Finite Group Databasebeta

← #25154826

Subgroups — #25154826

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#19139616C211yesmaximal, characteristic, complemented
2#19137542C211yesmaximal, characteristic
3#19135968C211yesmaximal, characteristic
4#19135968C211yesmaximal, characteristic
5#19135742C211yesmaximal, characteristic
6#19135732C211yesmaximal, characteristic
7#19135550C211yesmaximal, characteristic, complemented
8#19135546C211yesmaximal, characteristic, complemented
9#19135359C211yesmaximal, characteristic, complemented
10#19135181C211yesmaximal, characteristic, complemented
11#19135174C211yesmaximal, characteristic, complemented
12#19134729C211yesmaximal, characteristic, complemented
13#19134606C211yesmaximal, characteristic
14#19134421C211yesmaximal, characteristic
15C43×#1940C211yesmaximal, characteristic, complemented
16C2×#13063325C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063283—21no—
20C2×#13063257C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063247C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26#14582832—21no—
27#14582819—21no—
28#14582803—21no—
29#14582801C2211yescharacteristic
30#14582801C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582796—21no—
34#14582791—21no—
35#14582791—21no—
36#14582769C2211yescharacteristic
37#14582765C2211yescharacteristic
38#14582756—21no—
39C4×C4⋊Dic43C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86—21no—
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62#13063325—22no—
63#13063325—41no—
64#13063317—22no—
65#13063317—41no—
66C4×D172—22no—
67C4×D172Q814yescomplemented
68#13063283—44no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91#13063257—22no—
92#13063257—22no—
93#13063247—22no—
94#13063247—22no—
95#13063247—41no—
96#13063247—41no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C22×C8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C2×C4⋊C4×C43D411yescharacteristic
109C2×C4⋊C4×C43D411yescharacteristic
110C2×C42×C43C2311yescharacteristic
111C2×C42×C43C2311yescharacteristic
112C2×C42×C43C2311yescharacteristic
113C4⋊C8×C43—22no—
114C4⋊C8×C43—41no—
115C4⋊C8×C43—41no—
116#97×C43—22no—
117#95×C43D411yescharacteristic
118#95×C43D411yescharacteristic
119C23×D43—21no—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
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—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—41no—
160C42×C43—21no—
161C42×C43—21no—
162C42×C43—21no—
163C42×C43—21no—
164C42×C43C2×Q812yes—
165C42×C43#4112yes—
166(C2×D43)⋊C4—24no—
167(C2×D43)⋊C4—42no—
168(C2×D43)⋊C4—42no—
169(C2×D43)⋊C4—81no—
170(C2×D43)⋊C4—81no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—42no—
183C4⋊Dic43—42no—
184C4⋊Dic43—81no—
185C4⋊Dic43C2×Q812yes—
186C4⋊Dic43#4112yes—
187C4⋊Dic43#4112yes—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—81no—
192C4×Dic43—42no—
193C4×Dic43—42no—
194C4×Dic43—81no—
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—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
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×C43C22⋊Q812yes—
219C2×C4×C43C22⋊Q812yes—
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—22no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
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×Dic43—41no—
247C2×Dic43—41no—
248D172—22no—
249D172—22no—
250D172—41no—
251D172—41no—
252C4×D43—48no—
253Dic86—84no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—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—22no—
275C4×C43—22no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43#53311yescharacteristic
280C4×C43#54411yescharacteristic
281C4×C43#55511yescharacteristic
282C4×C43#55611yescharacteristic
283Dic43—42no—
284Dic43—42no—
285Dic43—42no—
286Dic43—81no—
287Dic43—81no—
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#1940D4311yescharacteristic, complemented
300#1920—431no—
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×#106—431no—
319C2×C4⋊C8C2×D4311yescharacteristic
320C2×C4⋊C8C2×D4311yescharacteristic
321C2×C4⋊C8C2×D4311yescharacteristic
322C2×#102—431no—
323C2×#102—431no—
324C2×#102—431no—
325C2×#102—431no—
326C2×#97C2×D4311yescharacteristic
327#398—861no—
328#395—861no—
329#391—861no—
330#390—431no—
331#390—431no—
332#389—431no—
