Finite Group Databasebeta

← #25097320

Subgroups — #25097320

Order 11008.

1590 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D43C211yesmaximal, characteristic
2C2×#14582935C211yesmaximal, characteristic, complemented
3C22×(C2×D43)⋊C8C211yesmaximal, characteristic
4#19136974C211yesmaximal, characteristic
5#19134793C212yesmaximal, complemented
6#19134791C212yesmaximal, complemented
7#19134786C212yesmaximal, complemented
8#19134781C212yesmaximal, complemented
9#19134312C211yesmaximal, characteristic, complemented
10#19134311C211yesmaximal, characteristic, complemented
11C2×C43×#427C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C23×C43⋊C8C2211yescharacteristic
14C2×#13063284C2211yescharacteristic
15C2×#13063284C2211yescharacteristic
16C2×#13063283C2212yes—
17C2×#13063282—21no—
18C2×#13063281—21no—
19#117×D43—24no—
20#117×D43—24no—
21C2×C4⋊C4×D43C2212yes—
22C2×C22⋊C4×D43—21no—
23C2×C42×D43—21no—
24#14582935—24no—
25C2×#13063258C2212yescomplemented
26C2×#13063256C2212yescomplemented
27C2×(C2×D43)⋊C8C418yescomplemented
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32#14582760—21no—
33#14582756C2212yes—
34#14582756C2212yes—
35#14582754—21no—
36C4×(C2×D43)⋊C4—21no—
37C4×(C2×D43)⋊C4—21no—
38#14582662C2212yescomplemented
39#14582662C2212yescomplemented
40#14582661C2212yescomplemented
41#14582661C2212yescomplemented
42C23×C8×C43C2211yescharacteristic
43C2×#117×C43C2211yescharacteristic
44C2×#117×C43C2211yescharacteristic
45C43×#427—24no—
46C2×#107×C43C2212yescomplemented
47C2×#106×C43C2212yescomplemented
48C24×D43D411yescharacteristic
49C23×Dic43D411yescharacteristic
50C22×C4×D43—22no—
51C22×C4×D43—22no—
52C22×C4×D43—22no—
53C22×C4×D43—22no—
54C22×C4×D43—22no—
55C22×C4×D43C2×C414yes—
56C22×C4×D43D411yescharacteristic
57C22×C4×D43D411yescharacteristic
58C22×C4×D43Q814yes—
59C22×C4×D43C2311yescharacteristic
60C22×C4×D43C2311yescharacteristic
61C22×C43⋊C8—22no—
62C22×C43⋊C8—22no—
63C22×C43⋊C8C2×C414yescomplemented
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063284—22no—
67#13063284—22no—
68#13063284—22no—
69#13063284D414yes—
70#13063283—24no—
71#13063283—24no—
72#13063282—28no—
73#13063281—28no—
74C2×C4⋊Dic43C2312yes—
75C2×C4⋊Dic43C2312yes—
76C2×Dic43⋊C4—22no—
77C4⋊C4×D43—24no—
78C4⋊C4×D43—24no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×(C2×D43)⋊C4—22no—
82C2×(C2×D43)⋊C4—22no—
83C2×(C2×D43)⋊C4—22no—
84C22⋊C4×D43—28no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—22no—
87C2×C4×Dic43—21no—
88C42×D43—28no—
89#13063258—24no—
90#13063256—24no—
91(C2×D43)⋊C8C2×C414yes—
92(C2×D43)⋊C8C2×C414yes—
93(C2×D43)⋊C8C2×C414yescomplemented
94(C2×D43)⋊C8C2×C414yescomplemented
95C43⋊#95—22no—
96C43⋊#95—22no—
97C23×C4×C43C2311yescharacteristic
98C22×C8×C43—22no—
99C22×C8×C43—22no—
100C22×C8×C43C2×C414yescomplemented
101C22×C8×C43C2311yescharacteristic
102C22×C8×C43C2311yescharacteristic
103#117×C43—22no—
104#117×C43—22no—
105#117×C43—22no—
106#117×C43D414yes—
107C2×C4⋊C4×C43C2312yes—
108C2×C4⋊C4×C43C2312yes—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C42×C43—21no—
112C2×C42×C43—21no—
113#107×C43—24no—
114#106×C43—24no—
115C24×C43C2×D411yescharacteristic
116C23×D43—22no—
117C23×D43—22no—
118C23×D43—24no—
119C23×D43—42no—
120C23×D43C4⋊C414yes—
121C23×D43C2×D411yescharacteristic
122C23×D43C2×D411yescharacteristic
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43C22×C412yes—
126C22×C4×C43C2×D412yes—
