Finite Group Databasebeta

← #35409305

Subgroups — #35409305

Order 21248.

826 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127760C211yesmaximal, characteristic
2#24910068C211yesmaximal, characteristic
3#24909817C211yesmaximal, characteristic
4#24908230C211yesmaximal, characteristic, complemented
5#24908228C211yesmaximal, characteristic, complemented
6#24908225C211yesmaximal, characteristic, complemented
7#24908218C211yesmaximal, characteristic, complemented
8#24907663C211yesmaximal, characteristic
9#24907659C211yesmaximal, characteristic
10#24907657C211yesmaximal, characteristic
11#24907649C211yesmaximal, characteristic
12#24907361C211yesmaximal, characteristic, complemented
13#24907361C211yesmaximal, characteristic, complemented
14C4×#14581724C211yesmaximal, characteristic, complemented
15C4×#107×C83C211yesmaximal, characteristic, complemented
16C2×#14581750C2211yescharacteristic
17C2×#14581749C2211yescharacteristic
18C2×C4⋊C4×D83C2211yescharacteristic
19#19127760C418yescomplemented
20C2×#14581725C2211yescharacteristic
21C2×#14581725C2211yescharacteristic
22C2×#14581724C2211yescharacteristic
23C2×#14581724C2211yescharacteristic
24C2×#14581723C2211yescharacteristic
25C2×#14581723C2211yescharacteristic
26C2×Dic83⋊C8C2211yescharacteristic
27C2×Dic83⋊C8C2211yescharacteristic
28C2×(C2×D83)⋊C8C2211yescharacteristic
29C2×(C2×D83)⋊C8C2211yescharacteristic
30C2×#14581703C2211yescharacteristic
31#19127592—21no—
32#19127590—21no—
33#19127585—21no—
34#19127583—21no—
35#19127570C2211yescharacteristic
36#19127566C2211yescharacteristic
37#19127558C2211yescharacteristic
38#19127558C2211yescharacteristic
39C4⋊C4×Dic83C2211yescharacteristic
40C4⋊C4×Dic83C2211yescharacteristic
41C4×Dic83⋊C4—21no—
42C4×C4⋊Dic83C2211yescharacteristic
43C4×C4⋊Dic83C2211yescharacteristic
44#19127552—21no—
45C4×(C2×D83)⋊C4—21no—
46#19127548—21no—
47#19127464C2211yescharacteristic
48#19127464C2211yescharacteristic
49#19127463C2211yescharacteristic
50#19127463C2211yescharacteristic
51#19127463C2211yescharacteristic
52#19127463C2211yescharacteristic
53C2×#107×C83C2211yescharacteristic
54C2×#107×C83C2211yescharacteristic
55C2×C4×C8×C83C2211yescharacteristic
56C4×C4⋊C4×C83C2211yescharacteristic
57C4×C4⋊C4×C83C2211yescharacteristic
58#340×C83C2211yescharacteristic
59#340×C83C2211yescharacteristic
60C22×C4×D83—21no—
61C22×C4×D83C2311yescharacteristic
62C22×C83⋊C8C2311yescharacteristic
63C22×C83⋊C8C2311yescharacteristic
64#14581750—22no—
65#14581750—22no—
66#14581749C2×C414yes—
67#14581749Q814yes—
68C2×C4⋊Dic83C2311yescharacteristic
69C2×C4⋊Dic83C2311yescharacteristic
70C2×C4⋊Dic83C2311yescharacteristic
71C2×C4⋊Dic83C2311yescharacteristic
72C2×Dic83⋊C4—21no—
73C2×Dic83⋊C4—21no—