333#389—431no—
334#389—861no—
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#340—431no—
352#340—431no—
353#340—431no—
354#336C2×D4311yescharacteristic
355#336C2×D4311yescharacteristic
356C43#2603211yescharacteristic, complemented, Sylow
357C22×Q8—861no—
358C22×D4—431no—
359C23×C4—861no—
360C22×C8C22×D4311yescharacteristic
361C22×C8C22×D4311yescharacteristic
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—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4D17211yescharacteristic
386C2×C4⋊C4D17211yescharacteristic
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C42—861no—
393C2×C42—861no—
394C2×C42—861no—
395C2×C42C22×D4311yescharacteristic
396C2×C42C22×D4311yescharacteristic
397C2×C42C22×D4311yescharacteristic
398#106—862no—
399#106—862no—
400C4⋊C8—22no—
401C4⋊C8—41no—
402C4⋊C8—41no—
403#102—862no—
404#102—862no—
405#102—1721no—
406#102—1721no—
407#97—22no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95D17211yescharacteristic
416#95D17211yescharacteristic
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—861no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—864no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—1722no—
436C22×C4—1722no—
437C22×C4C2×D17211yescharacteristic
438C22×C4C2×D17211yescharacteristic
439C22×C4C2×D17211yescharacteristic
440C22×C4C2×D17211yescharacteristic
441C22×C4C2×D17211yescharacteristic
442C22×C4C2×D17211yescharacteristic
443C22×C4C23×D4311yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C4⋊C4—22no—
457C4⋊C4—41no—
458C4⋊C4—432no—
459C4⋊C4—432no—
460C4⋊C4—432no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—3441no—
473C4⋊C4—3441no—
474C4⋊C4—1722no—
475C4⋊C4—1722no—
476C4⋊C4—1722no—
477C4⋊C4—1722no—
478C4⋊C4—1722no—
479C22⋊C4—864no—
480C22⋊C4—3441no—
481C22⋊C4—3441no—
482C22⋊C4—1722no—
483C22⋊C4—1722no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—3441no—
489C42—1722no—
490C42—1722no—
491C42#1062190012yes—
492C42Q8×D4312yes—
493C23—862no—
494C23—1721no—
495C23—1721no—
496C23—1721no—
497C23—1721no—
498C23—1721no—
499C23—1721no—
500C23C22×D17211yescharacteristic
501Q8—3444no—
502D4—862no—
503D4—862no—
504D4—1721no—
505D4—1721no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—862no—
522C2×C4—862no—
523C2×C4—862no—
524C2×C4—1728no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4#1306330512yes—
544C2×C4#1306330512yes—
545C2×C4#1306335312yes—
546C2×C4C2×Q8×D4311yescharacteristic
547C2×C4#41×D4311yescharacteristic
548C2×C4#41×D4311yescharacteristic
549C2×C4C2×#1062190011yescharacteristic
550C2×C4#1306337011yescharacteristic
551C2×C4#1306337311yescharacteristic
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C22—3441no—
557C22—3441no—
558C22—3441no—
559C22—3441no—
560C22—1722no—
561C22—1722no—
562C22—1722no—
563C22C2×#1306330511yescharacteristic
564C22#1458354411yescharacteristic
565C22#1458356111yescharacteristic
566C22C2×#1306335311yescharacteristic
567C22#1458369911yescharacteristic
568C22#1458371111yescharacteristic
569C22#1458371111yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—3441no—
577C4—3441no—
578C4—3441no—
579C4—3441no—
580C4—1722no—
581C4—1722no—
582C4—1722no—
583C4#1458345511yescharacteristic
584C4#1458352611yescharacteristic
585C4#1458361311yescharacteristic
586C4#1458362011yescharacteristic
587C2—3442no—
588C2#1913828411yescharacteristic
589C2#1914439411yescharacteristic
590C2#1914445911yescharacteristic
591C2#1914655811yescharacteristic
592C2#1914678311yescharacteristic
593C2#1914732611yescharacteristic
594C2#1914742411yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1940C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1940D43
hypocenterC43#26032
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
1. #19139616C2semidirect
7. #19135550C2semidirect
8. #19135546C2semidirect
9. #19135359C2semidirect
10. #19135181C2semidirect
11. #19135174C2semidirect
12. #19134729C2semidirect
15. C43×#1940C2semidirect
67. C4×D172Q8semidirect
299. #1940D43semidirect
356. C43#26032semidirect

Maximal subgroups

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

subgroupindex
#191396162
#191375422
#191359682
#191357422
#191357322
#191355502
#191355462
#191353592
#191351812
#191351742
#191347292
#191346062
#191344212
C43×#19402
#2603243