Finite Group Databasebeta

← #35374515

Subgroups — #35374515

Order 21248.

598 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#24917528C211yesmaximal, characteristic
2#24916572C211yesmaximal, characteristic
3#24916558C211yesmaximal, characteristic, complemented
4#24906337C211yesmaximal, characteristic, complemented
5#24906323C211yesmaximal, characteristic, complemented
6#24906316C211yesmaximal, characteristic, complemented
7#24906302C211yesmaximal, characteristic, complemented
8#24906279C211yesmaximal, characteristic, complemented
9#24906278C211yesmaximal, characteristic, complemented
10#24906267C211yesmaximal, characteristic, complemented
11#24906260C211yesmaximal, characteristic, complemented
12#24906246C211yesmaximal, characteristic, complemented
13#24905898C211yesmaximal, characteristic
14#24905763C211yesmaximal, characteristic, complemented
15C83×#1481C211yesmaximal, characteristic, complemented
16C4×#13050590C2211yescharacteristic
17#19128039C411yescharacteristic
18#19128039C411yescharacteristic
19#19127983C411yescharacteristic
20#19127978C411yescharacteristic
21#19127908C411yescharacteristic
22#19127903C411yescharacteristic
23#19127861C411yescharacteristic
24#19127861C411yescharacteristic
25#19127832—21no—
26#19127832—21no—
27#19127832C2211yescharacteristic
28#19127832C2211yescharacteristic
29Q8×C83⋊C8C2211yescharacteristic
30Q8×C83⋊C8C2211yescharacteristic
31#19127825C2211yescharacteristic
32#19127825C2211yescharacteristic
33C4×#13050580C2211yescharacteristic
34C4×#13050580C2211yescharacteristic
35C4×#13050577C2211yescharacteristic
36C4×#13050577C2211yescharacteristic
37#19127766C2211yescharacteristic
38#19127766C2211yescharacteristic
39C8×C22⋊D83—21no—
40C8×C22⋊D83—21no—
41#19127762—21no—
42#19127762—21no—
43#19127758C2211yescharacteristic
44#19127754C2211yescharacteristic
45#19127754C2211yescharacteristic
46#19127753—21no—
47C4⋊C8×D83—21no—
48#19127453C2211yescharacteristic
49#19127453C2211yescharacteristic
50#19127451C2211yescharacteristic
51#19127451C2211yescharacteristic
52#19127433C2211yescharacteristic
53#19127433C2211yescharacteristic
54#19127430C2211yescharacteristic
55#19127430C2211yescharacteristic
56#19127423C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127422C2211yescharacteristic
59C8×C83⋊C8C2211yescharacteristic
60#533×C83C2211yescharacteristic
61#431×C83C2211yescharacteristic
62C2×C4⋊C8×C83C2211yescharacteristic
63Q8⋊C8×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65Q8⋊C8×C83C2211yescharacteristic
66Q8⋊C8×C83C2211yescharacteristic
67C2×#13050590C2×C411yescharacteristic
68C2×#13050580C2×C411yescharacteristic
69C2×#13050580C2×C411yescharacteristic
70C2×#13050577C2×C411yescharacteristic
71C2×#13050577C2×C411yescharacteristic
72C2×C8×D83—21no—
73C2×C8×D83—21no—
74C4×Dic166C2×C411yescharacteristic
75C4×Dic166C2311yescharacteristic
76C4×D332C2×C411yescharacteristic
77C4×D332C2311yescharacteristic
78C4×C22⋊D83—21no—
79C4×C22⋊D83—21no—
80#14581751C2×C411yescharacteristic
81#14581749—21no—
82C42×D83—21no—
83#14581725C2×C411yescharacteristic
84#14581725C2×C411yescharacteristic
85#14581723C2×C411yescharacteristic
86#14581723C2×C411yescharacteristic
87C4⋊(C83⋊C8)—21no—
88C4⋊(C83⋊C8)—21no—
89C4⋊(C83⋊C8)—21no—
90C4⋊(C83⋊C8)—21no—
91C4⋊(C83⋊C8)C2×C411yescharacteristic
92C4⋊(C83⋊C8)C2×C411yescharacteristic
93C4⋊(C83⋊C8)D411yescharacteristic
94C4⋊(C83⋊C8)D411yescharacteristic
