Finite Group Databasebeta

← #35375546

Subgroups — #35375546

Order 21248.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917532C211yesmaximal, characteristic
2#24916482C211yesmaximal, characteristic
3#24916411C211yesmaximal, characteristic, complemented
4#24906364C211yesmaximal, characteristic, complemented
5#24906353C211yesmaximal, characteristic, complemented
6#24906338C211yesmaximal, characteristic, complemented
7#24906331C211yesmaximal, characteristic, complemented
8#24906308C211yesmaximal, characteristic, complemented
9#24906282C211yesmaximal, characteristic, complemented
10C8×#13050580C211yesmaximal, characteristic, complemented
11#24906247C211yesmaximal, characteristic, complemented
12#24905934C211yesmaximal, characteristic, complemented
13#24905849C211yesmaximal, characteristic
14#24905761C211yesmaximal, characteristic, complemented
15C83×#1584C211yesmaximal, characteristic, complemented
16#19128255C2211yescharacteristic
17C4×#13050591C2211yescharacteristic
18#19128044C411yescharacteristic
19#19128040C411yescharacteristic
20#19127984C411yescharacteristic
21#19127980C411yescharacteristic
22#19127909C411yescharacteristic
23#19127905C411yescharacteristic
24#19127866C411yescharacteristic
25#19127862C411yescharacteristic
26#19127829—21no—
27#19127828—21no—
28#19127828C2211yescharacteristic
29Q8×C83⋊C8C2211yescharacteristic
30Q8×C83⋊C8C2211yescharacteristic
31C8×Dic166C2211yescharacteristic
32C4×#13050580C2211yescharacteristic
33C4×#13050579C2211yescharacteristic
34C4×#13050577C2211yescharacteristic
35#19127780—21no—
36#19127780C2211yescharacteristic
37#19127778—21no—
38#19127778C2211yescharacteristic
39#19127757—21no—
40#19127757C2211yescharacteristic
41#19127752C2211yescharacteristic
42#19127752C2211yescharacteristic
43#19127726—21no—
44C4⋊C8×D83C2211yescharacteristic
45#19127658—21no—
46C4×#13050573—21no—
47C4×#13050573C2211yescharacteristic
48#19127453C2211yescharacteristic
49#19127452C2211yescharacteristic
50#19127451C2211yescharacteristic
51#19127433C2211yescharacteristic
52Q8⋊(C83⋊C8)C2211yescharacteristic
53Q8⋊(C83⋊C8)C2211yescharacteristic
54#19127431C2211yescharacteristic
55#19127430C2211yescharacteristic
56#19127428C2211yescharacteristic
57#19127422C2211yescharacteristic
58#19127422C2211yescharacteristic
59C8×C83⋊C8C2211yescharacteristic
60#446×C83C2211yescharacteristic
61C8×Q8×C83C2211yescharacteristic
62C4×Q16×C83C2211yescharacteristic
63#335×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65Q8⋊C8×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×#13050591C2×C411yescharacteristic
68C2×#13050580C2×C411yescharacteristic
69C2×#13050579C2×C411yescharacteristic
70C2×#13050577C2×C411yescharacteristic
71C2×#13050573—21no—
72C2×#13050573—21no—
73C2×#13050573D411yescharacteristic
