Finite Group Databasebeta

← #35462989

Subgroups — #35462989

Order 21248.

872 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127988C211yesmaximal, characteristic
2C2×#19127978C211yesmaximal, characteristic
3#24910374C211yesmaximal, characteristic
4#24908964C211yesmaximal, characteristic, complemented
5#24908959C211yesmaximal, characteristic, complemented
6#24908793C211yesmaximal, characteristic, complemented
7#24908788C211yesmaximal, characteristic, complemented
8#24908231C211yesmaximal, characteristic, complemented
9#24908187C211yesmaximal, characteristic, complemented
10#24907723C211yesmaximal, characteristic
11#24907709C211yesmaximal, characteristic
12#24907629C211yesmaximal, characteristic, complemented
13#24907460C211yesmaximal, characteristic
14#24907291C211yesmaximal, characteristic
15C83×#2551C211yesmaximal, characteristic, complemented
16C2×C4×D332C2211yescharacteristic
17C2×C4×D332C2211yescharacteristic
18C2×C4×D332C2211yescharacteristic
19#19127988—24no—
20#19127978—24no—
21C2×#14581725C2211yescharacteristic
22C2×#14581725C2211yescharacteristic
23C2×#14581725C2211yescharacteristic
24C2×#14581723C2211yescharacteristic
25C2×#14581723C2211yescharacteristic
26C2×#14581723C2211yescharacteristic
27C2×C4⋊(C83⋊C8)C2211yescharacteristic
28C2×C4⋊(C83⋊C8)C2211yescharacteristic
29C2×C4⋊(C83⋊C8)C2211yescharacteristic
30C2×#14581712C2211yescharacteristic
31C2×#14581712C2211yescharacteristic
32C2×#14581712C2211yescharacteristic
33C2×#14581712C2211yescharacteristic
34C2×#14581703C2211yescharacteristic
35#19127599C2211yescharacteristic
36#19127599C2211yescharacteristic
37#19127572—21no—
38#19127572—21no—
39#19127567C2211yescharacteristic
40#19127560—21no—
41#95×D83—21no—
42#19127463C2211yescharacteristic
43#19127463C2211yescharacteristic
44#19127463C2211yescharacteristic
45#19127463C2211yescharacteristic
46#19127463C2211yescharacteristic
47#19127463C2211yescharacteristic
48#19127456C2211yescharacteristic
49#19127456C2211yescharacteristic
50C2×C4⋊Q8×C83—21no—
51C2×C4⋊Q8×C83C2211yescharacteristic
52C2×C4⋊Q8×C83C2211yescharacteristic
53#395×C83—21no—
54#395×C83—21no—
55#389×C83—21no—
56#389×C83C2211yescharacteristic
57#389×C83C2211yescharacteristic
58#384×C83C2211yescharacteristic
59C4×C4⋊C4×C83C2211yescharacteristic
60C4×C4⋊C4×C83C2211yescharacteristic
61C22×D332C2311yescharacteristic
62C22×C4×D83—21no—
63C22×C4×D83—21no—
64C22×C4×D83—21no—
65C22×C83⋊C8C2311yescharacteristic
66C22×C83⋊C8C2311yescharacteristic
67C22×C83⋊C8C2311yescharacteristic
68C22×C83⋊C8C2311yescharacteristic
69C4×D332—22no—
70C4×D332—22no—
71C4×D332—22no—
72C4×D332—41no—
73C4×D332—41no—
74C4×D332Q814yescomplemented
75C2×C4⋊Dic83C2311yescharacteristic
76C2×C4⋊Dic83C2311yescharacteristic
77C2×C4⋊Dic83C2311yescharacteristic
78C2×Dic83⋊C4—21no—
79C2×Dic83⋊C4—21no—
80C2×(C2×D83)⋊C4—21no—
81C2×(C2×D83)⋊C4—21no—
82C2×(C2×D83)⋊C4—21no—
83#14581725—22no—
