Finite Group Databasebeta

← #25096066

Subgroups — #25096066

Order 11008.

1514 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621902C211yesmaximal, characteristic
2C2×C4⋊C8×D43C211yesmaximal, characteristic, complemented
3C2×#14582894C212yesmaximal
4#19137000C211yesmaximal, characteristic, complemented
5#19134608C212yesmaximal, complemented
6#19134604C212yesmaximal, complemented
7#19134600C211yesmaximal, characteristic, complemented
8#19134596C211yesmaximal, characteristic, complemented
9#19134592C211yesmaximal, characteristic, complemented
10#19134310C212yesmaximal, complemented
11C43×#1803C211yesmaximal, characteristic, complemented
12C22×#10621902C2211yescharacteristic
13C22×C8×D43C2212yes—
14C4×#10621902—24no—
15C4×#10621902C418yescomplemented
16C2×Q8×Dic43C2211yescharacteristic
17C2×C4×D172—21no—
18C2×C4×D172C2211yescharacteristic
19C2×#13063287—21no—
20C2×#13063287C2211yescharacteristic
21C2×#13063283—21no—
22C2×#13063283C2212yes—
23C2×#13063283C2211yescharacteristic
24C2×C42×D43—21no—
25C2×C42×D43C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×Dic43⋊C8C2212yes—
28C4⋊C8×D43—24no—
29#14582894—28no—
30C2×#13063249C2212yes—
31C2×#13063247C2212yes—
32C2×#13063245C2212yes—
33#14582769C2211yescharacteristic
34#14582764C2212yes—
35#14582756—21no—
36#14582756—21no—
37C4⋊C4×Dic43—21no—
38C4⋊C4×Dic43—21no—
39#14582662C2212yes—
40#14582661C2212yes—
41#14582661C2212yes—
42C2×C4×Q8×C43C2211yescharacteristic
43C2×C4⋊C8×C43C2211yescharacteristic
44C2×#103×C43C2212yes—
45C43×#384C2211yescharacteristic
46C43×#340C2212yes—
47C2×#10621902—22no—
48C2×#10621902—22no—
49C2×#10621902—22no—
50C2×#10621902C2×C414yes—
51C2×#10621902D414yes—
52C2×#10621902Q814yes—
53C22×D172—21no—
54C22×D172C2311yescharacteristic
55C22×C4×D43—21no—
56C22×C4×D43—21no—
57C22×C4×D43—21no—
58C22×C4×D43D411yescharacteristic
59C22×C4×D43D411yescharacteristic
60C22×C4×D43C2311yescharacteristic
61C22×C43⋊C8C2312yes—
62C2×C8×D43—24no—
63C2×C8×D43—24no—
64C2×C8×D43—24no—
65Q8×Dic43—22no—
66Q8×Dic43C2×C414yes—
67C4×D172—28no—
68C4×D172—22no—
69C4×D172C2×C414yes—
70#13063287—28no—
71#13063287—22no—
72#13063287C2×C414yes—
73#13063283—22no—
74#13063283—28no—
75#13063283—24no—
76#13063283—24no—
77#13063283C2×C414yes—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2312yes—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—22no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—22no—
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93C42×D43—28no—
94C42×D43C2×C414yes—
95C42×D43D414yes—
96C4⋊(C43⋊C8)—22no—
97Dic43⋊C8—24no—
98#13063249—24no—
99#13063247—24no—
100#13063245—24no—
101C43⋊#95—22no—
102C43⋊#95—22no—
103C22×Q8×C43C2311yescharacteristic
104C22×C8×C43C2312yes—
105C4×Q8×C43—22no—
106C4×Q8×C43C2×C414yes—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2312yes—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C42×C43—21no—
113C2×C42×C43C2311yescharacteristic
114C4⋊C8×C43—22no—
115#103×C43—24no—
116C23×D43—21no—
117C23×D43C2×D411yescharacteristic
118C2×Q8×C43—21no—
119C2×Q8×C43—21no—
120C2×Q8×C43—21no—
121C2×Q8×C43C22×C412yes—
122C2×Q8×C43C2×D412yes—
123C2×Q8×C43C2×Q812yes—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—22no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2411yescharacteristic
130C22×Dic43—21no—
131C22×Dic43—22no—