74C2×#13050573D411yescharacteristic
75C2×C8×D83—21no—
76#14581791C2×C411yescharacteristic
77#14581790C2×C411yescharacteristic
78#14581782—21no—
79#14581772C2×C411yescharacteristic
80#14581770—21no—
81#14581768C2×C411yescharacteristic
82Q8×Dic83C2×C411yescharacteristic
83C4×Dic166—21no—
84C4×Dic166C2311yescharacteristic
85C4×D332—21no—
86C4×D332C2311yescharacteristic
87#14581754—21no—
88#14581754C2×C411yescharacteristic
89#14581750—21no—
90#14581750C2×C411yescharacteristic
91#14581749—21no—
92C42×D83—21no—
93C42×D83C2311yescharacteristic
94#14581725C2×C411yescharacteristic
95#14581724C2×C411yescharacteristic
96#14581723C2×C411yescharacteristic
97C4⋊(C83⋊C8)—21no—
98C4⋊(C83⋊C8)—21no—
99C4⋊(C83⋊C8)C2311yescharacteristic
100C4⋊(C83⋊C8)C2311yescharacteristic
101Dic83⋊C8—21no—
102Dic83⋊C8—21no—
103Dic83⋊C8—21no—
104Dic83⋊C8—21no—
105Dic83⋊C8C2×C411yescharacteristic
106Dic83⋊C8C2×C411yescharacteristic
107#14581717C2×C411yescharacteristic
108#14581716C2×C411yescharacteristic
109#14581716C2×C411yescharacteristic
110#14581715C2×C411yescharacteristic
111#14581714C2×C411yescharacteristic
112#14581712C2×C411yescharacteristic
113(C2×D83)⋊C8—21no—
114(C2×D83)⋊C8—21no—
115(C2×D83)⋊C8—21no—
116(C2×D83)⋊C8—21no—
117(C2×D83)⋊C8C2×C411yescharacteristic
118(C2×D83)⋊C8C2×C411yescharacteristic
119#14581702—21no—
120#14581702—21no—
121#14581702D411yescharacteristic
122#14581702D411yescharacteristic
123C4×C83⋊C8—21no—
124C4×C83⋊C8—21no—
125C4×C83⋊C8C2311yescharacteristic
126C4×C83⋊C8C2311yescharacteristic
127C4×C83⋊C8C2311yescharacteristic
128C8×Dic83—21no—
129C2×Q16×C83C2×C411yescharacteristic
130C4×Q8×C83C2311yescharacteristic
131C4×Q8×C83C2311yescharacteristic
132#107×C83C2×C411yescharacteristic
133C4⋊C8×C83—21no—
134C4⋊C8×C83—21no—
135C4⋊C8×C83C2311yescharacteristic
136C4⋊C8×C83C2311yescharacteristic
137#103×C83C2×C411yescharacteristic
138#103×C83C2×C411yescharacteristic
139#97×C83—21no—
140C4×C8×C83—21no—
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#13050591—22no—
145#13050591—41no—
146C2×Dic166—21no—
147C2×Dic166C22×C411yescharacteristic
148C2×D332—21no—
149C2×D332C22×C411yescharacteristic
150C2×C4×D83—21no—
151C2×C4×D83—21no—
152C2×C4×D83—21no—
153C2×C4×D83C22×C411yescharacteristic
154C2×C4×D83C2×D411yescharacteristic
155C2×C4×D83#4111yescharacteristic
156#13050580—22no—
157#13050579—41no—
158#13050577—41no—
159#13050573—22no—
160#13050573—41no—
161#13050573—42no—
162#13050573—42no—
163C2×C83⋊C8—21no—
164C2×C83⋊C8—21no—
165C2×C83⋊C8—21no—
166C2×C83⋊C8C22×C411yescharacteristic
167C2×C83⋊C8C22×C411yescharacteristic
168C2×C83⋊C8C2×D411yescharacteristic
169C2×C83⋊C8C2×D411yescharacteristic
170C8×D83—42no—
171C4⋊Dic83—21no—
172C4⋊Dic83—21no—
173C4⋊Dic83C22×C411yescharacteristic
174C4⋊Dic83C22×C411yescharacteristic
175Dic83⋊C4—21no—
176Dic83⋊C4—21no—
