Finite Group Databasebeta

← #35374477

Subgroups — #35374477

Order 21248.

596 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917545C211yesmaximal, characteristic
2#24916608C211yesmaximal, characteristic
3#24916543C211yesmaximal, characteristic, complemented
4#24906340C211yesmaximal, characteristic, complemented
5#24906333C211yesmaximal, characteristic, complemented
6#24906312C211yesmaximal, characteristic, complemented
7#24906305C211yesmaximal, characteristic, complemented
8#24906281C211yesmaximal, characteristic, complemented
9#24906274C211yesmaximal, characteristic, complemented
10#24906269C211yesmaximal, characteristic, complemented
11#24906262C211yesmaximal, characteristic, complemented
12#24905891C211yesmaximal, characteristic, complemented
13#24905869C211yesmaximal, characteristic
14#24905763C211yesmaximal, characteristic, complemented
15C83×#1574C211yesmaximal, characteristic, complemented
16#19128235C2211yescharacteristic
17C2×C4×Dic166C2211yescharacteristic
18#19128032C411yescharacteristic
19#19128015C411yescharacteristic
20#19128009C411yescharacteristic
21#19128009C411yescharacteristic
22#19127924C411yescharacteristic
23#19127924C411yescharacteristic
24#19127859C411yescharacteristic
25#19127842C411yescharacteristic
26#19127828C2211yescharacteristic
27C8×Dic166—21no—
28C8×Dic166—21no—
29#19127825C2211yescharacteristic
30#19127825C2211yescharacteristic
31#19127825C2211yescharacteristic
32#19127825C2211yescharacteristic
33#19127825C2211yescharacteristic
34C4×Dic332C2211yescharacteristic
35C4×Dic332C2211yescharacteristic
36C4×#13050579C2211yescharacteristic
37C4×#13050579C2211yescharacteristic
38#19127778C2211yescharacteristic
39#19127777—21no—
40#19127770—21no—
41#19127766C2211yescharacteristic
42#19127761—21no—
43#19127754C2211yescharacteristic
44#19127754C2211yescharacteristic
45#19127751—21no—
46#19127751—21no—
47#19127726—21no—
48#19127431C2211yescharacteristic
49#19127431C2211yescharacteristic
50#19127431C2211yescharacteristic
51#19127431C2211yescharacteristic
52#19127431C2211yescharacteristic
53#19127431C2211yescharacteristic
54#19127428C2211yescharacteristic
55#19127428C2211yescharacteristic
56#19127423C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127422C2211yescharacteristic
59C8×C83⋊C8C2211yescharacteristic
60#431×C83C2211yescharacteristic
61#431×C83C2211yescharacteristic
62#423×C83C2211yescharacteristic
63#335×C83C2211yescharacteristic
64#335×C83C2211yescharacteristic
65#334×C83C2211yescharacteristic
66#334×C83C2211yescharacteristic
67C22×Dic166C2×C411yescharacteristic
68C2×Dic332C2×C411yescharacteristic
69C2×Dic332C2×C411yescharacteristic
70C2×#13050579C2×C411yescharacteristic
71C2×#13050579C2×C411yescharacteristic
72C2×#13050573—21no—
73C2×C8×D83—21no—
74#14581786—21no—