95C4⋊(C83⋊C8)C2311yescharacteristic
96C4⋊(C83⋊C8)C2311yescharacteristic
97Dic83⋊C8—21no—
98Dic83⋊C8—21no—
99#14581716C2×C411yescharacteristic
100#14581716C2×C411yescharacteristic
101#14581716C2×C411yescharacteristic
102#14581716C2×C411yescharacteristic
103#14581715C2×C411yescharacteristic
104#14581715C2×C411yescharacteristic
105#14581712C2×C411yescharacteristic
106#14581712C2×C411yescharacteristic
107C22⋊(C83⋊C8)—21no—
108C22⋊(C83⋊C8)C2×C411yescharacteristic
109C22⋊(C83⋊C8)C2×C411yescharacteristic
110C22⋊(C83⋊C8)D411yescharacteristic
111C22⋊(C83⋊C8)D411yescharacteristic
112(C2×D83)⋊C8—21no—
113(C2×D83)⋊C8—21no—
114#14581703—21no—
115#14581703—21no—
116#14581703—21no—
117C4×C83⋊C8—21no—
118C4×C83⋊C8—21no—
119C4×C83⋊C8C2311yescharacteristic
120C4×C83⋊C8C2311yescharacteristic
121C4×C83⋊C8C2311yescharacteristic
122C4×C83⋊C8C2311yescharacteristic
123C8×Dic83—21no—
124C8×Dic83—21no—
125C22×C8×C83—21no—
126C4⋊Q8×C83C2×C411yescharacteristic
127C4⋊Q8×C83C2×C411yescharacteristic
128#125×C83—21no—
129C22⋊Q8×C83—21no—
130C22⋊Q8×C83C2×C411yescharacteristic
131C22⋊Q8×C83C2×C411yescharacteristic
132C4×Q8×C83—21no—
133C4×Q8×C83C2311yescharacteristic
134C4×Q8×C83C2311yescharacteristic
135#117×C83—21no—
136C2×C42×C83C2311yescharacteristic
137C4⋊C8×C83—21no—
138C4⋊C8×C83—21no—
139C4⋊C8×C83C2311yescharacteristic
140C4⋊C8×C83C2311yescharacteristic
141C22⋊C8×C83—21no—
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#13050590—22no—
145#13050590—22no—
146C2×Dic166C22×C411yescharacteristic
147C2×D332C22×C411yescharacteristic
148C2×C22⋊D83—21no—
149C2×C4×D83—21no—
150C2×C4×D83—21no—
151C2×C4×D83—21no—
152#13050580—22no—
153#13050580—22no—
154#13050577—22no—
155#13050577—22no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8C22×C411yescharacteristic
159C2×C83⋊C8C22×C411yescharacteristic
160C2×C83⋊C8C22×C411yescharacteristic
161C2×C83⋊C8C22×C411yescharacteristic
162C2×C83⋊C8C2×D411yescharacteristic
163C2×C83⋊C8C2×D411yescharacteristic
164C2×C83⋊C8C2×D411yescharacteristic
165C2×C83⋊C8C2×D411yescharacteristic
166C8×D83—81no—
167C8×D83—81no—
168C4⋊Dic83C22×C411yescharacteristic
169C4⋊Dic83C22×C411yescharacteristic
170Dic83⋊C4—21no—
171Dic83⋊C4—21no—
172C22⋊Dic83—21no—
173(C2×D83)⋊C4—21no—
174(C2×D83)⋊C4—21no—
175C4×Dic83—21no—
176C4×Dic83—21no—
177C4×Dic83—21no—
178C2×Q8×C83—21no—
179C2×Q8×C83C22×C411yescharacteristic
180C2×Q8×C83C22×C411yescharacteristic
181C22×C4×C83C22×C411yescharacteristic
182C22×C4×C83C2×D411yescharacteristic
183C22×C4×C83#4111yescharacteristic
184C2×C8×C83—21no—
185C2×C8×C83—21no—
186C2×C8×C83—21no—
187C2×C8×C83—21no—
188C2×C8×C83—81no—
189C4⋊C4×C83—21no—
190C4⋊C4×C83—21no—
191C4⋊C4×C83—21no—
192C4⋊C4×C83—21no—
193C4⋊C4×C83—21no—
194C4⋊C4×C83—21no—
195C4⋊C4×C83—21no—
196C4⋊C4×C83C22×C411yescharacteristic
197C4⋊C4×C83C22×C411yescharacteristic
198C22⋊C4×C83—21no—
199C22⋊C4×C83—21no—
200C42×C83—21no—
201C42×C83—21no—
202C42×C83C22×C411yescharacteristic
203C42×C83C2×D411yescharacteristic
204C42×C83#4111yescharacteristic
205C42×C83C2411yescharacteristic
206C23×C83C4×D411yescharacteristic
207C22×D83—21no—
208Q8×C83—21no—
209Q8×C83—21no—
210Q8×C83—21no—
211Q8×C83—21no—
212Q8×C83—81no—
213C2×C4×C83—21no—
214C2×C4×C83—21no—
215C2×C4×C83—21no—
216C2×C4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—41no—
222C2×C4×C83C4×D411yescharacteristic
223C2×C4×C83C4×D411yescharacteristic
