Finite Group Databasebeta

← #35462706

Subgroups — #35462706

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#24910434C211yesmaximal, characteristic
2#24908848C211yesmaximal, characteristic
3#24908834C211yesmaximal, characteristic
4#24908606C211yesmaximal, characteristic
5#24908606C211yesmaximal, characteristic
6#24908421C211yesmaximal, characteristic, complemented
7#24908421C211yesmaximal, characteristic, complemented
8#24908231C211yesmaximal, characteristic, complemented
9#24908187C211yesmaximal, characteristic, complemented
10#24908045C211yesmaximal, characteristic, complemented
11#24908031C211yesmaximal, characteristic, complemented
12#24907598C211yesmaximal, characteristic, complemented
13#24907460C211yesmaximal, characteristic
14#24907291C211yesmaximal, characteristic
15C83×#2552C211yesmaximal, characteristic, complemented
16C2×C4×D332C2211yescharacteristic
17C2×#14581725C2211yescharacteristic
18C2×#14581723C2211yescharacteristic
19C2×C4⋊(C83⋊C8)C2211yescharacteristic
20C2×C4⋊(C83⋊C8)C2211yescharacteristic
21C2×C4⋊(C83⋊C8)C2211yescharacteristic
22C2×#14581712C2211yescharacteristic
23C2×#14581712C2211yescharacteristic
24C2×#14581712C2211yescharacteristic
25C2×#14581712C2211yescharacteristic
26C2×#14581703C2211yescharacteristic
27#19127603C2211yescharacteristic
28#19127603C2211yescharacteristic
29#19127591—21no—
30#19127591—21no—
31#19127567C2211yescharacteristic
32#19127563—21no—
33C4×C4⋊Dic83C2211yescharacteristic
34C4×C4⋊Dic83C2211yescharacteristic
35#19127548—21no—
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
49C2×#125×C83C2211yescharacteristic
50#398×C83—21no—
51#398×C83—21no—
52#389×C83—21no—
53#389×C83C2211yescharacteristic
54#389×C83C2211yescharacteristic
55#384×C83—21no—
56#384×C83C2211yescharacteristic
57C4×C4⋊C4×C83C2211yescharacteristic
58C4×C4⋊C4×C83C2211yescharacteristic
59C22×D332C2311yescharacteristic
60C22×C4×D83—21no—
61C22×C83⋊C8C2311yescharacteristic
62C22×C83⋊C8C2311yescharacteristic
63C22×C83⋊C8C2311yescharacteristic
64C22×C83⋊C8C2311yescharacteristic
65C4×D332—22no—
66C4×D332Q814yes—
67C2×C4⋊Dic83C2311yescharacteristic
68C2×C4⋊Dic83C2311yescharacteristic
69C2×C4⋊Dic83C2311yescharacteristic
70C2×(C2×D83)⋊C4—21no—
71C2×(C2×D83)⋊C4—21no—
72C2×(C2×D83)⋊C4—21no—
73C2×(C2×D83)⋊C4—21no—
74C2×(C2×D83)⋊C4—21no—
75C2×C4×Dic83—21no—
76C2×C4×Dic83—21no—
77#14581725—22no—
78#14581723—22no—
79C4⋊(C83⋊C8)—22no—
80C4⋊(C83⋊C8)—41no—
81C4⋊(C83⋊C8)—41no—
82#14581712—22no—
83#14581712—22no—
84#14581712—41no—
85#14581712—41no—
86#14581703—22no—
87C83⋊#95—21no—
88C83⋊#95—21no—
89C83⋊#95—21no—
90C83⋊#95—21no—
91#125×C83—22no—
92#125×C83—22no—
93#125×C83—41no—
94#125×C83—41no—
95C2×C4⋊C4×C83—21no—
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—21no—
102C2×C4⋊C4×C83—21no—
103C2×C4⋊C4×C83D411yescharacteristic
104C2×C4⋊C4×C83D411yescharacteristic
