Finite Group Databasebeta

← #25101649

Subgroups — #25101649

Order 11008.

1538 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583444C211yesmaximal, characteristic
2C2×#14582949C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
4#19135545C212yesmaximal, complemented
5#19135520C212yesmaximal, complemented
6#19134913C211yesmaximal, characteristic, complemented
7#19134912C211yesmaximal, characteristic, complemented
8#19134910C211yesmaximal, characteristic, complemented
9#102×Dic43C212yesmaximal, complemented
10#19134409C212yesmaximal, complemented
11C43×#1874C211yesmaximal, characteristic, complemented
12C22×#10621900—21no—
13#14583444—24no—
14#14583444C418yescomplemented
15C2×#13063324C2211yescharacteristic
16C2×#13063321C2211yescharacteristic
17C2×#13063311—21no—
18C2×#13063299C2211yescharacteristic
19C2×#13063297—21no—
20C2×D4×Dic43C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×(C22⋊D43)⋊C4—21no—
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4×Dic43—21no—
25C22×C4×Dic43C2211yescharacteristic
26#14582949—24no—
27C2×Dic43⋊C8C2212yes—
28C2×#13063247C2212yes—
29C2×#13063246C2212yes—
30C2×#13063245C2212yes—
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×C8×Dic43C2212yes—
33C4⋊C4×Dic43—21no—
34C4⋊C4×Dic43—21no—
35C4⋊C4×Dic43C2212yes—
36C4⋊C4×Dic43C2212yes—
37C2×C43⋊#95—21no—
38#14582662C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C2×#121×C43C2211yescharacteristic
42C22×C4⋊C4×C43C2211yescharacteristic
43C2×#102×C43C2212yes—
44C2×C22⋊C8×C43C2211yescharacteristic
45C43×#340C2212yes—
46C2×#10621900—28no—
47C2×#10621900—44no—
48C2×#10621900—44no—
49C22×Dic86—21no—
50C22×D172C2311yescharacteristic
51C22×C22⋊D43—21no—
52C22×C22⋊D43—21no—
53C22×C22⋊D43—21no—
54C23×Dic43—21no—
55C23×Dic43—21no—
56C23×Dic43D411yescharacteristic
57C23×Dic43D411yescharacteristic
58C22×C4×D43—21no—
59C22×C43⋊C8C2312yes—
60#13063324—22no—
61#13063324C2×C414yescomplemented
62#13063321—22no—
63#13063321C2×C414yescomplemented
64#13063311—28no—
65#13063299—22no—
66#13063299C2×C414yes—
67#13063297—28no—
68D4×Dic43—22no—
69D4×Dic43C2×C414yescomplemented
70#13063287—22no—
71#13063287C2×C414yescomplemented
72(C22⋊D43)⋊C4—28no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—24no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2312yes—
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×C4×Dic43—22no—
82C2×C4×Dic43—22no—
83C2×C4×Dic43—44no—
84C2×C4×Dic43C2×C414yes—
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43D414yes—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90Dic43⋊C8—24no—
91#13063247—24no—
92#13063246—24no—
93#13063245—24no—
94C22⋊(C43⋊C8)—22no—
95C8×Dic43—24no—
96C43⋊#95—22no—
97C43⋊#95—22no—
98C22×D4×C43—21no—
99C22×D4×C43C2311yescharacteristic
100C23×C4×C43—21no—
101C23×C4×C43C2311yescharacteristic
102C22×C8×C43C2312yes—
103#121×C43—22no—
104#121×C43C2×C414yes—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—24no—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2312yes—
109C2×C22⋊C4×C43—21no—
110#102×C43—24no—
111C22⋊C8×C43—22no—
112C24×C43—21no—
113C24×C43C2×D411yescharacteristic
114C23×D43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—24no—
117C2×D4×C43—22no—
118C2×D4×C43—22no—
119C2×D4×C43—42no—
120C2×D4×C43—42no—
121C2×D4×C43C22×C412yes—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—24no—
125C22×C4×C43—21no—
126C22×C4×C43—22no—
127C22×C4×C43—42no—
