Finite Group Databasebeta

← #25067629

Subgroups — #25067629

Order 11008.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144638C211yesmaximal, characteristic
2M16×D172C211yesmaximal, characteristic, complemented
3#19133507C211yesmaximal, characteristic, complemented
4#19133485C211yesmaximal, characteristic, complemented
5#19133473C211yesmaximal, characteristic, complemented
6#19133457C211yesmaximal, characteristic, complemented
7#19133429C211yesmaximal, characteristic, complemented
8#19133424C211yesmaximal, characteristic, complemented
9#19133405C211yesmaximal, characteristic, complemented
10C8×#10621882C211yesmaximal, characteristic, complemented
11#19133383C211yesmaximal, characteristic, complemented
12#19133060C211yesmaximal, characteristic, complemented
13#19132985C211yesmaximal, characteristic, complemented
14#19132892C211yesmaximal, characteristic, complemented
15C43×#2969C211yesmaximal, characteristic, complemented
16C2×M16×D43—21no—
17C2×C4×D172C2211yescharacteristic
18#14583232C411yescharacteristic
19#14583215C411yescharacteristic
20#14583196C411yescharacteristic
21#14583196C411yescharacteristic
22#14583111C411yescharacteristic
23#14583111C411yescharacteristic
24#14583049C411yescharacteristic
25#14583032C411yescharacteristic
26C4×#10621884C2211yescharacteristic
27C4×#10621884C2211yescharacteristic
28C4×#10621882C2211yescharacteristic
29C4×#10621882C2211yescharacteristic
30#14582978C2211yescharacteristic
31#14582978C2211yescharacteristic
32#14582972—21no—
33#14582972—21no—
34C8×D172C2211yescharacteristic
35C8×D172C2211yescharacteristic
36#14582952C2211yescharacteristic
37#14582952C2211yescharacteristic
38#14582923C2211yescharacteristic
39#14582862—21no—
40#14582651C2211yescharacteristic, complemented
41#14582651C2211yescharacteristic, complemented
42#14582649C2211yescharacteristic, complemented
43#14582649C2211yescharacteristic, complemented
44Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
45Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
46D4⋊(C43⋊C8)C2211yescharacteristic, complemented
47D4⋊(C43⋊C8)C2211yescharacteristic, complemented
48#14582626C2211yescharacteristic
49#14582626C2211yescharacteristic
50#14582626C2211yescharacteristic
51#14582626C2211yescharacteristic
52#14582621C2211yescharacteristic, complemented
53#14582621C2211yescharacteristic, complemented
54#14582620C2211yescharacteristic, complemented
55C8×C43⋊C8C2211yescharacteristic, complemented
56C43×#529C2211yescharacteristic
57C43×#446C2211yescharacteristic, complemented
58C8×Q8×C43C2211yescharacteristic, complemented
59C43×#436—21no—
60C43×#436C2211yescharacteristic, complemented
61C43×#435—21no—
62C8×D4×C43C2211yescharacteristic, complemented
63C43×#433—21no—
64C43×#431C2211yescharacteristic
65C43×#405—21no—
66C4×M16×C43C2211yescharacteristic
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—
76M16×D43—44no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79C4×D172—21no—
80C4×D172—21no—
81C4×D172C2×C411yescharacteristic
82C4×D172C2×C411yescharacteristic
83C4×D172C2311yescharacteristic
84C4×D172C2311yescharacteristic
85C2×C4⋊Dic43C2×C411yescharacteristic
86C2×(C2×D43)⋊C4—21no—
87#13063258C2×C411yescharacteristic
88#13063258C2×C411yescharacteristic
89#13063256C2×C411yescharacteristic
90#13063256C2×C411yescharacteristic
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)C2×C411yescharacteristic
94C4⋊(C43⋊C8)C2×C411yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063249C2×C411yescharacteristic
98#13063249C2×C411yescharacteristic
99#13063246C2×C411yescharacteristic
100#13063246C2×C411yescharacteristic