105C2×C4⋊C4×C83C2311yescharacteristic
106C2×C4⋊C4×C83C2311yescharacteristic
107C2×C4⋊C4×C83C2311yescharacteristic
108C2×C4⋊C4×C83C2311yescharacteristic
109C2×C42×C83—21no—
110C2×C42×C83C2311yescharacteristic
111C2×C42×C83C2311yescharacteristic
112C2×C42×C83C2311yescharacteristic
113#95×C83—21no—
114#95×C83—21no—
115#95×C83—21no—
116#95×C83D411yescharacteristic
117#95×C83D411yescharacteristic
118C23×D83—21no—
119C2×D332—21no—
120C2×D332—21no—
121C2×D332—21no—
122C2×D332—21no—
123C2×D332—21no—
124C2×D332C2×Q812yes—
125C22×Dic83—21no—
126C22×Dic83—21no—
127C22×Dic83—21no—
128C2×C4×D83—24no—
129C2×C4×D83—81no—
130C2×C4×D83—81no—
131C2×C83⋊C8—21no—
132C2×C83⋊C8—21no—
133C2×C83⋊C8—21no—
134C2×C83⋊C8—21no—
135C2×C83⋊C8—21no—
136C2×C83⋊C8—21no—
137C2×C83⋊C8—21no—
138C2×C83⋊C8—21no—
139C2×C83⋊C8—21no—
140C2×C83⋊C8—21no—
141C2×C83⋊C8—21no—
142C2×C83⋊C8—21no—
143C4⋊Dic83—21no—
144C4⋊Dic83—21no—
145C4⋊Dic83—21no—
146C4⋊Dic83—21no—
147C4⋊Dic83—21no—
148C4⋊Dic83C2×Q812yes—
149(C2×D83)⋊C4—24no—
150(C2×D83)⋊C4—42no—
151(C2×D83)⋊C4—42no—
152(C2×D83)⋊C4—81no—
153(C2×D83)⋊C4—81no—
154C4×Dic83—81no—
155C4×Dic83—81no—
156C22×C4×C83—21no—
157C22×C4×C83—21no—
158C22×C4×C83—21no—
159C22×C4×C83—21no—
160C22×C4×C83C2×D411yescharacteristic
161C22×C4×C83C2×D411yescharacteristic
162C22×C4×C83C2×D411yescharacteristic
163C22×C4×C83C2×D411yescharacteristic
164C22×C4×C83C2×D411yescharacteristic
165C22×C4×C83C2×D411yescharacteristic
166C22×C4×C83C2411yescharacteristic
167C4⋊C4×C83—21no—
168C4⋊C4×C83—21no—
169C4⋊C4×C83—21no—
170C4⋊C4×C83—21no—
171C4⋊C4×C83—21no—
172C4⋊C4×C83—21no—
173C4⋊C4×C83—41no—
174C4⋊C4×C83—41no—
175C4⋊C4×C83—42no—
176C4⋊C4×C83—42no—
177C4⋊C4×C83—42no—
178C4⋊C4×C83—42no—
179C4⋊C4×C83—42no—
180C4⋊C4×C83—81no—
181C4⋊C4×C83—81no—
182C4⋊C4×C83—81no—
183C4⋊C4×C83#4112yes—
184C4⋊C4×C83#4112yes—
185C42×C83—21no—
186C42×C83—21no—
187C42×C83—21no—
188C42×C83—21no—
189C42×C83—42no—
190C42×C83C2×Q812yes—
191C42×C83#4112yes—
192C23×C83C22×D411yescharacteristic
193C22×D83—22no—
194C22×D83—41no—
195C22×D83—41no—
196C22×D83—41no—
197C22×D83—41no—
198C22×D83—41no—
199C22×D83—41no—
200C2×C4×C83—21no—
201C2×C4×C83—21no—
202C2×C4×C83—21no—
203C2×C4×C83—21no—
204C2×C4×C83—21no—
205C2×C4×C83—21no—
206C2×C4×C83—21no—
207C2×C4×C83—21no—
208C2×C4×C83—22no—
209C2×C4×C83—22no—
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—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×C83C22⋊Q812yes—
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—41no—
238C2×Dic83—41no—
239C2×Dic83—41no—
240C2×Dic83—41no—
241C2×Dic83—41no—
242C2×Dic83—41no—
243C2×Dic83—41no—
244C2×Dic83—41no—
245D332—22no—
246D332—22no—
247D332—41no—
248D332—41no—
249C4×D83—84no—
250C83⋊C8—41no—
251C83⋊C8—41no—
252C83⋊C8—41no—
253C83⋊C8—41no—
254C22×C83C2×C22⋊Q811yescharacteristic
255C22×C83#54611yescharacteristic
256C22×C83#54811yescharacteristic
