Finite Group Databasebeta

← #25130898

Subgroups — #25130898

Order 11008.

1478 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583176C211yesmaximal, characteristic, complemented
2C2×#14583091C211yesmaximal, characteristic, complemented
3C4×#13063299C211yesmaximal, characteristic, complemented
4#19135774C212yesmaximal, complemented
5#19135591C212yesmaximal, complemented
6#19135548C211yesmaximal, characteristic, complemented
7#19135523C211yesmaximal, characteristic, complemented
8#19134943C212yesmaximal, complemented
9#19134842C212yesmaximal, complemented
10#19134575C211yesmaximal, characteristic, complemented
11C2×C43×#532C211yesmaximal, characteristic, complemented
12C22×#10621882C2212yes—
13C2×#13063299C2211yescharacteristic
14C2×C4×D172C2211yescharacteristic
15C2×C4×C22⋊D43—21no—
16#14583176—24no—
17#14583091—24no—
18C2×#13063258C2212yes—
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×#13063246C2212yes—
22C2×#13063246C2212yes—
23C2×#13063246C2212yes—
24C2×#13063245C2212yes—
25C2×C22⋊(C43⋊C8)C2212yes—
26#14582801C2211yescharacteristic
27#14582797C2211yescharacteristic
28#14582790—21no—
29#14582778—21no—
30#14582759C2211yescharacteristic
31C4×C4⋊Dic43C2211yescharacteristic
32C4×(C2×D43)⋊C4—21no—
33#14582661C2212yes—
34#14582661C2212yes—
35#14582654C2212yes—
36C22×#41×C43—21no—
37C43×#532—24no—
38C43×#532—24no—
39C2×C4⋊Q8×C43C2211yescharacteristic
40C2×#127×C43C2211yescharacteristic
41C2×#124×C43—21no—
42C2×#121×C43—21no—
43C2×#121×C43C2212yes—
44C2×C4×D4×C43—21no—
45C2×C4×D4×C43C2212yes—
46C22×C42×C43C2211yescharacteristic
47C22×D172C2311yescharacteristic
48C22×C22⋊D43—21no—
49C22×C4×D43—21no—
50C2×#10621882—24no—
51C2×#10621882—24no—
52C2×#10621882—42no—
53C22×C43⋊C8C2312yes—
54C22×C43⋊C8C2312yes—
55#13063299—22no—
56#13063299—22no—
57C4×D172—22no—
58C4×D172—22no—
59C4×C22⋊D43—44no—
60C2×C4⋊Dic43C2311yescharacteristic
61C2×C4⋊Dic43C2311yescharacteristic
62C2×C4⋊Dic43C2311yescharacteristic
63C2×Dic43⋊C4—21no—
64C2×C22⋊Dic43—21no—
65C2×(C2×D43)⋊C4—21no—
66C2×(C2×D43)⋊C4—21no—
67C2×(C2×D43)⋊C4—21no—
68C2×(C2×D43)⋊C4—21no—
69C2×C4×Dic43—21no—
70#13063258—24no—
71C4⋊(C43⋊C8)—22no—
72C4⋊(C43⋊C8)—22no—
73#13063246—24no—
74#13063246—24no—
75#13063246—42no—
76#13063245—24no—
77C22⋊(C43⋊C8)—42no—
78C43⋊#95—21no—
79C43⋊#95—21no—
80C43⋊#95—21no—
81C2×#41×C43—28no—
82C2×#41×C43—44no—
83C2×#41×C43—44no—
84C22×Q8×C43—21no—
85C22×D4×C43—22no—
86C22×D4×C43—21no—
87C22×D4×C43—21no—
88C22×D4×C43C2312yes—
89C23×C4×C43—22no—
90C23×C4×C43D411yescharacteristic
91C23×C4×C43D411yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C4⋊Q8×C43—22no—
94C4⋊Q8×C43D414yescomplemented
95#127×C43—22no—
96#127×C43D414yescomplemented
97#124×C43—28no—
98#121×C43—28no—
99#121×C43—24no—
100#121×C43—24no—
101C4×D4×C43—28no—
102C4×D4×C43—24no—
103C4×D4×C43—24no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43C2312yes—
106C2×C22⋊C4×C43—22no—
107C2×C22⋊C4×C43—22no—
108C2×C42×C43—22no—
109C2×C42×C43—22no—
110C2×C42×C43D411yescharacteristic
111C2×C42×C43D411yescharacteristic
112C2×C42×C43C2311yescharacteristic
113C2×C42×C43C2311yescharacteristic
114C24×C43—22no—
115C24×C43C2×D411yescharacteristic
116C23×D43—21no—
117#41×C43—432no—
118C2×Q8×C43—24no—
119C2×Q8×C43—42no—
120C2×Q8×C43—42no—
121C2×D4×C43—28no—
122C2×D4×C43—24no—
123C2×D4×C43—24no—
124C2×D4×C43—22no—
