Finite Group Databasebeta

← #35462468

Subgroups — #35462468

Order 21248.

696 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24910346C211yesmaximal, characteristic
2#24909030C211yesmaximal, characteristic, complemented
3#24908965C211yesmaximal, characteristic, complemented
4#24908965C211yesmaximal, characteristic, complemented
5#24908798C211yesmaximal, characteristic, complemented
6#24908421C211yesmaximal, characteristic, complemented
7#24908229C211yesmaximal, characteristic, complemented
8#24908038C211yesmaximal, characteristic, complemented
9#24908038C211yesmaximal, characteristic, complemented
10#24907656C211yesmaximal, characteristic
11#24907648C211yesmaximal, characteristic
12#24907555C211yesmaximal, characteristic
13#24907494C211yesmaximal, characteristic
14#24907182C211yesmaximal, characteristic
15C83×#2442C211yesmaximal, characteristic
16C22×#13050574C2211yescharacteristic
17C2×#14581751C2211yescharacteristic
18C2×#14581725C2211yescharacteristic
19C2×#14581723C2211yescharacteristic
20C2×#14581723C2211yescharacteristic
21C2×#14581723C2211yescharacteristic
22C2×C4⋊(C83⋊C8)C2211yescharacteristic
23C2×C4⋊(C83⋊C8)C2211yescharacteristic
24C2×C22⋊(C83⋊C8)C2211yescharacteristic
25#19127599C2211yescharacteristic
26#19127599C2211yescharacteristic
27#19127589—21no—
28#19127589—21no—
29#19127565—21no—
30#19127561C2211yescharacteristic
31C4×C4⋊Dic83C2211yescharacteristic
32C4×C4⋊Dic83C2211yescharacteristic
33#19127546—21no—
34#19127463C2211yescharacteristic
35#19127463C2211yescharacteristic
36#19127463C2211yescharacteristic
37#19127463C2211yescharacteristic
38#19127463C2211yescharacteristic
39#19127463C2211yescharacteristic
40#19127463C2211yescharacteristic
41#19127463C2211yescharacteristic
42#19127463C2211yescharacteristic
43#19127463C2211yescharacteristic
44#19127463C2211yescharacteristic
45#19127463C2211yescharacteristic
46#19127456C2211yescharacteristic
47#19127456C2211yescharacteristic
48C2×#125×C83C2211yescharacteristic
49C22×C4⋊C4×C83C2211yescharacteristic
50#400×C83—21no—
51#398×C83—21no—
52#389×C83C2211yescharacteristic
53#389×C83C2211yescharacteristic
54#385×C83—21no—
55#382×C83C2211yescharacteristic
56#380×C83—21no—
57#380×C83C2211yescharacteristic
58C4×C22⋊C4×C83C2211yescharacteristic
59C2×#13050574—22no—
60C2×#13050574—22no—
61C2×#13050574—41no—
62C22×C83⋊C8C2311yescharacteristic
63C22×C83⋊C8C2311yescharacteristic
64C22×C83⋊C8C2311yescharacteristic
65C22×C83⋊C8C2311yescharacteristic
66#14581751—22no—
67#14581751Q814yes—
68C2×C4⋊Dic83C2311yescharacteristic
69C2×C4⋊Dic83C2311yescharacteristic
70C2×C4⋊Dic83C2311yescharacteristic
71C2×C4⋊Dic83C2311yescharacteristic
72C2×Dic83⋊C4—21no—
73C2×Dic83⋊C4—21no—
74C2×C22⋊Dic83—21no—
75C2×C22⋊Dic83—21no—
76C2×C4×Dic83—21no—
77C2×C4×Dic83—21no—
78C2×C4×Dic83—21no—
79#14581725—41no—
80#14581723—22no—
81#14581723—22no—
82#14581723—41no—
83C4⋊(C83⋊C8)—22no—
84C4⋊(C83⋊C8)—41no—
85C22⋊(C83⋊C8)—22no—
86C83⋊#95—21no—
87C83⋊#95—21no—
88C83⋊#95—21no—
89C83⋊#95—21no—
90C83⋊#95—21no—
91C23×C4×C83—21no—
92C23×C4×C83C2311yescharacteristic
93#125×C83—22no—
94#125×C83—41no—
95C2×C4⋊C4×C83—22no—
96C2×C4⋊C4×C83—21no—
97C2×C4⋊C4×C83—21no—
98C2×C4⋊C4×C83—21no—
99C2×C4⋊C4×C83—21no—
100C2×C4⋊C4×C83—21no—
101C2×C4⋊C4×C83—41no—
102C2×C4⋊C4×C83C2311yescharacteristic
103C2×C4⋊C4×C83C2311yescharacteristic
