Finite Group Databasebeta

← #25132658

Subgroups — #25132658

Order 11008.

1378 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D43C211yesmaximal, characteristic, complemented
2C2×#14583180C211yesmaximal, characteristic, complemented
3C2×#14583176C211yesmaximal, characteristic, complemented
4C4×#13063300C211yesmaximal, characteristic
5#19135922C212yesmaximal, complemented
6#19135730C212yesmaximal, complemented
7#19135547C211yesmaximal, characteristic, complemented
8#19134911C212yesmaximal
9#19134784C212yesmaximal, complemented
10#19134572C211yesmaximal, characteristic, complemented
11C43×#1988C211yesmaximal, characteristic, complemented
12C22×Q8×D43—21no—
13C2×#13063325C2211yescharacteristic
14C2×#13063324—21no—
15C2×#13063324C2212yes—
16C2×#13063323—21no—
17C4⋊Q8×D43—24no—
18C4⋊Q8×D43—24no—
19C2×#13063300C2211yescharacteristic
20C2×C4×D172—21no—
21C2×C4×D172C2211yescharacteristic
22C2×C4⋊C4×D43—21no—
23C2×C4⋊C4×D43C2212yes—
24C2×C42×D43C2211yescharacteristic
25#14583180—24no—
26#14583176—24no—
27C2×#13063259C2212yes—
28C2×#13063258C2212yes—
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063247C2212yes—
31C2×#13063245C2212yes—
32C2×(C2×D43)⋊C8C2212yes—
33#14582800C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582791—21no—
36#14582777—21no—
37#14582756C2211yescharacteristic
38C4×(C2×D43)⋊C4—21no—
39#14582661C2212yes—
40#14582661C2212yes—
41#14582653C2212yes—
42C2×C4⋊Q8×C43C2211yescharacteristic
43C2×C4⋊C8×C43C2211yescharacteristic
44C4×C4⋊C4×C43C2211yescharacteristic
45C43×#340C2212yes—
46C43×#340C2212yes—
47C22×Dic86—21no—
48C22×Dic86—22no—
49C2×Q8×D43—28no—
50C2×Q8×D43—44no—
51C2×Q8×D43—44no—
52C22×D172—21no—
53C22×D172C2311yescharacteristic
54C22×C4×D43—22no—
55C22×C4×D43—21no—
56C22×C4×D43D411yescharacteristic
57C22×C4×D43D411yescharacteristic
58C22×C4×D43C2311yescharacteristic
59C22×C43⋊C8C2312yes—
60#13063325—22no—
61#13063325D414yescomplemented
62#13063324—28no—
63#13063324—24no—
64#13063324—24no—
65#13063323—28no—
66#13063300—22no—
67#13063300Q814yescomplemented
68C4×D172—22no—
69C4×D172—22no—
70C4×D172—44no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2312yes—
75C2×Dic43⋊C4—22no—
76C2×Dic43⋊C4—22no—
77C4⋊C4×D43—28no—
78C4⋊C4×D43—24no—
79C4⋊C4×D43—24no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88C42×D43—22no—
89C42×D43—22no—
90#13063259—24no—
91#13063258—24no—
92C4⋊(C43⋊C8)—22no—
93#13063247—24no—
94#13063245—24no—
95(C2×D43)⋊C8—24no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C22×Q8×C43—21no—
99C22×C8×C43C2312yes—
100C4⋊Q8×C43—22no—
101C4⋊Q8×C43D414yescomplemented
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2312yes—
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C42×C43—21no—
107C2×C42×C43C2311yescharacteristic
108C4⋊C8×C43—22no—
109#95×C43—21no—
110C23×D43—21no—
111C23×D43C2×D411yescharacteristic
112C2×Q8×C43—24no—
113C2×Q8×C43—42no—
114C2×Q8×C43—42no—
115C22×C4×C43—21no—
116C22×C4×C43—22no—
117C22×C4×C43—21no—
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2411yescharacteristic
121C22×Dic43—22no—
122C22×Dic43—21no—
123C22×Dic43C2×D411yescharacteristic
124C22×Dic43C2×D411yescharacteristic
125C22×Dic43C2×D411yescharacteristic
126Q8×D43—432no—
127C2×D172—21no—
128C2×D172—24no—
129C2×D172—21no—
