Finite Group Databasebeta

← #35466528

Subgroups — #35466528

Order 21248.

712 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24910412C211yesmaximal, characteristic
2#24908894C211yesmaximal, characteristic, complemented
3#24908894C211yesmaximal, characteristic, complemented
4#24908889C211yesmaximal, characteristic, complemented
5#24908889C211yesmaximal, characteristic, complemented
6#24908433C211yesmaximal, characteristic, complemented
7#24908421C211yesmaximal, characteristic, complemented
8#24908262C211yesmaximal, characteristic
9#24908221C211yesmaximal, characteristic, complemented
10#24907660C211yesmaximal, characteristic, complemented
11#24907660C211yesmaximal, characteristic, complemented
12#24907555C211yesmaximal, characteristic, complemented
13#24907555C211yesmaximal, characteristic, complemented
14#24907361C211yesmaximal, characteristic, complemented
15C83×#2562C211yesmaximal, characteristic
16C2×#14581751C2211yescharacteristic
17C2×#14581751C2211yescharacteristic
18C2×#14581725C2211yescharacteristic
19C2×#14581725C2211yescharacteristic
20C2×#14581725C2211yescharacteristic
21C2×#14581723C2211yescharacteristic
22C2×C4⋊(C83⋊C8)C2211yescharacteristic
23C2×C22⋊(C83⋊C8)C2211yescharacteristic
24C2×C22⋊(C83⋊C8)C2211yescharacteristic
25C2×C22⋊(C83⋊C8)C2211yescharacteristic
26C2×C22⋊(C83⋊C8)C2211yescharacteristic
27C2×#14581703C2211yescharacteristic
28#19127604—21no—
29#19127594—21no—
30#19127594—21no—
31#19127571C2211yescharacteristic
32#19127561C2211yescharacteristic
33#19127561C2211yescharacteristic
34C4⋊C4×Dic83—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#19127463C2211yescharacteristic
47#19127463C2211yescharacteristic
48C2×#125×C83C2211yescharacteristic
49C2×C4×D4×C83C2211yescharacteristic
50#400×C83—21no—
51#394×C83—21no—
52#388×C83—21no—
53#388×C83—21no—
54#380×C83C2211yescharacteristic
55#380×C83C2211yescharacteristic
56#380×C83C2211yescharacteristic
57#380×C83C2211yescharacteristic
58C4×C4⋊C4×C83C2211yescharacteristic
59C22×C83⋊C8C2311yescharacteristic
60C22×C83⋊C8C2311yescharacteristic
61C22×C83⋊C8C2311yescharacteristic
62C22×C83⋊C8C2311yescharacteristic
63#14581751—22no—
64#14581751—22no—
65#14581751—41no—
66#14581751—41no—
67C2×C4⋊Dic83—21no—
68C2×C4⋊Dic83—21no—
69C2×C4⋊Dic83C2311yescharacteristic
70C2×C4⋊Dic83C2311yescharacteristic
71C2×C4⋊Dic83C2311yescharacteristic
72C2×C4⋊Dic83C2311yescharacteristic
73C2×C22⋊Dic83—21no—
74C2×C22⋊Dic83—21no—
75C2×C22⋊Dic83—21no—
76C2×C22⋊Dic83—21no—
77C2×C4×Dic83—21no—
78C2×C4×Dic83—21no—
79C2×C4×Dic83—21no—
80#14581725—22no—
81#14581725—41no—
82#14581725—41no—
83#14581723—22no—
84C4⋊(C83⋊C8)—22no—
85C22⋊(C83⋊C8)—22no—
86C22⋊(C83⋊C8)—22no—
87C22⋊(C83⋊C8)—41no—
88C22⋊(C83⋊C8)—41no—
89#14581703—22no—
90C83⋊#95—21no—
91C83⋊#95—21no—
92C83⋊#95—21no—
93C22×D4×C83D411yescharacteristic
94C23×C4×C83C2311yescharacteristic
95C23×C4×C83C2311yescharacteristic
96#125×C83—22no—
97#125×C83—22no—
98C4×D4×C83—22no—
99C4×D4×C83—22no—
100C2×C4⋊C4×C83—21no—
101C2×C4⋊C4×C83—21no—
102C2×C4⋊C4×C83D411yescharacteristic
103C2×C4⋊C4×C83C2311yescharacteristic
104C2×C4⋊C4×C83C2311yescharacteristic
105C2×C4⋊C4×C83C2311yescharacteristic
106C2×C4⋊C4×C83C2311yescharacteristic
107C2×C22⋊C4×C83—21no—
108C2×C22⋊C4×C83—21no—
109C2×C22⋊C4×C83—21no—
110C2×C22⋊C4×C83—21no—
