Finite Group Databasebeta

← #25133095

Subgroups — #25133095

Order 11008.

1070 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×#14583203C211yesmaximal, characteristic, complemented
2C2×C4×#10621883C211yesmaximal, characteristic
3#19139961C211yesmaximal, characteristic, complemented
4#19135930C211yesmaximal, characteristic, complemented
5#19135925C211yesmaximal, characteristic, complemented
6#19135743C211yesmaximal, characteristic, complemented
7#19135733C211yesmaximal, characteristic, complemented
8#19135561C211yesmaximal, characteristic, complemented
9#19135532C211yesmaximal, characteristic, complemented
10#19134929C211yesmaximal, characteristic
11#19134929C211yesmaximal, characteristic
12#19134856C211yesmaximal, characteristic
13#19134842C211yesmaximal, characteristic
14#19134605C211yesmaximal, characteristic
15C2×C43×#554C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18#14583203—24no—
19C4×#10621883—24no—
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582837—21no—
32#14582818—21no—
33#14582805C2211yescharacteristic
34#14582805C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582780—21no—
38#14582780—21no—
39#14582765C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C43×#554—24no—
51C43×#554—24no—
52C2×C4⋊Q8×C43C2211yescharacteristic
53C2×#125×C43C2211yescharacteristic
54C2×#125×C43C2211yescharacteristic
55C2×C22⋊Q8×C43—21no—
56C2×C22⋊Q8×C43—21no—
57C2×C22⋊Q8×C43—21no—
58C2×C4×Q8×C43C2211yescharacteristic
59C2×C4×D4×C43C2211yescharacteristic
60C2×C4×D4×C43C2211yescharacteristic
61C2×C4×D4×C43C2211yescharacteristic
62C22×C4⋊C4×C43—21no—
63C22×Dic86C2311yescharacteristic
64C2×#10621883—22no—
65C2×#10621883—22no—
66C2×#10621883Q814yescomplemented
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C4×Dic86—22no—
72C4×Dic86—22no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×C4×Dic43—21no—
80#13063258—22no—
81#13063256—22no—
82#13063256—22no—
83C4⋊(C43⋊C8)—22no—
84#13063248—22no—
85#13063248—22no—
86#13063248—22no—
87#13063246—22no—
88#13063246—22no—
89#13063246—22no—
90C4×C43⋊C8—22no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C22×Q8×C43—21no—
100C22×Q8×C43D411yescharacteristic
101C22×D4×C43C2311yescharacteristic
102C23×C4×C43—21no—
103C23×C4×C43—21no—
104C23×C4×C43—21no—
105C4⋊Q8×C43—22no—
106C4⋊Q8×C43—22no—
107#125×C43—22no—
108#125×C43—22no—
109#125×C43—22no—
110#125×C43D414yes—
111C22⋊Q8×C43—28no—
112C22⋊Q8×C43—28no—
113C22⋊Q8×C43—28no—
114C4×Q8×C43—22no—
115C4×Q8×C43—22no—
116C4×D4×C43—22no—
117C4×D4×C43—22no—
118C4×D4×C43—22no—
119C4×D4×C43—22no—
120C4×D4×C43—22no—
121C4×D4×C43D414yes—
122C2×C4⋊C4×C43—28no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43D411yescharacteristic
129C2×C4⋊C4×C43D411yescharacteristic
130C2×C4⋊C4×C43D411yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C42×C43C2311yescharacteristic
138C2×C42×C43C2311yescharacteristic
139C2×C42×C43C2311yescharacteristic
140C24×C43—21no—
141C2×Q8×C43—24no—
142C2×Q8×C43—22no—
143C2×Q8×C43—22no—
144C2×Q8×C43—41no—
145C2×Q8×C43—81no—
146C2×Q8×C43—81no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C2×D412yes—
151C2×D4×C43C2×Q812yes—
152C2×D4×C43#4112yes—
153C22×C4×C43—24no—
154C22×C4×C43—24no—
155C22×C4×C43—24no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—42no—
160C22×C4×C43—42no—
161C22×C4×C43—81no—
162C22×C4×C43—81no—
163C22×C4×C43—81no—
164C22×C4×C43—81no—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2411yescharacteristic
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86C2×Q812yes—
182C4⋊C4×C43—24no—
183C4⋊C4×C43—24no—
184C4⋊C4×C43—24no—
185C4⋊C4×C43—22no—
186C4⋊C4×C43—24no—
187C4⋊C4×C43—24no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—22no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43C2×D412yes—
194C4⋊C4×C43C2×D412yes—
195C4⋊C4×C43C2×D412yes—
196C22⋊C4×C43—24no—
197C22⋊C4×C43—24no—
198C22⋊C4×C43—24no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43—21no—
203C42×C43C2×D412yes—
204C42×C43C2×D412yes—
205#10621883—28no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212Dic43⋊C4—42no—
