Finite Group Databasebeta

← #25199436

Subgroups — #25199436

Order 11008.

868 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063299C211yesmaximal, characteristic
2#19136026C211yesmaximal, characteristic, complemented
3#19135795C211yesmaximal, characteristic, complemented
4#19135784C211yesmaximal, characteristic
5#19135596C211yesmaximal, characteristic
6#19135226C211yesmaximal, characteristic, complemented
7#19135215C211yesmaximal, characteristic, complemented
8#19135180C211yesmaximal, characteristic, complemented
9#19135163C211yesmaximal, characteristic, complemented
10#19134950C211yesmaximal, characteristic, complemented
11#19134932C211yesmaximal, characteristic, complemented
12#19134849C211yesmaximal, characteristic, complemented
13#19134841C211yesmaximal, characteristic, complemented
14#19134663C211yesmaximal, characteristic, complemented
15C4×C22⋊Q8×C43C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063299C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×C4×C22⋊D43—21no—
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31#14582801C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582790—21no—
34#14582778—21no—
35#14582759C2211yescharacteristic
36C4×C4⋊Dic43C2211yescharacteristic
37C4×(C2×D43)⋊C4—21no—
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C22⋊Q8×C43C2211yescharacteristic
49C2×C4×Q8×C43C2211yescharacteristic
50C22×C42×C43C2211yescharacteristic
51C43×#391C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#387—21no—
54C43×#385—21no—
55C43×#380C2211yescharacteristic
56C4×C4⋊C4×C43—21no—
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C22⋊C4×C43—21no—
59C22×D172C2311yescharacteristic
60C22×C22⋊D43—21no—
61C22×C4×D43—21no—
62C2×#10621884—22no—
63C2×#10621884—22no—
64C2×#10621884—41no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063299—22no—
70#13063299—22no—
71C4×D172—41no—
72C4×D172—41no—
73C4×C22⋊D43—44no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×C4×Dic43—21no—
84#13063258—22no—
85#13063258—41no—
86#13063256—22no—
87#13063249—22no—
88#13063249—22no—
89#13063249—41no—
90#13063245—22no—
91#13063245—22no—
92#13063245—41no—
93C22⋊(C43⋊C8)—41no—
94C22⋊(C43⋊C8)—41no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C22×Q8×C43C2311yescharacteristic
99C23×C4×C43D411yescharacteristic
100C23×C4×C43D411yescharacteristic
101C23×C4×C43C2311yescharacteristic
102C22⋊Q8×C43—22no—
103C22⋊Q8×C43—22no—
104C4×Q8×C43—41no—
105C4×Q8×C43—41no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C42×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43—41no—
117C2×C42×C43—41no—
118C2×C42×C43D411yescharacteristic
119C2×C42×C43D411yescharacteristic
120C2×C42×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127C24×C43C2×D411yescharacteristic
128C23×D43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43#4112yes—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—22no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—41no—
149C22×C4×C43—41no—
150C22×C4×C43—41no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C2×C22⋊D43—24no—
158C2×C22⋊D43—42no—
159C2×C22⋊D43—42no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172#4112yes—
169C2×C4×D43—42no—
170C2×C4×D43—42no—
171C2×C4×D43—42no—
172C4⋊C4×C43—24no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—42no—
179C4⋊C4×C43—42no—
180C4⋊C4×C43#4112yes—
181C22⋊C4×C43—24no—
182C22⋊C4×C43—42no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—41no—
188C42×C43—41no—
189C42×C43—42no—
190C42×C43—42no—
191C22⋊Dic43—42no—
192#10621884—44no—
193(C2×D43)⋊C4—24no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—42no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43#4112yes—
203Dic43⋊C4—42no—
204C4×Dic43—42no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43#13712yes—
224C23×C43C22×D411yescharacteristic