75#14581784C2×C411yescharacteristic
76#14581780C2×C411yescharacteristic
77#14581775—21no—
78#14581771C2×C411yescharacteristic
79#14581766C2×C411yescharacteristic
80C4×Dic166—21no—
81C4×Dic166—21no—
82C4×Dic166C2×C411yescharacteristic
83C4×Dic166C2×C411yescharacteristic
84C4×Dic166C2311yescharacteristic
85C4×Dic166C2311yescharacteristic
86C4×Dic166C2311yescharacteristic
87C4×D332C2311yescharacteristic
88C4×C22⋊D83—21no—
89#14581749—21no—
90C2×C4⋊Dic83C2×C411yescharacteristic
91C2×Dic83⋊C4—21no—
92C2×C4×Dic83—21no—
93#14581726C2×C411yescharacteristic
94#14581726C2×C411yescharacteristic
95#14581724C2×C411yescharacteristic
96#14581724C2×C411yescharacteristic
97C4⋊(C83⋊C8)—21no—
98C4⋊(C83⋊C8)D411yescharacteristic
99C4⋊(C83⋊C8)D411yescharacteristic
100Dic83⋊C8—21no—
101Dic83⋊C8—21no—
102Dic83⋊C8—21no—
103Dic83⋊C8—21no—
104Dic83⋊C8—21no—
105Dic83⋊C8—21no—
106#14581717C2×C411yescharacteristic
107#14581717C2×C411yescharacteristic
108#14581717C2×C411yescharacteristic
109#14581717C2×C411yescharacteristic
110#14581717C2×C411yescharacteristic
111#14581717C2×C411yescharacteristic
112#14581714C2×C411yescharacteristic
113#14581714C2×C411yescharacteristic
114C22⋊(C83⋊C8)—21no—
115C22⋊(C83⋊C8)D411yescharacteristic
116C22⋊(C83⋊C8)D411yescharacteristic
117(C2×D83)⋊C8—21no—
118(C2×D83)⋊C8—21no—
119#14581702—21no—
120C4×C83⋊C8C2311yescharacteristic
121C4×C83⋊C8C2311yescharacteristic
122C4×C83⋊C8C2311yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C8×Dic83—21no—
125C8×Dic83—21no—
126C8×Dic83—21no—
127C8×Dic83—21no—
128C8×Dic83—21no—
129C2×M16×C83—21no—
130C2×C42×C83C2311yescharacteristic
131C4⋊C8×C83—21no—
132C4⋊C8×C83C2×C411yescharacteristic
133C4⋊C8×C83C2×C411yescharacteristic
134C4⋊C8×C83C2311yescharacteristic
135C4⋊C8×C83C2311yescharacteristic
136C4⋊C8×C83C2311yescharacteristic
137C4⋊C8×C83C2311yescharacteristic
138C22⋊C8×C83—21no—
139C22⋊C8×C83C2×C411yescharacteristic
140C22⋊C8×C83C2×C411yescharacteristic
141C4×C8×C83—21no—
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C2×Dic166—21no—
145C2×Dic166—22no—
146C2×Dic166—22no—
147C2×Dic166C22×C411yescharacteristic
148C2×Dic166C22×C411yescharacteristic
149C2×Dic166C22×C411yescharacteristic
150C2×D332C22×C411yescharacteristic
151C2×C22⋊D83—21no—
152C22×Dic83—21no—
153C22×Dic83—21no—
154C2×C4×D83—21no—
155Dic332—22no—
156Dic332—22no—
157#13050579—22no—
158#13050579—22no—
159#13050573—81no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8C2×D411yescharacteristic
163C2×C83⋊C8C2×D411yescharacteristic
164C2×C83⋊C8C2×D411yescharacteristic
165C2×C83⋊C8C2×D411yescharacteristic
166C8×D83—81no—
167C4⋊Dic83—21no—
168C4⋊Dic83C22×C411yescharacteristic
169C4⋊Dic83C22×C411yescharacteristic
170C4⋊Dic83C22×C411yescharacteristic
171C4⋊Dic83C22×C411yescharacteristic
172Dic83⋊C4—21no—
173Dic83⋊C4—21no—
174Dic83⋊C4—21no—