130C2×D172—21no—
131C2×D172—21no—
132C2×D172—21no—
133C2×D172—42no—
134C2×D172—42no—
135C2×D172C2×Q812yescomplemented
136C2×C4×D43—22no—
137C2×C4×D43—22no—
138C2×C4×D43—22no—
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—21no—
143C2×C4×D43—22no—
144C2×C4×D43—28no—
145C2×C4×D43—22no—
146C2×C4×D43—44no—
147C2×C4×D43—42no—
148C2×C4×D43—42no—
149C2×C4×D43—42no—
150C2×C4×D43—44no—
151C2×C4×D43D814yes—
152C2×C4×D43C2×Q812yes—
153C2×C4×D43#4112yes—
154C2×Dic86—28no—
155C2×Dic86—24no—
156C2×Dic86—44no—
157C2×Dic86—42no—
158C2×Dic86—42no—
159C2×Dic86—44no—
160C2×C8×C43—22no—
161C2×C8×C43—22no—
162C2×C8×C43—22no—
163C4⋊C4×C43—24no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43C2×D414yes—
169C4⋊C4×C43C2×Q812yescomplemented
170C42×C43—42no—
171C42×C43C2×D412yes—
172C42×C43C2×D412yes—
173(C2×D43)⋊C4—24no—
174(C2×D43)⋊C4—42no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—42no—
178C4⋊Dic43—24no—
179C4⋊Dic43—22no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—42no—
183C4⋊Dic43C2×D414yes—
184Dic43⋊C4—28no—
185Dic43⋊C4—28no—
186C4×Dic43—22no—
187C4×Dic43—22no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—22no—
193C23×C43C22×D411yescharacteristic
194C22×D43—21no—
195C22×D43—21no—
196C22×D43—21no—
197C22×D43—21no—
198C22×D43—22no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43C22⋊Q812yes—
206C22×D43C2×D812yes—
207C22×D43#13712yes—
208Q8×C43—48no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—24no—
212C2×C4×C43—22no—
213C2×C4×C43—41no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43#12012yes—
221C2×C4×C43#12012yes—
222C2×C4×C43C2×D812yes—
223C2×C4×C43AGL(1,ℤ/8)12yes—
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C22×Q811yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C432−1+411yescharacteristic
229C2×C4×C432−1+411yescharacteristic
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—24no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43C22⋊Q812yes—
243C2×Dic43C2×D812yes—
244C2×Dic43#13712yes—
245D172—22no—
246D172—22no—
247D172—48no—
248D172—41no—
249D172—41no—
250C4×D43—28no—
251C4×D43—22no—
252C4×D43—22no—
253C4×D43—22no—
254C4×D43—22no—
255C4×D43—28no—
256C4×D43—416no—
257C4×D43—84no—
258Dic86—416no—
259Dic86—48no—
260C8×C43—42no—
261C43⋊C8—42no—
262#24298—431nomaximal, Sylow
263C22×C43C2×#12011yescharacteristic
264C22×C43C2×C22⋊Q811yescharacteristic
265C22×C43#53611yescharacteristic
266C22×C43C22×D811yescharacteristic
267C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
268C22×C43C2×#13711yescharacteristic
269C22×C43C2×#13711yescharacteristic
270C2×D43—22no—
271C2×D43—22no—
272C2×D43—22no—
273C2×D43—22no—
274C2×D43—22no—
275C2×D43—22no—
276C2×D43—42no—
277C2×D43—42no—
278C2×D43—42no—
279C2×D43—81no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43#47414yescomplemented
284C4×C43—22no—
285C4×C43—44no—
286C4×C43—42no—
287C4×C43—81no—
288C4×C43#44714yes—
289C4×C43#54811yescharacteristic
290C4×C43#54811yescharacteristic
291C4×C43D4×Q811yescharacteristic
292C4×C43D4×Q811yescharacteristic
293Dic43—22no—
294Dic43—22no—
295Dic43—22no—
296Dic43—44no—
297Dic43—81no—
298C22×C4⋊Q8—431no—
299C2×#474—431no—
300C2×#474—431no—
301C4×#121—431no—
302#2057—432no—
303#2023—432no—
304#1988—431no—
