Finite Group Databasebeta

← #25148788

Subgroups — #25148788

Order 11008.

1474 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583133C212yesmaximal, complemented
2#19142926C211yesmaximal, characteristic, complemented
3#19135920C211yesmaximal, characteristic, complemented
4#19135826C211yesmaximal, characteristic, complemented
5#19135728C211yesmaximal, characteristic, complemented
6#19135666C211yesmaximal, characteristic, complemented
7#19135024C212yesmaximal, complemented
8#19134943C212yesmaximal, complemented
9#19134842C212yesmaximal, complemented
10C2×#14582654C211yesmaximal, characteristic, complemented
11C2×C43×#532C211yesmaximal, characteristic, complemented
12C22×#10621882C2212yes—
13C23×C43⋊C8C2212yes—
14C2×#13063308—21no—
15C2×#13063299C2211yescharacteristic
16#14583133—28no—
17C2×#13063258C2212yes—
18C2×#13063246C2212yes—
19C2×#13063246C2212yes—
20C2×#13063246C2212yes—
21C2×#13063245C2212yes—
22#14582801C2211yescharacteristic
23#14582801C2211yescharacteristic
24#14582797C2211yescharacteristic
25#14582797C2211yescharacteristic
26#14582790—21no—
27#14582790—21no—
28#14582778—21no—
29#14582759C2211yescharacteristic
30#14582661C2212yes—
31#14582661C2212yes—
32#14582654C2211yescharacteristic
33#14582654C2212yes—
34#14582654C2211yescharacteristic
35C22×#41×C43—21no—
36C43×#532—28no—
37C2×C4⋊Q8×C43C2211yescharacteristic
38C2×#127×C43C2211yescharacteristic
39C2×#124×C43—21no—
40C2×#121×C43—21no—
41C2×#121×C43C2212yes—
42C2×C4×D4×C43—21no—
43C2×C4×D4×C43C2212yes—
44C22×C42×C43C2211yescharacteristic
45C22×D172C2311yescharacteristic
46C22×C22⋊D43—21no—
47C2×#10621882—24no—
48C2×#10621882—24no—
49C2×#10621882—42no—
50C22×C43⋊C8—24no—
51C22×C43⋊C8—24no—
52C22×C43⋊C8—42no—
53C22×C43⋊C8C2312yes—
54C22×C43⋊C8C2312yes—
55#13063308—44no—
56#13063299—24no—
57C2×C4⋊Dic43C2311yescharacteristic
58C2×C4⋊Dic43C2311yescharacteristic
59C2×C4⋊Dic43C2311yescharacteristic
60C2×Dic43⋊C4—21no—
61C2×Dic43⋊C4—21no—
62C2×C22⋊Dic43—21no—
63C2×(C2×D43)⋊C4—21no—
64C2×(C2×D43)⋊C4—21no—
65C2×(C2×D43)⋊C4—21no—
66C2×(C2×D43)⋊C4—21no—
67C2×(C2×D43)⋊C4—21no—
68#13063258—24no—
69#13063246—24no—
70#13063246—24no—
71#13063246—42no—
72#13063245—24no—
73C43⋊#95—21no—
74C43⋊#95—21no—
75C43⋊#95—21no—
76C2×#41×C43—28no—
77C2×#41×C43—44no—
78C2×#41×C43—44no—
79C22×Q8×C43—21no—
80C22×D4×C43—22no—
81C22×D4×C43—21no—
82C22×D4×C43—21no—
83C22×D4×C43C2312yes—
84C23×C4×C43—22no—
85C23×C4×C43D411yescharacteristic
86C23×C4×C43D411yescharacteristic
87C23×C4×C43C2311yescharacteristic
88C4⋊Q8×C43—24no—
89#127×C43—24no—
90#124×C43—28no—
91#121×C43—28no—
92#121×C43—24no—
93#121×C43D418yes—
94C4×D4×C43—28no—
95C4×D4×C43—24no—
96C4×D4×C43—24no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43C2312yes—
99C2×C22⋊C4×C43—22no—
100C2×C22⋊C4×C43—22no—
101C2×C42×C43—24no—
102C2×C42×C43D411yescharacteristic
103C2×C42×C43D411yescharacteristic
104C2×C42×C43C2311yescharacteristic
105C2×C42×C43C2311yescharacteristic
106C24×C43—22no—
107C24×C43C2×D411yescharacteristic
108C23×D43—21no—
109#41×C43—432no—
110C2×Q8×C43—24no—
111C2×Q8×C43—42no—
112C2×Q8×C43—42no—
113C2×D4×C43—24no—
114C2×D4×C43—24no—
115C2×D4×C43—22no—
116C2×D4×C43—28no—