175Dic83⋊C4—21no—
176Dic83⋊C4—21no—
177Dic83⋊C4—21no—
178Dic83⋊C4—21no—
179Dic83⋊C4—21no—
180C22⋊Dic83—21no—
181(C2×D83)⋊C4—21no—
182(C2×D83)⋊C4—21no—
183(C2×D83)⋊C4—21no—
184(C2×D83)⋊C4—21no—
185C4×Dic83—21no—
186C4×Dic83—21no—
187C4×Dic83—21no—
188C4×Dic83—21no—
189C4×Dic83—21no—
190C22×C4×C83C22×C411yescharacteristic
191C22×C4×C83C2×D411yescharacteristic
192C22×C4×C83#4111yescharacteristic
193M16×C83—81no—
194C2×C8×C83—21no—
195C2×C8×C83—21no—
196C2×C8×C83—21no—
197C2×C8×C83—21no—
198C2×C8×C83C22×C411yescharacteristic
199C2×C8×C83C22×C411yescharacteristic
200C2×C8×C83C22×C411yescharacteristic
201C2×C8×C83C22×C411yescharacteristic
202C42×C83C22×C411yescharacteristic
203C42×C83C2×D411yescharacteristic
204C42×C83#4111yescharacteristic
205C42×C83C2411yescharacteristic
206C23×C83C4×D411yescharacteristic
207C22×D83—21no—
208C2×C4×C83—21no—
209C2×C4×C83—21no—
210C2×C4×C83—21no—
211C2×C4×C83—21no—
212C2×C4×C83—41no—
213C2×C4×C83C4×D411yescharacteristic
214C2×C4×C83C4×D411yescharacteristic
215C2×C4×C83C4×D411yescharacteristic
216C2×C4×C83C23×C411yescharacteristic
217C2×C4×C83C22×D411yescharacteristic
218C2×C4×C83C2×#4111yescharacteristic
219C22⋊D83—81no—
220C2×Dic83—24no—
221C2×Dic83—21no—
222C2×Dic83—21no—
223C2×Dic83—21no—
224C2×Dic83—21no—
225C2×Dic83—21no—
226C2×Dic83—21no—
227C2×Dic83—21no—
228C2×Dic83—81no—
229D332—21no—
230D332—21no—
231C4×D83—41no—
232C4×D83—41no—
233Dic166—24no—
234Dic166—21no—
235Dic166—21no—
236Dic166—21no—
237Dic166—21no—
238Dic166#13112yes—
239Dic166#13112yes—
240C8×C83—21no—
241C8×C83—21no—
242C8×C83—21no—
243C8×C83—21no—
244C8×C83—41no—
245C8×C83—41no—
246C8×C83—41no—
247C8×C83—41no—
248C83⋊C8—21no—
249C83⋊C8—21no—
250C83⋊C8—21no—
251C83⋊C8—21no—
252C83⋊C8—41no—
253C83⋊C8—41no—
254C22×C83—21no—
255C22×C83—21no—
256C22×C83—21no—
257C22×C83C2×C4×D411yescharacteristic
258C2×D83—41no—
259C2×D83—41no—
260C2×D83—41no—
261C4×C83—21no—
262C4×C83—21no—
263C4×C83—21no—
264C4×C83—21no—
265C4×C83C2×#13111yescharacteristic
266C4×C83C2×#13111yescharacteristic
267C4×C83#57711yescharacteristic
268C4×C83#57811yescharacteristic
269Dic83—22no—
270Dic83—22no—
271Dic83—41no—
272Dic83—41no—
273Dic83—41no—
274Dic83—41no—
275Dic83—41no—
276#17919—831nomaximal, Sylow
277C2×C83—41no—
278C2×C83#292911yescharacteristic
279C2×C83#294711yescharacteristic
280C2×C83#295711yescharacteristic
281D83—81no—
282#3108—831no—
283#2993—831no—
284#2982—831no—
285#1588—831no—
286#1587—831no—
287#1584—831no—
288#1583—831no—
289#1579—831no—
290SD16⋊C8—831no—
291C8×Q16—831no—
292C8×SD16—831no—
293#1574D8311yescharacteristic, complemented
294#1487—831no—
295#1482—831no—
296#1454—831no—
297C83#1791911yescharacteristic, complemented, Sylow
298#529—831no—
299C2×C4×Q8—831no—
300#483—831no—
301#480—831no—
302#479—831no—
303#479—831no—
