Finite Group Databasebeta

← #25099655

Subgroups — #25099655

Order 11008.

922 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
1C2×#14583000C211yesmaximal, characteristic
2#19137057C211yesmaximal, characteristic
3C4×Q8×Dic43C211yesmaximal, characteristic, complemented
4#19135219C211yesmaximal, characteristic
5#19135218C211yesmaximal, characteristic
6#19135188C211yesmaximal, characteristic, complemented
7#19135165C211yesmaximal, characteristic, complemented
8#19134952C211yesmaximal, characteristic
9#19134861C211yesmaximal, characteristic, complemented
10#19134849C211yesmaximal, characteristic, complemented
11#19134491C211yesmaximal, characteristic, complemented
12#19134427C211yesmaximal, characteristic, complemented
13#19134422C211yesmaximal, characteristic
14#19134342C211yesmaximal, characteristic, complemented
15C43×#1880C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063281—21no—
20#14583000C418yescomplemented
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30#14582802C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582793—21no—
34#14582787—21no—
35C4⋊C4×Dic43—21no—
36C4⋊C4×Dic43—21no—
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4×C4⋊Dic43—21no—
41C4×C4⋊Dic43C2211yescharacteristic
42C22⋊C4×Dic43—21no—
43C42×Dic43—21no—
44C42×Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63Q8×Dic43—22no—
64Q8×Dic43—22no—
65Q8×Dic43—22no—
66Q8×Dic43C2×C414yes—
67D4×Dic43—22no—
68D4×Dic43C2×C414yes—
69#13063281—44no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43D411yescharacteristic
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43D411yescharacteristic
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063259C2×C414yes—
94#13063258—22no—
95#13063256—22no—
96#13063249—22no—
97#13063249C2×C414yes—
98#13063246—22no—
99#13063246C2×C414yes—
100#13063235—22no—
101#13063235C2×C414yes—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×Q8×C43C2311yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C2×SD16×C43—22no—
111C2×SD16×C43—22no—
112C2×SD16×C43C2×C414yes—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C4×Q8×C43—22no—
116C4×Q8×C43—22no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C42×C43—21no—
123C2×C42×C43C2311yescharacteristic
124#103×C43—22no—
125#102×C43—22no—
126C24×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43C22×C412yes—
131C2×Q8×C43#4112yes—
132C2×Q8×C43#4112yes—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43C22×C412yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—24no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156SD16×C43—28no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43C22×C412yes—
163C4⋊C4×C43—24no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43#4112yes—
168C22⋊C4×C43—42no—
169C22⋊C4×C43—42no—
170C42×C43—24no—
171C42×C43—21no—
172C42×C43—21no—
173C22⋊Dic43—24no—
174C22⋊Dic43—42no—
175C22⋊Dic43—42no—
176C4⋊Dic43—24no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—24no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43C22×C412yes—
184C4⋊Dic43C22×C412yes—
185C4⋊Dic43#4112yes—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188C4×Dic43—24no—
189C4×Dic43—22no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—24no—
193C4×Dic43—22no—
194C4×Dic43—41no—
195C4×Dic43—41no—
196C4×Dic43—42no—
197C4×Dic43—42no—
198C4×Dic43—42no—
199C4×Dic43—42no—
200C4×Dic43C22×C412yes—
201C4×Dic43#4112yes—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8C22×C412yes—
208C23×C43—22no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43C22×D411yescharacteristic
216Q8×C43—22no—
