Finite Group Databasebeta

← #35462704

Subgroups — #35462704

Order 21248.

692 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24912498C211yesmaximal, characteristic, complemented
2#24908851C211yesmaximal, characteristic
3#24908837C211yesmaximal, characteristic
4#24908609C211yesmaximal, characteristic
5#24908609C211yesmaximal, characteristic
6#24908420C211yesmaximal, characteristic, complemented
7#24908420C211yesmaximal, characteristic, complemented
8#24908229C211yesmaximal, characteristic, complemented
9#24908187C211yesmaximal, characteristic, complemented
10#24908048C211yesmaximal, characteristic, complemented
11#24908034C211yesmaximal, characteristic, complemented
12#24907596C211yesmaximal, characteristic, complemented
13#24907463C211yesmaximal, characteristic
14#24907288C211yesmaximal, characteristic
15C83×#2357C211yesmaximal, characteristic
16C2×#14581784C2211yescharacteristic
17C2×#14581784C2211yescharacteristic
18C2×#14581725C2211yescharacteristic
19C2×#14581723C2211yescharacteristic
20C2×C4⋊(C83⋊C8)C2211yescharacteristic
21C2×C4⋊(C83⋊C8)C2211yescharacteristic
22C2×C4⋊(C83⋊C8)C2211yescharacteristic
23C2×#14581713C2211yescharacteristic
24C2×#14581713C2211yescharacteristic
25C2×#14581713C2211yescharacteristic
26C2×#14581713C2211yescharacteristic
27C2×#14581703C2211yescharacteristic
28#19127635—21no—
29#19127635—21no—
30#19127599C2211yescharacteristic
31#19127599C2211yescharacteristic
32#19127597—21no—
33#19127571C2211yescharacteristic
34#19127570—21no—
35C4×C4⋊Dic83C2211yescharacteristic
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×C4×D4×C83C2211yescharacteristic
49#390×C83C2211yescharacteristic
50#390×C83C2211yescharacteristic
51#388×C83—21no—
52#388×C83—21no—
53#382×C83C2211yescharacteristic
54#381×C83—21no—
55C4×C4⋊C4×C83C2211yescharacteristic
56C4×C4⋊C4×C83C2211yescharacteristic
57C4×C4⋊C4×C83C2211yescharacteristic
58C4×C22⋊C4×C83—21no—
59C22×C83⋊C8C2311yescharacteristic
60C22×C83⋊C8C2311yescharacteristic
61C22×C83⋊C8C2311yescharacteristic
62C22×C83⋊C8C2311yescharacteristic
63#14581784—22no—
64#14581784—22no—
65#14581784—41no—
66#14581784—41no—
67C2×C4⋊Dic83—21no—
68C2×C4⋊Dic83—21no—
69C2×C4⋊Dic83C2311yescharacteristic
70C2×C4⋊Dic83C2311yescharacteristic
71C2×C4⋊Dic83C2311yescharacteristic
72C2×C4⋊Dic83C2311yescharacteristic
73C2×Dic83⋊C4—21no—
74C2×Dic83⋊C4—21no—
75C2×Dic83⋊C4—21no—
76C2×Dic83⋊C4—21no—
77C2×Dic83⋊C4—21no—
78C2×Dic83⋊C4—21no—
79C2×C4×Dic83—21no—
80#14581725—22no—
81#14581723—22no—
82C4⋊(C83⋊C8)—22no—
83C4⋊(C83⋊C8)—41no—
84C4⋊(C83⋊C8)—41no—
85#14581713—22no—
86#14581713—22no—
87#14581713—41no—
88#14581713—41no—
89#14581703—22no—
90C83⋊#95—21no—
91C83⋊#95—21no—
92C83⋊#95—21no—
93C22×D4×C83C2311yescharacteristic
94C23×C4×C83—21no—
95C4×D4×C83—22no—
96C4×D4×C83Q814yes—
97C2×C4⋊C4×C83D411yescharacteristic
98C2×C4⋊C4×C83D411yescharacteristic
99C2×C4⋊C4×C83C2311yescharacteristic
100C2×C4⋊C4×C83C2311yescharacteristic
101C2×C4⋊C4×C83C2311yescharacteristic
102C2×C22⋊C4×C83—21no—
103C2×C22⋊C4×C83—21no—
104C2×C22⋊C4×C83—21no—
