Finite Group Databasebeta

← #25154827

Subgroups — #25154827

Order 11008.

736 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139618C211yesmaximal, characteristic, complemented
2#19137540C211yesmaximal, characteristic
3#19135966C211yesmaximal, characteristic
4#19135964C211yesmaximal, characteristic
5#19135740C211yesmaximal, characteristic
6#19135732C211yesmaximal, characteristic
7#19135551C211yesmaximal, characteristic, complemented
8#19135547C211yesmaximal, characteristic, complemented
9#19135355C211yesmaximal, characteristic, complemented
10#19135317C211yesmaximal, characteristic, complemented
11#19135176C211yesmaximal, characteristic, complemented
12#19134727C211yesmaximal, characteristic, complemented
13#19134604C211yesmaximal, characteristic
14#19134419C211yesmaximal, characteristic
15C43×#1920C211yesmaximal, characteristic, complemented
16C2×#13063325C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19C2×#13063282—21no—
20C2×#13063256C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29#14582832—21no—
30#14582820—21no—
31#14582803—21no—
32#14582801C2211yescharacteristic
33#14582800C2211yescharacteristic
34#14582798—21no—
35#14582798C2211yescharacteristic
36#14582790—21no—
37#14582788—21no—
38#14582768C2211yescharacteristic
39#14582764C2211yescharacteristic
40#14582758—21no—
41C4⋊C4×Dic43C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×Dic43⋊C4C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86—21no—
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063325—22no—
65#13063325—41no—
66#13063316—22no—
67#13063316—41no—
68#13063287—22no—
69#13063287Q814yescomplemented
70#13063282—44no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4D411yescharacteristic
81C2×Dic43⋊C4D411yescharacteristic
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063256—22no—
92C4⋊(C43⋊C8)—41no—
93Dic43⋊C8—22no—
94Dic43⋊C8—41no—
95#13063247—22no—
96#13063247—41no—
97#13063245—22no—
98#13063245—41no—
99#13063235—22no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116#106×C43—22no—
117#95×C43—21no—
118#95×C43—21no—
119C23×D43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43C2×D411yescharacteristic
131C22×Dic43C2×D411yescharacteristic
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172C2×Q812yes—
140C2×C4×D43—24no—
141C2×C4×D43—42no—
142C2×C4×D43—42no—
143C2×Dic86—42no—
144C2×Dic86—42no—
145C2×Dic86—81no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—42no—
159C4⋊C4×C43C2×Q812yes—
160C4⋊C4×C43#4112yes—
161C42×C43—21no—
162C42×C43—21no—
163C42×C43—42no—
164(C2×D43)⋊C4—24no—
165(C2×D43)⋊C4—42no—
166(C2×D43)⋊C4—42no—
167(C2×D43)⋊C4—81no—
168(C2×D43)⋊C4—81no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—42no—
175C4⋊Dic43—42no—
176C4⋊Dic43—81no—
177C4⋊Dic43#4112yes—
178Dic43⋊C4—22no—
179Dic43⋊C4—41no—
180Dic43⋊C4—42no—
181Dic43⋊C4—42no—
182Dic43⋊C4—81no—
183C4×Dic43—21no—
184C4×Dic43—21no—
185C4×Dic43—42no—
186C4×Dic43—81no—
187C4×Dic43C2×Q812yes—
188C4×Dic43#4112yes—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C23×C43C22×D411yescharacteristic
196C22×D43—22no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—41no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—22no—
206C2×C4×C43—21no—
207C2×C4×C43—22no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43AGL(1,ℤ/8)12yes—
