Finite Group Databasebeta

← #25115791

Subgroups — #25115791

Order 11008.

902 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582986C211yesmaximal, characteristic
2#19137548C211yesmaximal, characteristic, complemented
3#19137496C211yesmaximal, characteristic
4#19135286C211yesmaximal, characteristic, complemented
5#19135284C211yesmaximal, characteristic, complemented
6#19135182C211yesmaximal, characteristic, complemented
7#19134930C211yesmaximal, characteristic
8#19134928C211yesmaximal, characteristic
9#19134721C211yesmaximal, characteristic, complemented
10#19134599C211yesmaximal, characteristic, complemented
11#19134594C211yesmaximal, characteristic
12#19134461C211yesmaximal, characteristic, complemented
13#19134423C211yesmaximal, characteristic
14#19134419C211yesmaximal, characteristic
15C43×#1920C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×#13063290C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C2×C4⋊C4×D43—21no—
22#14582986C418yescomplemented
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063236C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582805C2211yescharacteristic
34#14582804C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582783—21no—
37#14582781—21no—
38#14582773—21no—
39#14582770—21no—
40#14582768C2211yescharacteristic
41#14582768C2211yescharacteristic
42#14582763—21no—
43#14582758—21no—
44C4⋊C4×Dic43C2211yescharacteristic
45C4×Dic43⋊C4—21no—
46C4×Dic43⋊C4C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C43×#389C2211yescharacteristic
55C4×C4⋊C4×C43C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C2×#10621873—22no—
66C2×#10621873—22no—
67C2×#10621873C2×C414yes—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063290—22no—
71#13063290C2×C414yescomplemented
72C4×D172—22no—
73C4×D172—41no—
74#13063287—22no—
75#13063287—22no—
76#13063287—41no—
77#13063287C2×C414yes—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4D411yescharacteristic
87C2×Dic43⋊C4D411yescharacteristic
88C4⋊C4×D43—44no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43C2311yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96Dic43⋊C8—22no—
97#13063250—41no—
98#13063248—41no—
99#13063248C2×C414yescomplemented
100#13063247—22no—
101#13063245—22no—
102#13063245C2×C414yes—
103#13063236—41no—
104#13063235—41no—
105C8×Dic43C2×C414yescomplemented
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95D411yescharacteristic
113C43⋊#95D411yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C42×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#106×C43C2×C414yescomplemented
124#95×C43—21no—
125#95×C43—21no—
126C23×D43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172C22×C412yes—
145C2×D172#4112yes—
146C2×D172#4112yes—
147C2×C4×D43—24no—
148C2×C4×D43—42no—
149C2×C4×D43—42no—
150C2×C4×D43—42no—
151C2×C4×D43—42no—
152C2×C4×D43—42no—
153C2×C4×D43—42no—
154C2×C4×D43—81no—
155C2×C4×D43—81no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86C22×C412yes—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43C22×C412yes—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—42no—
175C4⋊C4×C43C22×C412yes—
176C4⋊C4×C43C22×C412yes—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—81no—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—42no—
182(C2×D43)⋊C4—42no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—42no—
188Dic43⋊C4—24no—
189Dic43⋊C4—22no—
190Dic43⋊C4—22no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193Dic43⋊C4—81no—
194Dic43⋊C4—81no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—24no—
198C4×Dic43—81no—
199C4×Dic43C22×C412yes—
200C4×Dic43#4112yes—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8C22×C412yes—
207#10621873—28no—