224C2×C4×C83C4×D411yescharacteristic
225C2×C4×C83C23×C411yescharacteristic
226C2×C4×C83C22×D411yescharacteristic
227C2×C4×C83C2×#4111yescharacteristic
228C22⋊D83—24no—
229C2×Dic83—21no—
230C2×Dic83—21no—
231C2×Dic83—21no—
232D332—21no—
233D332#13112yes—
234C4×D83—24no—
235C4×D83—41no—
236C4×D83—41no—
237C4×D83—81no—
238Dic166—21no—
239Dic166#13112yes—
240C8×C83—41no—
241C8×C83—41no—
242C8×C83—41no—
243C8×C83—41no—
244C83⋊C8—21no—
245C83⋊C8—21no—
246C83⋊C8—21no—
247C83⋊C8—21no—
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—22no—
259C2×D83—41no—
260C2×D83—41no—
261C4×C83—21no—
262C4×C83—21no—
263C4×C83—21no—
264C4×C83—21no—
265C4×C83—41no—
266C4×C83—41no—
267C4×C83—41no—
268C4×C83—41no—
269C4×C83C2×#13111yescharacteristic
270C4×C83C2×#13111yescharacteristic
271C4×C83#57711yescharacteristic
272C4×C83#57811yescharacteristic
273Dic83—22no—
274Dic83—41no—
275Dic83—41no—
276#17921—831nomaximal, Sylow
277C2×C83—41no—
278C2×C83#292911yescharacteristic
279C2×C83#294711yescharacteristic
280C2×C83#295711yescharacteristic
281D83—42no—
282#3107—831no—
283#2988—831no—
284#2985—831no—
285#1587—831no—
286#1585—831no—
287#1584—831no—
288#1582—831no—
289#1579—831no—
290SD16⋊C8—831no—
291C8×Q16—831no—
292C8×SD16—831no—
293#1573—831no—
294#1488—831no—
295#1481D8311yescharacteristic, complemented
296#1454—831no—
297C83#1792111yescharacteristic, complemented, Sylow
298#533C2×D8311yescharacteristic
299C4×#41—831no—
300#485—831no—
301#485—831no—
302#475—831no—
303#474—831no—
304#462—831no—
305#461—831no—
306#452—831no—
307#452—831no—
308#446—831no—
309#446—831no—
310#446—1661no—
311#446—1661no—
312C8×Q8—831no—
313C8×Q8—831no—
314C8×Q8—831no—
315C8×Q8—831no—
316C4×Q16—831no—
317C4×Q16—831no—
318C4×SD16—831no—
319C4×SD16—831no—
320C8×D4—831no—
321C8×D4—831no—
322C8×D4—1661no—
323C8×D4—1661no—
324#433—1661no—
325#433—1661no—
326#432—831no—
327#431—831no—
328#431—831no—
329#431—1661no—
330#431C2×D8311yescharacteristic
331C2×C4⋊C8—1661no—
332C2×C4⋊C8C2×D8311yescharacteristic
333#335—831no—
334#335—831no—
335#334—831no—
336#334—831no—
337Q8⋊C8—831no—
338Q8⋊C8—831no—
339Q8⋊C8C2×D8311yescharacteristic
340Q8⋊C8C2×D8311yescharacteristic
341Q8⋊C8C2×D8311yescharacteristic
342Q8⋊C8C2×D8311yescharacteristic
343D4⋊C8—831no—
344D4⋊C8—831no—
345#322—831no—
346#322—831no—
347#322—831no—
348C82—831no—
349C2×#41—831no—
350C2×Q16—831no—
351C2×Q16—831no—
352C2×SD16—831no—
353C2×SD16—831no—
354C22×C8—21no—
355C22×C8—1661no—
356C22×C8—1661no—
357C4⋊Q8C4×D8311yescharacteristic
358C4⋊Q8C4×D8311yescharacteristic
359#125—21no—
360C22⋊Q8—21no—
361C22⋊Q8C4×D8311yescharacteristic
362C22⋊Q8C4×D8311yescharacteristic
363C4×Q8—21no—
364C4×Q8—831no—
365C4×Q8—831no—
366C4×Q8C22×D8311yescharacteristic
367C4×Q8C22×D8311yescharacteristic
368C4×D4—831no—
369C4×D4—831no—
370C4×D4—1661no—
371C4×D4—1661no—
372#117—21no—
373#117—831no—
374#117—1661no—
375C2×C42—1661no—
376C2×C42C22×D8311yescharacteristic
377#107—831no—
378#107—831no—
379#106—831no—
380#106—831no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—831no—
384C4⋊C8—831no—
385C4⋊C8—831no—
386C4⋊C8—831no—
387C4⋊C8—831no—
388C4⋊C8—831no—
389C4⋊C8—1661no—
390C4⋊C8—1661no—
391C4⋊C8—1661no—
392C4⋊C8—1661no—
393C4⋊C8—1661no—
394C4⋊C8—1661no—
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—831no—
409C22⋊C8—831no—
410C22⋊C8—1661no—
411C22⋊C8—1661no—
412C22⋊C8—1661no—
413#97—1661no—
414#97—1661no—