105C2×C22⋊C4×C83—21no—
106C2×C22⋊C4×C83—21no—
107C2×C42×C83—21no—
108C2×C42×C83—21no—
109C2×C42×C83C2311yescharacteristic
110C2×C42×C83C2311yescharacteristic
111C2×C42×C83C2311yescharacteristic
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—
122C2×C83⋊C8—21no—
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—
134C4⋊Dic83—21no—
135C4⋊Dic83—21no—
136C4⋊Dic83—21no—
137C4⋊Dic83—21no—
138C4⋊Dic83—21no—
139C4⋊Dic83—21no—
140C4⋊Dic83—42no—
141C4⋊Dic83—81no—
142C4⋊Dic83#4112yes—
143C4⋊Dic83#4112yes—
144Dic83⋊C4—42no—
145Dic83⋊C4—42no—
146Dic83⋊C4—42no—
147Dic83⋊C4—42no—
148Dic83⋊C4—81no—
149Dic83⋊C4—81no—
150C4×Dic83—42no—
151C24×C83—21no—
152C2×D4×C83—21no—
153C2×D4×C83—21no—
154C2×D4×C83—21no—
155C2×D4×C83—21no—
156C2×D4×C83—21no—
157C2×D4×C83C2×Q812yes—
158C22×C4×C83—21no—
159C22×C4×C83—24no—
160C22×C4×C83—21no—
161C22×C4×C83—21no—
162C22×C4×C83—81no—
163C22×C4×C83—81no—
164C22×C4×C83C2×D411yescharacteristic
165C22×C4×C83C2×D411yescharacteristic
166C22×C4×C83C2×D411yescharacteristic
167C22×C4×C83C2×D411yescharacteristic
168C22×C4×C83C2×D411yescharacteristic
169C22×C4×C83C2×D411yescharacteristic
170C22×C4×C83C2411yescharacteristic
171C4⋊C4×C83—21no—
172C4⋊C4×C83—21no—
173C4⋊C4×C83—21no—
174C4⋊C4×C83—21no—
175C4⋊C4×C83—21no—
176C4⋊C4×C83—41no—
177C4⋊C4×C83—41no—
178C4⋊C4×C83C2×Q812yes—
179C22⋊C4×C83—24no—
180C22⋊C4×C83—42no—
181C22⋊C4×C83—42no—
182C22⋊C4×C83—81no—
183C22⋊C4×C83—81no—
184C42×C83—21no—
185C42×C83—21no—
186C42×C83—21no—
187C42×C83—21no—
188C42×C83—81no—
189C42×C83—81no—
190C42×C83C2×Q812yes—
191C42×C83#4112yes—
192C23×C83—22no—
193C23×C83—41no—
194C23×C83—41no—
195C23×C83—41no—
196C23×C83—41no—
197C23×C83—41no—
198C23×C83—41no—
199C23×C83C22×D411yescharacteristic
200D4×C83—22no—
201D4×C83—22no—
202D4×C83—41no—
203D4×C83—41no—
204C2×C4×C83—21no—
205C2×C4×C83—21no—
206C2×C4×C83—21no—
207C2×C4×C83—21no—
208C2×C4×C83—22no—
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—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
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—41no—
229C2×C4×C83—84no—
230C2×C4×C83C22⋊Q812yes—
231C2×C4×C83C22⋊Q812yes—
232C2×C4×C83C22×Q811yescharacteristic
233C2×C4×C83C2×#4111yescharacteristic
234C2×C4×C83C2×#4111yescharacteristic
235C2×C4×C83C2×#4111yescharacteristic
236C2×C4×C83H(5,𝔽2)11yescharacteristic
237C2×C4×C832−1+411yescharacteristic
238C2×Dic83—22no—
239C2×Dic83—22no—
240C2×Dic83—41no—
241C2×Dic83—41no—
242C2×Dic83—41no—
243C2×Dic83—41no—
244C2×Dic83—41no—
245C2×Dic83—41no—
246C2×Dic83—41no—
247C2×Dic83—41no—
248C2×Dic83—41no—
249C2×Dic83—41no—
250C83⋊C8—41no—
251C83⋊C8—41no—
252C83⋊C8—41no—
253C83⋊C8—41no—
254C22×C83—42no—
255C22×C83—42no—
256C22×C83—42no—
257C22×C83—81no—
258C22×C83—81no—
259C22×C83—81no—
260C22×C83—81no—
261C22×C83C2×C22⋊Q811yescharacteristic
262C22×C83#54611yescharacteristic
263C22×C83#54811yescharacteristic
264C22×C83#57511yescharacteristic
265C22×C83#57511yescharacteristic
266C22×C83#57611yescharacteristic
267C22×C83#57711yescharacteristic
268C4×C83—22no—
269C4×C83—22no—
270C4×C83—42no—
