Finite Group Databasebeta

← #25199258

Subgroups — #25199258

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#19137339C211yesmaximal, characteristic, complemented
2#19137234C211yesmaximal, characteristic
3#19136080C211yesmaximal, characteristic, complemented
4#19136012C211yesmaximal, characteristic
5#19135922C211yesmaximal, characteristic, complemented
6#19135730C211yesmaximal, characteristic
7#19135216C211yesmaximal, characteristic
8#19135215C211yesmaximal, characteristic
9#19135190C211yesmaximal, characteristic, complemented
10#19135184C211yesmaximal, characteristic, complemented
11#19135165C211yesmaximal, characteristic, complemented
12#19134853C211yesmaximal, characteristic
13#19134843C211yesmaximal, characteristic
14#19134739C211yesmaximal, characteristic, complemented
15C43×#1919C211yesmaximal, characteristic, complemented
16C2×#13063324C2211yescharacteristic
17C2×#13063287C2211yescharacteristic
18C2×#13063259C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063247C2211yescharacteristic
22C2×#13063247C2211yescharacteristic
23C2×#13063245C2211yescharacteristic
24C2×#13063245C2211yescharacteristic
25#14582805—21no—
26#14582803—21no—
27#14582801C2211yescharacteristic
28#14582800C2211yescharacteristic
29#14582798C2211yescharacteristic
30#14582798C2211yescharacteristic
31#14582795C2211yescharacteristic
32#14582791—21no—
33#14582789—21no—
34#14582786—21no—
35#14582783—21no—
36#14582764C2211yescharacteristic
37#14582761—21no—
38#14582756—21no—
39C4⋊C4×Dic43C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41#14582745C2211yescharacteristic
42#14582662C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
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#13063324—22no—
65#13063324—22no—
66#13063287—22no—
67#13063287—22no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43C2311yescharacteristic
83C2×C4×Dic43C2311yescharacteristic
84#13063259—22no—
85#13063258—22no—
86#13063258—22no—
87#13063247—22no—
88#13063247—22no—
89#13063245—22no—
90#13063245—22no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95D411yescharacteristic
99C43⋊#95D411yescharacteristic
100C43⋊#95D411yescharacteristic
101C43⋊#95D411yescharacteristic
102C22×C8×C43C2311yescharacteristic
103C22×C8×C43C2311yescharacteristic
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C42×C43—21no—
110C2×C42×C43C2311yescharacteristic
111#106×C43—22no—
112#95×C43—21no—
113#95×C43—21no—
114C23×D43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2411yescharacteristic
122C22×Dic43—21no—
123C22×Dic43—21no—
124C22×Dic43—21no—
125C22×Dic43C2×D411yescharacteristic
126C22×Dic43C2×D411yescharacteristic
127C22×Dic43C2×D411yescharacteristic
128C22×Dic43C2×D411yescharacteristic
129C2×D172—21no—
130C2×D172—21no—
131C2×D172—21no—
132C2×D172—21no—
133C2×D172—21no—
134C2×D172#4112yes—
135C2×C4×D43—24no—
136C2×C4×D43—81no—
137C2×C4×D43—81no—
138C2×Dic86—24no—
139C2×Dic86—81no—
140C2×Dic86—81no—
141C2×C8×C43—21no—
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—81no—
154C4⋊C4×C43#4112yes—
155C4⋊C4×C43#4112yes—
156C42×C43—21no—
157C42×C43—21no—
158C42×C43—81no—
159(C2×D43)⋊C4—24no—
160(C2×D43)⋊C4—81no—
161(C2×D43)⋊C4—81no—
162(C2×D43)⋊C4—81no—
163(C2×D43)⋊C4—81no—
164C4⋊Dic43—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—81no—
170C4⋊Dic43—81no—
171C4⋊Dic43#4112yes—
172Dic43⋊C4—24no—
173Dic43⋊C4—81no—
174C4×Dic43—21no—
175C4×Dic43—21no—
176C4×Dic43—21no—
177C4×Dic43—21no—
178C4×Dic43—81no—
179C4×Dic43—81no—
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—
194C2×C4×C43—22no—
195C2×C4×C43—22no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43C2×#4111yescharacteristic
213C2×C4×C43C2×#4111yescharacteristic
214C2×C4×C43C2×#4111yescharacteristic
215C2×C4×C43C2×#4111yescharacteristic
216C2×C4×C432−1+411yescharacteristic
217C2×C4×C432−1+411yescharacteristic
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—22no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239D172—22no—
240D172—22no—
241D172—41no—
242D172—41no—
243C4×D43—84no—
244Dic86—84no—
245C8×C43—41no—
246C8×C43—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—42no—
265C4×C43—42no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43#55211yescharacteristic
271C4×C43#55211yescharacteristic
272C4×C43#55611yescharacteristic
273C4×C43#55611yescharacteristic
274Dic43—41no—
275Dic43—41no—
276Dic43—41no—
277Dic43—42no—
278Dic43—41no—
279Dic43—81no—
280Dic43—81no—
281#2331—431no—
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#1919D4311yescharacteristic, complemented
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⋊Q8—431no—
305C2×C4×D4—431no—
306C2×#107—431no—
307C2×#107—431no—
308C2×#107—431no—
309C2×#106C2×D4311yescharacteristic