128C22×C4×C43—42no—
129C22×C4×C43C22×C412yes—
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C2×C22⋊D43—24no—
134C2×C22⋊D43—24no—
135C2×C22⋊D43—24no—
136C2×C22⋊D43—42no—
137C2×C22⋊D43—42no—
138C2×C22⋊D43—42no—
139C2×C22⋊D43—42no—
140C2×C22⋊D43—42no—
141C2×C22⋊D43—42no—
142C22×Dic43—24no—
143C22×Dic43—24no—
144C22×Dic43—22no—
145C22×Dic43—21no—
146C22×Dic43—41no—
147C22×Dic43—41no—
148C22×Dic43—42no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43C22⋊C414yes—
153C22×Dic43C22⋊C414yes—
154C22×Dic43D814yes—
155C22×Dic43SD1614yes—
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160#10621900—432no—
161C2×D172—21no—
162C2×D172—22no—
163C2×D172—22no—
164C2×D172C22×C412yes—
165C2×C4×D43—24no—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
168C2×Dic86—24no—
169C2×Dic86—42no—
170C2×Dic86—42no—
171C2×C8×C43—22no—
172C2×C8×C43—22no—
173C2×C8×C43—22no—
174C4⋊C4×C43—24no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43C22×C412yes—
178C4⋊C4×C43#4114yescomplemented
179C22⋊C4×C43—24no—
180C22⋊Dic43—24no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—24no—
183C4⋊Dic43—24no—
184C4⋊Dic43—21no—
185C4⋊Dic43—22no—
186C4⋊Dic43C22×C412yes—
187C4⋊Dic43#4114yescomplemented
188Dic43⋊C4—24no—
189C4×Dic43—44no—
190C4×Dic43—44no—
191C4×Dic43C22⋊C414yes—
192C4×Dic43C22⋊C414yes—
193C4×Dic43C22×C412yes—
194C4×Dic43C22×C412yes—
195C4×Dic43C2×D412yes—
196C4×Dic43C2×D412yes—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—22no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—22no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43C2×C22⋊C412yes—
212C23×C43C2×D812yes—
213C23×C43C2×SD1612yes—
214C23×C43C22×D411yescharacteristic
215C22×D43—22no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222D4×C43—24no—
223D4×C43—48no—
224D4×C43—42no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—24no—
228C2×C4×C43—24no—
229C2×C4×C43—22no—
230C2×C4×C43—24no—
231C2×C4×C43—48no—
232C2×C4×C43—42no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—42no—
236C2×C4×C43C2×C22⋊C412yes—
237C2×C4×C43C23×C411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C2×#4112yes—
240C2×C4×C43C2×#4112yes—
241C22⋊D43—48no—
242C22⋊D43—48no—
243C22⋊D43—48no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—22no—
249C2×Dic43—24no—
250C2×Dic43—44no—
251C2×Dic43—48no—
252C2×Dic43—42no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—42no—
256C2×Dic43—48no—
257C2×Dic43#102116yescomplemented
258C2×Dic43C2×C22⋊C412yes—
259C2×Dic43C2×C22⋊C412yes—
260C2×Dic43C2×C22⋊C412yes—
261C2×Dic43C2×C22⋊C412yes—
262C2×Dic43C2×D812yes—
263C2×Dic43C2×D812yes—
264C2×Dic43C2×SD1612yes—
265C2×Dic43C2×SD1612yes—
266D172—24no—
267D172—42no—
268C4×D43—48no—
269Dic86—48no—
270C8×C43—42no—
271C43⋊C8—42no—
272#21386—431nomaximal, Sylow
273C22×C43—22no—
274C22×C43—22no—
275C22×C43—22no—
276C22×C43—22no—
277C22×C43—22no—
278C22×C43—22no—
279C22×C43—42no—
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43C2×#10214yes—
287C22×C43C22×C22⋊C411yescharacteristic
288C22×C43#52511yescharacteristic
289C22×C43#52511yescharacteristic
290C22×C43C22×D811yescharacteristic
291C22×C43C22×SD1611yescharacteristic
292C22×C43#57511yescharacteristic
293C22×C43#57511yescharacteristic
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C4×C43—22no—
302C4×C43—44no—
303C4×C43—42no—
304C4×C43C4×#4112yes—
305C4×C43#53212yes—
306Dic43—22no—
307Dic43—22no—
308Dic43—44no—
309Dic43—42no—
