Finite Group Databasebeta

← #25153211

Subgroups — #25153211

Order 11008.

1446 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063324C211yesmaximal, characteristic, complemented
2C2×#14583244C212yesmaximal, complemented
3#19142938C211yesmaximal, characteristic
4#19135730C212yesmaximal, complemented
5#19135729C212yesmaximal, complemented
6#19135554C212yesmaximal, complemented
7#19134913C211yesmaximal, characteristic, complemented
8#19134912C211yesmaximal, characteristic, complemented
9#19134910C211yesmaximal, characteristic, complemented
10C22⋊C8×Dic43C211yesmaximal, characteristic, complemented
11C43×#1874C211yesmaximal, characteristic, complemented
12C23×Dic86—21no—
13C2×#13063324—28no—
14C2×#13063324—21no—
15C2×#13063324—21no—
16C2×#13063324C2212yes—
17C2×#13063324C2212yes—
18C2×#13063321C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×#13063297—21no—
21C2×#13063297—21no—
22C22×C4⋊Dic43C2211yescharacteristic
23C22×Dic43⋊C4—21no—
24C22×C4×Dic43C2211yescharacteristic
25#14583244—28no—
26C2×#13063247C2212yes—
27C2×#13063246C2212yes—
28C2×#13063245C2212yes—
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C8×Dic43C2212yes—
31#14582802C2211yescharacteristic
32#14582800C2211yescharacteristic
33#14582799—21no—
34#14582799—21no—
35#14582768C2211yescharacteristic
36#14582662C2212yes—
37#14582661C2212yes—
38#14582661C2212yes—
39#14582653C2212yes—
40C2×#121×C43C2211yescharacteristic
41C22×C4⋊C4×C43C2211yescharacteristic
42C2×#102×C43C2212yes—
43C2×C22⋊C8×C43C2211yescharacteristic
44C43×#340C2212yes—
45C22×Dic86—28no—
46C22×Dic86—22no—
47C22×Dic86—22no—
48C22×Dic86—44no—
49C22×Dic86—44no—
50C22×D172C2311yescharacteristic
51C22×C22⋊D43—21no—
52C22×C22⋊D43—21no—
53C22×C22⋊D43—21no—
54C23×Dic43—21no—
55C23×Dic43D411yescharacteristic
56C23×Dic43D411yescharacteristic
57C22×C43⋊C8C2312yes—
58#13063324—28no—
59#13063324—28no—
60#13063324—24no—
61#13063324—24no—
62#13063324—24no—
63#13063324D418yescomplemented
64#13063321—24no—
65#13063299—22no—
66#13063299—22no—
67#13063297—44no—
68#13063297—44no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—24no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2312yes—
73C2×Dic43⋊C4—28no—
74C2×Dic43⋊C4—22no—
75C2×Dic43⋊C4—22no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×C4×Dic43—24no—
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88#13063247—24no—
89#13063246—24no—
90#13063245—24no—
91C22⋊(C43⋊C8)—22no—
92C8×Dic43—24no—
93C22×D4×C43—21no—
94C22×D4×C43C2311yescharacteristic
95C23×C4×C43—21no—
96C23×C4×C43C2311yescharacteristic
97C22×C8×C43C2312yes—
98#121×C43—22no—
99#121×C43—22no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—24no—
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2312yes—
104C2×C22⋊C4×C43—21no—
105#102×C43—24no—
106C22⋊C8×C43—22no—
107C24×C43—21no—
108C24×C43C2×D411yescharacteristic
109C23×D43—21no—
110C2×D4×C43—22no—
111C2×D4×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43—22no—
114C2×D4×C43—42no—
115C2×D4×C43—42no—
116C2×D4×C43—42no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—24no—
120C22×C4×C43—22no—
121C22×C4×C43—21no—
122C22×C4×C43—42no—
123C22×C4×C43—42no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43#4112yes—
126C22×C4×C43#4112yes—
127C22×C4×C43C2411yescharacteristic
128C2×C22⋊D43—42no—
129C2×C22⋊D43—42no—
130C2×C22⋊D43—42no—
131C2×C22⋊D43—42no—
132C2×C22⋊D43—42no—
133C2×C22⋊D43—42no—
134C2×C22⋊D43—42no—
135C2×C22⋊D43—42no—
136C2×C22⋊D43—42no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—24no—
142C22×Dic43—22no—
143C22×Dic43—21no—
144C22×Dic43—42no—
145C22×Dic43—42no—
146C22×Dic43D814yes—
147C22×Dic43SD1614yes—
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C2×D172—22no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—22no—
156C2×Dic86—28no—
157C2×Dic86—28no—
158C2×Dic86—44no—
159C2×Dic86—432no—
160C2×Dic86—44no—
161C2×Dic86—44no—
162C2×Dic86—44no—
163C2×C8×C43—22no—
164C2×C8×C43—22no—
165C2×C8×C43—22no—
166C4⋊C4×C43—24no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43C2×D414yes—
171C22⋊C4×C43—42no—
172C22⋊Dic43—42no—
173C22⋊Dic43—42no—
174(C2×D43)⋊C4—42no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177C4⋊Dic43—24no—