304#464—831no—
305#464—831no—
306#451—831no—
307#448—831no—
308#446—831no—
309C8×Q8—831no—
310C8×Q8—831no—
311C8×Q8—831no—
312C8×Q8—831no—
313C8×Q8—831no—
314C8×Q8—1661no—
315C8×Q8—1661no—
316C4×Q16—831no—
317C4×Q16—831no—
318C4×SD16—831no—
319C4×SD16—831no—
320#436—831no—
321#436—1661no—
322#435—1661no—
323C8×D4—831no—
324#433—1661no—
325#431—831no—
326#431—831no—
327#431—1661no—
328#431—1661no—
329#431C2×D8311yescharacteristic
330#431C2×D8311yescharacteristic
331#424—1661no—
332#423C2×D8311yescharacteristic
333#335C2×D8311yescharacteristic
334#335C2×D8311yescharacteristic
335#334C2×D8311yescharacteristic
336#334C2×D8311yescharacteristic
337Q8⋊C8—831no—
338Q8⋊C8—831no—
339Q8⋊C8—831no—
340Q8⋊C8—831no—
341Q8⋊C8—831no—
342Q8⋊C8—831no—
343D4⋊C8—831no—
344D4⋊C8—831no—
345#322—831no—
346#322—831no—
347#322—831no—
348C82—831no—
349C22×Q8—831no—
350C2×Q16—831no—
351C2×Q16—831no—
352C2×SD16—831no—
353C2×SD16—831no—
354C2×M16—21no—
355C2×M16—1661no—
356C22×C8—1661no—
357#126—1661no—
358#125—831no—
359#124—831no—
360#123—1661no—
361C22⋊Q8—831no—
362#121—831no—
363C4×Q8—831no—
364C4×Q8—831no—
365C4×Q8—831no—
366C4×Q8—831no—
367C4×Q8—831no—
368C4×Q8—1661no—
369C4×Q8—1661no—
370C4×D4—831no—
371C4×D4—1661no—
372#117—1661no—
373C2×C4⋊C4—831no—
374C2×C4⋊C4—1661no—
375C2×C42—1661no—
376C2×C42C22×D8311yescharacteristic
377#107—831no—
378#107—831no—
379#106—831no—
380#106—831no—
381C4⋊C8—21no—
382C4⋊C8—831no—
383C4⋊C8—831no—
384C4⋊C8—1661no—
385C4⋊C8—1661no—
386C4⋊C8—1661no—
387C4⋊C8—1661no—
388C4⋊C8—1661no—
389C4⋊C8—1661no—
390C4⋊C8—1661no—
391C4⋊C8C4×D8311yescharacteristic
392C4⋊C8C4×D8311yescharacteristic
393C4⋊C8C22×D8311yescharacteristic
394C4⋊C8C22×D8311yescharacteristic
395C4⋊C8C22×D8311yescharacteristic
396C4⋊C8C22×D8311yescharacteristic
397#103—831no—
398#103—831no—
399#103—831no—
400#103—831no—
401#103—831no—
402#103—831no—
403#102—831no—
404#102—831no—
405C22⋊C8—21no—
406C22⋊C8—831no—
407C22⋊C8—831no—
408C22⋊C8—1661no—
409C22⋊C8—1661no—
410C22⋊C8—1661no—
411C22⋊C8C4×D8311yescharacteristic
412C22⋊C8C4×D8311yescharacteristic
413#97—1661no—
414C4×C8—21no—
415C4×C8—831no—
416C4×C8—831no—
417C4×C8—831no—
418C4×C8—831no—
419C4×C8—1661no—
420C4×C8—1661no—
421C4×C8—1661no—
422C4×C8—1661no—
423C4×C8—1661no—
424C4×C8C22×D8311yescharacteristic
425C4×C8C22×D8311yescharacteristic
426C2×Q8—831no—
427C2×Q8—831no—
428C2×Q8—831no—
429C2×Q8—1662no—
430C2×Q8—1662no—
431C2×Q8—1661no—
432C2×D4—831no—
433C2×D4—1661no—
434C22×C4—1661no—
435C22×C4—1661no—
436C22×C4—1661no—
437C22×C4C2×C4×D8311yescharacteristic
438C22×C4D4×D8311yescharacteristic
439C22×C4#1305059111yescharacteristic
440Q16—1662no—
441Q16—1662no—
442SD16—1662no—
443SD16—1662no—
444M16—81no—
445M16—6641no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—831no—
451C2×C8—831no—
452C2×C8—831no—
