301—21no—
18C2×#13063301C411yescharacteristic, complemented
19C2×Q8×Dic43C411yescharacteristic, complemented
20C2×C4×C22⋊D43—21no—
21C2×C4×C22⋊D43C2211yescharacteristic
22C2×#13063249—22no—
23C2×#13063239—21no—
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25#14582759C2211yescharacteristic
26#14582665—21no—
27#14582637—22no—
28#14582635—22no—
29#14582624—21no—
30#14582622—21no—
31C23×Q8×C43C2211yescharacteristic
32C2×#103×C43—22no—
33C2×C22⋊C8×C43C2211yescharacteristic
34C43×#380C2211yescharacteristic
35C22×Dic86—21no—
36C22×Dic86C2×C411yescharacteristic
37C2×Q8×D43—22no—
38C2×Q8×D43—22no—
39C2×Q8×D43—44no—
40C22×C22⋊D43D411yescharacteristic
41C22×C4×D43—21no—
42C22×C4×D43C2×C411yescharacteristic
43C22×C43⋊C8—21no—
44#13063323—24no—
45#13063323—24no—
46#13063323—22no—
47#13063323—22no—
48#13063304—24no—
49#13063304—24no—
50#13063304—21no—
51#13063304—21no—
52#13063304D412yes—
53#13063304D412yes—
54#13063301—24no—
55#13063301—24no—
56#13063301—22no—
57#13063301—22no—
58Q8×Dic43—22no—
59Q8×Dic43—22no—
60C4×C22⋊D43—24no—
61C4×C22⋊D43—24no—
62C4×C22⋊D43—21no—
63C4×C22⋊D43—21no—
64C4×C22⋊D43—21no—
65C4×C22⋊D43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2×C411yescharacteristic
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4D411yescharacteristic
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43D411yescharacteristic
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4D411yescharacteristic
79C2×C4×Dic43—21no—
80C2×C4×Dic43C2×C411yescharacteristic
81#13063249—44no—
82#13063239—42no—
83C22⋊(C43⋊C8)—21no—
84C22⋊(C43⋊C8)—21no—
85C43⋊#95—21no—
86C22×Q8×C43—21no—
87C22×Q8×C43—21no—
88C22×Q8×C43—21no—
89C22×Q8×C43—44no—
90C22×Q8×C43C2×C411yescharacteristic
91C22×Q8×C43C2×C411yescharacteristic
92C22×Q8×C43D412yes—
93C22×Q8×C43D412yes—
94C23×C4×C43—21no—
95C23×C4×C43C2311yescharacteristic
96C22×C8×C43—21no—
97C2×C4⋊C4×C43—21no—
98C2×C22⋊C4×C43—21no—
99#103×C43—44no—
100C22⋊C8×C43—21no—
101C22⋊C8×C43—21no—
102#95×C43—21no—
103C24×C43C2×D411yescharacteristic
104C23×D43C22⋊C411yescharacteristic
105C2×Q8×C43—24no—
106C2×Q8×C43—21no—
107C2×Q8×C43—21no—
108C2×Q8×C43—22no—
109C2×Q8×C43—22no—
110C2×Q8×C43—24no—
111C2×Q8×C43—24no—
112C2×Q8×C43—42no—
113C2×Q8×C43—42no—
114C2×Q8×C43—42no—
115C2×Q8×C43—44no—
116C2×Q8×C43—44no—
117C2×Q8×C43—44no—
118C2×Q8×C43C22⋊C412yes—
119C2×Q8×C43C22⋊C412yes—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—42no—
125C22×C4×C43—44no—
126C22×C4×C43—41no—
127C22×C4×C43C22×C411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C2×C22⋊D43—21no—
134C2×C22⋊D43—21no—
135C2×C22⋊D43—21no—
136C2×C22⋊D43—21no—
137C2×C22⋊D43SD1612yes—
138C2×C22⋊D43Q1612yes—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—41no—
142C22×Dic43C22⋊C411yescharacteristic
143C22×Dic43C22⋊C411yescharacteristic
144C22×Dic43C22⋊C411yescharacteristic
145Q8×D43—44no—
146Q8×D43—48no—
147Q8×D43—44no—