213Dic43⋊C4—42no—
214Dic43⋊C4—42no—
215C4×Dic43—42no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8C2×Q812yes—
228C23×C43—22no—
229C23×C43—22no—
230C23×C43—22no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43C22×D411yescharacteristic
236Q8×C43—44no—
237Q8×C43—84no—
238D4×C43—22no—
239D4×C43—22no—
240D4×C43—22no—
241D4×C43C22⋊Q814yes—
242C2×C4×C43—21no—
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—22no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—48no—
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—84no—
268C2×C4×C43—84no—
269C2×C4×C43#12012yes—
270C2×C4×C43#12012yes—
271C2×C4×C43#13512yes—
272C2×C4×C43C22×D411yescharacteristic
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C22×Q811yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C432−1+411yescharacteristic
277C2×C4×C432−1+411yescharacteristic
278C2×Dic43—22no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290Dic86—22no—
291Dic86—22no—
292Dic86—41no—
293Dic86—41no—
294C43⋊C8—22no—
295C43⋊C8—41no—
296C43⋊C8—41no—
297C43⋊C8—41no—
298#24337—431nomaximal, Sylow
299C22×C43—24no—
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—42no—
305C22×C43—42no—
306C22×C43C2×#12011yescharacteristic
307C22×C43#54811yescharacteristic
308C22×C43D4×Q811yescharacteristic
309C22×C43C2×#13511yescharacteristic
310C22×C43#57511yescharacteristic
311C22×C43#57711yescharacteristic
312C22×C43#57711yescharacteristic
313C4×C43—22no—
314C4×C43—22no—
315C4×C43—22no—
316C4×C43—41no—
317C4×C43—42no—
318C4×C43—41no—
319C4×C43—41no—
320C4×C43—42no—
321C4×C43—42no—
322C4×C43C2×C22⋊Q811yescharacteristic
323C4×C43#53611yescharacteristic
324C4×C43#54811yescharacteristic
325C4×C43D4×Q811yescharacteristic
326Dic43—42no—
327Dic43—81no—
328Dic43—81no—
329Dic43—81no—
330C2×#554D4311yescharacteristic
331C2×#479—431no—
332C2×C4×SD16—431no—
333#2581—431no—
334#2059—431no—
335#2058—431no—
336#2026—431no—
337#2024—431no—
338#1991—431no—
339#1984—431no—
340#1877—431no—
341#1877—431no—
342#1864—431no—
343#1862—431no—
344#1804—431no—
345C2×C43—44no—
346C2×C43#240911yescharacteristic
347C2×C43#300211yescharacteristic
348C2×C43#300911yescharacteristic
349C2×C43#336011yescharacteristic
350C2×C43#337611yescharacteristic
351C2×C43#338111yescharacteristic
352C2×C43#338811yescharacteristic
353C22×SD16—431no—
354#554—24no—
355#554—24no—
356C2×C4⋊Q8C2×D4311yescharacteristic
357C2×#125C2×D4311yescharacteristic
358C2×#125C2×D4311yescharacteristic
359C2×C22⋊Q8—21no—
360C2×C22⋊Q8—21no—
361C2×C22⋊Q8—21no—
362C2×C4×Q8—431no—
363C2×C4×Q8C2×D4311yescharacteristic
364C2×C4×D4C2×D4311yescharacteristic
365C2×C4×D4C2×D4311yescharacteristic
366C2×C4×D4C2×D4311yescharacteristic
367C22×C4⋊C4—21no—
368#479—864no—
369C4×SD16—864no—
370C2×#107—431no—
371C2×#106—431no—
372C2×#106—431no—
373C2×C4⋊C8—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×#103—431no—
377C2×#102—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×C4×C8—431no—
381#400—861no—
382#395—861no—
383#391—431no—
384#391—431no—
385#389—431no—
386#389—431no—
387#387—861no—
388#387—861no—
389#382—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340—431no—
395#340—431no—
396#336—431no—
397#336—431no—
398#336—431no—
399#336—431no—
400C43#2433711yescharacteristic, complemented, Sylow
401C22×Q8—21no—
402C22×Q8—431no—
403C22×Q8C22⋊D4311yescharacteristic
404C22×D4C22×D4311yescharacteristic
405C23×C4—21no—
406C23×C4—21no—
407C23×C4—21no—
408C2×SD16—434no—
409C2×SD16—862no—
410C2×SD16—862no—
411C22×C8—431no—
412C22×C8—431no—
413C22×C8—431no—
414C22×C8—431no—
415C4⋊Q8—22no—
416C4⋊Q8—22no—
417#125—22no—
418#125—22no—
419#125—22no—
420#125C22⋊D4314yes—
421C22⋊Q8—28no—
422C22⋊Q8—28no—
423C22⋊Q8—28no—
424C4×Q8—22no—
425C4×Q8—22no—
426C4×Q8—862no—
427C4×Q8—862no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4C22⋊D4314yes—
434C2×C4⋊C4—28no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4C22⋊D4311yescharacteristic
447C2×C4⋊C4C22⋊D4311yescharacteristic
448C2×C4⋊C4C22⋊D4311yescharacteristic
