Finite Group Databasebeta

← #25153755

Subgroups — #25153755

Order 11008.

946 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#103×D43C211yesmaximal, characteristic
2#19138315C211yesmaximal, characteristic
3Q8×(C2×D43)⋊C4C211yesmaximal, characteristic
4#19136144C211yesmaximal, characteristic, complemented
5#19135985C211yesmaximal, characteristic, complemented
6#19135975C211yesmaximal, characteristic, complemented
7#19135743C211yesmaximal, characteristic, complemented
8#19134865C211yesmaximal, characteristic, complemented
9#19134849C211yesmaximal, characteristic, complemented
10#19134781C211yesmaximal, characteristic
11#19134771C211yesmaximal, characteristic
12#19134617C211yesmaximal, characteristic
13#19134608C211yesmaximal, characteristic, complemented
14#19134528C211yesmaximal, characteristic
15C2×C43×#479C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×C4⋊C4×D43C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29#103×D43—24no—
30C2×(C2×D43)⋊C8C2211yescharacteristic
31#14582837—21no—
32#14582832—21no—
33#14582805—21no—
34#14582805C2211yescharacteristic
35#14582804—21no—
36#14582804C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582770—21no—
40#14582764C2211yescharacteristic
41#14582756—21no—
42#14582756—21no—
43#14582756C2211yescharacteristic
44#14582756C2211yescharacteristic
45C4×(C2×D43)⋊C4—21no—
46C4×(C2×D43)⋊C4C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#125×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C43×#479—24no—
56C2×#107×C43C2211yescharacteristic
57C2×#106×C43C2211yescharacteristic
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C2×Q8×D43—22no—
64C2×Q8×D43—22no—
65C2×Q8×D43—22no—
66C2×Q8×D43—41no—
67C2×Q8×D43—41no—
68C2×Q8×D43Q814yes—
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C22×C4×D43C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C2×C8×D43—22no—
75C2×C8×D43—22no—
76C2×C8×D43—41no—
77Q8×Dic43—22no—
78Q8×Dic43—41no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C4⋊C4×D43—22no—
87C4⋊C4×D43—41no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4D411yescharacteristic
91C2×(C2×D43)⋊C4D411yescharacteristic
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94#13063258—41no—
95#13063257—41no—
96Dic43⋊C8—41no—
97#13063250—22no—
98#13063250—41no—
99#13063249—22no—
100#13063249—22no—
101#13063248—22no—
102#13063248—41no—
103(C2×D43)⋊C8—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95D411yescharacteristic
115C43⋊#95D411yescharacteristic
116C22×Q8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119#125×C43—22no—
120#125×C43—41no—
121C4×Q8×C43—22no—
122C4×Q8×C43—41no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131#107×C43—22no—
132#106×C43—22no—
133C4⋊C8×C43—22no—
134#103×C43—22no—
135#103×C43D414yes—
136C23×D43C2×D411yescharacteristic
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43C2×D412yes—
141C2×Q8×C43C2×Q812yes—
142C2×Q8×C43#4112yes—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157Q8×D43—28no—
158Q8×D43—44no—
159Q8×D43—44no—
160Q8×D43—44no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—24no—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
168C2×C4×D43—42no—
169C2×C4×D43—42no—
170C2×C4×D43—81no—
171C2×C4×D43C2×Q812yes—
172C2×C4×D43#4112yes—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—24no—
179C2×Dic86—42no—
180C2×Dic86—42no—
181C2×Dic86C2×Q812yes—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43C2×D412yes—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—42no—
194C4⋊C4×C43—42no—
195C4⋊C4×C43—42no—
196C4⋊C4×C43C2×D412yes—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—42no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—42no—
203(C2×D43)⋊C4—42no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—42no—
211C4⋊Dic43—81no—
212Dic43⋊C4—42no—
213Dic43⋊C4—81no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—42no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C8×D43—44no—