117C2×D4×C43—22no—
118C2×D4×C43—22no—
119C2×D4×C43—22no—
120C2×D4×C43—22no—
121C2×D4×C43—42no—
122C2×D4×C43—42no—
123C2×D4×C43—42no—
124C2×D4×C43—42no—
125C2×D4×C43—44no—
126C2×D4×C43—44no—
127C2×D4×C43C2×D414yes—
128C22×C4×C43—22no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—28no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—41no—
138C22×C4×C43—44no—
139C22×C4×C43—44no—
140C22×C4×C43D814yescomplemented
141C22×C4×C43C2×D414yes—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C2×C22⋊D43—42no—
149C2×C22⋊D43—42no—
150C2×C22⋊D43—42no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C2×D172—22no—
155C2×D172—22no—
156C2×D172—21no—
157C2×D172—21no—
158C4⋊C4×C43—24no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43C2×D414yes—
161C22⋊C4×C43—28no—
162C22⋊C4×C43—28no—
163C42×C43—22no—
164C42×C43—22no—
165C42×C43—22no—
166C42×C43—22no—
167C22⋊Dic43—42no—
168#10621882—48no—
169(C2×D43)⋊C4—42no—
170(C2×D43)⋊C4—42no—
171(C2×D43)⋊C4—42no—
172(C2×D43)⋊C4—42no—
173(C2×D43)⋊C4—42no—
174C4⋊Dic43—22no—
175C4⋊Dic43—22no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178Dic43⋊C4—42no—
179Dic43⋊C4—42no—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—22no—
182C2×C43⋊C8—22no—
183C2×C43⋊C8—22no—
184C2×C43⋊C8—22no—
185C2×C43⋊C8—48no—
186C2×C43⋊C8#4114yescomplemented
187C23×C43—21no—
188C23×C43—21no—
189C23×C43—21no—
190C23×C43—21no—
191C23×C43—24no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43—42no—
196C23×C43—42no—
197C23×C43—42no—
198C23×C43#12012yes—
199C23×C43C2×D812yes—
200C23×C43AGL(1,ℤ/8)12yes—
201C23×C43C22×D411yescharacteristic
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209Q8×C43—48no—
210D4×C43—24no—
211D4×C43—24no—
212D4×C43—48no—
213D4×C43—48no—
214D4×C43—416no—
215D4×C43—42no—
216D4×C43—42no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—28no—
226C2×C4×C43—24no—
227C2×C4×C43—24no—
228C2×C4×C43—21no—
229C2×C4×C43—24no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—44no—
233C2×C4×C43—416no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43#12012yes—
237C2×C4×C43C2×D812yes—
238C2×C4×C43C2×D812yes—
239C2×C4×C43#13512yes—
240C2×C4×C43C22×D412yes—
241C2×C4×C43C2×#4112yes—
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×C4×C432−1+411yescharacteristic
244C22⋊D43—84no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254D172—42no—
255D172—42no—
256C43⋊C8—24no—
257C43⋊C8—42no—
258#25496—431nomaximal, Sylow
259C22×C43—22no—
260C22×C43—22no—
261C22×C43—22no—
262C22×C43—22no—
263C22×C43—22no—
264C22×C43—22no—
265C22×C43—44no—
266C22×C43—44no—
267C22×C43—44no—
268C22×C43—82no—
269C22×C43—82no—
270C22×C43—82no—
271C22×C43—82no—
272C22×C43#44714yes—
273C22×C43C2×#12011yescharacteristic
274C22×C43#53211yescharacteristic
275C22×C43#53711yescharacteristic
276C22×C43C22×D811yescharacteristic
277C22×C43C2×#13511yescharacteristic
278C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C43#57511yescharacteristic
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—81no—
284C2×D43—81no—
285C2×D43—81no—
286C2×D43—81no—
287C4×C43—22no—
288C4×C43—22no—
289C4×C43—22no—
290C4×C43—22no—
291C4×C43—44no—
292C4×C43—41no—
293C4×C43#54612yes—
294C4×C43#54712yes—