125C2×D4×C43—22no—
126C2×D4×C43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43—44no—
130C2×D4×C43—42no—
131C2×D4×C43—42no—
132C2×D4×C43—42no—
133C2×D4×C43—42no—
134C2×D4×C43—44no—
135C2×D4×C43C2×D414yes—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—28no—
139C22×C4×C43—22no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—22no—
147C22×C4×C43—41no—
148C22×C4×C43—41no—
149C22×C4×C43—44no—
150C22×C4×C43—44no—
151C22×C4×C43D814yescomplemented
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C2×C22⋊D43—24no—
159C2×C22⋊D43—42no—
160C2×C22⋊D43—42no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172#4112yescomplemented
170C2×C4×D43—42no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C4⋊C4×C43—24no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43C2×D414yes—
176C22⋊C4×C43—28no—
177C22⋊C4×C43—28no—
178C42×C43—22no—
179C42×C43—22no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43C2×D412yes—
183C42×C43C2×D412yes—
184C22⋊Dic43—42no—
185#10621882—48no—
186(C2×D43)⋊C4—24no—
187(C2×D43)⋊C4—42no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43#4112yescomplemented
196Dic43⋊C4—42no—
197C4×Dic43—42no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—22no—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—22no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—24no—
211C23×C43—42no—
212C23×C43—42no—
213C23×C43—42no—
214C23×C43—42no—
215C23×C43—42no—
216C23×C43—42no—
217C23×C43C2×D812yes—
218C23×C43C22×D411yescharacteristic
219C22×D43—22no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226Q8×C43—48no—
227D4×C43—24no—
228D4×C43—24no—
229D4×C43—48no—
230D4×C43—416no—
231D4×C43—42no—
232D4×C43—42no—
233D4×C43—48no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—28no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—24no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—44no—
247C2×C4×C43—416no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43#12012yes—
255C2×C4×C43#12012yes—
256C2×C4×C43C2×D812yes—
257C2×C4×C43C2×D812yes—
258C2×C4×C43AGL(1,ℤ/8)12yes—
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43H(5,𝔽2)11yescharacteristic
264C2×C4×C432−1+411yescharacteristic
265C22⋊D43—48no—
266C2×Dic43—22no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275D172—22no—
276D172—22no—
277D172—41no—
278D172—41no—
279C4×D43—84no—
280C43⋊C8—42no—
281C43⋊C8—42no—
282#24150—431nomaximal, Sylow
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—22no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—44no—
291C22×C43—44no—
292C22×C43—44no—
293C22×C43—82no—
294C22×C43—82no—
295C22×C43—82no—
296C22×C43—82no—
297C22×C43C2×#12011yescharacteristic
298C22×C43#52511yescharacteristic
299C22×C43#53711yescharacteristic
300C22×C43C22×D811yescharacteristic
301C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
302C22×C43#57511yescharacteristic
303C22×C43#57511yescharacteristic
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—81no—
311C4×C43—22no—
312C4×C43—22no—
313C4×C43—41no—
314C4×C43—44no—
315C4×C43—41no—
316C4×C43#44714yes—
317C4×C43#54611yescharacteristic
318C4×C43#54711yescharacteristic
319C4×C43#54811yescharacteristic
320C4×C43#55011yescharacteristic
321Dic43—42no—
322Dic43—81no—
323Dic43—81no—
324C2×#532D4311yescharacteristic, complemented
325C2×#474—431no—
326C2×#459—431no—
327C4×#121—431no—