84#14581725—22no—
85#14581725—41no—
86#14581723—22no—
87#14581723—22no—
88#14581723—41no—
89C4⋊(C83⋊C8)—22no—
90C4⋊(C83⋊C8)—22no—
91C4⋊(C83⋊C8)—22no—
92#14581712—22no—
93#14581712—22no—
94#14581712D414yes—
95#14581712Q814yescomplemented
96#14581703—22no—
97C83⋊#95—21no—
98C83⋊#95—21no—
99C83⋊#95—21no—
100C83⋊#95—21no—
101C22×Q8×C83—21no—
102C22×Q8×C83—21no—
103C4⋊Q8×C83—22no—
104C4⋊Q8×C83—22no—
105C4⋊Q8×C83—41no—
106C4⋊Q8×C83—41no—
107C4⋊Q8×C83—44no—
108C2×C4⋊C4×C83—21no—
109C2×C4⋊C4×C83—21no—
110C2×C4⋊C4×C83—21no—
111C2×C4⋊C4×C83—21no—
112C2×C4⋊C4×C83—21no—
113C2×C4⋊C4×C83—21no—
114C2×C4⋊C4×C83D411yescharacteristic
115C2×C4⋊C4×C83D411yescharacteristic
116C2×C4⋊C4×C83C2311yescharacteristic
117C2×C4⋊C4×C83C2311yescharacteristic
118C2×C4⋊C4×C83C2311yescharacteristic
119C2×C4⋊C4×C83C2311yescharacteristic
120C2×C42×C83—21no—
121C2×C42×C83C2311yescharacteristic
122C2×C42×C83C2311yescharacteristic
123C2×C42×C83C2311yescharacteristic
124#95×C83—21no—
125#95×C83—21no—
126#95×C83—21no—
127#95×C83D411yescharacteristic
128#95×C83D411yescharacteristic
129C23×D83—21no—
130C2×D332—21no—
131C2×D332—21no—
132C2×D332—21no—
133C2×D332C2×D412yes—
134C2×D332C2×Q812yes—
135C2×D332C2×Q812yes—
136C22×Dic83—21no—
137C22×Dic83—21no—
138C22×Dic83—21no—
139C2×C4×D83—24no—
140C2×C4×D83—42no—
141C2×C4×D83—42no—
142C2×C4×D83—42no—
143C2×C4×D83—42no—
144C2×C4×D83—81no—
145C2×C4×D83—81no—
146C2×C4×D83—81no—
147C2×C4×D83—81no—
148C2×C83⋊C8—21no—
149C2×C83⋊C8—21no—
150C2×C83⋊C8—21no—
151C2×C83⋊C8—21no—
152C2×C83⋊C8—21no—
153C2×C83⋊C8—21no—
154C2×C83⋊C8—21no—
155C2×C83⋊C8—21no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8C2×D412yes—
159C2×C83⋊C8C2×Q812yes—
160C4⋊Dic83—21no—
161C4⋊Dic83—21no—
162C4⋊Dic83—21no—
163C4⋊Dic83—21no—
164C4⋊Dic83—21no—
165C4⋊Dic83C2×Q812yes—
166Dic83⋊C4—81no—
167Dic83⋊C4—81no—
168(C2×D83)⋊C4—24no—
169(C2×D83)⋊C4—42no—
170(C2×D83)⋊C4—42no—
171C2×Q8×C83—42no—
172C2×Q8×C83—42no—
173C2×Q8×C83—42no—
174C2×Q8×C83—42no—
175C2×Q8×C83—81no—
176C2×Q8×C83—81no—
177C22×C4×C83—21no—
178C22×C4×C83—21no—
179C22×C4×C83—21no—
180C22×C4×C83—21no—
181C22×C4×C83C2×D411yescharacteristic
182C22×C4×C83C2×D411yescharacteristic
183C22×C4×C83C2×D411yescharacteristic
184C22×C4×C83C2×D411yescharacteristic
185C22×C4×C83C2×D411yescharacteristic
186C22×C4×C83C2×D411yescharacteristic
187C22×C4×C83C2411yescharacteristic
188C4⋊C4×C83—22no—
189C4⋊C4×C83—22no—
190C4⋊C4×C83—21no—
191C4⋊C4×C83—21no—
192C4⋊C4×C83—21no—
193C4⋊C4×C83—21no—
194C4⋊C4×C83—21no—
195C4⋊C4×C83—21no—
196C4⋊C4×C83—42no—
197C4⋊C4×C83—42no—
198C4⋊C4×C83—42no—
199C4⋊C4×C83—42no—
200C4⋊C4×C83—42no—
201C4⋊C4×C83—81no—
202C4⋊C4×C83C2×D412yes—
203C4⋊C4×C83C2×Q812yes—
204C42×C83—21no—
205C42×C83—21no—
206C42×C83—21no—
207C42×C83—21no—
208C42×C83—42no—
209C42×C83C2×Q812yes—
210C42×C83#4112yes—
211C23×C83C22×D411yescharacteristic
212C22×D83—22no—
213C22×D83—22no—
214C22×D83—22no—