225C22×D43—22no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232Q8×C43—22no—
233Q8×C43—22no—
234Q8×C43—41no—
235Q8×C43—41no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—44no—
252C2×C4×C43—44no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43#13512yes—
268C2×C4×C43AGL(1,ℤ/8)12yes—
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C43C2×#4111yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43H(5,𝔽2)11yescharacteristic
274C2×C4×C43H(5,𝔽2)11yescharacteristic
275C22⋊D43—48no—
276C2×Dic43—22no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285D172—22no—
286D172—22no—
287D172—41no—
288D172—41no—
289C4×D43—84no—
290C43⋊C8—41no—
291C43⋊C8—41no—
292C43⋊C8—41no—
293C43⋊C8—41no—
294#29414—431nomaximal, Sylow
295C22×C43—22no—
296C22×C43—22no—
297C22×C43—22no—
298C22×C43—41no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43#52511yescharacteristic
303C22×C43#52511yescharacteristic
304C22×C43#53411yescharacteristic
305C22×C43C2×#13511yescharacteristic
306C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C43C2×#13711yescharacteristic
308C22×C43#57511yescharacteristic
309C2×D43—42no—
310C2×D43—42no—
311C2×D43—42no—
312C2×D43—81no—
313C2×D43—81no—
314C2×D43—81no—
315C2×D43—81no—
316C4×C43—22no—
317C4×C43—22no—
318C4×C43—42no—
319C4×C43—41no—
320C4×C43—42no—
321C4×C43—41no—
322C4×C43—41no—
323C4×C43—81no—
324C4×C43—81no—
325C4×C43#55111yescharacteristic
326C4×C43#55311yescharacteristic
327C4×C43#55311yescharacteristic
328C4×C43#55911yescharacteristic
329Dic43—42no—
330Dic43—81no—
331Dic43—81no—
332C4×C22⋊Q8D4311yescharacteristic, complemented
333C4×#121—431no—
334#2076—431no—
335#2036—431no—
336#2034—431no—
337#2000—431no—
338#1927—431no—
339#1925—431no—
340#1920—431no—
341#1918—431no—
342#1880—431no—
343#1877—431no—
344#1863—431no—
345#1862—431no—
346#1817—431no—
347C2×C43—42no—
348C2×C43#260011yescharacteristic
349C2×C43#310211yescharacteristic
350C2×C43#310611yescharacteristic
351C2×C43#311011yescharacteristic
352C2×C43#311711yescharacteristic
353C2×C43#319011yescharacteristic
354C2×C43#319411yescharacteristic
355D43—82no—
356C22×SD16—431no—
357C2×C22⋊Q8C2×D4311yescharacteristic
358C2×#121—431no—
359C2×C4×Q8C2×D4311yescharacteristic
360C2×C4×D4—431no—
361C2×C4×D4—861no—
362C22×C42C2×D4311yescharacteristic
363C2×#107—431no—
364C2×#107—431no—
365C2×#106—431no—
366C2×#103—431no—
367C2×#103—431no—
368C2×#103—431no—
369C2×#102—431no—
370C2×#102—431no—
371C2×#102—431no—
372C2×C22⋊C8—431no—
373C2×C22⋊C8—431no—
374#391C2×D4311yescharacteristic
375#390—431no—
376#389—431no—
377#389C2×D4311yescharacteristic
378#388—861no—
379#387—21no—
380#386—861no—
381#385—21no—
382#380—431no—
383#380C2×D4311yescharacteristic
384C4×C4⋊C4—21no—
385C4×C4⋊C4—431no—
386C4×C4⋊C4C2×D4311yescharacteristic
387C4×C22⋊C4—21no—
388C4×C22⋊C4—861no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340—431no—
395#336—431no—
396#336—431no—
397#336—431no—
398#336—431no—
399C43#2941411yescharacteristic, complemented, Sylow
400C22×Q8C22×D4311yescharacteristic
401C22×D4—431no—
402C22×D4—861no—
403C23×C4—861no—
404C23×C4C22⋊D4311yescharacteristic
405C23×C4C22⋊D4311yescharacteristic
406C23×C4C22×D4311yescharacteristic
407C2×SD16—862no—
408C2×SD16—862no—
409C2×SD16—1721no—
410C22×C8—431no—
411C22×C8—431no—
412C22×C8—431no—
413C22×C8—431no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416#121—862no—
417#121—862no—
418C4×Q8—41no—
419C4×Q8—41no—
420C4×D4—1721no—
421C4×D4—1721no—
422C4×D4—1724no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—41no—
443C2×C42—41no—
444C2×C42—861no—
445C2×C42C22⋊D4311yescharacteristic
446C2×C42C22⋊D4311yescharacteristic
447C2×C42C22×D4311yescharacteristic
448C2×C42C22×D4311yescharacteristic
449#107—862no—
450#107—1721no—
451#106—862no—
452#103—862no—
453#103—862no—
454#103—1721no—