127C22×C4×C43C2×D412yes—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×Q812yes—
130C22×C4×C43#4112yes—
131C22×C4×C43#4112yes—
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43C4⋊C414yes—
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C2×C4×D43—28no—
141C2×C4×D43—28no—
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—28no—
145C2×C4×D43—28no—
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—28no—
157C2×C4×D43—44no—
158C2×C4×D43—44no—
159C2×C4×D43C4⋊C414yes—
160C2×C4×D43C4⋊C414yes—
161C2×C4×D43C22×C412yes—
162C2×C4×D43C22×C412yes—
163C2×C4×D43C2×Q812yes—
164C2×C4×D43C2×Q812yes—
165C2×C8×C43—28no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43C22×C412yes—
171C2×C8×C43C22×C412yes—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43C2×D414yes—
176C22⋊C4×C43—24no—
177C22⋊C4×C43—42no—
178C42×C43—24no—
179C42×C43—42no—
180C22⋊Dic43—24no—
181C22⋊Dic43—42no—
182(C2×D43)⋊C4—28no—
183(C2×D43)⋊C4—44no—
184(C2×D43)⋊C4—44no—
185C4⋊Dic43—22no—
186C4⋊Dic43—22no—
187C4⋊Dic43—22no—
188C4⋊Dic43C2×D414yes—
189Dic43⋊C4—28no—
190C4×Dic43—28no—
191C4×Dic43—24no—
192C4×Dic43—42no—
193C2×C43⋊C8—28no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C22×C412yes—
199C2×C43⋊C8C22×C412yes—
200C23×C43—22no—
201C23×C43—22no—
202C23×C43C2×C4⋊C412yes—
203C23×C43#12012yes—
204C23×C43#12312yes—
205C23×C43C22×D411yescharacteristic
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—22no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—22no—
212C22×D43—22no—
213C22×D43—28no—
214C22×D43—28no—
215C22×D43—44no—
216C22×D43—48no—
217C22×D43—48no—
218C22×D43C2×C4⋊C412yes—
219C22×D43C2×C4⋊C412yes—
220C22×D43#13514yes—
221C2×C4×C43—24no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43C2×C4⋊C412yes—
228C2×C4×C43C4×D414yes—
229C2×C4×C43C4×D414yes—
230C2×C4×C43#12012yes—
231C2×C4×C43C22⋊Q814yes—
232C2×C4×C43C22⋊Q814yes—
233C2×C4×C43#12312yes—
234C2×C4×C43C23×C411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C22×Q811yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—28no—
245C2×Dic43—24no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43C2×C4⋊C412yes—
252C2×Dic43C2×C4⋊C412yes—
253C4×D43—22no—
254C4×D43—22no—
255C4×D43—22no—
256C4×D43—22no—
257C4×D43—22no—
258C4×D43—22no—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—28no—
262C4×D43—28no—
263C4×D43—416no—
264C8×C43—22no—
265C8×C43—22no—
266C43⋊C8—22no—
267C43⋊C8—22no—
268#20843—431nomaximal, Sylow
269C22×C43—24no—
270C22×C43—22no—
271C22×C43—22no—
272C22×C43—24no—
273C22×C43#38514yes—
274C22×C43C22×C4⋊C411yescharacteristic
275C22×C43C2×#12011yescharacteristic
276C22×C43C2×#12311yescharacteristic
277C22×C43C2×#13512yes—
278C22×C43#57512yes—
279C2×D43—24no—
280C2×D43—22no—
281C2×D43—24no—
282C2×D43—22no—
283C2×D43—22no—
284C2×D43—22no—
285C2×D43—22no—
286C2×D43—416no—
287C2×D43—42no—
288C2×D43—42no—
289C2×D43#42714yescomplemented
290C4×C43—44no—
291C4×C43—82no—
292C4×C43#38514yes—
293C4×C43C2×C4×D411yescharacteristic
294C4×C43C2×C4×D411yescharacteristic
295C4×C43C2×C22⋊Q811yescharacteristic
296C4×C43C2×C22⋊Q811yescharacteristic
297Dic43—22no—
298Dic43—22no—
299Dic43—44no—
300Dic43—82no—
301C22×#117—431no—
302C2×#427—431no—
303C2×#427D4311yescharacteristic, complemented
304C22×C22⋊C8—431no—
305#2280—431no—
306#1854—432no—
307#1854—432no—
308#1853—432no—
309#1852—432no—
310#1735—431no—
311#1735—431no—
312C2×C43—24no—
313C2×C43C2×#38511yescharacteristic