208C23×C43C22×D411yescharacteristic
209C22×D43—22no—
210C22×D43—22no—
211C22×D43—22no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43C23×C411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C2×C4×C432−1+411yescharacteristic
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—22no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43C4×D412yes—
258C2×Dic43C4×D412yes—
259C2×Dic43AGL(1,ℤ/8)12yes—
260C2×Dic43#13712yes—
261D172—22no—
262D172—22no—
263D172—22no—
264D172#11714yes—
265C4×D43—48no—
266C4×D43—84no—
267C4×D43—84no—
268Dic86—22no—
269Dic86—22no—
270Dic86—41no—
271Dic86—41no—
272C8×C43—22no—
273C8×C43—41no—
274C43⋊C8—22no—
275C43⋊C8—41no—
276#22762—431nomaximal, Sylow
277C22×C43C2×C4×D411yescharacteristic
278C22×C43#54611yescharacteristic
279C22×C43#54811yescharacteristic
280C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C43C2×#13711yescharacteristic
282C22×C43#57711yescharacteristic
283C22×C43#57711yescharacteristic
284C2×D43—24no—
285C2×D43—42no—
286C2×D43—42no—
287C2×D43—42no—
288C2×D43—42no—
289C2×D43—42no—
290C2×D43—42no—
291C4×C43—41no—
292C4×C43—42no—
293C4×C43—42no—
294C4×C43—41no—
295C4×C43—81no—
296C4×C43—81no—
297C4×C43C2×#11711yescharacteristic
298C4×C43#52011yescharacteristic
299C4×C43#55211yescharacteristic
300C4×C43#55311yescharacteristic
301Dic43—22no—
302Dic43—41no—
303Dic43—42no—
304Dic43—41no—
305Dic43—81no—
306Dic43—81no—
307Dic43#44014yes—
308C2×C4×SD16—431no—
309#2355—431no—
310D4×C4⋊C4—431no—
311#1935—431no—
312#1935—431no—
313#1920—431no—
314#1920D4311yescharacteristic, complemented
315#1877—431no—
316#1877—431no—
317#1834—431no—
318#1803—431no—
319#1802—431no—
320#1770—431no—
321#1762—431no—
322#1762—431no—
323C2×C43#235211yescharacteristic
324C2×C43C2×#44011yescharacteristic
325C2×C43#295211yescharacteristic
326C2×C43#332411yescharacteristic
327C2×C43#333111yescharacteristic
328C2×C43#337211yescharacteristic
329C2×C43#337311yescharacteristic
330D43—44no—
331C22×SD16—431no—
332C2×C4×Q8—431no—
333C2×C4×D4—431no—
334C2×C4×D4—431no—
335C2×C4×D4—431no—
336C22×C4⋊C4—861no—
337C4×SD16—438no—
338C2×#106C2×D4311yescharacteristic
339C2×C4⋊C8—431no—
340C2×#103—431no—
341C2×#103—431no—
342C2×#103—431no—
343C2×#102—431no—
344C2×#102—431no—
345C2×#102—431no—
346C2×#97—431no—
347C2×#97—431no—
348C2×C4×C8—431no—
349#391—431no—
350#391—431no—
351#389—431no—
352#389C2×D4311yescharacteristic
353#387—861no—
354#387—861no—
355#385—861no—
356#385—861no—
357#384—431no—
358#384—431no—
359#382—861no—
360#380—861no—
361C4×C4⋊C4—431no—
362C4×C4⋊C4—431no—
363C4×C4⋊C4—861no—
364C4×C4⋊C4C2×D4311yescharacteristic
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340C2×D4311yescharacteristic
371#340C2×D4311yescharacteristic
372#340C2×D4311yescharacteristic
373#336—431no—
374#336C2×D4311yescharacteristic
375C43#2276211yescharacteristic, complemented, Sylow
376C22×Q8—431no—
377C22×D4—431no—
378C23×C4—861no—
379C23×C4—861no—
380C23×C4—861no—
381C2×SD16—434no—
382C2×SD16—862no—
383C2×SD16—862no—
384C22×C8—431no—
385C22×C8—431no—
386C22×C8C22×D4311yescharacteristic
387C22×C8C22×D4311yescharacteristic
388C4×Q8—434no—
389C4×Q8—862no—
390C4×D4—434no—
391C4×D4—862no—
392C4×D4—862no—
393C4×D4—862no—
394C4×D4—1721no—
395C4×D4—1721no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—1724no—
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C42—21no—
416C2×C42—431no—
417C2×C42—431no—
418C2×C42—861no—
419C2×C42—861no—
420C2×C42C22×D4311yescharacteristic
421#106C4×D4314yescomplemented
422C4⋊C8—862no—
423#103—434no—
424#103—1721no—
425#103—1721no—
426#102—434no—
427#102—862no—
428#102—862no—
429#97—1721no—
430#97—1721no—
431C4×C8—434no—
432#95—21no—
433#95—21no—
434#95—431no—
