Finite Group Databasebeta

← #25118849

Subgroups — #25118849

Order 11008.

1030 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583103C211yesmaximal, characteristic
2C2×C4×#10621884C211yesmaximal, characteristic
3C2×#14582986C211yesmaximal, characteristic
4#19137649C211yesmaximal, characteristic, complemented
5#19137496C211yesmaximal, characteristic
6#19135395C211yesmaximal, characteristic, complemented
7#19135355C211yesmaximal, characteristic, complemented
8#19135273C211yesmaximal, characteristic, complemented
9#19135270C211yesmaximal, characteristic, complemented
10#19134928C211yesmaximal, characteristic
11#19134926C211yesmaximal, characteristic
12#19134864C211yesmaximal, characteristic, complemented
13#19134456C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic
15C43×#1865C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063323C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23C2×C4⋊C4×D43—21no—
24#14583103C418yescomplemented
25C4×#10621884—24no—
26#14582986—24no—
27C2×#13063256C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×C4×C43⋊C8C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37C2×C8×Dic43C2211yescharacteristic
38#14582806C2211yescharacteristic
39#14582805C2211yescharacteristic
40#14582798C2211yescharacteristic
41#14582794—21no—
42#14582783—21no—
43#14582780—21no—
44#14582773—21no—
45#14582770—21no—
46#14582768C2211yescharacteristic
47#14582758—21no—
48C4⋊C4×Dic43C2211yescharacteristic
49C4×Dic43⋊C4—21no—
50C4×Dic43⋊C4C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C2×#10621873—22no—
68C2×#10621873—22no—
69C2×#10621873C2×C414yes—
70C2×#10621884—22no—
71C2×#10621884—22no—
72C2×#10621884C2×C414yes—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063323—22no—
76#13063323C2×C414yescomplemented
77#13063290—22no—
78#13063290—41no—
79C4×D172—22no—
80C4×D172—41no—
81#13063287—22no—
82#13063287—22no—
83#13063287—41no—
84#13063287C2×C414yes—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4D411yescharacteristic
94C2×Dic43⋊C4D411yescharacteristic
95C4⋊C4×D43—44no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43C2311yescharacteristic
102C2×C4×Dic43C2311yescharacteristic
103#13063256—22no—
104Dic43⋊C8C2×C414yescomplemented
105#13063250—41no—
106#13063249—22no—
107#13063248—22no—
108#13063248C2×C414yescomplemented
109#13063247—22no—
110#13063245D414yes—
111C4×C43⋊C8—22no—
112C8×Dic43—22no—
113C8×Dic43—22no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95D411yescharacteristic
121C43⋊#95D411yescharacteristic
122C22×Q8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C4×Q8×C43—22no—
126C4×Q8×C43—41no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#106×C43—22no—
135#103×C43—41no—
136#103×C43C2×C414yescomplemented
137#95×C43—21no—
138C23×D43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43C22×C412yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172C22×C412yes—
163C2×D172C2×D412yes—
164C2×D172#4112yes—
165C2×C4×D43—24no—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
168C2×C4×D43—42no—
169C2×C4×D43—42no—
170C2×C4×D43—42no—
171C2×C4×D43—42no—
172C2×C4×D43—81no—
173C2×C4×D43—81no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86C22×C412yes—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43C22×C412yes—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—42no—
191C4⋊C4×C43—42no—
192C4⋊C4×C43C22×C412yes—
193C4⋊C4×C43C2×D412yes—
194C42×C43—21no—
195C42×C43—21no—
196C42×C43—42no—
197#10621884—28no—
198(C2×D43)⋊C4—24no—
199(C2×D43)⋊C4—42no—
200(C2×D43)⋊C4—42no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—42no—
206Dic43⋊C4—24no—
207Dic43⋊C4—24no—
208Dic43⋊C4—22no—
209Dic43⋊C4—42no—
210Dic43⋊C4—42no—
211Dic43⋊C4—81no—
212Dic43⋊C4SD1614yescomplemented
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—42no—
216C4×Dic43—42no—
217C4×Dic43C22×C412yes—
218C4×Dic43#4112yes—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8C22×C412yes—
224C2×C43⋊C8C2×D412yes—
225#10621873—28no—
226C23×C43C22×D411yescharacteristic
227C22×D43—22no—