104C2×C4⋊C4×C83C2311yescharacteristic
105C2×C4⋊C4×C83C2311yescharacteristic
106C2×C22⋊C4×C83—21no—
107C2×C22⋊C4×C83D411yescharacteristic
108C2×C22⋊C4×C83D411yescharacteristic
109C2×C42×C83C2311yescharacteristic
110C2×C42×C83C2311yescharacteristic
111#95×C83—21no—
112#95×C83—21no—
113#95×C83—21no—
114#95×C83—21no—
115#95×C83—21no—
116#95×C83D411yescharacteristic
117#95×C83D411yescharacteristic
118C22×Dic83—21no—
119C22×Dic83—21no—
120C22×Dic83—21no—
121C22×Dic83—21no—
122#13050574—44no—
123C2×C83⋊C8—21no—
124C2×C83⋊C8—21no—
125C2×C83⋊C8—21no—
126C2×C83⋊C8—21no—
127C2×C83⋊C8—21no—
128C2×C83⋊C8—21no—
129C2×C83⋊C8—21no—
130C2×C83⋊C8—21no—
131C2×C83⋊C8—21no—
132C2×C83⋊C8—21no—
133C2×C83⋊C8—21no—
134C2×C83⋊C8#4112yes—
135C4⋊Dic83—21no—
136C4⋊Dic83—21no—
137C4⋊Dic83—21no—
138C4⋊Dic83—21no—
139C4⋊Dic83—21no—
140C4⋊Dic83—21no—
141C4⋊Dic83C2×Q812yes—
142C4⋊Dic83C2×Q812yes—
143Dic83⋊C4—81no—
144Dic83⋊C4—81no—
145C22⋊Dic83—24no—
146C22⋊Dic83—81no—
147C4×Dic83—24no—
148C4×Dic83—42no—
149C4×Dic83—42no—
150C24×C83C2×D411yescharacteristic
151C22×C4×C83—21no—
152C22×C4×C83—21no—
153C22×C4×C83—21no—
154C22×C4×C83—21no—
155C22×C4×C83—21no—
156C22×C4×C83—21no—
157C22×C4×C83—21no—
158C22×C4×C83—21no—
159C22×C4×C83—42no—
160C22×C4×C83—42no—
161C22×C4×C83—81no—
162C22×C4×C83C2×D411yescharacteristic
163C22×C4×C83C2×D411yescharacteristic
164C22×C4×C83C2×D411yescharacteristic
165C22×C4×C83C2×D411yescharacteristic
166C22×C4×C83C2×D411yescharacteristic
167C22×C4×C83C2×Q812yes—
168C22×C4×C83#4112yes—
169C22×C4×C83C2411yescharacteristic
170C4⋊C4×C83—21no—
171C4⋊C4×C83—21no—
172C4⋊C4×C83—21no—
173C4⋊C4×C83—21no—
174C4⋊C4×C83—21no—
175C4⋊C4×C83—21no—
176C4⋊C4×C83—21no—
177C4⋊C4×C83—42no—
178C4⋊C4×C83—42no—
179C4⋊C4×C83—42no—
180C4⋊C4×C83—81no—
181C4⋊C4×C83—81no—
182C4⋊C4×C83#4112yes—
183C22⋊C4×C83—41no—
184C22⋊C4×C83—41no—
185C22⋊C4×C83—42no—
186C42×C83—21no—
187C42×C83—21no—
188C42×C83—21no—
189C42×C83—21no—
190C23×C83—21no—
191C23×C83—21no—
192C23×C83—21no—
193C23×C83—21no—
194C23×C83—21no—
195C23×C83—21no—
196C23×C83C22⋊Q812yes—
197C23×C83C22×D411yescharacteristic
198C2×C4×C83—21no—
199C2×C4×C83—21no—
200C2×C4×C83—22no—
201C2×C4×C83—22no—
202C2×C4×C83—22no—
203C2×C4×C83—22no—
204C2×C4×C83—21no—
205C2×C4×C83—21no—
206C2×C4×C83—22no—
207C2×C4×C83—21no—
208C2×C4×C83—21no—
209C2×C4×C83—21no—
210C2×C4×C83—21no—
211C2×C4×C83—21no—
212C2×C4×C83—21no—
213C2×C4×C83—21no—
214C2×C4×C83—21no—
215C2×C4×C83—21no—
216C2×C4×C83—21no—
217C2×C4×C83—41no—
218C2×C4×C83—41no—
219C2×C4×C83—41no—
220C2×C4×C83—41no—
221C2×C4×C83—41no—
222C2×C4×C83—41no—
223C2×C4×C83—41no—
224C2×C4×C83—41no—
225C2×C4×C83—41no—
226C2×C4×C83—41no—
227C2×C4×C83—41no—
228C2×C4×C83—84no—
229C2×C4×C83C22⋊Q812yes—
230C2×C4×C83C22×Q811yescharacteristic
231C2×C4×C83C2×#4111yescharacteristic
232C2×C4×C83C2×#4111yescharacteristic
233C2×C4×C83C2×#4111yescharacteristic
234C2×C4×C83H(5,𝔽2)11yescharacteristic
235C2×C4×C832−1+411yescharacteristic
236C2×Dic83—22no—
237C2×Dic83—22no—
238C2×Dic83—41no—
239C2×Dic83—41no—
240C2×Dic83—41no—
241C2×Dic83—41no—
242C2×Dic83—41no—
243C2×Dic83—41no—
244C2×Dic83—41no—
245C2×Dic83—41no—
246C2×Dic83—41no—
247C2×Dic83—41no—
248C83⋊C8—22no—
249C83⋊C8—41no—
250C83⋊C8—41no—
251C83⋊C8—41no—
252C22×C83—22no—
253C22×C83—22no—
254C22×C83—22no—
255C22×C83—41no—
256C22×C83—41no—
257C22×C83—41no—
258C22×C83—41no—