111C2×C22⋊C4×C83D411yescharacteristic
112C2×C22⋊C4×C83D411yescharacteristic
113C2×C42×C83—21no—
114C2×C42×C83C2311yescharacteristic
115#95×C83—21no—
116#95×C83—21no—
117#95×C83—21no—
118#95×C83—21no—
119#95×C83—21no—
120C22×Dic83—21no—
121C22×Dic83—21no—
122C22×Dic83—21no—
123C22×Dic83—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—21no—
135C2×C83⋊C8#4112yes—
136C4⋊Dic83—21no—
137C4⋊Dic83—21no—
138C4⋊Dic83—21no—
139C4⋊Dic83—21no—
140C4⋊Dic83—21no—
141C4⋊Dic83—21no—
142C4⋊Dic83—21no—
143C4⋊Dic83—42no—
144C4⋊Dic83—81no—
145C4⋊Dic83#4112yes—
146C22⋊Dic83—42no—
147C22⋊Dic83—42no—
148C22⋊Dic83—81no—
149C22⋊Dic83—81no—
150C4×Dic83—42no—
151C4×Dic83—42no—
152C4×Dic83—42no—
153C24×C83C2×D411yescharacteristic
154C24×C83C2×D411yescharacteristic
155C2×D4×C83—22no—
156C2×D4×C83—41no—
157C2×D4×C83—41no—
158C22×C4×C83—21no—
159C22×C4×C83—21no—
160C22×C4×C83—21no—
161C22×C4×C83—21no—
162C22×C4×C83—21no—
163C22×C4×C83—21no—
164C22×C4×C83—21no—
165C22×C4×C83—21no—
166C22×C4×C83—21no—
167C22×C4×C83—21no—
168C22×C4×C83—21no—
169C22×C4×C83—21no—
170C22×C4×C83—21no—
171C22×C4×C83—21no—
172C22×C4×C83—21no—
173C22×C4×C83—21no—
174C22×C4×C83C2×D411yescharacteristic
175C22×C4×C83C2×D411yescharacteristic
176C22×C4×C83C2×D411yescharacteristic
177C22×C4×C83C2×D411yescharacteristic
178C22×C4×C83C2411yescharacteristic
179C4⋊C4×C83—22no—
180C4⋊C4×C83—21no—
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—42no—
189C4⋊C4×C83—42no—
190C22⋊C4×C83—22no—
191C22⋊C4×C83—22no—
192C22⋊C4×C83—42no—
193C22⋊C4×C83—42no—
194C22⋊C4×C83—81no—
195C22⋊C4×C83—81no—
196C42×C83—81no—
197C42×C83#4112yes—
198C42×C83#4112yes—
199C23×C83—21no—
200C23×C83—21no—
201C23×C83—21no—
202C23×C83—21no—
203C23×C83—21no—
204C23×C83—21no—
205C23×C83—21no—
206C23×C83—21no—
207C23×C83—21no—
208C23×C83—21no—
209C23×C83—21no—
210C23×C83—21no—
211C23×C83—21no—
212C23×C83—21no—
213C23×C83C22×D411yescharacteristic
214D4×C83—44no—
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—21no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—21no—
225C2×C4×C83—41no—
226C2×C4×C83—41no—
227C2×C4×C83—41no—
228C2×C4×C83—41no—
229C2×C4×C83—41no—
230C2×C4×C83—41no—
231C2×C4×C83—41no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83—41no—
235C2×C4×C83—41no—
236C2×C4×C83—41no—
237C2×C4×C83—41no—
238C2×C4×C83—41no—
239C2×C4×C83—41no—
240C2×C4×C83—41no—
241C2×C4×C83—41no—
242C2×C4×C83—41no—
243C2×C4×C83—41no—
244C2×C4×C83—41no—
245C2×C4×C83#12312yes—
246C2×C4×C83#12312yes—
247C2×C4×C83C2×#4111yescharacteristic
248C2×C4×C83C2×#4111yescharacteristic
249C2×C4×C83C2×#4111yescharacteristic
250C2×C4×C83C2×#4111yescharacteristic
251C2×C4×C83H(5,𝔽2)11yescharacteristic
252C2×C4×C832−1+411yescharacteristic
253C2×Dic83—22no—
254C2×Dic83—41no—
255C2×Dic83—41no—
256C2×Dic83—41no—
257C2×Dic83—41no—
258C2×Dic83—41no—
259C2×Dic83—41no—
260C2×Dic83—41no—
261C2×Dic83—41no—
262C2×Dic83—41no—
263C2×Dic83—41no—
264C2×Dic83—41no—
265C83⋊C8—22no—
266C83⋊C8—41no—
267C83⋊C8—41no—
268C83⋊C8—41no—
269C22×C83—41no—
270C22×C83—41no—
271C22×C83—41no—
272C22×C83—41no—
273C22×C83—41no—
274C22×C83—41no—
275C22×C83—41no—
276C22×C83—41no—
277C22×C83—41no—
278C22×C83—41no—
279C22×C83—41no—
280C22×C83—41no—
281C22×C83—41no—
282C22×C83—41no—
283C22×C83C2×#12311yescharacteristic
284C22×C83#54611yescharacteristic
285C22×C83#54711yescharacteristic
