Finite Group Databasebeta

← #25067759

Subgroups — #25067759

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144638C211yesmaximal, characteristic
2#19143755C211yesmaximal, characteristic, complemented
3#19143632C211yesmaximal, characteristic, complemented
4#19133482C211yesmaximal, characteristic, complemented
5#19133477C211yesmaximal, characteristic, complemented
6#19133470C211yesmaximal, characteristic, complemented
7#19133462C211yesmaximal, characteristic, complemented
8#19133456C211yesmaximal, characteristic, complemented
9#19133455C211yesmaximal, characteristic, complemented
10#19133392C211yesmaximal, characteristic, complemented
11#19133387C211yesmaximal, characteristic, complemented
12#19133381C211yesmaximal, characteristic, complemented
13C2×#14582628C211yesmaximal, characteristic, complemented
14#19132878C211yesmaximal, characteristic, complemented
15C43×#1494C211yesmaximal, characteristic, complemented
16C2×C4×D172C2211yescharacteristic
17#14583232C411yescharacteristic
18#14583215C411yescharacteristic
19#14583196C411yescharacteristic
20#14583196C411yescharacteristic
21#14583111C411yescharacteristic
22#14583111C411yescharacteristic
23#14583049C411yescharacteristic
24#14583032C411yescharacteristic
25#14583030C2211yescharacteristic, complemented
26Q8×C43⋊C8C2211yescharacteristic, complemented
27C4×#10621884C2211yescharacteristic
28C4×#10621884C2211yescharacteristic
29C4×#10621882C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582977C2211yescharacteristic, complemented
32#14582976C2211yescharacteristic
33#14582976C2211yescharacteristic
34#14582972—21no—
35#14582972—21no—
36#14582971—21no—
37D4×C43⋊C8—21no—
38D4×C43⋊C8C2211yescharacteristic, complemented
39#14582964C2211yescharacteristic
40#14582964C2211yescharacteristic
41#14582960—21no—
42#14582952C2211yescharacteristic
43#14582952C2211yescharacteristic
44#14582926—21no—
45C2×C4⋊(C43⋊C8)C2211yescharacteristic
46#14582861—21no—
47C22⋊C8×D43—21no—
48#14582651C2211yescharacteristic, complemented
49#14582651C2211yescharacteristic, complemented
50#14582649C2211yescharacteristic, complemented
51#14582649C2211yescharacteristic, complemented
52#14582628C2211yescharacteristic
53#14582628C2211yescharacteristic
54#14582628C2211yescharacteristic
55#14582628C2211yescharacteristic
56#14582620C2211yescharacteristic, complemented
57#14582620C2211yescharacteristic, complemented
58C8×C43⋊C8C2211yescharacteristic, complemented
59C8×C43⋊C8C2211yescharacteristic, complemented
60C43×#529C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic, complemented
64C43×Q8⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic, complemented
66C43×D4⋊C8C2211yescharacteristic, complemented
67C22×D172C2×C411yescharacteristic
68C22×C4×D43—21no—
69C2×#10621884C2×C411yescharacteristic
70C2×#10621884C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72C2×#10621882C2×C411yescharacteristic
73C2×#10621877—21no—
74C2×#10621872—21no—
75C2×#10621872—21no—
76C22×C43⋊C8—21no—
77C22×C43⋊C8—21no—
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80C4×D172—21no—
81C4×D172—21no—
82C4×D172C2×C411yescharacteristic
83C4×D172C2×C411yescharacteristic
84C4×D172C2311yescharacteristic
85C4×D172C2311yescharacteristic
86C2×C4⋊Dic43C2×C411yescharacteristic
87C2×(C2×D43)⋊C4—21no—
88#13063258C2×C411yescharacteristic
89#13063258C2×C411yescharacteristic
90#13063256C2×C411yescharacteristic
91#13063256C2×C411yescharacteristic
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2×C411yescharacteristic