257C22×C83#57511yescharacteristic
258C22×C83#57511yescharacteristic
259C22×C83#57611yescharacteristic
260C22×C83#57711yescharacteristic
261C2×D83—42no—
262C2×D83—42no—
263C2×D83—42no—
264C2×D83—81no—
265C2×D83—81no—
266C2×D83—81no—
267C2×D83—81no—
268C4×C83—22no—
269C4×C83—22no—
270C4×C83—42no—
271C4×C83—41no—
272C4×C83—41no—
273C4×C83—42no—
274C4×C83—41no—
275C4×C83—41no—
276C4×C83—81no—
277C4×C83—81no—
278C4×C83#53311yescharacteristic
279C4×C83#54411yescharacteristic
280C4×C83#55511yescharacteristic
281C4×C83#55611yescharacteristic
282Dic83—42no—
283Dic83—81no—
284Dic83—81no—
285#26037—831nomaximal, Sylow
286C2×C83#243911yescharacteristic
287C2×C83#308011yescharacteristic
288C2×C83#308111yescharacteristic
289C2×C83#330711yescharacteristic
290C2×C83#330911yescharacteristic
291C2×C83#337011yescharacteristic
292C2×C83#337111yescharacteristic
293D83—82no—
294#2552D8311yescharacteristic, complemented
295#2357—831no—
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×#125C2×D8311yescharacteristic
311C2×#125C2×D8311yescharacteristic
312C2×C4×D4—831no—
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—21no—
324#398—21no—
325#390—831no—
326#390—831no—
327#389—21no—
328#389C2×D8311yescharacteristic
329#389C2×D8311yescharacteristic
330#388—1661no—
331#388—1661no—
332#384—21no—
333#384C2×D8311yescharacteristic
334#382—831no—
335#381—1661no—
336C4×C4⋊C4—831no—
337C4×C4⋊C4—831no—
338C4×C4⋊C4C2×D8311yescharacteristic
339C4×C4⋊C4C2×D8311yescharacteristic
340C4×C22⋊C4—1661no—
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×D4—831no—
354C23×C4—1661no—
355C22×C8—831no—
356C22×C8—831no—
357C22×C8—831no—
358C22×C8—831no—
359#125—22no—
360#125—22no—
361#125—41no—
362#125—41no—
363C4×D4—834no—
364C4×D4—1662no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—831no—
374C2×C4⋊C4—831no—
375C2×C4⋊C4—831no—
376C2×C4⋊C4C22⋊D8311yescharacteristic
377C2×C4⋊C4C22⋊D8311yescharacteristic
378C2×C4⋊C4C22×D8311yescharacteristic
379C2×C4⋊C4C22×D8311yescharacteristic
380C2×C4⋊C4C22×D8311yescharacteristic
381C2×C4⋊C4C22×D8311yescharacteristic
382C2×C22⋊C4—1661no—
383C2×C22⋊C4—1661no—
384C2×C22⋊C4—1661no—
385C2×C22⋊C4—1661no—
386C2×C22⋊C4—1661no—
387C2×C42—21no—
388C2×C42—1661no—
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—1661no—
407#95—1661no—
408#95—1661no—
409#95—1661no—
410#95C22⋊D8311yescharacteristic
411#95C22⋊D8311yescharacteristic
412C24—1661no—
413C2×D4—832no—
414C2×D4—1661no—
415C2×D4—1661no—
416C2×D4—1661no—
417C2×D4—1661no—
418C2×D4—1661no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—6641no—
424C22×C4—6641no—
425C22×C4—1661no—
426C22×C4—1661no—
427C22×C4—1661no—
428C22×C4—1664no—
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—21no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—42no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—42no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4—81no—