314C2×C43C2×#42711yescharacteristic
315C2×C43#291111yescharacteristic
316C2×C43#300212yes—
317C2×C43#309112yes—
318D43—24no—
319D43—42no—
320C24×C4—431no—
321C23×C8—431no—
322C23×C8C2×D4311yescharacteristic
323C2×#117—431no—
324C2×#117—431no—
325C2×#117—432no—
326C2×#117—861no—
327C2×#117—861no—
328C2×#117—864no—
329C2×#117—864no—
330C2×#117C2×D4311yescharacteristic
331C2×#117C2×D4311yescharacteristic
332C22×C4⋊C4—432no—
333C22×C22⋊C4—861no—
334C22×C42—861no—
335#427—24no—
336#427—864no—
337C2×#107—432no—
338C2×#107C2×D4312yescomplemented
339C2×#106—432no—
340C2×#106C2×D4312yescomplemented
341C2×C22⋊C8—431no—
342C2×C22⋊C8—431no—
343C2×C22⋊C8—431no—
344C2×C22⋊C8—431no—
345C2×C22⋊C8—438no—
346#381—861no—
347#380—432no—
348#380—432no—
349#379—861no—
350C4×C22⋊C4—861no—
351C4×C22⋊C4—861no—
352#340—432no—
353#340—432no—
354#340—432no—
355#340—432no—
356C43#2084311yescharacteristic, complemented, Sylow
357C25—431no—
358C23×C4—431no—
359C23×C4—434no—
360C23×C4—431no—
361C23×C4—431no—
362C23×C4—434no—
363C23×C4—431no—
364C23×C4—431no—
365C23×C4—862no—
366C23×C4—862no—
367C23×C4—862no—
368C23×C4—862no—
369C23×C4—862no—
370C23×C4C22×D4311yescharacteristic
371C22×C8—22no—
372C22×C8—22no—
373C22×C8—434no—
374C22×C8—431no—
375C22×C8—431no—
376C22×C8—862no—
377C22×C8—862no—
378C22×C8C4×D4314yescomplemented
379C22×C8C22×D4311yescharacteristic
380C22×C8C22×D4311yescharacteristic
381#117—22no—
382#117—22no—
383#117—22no—
384#117—434no—
385#117—868no—
386#117—868no—
387#117—864no—
388#117—862no—
389#117—864no—
390#117—862no—
391#117—862no—
392#117C22⋊D4314yes—
393C2×C4⋊C4—432no—
394C2×C4⋊C4—432no—
395C2×C4⋊C4—864no—
396C2×C4⋊C4—862no—
397C2×C4⋊C4—864no—
398C2×C4⋊C4C22×D4312yes—
399C2×C4⋊C4C22×D4312yes—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—868no—
403C2×C22⋊C4—862no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—862no—
406C2×C22⋊C4—862no—
407C2×C22⋊C4—861no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—868no—
411C2×C42—862no—
412C2×C42—861no—
413C2×C42—861no—
414#107—24no—
415#107—864no—
416#106—24no—
417#106—864no—
418C22⋊C8—434no—
419C22⋊C8—434no—
420C22⋊C8—434no—
421C22⋊C8—434no—
422#95—862no—
423#95—862no—
424C24—431no—
425C24—431no—
426C24—434no—
427C24—864no—
428C24—862no—
429C24—862no—
430C24—1722no—
431C24D4×D4311yescharacteristic
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—434no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—434no—
438C22×C4—434no—
439C22×C4—432no—
440C22×C4—432no—
441C22×C4—432no—
442C22×C4—432no—
443C22×C4—868no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—868no—
447C22×C4—868no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—868no—
451C22×C4—868no—
452C22×C4—862no—
453C22×C4—862no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—862no—
463C22×C4—862no—
464C22×C4—1724no—
465C22×C4—1724no—
466C22×C4C2×C4×D4312yes—
467C22×C4#1062189812yes—
468C22×C4D4×D4312yes—
469C22×C4D4×D4311yescharacteristic
470C22×C4Q8×D4312yes—
471C22×C4#1062190212yes—
472C22×C4C2×C22⋊D4312yes—
473C22×C4C23×D4311yescharacteristic
474C2×C8—28no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—432no—
480C2×C8—432no—
481C2×C8—868no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8C2×C4×D4312yes—
487C2×C8C2×C4×D4312yes—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—434no—
492C4⋊C4—868no—
493C4⋊C4—862no—
494C4⋊C4—862no—
495C4⋊C4—862no—
496C4⋊C4C2×C22⋊D4314yes—