215C22×D83—41no—
216C22×D83—41no—
217C22×D83—41no—
218C22×D83—41no—
219Q8×C83—84no—
220Q8×C83—84no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—21no—
225C2×C4×C83—21no—
226C2×C4×C83—21no—
227C2×C4×C83—21no—
228C2×C4×C83—21no—
229C2×C4×C83—21no—
230C2×C4×C83—21no—
231C2×C4×C83—22no—
232C2×C4×C83—22no—
233C2×C4×C83—21no—
234C2×C4×C83—21no—
235C2×C4×C83—21no—
236C2×C4×C83—21no—
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—41no—
246C2×C4×C83—41no—
247C2×C4×C83C22⋊Q812yes—
248C2×C4×C83C22⋊Q812yes—
249C2×C4×C83AGL(1,ℤ/8)12yes—
250C2×C4×C83#13712yes—
251C2×C4×C83C22×D411yescharacteristic
252C2×C4×C83C22×Q811yescharacteristic
253C2×C4×C83C22×Q811yescharacteristic
254C2×C4×C83C2×#4111yescharacteristic
255C2×C4×C83H(5,𝔽2)11yescharacteristic
256C2×C4×C832−1+411yescharacteristic
257C2×Dic83—22no—
258C2×Dic83—41no—
259C2×Dic83—41no—
260C2×Dic83—41no—
261C2×Dic83—41no—
262C2×Dic83—41no—
263C2×Dic83—41no—
264C2×Dic83—41no—
265C2×Dic83—41no—
266D332—22no—
267D332—22no—
268D332—22no—
269D332C4⋊Q814yescomplemented
270C4×D83—84no—
271C4×D83—84no—
272C4×D83—84no—
273C83⋊C8—22no—
274C83⋊C8—22no—
275C83⋊C8—41no—
276C83⋊C8—41no—
277C22×C83C2×C22⋊Q811yescharacteristic
278C22×C83D4211yescharacteristic
279C22×C83D4×Q811yescharacteristic
280C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C83C2×#13711yescharacteristic
282C22×C83#57611yescharacteristic
283C22×C83#57711yescharacteristic
284C2×D83—24no—
285C2×D83—42no—
286C2×D83—42no—
287C2×D83—42no—
288C2×D83—42no—
289C2×D83—42no—
290C2×D83—42no—
291C4×C83—22no—
292C4×C83—22no—
293C4×C83—22no—
294C4×C83—22no—
295C4×C83—42no—
296C4×C83—41no—
297C4×C83—42no—
298C4×C83—41no—
299C4×C83—81no—
300C4×C83—81no—
301C4×C83C2×C4⋊Q811yescharacteristic
302C4×C83#54411yescharacteristic
303C4×C83#54711yescharacteristic
304C4×C83#55411yescharacteristic
305Dic83—42no—
306Dic83—81no—
307Dic83—81no—
308#26058—831nomaximal, Sylow
309C2×C83#244011yescharacteristic
310C2×C83#307911yescharacteristic
311C2×C83#308111yescharacteristic
312C2×C83#326411yescharacteristic
313C2×C83#326611yescharacteristic
314C2×C83#338411yescharacteristic
315C2×C83#338511yescharacteristic
316D83—44no—
317C2×#476—831no—
318C2×#474—831no—
319#2551D8311yescharacteristic, complemented
320#2349—831no—
321#2088—831no—
322#2087—831no—
323#2058—831no—
324#2057—831no—
325#1949—831no—
326#1940—831no—
327#1864—831no—
328#1862—831no—
329#1847—831no—
330#1802—831no—
331#1762—831no—
332C83#2605811yescharacteristic, complemented, Sylow
333C2×C4⋊Q8—21no—
334C2×C4⋊Q8C2×D8311yescharacteristic
335C2×C4⋊Q8C2×D8311yescharacteristic
336C2×C4×D4—831no—
337C2×C4×D4—831no—
338C2×C4×D4—831no—
339#476—1664no—
340#474—1664no—
341C2×#107—831no—
342C2×#107—831no—
343C2×#107—831no—
344C2×#106—831no—
345C2×#106—831no—
346C2×#106—831no—
347C2×C4⋊C8—831no—
348C2×C4⋊C8—831no—
349C2×C4⋊C8—831no—
350C2×#102—831no—
351C2×#102—831no—
352C2×#102—831no—