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234Q8×C43—22no—
235Q8×C43—22no—
236Q8×C43—41no—
237Q8×C43—41no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43C2×SD1612yes—
256C2×C4×C43C23×C411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C2×C4×C432−1+411yescharacteristic
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—22no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43C4×D412yes—
279C2×Dic43C4×D412yes—
280C2×Dic43C2×SD1612yes—
281C2×Dic43C2×SD1612yes—
282C2×Dic43#13512yes—
283D172—22no—
284D172—22no—
285D172—22no—
286D172C4×D414yes—
287C4×D43—48no—
288C4×D43—84no—
289C4×D43—84no—
290Dic86—22no—
291Dic86—22no—
292Dic86—41no—
293Dic86—41no—
294C8×C43—22no—
295C8×C43—41no—
296C43⋊C8—22no—
297C43⋊C8—22no—
298#22996—431nomaximal, Sylow
299C22×C43C2×C4×D411yescharacteristic
300C22×C43D4211yescharacteristic
301C22×C43#54811yescharacteristic
302C22×C43C22×SD1611yescharacteristic
303C22×C43C2×#13511yescharacteristic
304C22×C43#57711yescharacteristic
305C22×C43#57811yescharacteristic
306C2×D43—24no—
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—42no—
311C2×D43—42no—
312C2×D43—42no—
313C4×C43—22no—
314C4×C43—42no—
315C4×C43—42no—
316C4×C43—41no—
317C4×C43—42no—
318C4×C43—81no—
319C4×C43C2×C4×D411yescharacteristic
320C4×C43#52011yescharacteristic
321C4×C43#54711yescharacteristic
322C4×C43#55311yescharacteristic
323Dic43—22no—
324Dic43—22no—
325Dic43—42no—
326Dic43—41no—
327Dic43—81no—
328Dic43—81no—
329Dic43C4×SD1614yescomplemented
330C2×#461—431no—
331C2×C4×SD16—431no—
332C2×C4×SD16—431no—
333#2365—431no—
334D4×C4⋊C4—431no—
335#1956—431no—
336#1948—431no—
337#1933—431no—
338#1933—431no—
339#1877—431no—
340#1877—431no—
341#1865—431no—
342#1865D4311yescharacteristic, complemented
343C8×C4⋊C4—431no—
344C4×#102—431no—
345C2×C43#236111yescharacteristic
346C2×C43C2×C4×SD1611yescharacteristic
347C2×C43#294711yescharacteristic
348C2×C43D4×SD1611yescharacteristic
349C2×C43#328311yescharacteristic
350C2×C43#335911yescharacteristic
351C2×C43#336011yescharacteristic
352D43—44no—
353C22×SD16—431no—
354C22×SD16—431no—
355C2×C4⋊Q8—431no—
356C2×C4×Q8—431no—
357C2×C4×Q8C2×D4311yescharacteristic
358C2×C4×D4—431no—
359C2×C4×D4—431no—
360C2×C4×D4—431no—
361C22×C4⋊C4—861no—
362#461—438no—
363C4×SD16—864no—
364C4×SD16—864no—
365C2×#106—431no—
366C2×#106C2×D4311yescharacteristic
367C2×C4⋊C8—431no—
368C2×#103—431no—
369C2×#103—431no—
370C2×#103—431no—
371C2×#103—431no—
372C2×#103C2×D4311yescharacteristic
373C2×#103C2×D4311yescharacteristic
374C2×#102—431no—
375C2×#102—431no—
376C2×C4×C8—431no—
377C2×C4×C8—431no—
378C2×C4×C8—431no—
379#391—431no—
380#391—431no—
381#389—431no—
382#389—861no—
383#389C2×D4311yescharacteristic
384#387—861no—
385#387—861no—
386#385—861no—
387#385—861no—
388#384—431no—
389#380—861no—
390C4×C4⋊C4—431no—
391C4×C4⋊C4—431no—
392C4×C4⋊C4—861no—
393#340—431no—
394#340—431no—
395#340—431no—
396#340C2×D4311yescharacteristic
397#336—431no—
398#336C2×D4311yescharacteristic
399C43#2299611yescharacteristic, complemented, Sylow
400C22×Q8—431no—
401C22×Q8C22×D4311yescharacteristic
402C22×D4—431no—
403C23×C4—861no—
404C23×C4—861no—
405C23×C4—861no—
406C2×SD16—434no—
407C2×SD16—434no—
408C2×SD16—862no—
409C2×SD16—862no—
410C2×SD16—862no—
411C2×SD16—862no—
412C22×C8—431no—
413C22×C8—431no—
414C22×C8C22×D4311yescharacteristic
415C22×C8C22×D4311yescharacteristic
416C4⋊Q8—434no—
417C4⋊Q8—862no—
418C4×Q8—22no—
419C4×Q8—41no—
420C4×Q8—862no—
421C4×Q8—1721no—
422C4×D4—434no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—1721no—
427C4×D4—1721no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—1724no—
441C2×C4⋊C4C22×D4311yescharacteristic
442C2×C4⋊C4C22×D4311yescharacteristic
443C2×C4⋊C4C22×D4311yescharacteristic
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C42—21no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—861no—
451C2×C42—861no—
452C2×C42C22×D4311yescharacteristic
453#106—22no—
454#106—862no—
455C4⋊C8—434no—
456#103—41no—
457#103—434no—
458#103—862no—
459#103—862no—
460#103—1721no—
461#103C4×D4314yescomplemented
462#102—434no—
463#102—862no—