148C2×C4×D43—24no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—44no—
152C2×C4×D43—42no—
153C2×Dic86—24no—
154C2×Dic86—21no—
155C2×Dic86—44no—
156C2×Dic86—42no—
157C2×Dic86C22⋊C412yes—
158C2×C8×C43—42no—
159C2×C8×C43—41no—
160C4⋊C4×C43—42no—
161C22⋊C4×C43—41no—
162C22⋊C4×C43—41no—
163C22⋊Dic43—22no—
164C22⋊Dic43—22no—
165C22⋊Dic43—21no—
166C22⋊Dic43—21no—
167C22⋊Dic43—41no—
168C22⋊Dic43—41no—
169(C2×D43)⋊C4—24no—
170(C2×D43)⋊C4—21no—
171(C2×D43)⋊C4—21no—
172C4⋊Dic43—24no—
173C4⋊Dic43—21no—
174C4⋊Dic43—42no—
175C4⋊Dic43C22⋊C412yes—
176Dic43⋊C4—24no—
177Dic43⋊C4—24no—
178Dic43⋊C4—24no—
179Dic43⋊C4—22no—
180Dic43⋊C4—22no—
181Dic43⋊C4—21no—
182Dic43⋊C4—21no—
183C4×Dic43—24no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C2×C43⋊C8—42no—
187C2×C43⋊C8—41no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43C2×C22⋊C411yescharacteristic
191C23×C43#12011yescharacteristic
192C23×C43#12011yescharacteristic
193C23×C43C2×SD1611yescharacteristic
194C23×C43C2×Q1611yescharacteristic
195C23×C43#13711yescharacteristic
196C23×C43#13711yescharacteristic
197C22×D43—21no—
198C22×D43—21no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43#10312yescomplemented
202Q8×C43—24no—
203Q8×C43—22no—
204Q8×C43—22no—
205Q8×C43—22no—
206Q8×C43—44no—
207Q8×C43—44no—
208Q8×C43—42no—
209Q8×C43#9914yescomplemented
210C2×C4×C43—24no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—44no—
220C2×C4×C43—44no—
221C2×C4×C43—42no—
222C2×C4×C43—81no—
223C2×C4×C43—81no—
224C2×C4×C43—81no—
225C2×C4×C43C2×C22⋊C411yescharacteristic
226C2×C4×C43C2×C22⋊C411yescharacteristic
227C2×C4×C43#12011yescharacteristic
228C2×C4×C43#12011yescharacteristic
229C22⋊D43—22no—
230C22⋊D43—22no—
231C22⋊D43—22no—
232C22⋊D43—22no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—22no—
237C2×Dic43—21no—
238C2×Dic43—22no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—81no—
244C2×Dic43—81no—
245C2×Dic43—81no—
246C2×Dic43#10312yescomplemented
247C4×D43—42no—
248C4×D43—48no—
249C4×D43—42no—
250Dic86—48no—
251Dic86—42no—
252Dic86—42no—
253C8×C43—81no—
254C43⋊C8—81no—
255#8379—431nomaximal, Sylow
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43#37911yescharacteristic
267C22×C43C2×#10311yescharacteristic
268C22×C43#41911yescharacteristic
269C22×C43#44811yescharacteristic
270C22×C43#44811yescharacteristic
271C22×C43#45111yescharacteristic
272C22×C43#45111yescharacteristic
273C2×D43—22no—
274C2×D43—42no—
275C2×D43—41no—
276C2×D43—41no—
277C2×D43—42no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—24no—
281C4×C43—21no—
282C4×C43—42no—
283C4×C43—161no—
284C4×C43C2×#9912yes—
285Dic43—22no—
286Dic43—41no—
287Dic43—42no—
288Dic43—41no—
289Dic43—42no—
290Dic43—161no—
291C2×D4×Q8—431no—
292#1799—431no—
293#1787—431no—
294#1787D4311yescharacteristic, complemented
295#1520—431no—
296#1520—431no—
297#1459—431no—
298C2×C43—21no—
299C2×C43—21no—
300C2×C43—21no—
301C2×C43—21no—
302C2×C43—21no—
303C2×C43—21no—
