Finite Group Databasebeta

← #25116034

Subgroups — #25116034

Order 11008.

866 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582999C211yesmaximal, characteristic
2#19137515C211yesmaximal, characteristic, complemented
3#19135295C211yesmaximal, characteristic
4#19135281C211yesmaximal, characteristic
5#19135187C211yesmaximal, characteristic, complemented
6#19135166C211yesmaximal, characteristic, complemented
7#19134953C211yesmaximal, characteristic
8#19134953C211yesmaximal, characteristic
9#19134730C211yesmaximal, characteristic, complemented
10#19134605C211yesmaximal, characteristic
11#19134597C211yesmaximal, characteristic, complemented
12#19134470C211yesmaximal, characteristic, complemented
13#19134428C211yesmaximal, characteristic, complemented
14C4×#13063248C211yesmaximal, characteristic, complemented
15C43×#2354C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20#14582999C418yescomplemented
21C2×#13063258C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30C2×#13063236C2211yescharacteristic
31C2×C4×C43⋊C8C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582794—21no—
35#14582794—21no—
36#14582765C2211yescharacteristic
37#14582763—21no—
38#14582750—21no—
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49C2×C4×D4×C43C2211yescharacteristic
50C2×#117×C43—21no—
51C43×#390C2211yescharacteristic
52C43×#390C2211yescharacteristic
53C43×#388—21no—
54C43×#388—21no—
55C43×#384C2211yescharacteristic
56C43×#380—21no—
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C2×#10621883—22no—
62C2×#10621883—22no—
63C2×#10621883C2×C414yes—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C4×Dic86—22no—
69C4×Dic86—22no—
70C4×Dic86—22no—
71C4×Dic86—41no—
72C4×Dic86—41no—
73C4×Dic86C2×C414yes—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85#13063258C2×C414yes—
86C4⋊(C43⋊C8)—22no—
87#13063248—22no—
88#13063248—22no—
89#13063248C2×C414yes—
90#13063246—41no—
91#13063246—41no—
92#13063246C2×C414yes—
93#13063236—41no—
94#13063236C2×C414yes—
95C4×C43⋊C8—41no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C22×D4×C43C2311yescharacteristic
101C23×C4×C43—21no—
102C4×D4×C43—22no—
103C4×D4×C43C2×C414yes—
104#117×C43—44no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43D411yescharacteristic
108C2×C4⋊C4×C43D411yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C42×C43—21no—
118C2×C42×C43—21no—
119C2×C42×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122#95×C43—21no—
123#95×C43—21no—
124#95×C43D411yescharacteristic
125#95×C43D411yescharacteristic
126C24×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43C22×C412yes—
133C22×C4×C43—24no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—42no—
138C22×C4×C43—42no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86C22×C412yes—
154C2×Dic86#4112yes—
155C2×Dic86#4112yes—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—41no—
163C4⋊C4×C43—42no—
164C4⋊C4×C43—81no—
165C4⋊C4×C43C22×C412yes—
166C22⋊C4×C43—24no—
167C22⋊C4×C43—42no—
168C22⋊C4×C43—42no—
169C22⋊C4×C43—81no—
170C22⋊C4×C43—81no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43—42no—
176C42×C43—42no—
177C42×C43C22×C412yes—
178C42×C43#4112yes—
179#10621883—28no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43C22×C412yes—
186Dic43⋊C4—24no—
187Dic43⋊C4—42no—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191C4×Dic43—24no—
192C4×Dic43—42no—
193C4×Dic43—42no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C22×C412yes—
205C2×C43⋊C8C22×C412yes—
206C23×C43—22no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43C22×D411yescharacteristic
214D4×C43—22no—
215D4×C43—22no—
216D4×C43—41no—
217D4×C43—41no—
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—22no—
225C2×C4×C43—21no—
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—21no—
234C2×C4×C43—48no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43C4×D412yes—
244C2×C4×C43C4×D412yes—
245C2×C4×C43AGL(1,ℤ/8)12yes—
246C2×C4×C43C23×C411yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C2×C4×C432−1+411yescharacteristic
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264Dic86—22no—
265Dic86—22no—
266Dic86—22no—
267Dic86#11714yescomplemented
268C43⋊C8—22no—
269C43⋊C8—22no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272#22781—431nomaximal, Sylow
273C22×C43—42no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43C2×C4×D411yescharacteristic
281C22×C43#54611yescharacteristic
282C22×C43#54811yescharacteristic
283C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
284C22×C43#57511yescharacteristic
285C22×C43#57711yescharacteristic
286C22×C43#57811yescharacteristic
287C4×C43—22no—
288C4×C43—22no—
289C4×C43—22no—
290C4×C43—42no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—81no—
295C4×C43—81no—
296C4×C43C2×#11711yescharacteristic
297C4×C43#52011yescharacteristic
298C4×C43#55211yescharacteristic
299C4×C43#55311yescharacteristic
300Dic43—24no—
301Dic43—42no—
302Dic43—81no—
303Dic43—81no—
304C2×#440—431no—
305#2354D4311yescharacteristic
306#2351—431no—
307#1936—431no—
308#1934—431no—
309#1921—431no—
310#1918—431no—
311#1880—431no—
312#1880—431no—
313#1836—431no—
314#1804—431no—
315#1803—431no—
316#1771—431no—
317#1763—431no—
318C4×#103—431no—
319C2×C43—82no—
320C2×C43#235211yescharacteristic
321C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