221C2×C4×C43C22×Q811yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43H(5,𝔽2)11yescharacteristic
226C2×C4×C432−1+411yescharacteristic
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—22no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43C22⋊Q812yes—
247C2×Dic43C22⋊Q812yes—
248D172—22no—
249D172—22no—
250D172—41no—
251D172—41no—
252C4×D43—48no—
253Dic86—84no—
254C8×C43—41no—
255C8×C43—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258#26032—431nomaximal, Sylow
259C22×C43C2×C22⋊Q811yescharacteristic
260C22×C43#54611yescharacteristic
261C22×C43#54811yescharacteristic
262C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C43#57511yescharacteristic
264C22×C43#57711yescharacteristic
265C22×C43#57711yescharacteristic
266C2×D43—42no—
267C2×D43—42no—
268C2×D43—42no—
269C2×D43—81no—
270C2×D43—81no—
271C2×D43—81no—
272C2×D43—81no—
273C4×C43—22no—
274C4×C43—42no—
275C4×C43—42no—
276C4×C43—41no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43#53311yescharacteristic
280C4×C43#54411yescharacteristic
281C4×C43#55511yescharacteristic
282C4×C43#55611yescharacteristic
283Dic43—22no—
284Dic43—22no—
285Dic43—42no—
286Dic43—41no—
287Dic43—41no—
288Dic43—81no—
289Dic43—81no—
290#2550—431no—
291#2354—431no—
292#2065—431no—
293#2065—431no—
294#2025—431no—
295#2023—431no—
296#1989—431no—
297#1988—431no—
298#1948—431no—
299#1940—431no—
300#1920D4311yescharacteristic, complemented
301#1919—431no—
302#1836—431no—
303#1804—431no—
304#1762—431no—
305C2×C43#243911yescharacteristic
306C2×C43#307711yescharacteristic
307C2×C43#308411yescharacteristic
308C2×C43#330611yescharacteristic
309C2×C43#332111yescharacteristic
310C2×C43#336811yescharacteristic
311C2×C43#337611yescharacteristic
312D43—82no—
313C2×C4⋊Q8—431no—
314C2×#125—431no—
315C2×C4×D4—431no—
316C2×#117—861no—
317C2×#106—431no—
318C2×#106C2×D4311yescharacteristic
319C2×C4⋊C8—431no—
320C2×C4⋊C8—431no—
321C2×C4⋊C8—431no—
322C2×#102—431no—
323C2×#102—431no—
324C2×#102—431no—
325C2×#102—431no—
326C2×#97—431no—
327#398—861no—
328#395—861no—
329#391—861no—
330#390—431no—
331#390—431no—
332#389—431no—
333#389—861no—
334#389C2×D4311yescharacteristic
335#388—861no—
336#388—861no—
337#384—431no—
338#382—431no—
339#380—861no—
340C4×C4⋊C4—431no—
341C4×C4⋊C4—431no—
342C4×C4⋊C4—431no—
343C4×C4⋊C4C2×D4311yescharacteristic
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340C2×D4311yescharacteristic
352#340C2×D4311yescharacteristic
353#340C2×D4311yescharacteristic
354#336—431no—
355#336C2×D4311yescharacteristic
356C43#2603211yescharacteristic, complemented, Sylow
357C22×Q8—861no—
358C22×D4—431no—
359C23×C4—861no—
360C22×C8—431no—
361C22×C8—431no—
362C22×C8C22×D4311yescharacteristic
363C22×C8C22×D4311yescharacteristic
364C4⋊Q8—862no—
365C4⋊Q8—1721no—
366#125—862no—
367#125—1721no—
368C4×D4—434no—
369C4×D4—862no—
370#117—1724no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C42—21no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—861no—
396C2×C42—861no—
397C2×C42C22×D4311yescharacteristic
398#106—22no—
399#106—862no—
400C4⋊C8—862no—
401C4⋊C8—1721no—
402C4⋊C8—1721no—
403#102—862no—
404#102—862no—
405#102—1721no—
406#102—1721no—
407#97—862no—
408#95—21no—
409#95—21no—
410#95—431no—
411#95—431no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417C24—861no—