353C2×#102—831no—
354C2×#97—831no—
355#395—21no—
356#395—21no—
357#389—21no—
358#389—831no—
359#389—831no—
360#389C2×D8311yescharacteristic
361#389C2×D8311yescharacteristic
362#385—1661no—
363#385—1661no—
364#384C2×D8311yescharacteristic
365#382—831no—
366#380—1661no—
367C4×C4⋊C4C2×D8311yescharacteristic
368C4×C4⋊C4C2×D8311yescharacteristic
369C2×#95—1661no—
370#340—831no—
371#340—831no—
372#340—831no—
373#340—831no—
374#340—831no—
375#340—831no—
376#336—831no—
377#336—831no—
378C22×Q8—21no—
379C22×Q8—21no—
380C22×D4—831no—
381C23×C4—1661no—
382C23×C4—1661no—
383C23×C4—1661no—
384C22×C8—831no—
385C22×C8—831no—
386C22×C8—831no—
387C22×C8—831no—
388C4⋊Q8—22no—
389C4⋊Q8—22no—
390C4⋊Q8—41no—
391C4⋊Q8—41no—
392C4⋊Q8—44no—
393C4×D4—3321no—
394C4×D4—3321no—
395C4×D4—834no—
396C4×D4—1662no—
397C4×D4—1662no—
398C4×D4—1662no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—831no—
406C2×C4⋊C4—831no—
407C2×C4⋊C4—831no—
408C2×C4⋊C4—1661no—
409C2×C4⋊C4—1661no—
410C2×C4⋊C4C22⋊D8311yescharacteristic
411C2×C4⋊C4C22⋊D8311yescharacteristic
412C2×C4⋊C4C22×D8311yescharacteristic
413C2×C4⋊C4C22×D8311yescharacteristic
414C2×C4⋊C4C22×D8311yescharacteristic
415C2×C4⋊C4C22×D8311yescharacteristic
416C2×C22⋊C4—1661no—
417C2×C22⋊C4—1661no—
418C2×C22⋊C4—1661no—
419C2×C42—21no—
420C2×C42C22×D8311yescharacteristic
421C2×C42C22×D8311yescharacteristic
422C2×C42C22×D8311yescharacteristic
423#107—3321no—
424#107—1662no—
425#107—1662no—
426#106—3321no—
427#106—1662no—
428#106—1662no—
429C4⋊C8—1662no—
430C4⋊C8—1662no—
431C4⋊C8—1662no—
432#102—834no—
433#102—834no—
434#102—1662no—
435#102—1662no—
436#97—1662no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—1661no—
441#95—1661no—
442#95—1661no—
443#95—1661no—
444#95C22⋊D8311yescharacteristic
445#95C22⋊D8311yescharacteristic
446C24—1661no—
447C2×Q8—42no—
448C2×Q8—42no—
449C2×Q8—42no—
450C2×Q8—42no—
451C2×Q8—81no—
452C2×Q8—81no—
453C2×D4—832no—
454C2×D4—832no—
455C2×D4—832no—
456C2×D4—1661no—
457C2×D4—1661no—
458C2×D4—1661no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—3322no—
464C22×C4—3322no—
465C22×C4—3322no—
466C22×C4—3322no—
467C22×C4—6641no—
468C22×C4—6641no—
469C22×C4—6641no—
470C22×C4—6641no—
471C22×C4—1661no—
472C22×C4—1661no—
473C22×C4—1661no—
474C22×C4—1664no—
475C22×C4C2×C22⋊D8311yescharacteristic
476C22×C4C2×C22⋊D8311yescharacteristic
477C22×C4C2×C22⋊D8311yescharacteristic
478C22×C4C2×C22⋊D8311yescharacteristic
479C22×C4C2×C22⋊D8311yescharacteristic
480C22×C4C2×C22⋊D8311yescharacteristic
481C22×C4C23×D8311yescharacteristic
482C2×C8—832no—
483C2×C8—832no—
484C2×C8—1661no—
485C2×C8—1661no—
486C2×C8—1661no—
487C2×C8—1661no—
488C2×C8—1661no—
489C2×C8—1661no—
490C2×C8—1661no—
491C2×C8—1661no—
492C2×C8—1661no—
493C2×C8—1661no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—81no—
508C4⋊C4—832no—
509C4⋊C4—6641no—
510C4⋊C4—6641no—
511C4⋊C4—1661no—
512C4⋊C4—1661no—