101#13063245C2×C411yescharacteristic
102#13063245C2×C411yescharacteristic
103#13063245C2×C411yescharacteristic
104#13063245C2×C411yescharacteristic
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)C2×C411yescharacteristic
107C22⋊(C43⋊C8)C2×C411yescharacteristic
108(C2×D43)⋊C8—21no—
109(C2×D43)⋊C8—21no—
110(C2×D43)⋊C8—21no—
111(C2×D43)⋊C8—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C2×M16×C43—21no—
117C2×M16×C43D411yescharacteristic
118C2×M16×C43D411yescharacteristic
119C22×C8×C43—21no—
120#126×C43—21no—
121#125×C43C2×C411yescharacteristic
122#124×C43C2×C411yescharacteristic
123#123×C43—21no—
124C22⋊Q8×C43C2×C411yescharacteristic
125#121×C43C2×C411yescharacteristic
126C4×Q8×C43C2311yescharacteristic
127C4×D4×C43—21no—
128C4×D4×C43C2311yescharacteristic
129#117×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—21no—
132C4⋊C8×C43—21no—
133C4⋊C8×C43C2311yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138#97×C43—21no—
139#97×C43D411yescharacteristic
140#97×C43D411yescharacteristic
141C4×C8×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C2×Q8×C43C22×C411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C22×C411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43#4111yescharacteristic
153C22×Dic43—21no—
154C2×D172—21no—
155C2×D172—22no—
156C2×D172—41no—
157C2×D172C22×C411yescharacteristic
158C2×D172C22×C411yescharacteristic
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165M16×C43—22no—
166M16×C43—41no—
167M16×C43—42no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—42no—
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43C22×C411yescharacteristic
180C4⋊C4×C43C22×C411yescharacteristic
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C42×C43—21no—
187C42×C43C22×C411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43#4111yescharacteristic
190C42×C43C2411yescharacteristic
191#10621884—22no—
192#10621884—41no—
193#10621882—22no—
194#10621882—41no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—21no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43C22×C411yescharacteristic
201C4⋊Dic43C22×C411yescharacteristic
202#10621877—42no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8C22×C411yescharacteristic
208C2×C43⋊C8C22×C411yescharacteristic
209C2×C43⋊C8C22×C411yescharacteristic
210C2×C43⋊C8C22×C411yescharacteristic
211#10621872—42no—
212#10621872—42no—
213C8×D43—42no—
214C8×D43—42no—
215C23×C43—21no—
216C23×C43C4×D411yescharacteristic
217C22×D43—21no—
218C22×D43—21no—
219C22×D43—42no—
220C22×D43—42no—
221C22×D43—81no—
222Q8×C43—21no—
223Q8×C43—21no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—81no—
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—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43C4×D411yescharacteristic
238C2×C4×C43C4×D411yescharacteristic
239C2×C4×C43C4×D411yescharacteristic
240C2×C4×C43C23×C411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—42no—
246D172—21no—
247D172—21no—
248D172—21no—
249D172—42no—
250D172#13112yes—
251C4×D43—42no—
252C4×D43—42no—
253C4×D43—41no—
254C4×D43—41no—
255C4×D43—41no—
256C4×D43—41no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43AGL(1,ℤ/8)12yes—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—21no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271#18006—431nomaximal, Sylow
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43C2×C4×D411yescharacteristic
279C2×D43—22no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—84no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43C2×#13111yescharacteristic
294C4×C43#56811yescharacteristic