455#102—862no—
456#102—862no—
457#102—1721no—
458C22⋊C8—1721no—
459C22⋊C8—1721no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—861no—
466#95—861no—
467#95—861no—
468C24—861no—
469C24C2×C22⋊D4311yescharacteristic
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8#1062189812yes—
476C2×D4—432no—
477C2×D4—864no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—1722no—
484C2×D4—1722no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—1722no—
505C22×C4—1722no—
506C22×C4—1722no—
507C22×C4C2×C22⋊D4311yescharacteristic
508C22×C4C2×C22⋊D4311yescharacteristic
509C22×C4C2×C22⋊D4311yescharacteristic
510C22×C4C2×C22⋊D4311yescharacteristic
511C22×C4C2×C22⋊D4311yescharacteristic
512C22×C4C23×D4311yescharacteristic
513SD16—1724no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C4⋊C4—24no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—432no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—1722no—
541C4⋊C4#1062189812yes—
542C22⋊C4—24no—
543C22⋊C4—42no—
544C22⋊C4—864no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C22⋊C4—1722no—
548C22⋊C4—1722no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—41no—
554C42—41no—
555C42—42no—
556C42—42no—
557C42—1722no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—862no—
565C23—1721no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23—1721no—
571C23#1306335612yes—
572C23C22×C22⋊D4311yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577D4—862no—
578D4—862no—
579D4—1728no—
580D4—1721no—
581D4—1721no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—44no—
598C2×C4—44no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—862no—
614C2×C4—3444no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4#1306334512yes—
624C2×C4#1306335012yes—
625C2×C4#41×D4311yescharacteristic
626C2×C4#41×D4311yescharacteristic
627C2×C4C2×#1062189811yescharacteristic
628C2×C4C2×#1062189811yescharacteristic
629C2×C4#1306337011yescharacteristic
630C2×C4#1306337011yescharacteristic
631C8—1721no—
632C8—1721no—
633C8—1721no—
634C8—1721no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—3441no—
643C22—3441no—
644C22—3441no—
645C22—3441no—
646C22—1722no—
647C22—1722no—
648C22—1722no—
649C22#1458340611yescharacteristic
650C22#1458341011yescharacteristic
651C22#1458345811yescharacteristic
652C22C2×#1306334511yescharacteristic
653C22C2×#1306335011yescharacteristic
654C22C2×#1306335611yescharacteristic
655C22#1458369711yescharacteristic
656C4—22no—
657C4—22no—
658C4—41no—
659C4—42no—
660C4—41no—
661C4—41no—
662C4—42no—
663C4—81no—
664C4—81no—
665C4—3441no—
666C4—3441no—
667C4—1722no—
668C4#1458357811yescharacteristic
669C4#1458359811yescharacteristic
670C4#1458359911yescharacteristic
671C4#1458363211yescharacteristic
672C2—42no—
673C2—3442no—
674C2#1914017711yescharacteristic
675C2#1914460711yescharacteristic
676C2#1914465511yescharacteristic
677C2#1914469011yescharacteristic
678C2#1914476611yescharacteristic
679C2#1914537611yescharacteristic
680C2#1914540511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×C22⋊Q8×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenterC4×C22⋊Q8D43
hypocenterC43#29414
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #19136026C2semidirect
3. #19135795C2semidirect
6. #19135226C2semidirect
7. #19135215C2semidirect
8. #19135180C2semidirect
9. #19135163C2semidirect
10. #19134950C2semidirect
11. #19134932C2semidirect
12. #19134849C2semidirect
13. #19134841C2semidirect
14. #19134663C2semidirect
15. C4×C22⋊Q8×C43C2semidirect
332. C4×C22⋊Q8D43semidirect
399. C43#29414semidirect

Maximal subgroups

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

subgroupindex
C4×#130632992
#191360262
#191357952
#191357842
#191355962
#191352262
#191352152
#191351802
#191351632
#191349502
#191349322
#191348492
#191348412
#191346632
C4×C22⋊Q8×C432
#2941443