178C4⋊Dic43—22no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43C2×D414yes—
182Dic43⋊C4—28no—
183Dic43⋊C4—28no—
184Dic43⋊C4—42no—
185Dic43⋊C4—42no—
186C4×Dic43—22no—
187C4×Dic43—22no—
188C4×Dic43—22no—
189C4×Dic43C2×D414yes—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—22no—
193C23×C43—21no—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43#12412yes—
205C23×C43C2×D812yes—
206C23×C43C2×SD1612yes—
207C23×C43C22×D411yescharacteristic
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215D4×C43—42no—
216D4×C43—42no—
217D4×C43—84no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—24no—
221C2×C4×C43—24no—
222C2×C4×C43—24no—
223C2×C4×C43—48no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43#12412yes—
230C2×C4×C43C22×D412yes—
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C432−1+412yes—
234C22⋊D43—84no—
235C22⋊D43—84no—
236C22⋊D43—84no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—28no—
242C2×Dic43—28no—
243C2×Dic43—24no—
244C2×Dic43—48no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43#12012yes—
251C2×Dic43#12012yes—
252C2×Dic43C2×D812yes—
253C2×Dic43C2×D812yes—
254C2×Dic43C2×SD1612yes—
255C2×Dic43C2×SD1612yes—
256C2×Dic43AGL(1,ℤ/8)12yes—
257C2×Dic43#13712yes—
258D172—42no—
259D172—42no—
260Dic86—416no—
261Dic86—416no—
262C8×C43—42no—
263C43⋊C8—42no—
264#25903—431nomaximal, Sylow
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—22no—
269C22×C43—22no—
270C22×C43—22no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43#48614yescomplemented
279C22×C43C2×#12011yescharacteristic
280C22×C43C2×#12411yescharacteristic
281C22×C43#53611yescharacteristic
282C22×C43C22×D811yescharacteristic
283C22×C43C22×SD1611yescharacteristic
284C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C43C2×#13711yescharacteristic
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—81no—
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—81no—
293C4×C43—22no—
294C4×C43—44no—
295C4×C43—81no—
296C4×C43#54812yes—
297C4×C43#54812yes—
298Dic43—22no—
299Dic43—22no—
300Dic43—44no—
301Dic43—81no—
302Dic43#44714yes—
303Dic43#44814yes—
304C22×C4⋊Q8—431no—
305C2×#486—432no—
306#2856—431no—
307#2023—432no—
308#2023—432no—
309#1990—432no—
310#1874—431no—
311#1874—431no—
312#1874—431no—
313#1874D4311yescharacteristic, complemented
314C4×C22⋊C8—431no—
315C2×C43—24no—
316C2×C43—161no—
317C2×C43#243611yescharacteristic
318C2×C43C2×#44711yescharacteristic
319C2×C43C2×#44811yescharacteristic
320C2×C43C2×#48611yescharacteristic
321C2×C43#314111yescharacteristic
322C2×C43#322611yescharacteristic
323C2×C43#322711yescharacteristic
324D43—161no—
325C23×Q8—861no—
326C2×C4⋊Q8—432no—
327C2×C4⋊Q8—432no—
328C2×C4⋊Q8—861no—
329C2×C4⋊Q8—861no—
330C2×C4⋊Q8—868no—
331C2×#127—431no—
332C2×#121—431no—
333C2×#121—861no—
334C2×#121—861no—
335C2×#121C2×D4311yescharacteristic
336C22×C4⋊C4—431no—
337C22×C4⋊C4—861no—
338C22×C4⋊C4C2×D4311yescharacteristic
339C22×C42—431no—
340#486—868no—
341C2×#102—432no—
342C2×#102—432no—
343C2×#102—432no—
344C2×#102C2×D4312yes—
345C2×C22⋊C8—431no—
346C2×C22⋊C8C2×D4311yescharacteristic
347C2×C4×C8—432no—
348#390—431no—
349#390—431no—
350#390—861no—
351#390—861no—
352#384—431no—
353#340—432no—
354#340—432no—
355#340—432no—
356#340C2×D4312yes—
357#336—432no—
358C43#2590311yescharacteristic, complemented, Sylow
359C22×Q8—862no—
360C22×Q8—862no—
361C22×Q8—868no—
362C22×Q8—1724no—
363C22×Q8—1724no—
364C22×D4—21no—
365C22×D4—431no—
366C22×D4—861no—
367C22×D4—861no—
368C22×D4—861no—
369C22×D4C22×D4311yescharacteristic
370C23×C4—21no—
371C23×C4—431no—
372C23×C4—431no—
373C23×C4—861no—
374C23×C4C22×D4311yescharacteristic
375C22×C8—432no—
376C22×C8C22×D4312yes—
377C4⋊Q8—438no—
378C4⋊Q8—864no—
379C4⋊Q8—864no—
380C4⋊Q8—868no—
381C4⋊Q8—868no—
382C4⋊Q8—864no—
383#127—864no—
384#121—22no—
385#121—22no—
386#121—862no—
387#121—862no—
388#121—1724no—
389#121—1724no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—432no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—864no—
395C2×C4⋊C4—862no—
396C2×C4⋊C4—862no—
397C2×C4⋊C4—868no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4312yes—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C42—431no—