259C22×C83C2×C22⋊Q811yescharacteristic
260C22×C83#54611yescharacteristic
261C22×C83#54711yescharacteristic
262C22×C83#57511yescharacteristic
263C22×C83#57511yescharacteristic
264C22×C83#57711yescharacteristic
265C22×C83#57711yescharacteristic
266C4×C83—22no—
267C4×C83—41no—
268C4×C83—41no—
269C4×C83—41no—
270C4×C83—41no—
271C4×C83—42no—
272C4×C83—81no—
273C4×C83—81no—
274C4×C83—81no—
275C4×C83#53311yescharacteristic
276C4×C83#54411yescharacteristic
277C4×C83#55111yescharacteristic
278C4×C83#55211yescharacteristic
279Dic83—42no—
280Dic83—42no—
281Dic83—81no—
282Dic83—81no—
283#26019—831nomaximal, Sylow
284C2×C83—42no—
285C2×C83#243811yescharacteristic
286C2×C83#308011yescharacteristic
287C2×C83#308411yescharacteristic
288C2×C83#332111yescharacteristic
289C2×C83#332311yescharacteristic
290C2×C83#334811yescharacteristic
291C2×C83#335111yescharacteristic
292#2442D8311yescharacteristic
293#2346—831no—
294#2101—831no—
295#2088—831no—
296#2088—831no—
297#2059—831no—
298#1989—831no—
299#1949—831no—
300#1919—831no—
301#1919—831no—
302#1853—831no—
303#1851—831no—
304#1825—831no—
305#1809—831no—
306#1736—831no—
307C83#2601911yescharacteristic, complemented, Sylow
308C22×M16—831no—
309C2×#125C2×D8311yescharacteristic
310C2×#117—831no—
311C22×C4⋊C4C2×D8311yescharacteristic
312C2×#107—831no—
313C2×#106—831no—
314C2×#106—831no—
315C2×#106—831no—
316C2×C4⋊C8—831no—
317C2×C4⋊C8—831no—
318C2×C22⋊C8—831no—
319#400—21no—
320#398—21no—
321#389—831no—
322#389—831no—
323#389C2×D8311yescharacteristic
324#389C2×D8311yescharacteristic
325#388—1661no—
326#388—1661no—
327#385—21no—
328#382—1661no—
329#382C2×D8311yescharacteristic
330#380—21no—
331#380—831no—
332#380C2×D8311yescharacteristic
333C4×C4⋊C4—831no—
334C4×C4⋊C4—831no—
335C4×C22⋊C4C2×D8311yescharacteristic
336#376—1661no—
337#340—831no—
338#340—831no—
339#340—831no—
340#340—831no—
341#340—831no—
342#340—831no—
343#340—831no—
344#340—831no—
345#340—831no—
346#340—831no—
347#340—831no—
348#340—831no—
349#336—831no—
350#336—831no—
351C23×C4—21no—
352C23×C4C22×D8311yescharacteristic
353C2×M16—3321no—
354C2×M16—1662no—
355C2×M16—1662no—
356C22×C8—831no—
357C22×C8—831no—
358C22×C8—831no—
359C22×C8—831no—
360#125—22no—
361#125—41no—
362#117—834no—
363#117—1662no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—41no—
371C2×C4⋊C4—831no—
372C2×C4⋊C4—831no—
373C2×C4⋊C4—831no—
374C2×C4⋊C4—831no—
375C2×C4⋊C4—1661no—
376C2×C4⋊C4—1661no—
377C2×C4⋊C4C22×D8311yescharacteristic
378C2×C4⋊C4C22×D8311yescharacteristic
379C2×C4⋊C4C22×D8311yescharacteristic
380C2×C4⋊C4C22×D8311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—1661no—
383C2×C22⋊C4—1661no—
384C2×C22⋊C4C22⋊D8311yescharacteristic
385C2×C22⋊C4C22⋊D8311yescharacteristic
386C2×C42—1661no—
387C2×C42—1661no—
388C2×C42—1661no—
389C2×C42C22×D8311yescharacteristic
390C2×C42C22×D8311yescharacteristic
391#107—3321no—
392#106—3321no—
393#106—1662no—
394#106—1662no—
395C4⋊C8—3321no—
396C4⋊C8—1662no—
397C22⋊C8—1662no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—1661no—
404#95—1661no—
405#95—1661no—
406#95—1661no—
407#95—1661no—
408#95C22⋊D8311yescharacteristic
409#95C22⋊D8311yescharacteristic
410C24C2×C22⋊D8311yescharacteristic
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—81no—
422C22×C4—1661no—
423C22×C4—1661no—
424C22×C4—1661no—
425C22×C4—1661no—
426C22×C4C2×C22⋊D8311yescharacteristic