453C2×C8—831no—
454C2×C8—6641no—
455C2×C8—1661no—
456C2×C8—1661no—
457C2×C8C2×C4×D8311yescharacteristic
458C2×C8C2×C4×D8311yescharacteristic
459C2×C8C2×C4×D8311yescharacteristic
460C2×C8C2×C4×D8311yescharacteristic
461C4⋊C4—831no—
462C4⋊C4—831no—
463C4⋊C4—831no—
464C4⋊C4—831no—
465C4⋊C4—1661no—
466C4⋊C4—1661no—
467C4⋊C4—1661no—
468C4⋊C4—1661no—
469C4⋊C4—1661no—
470C4⋊C4—1661no—
471C4⋊C4—1661no—
472C4⋊C4—1661no—
473C4⋊C4—1661no—
474C22⋊C4—1661no—
475C22⋊C4—1661no—
476C22⋊C4—1661no—
477C22⋊C4—1661no—
478C22⋊C4—1661no—
479C42—1661no—
480C42—1661no—
481C42—1661no—
482C42—1661no—
483C42—1661no—
484C42C2×C4×D8311yescharacteristic
485C42D4×D8311yescharacteristic
486C42#1305059111yescharacteristic
487C42C23×D8311yescharacteristic
488C23—1661no—
489C23#1458175411yescharacteristic
490Q8—832no—
491Q8—832no—
492Q8—1664no—
493Q8—1661no—
494Q8—1661no—
495Q8—1661no—
496Q8—1661no—
497D4—6641no—
498D4—1661no—
499D4—1661no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—3321no—
506C2×C4—3321no—
507C2×C4—6641no—
508C2×C4—1661no—
509C2×C4—1661no—
510C2×C4—1661no—
511C2×C4—1661no—
512C2×C4—1661no—
513C2×C4—1664no—
514C2×C4—1661no—
515C2×C4—1661no—
516C2×C4#1458175411yescharacteristic
517C2×C4#1458175411yescharacteristic
518C2×C4#1458175411yescharacteristic
519C2×C4C22×C4×D8311yescharacteristic
520C2×C4C2×D4×D8311yescharacteristic
521C2×C4C2×#1305059111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—3321no—
531C8—3321no—
532C8—1661no—
533C8—1661no—
534C8—1661no—
535C8—1661no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—3321no—
540C22—3321no—
541C22—3321no—
542C22C2×#1458175411yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—3321no—
548C4—3321no—
549C4—3321no—
550C4—3321no—
551C4—3321no—
552C4—1662no—
553C4—1662no—
554C4#131×D8311yescharacteristic
555C4#131×D8311yescharacteristic
556C4#1912851111yescharacteristic
557C4#1912851711yescharacteristic
558C2—41no—
559C2—6641no—
560C2#2491615611yescharacteristic
561C2#2491630411yescharacteristic
562C2#2491637911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1574C2
socleC22×C83C2×C4×D4
prime radical#14581766C2×C4
cosocleC42×C83C24
hypercenter#1574D83
hypocenterC83#17919
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
3. #24916543C2semidirect
4. #24906340C2semidirect
5. #24906333C2semidirect
6. #24906312C2semidirect
7. #24906305C2semidirect
8. #24906281C2semidirect
9. #24906274C2semidirect
10. #24906269C2semidirect
11. #24906262C2semidirect
12. #24905891C2semidirect
14. #24905763C2semidirect
15. C83×#1574C2semidirect
293. #1574D83semidirect
297. C83#17919semidirect

Maximal subgroups

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

subgroupindex
#249175452
#249166082
#249165432
#249063402
#249063332
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