74C2×Dic83⋊C4—21no—
75C2×Dic83⋊C4D411yescharacteristic
76C2×Dic83⋊C4D411yescharacteristic
77C4⋊C4×D83—22no—
78C4⋊C4×D83—22no—
79C2×(C2×D83)⋊C4—21no—
80C2×(C2×D83)⋊C4—21no—
81C2×(C2×D83)⋊C4—21no—
82C2×(C2×D83)⋊C4D411yescharacteristic
83C2×(C2×D83)⋊C4D411yescharacteristic
84C2×C4×Dic83—21no—
85C2×C4×Dic83—21no—
86C2×C4×Dic83—21no—
87C2×C4×Dic83—21no—
88C2×C4×Dic83—21no—
89C2×C4×Dic83C2311yescharacteristic
90#14581725—22no—
91#14581725—22no—
92#14581724—22no—
93#14581724—22no—
94#14581723—22no—
95#14581723—22no—
96Dic83⋊C8C2×C414yescomplemented
97Dic83⋊C8C2×C414yescomplemented
98(C2×D83)⋊C8C2×C414yes—
99(C2×D83)⋊C8C2×C414yes—
100#14581703C2×C414yescomplemented
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×C83C2311yescharacteristic
112C2×C4⋊C4×C83C2311yescharacteristic
113C2×C4⋊C4×C83C2311yescharacteristic
114C2×C4⋊C4×C83C2311yescharacteristic
115C2×C42×C83—21no—
116C2×C42×C83—21no—
117C2×C42×C83C2311yescharacteristic
118#107×C83—22no—
119#107×C83—22no—
120C4×C8×C83C2×C414yescomplemented
121#95×C83—21no—
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×D83—24no—
136C2×C4×D83—81no—
137C2×C4×D83—81no—
138C2×C4×D83C22×C412yes—
139C2×C4×D83C2×Q812yes—
140C2×C83⋊C8—21no—
141C2×C83⋊C8—21no—
142C2×C83⋊C8—21no—
143C2×C83⋊C8—21no—
144C2×C83⋊C8C22×C412yes—
145C2×C83⋊C8C22×C412yes—
146C4⋊Dic83—21no—
147C4⋊Dic83—21no—
148C4⋊Dic83—21no—
149C4⋊Dic83—21no—
150C4⋊Dic83—21no—
151C4⋊Dic83—21no—
152C4⋊Dic83#4112yes—
153C4⋊Dic83#4112yes—
154Dic83⋊C4—24no—
155Dic83⋊C4—81no—
156Dic83⋊C4—81no—
157Dic83⋊C4C4⋊C414yes—
158Dic83⋊C4C4⋊C414yes—
159(C2×D83)⋊C4—24no—
160(C2×D83)⋊C4—81no—
161(C2×D83)⋊C4—81no—
162(C2×D83)⋊C4C4⋊C414yes—
163(C2×D83)⋊C4C4⋊C414yes—
164C4×Dic83—24no—
165C4×Dic83—81no—
166C4×Dic83—81no—
167C4×Dic83—81no—
168C4×Dic83—81no—
169C4×Dic83C22×C412yes—
170C4×Dic83C2×Q812yes—
171C22×C4×C83—21no—
172C22×C4×C83—21no—
173C22×C4×C83—21no—
174C22×C4×C83—21no—
175C22×C4×C83C2×D411yescharacteristic
176C22×C4×C83C2×D411yescharacteristic
177C22×C4×C83C2411yescharacteristic
178C2×C8×C83—21no—
179C2×C8×C83—21no—
180C2×C8×C83—21no—
181C2×C8×C83—21no—
182C2×C8×C83C22×C412yes—
183C2×C8×C83C22×C412yes—
184C4⋊C4×C83—21no—
185C4⋊C4×C83—21no—
186C4⋊C4×C83—21no—
187C4⋊C4×C83—21no—
188C4⋊C4×C83—21no—
189C4⋊C4×C83—21no—
190C4⋊C4×C83#4112yes—
191C4⋊C4×C83#4112yes—
192C42×C83—81no—
193C42×C83—81no—
194C42×C83C22×C412yes—
195C42×C83C2×Q812yes—
196C23×C83C22×D411yescharacteristic
197C22×D83—21no—
198C22×D83—21no—
199C22×D83—21no—
200C22×D83—21no—
201C22×D83—21no—
202C22×D83—21no—
203C22×D83C2×C4⋊C412yes—
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—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×C83—41no—
219C2×C4×C83—41no—
220C2×C4×C83C2×C4⋊C412yes—
221C2×C4×C83C2×C4⋊C412yes—