464C4⋊C4—832no—
465C4⋊C4—1661no—
466C4⋊C4—1661no—
467C4⋊C4—1661no—
468C4⋊C4—1661no—
469C4⋊C4—1661no—
470C4⋊C4#1305058912yes—
471C4⋊C4#1305059112yes—
472C22⋊C4—3322no—
473C22⋊C4—3322no—
474C22⋊C4—6641no—
475C22⋊C4—6641no—
476C22⋊C4—1664no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—42no—
482C42—6641no—
483C42—6641no—
484C42Q8×D8312yes—
485C42#1305059112yes—
486C23—3321no—
487C23—3321no—
488C23—3321no—
489C23—3321no—
490C23—3321no—
491C23—3321no—
492C23—1662no—
493C23C22×C22⋊D8311yescharacteristic
494D4—3321no—
495D4—3321no—
496D4—1662no—
497D4—1662no—
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—22no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
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—6644no—
535C2×C4—1662no—
536C2×C4#1458176812yes—
537C2×C4#1458176812yes—
538C2×C4C2×Q8×D8311yescharacteristic
539C2×C4C2×#1305058911yescharacteristic
540C2×C4C2×#1305059111yescharacteristic
541C2×C4C2×#1305059111yescharacteristic
542C2×C4#1458183711yescharacteristic
543C2×C4#1458184011yescharacteristic
544C8—3321no—
545C8—3321no—
546C8—3321no—
547C8—3321no—
548C22—3322no—
549C22—3322no—
550C22—3322no—
551C22—6641no—
552C22—6641no—
553C22—6641no—
554C22—6641no—
555C22C2×#1458176811yescharacteristic
556C22#1912834511yescharacteristic
557C22#1912836211yescharacteristic
558C22#1912849911yescharacteristic
559C22#1912849911yescharacteristic
560C22#1912850411yescharacteristic
561C22#1912850911yescharacteristic
562C4—22no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—42no—
567C4—42no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—3322no—
573C4—6641no—
574C4—6641no—
575C4#1912825611yescharacteristic
576C4#1912832811yescharacteristic
577C4#1912841711yescharacteristic
578C4#1912842511yescharacteristic
579C2—6642no—
580C2#2491115011yescharacteristic
581C2#2491728111yescharacteristic
582C2#2491728811yescharacteristic
583C2#2491943911yescharacteristic
584C2#2491946911yescharacteristic
585C2#2492021611yescharacteristic
586C2#2492023111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#2552C2
socleC23×C83C22×D4
prime radicalC22×D332C23
hypercenter#2552D83
hypocenterC83#26037
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2552

Complements

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

NH ≅ G/Ntype
6. #24908421C2semidirect
7. #24908421C2semidirect
8. #24908231C2semidirect
9. #24908187C2semidirect
10. #24908045C2semidirect
11. #24908031C2semidirect
12. #24907598C2semidirect
15. C83×#2552C2semidirect
294. #2552D83semidirect
309. C83#26037semidirect

Maximal subgroups

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

subgroupindex
#249104342
#249088482
#249088342
#249086062
#249084212
#249082312
#249081872
#249080452
#249080312
#249075982
#249074602
#249072912
C83×#25522
#2603783