271C4×C83—41no—
272C4×C83—41no—
273C4×C83—41no—
274C4×C83—41no—
275C4×C83—81no—
276C4×C83—81no—
277C4×C83#53311yescharacteristic
278C4×C83#54411yescharacteristic
279C4×C83#55511yescharacteristic
280C4×C83#55611yescharacteristic
281Dic83—42no—
282Dic83—42no—
283Dic83—81no—
284Dic83—81no—
285#26037—831nomaximal, Sylow
286C2×C83—82no—
287C2×C83#243911yescharacteristic
288C2×C83#308011yescharacteristic
289C2×C83#308111yescharacteristic
290C2×C83#330711yescharacteristic
291C2×C83#330911yescharacteristic
292C2×C83#337011yescharacteristic
293C2×C83#337111yescharacteristic
294#2552—831no—
295#2357D8311yescharacteristic
296#2067—831no—
297#2065—831no—
298#2025—831no—
299#2025—831no—
300#1989—831no—
301#1989—831no—
302#1949—831no—
303#1940—831no—
304#1920—831no—
305#1918—831no—
306#1836—831no—
307#1802—831no—
308#1762—831no—
309C83#2603711yescharacteristic, complemented, Sylow
310C2×#125—831no—
311C2×#125—831no—
312C2×C4×D4C2×D8311yescharacteristic
313C2×#107—831no—
314C2×#106—831no—
315C2×C4⋊C8—831no—
316C2×C4⋊C8—831no—
317C2×C4⋊C8—831no—
318C2×#102—831no—
319C2×#102—831no—
320C2×#102—831no—
321C2×#102—831no—
322C2×#97—831no—
323#398—1661no—
324#398—1661no—
325#390C2×D8311yescharacteristic
326#390C2×D8311yescharacteristic
327#389—831no—
328#389—831no—
329#389—1661no—
330#388—21no—
331#388—21no—
332#384—831no—
333#384—1661no—
334#382C2×D8311yescharacteristic
335#381—21no—
336C4×C4⋊C4—831no—
337C4×C4⋊C4C2×D8311yescharacteristic
338C4×C4⋊C4C2×D8311yescharacteristic
339C4×C4⋊C4C2×D8311yescharacteristic
340C4×C22⋊C4—21no—
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#340—831no—
350#340—831no—
351#336—831no—
352#336—831no—
353C22×D4C22×D8311yescharacteristic
354C23×C4—21no—
355C22×C8—831no—
356C22×C8—831no—
357C22×C8—831no—
358C22×C8—831no—
359#125—3321no—
360#125—3321no—
361#125—1662no—
362#125—1662no—
363C4×D4—22no—
364C4×D4Dic16614yes—
365C2×C4⋊C4—831no—
366C2×C4⋊C4—831no—
367C2×C4⋊C4—831no—
368C2×C4⋊C4—831no—
369C2×C4⋊C4—1661no—
370C2×C4⋊C4—1661no—
371C2×C4⋊C4—1661no—
372C2×C4⋊C4—1661no—
373C2×C4⋊C4—1661no—
374C2×C4⋊C4—1661no—
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×C4⋊C4C22×D8311yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—1661no—
390C2×C42C22×D8311yescharacteristic
391C2×C42C22×D8311yescharacteristic
392C2×C42C22×D8311yescharacteristic
393#107—1662no—
394#106—1662no—
395C4⋊C8—3321no—
396C4⋊C8—3321no—
397C4⋊C8—1662no—
398#102—3321no—
399#102—3321no—
400#102—1662no—
401#102—1662no—
402#97—1662no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—1661no—
408#95—1661no—
409#95—1661no—
410#95C22⋊D8311yescharacteristic
411#95C22⋊D8311yescharacteristic
412C24—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4C2×Dic16612yes—
419C22×C4—21no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—81no—
424C22×C4—81no—
425C22×C4—1661no—
426C22×C4—1661no—
427C22×C4—1661no—
428C22×C4—1661no—
429C22×C4C2×C22⋊D8311yescharacteristic
430C22×C4C2×C22⋊D8311yescharacteristic
431C22×C4C2×C22⋊D8311yescharacteristic
432C22×C4C2×C22⋊D8311yescharacteristic
