Finite Group Databasebeta

← #25133101

Subgroups — #25133101

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×#14583608C211yesmaximal, characteristic
2C2×#14583206C211yesmaximal, characteristic, complemented
3#19139957C211yesmaximal, characteristic, complemented
4#19135935C211yesmaximal, characteristic, complemented
5#19135926C211yesmaximal, characteristic, complemented
6#19135744C211yesmaximal, characteristic, complemented
7#19135734C211yesmaximal, characteristic, complemented
8#19135560C211yesmaximal, characteristic, complemented
9#19135531C211yesmaximal, characteristic, complemented
10#19134931C211yesmaximal, characteristic
11#19134931C211yesmaximal, characteristic
12#19134854C211yesmaximal, characteristic
13#19134840C211yesmaximal, characteristic
14#19134605C211yesmaximal, characteristic
15C2×C4×SD16×C43C211yesmaximal, characteristic
16#14583608—24no—
17#14583608—24no—
18C2×#13063324C2211yescharacteristic
19C2×#13063317C2211yescharacteristic
20C2×#13063316C2211yescharacteristic
21C2×#13063304—21no—
22C2×#13063302—21no—
23C2×#13063302—21no—
24C2×C4×Dic86C2211yescharacteristic
25C2×D4×Dic43C2211yescharacteristic
26C2×D4×Dic43C2211yescharacteristic
27C22×Dic43⋊C4—21no—
28#14583206—24no—
29C2×#13063258C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36#14582838—21no—
37#14582819—21no—
38#14582806C2211yescharacteristic
39#14582806C2211yescharacteristic
40#14582795C2211yescharacteristic
41#14582795C2211yescharacteristic
42#14582783—21no—
43#14582783—21no—
44#14582765C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C4×SD16×C43—24no—
59C2×#106×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86D411yescharacteristic
65C23×Dic43—21no—
66C23×Dic43—21no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063324—22no—
70#13063324—22no—
71#13063317—22no—
72#13063317D414yes—
73#13063316—22no—
74#13063316—22no—
75#13063304—28no—
76#13063302—28no—
77#13063302—28no—
78C4×Dic86—22no—
79C4×Dic86—22no—
80D4×Dic43—22no—
81D4×Dic43—22no—
82D4×Dic43—22no—
83D4×Dic43—22no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43D411yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—28no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4D411yescharacteristic
98C2×Dic43⋊C4D411yescharacteristic
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C4×Dic43C2311yescharacteristic
102C2×C4×Dic43C2311yescharacteristic
103#13063258—22no—
104#13063256—22no—
105C4⋊(C43⋊C8)—22no—
106#13063249—22no—
107#13063249—22no—
108#13063246—22no—
109#13063246—22no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C22×Q8×C43C2311yescharacteristic
119C22×D4×C43C2311yescharacteristic
120C23×C4×C43—21no—
121C2×SD16×C43—22no—
122C2×SD16×C43—22no—
123C2×SD16×C43Q814yescomplemented
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C4×Q8×C43—22no—
127C4×Q8×C43—22no—
128C4×D4×C43—22no—
129C4×D4×C43D414yes—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C22⋊C4×C43—21no—
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136#106×C43—22no—
137#103×C43—22no—
138#102×C43—22no—
139C4×C8×C43—22no—
140C24×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×Q812yes—
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—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—81no—
158C22×C4×C43—81no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C22×Dic43—24no—
163C22×Dic43—24no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—42no—
169C22×Dic43—42no—
170C22×Dic43—81no—
171C22×Dic43—81no—
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175C22×Dic43C2×D411yescharacteristic
176C2×Dic86—22no—
177C2×Dic86—22no—
178C2×Dic86—24no—
