Finite Group Databasebeta

← #25199253

Subgroups — #25199253

Order 11008.

672 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137239C211yesmaximal, characteristic
2#19136077C211yesmaximal, characteristic, complemented
3#19136009C211yesmaximal, characteristic
4#19135920C211yesmaximal, characteristic, complemented
5#19135728C211yesmaximal, characteristic
6#19135215C211yesmaximal, characteristic
7#19135215C211yesmaximal, characteristic
8#19135187C211yesmaximal, characteristic, complemented
9#19135184C211yesmaximal, characteristic, complemented
10#19135173C211yesmaximal, characteristic, complemented
11#19135163C211yesmaximal, characteristic, complemented
12#19134855C211yesmaximal, characteristic
13#19134841C211yesmaximal, characteristic
14#19134740C211yesmaximal, characteristic, complemented
15C43×#2331C211yesmaximal, characteristic, complemented
16C2×C4×D172C2211yescharacteristic
17C2×#13063258C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×#13063245C2211yescharacteristic
22C2×#13063245C2211yescharacteristic
23C2×#13063245C2211yescharacteristic
24C2×#13063245C2211yescharacteristic
25#14582801C2211yescharacteristic
26#14582801C2211yescharacteristic
27#14582797C2211yescharacteristic
28#14582797C2211yescharacteristic
29#14582788—21no—
30#14582788—21no—
31#14582761—21no—
32#14582758—21no—
33C4×C4⋊Dic43C2211yescharacteristic
34#14582661C2211yescharacteristic
35#14582661C2211yescharacteristic
36#14582661C2211yescharacteristic
37#14582661C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582654C2211yescharacteristic
43#14582654C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C4⋊Q8×C43C2211yescharacteristic
49C43×#391—21no—
50C43×#391—21no—
51C43×#389C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#387—21no—
54C43×#387—21no—
55C43×#382C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#376C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C4×D43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C4×D172—22no—
66C4×D172—22no—
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×C4×Dic43—21no—
78#13063258—22no—
79#13063258—22no—
80#13063258—22no—
81#13063256—22no—
82#13063245—22no—
83#13063245—22no—
84#13063245—22no—
85#13063245—22no—
86C43⋊#95—21no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C22×Q8×C43—21no—
90C4⋊Q8×C43—22no—
91C4⋊Q8×C43—22no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43C2311yescharacteristic
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C42×C43—21no—
100C2×C42×C43—21no—
101C2×C42×C43C2311yescharacteristic
102C2×C42×C43C2311yescharacteristic
103C2×C42×C43C2311yescharacteristic
104#95×C43—21no—
105#95×C43—21no—
106#95×C43—21no—
107#95×C43—21no—
108#95×C43—21no—
109#95×C43—21no—
110#95×C43D411yescharacteristic
111#95×C43D411yescharacteristic
112#95×C43D411yescharacteristic
113#95×C43D411yescharacteristic
114C23×D43—21no—
115C2×Q8×C43—24no—
116C2×Q8×C43—81no—
117C2×Q8×C43—81no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2411yescharacteristic
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C2×D172—21no—
133C2×D172—21no—
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172#4112yes—
138C2×C4×D43—24no—
139C2×C4×D43—81no—
140C2×C4×D43—81no—
141C4⋊C4×C43—24no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—81no—
149C4⋊C4×C43—81no—
150C4⋊C4×C43#4112yes—
151C4⋊C4×C43#4112yes—
152C42×C43—21no—
153C42×C43—21no—
154C42×C43—21no—
155C42×C43—21no—
156C42×C43—21no—
157C42×C43—21no—
158C42×C43—81no—
159C42×C43—81no—
160(C2×D43)⋊C4—24no—
161(C2×D43)⋊C4—81no—
162(C2×D43)⋊C4—81no—
163(C2×D43)⋊C4—81no—
164(C2×D43)⋊C4—81no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43#4112yes—
171Dic43⋊C4—81no—
172Dic43⋊C4—81no—
173C4×Dic43—81no—
174C2×C43⋊C8—21no—
175C2×C43⋊C8—21no—
176C2×C43⋊C8—21no—
177C2×C43⋊C8—21no—