295C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
296C4×C43#57511yescharacteristic
297Dic43—41no—
298Dic43—41no—
299#3105—431no—
300#2969D4311yescharacteristic, complemented
301D4×M16—431no—
302#1594—431no—
303#1590—431no—
304#1588—431no—
305#1586—431no—
306#1582—431no—
307#1581—431no—
308SD16⋊C8—431no—
309C8×D8—431no—
310#1574—431no—
311#1495—431no—
312#1478—431no—
313#1453—431no—
314C2×C43—41no—
315C2×C43—81no—
316C2×C43#293311yescharacteristic
317C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
318C2×C43#295711yescharacteristic
319D43—42no—
320D43—81no—
321C22×M16—861no—
322#529C2×D4311yescharacteristic
323C2×C4×D4—431no—
324#484—431no—
325#481—431no—
326#478—431no—
327#478—431no—
328#463—431no—
329#463—431no—
330#450—431no—
331#447—431no—
332#446C2×D4311yescharacteristic, complemented
333C8×Q8C2×D4311yescharacteristic, complemented
334C4×SD16—431no—
335C4×SD16—431no—
336C4×D8—431no—
337C4×D8—431no—
338#436—21no—
339#436—431no—
340#436—431no—
341#436C2×D4311yescharacteristic, complemented
342#435—21no—
343#435—861no—
344#435—861no—
345C8×D4—431no—
346C8×D4—431no—
347C8×D4C2×D4311yescharacteristic, complemented
348#433—21no—
349#431—431no—
350#431—431no—
351#431C2×D4311yescharacteristic
352#423—431no—
353#407—861no—
354#405—21no—
355C4×M16C2×D4311yescharacteristic
356#335—431no—
357#335—431no—
358#334—431no—
359#334—431no—
360Q8⋊C8—431no—
361Q8⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8—431no—
364D4⋊C8—431no—
365D4⋊C8—431no—
366D4⋊C8—431no—
367D4⋊C8—431no—
368#322—431no—
369#322—431no—
370#322—431no—
371C82—431no—
372C43#1800611yescharacteristic, complemented, Sylow
373C22×D4—431no—
374C23×C4—861no—
375C2×SD16—431no—
376C2×SD16—431no—
377C2×D8—431no—
378C2×D8—431no—
379C2×M16—21no—
380C2×M16—861no—
381C2×M16—861no—
382C2×M16—861no—
383C2×M16—1724no—
384C2×M16C22⋊D4311yescharacteristic
385C2×M16C22⋊D4311yescharacteristic
386C22×C8—21no—
387C22×C8—861no—
388C22×C8—861no—
389#126—21no—
390#125C4×D4311yescharacteristic
391#124C4×D4311yescharacteristic
392#123—21no—
393C22⋊Q8C4×D4311yescharacteristic
394#121C4×D4311yescharacteristic
395C4×Q8C22×D4311yescharacteristic
396C4×D4—21no—
397C4×D4—431no—
398C4×D4—431no—
399C4×D4—431no—
400C4×D4—431no—
401C4×D4—861no—
402C4×D4—861no—
403C4×D4C22×D4311yescharacteristic
404#117—21no—
405C2×C4⋊C4—431no—
406C2×C22⋊C4—861no—
407C2×C42C22×D4311yescharacteristic
408#107—431no—
409#107—431no—
410#106—431no—
411#106—431no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—431no—
417C4⋊C8—431no—
418C4⋊C8—861no—
419C4⋊C8—861no—
420C4⋊C8C22×D4311yescharacteristic
421C4⋊C8C22×D4311yescharacteristic
422#103—431no—
423#103—431no—
424#102—431no—
425#102—431no—
426#102—431no—
427#102—431no—
428#102—431no—
429#102—431no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8—431no—
434C22⋊C8—431no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439C22⋊C8—861no—
440#97—21no—
441#97C22⋊D4311yescharacteristic
442#97C22⋊D4311yescharacteristic
443C4×C8—21no—
444C4×C8—21no—
445C4×C8—431no—
446C4×C8—431no—
447C4×C8—431no—
448C4×C8—431no—
449C4×C8C22×D4311yescharacteristic
450C4×C8C22×D4311yescharacteristic
451C24—861no—
452C2×Q8C2×C4×D4311yescharacteristic
453C2×D4—21no—
454C2×D4—431no—
455C2×D4—431no—
456C2×D4—862no—
457C2×D4—861no—
458C2×D4—1721no—
459C2×D4C2×C4×D4311yescharacteristic
460C22×C4—21no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—1722no—
467C22×C4—1722no—
468C22×C4C2×C4×D4311yescharacteristic
469C22×C4#1062189811yescharacteristic
470C22×C4C2×C22⋊D4311yescharacteristic
471SD16—862no—
472SD16—1721no—
473D8—862no—
474D8—1721no—
475M16—22no—