217Q8×C43—22no—
218Q8×C43—22no—
219Q8×C43#11714yescomplemented
220D4×C43—22no—
221D4×C43—22no—
222D4×C43—41no—
223D4×C43—41no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—22no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43#13712yes—
239C2×C4×C43C23×C411yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—21no—
254C2×Dic43—22no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—48no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43C4×D412yes—
268C2×Dic43C4×D412yes—
269C2×Dic43AGL(1,ℤ/8)12yes—
270C8×C43—22no—
271C8×C43—41no—
272C43⋊C8—22no—
273C43⋊C8—41no—
274#21124—431nomaximal, Sylow
275C22×C43—42no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43C2×C4×D411yescharacteristic
283C22×C43#52511yescharacteristic
284C22×C43#52511yescharacteristic
285C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C43C2×#13711yescharacteristic
287C22×C43#57511yescharacteristic
288C22×C43#57511yescharacteristic
289C4×C43—22no—
290C4×C43—24no—
291C4×C43—41no—
292C4×C43—42no—
293C4×C43—81no—
294C4×C43C2×#11711yescharacteristic
295C4×C43C4×#4111yescharacteristic
296C4×C43#52911yescharacteristic
297C4×C43#52911yescharacteristic
298Dic43—22no—
299Dic43—22no—
300Dic43—22no—
301Dic43—41no—
302Dic43—42no—
303Dic43—42no—
304Dic43—42no—
305Dic43—81no—
306C2×#440—431no—
307#2293—431no—
308C42×Q8—431no—
309#1926—431no—
310#1925—431no—
311#1921—431no—
312#1918—431no—
313#1880—431no—
314#1880D4311yescharacteristic
315#1865—431no—
316#1863—431no—
317#1776—431no—
318#1763—431no—
319#1762—431no—
320#1745—431no—
321C2×C43—82no—
322C2×C43#229011yescharacteristic
323C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
324C2×C43C4×#13711yescharacteristic
325C2×C43#311111yescharacteristic
326C2×C43#311211yescharacteristic
327C2×C43#311511yescharacteristic
328C2×C43#311711yescharacteristic
329C22×SD16C2×D4311yescharacteristic
330C2×C4×Q8—431no—
331C2×C4×Q8—431no—
332C2×C4×Q8C2×D4311yescharacteristic
333C2×C4×D4—431no—
334C2×#117—861no—
335#440—438no—
336C2×#107—431no—
337C2×#107—431no—
338C2×#106—431no—
339C2×#103—431no—
340C2×#103—431no—
341C2×#103C2×D4311yescharacteristic
342C2×#102—431no—
343C2×#102—431no—
344C2×#102C2×D4311yescharacteristic
345C2×#97—431no—
346C2×#97—431no—
347#390—431no—
348#390C2×D4311yescharacteristic
349#389—431no—
350#389—431no—
351#388—861no—
352#388—861no—
353C4×C4⋊C4—431no—
354C4×C4⋊C4—431no—
355C4×C4⋊C4—431no—
356C4×C4⋊C4—431no—
357C4×C4⋊C4—861no—
358C4×C4⋊C4—861no—
359C4×C4⋊C4—861no—
360C4×C22⋊C4—861no—
361C43—431no—
362C43—861no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340C2×D4311yescharacteristic
369#336—431no—
370#336—431no—
371#336—431no—
372#336C2×D4311yescharacteristic
373C43#2112411yescharacteristic, complemented, Sylow
374C22×Q8C22×D4311yescharacteristic
375C22×D4C22×D4311yescharacteristic
376C23×C4—861no—
377C2×SD16—22no—
378C2×SD16—22no—
379C2×SD16C4×D4314yes—
380C22×C8—431no—
381C22×C8—431no—
382C22×C8C22×D4311yescharacteristic
383C22×C8C22×D4311yescharacteristic
384C4×Q8—22no—
385C4×Q8—22no—
386C4×Q8—434no—
387C4×Q8—862no—
388C4×Q8—862no—
389C4×Q8—862no—
390C4×D4—434no—
391C4×D4—862no—
392#117—1724no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C42—21no—
410C2×C42—431no—
411C2×C42—431no—
412C2×C42—431no—
413C2×C42—431no—
414C2×C42—431no—
415C2×C42—431no—
416C2×C42—861no—
417C2×C42—861no—
418C2×C42—861no—
419C2×C42—861no—
420C2×C42—861no—
421C2×C42—861no—
422C2×C42C22×D4311yescharacteristic
423#107—434no—
424#107—862no—
425#106—862no—
426#103—22no—
427#103—434no—
428#103—862no—
429#102—22no—
430#102—434no—
431#102—862no—
432#97—434no—