304C2×C43#178111yescharacteristic
305C2×C43#178711yescharacteristic
306C2×C43#179611yescharacteristic
307D43—42no—
308C23×Q8—431no—
309C23×Q8C2×D4311yescharacteristic
310D4×Q8—862no—
311D4×Q8—862no—
312D4×Q8—862no—
313D4×Q8—862no—
314C2×C4⋊Q8—431no—
315C2×C4⋊Q8—861no—
316C2×C22⋊Q8—431no—
317C2×C22⋊Q8—431no—
318C2×C22⋊Q8—861no—
319C2×C22⋊Q8—861no—
320C2×C4×Q8—431no—
321C2×C4×D4—431no—
322C2×C4×D4—861no—
323C2×#103—22no—
324C2×#103—862no—
325C2×#99—861no—
326C2×C22⋊C8—431no—
327C2×C22⋊C8C2×D4311yescharacteristic
328#380—431no—
329#380C2×D4311yescharacteristic
330#342—861no—
331#328—862no—
332#328—862no—
333#324—861no—
334#323—861no—
335C43#837911yescharacteristic, complemented, Sylow
336C22×Q8—21no—
337C22×Q8—21no—
338C22×Q8—21no—
339C22×Q8—44no—
340C22×Q8—431no—
341C22×Q8—861no—
342C22×Q8—862no—
343C22×Q8—862no—
344C22×Q8—1724no—
345C22×Q8C4×D4311yescharacteristic
346C22×Q8C4×D4311yescharacteristic
347C22×Q8D17212yes—
348C22×Q8C22⋊D4312yes—
349C22×D4—431no—
350C23×C4—21no—
351C23×C4—431no—
352C23×C4—861no—
353C23×C4C22×D4311yescharacteristic
354C22×C8—21no—
355C22×C8—861no—
356C4⋊Q8—862no—
357C4⋊Q8—864no—
358C4⋊Q8—864no—
359C4⋊Q8—862no—
360C22⋊Q8—432no—
361C22⋊Q8—432no—
362C22⋊Q8—862no—
363C22⋊Q8—864no—
364C22⋊Q8—864no—
365C22⋊Q8—864no—
366C22⋊Q8—864no—
367C22⋊Q8—862no—
368C22⋊Q8—861no—
369C22⋊Q8—861no—
370C4×Q8—862no—
371C4×Q8—862no—
372C4×D4—864no—
373C4×D4—864no—
374C4×D4—861no—
375C4×D4—861no—
376C4×D4—861no—
377C4×D4—861no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—431no—
389C2×C22⋊C4—431no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C42—431no—
394C2×C42—861no—
395#103—44no—
396#103—1724no—
397#99—1722no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400C22⋊C8—861no—
401C22⋊C8—861no—
402#95—21no—
403#95—861no—
404C24—431no—
405C24D4×D4311yescharacteristic
406C2×Q8—24no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—24no—
412C2×Q8—24no—
413C2×Q8—42no—
414C2×Q8—42no—
415C2×Q8—42no—
416C2×Q8—44no—
417C2×Q8—44no—
418C2×Q8—44no—
419C2×Q8—432no—
420C2×Q8—864no—
421C2×Q8—861no—
422C2×Q8—1722no—
423C2×Q8—1724no—
424C2×Q8—1728no—
425C2×Q8—1724no—
426C2×Q8—1724no—
427C2×Q8(C2×D43)⋊C412yes—
428C2×Q8(C2×D43)⋊C412yes—
429C2×D4—432no—
430C2×D4—432no—
431C2×D4—861no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4—861no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—42no—
440C22×C4—44no—
441C22×C4—41no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—864no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—1724no—
451C22×C4—1722no—
452C22×C4—1721no—
453C22×C4C2×C4×D4311yescharacteristic
454C22×C4C2×D17211yescharacteristic
455C22×C4D4×D4311yescharacteristic
456C22×C4D4×D4311yescharacteristic
457C22×C4D4×D4311yescharacteristic
458C22×C4C2×C22⋊D4311yescharacteristic
459C2×C8—42no—
460C2×C8—41no—
461C2×C8—1722no—
462C2×C8—1721no—
463C4⋊C4—42no—
464C4⋊C4—432no—
465C4⋊C4—864no—
466C4⋊C4—864no—
467C4⋊C4—864no—
