Finite Group Databasebeta

← #25148796

Subgroups — #25148796

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×#14583449C211yesmaximal, characteristic, complemented
2C2×#14583133C212yesmaximal, complemented
3#19135923C211yesmaximal, characteristic, complemented
4#19135829C211yesmaximal, characteristic, complemented
5#19135731C211yesmaximal, characteristic, complemented
6#19135665C211yesmaximal, characteristic, complemented
7#19135021C212yesmaximal, complemented
8#19134946C212yesmaximal, complemented
9#19134841C212yesmaximal, complemented
10C2×#14582654C211yesmaximal, characteristic, complemented
11C43×#2854C211yesmaximal, characteristic, complemented
12C22×#10621898—21no—
13C22×#10621882C2212yes—
14C23×C43⋊C8C2212yes—
15#14583449—28no—
16C2×#13063325C2211yescharacteristic
17C2×#13063322C2211yescharacteristic
18C2×#13063313—21no—
19C2×#13063299—21no—
20C2×#13063299C2212yes—
21C2×C4×D172—21no—
22C2×C4×D172C2212yes—
23#14583133—28no—
24C2×#13063258C2212yes—
25C2×#13063246C2212yes—
26C2×#13063245C2212yes—
27C2×#13063245C2212yes—
28C2×#13063245C2212yes—
29#14582661C2212yes—
30#14582661C2212yes—
31#14582654C2211yescharacteristic
32#14582654C2212yes—
33#14582654C2211yescharacteristic
34C2×#123×C43—21no—
35C2×#121×C43C2211yescharacteristic
36C22×C42×C43C2211yescharacteristic
37C43×#390C2211yescharacteristic
38C43×#390C2211yescharacteristic
39C43×#389C2211yescharacteristic
40C43×#389C2211yescharacteristic
41C43×#388—21no—
42C43×#388—21no—
43C43×#386—21no—
44C43×#380C2211yescharacteristic
45C2×#10621898—28no—
46C2×#10621898—44no—
47C2×#10621898—44no—
48C22×Dic86—21no—
49C22×D172—21no—
50C22×D172—21no—
51C22×D172C2312yes—
52C22×C22⋊D43—22no—
53C22×C4×D43—22no—
54C2×#10621882—24no—
55C2×#10621882—24no—
56C2×#10621882—42no—
57C22×C43⋊C8—24no—
58C22×C43⋊C8—24no—
59C22×C43⋊C8—42no—
60C22×C43⋊C8C2312yes—
61C22×C43⋊C8C2312yes—
62#13063325—24no—
63#13063322—24no—
64#13063313—28no—
65#13063299—28no—
66#13063299—24no—
67#13063299D418yes—
68C4×D172—28no—
69C4×D172—24no—
70C4×D172—24no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2312yes—
73C2×(C2×D43)⋊C4—22no—
74C2×(C2×D43)⋊C4—22no—
75#13063258—24no—
76#13063246—24no—
77#13063245—24no—
78#13063245—24no—
79#13063245—42no—
80C22×D4×C43—21no—
81C22×D4×C43C2311yescharacteristic
82C23×C4×C43D411yescharacteristic
83C23×C4×C43D411yescharacteristic
84C23×C4×C43C2311yescharacteristic
85#123×C43—44no—
86#121×C43—24no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C4⋊C4×C43C2311yescharacteristic
91C2×C4⋊C4×C43C2311yescharacteristic
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43—21no—
98C2×C42×C43—24no—
99C2×C42×C43D411yescharacteristic
100C2×C42×C43D411yescharacteristic
101C2×C42×C43C2311yescharacteristic
102C2×C42×C43C2311yescharacteristic
103#95×C43—21no—
104#95×C43—21no—
105#95×C43—21no—
106C24×C43—21no—
107C24×C43C2×D411yescharacteristic
108C23×D43—22no—
109C2×D4×C43—22no—
110C2×D4×C43—22no—
111C2×D4×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43—42no—
114C2×D4×C43—42no—
115C2×D4×C43—42no—
116C22×C4×C43—22no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—41no—
127C22×C4×C43D814yescomplemented
128C22×C4×C43C2×D414yes—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C2×C22⋊D43—28no—
136C2×C22⋊D43—44no—
137C2×C22⋊D43—44no—
138C22×Dic43—22no—
139#10621898—432no—
140C2×D172—24no—
141C2×D172—24no—
142C2×D172—22no—
143C2×D172—22no—
144C2×D172—22no—
145C2×D172—22no—
146C2×D172—22no—
147C2×D172—42no—
148C2×D172—42no—
149C2×D172—42no—
150C2×D172—42no—
151C2×D172C2×D414yes—
152C2×C4×D43—28no—
153C2×C4×D43—44no—