433#97—862no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440C24—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8C2×C4×D4312yes—
445C2×Q8#1062190012yes—
446C2×Q8#1062190012yes—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4C2×C4×D4312yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—864no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—1722no—
466C22×C4—1722no—
467C22×C4D4×D4311yescharacteristic
468C22×C4D4×D4311yescharacteristic
469C22×C4C23×D4311yescharacteristic
470SD16—28no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—432no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8C2×C4×D4312yes—
483C4⋊C4—24no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—432no—
488C4⋊C4—432no—
489C4⋊C4—432no—
490C4⋊C4—864no—
491C4⋊C4—864no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—1722no—
498C4⋊C4—1722no—
499C4⋊C4#1062190012yes—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C22⋊C4—864no—
503C22⋊C4—1722no—
504C22⋊C4—1722no—
505C42—24no—
506C42—21no—
507C42—21no—
508C42—432no—
509C42—432no—
510C42—862no—
511C42—864no—
512C42—864no—
513C42—862no—
514C42—861no—
515C42—861no—
516C42—1721no—
517C42—1721no—
518C42—1722no—
519C42—1722no—
520C42—1722no—
521C42—1722no—
522C23—22no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23C2×D4×D4311yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—22no—
533Q8#1306328114yescomplemented
534D4—22no—
535D4—22no—
536D4—41no—
537D4—41no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—432no—
553C2×C4—432no—
554C2×C4—432no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—1728no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4#1306335412yes—
578C2×C4C22×C4×D4311yescharacteristic
579C2×C4#41×D4311yescharacteristic
580C2×C4#41×D4311yescharacteristic
581C2×C4C2×#1062190011yescharacteristic
582C2×C4C2×#1062190011yescharacteristic
583C2×C4C2×#1062190011yescharacteristic
584C8—22no—
585C8—41no—
586C8—862no—
587C8—1721no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22C4×D4×D4311yescharacteristic
596C22#1458340511yescharacteristic
597C22#1458340911yescharacteristic
598C22AGL(1,ℤ/8)×D4311yescharacteristic
599C22C2×#1306335411yescharacteristic
600C22#1458369611yescharacteristic
601C22#1458369811yescharacteristic
602C4—24no—
603C4—22no—
604C4—41no—
605C4—42no—
606C4—81no—
607C4—862no—
608C4—862no—
609C4—862no—
610C4—3441no—
611C4—1722no—
612C4—1722no—
613C4—1721no—
614C4—1722no—
615C4C2×#1306328111yescharacteristic
616C4C4×#1062190011yescharacteristic
617C4#1458342611yescharacteristic
618C4#1458343011yescharacteristic
619C2—82no—
620C2#1913703511yescharacteristic
621C2#1914340011yescharacteristic
622C2C4×#1306335411yescharacteristic
623C2#1914470311yescharacteristic
624C2#1914471611yescharacteristic
625C2#1914473911yescharacteristic
626C2#1914476111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1880C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1880D43
hypocenterC43#21124
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
3. C4×Q8×Dic43C2semidirect
6. #19135188C2semidirect
7. #19135165C2semidirect
9. #19134861C2semidirect
10. #19134849C2semidirect
11. #19134491C2semidirect
12. #19134427C2semidirect
14. #19134342C2semidirect
20. #14583000C4semidirect
219. Q8×C43#117semidirect
373. C43#21124semidirect
533. Q8#13063281semidirect

Maximal subgroups

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

subgroupindex
C2×#145830002
#191370572
C4×Q8×Dic432
#191352192
#191352182
#191351882
#191351652
#191349522
#191348612
#191348492
#191344912
#191344272
#191344222
#191343422
C43×#18802
#2112443