310Dic43C2×#10214yes—
311Dic43C2×#10214yes—
312C2×#532—431no—
313C2×#431—431no—
314C2×C4×C4⋊C4—431no—
315#1988—432no—
316#1982—432no—
317#1874—431no—
318#1874—431no—
319#1874—431no—
320#1874D4311yescharacteristic, complemented
321C4×#102—432no—
322C4×#102—432no—
323C2×C43—24no—
324C2×C43—82no—
325C2×C43#229711yescharacteristic
326C2×C43C22×#10211yescharacteristic
327C2×C43#289611yescharacteristic
328C2×C43#310011yescharacteristic
329C2×C43#310011yescharacteristic
330C2×C43#310311yescharacteristic
331C2×C43#310311yescharacteristic
332D43—82no—
333C22×#41—861no—
334#532—438no—
335#532—864no—
336C2×C4⋊Q8—431no—
337C2×#127—431no—
338C2×#124—861no—
339C2×#121—431no—
340C2×#121—861no—
341C2×#121C2×D4311yescharacteristic
342C2×C4×D4—431no—
343C2×C4×D4—431no—
344C2×C4×D4—861no—
345C22×C4⋊C4—431no—
346C22×C4⋊C4C2×D4311yescharacteristic
347C22×C42—431no—
348C22×C42—861no—
349#431—864no—
350C2×C4⋊C8—432no—
351C2×#102—432no—
352C2×#102—432no—
353C2×#102—432no—
354C2×#102C2×D4312yes—
355C2×C22⋊C8—431no—
356C2×C22⋊C8C2×D4311yescharacteristic
357C2×C4×C8—432no—
358C4×C4⋊C4—432no—
359C4×C4⋊C4—432no—
360C4×C4⋊C4—861no—
361C4×C4⋊C4—861no—
362C2×#95—861no—
363#340—432no—
364#340—432no—
365#340—432no—
366#340C2×D4312yes—
367C43#2138611yescharacteristic, complemented, Sylow
368C2×#41—868no—
369C2×#41—1724no—
370C2×#41—1724no—
371C22×Q8—861no—
372C22×D4—21no—
373C22×D4—431no—
374C22×D4—861no—
375C22×D4—861no—
376C22×D4—861no—
377C22×D4C22×D4311yescharacteristic
378C23×C4—21no—
379C23×C4—431no—
380C23×C4—431no—
381C23×C4—861no—
382C23×C4—861no—
383C23×C4—861no—
384C23×C4C22×D4311yescharacteristic
385C22×C8—432no—
386C22×C8C22×D4312yes—
387C4⋊Q8—434no—
388C4⋊Q8—862no—
389#127—434no—
390#127—862no—
391#124—868no—
392#121—22no—
393#121—434no—
394#121—868no—
395#121—862no—
396#121C4×D4314yes—
397C4×D4—434no—
398C4×D4—434no—
399C4×D4—868no—
400C4×D4—862no—
401C4×D4—862no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—432no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—864no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4312yes—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C42—434no—
416C2×C42—431no—
417C2×C42—431no—
418C2×C42—434no—
419C2×C42—431no—
420C2×C42—431no—
421C2×C42—862no—
422C2×C42—862no—
423C2×C42—1724no—
424C4⋊C8—864no—
425#102—24no—
426#102—864no—
427#102—864no—
428#102—864no—
429C22⋊C8—22no—
430C22⋊C8—862no—
431C4×C8—864no—
432#95—862no—
433#95—862no—
434C24—21no—
435C24—861no—
436C24D4×D4311yescharacteristic
437#41—17232no—
438C2×Q8—864no—
439C2×Q8—1722no—
440C2×Q8—1722no—
441C2×D4—24no—
442C2×D4—21no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—432no—
448C2×D4—864no—
449C2×D4—864no—
450C2×D4—864no—
451C2×D4—861no—
452C2×D4—862no—
453C2×D4—862no—
454C2×D4—1722no—
455C2×D4—1722no—
456C2×D4—1722no—
457C2×D4—1722no—
458C2×D4—1722no—
459C2×D4—1722no—
460C2×D4C2×C4×D4312yes—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—434no—
469C22×C4—434no—
470C22×C4—434no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—434no—
476C22×C4—864no—
477C22×C4—864no—
478C22×C4—864no—
479C22×C4—862no—
480C22×C4—861no—
481C22×C4—1722no—
482C22×C4—1722no—
483C22×C4—1722no—
484C22×C4—1722no—
485C22×C4—1721no—
486C22×C4—1721no—
487C22×C4—1722no—
488C22×C4—1722no—
489C22×C4C2×C4×D4312yes—
490C22×C4D4×D4311yescharacteristic
491C22×C4D4×D4312yes—
492C22×C4C23×D4311yescharacteristic