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135#10621902—28no—
136#10621902—28no—
137#10621902—28no—
138#10621902C4⋊C4116yescomplemented
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—24no—
143C2×D172—24no—
144C2×D172—24no—
145C2×D172C22×C412yes—
146C2×D172C2×D412yes—
147C2×D172C2×Q812yes—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—24no—
151C2×C4×D43—24no—
152C2×C4×D43—24no—
153C2×C4×D43—24no—
154C2×C4×D43—24no—
155C2×C4×D43—41no—
156C2×C4×D43—41no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43C22⋊C414yes—
162C2×C4×D43C22⋊C414yes—
163C2×C4×D43C22×C412yes—
164C2×C4×D43C2×D412yes—
165C2×C4×D43C2×D412yes—
166C2×C4×D43C2×Q812yes—
167C2×C4×D43#4112yes—
168C2×C4×D43#4112yes—
169C2×C8×C43—22no—
170C2×C8×C43—22no—
171C2×C8×C43—22no—
172C4⋊C4×C43—24no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43—42no—
178C4⋊C4×C43C22×C412yes—
179C42×C43—24no—
180C42×C43C22×C412yes—
181C42×C43C2×D412yes—
182(C2×D43)⋊C4—24no—
183(C2×D43)⋊C4—24no—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—44no—
186C4⋊Dic43—21no—
187C4⋊Dic43—24no—
188C4⋊Dic43—22no—
189C4⋊Dic43—22no—
190C4⋊Dic43—42no—
191C4⋊Dic43—42no—
192C4⋊Dic43C22×C412yes—
193C4×Dic43—24no—
194C4×Dic43—24no—
195C4×Dic43—44no—
196C4×Dic43C22⋊C414yes—
197C4×Dic43C22⋊C414yes—
198C4×Dic43C22×C412yes—
199C4×Dic43C2×D412yes—
200C2×C43⋊C8—22no—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—22no—
203C8×D43—48no—
204C23×C43C22×D411yescharacteristic
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—22no—
210C22×D43—22no—
211C22×D43—22no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43C2×C22⋊C412yes—
217C22×D43#12112yes—
218C22×D43C22⋊Q812yes—
219Q8×C43—22no—
220Q8×C43—22no—
221Q8×C43—22no—
222Q8×C43C2×C4⋊C414yes—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43C2×C22⋊C412yes—
235C2×C4×C43C2×C22⋊C412yes—
236C2×C4×C43#13512yes—
237C2×C4×C43#13512yes—
238C2×C4×C43C23×C411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×Q811yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—22no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43C2×C22⋊C412yes—
255C2×Dic43C2×C22⋊C412yes—
256C2×Dic43C2×C22⋊C412yes—
257C2×Dic43#12112yes—
258C2×Dic43C22⋊Q812yes—
259D172—216no—
260D172—22no—
261D172—22no—
262D172—22no—
263D172C2×C4⋊C414yes—
264C4×D43—28no—
265C4×D43—216no—
266C4×D43—44no—
267C4×D43—48no—
268C4×D43—48no—
269C4×D43C2×C4⋊C414yes—
270C4×D43#11714yes—
271C4×D43#12114yes—
272C4×D43C22⋊Q814yes—
273C8×C43—42no—
274C43⋊C8—42no—
275#20645—431nomaximal, Sylow
276C22×C43C22×C22⋊C411yescharacteristic
277C22×C43C2×#12111yescharacteristic
278C22×C43C2×C22⋊Q811yescharacteristic
279C22×C43C2×#13511yescharacteristic
280C22×C43C2×#13511yescharacteristic
281C22×C43#57511yescharacteristic
282C22×C43#57511yescharacteristic
283C2×D43—22no—
284C2×D43—22no—
285C2×D43—22no—
286C2×D43—22no—
287C2×D43—22no—
288C2×D43—22no—
289C2×D43—24no—
290C2×D43—42no—
291C2×D43—42no—
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—42no—
295C2×D43—42no—
296C2×D43#38014yes—
297C4×C43—22no—
298C4×C43—24no—
299C4×C43—42no—
300C4×C43—82no—
301C4×C43#41614yescomplemented
302C4×C43C22×C4⋊C411yescharacteristic
303C4×C43C2×#11711yescharacteristic
304C4×C43C2×#12111yescharacteristic
305C4×C43C2×C22⋊Q811yescharacteristic
306Dic43—22no—
307Dic43—22no—
308Dic43—42no—
309Dic43—82no—
310Dic43#38014yes—
311C2×C4×#41—431no—