224C23×C43C22×D411yescharacteristic
225C22×D43—21no—
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43C22⋊Q812yes—
230C22×D43#13512yes—
231C22×D43#13712yes—
232Q8×C43—22no—
233Q8×C43—22no—
234Q8×C43—22no—
235Q8×C43C22⋊Q814yes—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
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×C43C22×D411yescharacteristic
255C2×C4×C43C22×Q811yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—41no—
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×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43C22⋊Q812yes—
281C4×D43—22no—
282C4×D43—22no—
283C4×D43—22no—
284C4×D43—22no—
285C4×D43—48no—
286C4×D43—84no—
287Dic86—22no—
288Dic86—22no—
289Dic86—48no—
290Dic86—41no—
291Dic86—41no—
292C8×C43—22no—
293C8×C43—41no—
294C43⋊C8—41no—
295C43⋊C8—41no—
296#25957—431nomaximal, Sylow
297C22×C43C2×C22⋊Q811yescharacteristic
298C22×C43D4211yescharacteristic
299C22×C43#54611yescharacteristic
300C22×C43C2×#13511yescharacteristic
301C22×C43C2×#13711yescharacteristic
302C22×C43#57711yescharacteristic
303C22×C43#57811yescharacteristic
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—22no—
308C2×D43—22no—
309C2×D43—22no—
310C2×D43#47914yescomplemented
311C4×C43—24no—
312C4×C43—41no—
313C4×C43—42no—
314C4×C43—41no—
315C4×C43—81no—
316C4×C43—81no—
317C4×C43C2×C22⋊Q811yescharacteristic
318C4×C43#54311yescharacteristic
319C4×C43#54611yescharacteristic
320C4×C43#55111yescharacteristic
321Dic43—22no—
322Dic43—42no—
323Dic43—41no—
324Dic43—41no—
325Dic43—81no—
326Dic43—81no—
327Dic43—81no—
328C2×#479D4311yescharacteristic, complemented
329C22×#103—431no—
330#2442—431no—
331Q8×C22⋊C4—431no—
332#2097—431no—
333#2068—431no—
334#2066—431no—
335#2026—431no—
336#1865—431no—
337#1863—431no—
338#1852—431no—
339#1850—431no—
340#1807—431no—
341#1805—431no—
342#1787—431no—
343C2×C43#243711yescharacteristic
344C2×C43C2×#47911yescharacteristic
345C2×C43#308211yescharacteristic
346C2×C43#327011yescharacteristic
347C2×C43#328211yescharacteristic
348C2×C43#330011yescharacteristic
349C2×C43#332011yescharacteristic
350D43—24no—
351C23×Q8—431no—
352C23×C8—431no—
353C2×#125C2×D4311yescharacteristic
354C2×C4×Q8—431no—
355C2×C4×Q8C2×D4311yescharacteristic
356C22×C4⋊C4—431no—
357#479—24no—
358C2×#107—431no—
359C2×#107C2×D4311yescharacteristic
360C2×#106—431no—
361C2×#106C2×D4311yescharacteristic
362C2×C4⋊C8—431no—
363C2×C4⋊C8C2×D4311yescharacteristic
364C2×#103—431no—
365C2×#103—431no—
366C2×#103—431no—
367C2×#103—431no—
368C2×#103—431no—
369C2×#103—431no—
370C2×#103—864no—
371C2×#103C2×D4311yescharacteristic
372C2×#103C2×D4311yescharacteristic
373C2×C22⋊C8—431no—
374#400—861no—
375#398—861no—
376#391—431no—
377#391—431no—
378#391—861no—
379#391—861no—
380#389—431no—
381#389—431no—
382#385—861no—
383#382—431no—
384#380—431no—
385#380—431no—
386#380—861no—
387#380—861no—
388C4×C22⋊C4—431no—
389C4×C22⋊C4—861no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#336—431no—
395#336—431no—
396C43#2595711yescharacteristic, complemented, Sylow
397C22×Q8—434no—
398C22×Q8—431no—
399C22×Q8—861no—
400C22×Q8—862no—
401C22×Q8—862no—
402C22×Q8—862no—
403C22×Q8—1721no—
404C22×Q8—1721no—
405C22×Q8C22×D4311yescharacteristic
406C23×C4—431no—
407C23×C4—861no—
408C23×C4—861no—
409C22×C8—431no—
410C22×C8—431no—
411C22×C8—862no—
412C22×C8—862no—
413C22×C8—1721no—
414C22×C8C22×D4311yescharacteristic
415C22×C8C22×D4311yescharacteristic
416#125—22no—
417#125—41no—
418C4×Q8—22no—
419C4×Q8—41no—
420C4×Q8—862no—
421C4×Q8—1721no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—862no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—1721no—
434C2×C4⋊C4C22×D4311yescharacteristic
435C2×C4⋊C4C22×D4311yescharacteristic
436C2×C4⋊C4C22×D4311yescharacteristic
437C2×C22⋊C4—431no—
438C2×C22⋊C4—431no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C42—21no—
442C2×C42—431no—
443C2×C42—861no—