96C4⋊(C43⋊C8)C2×C411yescharacteristic
97C4⋊(C43⋊C8)D411yescharacteristic
98C4⋊(C43⋊C8)D411yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063249C2×C411yescharacteristic
102#13063249C2×C411yescharacteristic
103#13063246C2×C411yescharacteristic
104#13063246C2×C411yescharacteristic
105#13063245C2×C411yescharacteristic
106#13063245C2×C411yescharacteristic
107#13063245C2×C411yescharacteristic
108#13063245C2×C411yescharacteristic
109C22⋊(C43⋊C8)—21no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)C2×C411yescharacteristic
112C22⋊(C43⋊C8)C2×C411yescharacteristic
113C22⋊(C43⋊C8)D411yescharacteristic
114C22⋊(C43⋊C8)D411yescharacteristic
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119#13063236—21no—
120C4×C43⋊C8—21no—
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C22×C8×C43—21no—
126#126×C43—21no—
127#125×C43C2×C411yescharacteristic
128#124×C43C2×C411yescharacteristic
129#123×C43—21no—
130C22⋊Q8×C43C2×C411yescharacteristic
131#121×C43C2×C411yescharacteristic
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43—21no—
134C4×D4×C43C2311yescharacteristic
135#117×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C22⋊C8×C43—21no—
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C23×D43—21no—
145C2×Q8×C43C22×C411yescharacteristic
146C2×D4×C43—21no—
147C2×D4×C43C22×C411yescharacteristic
148C22×C4×C43—21no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43#4111yescharacteristic
152C22×Dic43—21no—
153C2×D172—21no—
154C2×D172—22no—
155C2×D172—41no—
156C2×D172C22×C411yescharacteristic
157C2×D172C22×C411yescharacteristic
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—81no—
163C2×C4×D43—81no—
164C2×C8×C43—24no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43C22×C411yescharacteristic
174C4⋊C4×C43C22×C411yescharacteristic
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C42×C43—21no—
181C42×C43C22×C411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43#4111yescharacteristic
184C42×C43C2411yescharacteristic
185#10621884—22no—
186#10621884—41no—
187#10621882—22no—
188#10621882—41no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43C22×C411yescharacteristic
195C4⋊Dic43C22×C411yescharacteristic
196#10621877—81no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—81no—
200C2×C43⋊C8—81no—
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209#10621872—81no—
210#10621872—81no—
211C8×D43—81no—
212C8×D43—81no—
213C23×C43—21no—
214C23×C43C4×D411yescharacteristic
215C22×D43—21no—
216C22×D43—21no—
217C22×D43—42no—
218C22×D43—42no—
219C22×D43—81no—
220Q8×C43—21no—
221Q8×C43—21no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—42no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43C4×D411yescharacteristic
236C2×C4×C43C4×D411yescharacteristic
237C2×C4×C43C4×D411yescharacteristic
238C2×C4×C43C23×C411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—81no—
244D172—21no—
245D172—21no—
246D172—21no—
247D172—42no—
248D172#13112yes—
249C4×D43—41no—
250C4×D43—41no—
251C4×D43—41no—
252C4×D43—41no—
253C4×D43—81no—
254C4×D43—81no—
255C8×C43—22no—
256C8×C43—22no—
257C8×C43—41no—
258C8×C43—41no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—21no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269#18014—431nomaximal, Sylow
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43#44312yes—
276C22×C43C2×C4×D411yescharacteristic
277C2×D43—22no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—84no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43C2×#13111yescharacteristic