312C22×C4⋊C8—431no—
313C2×#416—432no—
314#2285—431no—
315#1805—432no—
316#1804—432no—
317#1803—431no—
318#1803D4311yescharacteristic, complemented
319#1802—431no—
320#1802—431no—
321#1735—432no—
322C2×C43C2×#38011yescharacteristic
323C2×C43C2×#41611yescharacteristic
324C2×C43#289611yescharacteristic
325C2×C43#303511yescharacteristic
326C2×C43#303511yescharacteristic
327C2×C43#307611yescharacteristic
328C2×C43#307611yescharacteristic
329D43—24no—
330D43—44no—
331C22×#41—431no—
332C23×C8—432no—
333C4×#41—438no—
334C4×#41—864no—
335C2×C4×Q8—431no—
336C2×C4×Q8C2×D4311yescharacteristic
337C2×C4×D4—431no—
338C2×C4×D4—431no—
339C2×C4×D4—861no—
340C2×C4×D4—861no—
341C2×#117—431no—
342C2×#117—432no—
343C2×#117—861no—
344C22×C42—431no—
345C22×C42—861no—
346C2×C4⋊C8—432no—
347C2×C4⋊C8—431no—
348C2×C4⋊C8—864no—
349C2×C4⋊C8C2×D4311yescharacteristic
350#416—868no—
351C2×#103—432no—
352C2×#103C2×D4312yes—
353C2×#102—432no—
354C2×#102—432no—
355#384—431no—
356#384C2×D4311yescharacteristic
357#382—432no—
358#380—861no—
359#380—861no—
360C4×C4⋊C4—861no—
361C4×C4⋊C4—861no—
362#340—432no—
363#340—432no—
364#340—432no—
365#340C2×D4312yes—
366C43#2064511yescharacteristic, complemented, Sylow
367C2×#41—434no—
368C2×#41—434no—
369C2×#41—434no—
370C2×#41—862no—
371C2×#41—862no—
372C2×#41—862no—
373C22×Q8C22×D4311yescharacteristic
374C22×D4—431no—
375C22×D4—861no—
376C23×C4—431no—
377C23×C4—431no—
378C23×C4—431no—
379C23×C4—861no—
380C23×C4—861no—
381C23×C4—861no—
382C22×C8—432no—
383C22×C8—864no—
384C22×C8—864no—
385C22×C8—864no—
386C22×C8C22×D4312yes—
387C4×Q8—22no—
388C4×Q8—434no—
389C4×Q8—862no—
390C4×Q8C4×D4314yes—
391C4×D4—434no—
392C4×D4—434no—
393C4×D4—868no—
394C4×D4—862no—
395C4×D4—868no—
396C4×D4—862no—
397#117—434no—
398#117—868no—
399#117—862no—
400#117—864no—
401#117—864no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—432no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4C22×D4312yes—
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—862no—
416C2×C42—21no—
417C2×C42—431no—
418C2×C42—431no—
419C2×C42—431no—
420C2×C42—434no—
421C2×C42—434no—
422C2×C42—868no—
423C2×C42—861no—
424C2×C42—861no—
425C2×C42—862no—
426C2×C42C22×D4311yescharacteristic
427C4⋊C8—22no—
428C4⋊C8—864no—
429C4⋊C8—862no—
430#103—24no—
431#103—864no—
432#102—864no—
433#102—864no—
434#95—862no—
435#95—862no—
436C24—431no—
437C24—861no—
438#41—4316no—
439#41—868no—
440#41—868no—
441#41—868no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8C2×C4×D4312yes—
446C2×Q8D4×D4312yes—
447C2×Q8Q8×D4312yes—
448C2×D4—432no—
449C2×D4—432no—
450C2×D4—432no—
451C2×D4—864no—
452C2×D4—864no—
453C2×D4—864no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—431no—
461C22×C4—432no—
462C22×C4—432no—
463C22×C4—432no—
464C22×C4—432no—
465C22×C4—432no—
466C22×C4—432no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—434no—
470C22×C4—434no—
471C22×C4—864no—
472C22×C4—864no—
473C22×C4—864no—
474C22×C4—864no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—861no—
478C22×C4—864no—
479C22×C4—862no—
480C22×C4—1721no—
481C22×C4—1721no—
482C22×C4—1722no—
483C22×C4—1722no—
484C22×C4—1722no—
485C22×C4—1722no—
486C22×C4D4×D4311yescharacteristic
487C22×C4D4×D4311yescharacteristic
488C22×C4C23×D4311yescharacteristic
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—862no—
493C2×C8—862no—
494C2×C8—862no—