305#1988D4311yescharacteristic, complemented
306#1874—432no—
307#1852—432no—
308#1797—431no—
309C2×C43#240911yescharacteristic
310C2×C43C2×#44711yescharacteristic
311C2×C43#300411yescharacteristic
312C2×C43C2×#47411yescharacteristic
313C2×C43#307911yescharacteristic
314C2×C43#322611yescharacteristic
315C2×C43#323911yescharacteristic
316D43—24no—
317D43—82no—
318C23×Q8—861no—
319C2×C4⋊Q8—432no—
320C2×C4⋊Q8—431no—
321C2×C4⋊Q8—861no—
322C2×C4⋊Q8—861no—
323C2×C4⋊Q8—864no—
324C2×C4⋊Q8—864no—
325C2×C4⋊Q8C2×D4311yescharacteristic
326C2×#121—431no—
327C2×C4×D4—431no—
328C2×C4×D4—861no—
329C22×C4⋊C4—432no—
330C22×C4⋊C4—861no—
331C22×C42—431no—
332#474—864no—
333#474—864no—
334C2×#107—432no—
335C2×#107—432no—
336C2×C4⋊C8—431no—
337C2×C4⋊C8C2×D4311yescharacteristic
338C2×#102—432no—
339C2×#102—432no—
340C2×C22⋊C8—432no—
341#390—431no—
342#389—431no—
343#388—861no—
344#386—861no—
345#380—431no—
346C4×C4⋊C4C2×D4311yescharacteristic
347C4×C22⋊C4—861no—
348#340—432no—
349#340—432no—
350#340C2×D4312yes—
351#340C2×D4312yes—
352#336—432no—
353C43#2429811yescharacteristic, complemented, Sylow
354C22×Q8—21no—
355C22×Q8—862no—
356C22×Q8—868no—
357C22×Q8—861no—
358C22×Q8—1724no—
359C22×Q8—1724no—
360C22×D4—431no—
361C22×D4—861no—
362C23×C4—431no—
363C23×C4—431no—
364C23×C4—431no—
365C23×C4—862no—
366C23×C4—861no—
367C22×C8—432no—
368C22×C8C22×D4312yes—
369C4⋊Q8—22no—
370C4⋊Q8—434no—
371C4⋊Q8—864no—
372C4⋊Q8—868no—
373C4⋊Q8—868no—
374C4⋊Q8—864no—
375C4⋊Q8—862no—
376C4⋊Q8D17214yescomplemented
377#121—434no—
378#121—862no—
379C4×D4—862no—
380C4×D4—862no—
381C4×D4—1724no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—432no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—864no—
386C2×C4⋊C4—868no—
387C2×C4⋊C4—862no—
388C2×C4⋊C4—862no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—864no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4C22×D4311yescharacteristic
393C2×C4⋊C4C22×D4312yes—
394C2×C4⋊C4C22×D4311yescharacteristic
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C42—21no—
401C2×C42—431no—
402C2×C42—431no—
403C2×C42—431no—
404C2×C42—862no—
405C2×C42—862no—
406C2×C42C22×D4311yescharacteristic
407#107—864no—
408#107—864no—
409C4⋊C8—22no—
410C4⋊C8—862no—
411#102—864no—
412#102—864no—
413C22⋊C8—864no—
414#95—21no—
415#95—861no—
416#95—861no—
417C24—431no—
418C24—861no—
419C2×Q8—24no—
420C2×Q8—42no—
421C2×Q8—42no—
422C2×Q8—868no—
423C2×Q8—864no—
424C2×Q8—1724no—
425C2×Q8—1724no—
426C2×Q8—17232no—
427C2×Q8—1722no—
428C2×Q8—1722no—
429C2×D4—432no—
430C2×D4—864no—
431C2×D4—861no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—861no—
436C2×D4—1722no—
437C2×D4—1722no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—434no—
445C22×C4—432no—
446C22×C4—432no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—868no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—862no—
458C22×C4—861no—
459C22×C4—1724no—
460C22×C4—1724no—
461C22×C4—1722no—
462C22×C4—1722no—
463C22×C4—1722no—
464C22×C4D4×D4311yescharacteristic
465C22×C4D4×D4311yescharacteristic
466C22×C4C23×D4311yescharacteristic
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—862no—
471C2×C8—862no—
472C2×C8—862no—
473C4⋊C4—24no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—434no—
479C4⋊C4—868no—
480C4⋊C4—868no—