427C22×C4C2×C22⋊D8311yescharacteristic
428C22×C4C2×C22⋊D8311yescharacteristic
429C22×C4C2×C22⋊D8311yescharacteristic
430C22×C4C2×C22⋊D8311yescharacteristic
431C22×C4Q8×D8312yes—
432C22×C4#1305059112yes—
433C22×C4C23×D8311yescharacteristic
434M16—3324no—
435C2×C8—832no—
436C2×C8—1661no—
437C2×C8—1661no—
438C2×C8—1661no—
439C2×C8—1661no—
440C2×C8—1661no—
441C2×C8—1661no—
442C2×C8—1661no—
443C2×C8—1661no—
444C2×C8—1661no—
445C2×C8—1661no—
446C2×C8—1661no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—42no—
455C4⋊C4—42no—
456C4⋊C4—42no—
457C4⋊C4—81no—
458C4⋊C4—81no—
459C4⋊C4—832no—
460C4⋊C4—832no—
461C4⋊C4—6641no—
462C4⋊C4—6641no—
463C4⋊C4—1661no—
464C4⋊C4—1661no—
465C4⋊C4—1661no—
466C4⋊C4—1661no—
467C4⋊C4—1661no—
468C4⋊C4—1661no—
469C4⋊C4#1305058912yes—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—42no—
473C22⋊C4—6641no—
474C22⋊C4—1664no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—3322no—
480C42—3322no—
481C42—1664no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23#1458176812yes—
489C23C22×C22⋊D8311yescharacteristic
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
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—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—84no—
521C2×C4—3321no—
522C2×C4—3321no—
523C2×C4—3321no—
524C2×C4—3321no—
525C2×C4—3321no—
526C2×C4—3321no—
527C2×C4—3321no—
528C2×C4—3321no—
529C2×C4—3321no—
530C2×C4—3321no—
531C2×C4—1662no—
532C2×C4—1662no—
533C2×C4#1458176812yes—
534C2×C4C2×Q8×D8311yescharacteristic
535C2×C4#41×D8311yescharacteristic
536C2×C4C2×#1305058911yescharacteristic
537C2×C4C2×#1305059111yescharacteristic
538C2×C4#1458183711yescharacteristic
539C2×C4#1458183911yescharacteristic
540C8—3321no—
541C8—3321no—
542C8—3321no—
543C8—1662no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22C2×#1458176811yescharacteristic
552C22#1912834511yescharacteristic
553C22#1912835011yescharacteristic
554C22#1912849911yescharacteristic
555C22#1912849911yescharacteristic
556C22#1912850911yescharacteristic
557C22#1912851211yescharacteristic
558C4—22no—
559C4—41no—
560C4—41no—
561C4—42no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4—3322no—
568C4—3322no—
569C4—6641no—
570C4—6641no—
571C4#1912825311yescharacteristic
572C4#1912833011yescharacteristic
573C4#1912837811yescharacteristic
574C4#1912839311yescharacteristic
575C2—42no—
576C2#2491113511yescharacteristic
577C2#2491728111yescharacteristic
578C2#2491732111yescharacteristic
579C2#2491964911yescharacteristic
580C2#2491967911yescharacteristic
581C2#2491997211yescharacteristic
582C2#2492001711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#2442C2
socleC23×C83C22×D4
prime radicalC24×C83C2×D4
hypercenter#2442D83
hypocenterC83#26019
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2442

Complements

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

NH ≅ G/Ntype
2. #24909030C2semidirect
3. #24908965C2semidirect
4. #24908965C2semidirect
5. #24908798C2semidirect
6. #24908421C2semidirect
7. #24908229C2semidirect
8. #24908038C2semidirect
9. #24908038C2semidirect
307. C83#26019semidirect

Maximal subgroups

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

subgroupindex
#249103462
#249090302
#249089652
#249087982
#249084212
#249082292
#249080382
#249076562
#249076482
#249075552
#249074942
#249071822
C83×#24422
#2601983