286C22×C83#57511yescharacteristic
287C22×C83#57511yescharacteristic
288C22×C83#57611yescharacteristic
289C22×C83#57811yescharacteristic
290C4×C83—22no—
291C4×C83—22no—
292C4×C83—41no—
293C4×C83—41no—
294C4×C83—81no—
295C4×C83—81no—
296C4×C83—81no—
297C4×C83—81no—
298C4×C83#52911yescharacteristic
299C4×C83#54211yescharacteristic
300C4×C83#55611yescharacteristic
301C4×C83#55911yescharacteristic
302Dic83—42no—
303Dic83—81no—
304Dic83—81no—
305Dic83—81no—
306#26311—831nomaximal, Sylow
307C2×C83—81no—
308C2×C83—81no—
309C2×C83#244711yescharacteristic
310C2×C83#309311yescharacteristic
311C2×C83#309811yescharacteristic
312C2×C83#330911yescharacteristic
313C2×C83#331511yescharacteristic
314C2×C83#334711yescharacteristic
315C2×C83#334911yescharacteristic
316#2562D8311yescharacteristic
317#2354—831no—
318#2076—831no—
319#2076—831no—
320#2075—831no—
321#2075—831no—
322#1992—831no—
323#1989—831no—
324#1955—831no—
325#1947—831no—
326#1854—831no—
327#1854—831no—
328#1825—831no—
329#1825—831no—
330#1776—831no—
331C83#2631111yescharacteristic, complemented, Sylow
332C2×#125C2×D8311yescharacteristic
333C2×C4×D4C2×D8311yescharacteristic
334C2×#117—831no—
335C2×#117—831no—
336C2×#107—831no—
337C2×#107—831no—
338C2×#107—831no—
339C2×#106—831no—
340C2×C4⋊C8—831no—
341C2×C22⋊C8—831no—
342C2×C22⋊C8—831no—
343C2×C22⋊C8—831no—
344C2×C22⋊C8—831no—
345C2×#97—831no—
346#400—21no—
347#394—21no—
348#390—1661no—
349#388—21no—
350#388—21no—
351#388—1661no—
352#388—1661no—
353#384—831no—
354#380—831no—
355#380—831no—
356#380C2×D8311yescharacteristic
357#380C2×D8311yescharacteristic
358#380C2×D8311yescharacteristic
359#380C2×D8311yescharacteristic
360C4×C4⋊C4—831no—
361C4×C4⋊C4—1661no—
362C4×C4⋊C4C2×D8311yescharacteristic
363#340—831no—
364#340—831no—
365#340—831no—
366#340—831no—
367#340—831no—
368#340—831no—
369#340—831no—
370#340—831no—
371#340—831no—
372#340—831no—
373#340—831no—
374#340—831no—
375C22×D4C22⋊D8311yescharacteristic
376C23×C4C22×D8311yescharacteristic
377C23×C4C22×D8311yescharacteristic
378C22×C8—831no—
379C22×C8—831no—
380C22×C8—831no—
381C22×C8—831no—
382#125—22no—
383#125—22no—
384C4×D4—22no—
385C4×D4—22no—
386#117—3321no—
387#117—3321no—
388#117—1662no—
389#117—1662no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—831no—
393C2×C4⋊C4—831no—
394C2×C4⋊C4—831no—
395C2×C4⋊C4—831no—
396C2×C4⋊C4—1661no—
397C2×C4⋊C4—1661no—
398C2×C4⋊C4C22⋊D8311yescharacteristic
399C2×C4⋊C4C22×D8311yescharacteristic
400C2×C4⋊C4C22×D8311yescharacteristic
401C2×C4⋊C4C22×D8311yescharacteristic
402C2×C4⋊C4C22×D8311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—1661no—
408C2×C22⋊C4—1661no—
409C2×C22⋊C4—1661no—
410C2×C22⋊C4—1661no—
411C2×C22⋊C4C22⋊D8311yescharacteristic
412C2×C22⋊C4C22⋊D8311yescharacteristic
413C2×C42—21no—
414C2×C42—1661no—
415C2×C42—1661no—
416C2×C42—1661no—
417C2×C42C22×D8311yescharacteristic
418#107—3321no—
419#107—3321no—
420#107—1662no—
421#106—1662no—
422C4⋊C8—1662no—
423C22⋊C8—3321no—
424C22⋊C8—3321no—
425C22⋊C8—1662no—
426C22⋊C8—1662no—
427#97—1662no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—1661no—
434#95—1661no—
435#95—1661no—
436C24C2×C22⋊D8311yescharacteristic
437C24C2×C22⋊D8311yescharacteristic
438C2×D4—22no—
439C2×D4—41no—
440C2×D4—41no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—1661no—