154C2×C4×D43—44no—
155C2×Dic86—24no—
156C2×Dic86—42no—
157C2×Dic86—42no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—42no—
163C4⋊C4×C43—42no—
164C22⋊C4×C43—42no—
165C22⋊C4×C43—42no—
166C22⋊C4×C43—42no—
167C22⋊C4×C43—42no—
168C22⋊C4×C43—42no—
169C22⋊C4×C43—42no—
170C42×C43—22no—
171C42×C43—22no—
172C42×C43—22no—
173C42×C43—22no—
174#10621882—48no—
175(C2×D43)⋊C4—28no—
176(C2×D43)⋊C4—28no—
177C4⋊Dic43—24no—
178C4⋊Dic43—22no—
179C4⋊Dic43C2×D414yes—
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—41no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43#12012yes—
199C23×C43C2×D812yes—
200C23×C43AGL(1,ℤ/8)12yes—
201C23×C43C22×D411yescharacteristic
202C22×D43—24no—
203C22×D43—42no—
204C22×D43—42no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43—42no—
208C22×D43—42no—
209D4×C43—42no—
210D4×C43—42no—
211D4×C43—84no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—28no—
221C2×C4×C43—24no—
222C2×C4×C43—24no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—44no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
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—416no—
245C2×Dic43—24no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248D172—24no—
249D172—24no—
250D172—48no—
251D172—48no—
252D172—42no—
253D172—42no—
254C4×D43—416no—
255Dic86—48no—
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—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
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—44no—
281C2×D43—44no—
282C2×D43—44no—
283C2×D43—82no—
284C2×D43—82no—
285C2×D43—82no—
286C2×D43—82no—
287C4×C43—22no—
288C4×C43—22no—
289C4×C43—22no—
290C4×C43—22no—
291C4×C43—41no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43#54612yes—
296C4×C43#54712yes—
297Dic43—44no—
298C2×#532—431no—
299C2×#466—432no—
300#2854D4311yescharacteristic, complemented
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—161no—
311C2×C43#243011yescharacteristic
312C2×C43C2×#44711yescharacteristic
313C2×C43#300211yescharacteristic
314C2×C43#316911yescharacteristic
315C2×C43#318011yescharacteristic
316C2×C43#324511yescharacteristic
317C2×C43#324711yescharacteristic
318D43—84no—
319C22×#41—861no—
320C22×D8—432no—
321C23×C8—432no—
322#532—868no—
323C2×C4⋊Q8—431no—
324C2×#127—431no—
325C2×#124—861no—
326C2×#123—21no—
327C2×#121—432no—
328C2×#121—861no—
329C2×#121C2×D4311yescharacteristic
330C2×C4×D4—432no—
331C2×C4×D4—861no—
332C22×C42C2×D4311yescharacteristic
333#466—868no—
334C2×#107—432no—
335C2×#102—432no—
336C2×#102—432no—
337C2×#102—432no—
338C2×#102—432no—
339#390C2×D4311yescharacteristic
340#390C2×D4311yescharacteristic
341#389C2×D4311yescharacteristic
342#389C2×D4311yescharacteristic
343#388—21no—
344#388—21no—
345#386—21no—
346#380C2×D4311yescharacteristic
347#340—432no—
348#340—432no—
349#336—431no—
350#336—432no—
351#336—431no—
352C43#2549611yescharacteristic, complemented, Sylow
353C2×#41—868no—
354C2×#41—1724no—
355C2×#41—1724no—
356C22×Q8—861no—
357C22×D4—21no—
358C22×D4—432no—
359C22×D4—862no—
360C22×D4—861no—
361C22×D4—861no—
362C22×D4C22×D4311yescharacteristic
363C23×C4—862no—
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—864no—
376#127—864no—
377#124—868no—
378#123—44no—
379#121—24no—
380#121—438no—
381#121—868no—
382#121—864no—
383C4×D4—864no—
384C4×D4—864no—
385C4×D4—868no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—432no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4C22×D4311yescharacteristic
391C2×C4⋊C4C22×D4311yescharacteristic
392C2×C4⋊C4C22×D4311yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—862no—