418C2×Q8—3441no—
419C2×Q8—1722no—
420C2×Q8—1722no—
421C2×D4—432no—
422C2×D4—861no—
423C2×D4—861no—
424C2×D4—861no—
425C2×D4—861no—
426C2×D4—861no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—431no—
432C22×C4—431no—
433C22×C4—431no—
434C22×C4—431no—
435C22×C4—864no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—1722no—
440C22×C4—1722no—
441C22×C4D4×D4311yescharacteristic
442C22×C4D4×D4311yescharacteristic
443C22×C4C23×D4311yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—42no—
463C4⋊C4—432no—
464C4⋊C4—862no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—3441no—
471C4⋊C4—3441no—
472C4⋊C4—1721no—
473C4⋊C4—1722no—
474C4⋊C4—1722no—
475C4⋊C4—1722no—
476C4⋊C4—1722no—
477C4⋊C4#1062189812yes—
478C4⋊C4Q8×D4312yes—
479C22⋊C4—864no—
480C22⋊C4—3441no—
481C22⋊C4—3441no—
482C22⋊C4—1722no—
483C22⋊C4—1722no—
484C42—21no—
485C42—21no—
486C42—42no—
487C42—432no—
488C42—432no—
489C42—861no—
490C42—861no—
491C42—3441no—
492C42—1722no—
493C23—862no—
494C23—1721no—
495C23—1721no—
496C23—1721no—
497C23—1721no—
498C23—1721no—
499C23—1721no—
500C23C2×D4×D4311yescharacteristic
501Q8—3444no—
502D4—862no—
503D4—862no—
504D4—1721no—
505D4—1721no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—432no—
524C2×C4—432no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—862no—
536C2×C4—1728no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4#1306335212yes—
546C2×C4C2×Q8×D4311yescharacteristic
547C2×C4#41×D4311yescharacteristic
548C2×C4#41×D4311yescharacteristic
549C2×C4C2×#1062189811yescharacteristic
550C2×C4#1306337111yescharacteristic
551C2×C4#1306337211yescharacteristic
552C8—41no—
553C8—41no—
554C8—1721no—
555C8—1721no—
556C22—3441no—
557C22—3441no—
558C22—3441no—
559C22—3441no—
560C22—1722no—
561C22—1722no—
562C22—1722no—
563C22C22⋊Q8×D4311yescharacteristic
564C22#1458354111yescharacteristic
565C22#1458355811yescharacteristic
566C22C2×#1306335211yescharacteristic
567C22#1458369511yescharacteristic
568C22#1458370611yescharacteristic
569C22#1458370811yescharacteristic
570C4—22no—
571C4—41no—
572C4—42no—
573C4—42no—
574C4—81no—
575C4—81no—
576C4—862no—
577C4—862no—
578C4—3441no—
579C4—3441no—
580C4—1721no—
581C4—1721no—
582C4—1722no—
583C4#1458345311yescharacteristic
584C4#1458352911yescharacteristic
585C4#1458361211yescharacteristic
586C4#1458361611yescharacteristic
587C2—3442no—
588C2#1913828511yescharacteristic
589C2#1914439311yescharacteristic
590C2#1914446011yescharacteristic
591C2#1914655411yescharacteristic
592C2#1914678411yescharacteristic
593C2#1914732211yescharacteristic
594C2#1914742711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1920C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1920D43
hypocenterC43#26032
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
1. #19139618C2semidirect
7. #19135551C2semidirect
8. #19135547C2semidirect
9. #19135355C2semidirect
10. #19135317C2semidirect
11. #19135176C2semidirect
12. #19134727C2semidirect
15. C43×#1920C2semidirect
69. #13063287Q8semidirect
300. #1920D43semidirect
356. C43#26032semidirect

Maximal subgroups

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

subgroupindex
#191396182
#191375402
#191359662
#191359642
#191357402
#191357322
#191355512
#191355472
#191353552
#191353172
#191351762
#191347272
#191346042
#191344192
C43×#19202
#2603243