435#95—431no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442C24—861no—
443C2×Q8—432no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×D4—432no—
450C2×D4—432no—
451C2×D4—432no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—431no—
463C22×C4—864no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—3441no—
468C22×C4—3441no—
469C22×C4—1722no—
470C22×C4—1722no—
471C22×C4—1722no—
472C22×C4—1722no—
473C22×C4—1722no—
474C22×C4—1722no—
475C22×C4D4×D4311yescharacteristic
476C22×C4D4×D4311yescharacteristic
477C22×C4C23×D4311yescharacteristic
478SD16—868no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—432no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8C2×C4×D4312yes—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—42no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C4⋊C4—864no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—3441no—
506C4⋊C4—3441no—
507C4⋊C4—1722no—
508C4⋊C4—1722no—
509C4⋊C4—1722no—
510C4⋊C4C2×C4×D4312yes—
511C4⋊C4C2×C4×D4312yes—
512C22⋊C4—864no—
513C22⋊C4—1722no—
514C22⋊C4—1722no—
515C42—21no—
516C42—21no—
517C42—81no—
518C42—432no—
519C42—432no—
520C42—864no—
521C42—861no—
522C42—861no—
523C42—3441no—
524C23—862no—
525C23—862no—
526C23—862no—
527C23—1721no—
528C23—1721no—
529C23—1721no—
530C23—1721no—
531C23C2×D4×D4311yescharacteristic
532Q8—862no—
533Q8—862no—
534Q8—1721no—
535Q8—1721no—
536D4—434no—
537D4—862no—
538D4—862no—
539D4—862no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—432no—
559C2×C4—432no—
560C2×C4—432no—
561C2×C4—432no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—862no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—3444no—
572C2×C4—3444no—
573C2×C4—1728no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4C22×C4×D4311yescharacteristic
583C2×C4#41×D4311yescharacteristic
584C2×C4#41×D4311yescharacteristic
585C2×C4#41×D4311yescharacteristic
586C2×C4#1306337111yescharacteristic
587C2×C4#1306337311yescharacteristic
588C8—22no—
589C8—41no—
590C8—862no—
591C8—1721no—
592C22—864no—
593C22—1722no—
594C22—1722no—
595C22—1722no—
596C22—1722no—
597C22—1722no—
598C22—1722no—
599C22C4×D4×D4311yescharacteristic
600C22#1458354111yescharacteristic
601C22#1458355911yescharacteristic
602C22AGL(1,ℤ/8)×D4311yescharacteristic
603C22#137×D4311yescharacteristic
604C22#1458370511yescharacteristic
605C22#1458370611yescharacteristic
606C4—42no—
607C4—41no—
608C4—41no—
609C4—42no—
610C4—81no—
611C4—81no—
612C4—434no—
613C4—862no—
614C4—3441no—
615C4—3441no—
616C4—1721no—
617C4—1721no—
618C4—1722no—
619C4#117×D4311yescharacteristic
620C4#1458338111yescharacteristic
621C4#1458358111yescharacteristic
622C4#1458360011yescharacteristic
623C2—1724no—
624C2#1913751911yescharacteristic
625C2#440×D4311yescharacteristic
626C2#1914347311yescharacteristic
627C2#1914682411yescharacteristic
628C2#1914690911yescharacteristic
629C2#1914737911yescharacteristic
630C2#1914739011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1920C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1920D43
hypocenterC43#22762
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
2. #19137548C2semidirect
4. #19135286C2semidirect
5. #19135284C2semidirect
6. #19135182C2semidirect
9. #19134721C2semidirect
10. #19134599C2semidirect
12. #19134461C2semidirect
15. C43×#1920C2semidirect
22. #14582986C4semidirect
71. #13063290C2×C4semidirect
99. #13063248C2×C4semidirect
105. C8×Dic43C2×C4semidirect
123. #106×C43C2×C4semidirect
314. #1920D43semidirect
375. C43#22762semidirect
421. #106C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829862
#191375482
#191374962
#191352862
#191352842
#191351822
#191349302
#191349282
#191347212
#191345992
#191345942
#191344612
#191344232
#191344192
C43×#19202
#2276243