222C2×C4×C83C23×C411yescharacteristic
223C2×C4×C83C22×Q811yescharacteristic
224C2×C4×C83C2×#4111yescharacteristic
225C2×C4×C83C2×#4111yescharacteristic
226C2×C4×C83C2×#4111yescharacteristic
227C2×C4×C83C2×#4111yescharacteristic
228C2×Dic83—21no—
229C2×Dic83—21no—
230C2×Dic83—21no—
231C2×Dic83—21no—
232C2×Dic83—21no—
233C2×Dic83—21no—
234C2×Dic83—22no—
235C2×Dic83—22no—
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×Dic83—41no—
245C2×Dic83—41no—
246C2×Dic83C2×C4⋊C412yes—
247C2×Dic83C2×C4⋊C412yes—
248C2×Dic83C2×C4⋊C412yes—
249C4×D83—22no—
250C4×D83—22no—
251C4×D83—22no—
252C4×D83—22no—
253C4×D83—84no—
254C8×C83—22no—
255C8×C83—22no—
256C83⋊C8—22no—
257C83⋊C8—22no—
258C22×C83C22×C4⋊C411yescharacteristic
259C22×C83#52511yescharacteristic
260C22×C83#52511yescharacteristic
261C22×C83#57611yescharacteristic
262C22×C83#57711yescharacteristic
263C22×C83#57711yescharacteristic
264C22×C83#57811yescharacteristic
265C2×D83—22no—
266C2×D83—22no—
267C2×D83—22no—
268C2×D83—41no—
269C2×D83—41no—
270C2×D83—41no—
271C2×D83—41no—
272C4×C83—22no—
273C4×C83—22no—
274C4×C83—42no—
275C4×C83—42no—
276C4×C83—81no—
277C4×C83—81no—
278C4×C83C4×#4111yescharacteristic
279C4×C83C4×#4111yescharacteristic
280C4×C83#53311yescharacteristic
281C4×C83#53311yescharacteristic
282Dic83—22no—
283Dic83—22no—
284Dic83—22no—
285Dic83—42no—
286Dic83—42no—
287Dic83—81no—
288Dic83—81no—
289#21367—831nomaximal, Sylow
290C2×C83#229611yescharacteristic
291C2×C83#291211yescharacteristic
292C2×C83#291311yescharacteristic
293C2×C83#311811yescharacteristic
294C2×C83#311911yescharacteristic
295C2×C83#312011yescharacteristic
296C2×C83#312111yescharacteristic
297D83—42no—
298C2×#433—831no—
299#2314—831no—
300#2274—831no—
301#1949—831no—
302#1949—831no—
303#1948—831no—
304#1947—831no—
305#1854—831no—
306#1854—831no—
307#1853—831no—
308#1852—831no—
309#1776—831no—
310#1776—831no—
311C4×#107D8311yescharacteristic, complemented
312C4×#106—831no—
313C83#2136711yescharacteristic, complemented, Sylow
314C2×#117—831no—
315C2×#117—831no—
316C22×C4⋊C4—831no—
317#433—838no—
318C2×#107—831no—
319C2×#107—831no—
320C2×#107C2×D8311yescharacteristic
321C2×#107C2×D8311yescharacteristic
322C2×#106—831no—
323C2×#106—831no—
324C2×#106—831no—
325C2×#106—831no—
326C2×C4⋊C8—831no—
327C2×C4⋊C8—831no—
328C2×C22⋊C8—831no—
329C2×C22⋊C8—831no—
330C2×#97—831no—
331C2×C4×C8C2×D8311yescharacteristic
332#388—1661no—
333#388—1661no—
334#387—1661no—
335#387—1661no—
336#384—831no—
337#382—831no—
338#380—831no—
339#380—831no—
340C4×C4⋊C4—831no—
341C4×C4⋊C4—831no—
342C4×C4⋊C4—831no—
343C4×C4⋊C4—831no—
344C4×C4⋊C4—1661no—
345C4×C4⋊C4—1661no—
346C4×C4⋊C4C2×D8311yescharacteristic
347C4×C4⋊C4C2×D8311yescharacteristic
348C4×C22⋊C4—1661no—