328#2033—432no—
329#1999—432no—
330#1988—431no—
331#1982—431no—
332#1879—432no—
333#1862—432no—
334#1797—431no—
335C2×C43—42no—
336C2×C43—84no—
337C2×C43#240711yescharacteristic
338C2×C43C2×#44711yescharacteristic
339C2×C43#300511yescharacteristic
340C2×C43#310011yescharacteristic
341C2×C43#311511yescharacteristic
342C2×C43#324511yescharacteristic
343C2×C43#325111yescharacteristic
344D43—82no—
345C22×#41—21no—
346C22×D8—432no—
347#532—24no—
348#532—24no—
349C2×C4⋊Q8C2×D4311yescharacteristic
350C2×#127C2×D4311yescharacteristic
351C2×#124—21no—
352C2×#121—21no—
353C2×#121—431no—
354C2×#121C2×D4312yes—
355C2×C4×D4—21no—
356C2×C4×D4—431no—
357C2×C4×D4—861no—
358C2×C4×D4C2×D4312yes—
359C22×C42C2×D4311yescharacteristic
360#474—864no—
361#459—864no—
362C2×#107—432no—
363C2×C4⋊C8—431no—
364C2×C4⋊C8—431no—
365C2×#102—432no—
366C2×#102—432no—
367C2×#102—432no—
368C2×#102—432no—
369C2×C22⋊C8—432no—
370#390—431no—
371#389—431no—
372#388—861no—
373#386—861no—
374#380—431no—
375C4×C4⋊C4—431no—
376C4×C22⋊C4—861no—
377#340—432no—
378#340—432no—
379#336—432no—
380C43#2415011yescharacteristic, complemented, Sylow
381C2×#41—28no—
382C2×#41—44no—
383C2×#41—44no—
384C22×Q8—21no—
385C22×D4—22no—
386C22×D4—21no—
387C22×D4—21no—
388C22×D4—431no—
389C22×D4—861no—
390C22×D4C22×D4312yes—
391C23×C4—22no—
392C23×C4—861no—
393C23×C4C22⋊D4311yescharacteristic
394C23×C4C22⋊D4311yescharacteristic
395C23×C4C22×D4311yescharacteristic
396C2×D8—864no—
397C2×D8—864no—
398C2×D8—1722no—
399C22×C8—432no—
400C22×C8—432no—
401C4⋊Q8—22no—
402C4⋊Q8C22⋊D4314yescomplemented
403#127—22no—
404#127C22⋊D4314yescomplemented
405#124—28no—
406#121—28no—
407#121—24no—
408#121—24no—
409#121—862no—
410#121—862no—
411C4×D4—28no—
412C4×D4—24no—
413C4×D4—24no—
414C4×D4—862no—
415C4×D4—862no—
416C4×D4—1724no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4C22×D4312yes—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—861no—
433C2×C42C22⋊D4311yescharacteristic
434C2×C42C22⋊D4311yescharacteristic
435C2×C42C22×D4311yescharacteristic
436C2×C42C22×D4311yescharacteristic
437#107—864no—
438C4⋊C8—862no—
439C4⋊C8—862no—
440#102—864no—
441#102—864no—
442#102—864no—
443#102—1722no—
444C22⋊C8—1722no—
445#95—861no—
446#95—861no—
447#95—861no—
448C24—22no—
449C24—861no—
450C24C2×C22⋊D4311yescharacteristic
451#41—432no—
452C2×Q8—24no—
453C2×Q8—42no—
454C2×Q8—42no—
455C2×D4—28no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—44no—
466C2×D4—44no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—432no—
470C2×D4—864no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—1722no—
477C2×D4—1722no—
478C2×D4C2×C22⋊D4314yes—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—28no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—1722no—
498C22×C4—1722no—
499C22×C4—1722no—
500C22×C4#1062188214yescomplemented
501C22×C4C2×C22⋊D4311yescharacteristic
502C22×C4C2×C22⋊D4311yescharacteristic
503C22×C4C2×C22⋊D4311yescharacteristic
504C22×C4C2×C22⋊D4311yescharacteristic
505C22×C4C2×C22⋊D4311yescharacteristic
506C22×C4C23×D4311yescharacteristic
507D8—1728no—
508C2×C8—862no—
509C2×C8—862no—
510C2×C8—862no—
511C2×C8—862no—
512C2×C8—862no—
513C2×C8—862no—
514C4⋊C4—24no—
515C4⋊C4—22no—
516C4⋊C4—432no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—1722no—
523C4⋊C4C2×C22⋊D4314yes—
524C22⋊C4—28no—
525C22⋊C4—28no—
