Finite Group Databasebeta

← #35414812

Subgroups — #35414812

Order 21248.

754 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127726C211yesmaximal, characteristic
2#24910071C211yesmaximal, characteristic
3#24910068C211yesmaximal, characteristic
4#24908233C211yesmaximal, characteristic, complemented
5#24908231C211yesmaximal, characteristic, complemented
6#24908228C211yesmaximal, characteristic, complemented
7#24908228C211yesmaximal, characteristic, complemented
8#24908225C211yesmaximal, characteristic, complemented
9#24908224C211yesmaximal, characteristic, complemented
10#24908220C211yesmaximal, characteristic, complemented
11#24907497C211yesmaximal, characteristic
12#24907495C211yesmaximal, characteristic
13#24907489C211yesmaximal, characteristic
14#24907487C211yesmaximal, characteristic
15C83×#1947C211yesmaximal, characteristic, complemented
16C22×#13050573C2211yescharacteristic
17C22×C8×D83C2211yescharacteristic
18C2×#14581749C2211yescharacteristic
19C2×#14581726C2211yescharacteristic
20C2×#14581725C2211yescharacteristic
21C2×#14581724C2211yescharacteristic
22C2×#14581723C2211yescharacteristic
23C2×#14581723C2211yescharacteristic
24C2×#14581723C2211yescharacteristic
25#19127726C418yescomplemented
26C2×C4⋊(C83⋊C8)C2211yescharacteristic
27C2×Dic83⋊C8C2211yescharacteristic
28C2×Dic83⋊C8C2211yescharacteristic
29#19127592—21no—
30#19127591—21no—
31#19127591—21no—
32#19127590—21no—
33#19127585—21no—
34#19127583—21no—
35#19127582—21no—
36#19127582—21no—
37#19127570C2211yescharacteristic
38#19127567C2211yescharacteristic
39#19127566C2211yescharacteristic
40#19127558C2211yescharacteristic
41#19127558C2211yescharacteristic
42#19127558C2211yescharacteristic
43#19127558C2211yescharacteristic
44C4⋊C4×Dic83C2211yescharacteristic
45C4⋊C4×Dic83C2211yescharacteristic
46C4×C4⋊Dic83C2211yescharacteristic
47#19127464C2211yescharacteristic
48#19127464C2211yescharacteristic
49#19127463C2211yescharacteristic
50#19127463C2211yescharacteristic
51#19127463C2211yescharacteristic
52#19127463C2211yescharacteristic
53C2×#107×C83C2211yescharacteristic
54C2×#107×C83C2211yescharacteristic
55C2×C4⋊C8×C83C2211yescharacteristic
56#384×C83C2211yescharacteristic
57C4×C4⋊C4×C83C2211yescharacteristic
58#340×C83C2211yescharacteristic
59#340×C83C2211yescharacteristic
60C22×C4×D83C2311yescharacteristic
61C2×#13050573—41no—
62C2×#13050573—41no—
63C2×#13050573C2×C414yes—
64C22×C83⋊C8C2311yescharacteristic
65C22×C83⋊C8C2311yescharacteristic
66C2×C8×D83—41no—
67C2×C8×D83—41no—
68C2×C8×D83C2×C414yes—
69#14581749C2×C414yes—
70#14581749Q814yes—
71C2×C4⋊Dic83C2311yescharacteristic
72C2×C4⋊Dic83C2311yescharacteristic
73C2×C4⋊Dic83C2311yescharacteristic
74C2×C4⋊Dic83C2311yescharacteristic
75C2×Dic83⋊C4—21no—
76C2×Dic83⋊C4—21no—