349C4×C22⋊C4—1661no—
350#340—831no—
351#340—831no—
352#340—831no—
353#340—831no—
354#340—831no—
355#340—831no—
356#340C2×D8311yescharacteristic
357#340C2×D8311yescharacteristic
358C23×C4—831no—
359C23×C4—1661no—
360C22×C8—831no—
361C22×C8—831no—
362C22×C8C22×D8311yescharacteristic
363C22×C8C22×D8311yescharacteristic
364#117—834no—
365#117—834no—
366#117—1662no—
367#117—1662no—
368C2×C4⋊C4—831no—
369C2×C4⋊C4—831no—
370C2×C4⋊C4—831no—
371C2×C4⋊C4—831no—
372C2×C4⋊C4—831no—
373C2×C4⋊C4—831no—
374C2×C4⋊C4—1662no—
375C2×C4⋊C4—1661no—
376C2×C4⋊C4—1661no—
377C2×C4⋊C4—1661no—
378C2×C4⋊C4—1662no—
379C2×C4⋊C4C22×D8311yescharacteristic
380C2×C4⋊C4C22×D8311yescharacteristic
381C2×C4⋊C4C22×D8311yescharacteristic
382C2×C4⋊C4C22×D8311yescharacteristic
383C2×C22⋊C4—831no—
384C2×C22⋊C4—831no—
385C2×C22⋊C4—1661no—
386C2×C22⋊C4—1661no—
387C2×C22⋊C4—1661no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—831no—
391C2×C42—1661no—
392C2×C42—1661no—
393C2×C42—1661no—
394C2×C42—1661no—
395C2×C42—1661no—
396C2×C42C22×D8311yescharacteristic
397#107—22no—
398#107—22no—
399#107—1662no—
400#107—1662no—
401#106—1662no—
402#106—1662no—
403#106—1662no—
404#106—1662no—
405C4⋊C8—834no—
406C4⋊C8—834no—
407C22⋊C8—834no—
408C22⋊C8—834no—
409#97—834no—
410C4×C8C4×D8314yescomplemented
411#95—21no—
412#95—21no—
413#95—1661no—
414#95—1661no—
415#95—1661no—
416#95—1661no—
417#95—1661no—
418#95—1661no—
419#95—1661no—
420#95—1661no—
421C24—831no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—831no—
427C22×C4—831no—
428C22×C4—831no—
429C22×C4—832no—
430C22×C4—832no—
431C22×C4—6641no—
432C22×C4—6641no—
433C22×C4—1664no—
434C22×C4—1661no—
435C22×C4—1661no—
436C22×C4—1661no—
437C22×C4—1661no—
438C22×C4—1661no—
439C22×C4—1661no—
440C22×C4—1661no—
441C22×C4—1661no—
442C22×C4D4×D8311yescharacteristic
443C22×C4D4×D8311yescharacteristic
444C22×C4C23×D8311yescharacteristic
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—832no—
450C2×C8—832no—
451C2×C8—1661no—
452C2×C8—1661no—
453C2×C8—1661no—
454C2×C8—1661no—
455C2×C8C2×C4×D8312yes—
456C2×C8C2×C4×D8312yes—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—834no—
464C4⋊C4—834no—
465C4⋊C4—832no—
466C4⋊C4—832no—
467C4⋊C4—6641no—
468C4⋊C4—6641no—
469C4⋊C4—1664no—
470C4⋊C4—1661no—
471C4⋊C4—1661no—
472C4⋊C4—1661no—
473C4⋊C4—1661no—
474C4⋊C4—1661no—
475C4⋊C4—1661no—
476C4⋊C4#1305059012yes—
477C4⋊C4#1305059012yes—
478C22⋊C4—834no—
479C22⋊C4—834no—
480C22⋊C4—6641no—
481C22⋊C4—6641no—
482C22⋊C4—1664no—
483C42—81no—
484C42—81no—
485C42—832no—
486C42—832no—
487C42—6641no—
488C42—6641no—
489C42—6641no—
490C42—6641no—
491C42—1664no—
492C42C2×C4×D8312yes—
493C42Q8×D8312yes—
494C23—832no—
495C23—1661no—
496C23—1661no—
497C23—1661no—
498C23—1661no—