310C2×#102—431no—
311C2×#102—431no—
312C2×#102—431no—
313C2×#102—431no—
314#391—861no—
315#391—861no—
316#390—431no—
317#390—431no—
318#389—431no—
319#389—431no—
320#389—431no—
321#389C2×D4311yescharacteristic
322#388—861no—
323#388—861no—
324#387—861no—
325#387—861no—
326#382—431no—
327#381—861no—
328#380—861no—
329C4×C4⋊C4—431no—
330C4×C4⋊C4—431no—
331C4×C4⋊C4C2×D4311yescharacteristic
332#376—431no—
333#340—431no—
334#340—431no—
335#340—431no—
336#340—431no—
337#340—431no—
338#340C2×D4311yescharacteristic
339#340C2×D4311yescharacteristic
340#340C2×D4311yescharacteristic
341#336—431no—
342#336—431no—
343#336—431no—
344#336—431no—
345#336—431no—
346#336C2×D4311yescharacteristic
347C43#2940111yescharacteristic, complemented, Sylow
348C22×Q8—861no—
349C22×D4—431no—
350C23×C4—861no—
351C22×C8—431no—
352C22×C8—431no—
353C22×C8C22×D4311yescharacteristic
354C22×C8C22×D4311yescharacteristic
355C4⋊Q8—862no—
356C4⋊Q8—862no—
357C4×D4—862no—
358C4×D4—862no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—431no—
361C2×C4⋊C4—431no—
362C2×C4⋊C4—431no—
363C2×C4⋊C4—861no—
364C2×C4⋊C4—861no—
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—431no—
378C2×C42—431no—
379C2×C42—861no—
380C2×C42—861no—
381C2×C42C22×D4311yescharacteristic
382#107—862no—
383#107—862no—
384#107—862no—
385#106—22no—
386#102—862no—
387#102—862no—
388#102—862no—
389#102—862no—
390#95—21no—
391#95—21no—
392#95—431no—
393#95—431no—
394#95—431no—
395#95—431no—
396#95—861no—
397#95—861no—
398#95—861no—
399#95—861no—
400#95—861no—
401#95—861no—
402#95—861no—
403C24—861no—
404C2×Q8—864no—
405C2×Q8—3441no—
406C2×Q8—3441no—
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—431no—
418C22×C4—431no—
419C22×C4—431no—
420C22×C4—431no—
421C22×C4—864no—
422C22×C4—861no—
423C22×C4—861no—
424C22×C4—861no—
425C22×C4—3441no—
426C22×C4—3441no—
427C22×C4D4×D4311yescharacteristic
428C22×C4D4×D4311yescharacteristic
429C22×C4C23×D4311yescharacteristic
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—861no—
437C2×C8—861no—
438C2×C8—861no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—861no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—81no—
449C4⋊C4—432no—
450C4⋊C4—864no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—3441no—
457C4⋊C4—3441no—
458C4⋊C4—3441no—
459C4⋊C4#1062189812yes—
460C4⋊C4#1062190212yes—
461C22⋊C4—864no—
462C22⋊C4—3441no—
463C22⋊C4—3441no—
464C22⋊C4—3441no—
465C22⋊C4—3441no—
466C42—21no—
467C42—21no—
468C42—81no—
469C42—861no—
470C42—861no—
471C42—861no—
472C42—861no—
473C42—3441no—
474C42—3441no—
475C23—862no—
476C23—1721no—
477C23—1721no—
478C23—1721no—
479C23—1721no—
480C23—1721no—
481C23—1721no—
482C23C2×D4×D4311yescharacteristic
483Q8—3444no—
484D4—862no—
485D4—862no—
486D4—1721no—
487D4—1721no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—862no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—861no—
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×#1062190211yescharacteristic
532C2×C4#1306337211yescharacteristic
533C2×C4#1306337211yescharacteristic
534C8—41no—
535C8—41no—
536C8—1721no—
537C8—1721no—
538C22—3441no—
539C22—3441no—
540C22—3441no—
541C22—3441no—
542C22—1722no—
543C22—1722no—
544C22—1722no—
545C22#1458340811yescharacteristic
546C22#1458341211yescharacteristic
547C22#1458347111yescharacteristic
548C22#1458370111yescharacteristic
549C22#1458370311yescharacteristic
550C22#1458370511yescharacteristic
551C22#1458371511yescharacteristic
552C4—42no—
553C4—41no—
554C4—42no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—3441no—
559C4—3441no—
560C4—1721no—
561C4—1721no—
562C4—1721no—
563C4—1722no—
564C4—1721no—
565C4#1458358511yescharacteristic
566C4#1458358711yescharacteristic
567C4#1458361711yescharacteristic
568C4#1458362211yescharacteristic
569C2—3442no—
570C2#1914017111yescharacteristic
571C2#1914478511yescharacteristic
572C2#1914483111yescharacteristic
573C2#1914484011yescharacteristic
574C2#1914485511yescharacteristic
575C2#1914585211yescharacteristic
576C2#1914588411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1919C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1919D43
hypocenterC43#29401
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
1. #19137339C2semidirect
3. #19136080C2semidirect
5. #19135922C2semidirect
9. #19135190C2semidirect
10. #19135184C2semidirect
11. #19135165C2semidirect
14. #19134739C2semidirect
15. C43×#1919C2semidirect
291. #1919D43semidirect
347. C43#29401semidirect

Maximal subgroups

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

subgroupindex
#191373392
#191372342
#191360802
#191360122
#191359222
#191357302
#191352162
#191352152
#191351902
#191351842
#191351652
#191348532
#191348432
#191347392
C43×#19192
#2940143