77C2×Dic83⋊C4D411yescharacteristic
78C2×Dic83⋊C4D411yescharacteristic
79C2×(C2×D83)⋊C4—21no—
80C2×(C2×D83)⋊C4—21no—
81C2×(C2×D83)⋊C4—21no—
82C2×(C2×D83)⋊C4—21no—
83C2×(C2×D83)⋊C4D411yescharacteristic
84C2×(C2×D83)⋊C4D411yescharacteristic
85C2×C4×Dic83—21no—
86C2×C4×Dic83—21no—
87C2×C4×Dic83—21no—
88C2×C4×Dic83C2311yescharacteristic
89#14581726—41no—
90#14581725—41no—
91#14581724—41no—
92#14581723—41no—
93#14581723—41no—
94#14581723—41no—
95C4⋊(C83⋊C8)C2×C414yes—
96Dic83⋊C8C2×C414yes—
97Dic83⋊C8C2×C414yes—
98C83⋊#95—21no—
99C83⋊#95—21no—
100C83⋊#95—21no—
101C83⋊#95—21no—
102C83⋊#95—21no—
103C83⋊#95—21no—
104C83⋊#95—21no—
105C83⋊#95—21no—
106C83⋊#95—21no—
107C83⋊#95—21no—
108C83⋊#95—21no—
109C22×C8×C83C2311yescharacteristic
110C22×C8×C83C2311yescharacteristic
111C2×C4⋊C4×C83—21no—
112C2×C4⋊C4×C83—21no—
113C2×C4⋊C4×C83C2311yescharacteristic
114C2×C4⋊C4×C83C2311yescharacteristic
115C2×C4⋊C4×C83C2311yescharacteristic
116C2×C4⋊C4×C83C2311yescharacteristic
117C2×C42×C83—21no—
118C2×C42×C83C2311yescharacteristic
119#107×C83—41no—
120#107×C83—41no—
121C4⋊C8×C83C2×C414yes—
122#95×C83—21no—
123C23×D83C2×D411yescharacteristic
124C22×Dic83—21no—
125C22×Dic83—21no—
126C22×Dic83—21no—
127C22×Dic83—21no—
128C22×Dic83C2×D411yescharacteristic
129C22×Dic83C2×D411yescharacteristic
130C22×Dic83C2×D411yescharacteristic
131C2×C4×D83—21no—
132C2×C4×D83—21no—
133C2×C4×D83—21no—
134C2×C4×D83—21no—
135C2×C4×D83C22×C412yes—
136C2×C4×D83C2×Q812yes—
137#13050573—44no—
138C2×C83⋊C8—21no—
139C2×C83⋊C8—21no—
140C2×C83⋊C8—21no—
141C2×C83⋊C8—21no—
142C2×C83⋊C8C22×C412yes—
143C2×C83⋊C8C22×C412yes—
144C8×D83—44no—
145C4⋊Dic83—21no—
146C4⋊Dic83—21no—
147C4⋊Dic83—21no—
148C4⋊Dic83—21no—
149C4⋊Dic83—21no—
150C4⋊Dic83—21no—
151C4⋊Dic83—21no—
152C4⋊Dic83—21no—
153Dic83⋊C4—81no—
154Dic83⋊C4—81no—
155Dic83⋊C4C4⋊C414yes—
156Dic83⋊C4C4⋊C414yes—
157(C2×D83)⋊C4—81no—
158(C2×D83)⋊C4—81no—
159(C2×D83)⋊C4—81no—
160(C2×D83)⋊C4—81no—
161(C2×D83)⋊C4C4⋊C414yes—
162(C2×D83)⋊C4C4⋊C414yes—
163C4×Dic83—81no—
164C4×Dic83—81no—
165C4×Dic83—81no—
166C4×Dic83C22×C412yes—
167C4×Dic83C2×Q812yes—
168C22×C4×C83—21no—
169C22×C4×C83—21no—
170C22×C4×C83—21no—
171C22×C4×C83—21no—
172C22×C4×C83C2×D411yescharacteristic
173C22×C4×C83C2×D411yescharacteristic
174C22×C4×C83C2411yescharacteristic
175C2×C8×C83—21no—
176C2×C8×C83—21no—
177C2×C8×C83—21no—
178C2×C8×C83—21no—
179C2×C8×C83C22×C412yes—
180C2×C8×C83C22×C412yes—
181C4⋊C4×C83—21no—
182C4⋊C4×C83—21no—
183C4⋊C4×C83—21no—
184C4⋊C4×C83—21no—
185C4⋊C4×C83—21no—
186C4⋊C4×C83—21no—
187C4⋊C4×C83—21no—
188C4⋊C4×C83—21no—
189C4⋊C4×C83—81no—
190C4⋊C4×C83—81no—
191C42×C83—81no—
192C42×C83C22×C412yes—
193C42×C83C2×Q812yes—
194C23×C83C22×D411yescharacteristic
195C22×D83—21no—
196C22×D83—21no—
197C22×D83—21no—
198C22×D83—21no—