458C22×C4—1661no—
459C22×C4—1661no—
460C22×C4—1661no—
461C22×C4C2×C22⋊D8311yescharacteristic
462C22×C4C2×C22⋊D8311yescharacteristic
463C22×C4C2×C22⋊D8311yescharacteristic
464C22×C4C2×C22⋊D8311yescharacteristic
465C22×C4C23×D8311yescharacteristic
466C2×C8—832no—
467C2×C8—1661no—
468C2×C8—1661no—
469C2×C8—1661no—
470C2×C8—1661no—
471C2×C8—1661no—
472C2×C8—1661no—
473C2×C8—1661no—
474C2×C8—1661no—
475C2×C8—1661no—
476C2×C8—1661no—
477C2×C8—1661no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—3322no—
490C4⋊C4—832no—
491C4⋊C4—6641no—
492C4⋊C4—1661no—
493C4⋊C4—1661no—
494C4⋊C4—1661no—
495C4⋊C4—1661no—
496C4⋊C4—1661no—
497C4⋊C4—1661no—
498C4⋊C4—1661no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—42no—
502C22⋊C4—42no—
503C22⋊C4—81no—
504C22⋊C4—81no—
505C22⋊C4—3322no—
506C22⋊C4—3322no—
507C22⋊C4—6641no—
508C22⋊C4—6641no—
509C42—81no—
510C42—3322no—
511C42—3322no—
512C42—3322no—
513C42#1305058912yes—
514C42#1305058912yes—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23C22×C22⋊D8311yescharacteristic
530D4—44no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—3321no—
562C2×C4—3321no—
563C2×C4—3321no—
564C2×C4—3321no—
565C2×C4—3321no—
566C2×C4—3321no—
567C2×C4—3321no—
568C2×C4—3321no—
569C2×C4—3321no—
570C2×C4—3321no—
571C2×C4—3321no—
572C2×C4—1662no—
573C2×C4#1458177312yes—
574C2×C4#1458177312yes—
575C2×C4#41×D8311yescharacteristic
576C2×C4#41×D8311yescharacteristic
577C2×C4C2×#1305058911yescharacteristic
578C2×C4C2×#1305058911yescharacteristic
579C2×C4#1458183811yescharacteristic
580C2×C4#1458183911yescharacteristic
581C8—3321no—
582C8—3321no—
583C8—3321no—
584C8—1662no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22C2×#1458177311yescharacteristic
600C22#1912833911yescharacteristic
601C22#1912835011yescharacteristic
602C22#1912849911yescharacteristic
603C22#1912849911yescharacteristic
604C22#1912850411yescharacteristic
605C22#1912851611yescharacteristic
606C4—22no—
607C4—22no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4—81no—
614C4—3322no—
615C4—6641no—
616C4—6641no—
617C4—6641no—
618C4#1912823011yescharacteristic
619C4#1912832011yescharacteristic
620C4#1912842011yescharacteristic
621C4#1912843311yescharacteristic
622C2—81no—
623C2—81no—
624C2#2491124611yescharacteristic
625C2#2491739211yescharacteristic
626C2#2491743711yescharacteristic
627C2#2491946311yescharacteristic
628C2#2491955311yescharacteristic
629C2#2491995711yescharacteristic
630C2#2491999311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#2562C2
socleC23×C83C22×D4
prime radicalC22×D4×C83D4
hypercenter#2562D83
hypocenterC83#26311
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2562

Complements

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

NH ≅ G/Ntype
2. #24908894C2semidirect
3. #24908894C2semidirect
4. #24908889C2semidirect
5. #24908889C2semidirect
6. #24908433C2semidirect
7. #24908421C2semidirect
9. #24908221C2semidirect
10. #24907660C2semidirect
11. #24907660C2semidirect
12. #24907555C2semidirect
13. #24907555C2semidirect
14. #24907361C2semidirect
331. C83#26311semidirect

Maximal subgroups

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

subgroupindex
#249104122
#249088942
#249088892
#249084332
#249084212
#249082622
#249082212
#249076602
#249075552
#249073612
C83×#25622
#2631183