433C22×C4C2×C22⋊D8311yescharacteristic
434C22×C4C2×C22⋊D8311yescharacteristic
435C22×C4C23×D8311yescharacteristic
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—
447C2×C8—1661no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—3322no—
456C4⋊C4—3322no—
457C4⋊C4—3322no—
458C4⋊C4—3322no—
459C4⋊C4—3322no—
460C4⋊C4—832no—
461C4⋊C4—832no—
462C4⋊C4—6641no—
463C4⋊C4—6641no—
464C4⋊C4—6641no—
465C4⋊C4—1661no—
466C4⋊C4—1661no—
467C4⋊C4—1661no—
468C4⋊C4—1661no—
469C4⋊C4—1661no—
470C4⋊C4—1661no—
471C4⋊C4C2×Dic16612yes—
472C22⋊C4—24no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—81no—
476C22⋊C4—81no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—81no—
482C42—81no—
483C42—3322no—
484C42C2×Dic16612yes—
485C42#1305059012yes—
486C23—22no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23C22×C22⋊D8311yescharacteristic
494D4—22no—
495D4—22no—
496D4—41no—
497D4—41no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—84no—
524C2×C4—3321no—
525C2×C4—3321no—
526C2×C4—3321no—
527C2×C4—3321no—
528C2×C4—3321no—
529C2×C4—3321no—
530C2×C4—3321no—
531C2×C4—3321no—
532C2×C4—3321no—
533C2×C4—3321no—
534C2×C4—1662no—
535C2×C4—1662no—
536C2×C4#1458177112yes—
537C2×C4#1458177112yes—
538C2×C4C22×Dic16611yescharacteristic
539C2×C4#41×D8311yescharacteristic
540C2×C4#41×D8311yescharacteristic
541C2×C4C2×#1305059011yescharacteristic
542C2×C4#1458183811yescharacteristic
543C2×C4#1458183911yescharacteristic
544C8—3321no—
545C8—3321no—
546C8—3321no—
547C8—3321no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22C2×#1458177111yescharacteristic
556C22#1912833911yescharacteristic
557C22#1912835811yescharacteristic
558C22#1912849911yescharacteristic
559C22#1912849911yescharacteristic
560C22#1912850411yescharacteristic
561C22#1912851211yescharacteristic
562C4—22no—
563C4—22no—
564C4—42no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—3322no—
572C4—3322no—
573C4—6641no—
574C4—6641no—
575C4#1912825411yescharacteristic
576C4#1912832911yescharacteristic
577C4#1912841411yescharacteristic
578C4#1912841911yescharacteristic
579C2—82no—
580C2#2491114811yescharacteristic
581C2#2491728511yescharacteristic
582C2#2491729411yescharacteristic
583C2#2491943311yescharacteristic
584C2#2491946311yescharacteristic
585C2#2492021011yescharacteristic
586C2#2492022511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#2357C2
socleC23×C83C22×D4
prime radicalC22×D4×C83C23
hypercenter#2357D83
hypocenterC83#26037
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2357

Complements

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

NH ≅ G/Ntype
1. #24912498C2semidirect
6. #24908420C2semidirect
7. #24908420C2semidirect
8. #24908229C2semidirect
9. #24908187C2semidirect
10. #24908048C2semidirect
11. #24908034C2semidirect
12. #24907596C2semidirect
309. C83#26037semidirect

Maximal subgroups

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

subgroupindex
#249124982
#249088512
#249088372
#249086092
#249084202
#249082292
#249081872
#249080482
#249080342
#249075962
#249074632
#249072882
C83×#23572
#2603783