199C22×D83—21no—
200C22×D83—21no—
201C22×D83C2×C4⋊C412yes—
202C2×C4×C83—21no—
203C2×C4×C83—21no—
204C2×C4×C83—21no—
205C2×C4×C83—21no—
206C2×C4×C83—41no—
207C2×C4×C83—41no—
208C2×C4×C83—41no—
209C2×C4×C83—41no—
210C2×C4×C83—41no—
211C2×C4×C83—41no—
212C2×C4×C83—41no—
213C2×C4×C83—41no—
214C2×C4×C83—41no—
215C2×C4×C83—41no—
216C2×C4×C83—41no—
217C2×C4×C83—41no—
218C2×C4×C83C2×C4⋊C412yes—
219C2×C4×C83C2×C4⋊C412yes—
220C2×C4×C83C23×C411yescharacteristic
221C2×C4×C83C22×Q811yescharacteristic
222C2×C4×C83H(5,𝔽2)11yescharacteristic
223C2×C4×C83H(5,𝔽2)11yescharacteristic
224C2×C4×C832−1+411yescharacteristic
225C2×C4×C832−1+411yescharacteristic
226C2×Dic83—21no—
227C2×Dic83—21no—
228C2×Dic83—21no—
229C2×Dic83—21no—
230C2×Dic83—21no—
231C2×Dic83—21no—
232C2×Dic83—41no—
233C2×Dic83—41no—
234C2×Dic83—41no—
235C2×Dic83—41no—
236C2×Dic83—41no—
237C2×Dic83—41no—
238C2×Dic83—41no—
239C2×Dic83—41no—
240C2×Dic83—41no—
241C2×Dic83—41no—
242C2×Dic83—41no—
243C2×Dic83—41no—
244C2×Dic83C2×C4⋊C412yes—
245C2×Dic83C2×C4⋊C412yes—
246C2×Dic83C2×C4⋊C412yes—
247C4×D83—22no—
248C4×D83—22no—
249C4×D83—22no—
250C4×D83—22no—
251C8×C83—22no—
252C8×C83—22no—
253C83⋊C8—22no—
254C83⋊C8—22no—
255C22×C83C22×C4⋊C411yescharacteristic
256C22×C83#53711yescharacteristic
257C22×C83#53711yescharacteristic
258C22×C83#57611yescharacteristic
259C22×C83#57711yescharacteristic
260C22×C83#57711yescharacteristic
261C22×C83#57811yescharacteristic
262C2×D83—22no—
263C2×D83—22no—
264C2×D83—22no—
265C2×D83—41no—
266C2×D83—41no—
267C2×D83—41no—
268C2×D83—41no—
269C4×C83—22no—
270C4×C83—22no—
271C4×C83—81no—
272C4×C83—81no—
273C4×C83—81no—
274C4×C83—81no—
275C4×C83#51811yescharacteristic
276C4×C83#51911yescharacteristic
277C4×C83#54411yescharacteristic
278C4×C83#54411yescharacteristic
279Dic83—22no—
280Dic83—22no—
281Dic83—22no—
282Dic83—81no—
283Dic83—81no—
284Dic83—81no—
285Dic83—81no—
286#21966—831nomaximal, Sylow
287C2×C83#231611yescharacteristic
288C2×C83#291211yescharacteristic
289C2×C83#291311yescharacteristic
290C2×C83#325711yescharacteristic
291C2×C83#325711yescharacteristic
292C2×C83#325811yescharacteristic
293C2×C83#325811yescharacteristic
294D83—42no—
295C2×#424—831no—
296#2314—831no—
297#2314—831no—
298#1949—831no—
299#1949—831no—
300#1949—831no—
301#1949—831no—
302#1948—831no—
303#1948—831no—
304#1947—831no—
305#1947D8311yescharacteristic, complemented
306#1809—831no—
307#1809—831no—
308#1808—831no—
309#1807—831no—
310C83#2196611yescharacteristic, complemented, Sylow
311C22×M16—831no—
312C23×C8—831no—
313C2×#117—831no—
314C2×#107—831no—
315C2×#107—831no—
316C2×#107C2×D8311yescharacteristic
317C2×#107C2×D8311yescharacteristic
318C2×#106—831no—
319C2×#106—831no—
320C2×#106—831no—
321C2×#106—831no—
322#424—838no—
323C2×C4⋊C8—831no—