295Dic43—81no—
296Dic43—81no—
297Dic43—81no—
298C2×#532D4311yescharacteristic, complemented
299C2×#466—432no—
300#2854—431no—
301#2057—431no—
302#2041—431no—
303#2023—431no—
304#2011—431no—
305#1893—432no—
306#1879—432no—
307#1862—432no—
308C2×#336—431no—
309C2×C43—24no—
310C2×C43—84no—
311C2×C43#243011yescharacteristic
312C2×C43C2×#44711yescharacteristic
313C2×C43#300211yescharacteristic
314C2×C43#316911yescharacteristic
315C2×C43#318011yescharacteristic
316C2×C43#324511yescharacteristic
317C2×C43#324711yescharacteristic
318D43—161no—
319C22×#41—21no—
320C22×D8—432no—
321C23×C8—432no—
322#532—28no—
323C2×C4⋊Q8C2×D4311yescharacteristic
324C2×#127C2×D4311yescharacteristic
325C2×#124—21no—
326C2×#123—861no—
327C2×#121—21no—
328C2×#121—431no—
329C2×#121C2×D4312yes—
330C2×C4×D4—21no—
331C2×C4×D4C2×D4312yes—
332C22×C42C2×D4311yescharacteristic
333#466—868no—
334C2×#107—432no—
335C2×#102—432no—
336C2×#102—432no—
337C2×#102—432no—
338C2×#102—432no—
339#390—431no—
340#390—431no—
341#389—431no—
342#389—431no—
343#388—861no—
344#388—861no—
345#386—861no—
346#380—431no—
347#340—432no—
348#340—432no—
349#336—431no—
350#336—432no—
351#336—431no—
352C43#2549611yescharacteristic, complemented, Sylow
353C2×#41—28no—
354C2×#41—44no—
355C2×#41—44no—
356C22×Q8—21no—
357C22×D4—22no—
358C22×D4—21no—
359C22×D4—21no—
360C22×D4—431no—
361C22×D4—861no—
362C22×D4C22×D4312yes—
363C23×C4—22no—
364C23×C4C22⋊D4311yescharacteristic
365C23×C4C22⋊D4311yescharacteristic
366C23×C4C22×D4311yescharacteristic
367C2×D8—864no—
368C2×D8—864no—
369C2×D8—1722no—
370C22×C8—432no—
371C22×C8—432no—
372C22×C8—864no—
373C22×C8—864no—
374C22×C8—1722no—
375C4⋊Q8—24no—
376#127—24no—
377#124—28no—
378#123—1724no—
379#121—28no—
380#121—24no—
381#121—864no—
382#121C22⋊D4318yes—
383C4×D4—28no—
384C4×D4—24no—
385C4×D4—24no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4C22×D4312yes—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C42—24no—
402C2×C42C22⋊D4311yescharacteristic
403C2×C42C22⋊D4311yescharacteristic
404C2×C42C22×D4311yescharacteristic
405C2×C42C22×D4311yescharacteristic
406#107—864no—
407#102—864no—
408#102—864no—
409#102—864no—
410#102—1722no—
411#95—861no—
412#95—861no—
413#95—861no—
414C24—22no—
415C24—861no—
416C24C2×C22⋊D4311yescharacteristic
417#41—432no—
418C2×Q8—24no—
419C2×Q8—42no—
420C2×Q8—42no—
421C2×D4—24no—
422C2×D4—24no—
423C2×D4—28no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—42no—
430C2×D4—42no—
431C2×D4—44no—
432C2×D4—44no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4—862no—
436C2×D4—862no—
437C2×D4—861no—
438C2×D4—861no—
439C2×D4—1722no—
440C2×D4—1722no—
441C2×D4—1722no—
442C2×D4C2×C22⋊D4314yes—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—28no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—41no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4#1062188214yescomplemented
459C22×C4C2×C22⋊D4311yescharacteristic
460C22×C4C2×C22⋊D4311yescharacteristic
461C22×C4C2×C22⋊D4314yes—
462C22×C4C2×C22⋊D4311yescharacteristic
463C22×C4C2×C22⋊D4311yescharacteristic
464C22×C4C2×C22⋊D4311yescharacteristic
465C22×C4C23×D4311yescharacteristic
466D8—1728no—
467C2×C8—434no—
