Finite Group Databasebeta

← #25169189

Subgroups — #25169189

Order 11008.

726 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#19138443C211yesmaximal, characteristic
2#19137695C211yesmaximal, characteristic, complemented
3#19135964C211yesmaximal, characteristic
4#19135927C211yesmaximal, characteristic, complemented
5#19135738C211yesmaximal, characteristic
6#19135545C211yesmaximal, characteristic, complemented
7#19135334C211yesmaximal, characteristic, complemented
8#19135223C211yesmaximal, characteristic
9#19135214C211yesmaximal, characteristic
10#19135182C211yesmaximal, characteristic, complemented
11#19135177C211yesmaximal, characteristic, complemented
12#19135158C211yesmaximal, characteristic, complemented
13#19134857C211yesmaximal, characteristic
14#19134419C211yesmaximal, characteristic
15C43×#2059C211yesmaximal, characteristic, complemented
16C2×#13063324C2211yescharacteristic
17C2×#13063305—21no—
18C2×#13063287C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063247C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063245C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063235C2211yescharacteristic
27#14582821—21no—
28#14582812—21no—
29#14582801C2211yescharacteristic
30#14582800C2211yescharacteristic
31#14582798—21no—
32#14582798C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582785—21no—
36#14582785—21no—
37#14582773—21no—
38C4⋊C4×Dic43—21no—
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#125×C43C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86—21no—
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063324—22no—
65#13063324—41no—
66#13063305—44no—
67#13063287—22no—
68#13063287—41no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43D411yescharacteristic
73C2×C4⋊Dic43D411yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43C2311yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88#13063257—41no—
89#13063256—22no—
90Dic43⋊C8—41no—
91#13063247—41no—
92#13063247Q814yescomplemented
93#13063245—22no—
94#13063245—22no—
95#13063235—41no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95D411yescharacteristic
103C43⋊#95D411yescharacteristic
104C22×C8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106#125×C43—22no—
107#125×C43—22no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C42×C43C2311yescharacteristic
116#107×C43—22no—
117#106×C43—22no—
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—42no—
141C2×C4×D43—42no—
142C2×C4×D43—81no—
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×C43C2×Q812yes—
152C4⋊C4×C43—24no—
153C4⋊C4×C43—24no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—42no—
160C4⋊C4×C43#4112yes—
161C4⋊C4×C43#4112yes—
162C4⋊C4×C43#4112yes—
163C42×C43—21no—
164C42×C43—21no—
165(C2×D43)⋊C4—42no—
166(C2×D43)⋊C4—42no—
167(C2×D43)⋊C4—42no—
168(C2×D43)⋊C4—42no—
169(C2×D43)⋊C4—81no—
170C4⋊Dic43—21no—
171C4⋊Dic43—22no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—41no—
177C4⋊Dic43—42no—
178C4⋊Dic43—42no—
179C4⋊Dic43—81no—
180C4⋊Dic43C2×Q812yes—
181Dic43⋊C4—42no—
182C4×Dic43—21no—
183C4×Dic43—21no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C4×Dic43—42no—
187C4×Dic43—81no—
188C4×Dic43—81no—
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—22no—
207C2×C4×C43—22no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
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×C43—41no—
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—22no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
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×Dic43AGL(1,ℤ/8)12yes—
248D172—22no—
249D172—22no—
250D172—41no—
251D172—41no—
252C4×D43—84no—
253Dic86—84no—
254C8×C43—22no—
255C8×C43—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258#27026—431nomaximal, Sylow
259C22×C43#52511yescharacteristic
260C22×C43#54611yescharacteristic
261C22×C43D4×Q811yescharacteristic
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—41no—
274C4×C43—42no—
275C4×C43—41no—
276C4×C43—42no—
277C4×C43—42no—
278C4×C43—81no—
279C4×C43#53311yescharacteristic
280C4×C43#54211yescharacteristic
281C4×C43#55411yescharacteristic
282C4×C43#55611yescharacteristic
283Dic43—22no—
284Dic43—42no—
285Dic43—41no—
286Dic43—41no—
287Dic43—41no—
288Dic43—81no—
289Dic43—81no—
290#2452—431no—
291#2370—431no—
292#2065—431no—
293#2059D4311yescharacteristic, complemented
294#2058—431no—
295#2025—431no—
296#1988—431no—
297#1943—431no—
298#1926—431no—
299#1925—431no—
300#1920—431no—
301#1920—431no—
302#1917—431no—
303#1864—431no—
304#1762—431no—
305C2×C43#246511yescharacteristic
306C2×C43#311511yescharacteristic
307C2×C43#312511yescharacteristic