481C4⋊C4—864no—
482C4⋊C4—862no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—1722no—
486C4⋊C4C2×D17214yes—
487C4⋊C4Q8×D4312yescomplemented
488C22⋊C4—864no—
489C22⋊C4—1722no—
490C22⋊C4—1722no—
491C22⋊C4—1722no—
492C22⋊C4—1722no—
493C42—42no—
494C42—862no—
495C42—862no—
496C42—861no—
497C42—861no—
498C42C2×D17212yes—
499C42D4×D4312yes—
500C23—432no—
501C23—432no—
502C23—432no—
503C23—861no—
504C23—861no—
505C23—861no—
506C23—861no—
507C23—862no—
508C23—1721no—
509C23—1721no—
510C23—1721no—
511C23—1721no—
512C23—1721no—
513C23—1721no—
514C23C2×D4×D4311yescharacteristic
515Q8—48no—
516Q8—17216no—
517Q8—1728no—
518D4—862no—
519D4—862no—
520D4—1728no—
521D4—1721no—
522D4—1721no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—432no—
535C2×C4—432no—
536C2×C4—432no—
537C2×C4—868no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—862no—
545C2×C4—862no—
546C2×C4—862no—
547C2×C4—862no—
548C2×C4—868no—
549C2×C4—864no—
550C2×C4—3444no—
551C2×C4—17216no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1722no—
556C2×C4—1722no—
557C2×C4#1306329512yes—
558C2×C4#1306329512yes—
559C2×C4D8×D4312yes—
560C2×C4#1306335212yes—
561C2×C4C2×D4×D4311yescharacteristic
562C2×C4C22×D17211yescharacteristic
563C2×C4C2×Q8×D4311yescharacteristic
564C2×C4#41×D4311yescharacteristic
565C2×C4#1306337211yescharacteristic
566C2×C4#1306337311yescharacteristic
567C8—42no—
568C8—1722no—
569C22—434no—
570C22—862no—
571C22—862no—
572C22—862no—
573C22—862no—
574C22—862no—
575C22—862no—
576C22—3441no—
577C22—3441no—
578C22—3441no—
579C22—3441no—
580C22—1722no—
581C22—1722no—
582C22—1722no—
583C22C2×#1306329511yescharacteristic
584C22C22⋊Q8×D4311yescharacteristic
585C22#1458347211yescharacteristic
586C22C2×D8×D4311yescharacteristic
587C22C2×#1306335211yescharacteristic
588C22#137×D4311yescharacteristic
589C22#137×D4311yescharacteristic
590C4—22no—
591C4—44no—
592C4—42no—
593C4—81no—
594C4—862no—
595C4—862no—
596C4—862no—
597C4—3441no—
598C4—1724no—
599C4#1458303414yes—
600C4#1458355711yescharacteristic
601C4#1458356111yescharacteristic
602C4#1458356411yescharacteristic
603C4Q8×D17211yescharacteristic
604C2—864no—
605C2—3442no—
606C2#1913795811yescharacteristic
607C2C2×#1458303411yescharacteristic
608C2#1914383111yescharacteristic
609C2#474×D4311yescharacteristic
610C2#1914440511yescharacteristic
611C2#1914571511yescharacteristic
612C2#1914582911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1988C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenter#1988D43
hypocenterC43#24298
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Q8×D43C2semidirect
2. C2×#14583180C2semidirect
3. C2×#14583176C2semidirect
5. #19135922C2semidirect
6. #19135730C2semidirect
7. #19135547C2semidirect
9. #19134784C2semidirect
10. #19134572C2semidirect
11. C43×#1988C2semidirect
61. #13063325D4semidirect
67. #13063300Q8semidirect
101. C4⋊Q8×C43D4semidirect
135. C2×D172C2×Q8semidirect
169. C4⋊C4×C43C2×Q8semidirect
283. C2×D43#474semidirect
305. #1988D43semidirect
353. C43#24298semidirect
376. C4⋊Q8D172semidirect
487. C4⋊C4Q8×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D432
C2×#145831802
C2×#145831762
C4×#130633002
#191359222
#191357302
#191355472
#191349112
#191347842
#191345722
C43×#19882
#2429843