444C2×C42C22×D4311yescharacteristic
445#107—22no—
446#107—1721no—
447#106—22no—
448#106—1721no—
449C4⋊C8—22no—
450C4⋊C8—1721no—
451#103—22no—
452#103—862no—
453#103—862no—
454#103—862no—
455#103—862no—
456#103—1721no—
457#103—1721no—
458#103C22⋊D4314yes—
459C22⋊C8—862no—
460#95—431no—
461#95—431no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472C24—431no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—432no—
477C2×Q8—864no—
478C2×Q8—861no—
479C2×Q8—868no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8—861no—
483C2×Q8—861no—
484C2×Q8—1722no—
485C2×Q8—1722no—
486C2×Q8—1724no—
487C2×Q8—1724no—
488C2×Q8—1724no—
489C2×Q8Q8×D4312yes—
490C2×Q8#1062190212yes—
491C2×Q8C2×C22⋊D4312yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—431no—
497C22×C4—432no—
498C22×C4—432no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—864no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—861no—
510C22×C4—3441no—
511C22×C4—1722no—
512C22×C4—1722no—
513C22×C4—1722no—
514C22×C4—1722no—
515C22×C4D4×D4311yescharacteristic
516C22×C4D4×D4311yescharacteristic
517C22×C4C23×D4311yescharacteristic
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—1724no—
530C2×C8C2×C22⋊D4312yes—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—3441no—
546C4⋊C4—3441no—
547C4⋊C4—1722no—
548C4⋊C4—1722no—
549C4⋊C4C2×C22⋊D4312yes—
550C22⋊C4—862no—
551C22⋊C4—862no—
552C22⋊C4—1722no—
553C22⋊C4—1722no—
554C42—21no—
555C42—21no—
556C42—42no—
557C42—861no—
558C42—861no—
559C42—1722no—
560C23—432no—
561C23—432no—
562C23—432no—
563C23—861no—
564C23—861no—
565C23—861no—
566C23—861no—
567C23C2×D4×D4311yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—22no—
571Q8—862no—
572Q8—862no—
573Q8—1728no—
574Q8—1721no—
575Q8—1721no—
576Q8#1306330114yes—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—432no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—3444no—
610C2×C4—1728no—
611C2×C4—1721no—
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×C4C22×C22⋊D4311yescharacteristic
623C2×C4C2×Q8×D4311yescharacteristic
624C2×C4#41×D4311yescharacteristic
625C2×C4C2×#1062190211yescharacteristic
626C2×C4#1306337011yescharacteristic
627C2×C4#1306337111yescharacteristic
628C8—22no—
629C8—41no—
630C8—1721no—
631C8—1721no—
632C22—434no—
633C22—862no—
634C22—862no—
635C22—862no—
636C22—862no—
637C22—862no—
638C22—862no—
639C22C22⋊Q8×D4311yescharacteristic
640C22D4×C22⋊D4311yescharacteristic
641C22#1458354011yescharacteristic
642C22#135×D4311yescharacteristic
643C22#137×D4311yescharacteristic
644C22#1458370611yescharacteristic
645C22#1458371511yescharacteristic
646C4—24no—
647C4—41no—
648C4—42no—
649C4—41no—
650C4—81no—
651C4—81no—
652C4—862no—
653C4—3441no—
654C4—3441no—
655C4—3441no—
656C4—1721no—
657C4—1722no—
658C4—1721no—
659C4C2×#1306330111yescharacteristic
660C4#1458352411yescharacteristic
661C4#1458353711yescharacteristic
662C4#1458357611yescharacteristic
663C2—864no—
664C2#1913825811yescharacteristic
665C2#479×D4311yescharacteristic
666C2#1914443411yescharacteristic
667C2#1914615911yescharacteristic
668C2#1914629611yescharacteristic
669C2#1914647911yescharacteristic
670C2#1914676311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#479C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenterC2×#479D43
hypocenterC43#25957
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
4. #19136144C2semidirect
5. #19135985C2semidirect
6. #19135975C2semidirect
7. #19135743C2semidirect
8. #19134865C2semidirect
9. #19134849C2semidirect
13. #19134608C2semidirect
15. C2×C43×#479C2semidirect
310. C2×D43#479semidirect
328. C2×#479D43semidirect
396. C43#25957semidirect

Maximal subgroups

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

subgroupindex
C2×#103×D432
#191383152
Q8×(C2×D43)⋊C42
#191361442
#191359852
#191359752
#191357432
#191348652
#191348492
#191347812
#191347712
#191346172
#191346082
#191345282
C2×C43×#4792
#2595743