178C2×C43⋊C8—21no—
179C2×C43⋊C8—21no—
180C2×C43⋊C8—21no—
181C2×C43⋊C8—21no—
182C2×C43⋊C8—21no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8—21no—
185C2×C43⋊C8—21no—
186C23×C43C22×D411yescharacteristic
187C22×D43—22no—
188C22×D43—41no—
189C22×D43—41no—
190C22×D43—41no—
191C22×D43—41no—
192C22×D43—41no—
193C22×D43—41no—
194Q8×C43—84no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—22no—
200C2×C4×C43—22no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
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—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C432−1+411yescharacteristic
230C2×C4×C432−1+411yescharacteristic
231C2×Dic43—22no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240D172—22no—
241D172—22no—
242D172—41no—
243D172—41no—
244C4×D43—84no—
245C43⋊C8—41no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249#29401—431nomaximal, Sylow
250C22×C43#52511yescharacteristic
251C22×C43#52511yescharacteristic
252C22×C43#53611yescharacteristic
253C22×C43#57611yescharacteristic
254C22×C43#57611yescharacteristic
255C22×C43#57711yescharacteristic
256C22×C43#57811yescharacteristic
257C2×D43—42no—
258C2×D43—42no—
259C2×D43—42no—
260C2×D43—81no—
261C2×D43—81no—
262C2×D43—81no—
263C2×D43—81no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—42no—
268C4×C43—42no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43#55211yescharacteristic
275C4×C43#55211yescharacteristic
276C4×C43#55611yescharacteristic
277C4×C43#55611yescharacteristic
278Dic43—42no—
279Dic43—81no—
280Dic43—81no—
281#2331D4311yescharacteristic, complemented
282#2319—431no—
283#2085—431no—
284#2073—431no—
285#2057—431no—
286#2023—431no—
287#1925—431no—
288#1925—431no—
289#1921—431no—
290#1921—431no—
291#1919—431no—
292#1918—431no—
293#1864—431no—
294#1862—431no—
295#1840—431no—
296C2×C43#259911yescharacteristic
297C2×C43#311811yescharacteristic
298C2×C43#312111yescharacteristic
299C2×C43#312211yescharacteristic
300C2×C43#312411yescharacteristic
301C2×C43#324111yescharacteristic
302C2×C43#324311yescharacteristic
303D43—82no—
304C2×C4⋊Q8C2×D4311yescharacteristic
305C2×C4×D4—431no—
306C2×#107—431no—
307C2×#107—431no—
308C2×#107—431no—
309C2×#106—431no—
310C2×#102—431no—
311C2×#102—431no—
312C2×#102—431no—
313C2×#102—431no—
314#391—21no—
315#391—21no—
316#390—431no—
317#390—431no—
318#389—431no—
319#389—431no—
320#389C2×D4311yescharacteristic
321#389C2×D4311yescharacteristic
322#388—861no—
323#388—861no—
324#387—21no—
325#387—21no—
326#382C2×D4311yescharacteristic
327#381—861no—
328#380—861no—
329C4×C4⋊C4—431no—
330C4×C4⋊C4C2×D4311yescharacteristic
331C4×C4⋊C4C2×D4311yescharacteristic
332#376C2×D4311yescharacteristic
333#340—431no—
334#340—431no—
335#340—431no—
336#340—431no—
337#340—431no—
338#340—431no—
339#340—431no—
340#340—431no—
341#336—431no—
342#336—431no—
343#336—431no—
344#336—431no—
345#336—431no—
346#336—431no—
347C43#2940111yescharacteristic, complemented, Sylow
348C22×Q8—21no—
349C22×D4—431no—
350C23×C4—861no—
351C22×C8—431no—
352C22×C8—431no—
353C22×C8—431no—
354C22×C8—431no—
355C4⋊Q8—22no—
356C4⋊Q8—22no—
357C4×D4—862no—
358C4×D4—862no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—431no—
363C2×C4⋊C4—431no—
364C2×C4⋊C4—431no—
365C2×C4⋊C4—861no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4C22×D4311yescharacteristic
368C2×C4⋊C4C22×D4311yescharacteristic
369C2×C4⋊C4C22×D4311yescharacteristic
370C2×C4⋊C4C22×D4311yescharacteristic
371C2×C22⋊C4—861no—
372C2×C22⋊C4—861no—
373C2×C22⋊C4—861no—
374C2×C22⋊C4—861no—
375C2×C22⋊C4—861no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—861no—
379C2×C42C22×D4311yescharacteristic
380C2×C42C22×D4311yescharacteristic
381C2×C42C22×D4311yescharacteristic
382#107—862no—
383#107—862no—
384#107—862no—
385#106—862no—