468C2×C8—862no—
469C2×C8—862no—
470C2×C8—862no—
471C2×C8—862no—
472C2×C8—862no—
473C2×C8—1728no—
474C4⋊C4—24no—
475C4⋊C4—22no—
476C4⋊C4—862no—
477C4⋊C4—862no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—1722no—
481C4⋊C4—1722no—
482C4⋊C4C2×C22⋊D4314yes—
483C22⋊C4—28no—
484C22⋊C4—28no—
485C22⋊C4—1722no—
486C22⋊C4—1722no—
487C22⋊C4—1722no—
488C22⋊C4—1722no—
489C22⋊C4—1722no—
490C22⋊C4—1722no—
491C42—22no—
492C42—22no—
493C42—22no—
494C42—22no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—24no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—1721no—
507C23—1721no—
508C23—1721no—
509C23—1721no—
510C23—1721no—
511C23—1721no—
512C23—1721no—
513C23#1306329412yes—
514C23C2×#1062188212yes—
515C23#1306335112yes—
516C23C22×C22⋊D4311yescharacteristic
517Q8—48no—
518D4—24no—
519D4—24no—
520D4—48no—
521D4—48no—
522D4—416no—
523D4—42no—
524D4—42no—
525D4—3444no—
526D4—1722no—
527D4—1722no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—28no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—21no—
540C2×C4—24no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—44no—
544C2×C4—416no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4#1306329412yes—
557C2×C4C2×#1062188212yes—
558C2×C4C2×#1062188212yes—
559C2×C4#1306334512yes—
560C2×C4C22×C22⋊D4312yes—
561C2×C4#41×D4312yes—
562C2×C4#1306337111yescharacteristic
563C2×C4#1306337211yescharacteristic
564C8—864no—
565C8—1722no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—44no—
573C22—44no—
574C22—44no—
575C22—82no—
576C22—82no—
577C22—82no—
578C22—82no—
579C22—3441no—
580C22—3441no—
581C22—3441no—
582C22—3441no—
583C22—3441no—
584C22—3441no—
585C22—3441no—
586C22#1458303314yes—
587C22C2×#1306329411yescharacteristic
588C22#1458344511yescharacteristic
589C22#1458347711yescharacteristic
590C22C22×#1062188211yescharacteristic
591C22C2×#1306334511yescharacteristic
592C22C2×#1306335111yescharacteristic
593C22#1458369711yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—44no—
599C4—41no—
600C4—3441no—
601C4—3441no—
602C4—3441no—
603C4#1458353712yes—
604C4#1458354812yes—
605C2—24no—
606C2—84no—
607C2—6881no—
608C2#1913819911yescharacteristic
609C2C2×#1458303311yescharacteristic
610C2#1914381311yescharacteristic
611C2#1914517011yescharacteristic
612C2#1914528711yescharacteristic
613C2#1914590211yescharacteristic
614C2#1914591511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#532C2
socleC23×C43C22×D4
hypercenterC2×#532D43
hypocenterC43#25496
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×#14583133C2semidirect
2. #19142926C2semidirect
3. #19135920C2semidirect
4. #19135826C2semidirect
5. #19135728C2semidirect
6. #19135666C2semidirect
7. #19135024C2semidirect
8. #19134943C2semidirect
9. #19134842C2semidirect
10. C2×#14582654C2semidirect
11. C2×C43×#532C2semidirect
140. C22×C4×C43D8semidirect
186. C2×C43⋊C8#41semidirect
298. C2×#532D43semidirect
352. C43#25496semidirect
458. C22×C4#10621882semidirect

Maximal subgroups

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

subgroupindex
C2×#145831332
#191429262
#191359202
#191358262
#191357282
#191356662
#191350242
#191349432
#191348422
C2×#145826542
C2×C43×#5322
#2549643