415#97—1661no—
416C4×C8—831no—
417C4×C8—831no—
418C4×C8—831no—
419C4×C8—831no—
420C4×C8—1661no—
421C4×C8—1661no—
422C4×C8—1661no—
423C4×C8—1661no—
424C4×C8C22×D8311yescharacteristic
425C4×C8C22×D8311yescharacteristic
426#41—1662no—
427#41—1662no—
428C2×Q8—21no—
429C2×Q8—831no—
430C2×Q8C2×C4×D8311yescharacteristic
431C2×Q8C2×C4×D8311yescharacteristic
432C2×D4—831no—
433C2×D4—1661no—
434C22×C4—1661no—
435C22×C4—1661no—
436C22×C4—1661no—
437C22×C4C2×C4×D8311yescharacteristic
438C22×C4D4×D8311yescharacteristic
439C22×C4#1305058911yescharacteristic
440Q16—1662no—
441Q16—1662no—
442SD16—1662no—
443SD16—1662no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—81no—
449C2×C8—831no—
450C2×C8—831no—
451C2×C8—831no—
452C2×C8—831no—
453C2×C8—831no—
454C2×C8—831no—
455C2×C8—831no—
456C2×C8—831no—
457C2×C8—6641no—
458C2×C8—6641no—
459C2×C8—1661no—
460C2×C8—1661no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—831no—
469C4⋊C4—831no—
470C4⋊C4—1661no—
471C4⋊C4—1661no—
472C4⋊C4C2×C4×D8311yescharacteristic
473C4⋊C4C2×C4×D8311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—1661no—
477C22⋊C4—1661no—
478C22⋊C4—1661no—
479C42—21no—
480C42—21no—
481C42—1661no—
482C42—1661no—
483C42—1661no—
484C42C2×C4×D8311yescharacteristic
485C42D4×D8311yescharacteristic
486C42#1305058911yescharacteristic
487C42C23×D8311yescharacteristic
488C23—1661no—
489C23(C22⋊D83)⋊C411yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—832no—
496Q8—1661no—
497D4—832no—
498D4—1664no—
499D4—1661no—
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—3321no—
510C2×C4—3321no—
511C2×C4—6641no—
512C2×C4—1664no—
513C2×C4—1661no—
514C2×C4—1661no—
515C2×C4—1661no—
516C2×C4(C22⋊D83)⋊C411yescharacteristic
517C2×C4(C22⋊D83)⋊C411yescharacteristic
518C2×C4(C22⋊D83)⋊C411yescharacteristic
519C2×C4C22×C4×D8311yescharacteristic
520C2×C4C2×D4×D8311yescharacteristic
521C2×C4C2×#1305058911yescharacteristic
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—3321no—
527C8—3321no—
528C8—1661no—
529C8—1661no—
530C8—1661no—
531C8—1661no—
532C8—1661no—
533C8—1661no—
534C8—1661no—
535C8—1661no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—3321no—
540C22—3321no—
541C22—1662no—
542C22C2×(C22⋊D83)⋊C411yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—3321no—
552C4—3321no—
553C4—1662no—
554C4#131×D8311yescharacteristic
555C4#131×D8311yescharacteristic
556C4#1912850711yescharacteristic
557C4#1912851411yescharacteristic
558C2—41no—
559C2—3322no—
560C2#2491616011yescharacteristic
561C2#2491630011yescharacteristic
562C2#2491637611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1481C2
socleC22×C83C2×C4×D4
prime radicalC2×#13050590C2×C4
cosocleC42×C83C24
hypercenter#1481D83
hypocenterC83#17921
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
3. #24916558C2semidirect
4. #24906337C2semidirect
5. #24906323C2semidirect
6. #24906316C2semidirect
7. #24906302C2semidirect
8. #24906279C2semidirect
9. #24906278C2semidirect
10. #24906267C2semidirect
11. #24906260C2semidirect
12. #24906246C2semidirect
14. #24905763C2semidirect
15. C83×#1481C2semidirect
295. #1481D83semidirect
297. C83#17921semidirect

Maximal subgroups

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

subgroupindex
#249175282
#249165722
#249165582
#249063372
#249063232
#249063162
#249063022
#249062792
#249062782
#249062672
#249062602
#249062462
#249058982
#249057632
C83×#14812
#1792183