400C2×C22⋊C4—862no—
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—21no—
412#95—21no—
413#95—21no—
414C24—21no—
415C24—862no—
416C24C2×C22⋊D4311yescharacteristic
417#41—17232no—
418C2×Q8—864no—
419C2×Q8—1722no—
420C2×Q8—1722no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—42no—
428C2×D4—434no—
429C2×D4—864no—
430C2×D4—864no—
431C2×D4—868no—
432C2×D4—862no—
433C2×D4—862no—
434C2×D4—862no—
435C2×D4—862no—
436C2×D4—862no—
437C2×D4—1722no—
438C2×D4—1722no—
439C2×D4—1724no—
440C2×D4—1724no—
441C2×D4—1722no—
442C2×D4—1722no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—41no—
454C22×C4—868no—
455C22×C4—862no—
456C22×C4—1724no—
457C22×C4—1724no—
458C22×C4#1062188214yescomplemented
459C22×C4D4×D4314yes—
460C22×C4C2×C22⋊D4311yescharacteristic
461C22×C4C2×C22⋊D4311yescharacteristic
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—22no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—434no—
481C4⋊C4—864no—
482C4⋊C4—862no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—42no—
488C22⋊C4—42no—
489C22⋊C4—868no—
490C22⋊C4—868no—
491C42—22no—
492C42—22no—
493C42—22no—
494C42—22no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—864no—
507C23—1722no—
508C23—1722no—
509C23—1722no—
510C23—1722no—
511C23—1722no—
512C23—1722no—
513C23#1306329312yes—
514C23C2×#1062188212yes—
515C23#1306335012yes—
516C23C22×C22⋊D4311yescharacteristic
517Q8—1728no—
518D4—42no—
519D4—42no—
520D4—84no—
521D4—864no—
522D4—864no—
523D4—1728no—
524D4—1728no—
525D4—17216no—
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—21no—
541C2×C4—21no—
542C2×C4—44no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—864no—
553C2×C4—17216no—
554C2×C4—1722no—
555C2×C4—1722no—
556C2×C4#1306329312yes—
557C2×C4C2×#1062188212yes—
558C2×C4C2×#1062188212yes—
559C2×C4#1306334512yes—
560C2×C4C2×D4×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—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—3442no—
580C22—3442no—
581C22—3442no—
582C22—3442no—
583C22—1724no—
584C22—1724no—
585C22—1724no—
586C22#1458303214yes—
587C22C2×#1306329311yescharacteristic
588C22#1458344511yescharacteristic
589C22#1458347711yescharacteristic
590C22C22×#1062188211yescharacteristic
591C22C2×#1306334511yescharacteristic
592C22C2×#1306335011yescharacteristic
593C22#1458369711yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—41no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—1724no—
603C4#1458354112yes—
604C4#1458354712yes—
605C2—24no—
606C2—161no—
607C2—3444no—
608C2#1913820711yescharacteristic
609C2C2×#1458303211yescharacteristic
610C2#1914381111yescharacteristic
611C2#1914517011yescharacteristic
612C2#1914529411yescharacteristic
613C2#1914590211yescharacteristic
614C2#1914592111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2854C2
socleC23×C43C22×D4
hypercenter#2854D43
hypocenterC43#25496
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2854

Complements

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

NH ≅ G/Ntype
1. C2×#14583449C2semidirect
2. C2×#14583133C2semidirect
3. #19135923C2semidirect
4. #19135829C2semidirect
5. #19135731C2semidirect
6. #19135665C2semidirect
7. #19135021C2semidirect
8. #19134946C2semidirect
9. #19134841C2semidirect
10. C2×#14582654C2semidirect
11. C43×#2854C2semidirect
127. C22×C4×C43D8semidirect
186. C2×C43⋊C8#41semidirect
300. #2854D43semidirect
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×#145834492
C2×#145831332
#191359232
#191358292
#191357312
#191356652
#191350212
#191349462
#191348412
C2×#145826542
C43×#28542
#2549643