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—862no—
497C2×C8—862no—
498C2×C8—862no—
499C4⋊C4—24no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—432no—
503C4⋊C4—434no—
504C4⋊C4—864no—
505C4⋊C4—864no—
506C4⋊C4—861no—
507C4⋊C4—862no—
508C4⋊C4C2×C4×D4312yes—
509C4⋊C4#1062190014yescomplemented
510C22⋊C4—24no—
511C22⋊C4—864no—
512C22⋊C4—864no—
513C22⋊C4—864no—
514C42—434no—
515C42—434no—
516C42—432no—
517C42—432no—
518C42—432no—
519C42—432no—
520C42—1724no—
521C42—1724no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—22no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—862no—
534C23—1721no—
535C23—1721no—
536C23—1721no—
537C23—1721no—
538C23—1721no—
539C23—1721no—
540C23C22⋊C4×D4312yes—
541C23D8×D4312yes—
542C23SD16×D4312yes—
543C23C2×D4×D4311yescharacteristic
544Q8—1728no—
545D4—24no—
546D4—48no—
547D4—42no—
548D4—864no—
549D4—1728no—
550D4—1728no—
551D4—1728no—
552D4—1722no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—48no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—432no—
565C2×C4—432no—
566C2×C4—4316no—
567C2×C4—432no—
568C2×C4—432no—
569C2×C4—432no—
570C2×C4—432no—
571C2×C4—432no—
572C2×C4—432no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—862no—
578C2×C4—864no—
579C2×C4—1728no—
580C2×C4—1728no—
581C2×C4—1724no—
582C2×C4—1728no—
583C2×C4—1722no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1722no—
587C2×C4C22⋊C4×D4312yes—
588C2×C4C22×C4×D4311yescharacteristic
589C2×C4C2×D4×D4311yescharacteristic
590C2×C4#41×D4312yes—
591C2×C4C2×#1062190012yes—
592C8—42no—
593C8—1722no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—3441no—
608C22—3441no—
609C22—3441no—
610C22—3441no—
611C22—1722no—
612C22—1722no—
613C22—1722no—
614C22#102×D4314yes—
615C22C2×C22⋊C4×D4311yescharacteristic
616C22#1458340511yescharacteristic
617C22#1458340711yescharacteristic
618C22C2×D8×D4311yescharacteristic
619C22C2×SD16×D4311yescharacteristic
620C22#1458369511yescharacteristic
621C22#1458369811yescharacteristic
622C4—22no—
623C4—44no—
624C4—42no—
625C4—434no—
626C4—434no—
627C4—862no—
628C4—862no—
629C4—1724no—
630C4—1722no—
631C4C4×#1062190012yes—
632C4#1458344412yes—
633C2—24no—
634C2—82no—
635C2—3442no—
636C2#1913708011yescharacteristic
637C2C2×#102×D4311yescharacteristic
638C2#1914311111yescharacteristic
639C2#1914459011yescharacteristic
640C2#1914459211yescharacteristic
641C2#1914462111yescharacteristic
642C2#1914462311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1874C2
socleC23×C43C22×D4
prime radicalC2×#14583444C2
cosocleC22×C4×C43C24
hypercenter#1874D43
hypocenterC43#21386
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#14582949C2semidirect
3. C2×C4⋊C4×Dic43C2semidirect
4. #19135545C2semidirect
5. #19135520C2semidirect
6. #19134913C2semidirect
7. #19134912C2semidirect
8. #19134910C2semidirect
9. #102×Dic43C2semidirect
10. #19134409C2semidirect
11. C43×#1874C2semidirect
14. #14583444C4semidirect
61. #13063324C2×C4semidirect
63. #13063321C2×C4semidirect
69. D4×Dic43C2×C4semidirect
71. #13063287C2×C4semidirect
178. C4⋊C4×C43#41semidirect
187. C4⋊Dic43#41semidirect
257. C2×Dic43#102semidirect
320. #1874D43semidirect
367. C43#21386semidirect
509. C4⋊C4#10621900semidirect

Maximal subgroups

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

subgroupindex
C2×#145834442
C2×#145829492
C2×C4⋊C4×Dic432
#191355452
#191355202
#191349132
#191349122
#191349102
#102×Dic432
#191344092
C43×#18742
#2138643