322C2×C43#294711yescharacteristic
323C2×C43#330811yescharacteristic
324C2×C43#332111yescharacteristic
325C2×C43#336811yescharacteristic
326C2×C43#337711yescharacteristic
327C22×SD16—431no—
328C2×C4×Q8—431no—
329C2×C4×Q8—431no—
330C2×C4×Q8—431no—
331C2×C4×D4C2×D4311yescharacteristic
332C2×#117—21no—
333#440—438no—
334C2×#107—431no—
335C2×C4⋊C8—431no—
336C2×#103—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#102—431no—
340C2×#102—431no—
341C2×#102—431no—
342C2×#97—431no—
343C2×#97—431no—
344C2×C4×C8—431no—
345#390C2×D4311yescharacteristic
346#390C2×D4311yescharacteristic
347#389—431no—
348#389—431no—
349#389—861no—
350#389—861no—
351#388—21no—
352#388—21no—
353#384C2×D4311yescharacteristic
354#382—431no—
355#382—861no—
356#380—21no—
357C4×C4⋊C4—861no—
358C4×C4⋊C4C2×D4311yescharacteristic
359C4×C4⋊C4C2×D4311yescharacteristic
360C4×C4⋊C4C2×D4311yescharacteristic
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#336—431no—
370#336—431no—
371C43#2278111yescharacteristic, complemented, Sylow
372C22×Q8—431no—
373C22×D4C22×D4311yescharacteristic
374C23×C4—21no—
375C2×SD16—434no—
376C2×SD16—862no—
377C2×SD16—862no—
378C22×C8—431no—
379C22×C8—431no—
380C22×C8—431no—
381C22×C8—431no—
382C4×Q8—434no—
383C4×Q8—862no—
384C4×Q8—862no—
385C4×Q8—862no—
386C4×Q8—1721no—
387C4×Q8—1721no—
388C4×D4—22no—
389C4×D4C4×D4314yes—
390#117—44no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4C22⋊D4311yescharacteristic
402C2×C4⋊C4C22⋊D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—861no—
414C2×C42—861no—
415C2×C42—861no—
416C2×C42C22×D4311yescharacteristic
417C2×C42C22×D4311yescharacteristic
418C2×C42C22×D4311yescharacteristic
419#107—434no—
420C4⋊C8—862no—
421#103—434no—
422#103—862no—
423#103—862no—
424#102—434no—
425#102—1721no—
426#102—1721no—
427#97—434no—
428#97—1721no—
429C4×C8—1721no—
430#95—21no—
431#95—21no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95C22⋊D4311yescharacteristic
437#95C22⋊D4311yescharacteristic
438C24—21no—
439C2×Q8—432no—
440C2×Q8—432no—
441C2×Q8—432no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×Q8—861no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4C2×C4×D4312yes—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4C2×C22⋊D4311yescharacteristic
462C22×C4C2×C22⋊D4311yescharacteristic
463C22×C4C2×C22⋊D4311yescharacteristic
464C22×C4C2×C22⋊D4311yescharacteristic
465C22×C4C2×C22⋊D4311yescharacteristic
466C22×C4C2×C22⋊D4311yescharacteristic
467C22×C4C23×D4311yescharacteristic
468SD16—868no—
469C2×C8—432no—
470C2×C8—432no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—42no—
489C4⋊C4—81no—
490C4⋊C4—432no—
491C4⋊C4—864no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—1722no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4—1722no—
501C4⋊C4C2×C4×D4312yes—
502C22⋊C4—24no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—81no—
506C22⋊C4—81no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—42no—
512C42—42no—
513C42—864no—
514C42—1722no—
515C42—1722no—
516C42C2×C4×D4312yes—
517C42#1062189812yes—
518C23—22no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23C22×C22⋊D4311yescharacteristic
526Q8—434no—
527Q8—862no—
528Q8—862no—
529Q8—862no—
530D4—22no—
531D4—22no—
532D4—41no—
533D4—41no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—48no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4C4×C22⋊D4312yes—
572C2×C4C4×C22⋊D4312yes—
573C2×C4#1306335112yes—
574C2×C4C22×C4×D4311yescharacteristic
575C2×C4#41×D4311yescharacteristic
576C2×C4#41×D4311yescharacteristic
577C2×C4C2×#1062189811yescharacteristic
578C2×C4#1306337111yescharacteristic
579C2×C4#1306337211yescharacteristic
580C8—862no—
581C8—862no—
582C8—1721no—
583C8—1721no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22C2×C4×C22⋊D4311yescharacteristic
592C22#1458353711yescharacteristic
593C22#1458355611yescharacteristic
594C22C2×#1306335111yescharacteristic
595C22#1458369711yescharacteristic
596C22#1458371011yescharacteristic
597C22#1458371411yescharacteristic
598C4—22no—
599C4—22no—
600C4—22no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—42no—
605C4—81no—
606C4—81no—
607C4—864no—
608C4—3441no—
609C4—3441no—
610C4—1722no—
611C4#117×D4311yescharacteristic
612C4#1458337911yescharacteristic
613C4#1458358811yescharacteristic
614C4#1458359311yescharacteristic
615C2—82no—
616C2#1913752511yescharacteristic
617C2C4×#1306335111yescharacteristic
618C2#1914343411yescharacteristic
619C2#1914658011yescharacteristic
620C2#1914677511yescharacteristic
621C2#1914732011yescharacteristic
622C2#1914743111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2354C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#2354D43
hypocenterC43#22781
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #19137515C2semidirect
5. #19135187C2semidirect
6. #19135166C2semidirect
9. #19134730C2semidirect
11. #19134597C2semidirect
12. #19134470C2semidirect
13. #19134428C2semidirect
14. C4×#13063248C2semidirect
20. #14582999C4semidirect
267. Dic86#117semidirect
371. C43#22781semidirect

Maximal subgroups

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

subgroupindex
C2×#145829992
#191375152
#191352952
#191352812
#191351872
#191351662
#191349532
#191347302
#191346052
#191345972
#191344702
#191344282
C4×#130632482
C43×#23542
#2278143