179C2×Dic86—41no—
180C2×Dic86—81no—
181C2×Dic86—81no—
182SD16×C43—28no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43C2×Q812yes—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—42no—
193C4⋊C4×C43C2×D412yes—
194C22⋊C4×C43—24no—
195C42×C43—42no—
196C42×C43C2×D412yes—
197C42×C43C2×D412yes—
198C22⋊Dic43—24no—
199C22⋊Dic43—24no—
200C4⋊Dic43—24no—
201C4⋊Dic43—22no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43C2×D412yes—
209C4⋊Dic43C2×D412yes—
210Dic43⋊C4—24no—
211Dic43⋊C4—24no—
212Dic43⋊C4—22no—
213Dic43⋊C4—24no—
214Dic43⋊C4—24no—
215Dic43⋊C4—22no—
216Dic43⋊C4—42no—
217Dic43⋊C4—42no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
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—22no—
237Q8×C43—22no—
238Q8×C43—41no—
239Q8×C43—41no—
240D4×C43—22no—
241D4×C43—22no—
242D4×C43—22no—
243D4×C43C22⋊Q814yes—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—84no—
258C2×C4×C43#12012yes—
259C2×C4×C43#12012yes—
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C22×Q811yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C432−1+411yescharacteristic
265C2×C4×C432−1+411yescharacteristic
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—48no—
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—
290C2×Dic43—84no—
291C2×Dic43#13512yes—
292Dic86—44no—
293Dic86—84no—
294C8×C43—22no—
295C8×C43—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—42no—
316C4×C43—42no—
317C4×C43—81no—
318C4×C43C2×C22⋊Q811yescharacteristic
319C4×C43#53611yescharacteristic
320C4×C43#54811yescharacteristic
321C4×C43D4×Q811yescharacteristic
322Dic43—22no—
323Dic43—41no—
324Dic43—42no—
325Dic43—41no—
326Dic43—42no—
327Dic43—41no—
328Dic43—81no—
329Dic43—81no—
330C2×#554—431no—
331C2×#479—431no—
332C2×C4×SD16D4311yescharacteristic
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×SD16C2×D4311yescharacteristic
354#554—864no—
355#554—864no—
356C2×C4⋊Q8—431no—
357C2×#125—431no—
358C2×#125—431no—
359C2×C22⋊Q8—861no—
360C2×C22⋊Q8—861no—
361C2×C22⋊Q8—861no—
362C2×C4×Q8—431no—
363C2×C4×Q8C2×D4311yescharacteristic
364C2×C4×D4—431no—
365C2×C4×D4—431no—
366C2×C4×D4C2×D4311yescharacteristic
367C22×C4⋊C4—861no—
368#479—864no—
369C4×SD16—24no—
370C2×#107—431no—
371C2×#106—431no—
372C2×#106C2×D4311yescharacteristic
373C2×C4⋊C8—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×#103C2×D4311yescharacteristic
377C2×#102—431no—
378C2×#102—431no—
379C2×#102C2×D4311yescharacteristic
380C2×C4×C8C2×D4311yescharacteristic
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—431no—
402C22×Q8—861no—
403C22×Q8C22×D4311yescharacteristic
404C22×D4C22×D4311yescharacteristic
405C23×C4—21no—
406C23×C4—861no—
407C23×C4—861no—
408C2×SD16—22no—
409C2×SD16—22no—
410C2×SD16Dic8614yescomplemented
411C22×C8—431no—
412C22×C8—431no—
413C22×C8C22×D4311yescharacteristic
414C22×C8C22×D4311yescharacteristic
415C4⋊Q8—862no—
416C4⋊Q8—862no—
417#125—434no—
418#125—862no—
419#125—862no—
420#125—862no—
421C22⋊Q8—868no—
422C22⋊Q8—868no—
423C22⋊Q8—868no—
424C4×Q8—22no—
425C4×Q8—22no—
426C4×Q8—862no—
427C4×Q8—862no—
428C4×D4—22no—
429C4×D4—862no—
430C4×D4—862no—
431C4×D4—862no—
432C4×D4—862no—
433C4×D4C22⋊D4314yes—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—868no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4C22×D4311yescharacteristic
451C2×C4⋊C4C22×D4311yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C42—21no—
456C2×C42—431no—
457C2×C42—431no—
458C2×C42C22×D4311yescharacteristic
459#107—862no—
460#106—22no—
461#106—862no—
462C4⋊C8—862no—
463#103—22no—
464#103—862no—
465#103—862no—
466#102—22no—
467#102—862no—
468#102—862no—
469C4×C8—22no—