177Dic83⋊C4—21no—
178Dic83⋊C4—21no—
179Dic83⋊C4—21no—
180(C2×D83)⋊C4—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×Dic83C22×C411yescharacteristic
189C4×Dic83C2×D411yescharacteristic
190C4×Dic83#4111yescharacteristic
191C2×Q8×C83C22×C411yescharacteristic
192C2×Q8×C83C22×C411yescharacteristic
193Q16×C83—22no—
194C2×C8×C83—21no—
195C2×C8×C83—21no—
196C2×C8×C83—21no—
197C2×C8×C83C22×C411yescharacteristic
198C2×C8×C83C22×C411yescharacteristic
199C2×C8×C83C2×D411yescharacteristic
200C2×C8×C83C2×D411yescharacteristic
201C4⋊C4×C83—21no—
202C4⋊C4×C83—21no—
203C4⋊C4×C83C22×C411yescharacteristic
204C4⋊C4×C83C22×C411yescharacteristic
205C42×C83—21no—
206C42×C83—21no—
207C42×C83C2411yescharacteristic
208C22×D83—21no—
209C22×D83C4×D411yescharacteristic
210Q8×C83—21no—
211Q8×C83—21no—
212Q8×C83—21no—
213Q8×C83#13112yes—
214C2×C4×C83—21no—
215C2×C4×C83—21no—
216C2×C4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83C23×C411yescharacteristic
219C2×C4×C83C22×D411yescharacteristic
220C2×C4×C83C2×#4111yescharacteristic
221C2×Dic83—21no—
222C2×Dic83—21no—
223C2×Dic83—21no—
224C2×Dic83C4×D411yescharacteristic
225C2×Dic83C4×D411yescharacteristic
226C2×Dic83C4×D411yescharacteristic
227D332—21no—
228D332—21no—
229D332—42no—
230C4×D83—21no—
231C4×D83—21no—
232C4×D83—21no—
233C4×D83—21no—
234C4×D83—41no—
235C4×D83—42no—
236C4×D83—41no—
237C4×D83—41no—
238C4×D83—81no—
239Dic166—21no—
240Dic166—21no—
241Dic166—81no—
242C8×C83—21no—
243C8×C83—21no—
244C8×C83—21no—
245C8×C83—41no—
246C8×C83—41no—
247C8×C83—41no—
248C8×C83#13712yes—
249C83⋊C8—21no—
250C83⋊C8—21no—
251C83⋊C8—21no—
252C83⋊C8—21no—
253C83⋊C8—41no—
254C83⋊C8—41no—
255C83⋊C8—41no—
256C22×C83C2×C4×D411yescharacteristic
257C2×D83—21no—
258C2×D83—21no—
259C2×D83—21no—
260C2×D83—41no—
261C2×D83—41no—
262C2×D83—41no—
263C4×C83—22no—
264C4×C83—21no—
265C4×C83—41no—
266C4×C83—41no—
267C4×C83—41no—
268C4×C83C2×#13111yescharacteristic
269C4×C83#56811yescharacteristic
270C4×C83C2×#13711yescharacteristic
271C4×C83#57511yescharacteristic
272Dic83—21no—
273Dic83—21no—
274Dic83—21no—
275Dic83—41no—
276Dic83—41no—
277Dic83—41no—
278#18013—831nomaximal, Sylow
279C2×C83#293311yescharacteristic
280C2×C83C4×#13711yescharacteristic
281C2×C83#295711yescharacteristic
282D83—41no—
283D83—81no—
284#3107—831no—
285#2971—831no—
286#2962—831no—
287#1592—831no—
288#1590—831no—
289#1588—831no—
290#1587—831no—
291#1584D8311yescharacteristic, complemented
292#1583—831no—
293#1579—831no—
294C8×Q16—831no—
295#1573—831no—
296#1497—831no—
297#1477—831no—
298#1453—831no—
299C83#1801311yescharacteristic, complemented, Sylow
300#533—831no—
301C4×#41—831no—
302#485—831no—
303#485—831no—
304#475—831no—
305#474—831no—
306#462—831no—
307#461—831no—
308#452—831no—
309#452—831no—
310#446—831no—
311#446—1661no—