386#102—862no—
387#102—862no—
388#102—862no—
389#102—862no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—861no—
397#95—861no—
398#95—861no—
399#95C22⋊D4311yescharacteristic
400#95C22⋊D4311yescharacteristic
401#95C22⋊D4311yescharacteristic
402#95C22⋊D4311yescharacteristic
403C24—861no—
404C2×Q8—24no—
405C2×Q8—81no—
406C2×Q8—81no—
407C2×D4—432no—
408C2×D4—861no—
409C2×D4—861no—
410C2×D4—861no—
411C2×D4—861no—
412C2×D4—861no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—864no—
418C22×C4—861no—
419C22×C4—861no—
420C22×C4—861no—
421C22×C4—3441no—
422C22×C4—3441no—
423C22×C4C2×C22⋊D4311yescharacteristic
424C22×C4C2×C22⋊D4311yescharacteristic
425C22×C4C2×C22⋊D4311yescharacteristic
426C22×C4C2×C22⋊D4311yescharacteristic
427C22×C4C2×C22⋊D4311yescharacteristic
428C22×C4C2×C22⋊D4311yescharacteristic
429C22×C4C23×D4311yescharacteristic
430C2×C8—861no—
431C2×C8—861no—
432C2×C8—861no—
433C2×C8—861no—
434C2×C8—861no—
435C2×C8—861no—
436C2×C8—861no—
437C2×C8—861no—
438C2×C8—861no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—861no—
442C4⋊C4—24no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—81no—
450C4⋊C4—81no—
451C4⋊C4—432no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—3441no—
458C4⋊C4—3441no—
459C4⋊C4#1062189812yes—
460C4⋊C4#1062189812yes—
461C22⋊C4—864no—
462C22⋊C4—3441no—
463C22⋊C4—3441no—
464C22⋊C4—3441no—
465C22⋊C4—3441no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—81no—
473C42—81no—
474C42—3441no—
475C23—862no—
476C23—1721no—
477C23—1721no—
478C23—1721no—
479C23—1721no—
480C23—1721no—
481C23—1721no—
482C23C22×C22⋊D4311yescharacteristic
483Q8—84no—
484D4—862no—
485D4—862no—
486D4—1721no—
487D4—1721no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—862no—
519C2×C4—3444no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4#41×D4311yescharacteristic
529C2×C4#41×D4311yescharacteristic
530C2×C4C2×#1062189811yescharacteristic
531C2×C4C2×#1062189811yescharacteristic
532C2×C4#1306337311yescharacteristic
533C2×C4#1306337311yescharacteristic
534C8—1721no—
535C8—1721no—
536C8—1721no—
537C8—1721no—
538C22—3441no—
539C22—3441no—
540C22—3441no—
541C22—3441no—
542C22—1722no—
543C22—1722no—
544C22—1722no—
545C22#1458340611yescharacteristic
546C22#1458341011yescharacteristic
547C22#1458347311yescharacteristic
548C22#1458370211yescharacteristic
549C22#1458370211yescharacteristic
550C22#1458370711yescharacteristic
551C22#1458371411yescharacteristic
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—41no—
559C4—41no—
560C4—81no—
561C4—81no—
562C4—3441no—
563C4—3441no—
564C4—1722no—
565C4#1458359011yescharacteristic
566C4#1458359011yescharacteristic
567C4#1458362111yescharacteristic
568C4#1458362111yescharacteristic
569C2—3442no—
570C2#1914016611yescharacteristic
571C2#1914477311yescharacteristic
572C2#1914482411yescharacteristic
573C2#1914483811yescharacteristic
574C2#1914485111yescharacteristic
575C2#1914584811yescharacteristic
576C2#1914587811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2331C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2331D43
hypocenterC43#29401
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #2331

Complements

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

NH ≅ G/Ntype
2. #19136077C2semidirect
4. #19135920C2semidirect
8. #19135187C2semidirect
9. #19135184C2semidirect
10. #19135173C2semidirect
11. #19135163C2semidirect
14. #19134740C2semidirect
15. C43×#2331C2semidirect
281. #2331D43semidirect
347. C43#29401semidirect

Maximal subgroups

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

subgroupindex
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#191360092
#191359202
#191357282
#191352152
#191351872
#191351842
#191351732
#191351632
#191348552
#191348412
#191347402
C43×#23312
#2940143