308C2×C43#331011yescharacteristic
309C2×C43#332611yescharacteristic
310C2×C43#338411yescharacteristic
311C2×C43#338811yescharacteristic
312D43—82no—
313C2×C4⋊Q8—431no—
314C2×#125C2×D4311yescharacteristic
315C2×C22⋊Q8—861no—
316C2×C4×D4—431no—
317C2×#107C2×D4311yescharacteristic
318C2×#106—431no—
319C2×#106—431no—
320C2×#106C2×D4311yescharacteristic
321C2×C4⋊C8—431no—
322C2×#102—431no—
323C2×#102—431no—
324C2×#102—431no—
325C2×#102—431no—
326C2×#97—431no—
327#396—861no—
328#393—861no—
329#390—431no—
330#390—431no—
331#389—431no—
332#389—431no—
333#389—431no—
334#389—861no—
335#389C2×D4311yescharacteristic
336#387—861no—
337#387—861no—
338#385—861no—
339C4×C4⋊C4—431no—
340C4×C4⋊C4—431no—
341C4×C4⋊C4—431no—
342C4×C4⋊C4—431no—
343C4×C4⋊C4—861no—
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340C2×D4311yescharacteristic
351#340C2×D4311yescharacteristic
352#336—431no—
353#336—431no—
354#336—431no—
355#336C2×D4311yescharacteristic
356C43#2702611yescharacteristic, 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—22no—
367#125—22no—
368C22⋊Q8—1724no—
369C4×D4—862no—
370C4×D4—1721no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
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—431no—
393C2×C42—431no—
394C2×C42—861no—
395C2×C42—861no—
396C2×C42—861no—
397C2×C42C22×D4311yescharacteristic
398#107—22no—
399#106—22no—
400#106—862no—
401#106—1721no—
402C4⋊C8—1721no—
403#102—434no—
404#102—862no—
405#102—862no—
406#102—1721no—
407#97—1721no—
408#95—21no—
409#95—431no—
410#95—431no—
411#95—861no—
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—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—3441no—
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—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8Q8×D4312yes—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—42no—
464C4⋊C4—432no—
465C4⋊C4—862no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—3441no—
472C4⋊C4—1721no—
473C4⋊C4—1722no—
474C4⋊C4—1722no—
475C4⋊C4—1722no—
476C4⋊C4#1062190012yes—
477C4⋊C4#1062190012yes—
478C4⋊C4#1062190212yes—
479C22⋊C4—3441no—
480C22⋊C4—1722no—
481C22⋊C4—1722no—
482C22⋊C4—1722no—
483C22⋊C4—1722no—
484C42—21no—
485C42—21no—
486C42—861no—
487C42—861no—
488C42—861no—
489C42—861no—
490C42—3441no—
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—21no—
514C2×C4—22no—
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—41no—
524C2×C4—432no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—862no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—3444no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4C2×Q8×D4311yescharacteristic
547C2×C4C2×#1062190011yescharacteristic
548C2×C4C2×#1062190011yescharacteristic
549C2×C4C2×#1062190211yescharacteristic
550C2×C4#1306337111yescharacteristic
551C2×C4#1306337311yescharacteristic
552C8—22no—
553C8—41no—
554C8—1721no—
555C8—1721no—
556C22—3441no—
557C22—3441no—
558C22—3441no—
559C22—3441no—
560C22—1722no—
561C22—1722no—
562C22—1722no—
563C22#1458340511yescharacteristic
564C22#1458354011yescharacteristic
565C22#1458356411yescharacteristic
566C22AGL(1,ℤ/8)×D4311yescharacteristic
567C22#1458369611yescharacteristic
568C22#1458370611yescharacteristic
569C22#1458370811yescharacteristic
570C4—41no—
571C4—42no—
572C4—42no—
573C4—41no—
574C4—42no—
575C4—81no—
576C4—862no—
577C4—3441no—
578C4—3441no—
579C4—1721no—
580C4—1721no—
581C4—1721no—
582C4—1722no—
583C4#1458345411yescharacteristic
584C4#1458352211yescharacteristic
585C4#1458360711yescharacteristic
586C4#1458362311yescharacteristic
587C2—3442no—
588C2#1913861111yescharacteristic
589C2#1914473911yescharacteristic
590C2#1914486511yescharacteristic
591C2#1914661311yescharacteristic
592C2#1914684511yescharacteristic
593C2#1914749111yescharacteristic
594C2#1914754611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2059C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2059D43
hypocenterC43#27026
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2059

Complements

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

NH ≅ G/Ntype
2. #19137695C2semidirect
4. #19135927C2semidirect
6. #19135545C2semidirect
7. #19135334C2semidirect
10. #19135182C2semidirect
11. #19135177C2semidirect
12. #19135158C2semidirect
15. C43×#2059C2semidirect
92. #13063247Q8semidirect
293. #2059D43semidirect
356. C43#27026semidirect

Maximal subgroups

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

subgroupindex
#191384432
#191376952
#191359642
#191359272
#191357382
#191355452
#191353342
#191352232
#191352142
#191351822
#191351772
#191351582
#191348572
#191344192
C43×#20592
#2702643