449C2×C4⋊C4C22×D4311yescharacteristic
450C2×C4⋊C4C22×D4311yescharacteristic
451C2×C4⋊C4C22×D4311yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C42—861no—
456C2×C42C22×D4311yescharacteristic
457C2×C42C22×D4311yescharacteristic
458C2×C42C22×D4311yescharacteristic
459#107—862no—
460#106—862no—
461#106—862no—
462C4⋊C8—862no—
463#103—862no—
464#103—862no—
465#103—862no—
466#102—862no—
467#102—862no—
468#102—862no—
469C4×C8—862no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478C24—21no—
479C2×Q8—24no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—41no—
483C2×Q8—81no—
484C2×Q8—81no—
485C2×Q8—432no—
486C2×Q8—861no—
487C2×Q8—861no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8—861no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4Q8×D4312yes—
495C2×D4#1062190212yes—
496C2×D4C2×C22⋊D4312yes—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4—81no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4C2×C22⋊D4311yescharacteristic
514C22×C4C2×C22⋊D4311yescharacteristic
515C22×C4C2×C22⋊D4311yescharacteristic
516C22×C4C2×C22⋊D4311yescharacteristic
517C22×C4C2×C22⋊D4311yescharacteristic
518C22×C4C2×C22⋊D4311yescharacteristic
519C22×C4C23×D4311yescharacteristic
520SD16—868no—
521C2×C8—432no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8—861no—
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—24no—
536C4⋊C4—22no—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—1722no—
551C4⋊C4—1722no—
552C4⋊C4—1722no—
553C4⋊C4C2×C22⋊D4312yes—
554C4⋊C4C2×C22⋊D4312yes—
555C4⋊C4C2×C22⋊D4312yes—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—1722no—
564C42C2×C22⋊D4312yes—
565C42C2×C22⋊D4312yes—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23C22×C22⋊D4311yescharacteristic
574Q8—44no—
575Q8—84no—
576Q8—862no—
577Q8—862no—
578Q8—1721no—
579Q8—1721no—
580D4—22no—
581D4—22no—
582D4—22no—
583D4#1306330114yes—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—48no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—84no—
610C2×C4—84no—
611C2×C4—862no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
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#1306329412yes—
624C2×C4#1306329412yes—
625C2×C4#1306334512yes—
626C2×C4C22×C22⋊D4311yescharacteristic
627C2×C4C22×C22⋊D4311yescharacteristic
628C2×C4C2×Q8×D4311yescharacteristic
629C2×C4C2×#1062190211yescharacteristic
630C2×C4#1306337311yescharacteristic
631C2×C4#1306337311yescharacteristic
632C8—862no—
633C8—1721no—
634C8—1721no—
635C8—1721no—
636C22—24no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22C2×#1306329411yescharacteristic
644C22#1458356011yescharacteristic
645C22Q8×C22⋊D4311yescharacteristic
646C22C2×#1306334511yescharacteristic
647C22#1458369711yescharacteristic
648C22#1458371011yescharacteristic
649C22#1458371011yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—41no—
654C4—42no—
655C4—41no—
656C4—41no—
657C4—42no—
658C4—42no—
659C4—3441no—
660C4—3441no—
661C4—3441no—
662C4—1722no—
663C4C2×#1306330111yescharacteristic
664C4#1458347311yescharacteristic
665C4#1458356011yescharacteristic
666C4Q8×C22⋊D4311yescharacteristic
667C2—44no—
668C2#1913795411yescharacteristic
669C2#1914381311yescharacteristic
670C2#1914387211yescharacteristic
671C2#1914724411yescharacteristic
672C2#1914742211yescharacteristic
673C2#1914747011yescharacteristic
674C2#1914754011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#554C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenterC2×#554D43
hypocenterC43#24337
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#14583203C2semidirect
3. #19139961C2semidirect
4. #19135930C2semidirect
5. #19135925C2semidirect
6. #19135743C2semidirect
7. #19135733C2semidirect
8. #19135561C2semidirect
9. #19135532C2semidirect
66. C2×#10621883Q8semidirect
400. C43#24337semidirect

Maximal subgroups

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

subgroupindex
C2×#145832032
C2×C4×#106218832
#191399612
#191359302
#191359252
#191357432
#191357332
#191355612
#191355322
#191349292
#191348562
#191348422
#191346052
C2×C43×#5542
#2433743