497C22⋊C4—24no—
498C22⋊C4—42no—
499C22⋊C4—868no—
500C22⋊C4—864no—
501C22⋊C4—1724no—
502C22⋊C4—1724no—
503C22⋊C4—1722no—
504C42—24no—
505C42—42no—
506C42—868no—
507C42—864no—
508C42—1722no—
509C23—22no—
510C23—22no—
511C23—432no—
512C23—434no—
513C23—432no—
514C23—868no—
515C23—861no—
516C23—861no—
517C23—862no—
518C23—861no—
519C23—861no—
520C23—862no—
521C23—862no—
522C23—868no—
523C23—1724no—
524C23—1728no—
525C23—1728no—
526C23C4⋊C4×D4312yes—
527C23#1306329312yes—
528C23#1306331012yes—
529C23C2×D4×D4311yescharacteristic
530C2×C4—24no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—432no—
537C2×C4—432no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—868no—
543C2×C4—862no—
544C2×C4—862no—
545C2×C4—862no—
546C2×C4—862no—
547C2×C4—862no—
548C2×C4—862no—
549C2×C4—862no—
550C2×C4—862no—
551C2×C4—868no—
552C2×C4—868no—
553C2×C4—864no—
554C2×C4—17216no—
555C2×C4—1722no—
556C2×C4—1722no—
557C2×C4—1722no—
558C2×C4—1722no—
559C2×C4—1722no—
560C2×C4C4⋊C4×D4312yes—
561C2×C4C4×C22⋊D4314yes—
562C2×C4#1306328714yes—
563C2×C4#1306329312yes—
564C2×C4#1306330114yes—
565C2×C4#1306330314yes—
566C2×C4#1306331012yes—
567C2×C4C22×C4×D4311yescharacteristic
568C2×C4C2×D4×D4311yescharacteristic
569C2×C4C22×C22⋊D4311yescharacteristic
570C2×C4C2×Q8×D4311yescharacteristic
571C2×C4C2×#1062189811yescharacteristic
572C2×C4C2×#1062190211yescharacteristic
573C8—22no—
574C8—22no—
575C8—862no—
576C8—862no—
577C22—22no—
578C22—22no—
579C22—24no—
580C22—24no—
581C22—434no—
582C22—862no—
583C22—864no—
584C22—864no—
585C22—862no—
586C22—862no—
587C22—862no—
588C22—862no—
589C22—17216no—
590C22—1722no—
591C22—1722no—
592C22#1458277014yes—
593C22C2×C4⋊C4×D4311yescharacteristic
594C22C2×#1306329311yescharacteristic
595C22C2×#1306331011yescharacteristic
596C22#135×D4312yes—
597C22#1458369612yes—
598C4—44no—
599C4—82no—
600C4—862no—
601C4—862no—
602C4—3442no—
603C4—1724no—
604C4#1458277014yes—
605C4C2×C4×C22⋊D4311yescharacteristic
606C4C2×#1306328711yescharacteristic
607C4C2×#1306330111yescharacteristic
608C4C2×#1306330311yescharacteristic
609C2—24no—
610C2—864no—
611C2—1722no—
612C2C2×#1458277011yescharacteristic
613C2#427×D4311yescharacteristic
614C2#1914318311yescharacteristic
615C2#1914380912yes—
616C2#1914451212yes—
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#427C2
socleC23×C43C22×D4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenterC2×#427D43
hypocenterC43#20843
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. C2×#14582935C2semidirect
5. #19134793C2semidirect
6. #19134791C2semidirect
7. #19134786C2semidirect
8. #19134781C2semidirect
9. #19134312C2semidirect
10. #19134311C2semidirect
11. C2×C43×#427C2semidirect
25. C2×#13063258C22semidirect
26. C2×#13063256C22semidirect
27. C2×(C2×D43)⋊C8C4semidirect
38. #14582662C22semidirect
39. #14582662C22semidirect
40. #14582661C22semidirect
41. #14582661C22semidirect
46. C2×#107×C43C22semidirect
47. C2×#106×C43C22semidirect
63. C22×C43⋊C8C2×C4semidirect
93. (C2×D43)⋊C8C2×C4semidirect
94. (C2×D43)⋊C8C2×C4semidirect
100. C22×C8×C43C2×C4semidirect
289. C2×D43#427semidirect
303. C2×#427D43semidirect
338. C2×#107C2×D43semidirect
340. C2×#106C2×D43semidirect
356. C43#20843semidirect
378. C22×C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D432
C2×#145829352
C22×(C2×D43)⋊C82
#191369742
#191347932
#191347912
#191347862
#191347812
#191343122
#191343112
C2×C43×#4272
#2084343