495C2×C8—1728no—
496C4⋊C4—24no—
497C4⋊C4—21no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4—432no—
503C4⋊C4—864no—
504C4⋊C4—861no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—1722no—
508C4⋊C4—1722no—
509C4⋊C4C2×C4×D4312yes—
510C22⋊C4—864no—
511C22⋊C4—864no—
512C22⋊C4—864no—
513C22⋊C4—1724no—
514C42—24no—
515C42—434no—
516C42—434no—
517C42—432no—
518C42—432no—
519C42—864no—
520C42—864no—
521C42—1724no—
522C42C2×C4×D4312yes—
523C42D4×D4312yes—
524C23—432no—
525C23—432no—
526C23—432no—
527C23—861no—
528C23—861no—
529C23—861no—
530C23—861no—
531C23—862no—
532C23—862no—
533C23—862no—
534C23—1721no—
535C23—1721no—
536C23—1721no—
537C23—1721no—
538C23C2×D4×D4311yescharacteristic
539Q8—22no—
540Q8—22no—
541Q8—22no—
542Q8C4⋊C4×D4314yes—
543D4—434no—
544D4—8616no—
545D4—862no—
546D4—862no—
547D4—862no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—432no—
560C2×C4—432no—
561C2×C4—432no—
562C2×C4—434no—
563C2×C4—434no—
564C2×C4—434no—
565C2×C4—434no—
566C2×C4—432no—
567C2×C4—432no—
568C2×C4—8616no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—868no—
574C2×C4—862no—
575C2×C4—1724no—
576C2×C4—1728no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1728no—
583C2×C4C22⋊C4×D4312yes—
584C2×C4C22⋊C4×D4312yes—
585C2×C4#1306334612yes—
586C2×C4#1306334812yes—
587C2×C4C22×C4×D4311yescharacteristic
588C2×C4C2×D4×D4311yescharacteristic
589C2×C4C2×D4×D4311yescharacteristic
590C2×C4C2×Q8×D4311yescharacteristic
591C2×C4#41×D4311yescharacteristic
592C2×C4#41×D4311yescharacteristic
593C8—42no—
594C8—1722no—
595C22—434no—
596C22—862no—
597C22—862no—
598C22—862no—
599C22—862no—
600C22—862no—
601C22—862no—
602C22—864no—
603C22—1722no—
604C22—1722no—
605C22—1722no—
606C22—1722no—
607C22—1722no—
608C22—1722no—
609C22C2×C22⋊C4×D4311yescharacteristic
610C22#121×D4311yescharacteristic
611C22C22⋊Q8×D4311yescharacteristic
612C22C2×#1306334611yescharacteristic
613C22C2×#1306334811yescharacteristic
614C22#1458369511yescharacteristic
615C22#1458369811yescharacteristic
616C4—24no—
617C4—22no—
618C4—42no—
619C4—82no—
620C4—434no—
621C4—862no—
622C4—862no—
623C4—3442no—
624C4—1722no—
625C4#1458289414yescomplemented
626C4C2×C4⋊C4×D4311yescharacteristic
627C4#117×D4311yescharacteristic
628C4#121×D4311yescharacteristic
629C4C22⋊Q8×D4311yescharacteristic
630C2—864no—
631C2—1724no—
632C2#380×D4311yescharacteristic
633C2C2×#1458289411yescharacteristic
634C2#1914311111yescharacteristic
635C2#1914404511yescharacteristic
636C2#1914405311yescharacteristic
637C2#1914437811yescharacteristic
638C2#1914438611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1803C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
cosocleC22×C4×C43C24
hypercenter#1803D43
hypocenterC43#20645
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C8×D43C2semidirect
4. #19137000C2semidirect
5. #19134608C2semidirect
6. #19134604C2semidirect
7. #19134600C2semidirect
8. #19134596C2semidirect
9. #19134592C2semidirect
10. #19134310C2semidirect
11. C43×#1803C2semidirect
15. C4×#10621902C4semidirect
138. #10621902C4⋊C4semidirect
301. C4×C43#416semidirect
318. #1803D43semidirect
366. C43#20645semidirect
625. C4#14582894semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106219022
C2×C4⋊C8×D432
C2×#145828942
#191370002
#191346082
#191346042
#191346002
#191345962
#191345922
#191343102
C43×#18032
#2064543