324C2×C4⋊C8—831no—
325C2×C4⋊C8—831no—
326C2×C4⋊C8C2×D8311yescharacteristic
327#388—1661no—
328#388—1661no—
329#388—1661no—
330#388—1661no—
331#387—1661no—
332#387—1661no—
333#387—1661no—
334#387—1661no—
335#384—831no—
336#384C2×D8311yescharacteristic
337#382—831no—
338#382—831no—
339#380—831no—
340#380—831no—
341#380—831no—
342#380—831no—
343C4×C4⋊C4—831no—
344C4×C4⋊C4—831no—
345C4×C4⋊C4—831no—
346C4×C4⋊C4C2×D8311yescharacteristic
347#340—831no—
348#340—831no—
349#340—831no—
350#340—831no—
351#340—831no—
352#340—831no—
353#340C2×D8311yescharacteristic
354#340C2×D8311yescharacteristic
355C23×C4—831no—
356C2×M16—3321no—
357C2×M16—3321no—
358C2×M16—834no—
359C22×C8—3321no—
360C22×C8—3321no—
361C22×C8—834no—
362C22×C8—831no—
363C22×C8—831no—
364C22×C8C22×D8311yescharacteristic
365C22×C8C22×D8311yescharacteristic
366#117—834no—
367#117—834no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—831no—
371C2×C4⋊C4—831no—
372C2×C4⋊C4—831no—
373C2×C4⋊C4—831no—
374C2×C4⋊C4—831no—
375C2×C4⋊C4—831no—
376C2×C4⋊C4—1661no—
377C2×C4⋊C4—1661no—
378C2×C4⋊C4C22×D8311yescharacteristic
379C2×C4⋊C4C22×D8311yescharacteristic
380C2×C4⋊C4C22×D8311yescharacteristic
381C2×C4⋊C4C22×D8311yescharacteristic
382C2×C22⋊C4—831no—
383C2×C22⋊C4—831no—
384C2×C22⋊C4—1661no—
385C2×C22⋊C4—1661no—
386C2×C22⋊C4—1661no—
387C2×C22⋊C4—1661no—
388C2×C42—21no—
389C2×C42—831no—
390C2×C42—1661no—
391C2×C42—1661no—
392C2×C42—1661no—
393C2×C42C22×D8311yescharacteristic
394#107—41no—
395#107—41no—
396#107—3321no—
397#107—3321no—
398#106—3321no—
399#106—3321no—
400#106—3321no—
401#106—3321no—
402C4⋊C8—834no—
403C4⋊C8—834no—
404C4⋊C8—834no—
405C4⋊C8C4×D8314yes—
406#95—21no—
407#95—1661no—
408#95—1661no—
409#95—1661no—
410#95—1661no—
411#95—1661no—
412#95—1661no—
413#95—1661no—
414#95—1661no—
415#95—1661no—
416#95—1661no—
417#95—1661no—
418C24—831no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—831no—
424C22×C4—831no—
425C22×C4—831no—
426C22×C4—832no—
427C22×C4—832no—
428C22×C4—1661no—
429C22×C4—1661no—
430C22×C4—1661no—
431C22×C4—1661no—
432C22×C4—1661no—
433C22×C4—1661no—
434C22×C4—1661no—
435C22×C4—1661no—
436C22×C4D4×D8311yescharacteristic
437C22×C4D4×D8311yescharacteristic
438C22×C4C23×D8311yescharacteristic
439M16—3324no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—3324no—
445C2×C8—832no—
446C2×C8—832no—
447C2×C8—1661no—
448C2×C8—1661no—
449C2×C8—1661no—
450C2×C8—1661no—
451C2×C8C2×C4×D8312yes—
452C2×C8C2×C4×D8312yes—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4—834no—
464C4⋊C4—834no—
465C4⋊C4—6641no—
466C4⋊C4—6641no—
467C4⋊C4—1661no—
468C4⋊C4—1661no—
469C4⋊C4—1661no—
470C4⋊C4—1661no—
471C4⋊C4—1661no—
472C4⋊C4—1661no—
473C4⋊C4—1661no—
474C4⋊C4—1661no—
475C22⋊C4—834no—
476C22⋊C4—834no—
477C22⋊C4—6641no—