526C22⋊C4—864no—
527C22⋊C4—1722no—
528C22⋊C4—1722no—
529C22⋊C4—1722no—
530C22⋊C4—1722no—
531C42—22no—
532C42—22no—
533C42—21no—
534C42—21no—
535C42—1722no—
536C42C2×C22⋊D4312yes—
537C42C2×C22⋊D4312yes—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—24no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—862no—
552C23—1721no—
553C23—1721no—
554C23—1721no—
555C23—1721no—
556C23—1721no—
557C23—1721no—
558C23C2×#1062188212yes—
559C23C22×C22⋊D4311yescharacteristic
560Q8—48no—
561D4—24no—
562D4—24no—
563D4—48no—
564D4—416no—
565D4—42no—
566D4—42no—
567D4—48no—
568D4—862no—
569D4—862no—
570D4—1728no—
571D4—1721no—
572D4—1721no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—28no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—24no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—416no—
586C2×C4—44no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—862no—
594C2×C4—3444no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4#1306329412yes—
604C2×C4#1306329412yes—
605C2×C4C2×#1062188212yes—
606C2×C4C2×#1062188212yes—
607C2×C4#1306335112yes—
608C2×C4C22×C22⋊D4311yescharacteristic
609C2×C4C22×C22⋊D4311yescharacteristic
610C2×C4#41×D4311yescharacteristic
611C2×C4#41×D4311yescharacteristic
612C2×C4#1306337111yescharacteristic
613C2×C4#1306337211yescharacteristic
614C8—1722no—
615C8—1722no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—44no—
624C22—44no—
625C22—44no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—82no—
630C22—3441no—
631C22—3441no—
632C22—3441no—
633C22—3441no—
634C22—1722no—
635C22—1722no—
636C22—1722no—
637C22C2×#1306329411yescharacteristic
638C22#1458340611yescharacteristic
639C22#1458347711yescharacteristic
640C22C22×#1062188211yescharacteristic
641C22C2×#1306335111yescharacteristic
642C22#1458369711yescharacteristic
643C22#1458369711yescharacteristic
644C4—22no—
645C4—22no—
646C4—44no—
647C4—41no—
648C4—41no—
649C4—3441no—
650C4—3441no—
651C4—1722no—
652C4#1458303314yes—
653C4#1458353711yescharacteristic
654C4#1458354811yescharacteristic
655C4#1458355611yescharacteristic
656C4#1458356811yescharacteristic
657C2—42no—
658C2—84no—
659C2—3442no—
660C2#1913793411yescharacteristic
661C2C2×#1458303311yescharacteristic
662C2#1914383711yescharacteristic
663C2#1914459111yescharacteristic
664C2#1914474011yescharacteristic
665C2#1914590211yescharacteristic
666C2#1914595111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#532C2
socleC23×C43C22×D4
hypercenterC2×#532D43
hypocenterC43#24150
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×#14583176C2semidirect
2. C2×#14583091C2semidirect
3. C4×#13063299C2semidirect
4. #19135774C2semidirect
5. #19135591C2semidirect
6. #19135548C2semidirect
7. #19135523C2semidirect
8. #19134943C2semidirect
9. #19134842C2semidirect
10. #19134575C2semidirect
11. C2×C43×#532C2semidirect
94. C4⋊Q8×C43D4semidirect
96. #127×C43D4semidirect
151. C22×C4×C43D8semidirect
169. C2×D172#41semidirect
195. C4⋊Dic43#41semidirect
324. C2×#532D43semidirect
380. C43#24150semidirect
402. C4⋊Q8C22⋊D43semidirect
404. #127C22⋊D43semidirect
500. C22×C4#10621882semidirect

Maximal subgroups

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

subgroupindex
C2×#145831762
C2×#145830912
C4×#130632992
#191357742
#191355912
#191355482
#191355232
#191349432
#191348422
#191345752
C2×C43×#5322
#2415043