292C4×C43#56811yescharacteristic
293C4×C43#57611yescharacteristic
294C4×C43#57711yescharacteristic
295Dic43—41no—
296Dic43—41no—
297#3105—431no—
298#2994—431no—
299#2974—431no—
300#1590—431no—
301#1589—431no—
302#1588—431no—
303#1586—431no—
304#1586—431no—
305#1585—431no—
306C8×SD16—431no—
307C8×D8—431no—
308#1573—431no—
309#1494D4311yescharacteristic, complemented
310C2×D4⋊C8—431no—
311#1450—431no—
312C2×C43—22no—
313C2×C43—81no—
314C2×C43#293311yescharacteristic
315C2×C43#294611yescharacteristic
316C2×C43C2×#44311yescharacteristic
317D43—42no—
318D43—81no—
319#529C2×D4311yescharacteristic
320C2×C4×D4—431no—
321#484—431no—
322#481—431no—
323#478—431no—
324#478—431no—
325#463—431no—
326#463—431no—
327#450—431no—
328#447—431no—
329#446—431no—
330C8×Q8—431no—
331C4×SD16—431no—
332C4×SD16—431no—
333C4×D8—431no—
334C4×D8—431no—
335#436—431no—
336#436—431no—
337#436—431no—
338#435—861no—
339#435—861no—
340#435—861no—
341C8×D4—431no—
342C8×D4—431no—
343C8×D4—431no—
344C8×D4—861no—
345#433—861no—
346#432C2×D4311yescharacteristic
347#431—431no—
348#431—431no—
349#424—861no—
350C2×C4⋊C8—431no—
351#407—861no—
352C2×C22⋊C8—861no—
353C2×C4×C8C2×D4311yescharacteristic
354#335—431no—
355#335—431no—
356#334—431no—
357#334—431no—
358Q8⋊C8C2×D4311yescharacteristic, complemented
359Q8⋊C8C2×D4311yescharacteristic, complemented
360D4⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8—431no—
364D4⋊C8C2×D4311yescharacteristic, complemented
365D4⋊C8C2×D4311yescharacteristic, complemented
366#322—431no—
367#322—431no—
368C82—431no—
369C82—431no—
370C43#1801411yescharacteristic, complemented, Sylow
371C22×D4—431no—
372C23×C4—861no—
373C2×SD16—431no—
374C2×SD16—431no—
375C2×D8—431no—
376C2×D8—431no—
377C2×M16—861no—
378C2×M16—861no—
379C2×M16—861no—
380C22×C8—21no—
381C22×C8—861no—
382C22×C8—861no—
383C22×C8—861no—
384C22×C8—861no—
385#126—21no—
386#125C4×D4311yescharacteristic
387#124C4×D4311yescharacteristic
388#123—21no—
389C22⋊Q8C4×D4311yescharacteristic
390#121C4×D4311yescharacteristic
391C4×Q8C22×D4311yescharacteristic
392C4×D4—21no—
393C4×D4—431no—
394C4×D4—431no—
395C4×D4—431no—
396C4×D4—431no—
397C4×D4—861no—
398C4×D4—861no—
399C4×D4C22×D4311yescharacteristic
400#117—21no—
401C2×C4⋊C4—431no—
402C2×C22⋊C4—861no—
403C2×C42C22×D4311yescharacteristic
404#107—431no—
405#107—431no—
406#106—431no—
407#106—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—861no—
415C4⋊C8—861no—
416C4⋊C8—861no—
417C4⋊C8C22×D4311yescharacteristic
418C4⋊C8C22×D4311yescharacteristic
419#103—431no—
420#103—431no—
421#102—431no—
422#102—431no—
423#102—431no—
424#102—431no—
425#102—431no—
426#102—431no—
427C22⋊C8—21no—
428C22⋊C8—431no—
429C22⋊C8—431no—
430C22⋊C8—431no—
431C22⋊C8—431no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438#97—21no—
439#97—861no—
440C4×C8—21no—
441C4×C8—431no—
442C4×C8—431no—
443C4×C8—431no—
444C4×C8—431no—
445C4×C8—861no—
446C4×C8C22×D4311yescharacteristic
447C4×C8C22×D4311yescharacteristic
448C24—861no—
449C2×Q8C2×C4×D4311yescharacteristic
450C2×D4—21no—
451C2×D4—431no—
452C2×D4—431no—
453C2×D4—862no—
454C2×D4—861no—
455C2×D4—1721no—
456C2×D4C2×C4×D4311yescharacteristic
457C22×C4—21no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—3441no—
464C22×C4—3441no—
465C22×C4C2×C4×D4311yescharacteristic
466C22×C4D4×D4311yescharacteristic
467C22×C4#1062190011yescharacteristic
468SD16—862no—
469SD16—1721no—
470D8—862no—
471D8—1721no—