464C4×C8—862no—
465C4×C8—862no—
466C4×C8—862no—
467#95—21no—
468#95—431no—
469#95—431no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476C24—861no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—432no—
483C2×Q8—861no—
484C2×Q8—861no—
485C2×Q8—861no—
486C2×Q8—861no—
487C2×Q8—861no—
488C2×Q8C2×C4×D4312yes—
489C2×D4—432no—
490C2×D4—432no—
491C2×D4—432no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—864no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—3441no—
508C22×C4—3441no—
509C22×C4—1722no—
510C22×C4—1722no—
511C22×C4—1722no—
512C22×C4—1722no—
513C22×C4—1722no—
514C22×C4—1722no—
515C22×C4D4×D4311yescharacteristic
516C22×C4D4×D4311yescharacteristic
517C22×C4C23×D4311yescharacteristic
518SD16—868no—
519SD16—868no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—432no—
526C2×C8—432no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8C2×C4×D4312yes—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—434no—
539C4⋊C4—862no—
540C4⋊C4—864no—
541C4⋊C4—864no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—3441no—
547C4⋊C4—1722no—
548C4⋊C4—1722no—
549C4⋊C4—1722no—
550C4⋊C4C2×C4×D4312yes—
551C4⋊C4D4×D4312yes—
552C22⋊C4—864no—
553C22⋊C4—1722no—
554C22⋊C4—1722no—
555C42—21no—
556C42—21no—
557C42—42no—
558C42—432no—
559C42—432no—
560C42—861no—
561C42—861no—
562C42—1722no—
563C42—1722no—
564C23—862no—
565C23—862no—
566C23—862no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23—1721no—
571C23C2×D4×D4311yescharacteristic
572Q8—22no—
573Q8—22no—
574Q8—41no—
575Q8—41no—
576Q8—862no—
577Q8—862no—
578Q8—1721no—
579Q8—1721no—
580D4—434no—
581D4—862no—
582D4—862no—
583D4—862no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—432no—
602C2×C4—432no—
603C2×C4—432no—
604C2×C4—432no—
605C2×C4—432no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—862no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—3444no—
615C2×C4—3444no—
616C2×C4—1728no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4SD16×D4312yes—
626C2×C4C22×C4×D4311yescharacteristic
627C2×C4C2×D4×D4311yescharacteristic
628C2×C4#41×D4311yescharacteristic
629C2×C4#41×D4311yescharacteristic
630C2×C4#1306337011yescharacteristic
631C2×C4#1306337311yescharacteristic
632C8—22no—
633C8—41no—
634C8—862no—
635C8—862no—
636C22—864no—
637C22—1722no—
638C22—1722no—
639C22—1722no—
640C22—1722no—
641C22—1722no—
642C22—1722no—
643C22C4×D4×D4311yescharacteristic
644C22#1458353111yescharacteristic
645C22#1458355911yescharacteristic
646C22C2×SD16×D4311yescharacteristic
647C22#135×D4311yescharacteristic
648C22#1458370811yescharacteristic
649C22#1458371511yescharacteristic
650C4—22no—
651C4—41no—
652C4—42no—
653C4—42no—
654C4—42no—
655C4—81no—
656C4—434no—
657C4—862no—
658C4—862no—
659C4—3441no—
660C4—3441no—
661C4—1721no—
662C4—1722no—
663C4C4×D4×D4311yescharacteristic
664C4#1458338011yescharacteristic
665C4#1458355111yescharacteristic
666C4#1458359411yescharacteristic
667C2—1724no—
668C2#1913761411yescharacteristic
669C2C4×SD16×D4311yescharacteristic
670C2#1914343711yescharacteristic
671C2#1914628411yescharacteristic
672C2#1914631011yescharacteristic
673C2#1914723611yescharacteristic
674C2#1914724711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1865C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1865D43
hypocenterC43#22996
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
4. #19137649C2semidirect
6. #19135395C2semidirect
7. #19135355C2semidirect
8. #19135273C2semidirect
9. #19135270C2semidirect
12. #19134864C2semidirect
13. #19134456C2semidirect
15. C43×#1865C2semidirect
24. #14583103C4semidirect
76. #13063323C2×C4semidirect
104. Dic43⋊C8C2×C4semidirect
108. #13063248C2×C4semidirect
136. #103×C43C2×C4semidirect
212. Dic43⋊C4SD16semidirect
329. Dic43C4×SD16semidirect
342. #1865D43semidirect
399. C43#22996semidirect
461. #103C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831032
C2×C4×#106218842
C2×#145829862
#191376492
#191374962
#191353952
#191353552
#191352732
#191352702
#191349282
#191349262
#191348642
#191344562
#191344092
C43×#18652
#2299643