499C23—1661no—
500C23—1661no—
501C23C2×D4×D8311yescharacteristic
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—41no—
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—3321no—
519C2×C4—3321no—
520C2×C4—3321no—
521C2×C4—3321no—
522C2×C4—3321no—
523C2×C4—3321no—
524C2×C4—3321no—
525C2×C4—3321no—
526C2×C4—3321no—
527C2×C4—3321no—
528C2×C4—832no—
529C2×C4—832no—
530C2×C4—832no—
531C2×C4—6644no—
532C2×C4—1662no—
533C2×C4—1662no—
534C2×C4—1661no—
535C2×C4—1661no—
536C2×C4—1661no—
537C2×C4—1661no—
538C2×C4—1661no—
539C2×C4—1661no—
540C2×C4—1662no—
541C2×C4—1662no—
542C2×C4—1662no—
543C2×C4—1662no—
544C2×C4C4⋊C4×D8312yes—
545C2×C4C4⋊C4×D8312yes—
546C2×C4C22×C4×D8311yescharacteristic
547C2×C4C2×Q8×D8311yescharacteristic
548C2×C4#41×D8311yescharacteristic
549C2×C4#41×D8311yescharacteristic
550C2×C4C2×#1305059011yescharacteristic
551C2×C4C2×#1305059011yescharacteristic
552C8—22no—
553C8—22no—
554C8—1662no—
555C8—1662no—
556C22—3321no—
557C22—3321no—
558C22—3321no—
559C22—3321no—
560C22—1662no—
561C22—1662no—
562C22—1662no—
563C22C2×C4⋊C4×D8311yescharacteristic
564C22#1912821011yescharacteristic
565C22#1912821011yescharacteristic
566C22#1912850211yescharacteristic
567C22#1912850811yescharacteristic
568C22#1912850811yescharacteristic
569C22#1912851411yescharacteristic
570C4—22no—
571C4—22no—
572C4—42no—
573C4—42no—
574C4—81no—
575C4—81no—
576C4—3322no—
577C4—3322no—
578C4—6641no—
579C4—6641no—
580C4—1662no—
581C4—1662no—
582C4—1662no—
583C4#1912816911yescharacteristic
584C4C4×#1305059011yescharacteristic
585C4#1912825511yescharacteristic
586C4#1912825511yescharacteristic
587C2—3322no—
588C2#2490994311yescharacteristic
589C2#2491605511yescharacteristic
590C2#2491605911yescharacteristic
591C2#2491764311yescharacteristic
592C2#2491765811yescharacteristic
593C2#2491768311yescharacteristic
594C2#2491769811yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC4×#107×C83C2
socleC23×C83C22×D4
prime radicalC23×D83C2×D4
cosocleC22×C4×C83C24
hypercenterC4×#107D83
hypocenterC83#21367
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
4. #24908230C2semidirect
5. #24908228C2semidirect
6. #24908225C2semidirect
7. #24908218C2semidirect
12. #24907361C2semidirect
13. #24907361C2semidirect
14. C4×#14581724C2semidirect
15. C4×#107×C83C2semidirect
19. #19127760C4semidirect
96. Dic83⋊C8C2×C4semidirect
97. Dic83⋊C8C2×C4semidirect
100. #14581703C2×C4semidirect
120. C4×C8×C83C2×C4semidirect
311. C4×#107D83semidirect
313. C83#21367semidirect
410. C4×C8C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191277602
#249100682
#249098172
#249082302
#249082282
#249082252
#249082182
#249076632
#249076592
#249076572
#249076492
#249073612
C4×#145817242
C4×#107×C832
#2136783