312#446—1661no—
313#446C2×D8311yescharacteristic
314C8×Q8—831no—
315C8×Q8—831no—
316C8×Q8—831no—
317C8×Q8C2×D8311yescharacteristic
318C4×Q16—831no—
319C4×Q16C2×D8311yescharacteristic
320C4×SD16—831no—
321C4×SD16—831no—
322#436—831no—
323#436—831no—
324#436—1661no—
325#436—1661no—
326#432—831no—
327#432—1661no—
328#431—831no—
329#431—831no—
330#424—1661no—
331C2×C4⋊C8—831no—
332#405—1661no—
333C4×M16—831no—
334C4×M16—1661no—
335#335—831no—
336#335C2×D8311yescharacteristic
337#334—831no—
338#334—831no—
339Q8⋊C8—831no—
340Q8⋊C8—831no—
341Q8⋊C8—831no—
342Q8⋊C8—831no—
343Q8⋊C8C2×D8311yescharacteristic
344Q8⋊C8C2×D8311yescharacteristic
345D4⋊C8—831no—
346D4⋊C8—831no—
347#322—831no—
348#322—831no—
349#322C2×D8311yescharacteristic
350C82—831no—
351C2×#41—831no—
352C2×Q16—831no—
353C2×Q16C4×D8311yescharacteristic
354C2×SD16—831no—
355C2×SD16—831no—
356C2×M16—831no—
357C2×M16—831no—
358C2×M16—1661no—
359C2×M16—1661no—
360C22×C8—1661no—
361C4⋊Q8—831no—
362C4⋊Q8—831no—
363#125—1661no—
364C22⋊Q8—831no—
365C22⋊Q8—831no—
366C22⋊Q8—1661no—
367C4×Q8—831no—
368C4×Q8—831no—
369C4×Q8—1661no—
370C4×Q8C22×D8311yescharacteristic
371C4×Q8C22×D8311yescharacteristic
372C4×D4—831no—
373C4×D4—831no—
374C4×D4—1661no—
375C4×D4—1661no—
376#117—831no—
377#117—1661no—
378#117—1661no—
379C2×C42—831no—
380C2×C42—1661no—
381#107—831no—
382#107C4×D8311yescharacteristic
383#106—831no—
384#106—831no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—831no—
388C4⋊C8—831no—
389C4⋊C8—831no—
390C4⋊C8—831no—
391C4⋊C8—1661no—
392C4⋊C8—1661no—
393C4⋊C8—1661no—
394C4⋊C8—1661no—
395C4⋊C8—1661no—
396C4⋊C8—1661no—
397C4⋊C8C22×D8311yescharacteristic
398C4⋊C8C22×D8311yescharacteristic
399#103—831no—
400#103—831no—
401#103—831no—
402#103—831no—
403#103C4×D8311yescharacteristic
404#103C4×D8311yescharacteristic
405#102—831no—
406#102—831no—
407C22⋊C8—831no—
408C22⋊C8—831no—
409C22⋊C8—1661no—
410C22⋊C8—1661no—
411C22⋊C8—1661no—
412C22⋊C8—1661no—
413#97—21no—
414#97—831no—
415#97—831no—
416#97—1661no—
417#97—1661no—
418C4×C8—21no—
419C4×C8—831no—
420C4×C8—831no—
421C4×C8—831no—
422C4×C8—1661no—
423C4×C8—1661no—
424C4×C8—1661no—
425C4×C8C22×D8311yescharacteristic
426C4×C8C22×D8311yescharacteristic
427C4×C8C22×D8311yescharacteristic
428#41—3321no—
429#41—1662no—
430C2×Q8—831no—
431C2×Q8—1661no—
432C2×Q8C2×C4×D8311yescharacteristic
433C2×Q8C2×C4×D8311yescharacteristic
434C2×D4—831no—
435C2×D4—1661no—
436C22×C4—831no—
437C22×C4—831no—
438C22×C4—831no—
439C22×C4—1661no—
440C22×C4—1661no—
441C22×C4—1661no—
442Q16—22no—
443Q16—1662no—
444SD16—3321no—
445SD16—3321no—
446M16—3321no—
447M16—3322no—
448M16—3322no—
449M16—1662no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—3322no—
454C2×C8—831no—
455C2×C8—831no—
456C2×C8—831no—
457C2×C8—831no—
458C2×C8—1661no—
459C2×C8—1661no—