513C4⋊C4—1661no—
514C4⋊C4—1661no—
515C4⋊C4—1661no—
516C4⋊C4D4×D8312yes—
517C4⋊C4Q8×D8312yes—
518C22⋊C4—3322no—
519C22⋊C4—3322no—
520C22⋊C4—1664no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—42no—
526C42Q8×D8312yes—
527C42#1305059112yes—
528C23—3321no—
529C23—3321no—
530C23—3321no—
531C23—3321no—
532C23—1662no—
533C23—1662no—
534C23—1662no—
535C23C22×C22⋊D8311yescharacteristic
536Q8—84no—
537Q8—84no—
538D4—834no—
539D4—1662no—
540D4—1662no—
541D4—1662no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—3321no—
569C2×C4—3321no—
570C2×C4—3321no—
571C2×C4—3321no—
572C2×C4—3321no—
573C2×C4—3321no—
574C2×C4—3321no—
575C2×C4—3321no—
576C2×C4—6644no—
577C2×C4—6644no—
578C2×C4—6644no—
579C2×C4—1662no—
580C2×C4#1458176812yes—
581C2×C4#1458176812yes—
582C2×C4#1458181812yes—
583C2×C4#1458182312yes—
584C2×C4C2×D4×D8311yescharacteristic
585C2×C4C2×Q8×D8311yescharacteristic
586C2×C4C2×Q8×D8311yescharacteristic
587C2×C4C2×#1305059111yescharacteristic
588C2×C4#1458183711yescharacteristic
589C2×C4#1458184011yescharacteristic
590C8—3321no—
591C8—3321no—
592C8—1662no—
593C8—1662no—
594C22—3322no—
595C22—3322no—
596C22—3322no—
597C22—3322no—
598C22—3322no—
599C22—3322no—
600C22—1664no—
601C22C2×#1458176811yescharacteristic
602C22D4×C22⋊D8311yescharacteristic
603C22Q8×C22⋊D8311yescharacteristic
604C22C2×#1458181811yescharacteristic
605C22C2×#1458182311yescharacteristic
606C22#1912850411yescharacteristic
607C22#1912850911yescharacteristic
608C4—22no—
609C4—22no—
610C4—22no—
611C4—22no—
612C4—42no—
613C4—41no—
614C4—42no—
615C4—41no—
616C4—81no—
617C4—81no—
618C4—3322no—
619C4—6641no—
620C4—6641no—
621C4C4⋊Q8×D8311yescharacteristic
622C4#1912832811yescharacteristic
623C4#1912835411yescharacteristic
624C4#1912841211yescharacteristic
625C2—3324no—
626C2#2491116111yescharacteristic
627C2#2491727211yescharacteristic
628C2#2491728811yescharacteristic
629C2#2491893911yescharacteristic
630C2#2491897411yescharacteristic
631C2#2492035811yescharacteristic
632C2#2492036911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#2551C2
socleC23×C83C22×D4
prime radicalC22×D332C23
hypercenter#2551D83
hypocenterC83#26058
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2551

Complements

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

NH ≅ G/Ntype
4. #24908964C2semidirect
5. #24908959C2semidirect
6. #24908793C2semidirect
7. #24908788C2semidirect
8. #24908231C2semidirect
9. #24908187C2semidirect
12. #24907629C2semidirect
15. C83×#2551C2semidirect
74. C4×D332Q8semidirect
95. #14581712Q8semidirect
269. D332C4⋊Q8semidirect
319. #2551D83semidirect
332. C83#26058semidirect

Maximal subgroups

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

subgroupindex
C2×#191279882
C2×#191279782
#249103742
#249089642
#249089592
#249087932
#249087882
#249082312
#249081872
#249077232
#249077092
#249076292
#249074602
#249072912
C83×#25512
#2605883