476M16—41no—
477M16—42no—
478M16—1722no—
479M16—1722no—
480M16—1722no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—42no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—431no—
487C2×C8—431no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—1722no—
493C2×C8—1722no—
494C2×C8C2×C22⋊D4311yescharacteristic
495C2×C8C2×C22⋊D4311yescharacteristic
496C2×C8C2×C22⋊D4311yescharacteristic
497C2×C8C2×C22⋊D4311yescharacteristic
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—431no—
503C4⋊C4—431no—
504C4⋊C4—861no—
505C4⋊C4C2×C4×D4311yescharacteristic
506C4⋊C4C2×C4×D4311yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—861no—
513C22⋊C4—861no—
514C22⋊C4—861no—
515C22⋊C4—861no—
516C42—21no—
517C42C2×C4×D4311yescharacteristic
518C42#1062189811yescharacteristic
519C42C2×C22⋊D4311yescharacteristic
520C42C23×D4311yescharacteristic
521C23—21no—
522C23—861no—
523C23—861no—
524C23—3441no—
525C23—1722no—
526C23—1722no—
527C23C4×C22⋊D4311yescharacteristic
528Q8—21no—
529Q8—21no—
530D4—21no—
531D4—21no—
532D4—81no—
533D4—432no—
534D4—861no—
535D4—861no—
536D4—861no—
537D4—1722no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—1722no—
551C2×C4—1722no—
552C2×C4—1722no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4C4×C22⋊D4311yescharacteristic
558C2×C4C4×C22⋊D4311yescharacteristic
559C2×C4C4×C22⋊D4311yescharacteristic
560C2×C4C22×C4×D4311yescharacteristic
561C2×C4C22×C22⋊D4311yescharacteristic
562C2×C4C2×#1062189811yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—861no—
569C8—861no—
570C8—861no—
571C8—861no—
572C8—1721no—
573C8—1721no—
574C8—1721no—
575C8—1721no—
576C8#1306335012yes—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—862no—
584C22—3444no—
585C22—1721no—
586C22—1721no—
587C22—1721no—
588C22—1721no—
589C22—1721no—
590C22C2×C4×C22⋊D4311yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—1721no—
599C4—1721no—
600C4#131×D4311yescharacteristic
601C4#1458366411yescharacteristic
602C4C2×#1306335011yescharacteristic
603C4#1458369711yescharacteristic
604C2—41no—
605C2—81no—
606C2—3441no—
607C2—1722no—
608C2#1914331711yescharacteristic
609C2C4×#1306335011yescharacteristic
610C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2969C2
socleC22×C43C2×C4×D4
prime radical#14583032C4
cosocleC42×C43C24
hypercenter#2969D43
hypocenterC43#18006
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. M16×D172C2semidirect
3. #19133507C2semidirect
4. #19133485C2semidirect
5. #19133473C2semidirect
6. #19133457C2semidirect
7. #19133429C2semidirect
8. #19133424C2semidirect
9. #19133405C2semidirect
10. C8×#10621882C2semidirect
11. #19133383C2semidirect
12. #19133060C2semidirect
13. #19132985C2semidirect
14. #19132892C2semidirect
15. C43×#2969C2semidirect
40. #14582651C22semidirect
41. #14582651C22semidirect
42. #14582649C22semidirect
43. #14582649C22semidirect
44. Q8⋊(C43⋊C8)C22semidirect
45. Q8⋊(C43⋊C8)C22semidirect
46. D4⋊(C43⋊C8)C22semidirect
47. D4⋊(C43⋊C8)C22semidirect
52. #14582621C22semidirect
53. #14582621C22semidirect
54. #14582620C22semidirect
55. C8×C43⋊C8C22semidirect
57. C43×#446C22semidirect
58. C8×Q8×C43C22semidirect
60. C43×#436C22semidirect
62. C8×D4×C43C22semidirect
300. #2969D43semidirect
332. #446C2×D43semidirect
333. C8×Q8C2×D43semidirect
341. #436C2×D43semidirect
347. C8×D4C2×D43semidirect
372. C43#18006semidirect

Maximal subgroups

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

subgroupindex
#191446382
M16×D1722
#191335072
#191334852
#191334732
#191334572
#191334292
#191334242
#191334052
C8×#106218822
#191333832
#191330602
#191329852
#191328922
C43×#29692
#1800643