478C22⋊C4—6641no—
479C22⋊C4—6641no—
480C22⋊C4—6641no—
481C42—81no—
482C42—832no—
483C42—832no—
484C42—6641no—
485C42—6641no—
486C42—6641no—
487C42C2×C4×D8312yes—
488C42Q8×D8312yes—
489C23—832no—
490C23—1661no—
491C23—1661no—
492C23—1661no—
493C23—1661no—
494C23—1661no—
495C23—1661no—
496C23C2×D4×D8311yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—3321no—
514C2×C4—3321no—
515C2×C4—3321no—
516C2×C4—3321no—
517C2×C4—3321no—
518C2×C4—3321no—
519C2×C4—3321no—
520C2×C4—3321no—
521C2×C4—3321no—
522C2×C4—3321no—
523C2×C4—3321no—
524C2×C4—3321no—
525C2×C4—832no—
526C2×C4—832no—
527C2×C4—832no—
528C2×C4—1661no—
529C2×C4—1661no—
530C2×C4—1661no—
531C2×C4—1661no—
532C2×C4—1661no—
533C2×C4—1661no—
534C2×C4—1662no—
535C2×C4—1662no—
536C2×C4—1662no—
537C2×C4—1662no—
538C2×C4C4⋊C4×D8312yes—
539C2×C4C4⋊C4×D8312yes—
540C2×C4C22×C4×D8311yescharacteristic
541C2×C4C2×Q8×D8311yescharacteristic
542C2×C4#1458183711yescharacteristic
543C2×C4#1458183811yescharacteristic
544C2×C4#1458183911yescharacteristic
545C2×C4#1458184011yescharacteristic
546C8—22no—
547C8—22no—
548C8—1662no—
549C8—1662no—
550C22—3321no—
551C22—3321no—
552C22—3321no—
553C22—3321no—
554C22—1662no—
555C22—1662no—
556C22—1662no—
557C22C2×C4⋊C4×D8311yescharacteristic
558C22#1912828011yescharacteristic
559C22#1912828111yescharacteristic
560C22#1912850211yescharacteristic
561C22#1912851011yescharacteristic
562C22#1912851111yescharacteristic
563C22#1912851411yescharacteristic
564C4—22no—
565C4—22no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—6641no—
571C4—6641no—
572C4—6641no—
573C4—6641no—
574C4—1662no—
575C4—1662no—
576C4—1662no—
577C4#1912817311yescharacteristic
578C4#1912817711yescharacteristic
579C4#1912832811yescharacteristic
580C4#1912833111yescharacteristic
581C2—3322no—
582C2#2491007811yescharacteristic
583C2#2491605711yescharacteristic
584C2#2491605911yescharacteristic
585C2#2491887011yescharacteristic
586C2#2491888111yescharacteristic
587C2#2491888711yescharacteristic
588C2#2491888811yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1947C2
socleC23×C83C22×D4
prime radicalC23×D83C2×D4
cosocleC22×C4×C83C24
hypercenter#1947D83
hypocenterC83#21966
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
4. #24908233C2semidirect
5. #24908231C2semidirect
6. #24908228C2semidirect
7. #24908228C2semidirect
8. #24908225C2semidirect
9. #24908224C2semidirect
10. #24908220C2semidirect
15. C83×#1947C2semidirect
25. #19127726C4semidirect
305. #1947D83semidirect
310. C83#21966semidirect

Maximal subgroups

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

subgroupindex
C2×#191277262
#249100712
#249100682
#249082332
#249082312
#249082282
#249082252
#249082242
#249082202
#249074972
#249074952
#249074892
#249074872
C83×#19472
#2196683