472M16—3441no—
473M16—3441no—
474M16—3441no—
475C2×C8—24no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—431no—
487C2×C8—431no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—3441no—
491C2×C8—3441no—
492C2×C8—3441no—
493C2×C8—3441no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—431no—
499C4⋊C4—431no—
500C4⋊C4—861no—
501C4⋊C4C2×C4×D4311yescharacteristic
502C4⋊C4C2×C4×D4311yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—861no—
509C22⋊C4—861no—
510C22⋊C4—861no—
511C22⋊C4—861no—
512C42—21no—
513C42C2×C4×D4311yescharacteristic
514C42D4×D4311yescharacteristic
515C42#1062190011yescharacteristic
516C42C23×D4311yescharacteristic
517C23—21no—
518C23—861no—
519C23—861no—
520C23—3441no—
521C23—1722no—
522C23—1722no—
523C23(C22⋊D43)⋊C411yescharacteristic
524Q8—21no—
525Q8—21no—
526D4—21no—
527D4—21no—
528D4—42no—
529D4—432no—
530D4—861no—
531D4—861no—
532D4—861no—
533D4—1722no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—3441no—
547C2×C4—3441no—
548C2×C4—3441no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4(C22⋊D43)⋊C411yescharacteristic
554C2×C4(C22⋊D43)⋊C411yescharacteristic
555C2×C4(C22⋊D43)⋊C411yescharacteristic
556C2×C4C22×C4×D4311yescharacteristic
557C2×C4C2×D4×D4311yescharacteristic
558C2×C4C2×#1062190011yescharacteristic
559C8—22no—
560C8—22no—
561C8—41no—
562C8—41no—
563C8—861no—
564C8—861no—
565C8—861no—
566C8—861no—
567C8—861no—
568C8—861no—
569C8—861no—
570C8—861no—
571C8—1721no—
572C8—1721no—
573C22—21no—
574C22—21no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—862no—
579C22—3444no—
580C22—1721no—
581C22—1721no—
582C22—1721no—
583C22—1721no—
584C22—1721no—
585C22#1458301312yes—
586C22C2×(C22⋊D43)⋊C411yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—1721no—
595C4—1721no—
596C4#131×D4311yescharacteristic
597C4#1458366411yescharacteristic
598C4#1458370111yescharacteristic
599C4#1458370611yescharacteristic
600C2—22no—
601C2—81no—
602C2—3441no—
603C2—1722no—
604C2#1914332511yescharacteristic
605C2#1914343011yescharacteristic
606C2C2×#1458301311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1494C2
socleC22×C43C2×C4×D4
prime radical#14583032C4
cosocleC42×C43C24
hypercenter#1494D43
hypocenterC43#18014
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #19143755C2semidirect
3. #19143632C2semidirect
4. #19133482C2semidirect
5. #19133477C2semidirect
6. #19133470C2semidirect
7. #19133462C2semidirect
8. #19133456C2semidirect
9. #19133455C2semidirect
10. #19133392C2semidirect
11. #19133387C2semidirect
12. #19133381C2semidirect
13. C2×#14582628C2semidirect
14. #19132878C2semidirect
15. C43×#1494C2semidirect
25. #14583030C22semidirect
26. Q8×C43⋊C8C22semidirect
31. #14582977C22semidirect
38. D4×C43⋊C8C22semidirect
48. #14582651C22semidirect
49. #14582651C22semidirect
50. #14582649C22semidirect
51. #14582649C22semidirect
56. #14582620C22semidirect
57. #14582620C22semidirect
58. C8×C43⋊C8C22semidirect
59. C8×C43⋊C8C22semidirect
63. C43×Q8⋊C8C22semidirect
64. C43×Q8⋊C8C22semidirect
65. C43×D4⋊C8C22semidirect
66. C43×D4⋊C8C22semidirect
309. #1494D43semidirect
358. Q8⋊C8C2×D43semidirect
359. Q8⋊C8C2×D43semidirect
364. D4⋊C8C2×D43semidirect
365. D4⋊C8C2×D43semidirect
370. C43#18014semidirect

Maximal subgroups

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

subgroupindex
#191446382
#191437552
#191436322
#191334822
#191334772
#191334702
#191334622
#191334562
#191334552
#191333922
#191333872
#191333812
C2×#145826282
#191328782
C43×#14942
#1801443