460C2×C8—1661no—
461C2×C8C2×C4×D8311yescharacteristic
462C2×C8C2×C4×D8311yescharacteristic
463C2×C8D4×D8311yescharacteristic
464C2×C8D4×D8311yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—831no—
468C4⋊C4—831no—
469C4⋊C4—1661no—
470C4⋊C4—1661no—
471C4⋊C4—1661no—
472C4⋊C4—1661no—
473C4⋊C4—1661no—
474C4⋊C4—1661no—
475C4⋊C4—1661no—
476C4⋊C4C2×C4×D8311yescharacteristic
477C4⋊C4C2×C4×D8311yescharacteristic
478C22⋊C4—1661no—
479C22⋊C4—1661no—
480C22⋊C4—1661no—
481C22⋊C4—1661no—
482C22⋊C4—1661no—
483C42—21no—
484C42—21no—
485C42—831no—
486C42—831no—
487C42—831no—
488C42—1661no—
489C42—1661no—
490C42—1661no—
491C42C23×D8311yescharacteristic
492C23—831no—
493C23—1661no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—6641no—
498Q8—1661no—
499Q8—1661no—
500Q8#1458180012yes—
501D4—3322no—
502D4—1661no—
503D4—1661no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—3322no—
509C2×C4—3321no—
510C2×C4—3321no—
511C2×C4—3321no—
512C2×C4—831no—
513C2×C4—831no—
514C2×C4—831no—
515C2×C4—6641no—
516C2×C4—1661no—
517C2×C4—1661no—
518C2×C4—1661no—
519C2×C4—1661no—
520C2×C4—1661no—
521C2×C4—1661no—
522C2×C4—1661no—
523C2×C4C22×C4×D8311yescharacteristic
524C2×C4C2×D4×D8311yescharacteristic
525C2×C4#41×D8311yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—3321no—
533C8—3321no—
534C8—3321no—
535C8—1661no—
536C8—1661no—
537C8—1661no—
538C8—1661no—
539C8#1458182412yes—
540C22—3321no—
541C22—3321no—
542C22—3321no—
543C22—1661no—
544C22—1661no—
545C22—1661no—
546C22C4×D4×D8311yescharacteristic
547C4—21no—
548C4—22no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—3321no—
553C4—3321no—
554C4—3321no—
555C4—1661no—
556C4—1661no—
557C4—1661no—
558C4C2×#1458180011yescharacteristic
559C4#1912846611yescharacteristic
560C4C2×#1458182411yescharacteristic
561C4#1912849811yescharacteristic
562C2—3321no—
563C2—6641no—
564C2#2491618911yescharacteristic
565C2C4×#1458182411yescharacteristic
566C2#2491637711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1584C2
socleC22×C83C2×C4×D4
prime radicalC2×#13050591C2×C4
cosocleC42×C83C24
hypercenter#1584D83
hypocenterC83#18013
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
3. #24916411C2semidirect
4. #24906364C2semidirect
5. #24906353C2semidirect
6. #24906338C2semidirect
7. #24906331C2semidirect
8. #24906308C2semidirect
9. #24906282C2semidirect
10. C8×#13050580C2semidirect
11. #24906247C2semidirect
12. #24905934C2semidirect
14. #24905761C2semidirect
15. C83×#1584C2semidirect
291. #1584D83semidirect
299. C83#18013semidirect

Maximal subgroups

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

subgroupindex
#249175322
#249164822
#249164112
#249063642
#249063532
#249063382
#249063312
#249063082
#249062822
C8×#130505802
#249062472
#249059342
#249058492
#249057612
C83×#15842
#1801383