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—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—862no—
485C2×Q8—864no—
486C2×Q8—862no—
487C2×Q8—3441no—
488C2×Q8—3441no—
489C2×Q8—1721no—
490C2×Q8C2×Dic8612yes—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4C2×Dic8612yes—
495C2×D4#1062189812yes—
496C2×D4C2×C22⋊D4312yes—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—24no—
500C22×C4—21no—
501C22×C4—81no—
502C22×C4—81no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—864no—
508C22×C4—864no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—3441no—
514C22×C4—3441no—
515C22×C4—1722no—
516C22×C4—1722no—
517C22×C4D4×D4311yescharacteristic
518C22×C4D4×D4311yescharacteristic
519C22×C4C23×D4311yescharacteristic
520SD16—28no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8C2×Dic8612yes—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—42no—
537C4⋊C4—432no—
538C4⋊C4—432no—
539C4⋊C4—864no—
540C4⋊C4—864no—
541C4⋊C4—864no—
542C4⋊C4—862no—
543C4⋊C4—862no—
544C4⋊C4—862no—
545C4⋊C4—864no—
546C4⋊C4—864no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—1722no—
554C4⋊C4—1722no—
555C4⋊C4C2×C22⋊D4312yes—
556C22⋊C4—24no—
557C22⋊C4—864no—
558C22⋊C4—864no—
559C42—42no—
560C42—861no—
561C42—861no—
562C42—861no—
563C42—861no—
564C42D4×D4312yes—
565C42C2×C22⋊D4312yes—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23C2×D4×D4311yescharacteristic
574Q8—22no—
575Q8—22no—
576Q8—41no—
577Q8—41no—
578Q8—3444no—
579Q8—1724no—
580D4—22no—
581D4—22no—
582D4—22no—
583D4#1306330414yes—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—84no—
598C2×C4—432no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—3444no—
613C2×C4—1728no—
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—1721no—
624C2×C4#1306329312yes—
625C2×C4#1306329312yes—
626C2×C4C2×D4×D4311yescharacteristic
627C2×C4C22×C22⋊D4311yescharacteristic
628C2×C4C22×Dic8611yescharacteristic
629C2×C4C2×#1062189811yescharacteristic
630C2×C4#1306337211yescharacteristic
631C2×C4#1306337211yescharacteristic
632C8—22no—
633C8—41no—
634C8—1721no—
635C8—1721no—
636C22—24no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22C2×#1306329311yescharacteristic
644C22#1458355811yescharacteristic
645C22D4×Dic8611yescharacteristic
646C22#135×D4311yescharacteristic
647C22#1458369611yescharacteristic
648C22#1458370511yescharacteristic
649C22#1458370511yescharacteristic
650C4—22no—
651C4—22no—
652C4—42no—
653C4—42no—
654C4—81no—
655C4—862no—
656C4—3441no—
657C4—3441no—
658C4—1721no—
659C4—1722no—
660C4—1721no—
661C4—1721no—
662C4—1722no—
663C4C2×#1306330411yescharacteristic
664C4#1458347011yescharacteristic
665C4#1458355811yescharacteristic
666C4D4×Dic8611yescharacteristic
667C2—44no—
668C2#1913796011yescharacteristic
669C2#1914380911yescharacteristic
670C2#1914386811yescharacteristic
671C2#1914724511yescharacteristic
672C2#1914741811yescharacteristic
673C2#1914747111yescharacteristic
674C2#1914753611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenterC2×C4×SD16D43
hypocenterC43#24337
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#14583206C2semidirect
3. #19139957C2semidirect
4. #19135935C2semidirect
5. #19135926C2semidirect
6. #19135744C2semidirect
7. #19135734C2semidirect
8. #19135560C2semidirect
9. #19135531C2semidirect
123. C2×SD16×C43Q8semidirect
400. C43#24337semidirect
410. C2×SD16Dic86semidirect

Maximal subgroups

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

subgroupindex
C2×#145836082
C2×#145832062
#191399572
#191359352
#191359262
#191357442
#191357342
#191355602
#191355312
#191349312
#191348542
#191348402
#191346052
C2×C4×SD16×C432
#2433743