468C4⋊C4—864no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—862no—
472C4⋊C4—861no—
473C4⋊C4—862no—
474C4⋊C4—1722no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—864no—
478C22⋊C4—861no—
479C22⋊C4—862no—
480C22⋊C4—861no—
481C22⋊C4—862no—
482C22⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—1721no—
485C22⋊C4—1721no—
486C42—864no—
487C42—861no—
488C42—861no—
489C23—41no—
490C23—41no—
491C23—432no—
492C23—861no—
493C23—861no—
494C23—1721no—
495C23—1721no—
496C23C22⋊C4×D4311yescharacteristic
497C23#1306329311yescharacteristic
498C23#1306329511yescharacteristic
499C23SD16×D4311yescharacteristic
500C23Q16×D4311yescharacteristic
501C23#1306335411yescharacteristic
502C23#1306335711yescharacteristic
503Q8—24no—
504Q8—22no—
505Q8—22no—
506Q8—22no—
507Q8—44no—
508Q8—44no—
509Q8—42no—
510Q8—1722no—
511Q8—1728no—
512Q8—1722no—
513Q8#1306323914yescomplemented
514D4—862no—
515D4—862no—
516D4—862no—
517D4—862no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—432no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—862no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—862no—
540C2×C4—3441no—
541C2×C4—3441no—
542C2×C4—3441no—
543C2×C4—1728no—
544C2×C4—1722no—
545C2×C4—1722no—
546C2×C4—1722no—
547C2×C4—1722no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4C22⋊C4×D4311yescharacteristic
551C2×C4C2×(C2×D43)⋊C411yescharacteristic
552C2×C4#1306329311yescharacteristic
553C2×C4#1306329511yescharacteristic
554C8—81no—
555C8—3441no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—862no—
567C22—1722no—
568C22—1722no—
569C22—1721no—
570C22—1721no—
571C22#1458275411yescharacteristic
572C22#103×D4311yescharacteristic
573C22#1458290611yescharacteristic
574C22#1458303611yescharacteristic
575C22#1458303911yescharacteristic
576C22#1458305311yescharacteristic
577C22#1458305611yescharacteristic
578C4—21no—
579C4—21no—
580C4—24no—
581C4—21no—
582C4—42no—
583C4—161no—
584C4—862no—
585C4—1722no—
586C4—1721no—
587C4—1722no—
588C4—1721no—
589C4—6881no—
590C4C2×#1306323912yes—
591C2—21no—
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—1722no—
598C2#1913450911yescharacteristic
599C2#1913452811yescharacteristic
600C2#1913456711yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1787C2
socleC22×C43#379
prime radicalC22×C22⋊D43D4
cosocleC23×C4×C43C23
hypercenter#1787D43
hypocenterC43#8379
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
3. #19134530C2semidirect
4. #19133168C2semidirect
5. #19133166C2semidirect
7. C43×#1787C2semidirect
8. C22×Q8×D43C4semidirect
14. C2×#13063323C4semidirect
18. C2×#13063301C4semidirect
19. C2×Q8×Dic43C4semidirect
201. C22×D43#103semidirect
209. Q8×C43#99semidirect
246. C2×Dic43#103semidirect
294. #1787D43semidirect
335. C43#8379semidirect
513. Q8#13063239semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D432
#191345802
#191345302
#191331682
#191331662
#191329112
C43×#17872
#837943