410C2×C42—431no—
411C2×C42—431no—
412C2×C42—431no—
413C2×C42—864no—
414#102—24no—
415#102—864no—
416#102—864no—
417#102—864no—
418C22⋊C8—22no—
419C22⋊C8—862no—
420C4×C8—864no—
421C24—21no—
422C24—861no—
423C24D4×D4311yescharacteristic
424C2×Q8—868no—
425C2×Q8—868no—
426C2×Q8—1724no—
427C2×Q8—1724no—
428C2×Q8—1724no—
429C2×Q8—17232no—
430C2×Q8—1724no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—862no—
439C2×D4—861no—
440C2×D4—861no—
441C2×D4—862no—
442C2×D4—1722no—
443C2×D4—1722no—
444C2×D4—1722no—
445C2×D4—1722no—
446C2×D4—1722no—
447C2×D4—1722no—
448C2×D4—1722no—
449C2×D4—1722no—
450C2×D4—1722no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—434no—
461C22×C4—434no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—864no—
469C22×C4—862no—
470C22×C4—861no—
471C22×C4—1722no—
472C22×C4—1722no—
473C22×C4#1062189812yes—
474C22×C4D4×D4311yescharacteristic
475C22×C4#1062190012yes—
476C22×C4C23×D4311yescharacteristic
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—862no—
481C2×C8—862no—
482C2×C8—862no—
483C4⋊C4—24no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—434no—
488C4⋊C4—868no—
489C4⋊C4—868no—
490C4⋊C4—864no—
491C4⋊C4—862no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—1722no—
495C4⋊C4—1722no—
496C4⋊C4D4×D4314yes—
497C22⋊C4—42no—
498C22⋊C4—1722no—
499C22⋊C4—1722no—
500C22⋊C4—1722no—
501C22⋊C4—1722no—
502C22⋊C4—1722no—
503C42—434no—
504C42—862no—
505C42—862no—
506C42—862no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—1721no—
519C23—1721no—
520C23—1721no—
521C23—1721no—
522C23—1721no—
523C23—1721no—
524C23—1721no—
525C23#1306331112yes—
526C23D8×D4312yes—
527C23SD16×D4312yes—
528C23C2×D4×D4311yescharacteristic
529Q8—17216no—
530Q8—17216no—
531D4—42no—
532D4—42no—
533D4—84no—
534D4—3444no—
535D4—3444no—
536D4—3444no—
537D4—1722no—
538D4—1722no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—48no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—432no—
551C2×C4—432no—
552C2×C4—432no—
553C2×C4—432no—
554C2×C4—432no—
555C2×C4—432no—
556C2×C4—432no—
557C2×C4—432no—
558C2×C4—868no—
559C2×C4—868no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—864no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1728no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4#1306331112yes—
572C2×C4C2×D4×D4312yes—
573C2×C4C2×#1062190011yescharacteristic
574C2×C4C2×#1062189811yescharacteristic
575C2×C4#1306337212yes—
576C8—42no—
577C8—1722no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—3441no—
592C22—3441no—
593C22—3441no—
594C22—3441no—
595C22—3441no—
596C22—3441no—
597C22—3441no—
598C22#1458324414yescomplemented
599C22#120×D4311yescharacteristic
600C22C2×#1306331111yescharacteristic
601C22#1458347111yescharacteristic
602C22C2×D8×D4311yescharacteristic
603C22C2×SD16×D4311yescharacteristic
604C22AGL(1,ℤ/8)×D4311yescharacteristic
605C22#137×D4311yescharacteristic
606C4—22no—
607C4—44no—
608C4—81no—
609C4—434no—
610C4—434no—
611C4—862no—
612C4—862no—
613C4—3441no—
614C4—1724no—
615C4#1458355512yes—
616C4#1458355812yes—
617C2—24no—
618C2—161no—
619C2—6881no—
620C2#1913825111yescharacteristic
621C2#447×D4311yescharacteristic
622C2#448×D4311yescharacteristic
623C2C2×#1458324411yescharacteristic
624C2#1914498611yescharacteristic
625C2#1914571411yescharacteristic
626C2#1914572111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1874C2
socleC23×C43C22×D4
prime radical#19142938C2
hypercenter#1874D43
hypocenterC43#25903
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C22×#13063324C2semidirect
2. C2×#14583244C2semidirect
4. #19135730C2semidirect
5. #19135729C2semidirect
6. #19135554C2semidirect
7. #19134913C2semidirect
8. #19134912C2semidirect
9. #19134910C2semidirect
10. C22⋊C8×Dic43C2semidirect
11. C43×#1874C2semidirect
63. #13063324D4semidirect
278. C22×C43#486semidirect
313. #1874D43semidirect
358. C43#25903semidirect
598. C22#14583244semidirect

Maximal subgroups

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

subgroupindex
C22×#130633242
C2×#145832442
#191429382
#191357302
#191357292
#191355542
#191349132
#191349122
#191349102
C22⋊C8×Dic432
C43×#18742
#2590343