Finite Group Databasebeta

← #35416737

Subgroups — #35416737

Order 21248.

628 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24916404C211yesmaximal, characteristic, complemented
2#24916114C211yesmaximal, characteristic
3#24908408C211yesmaximal, characteristic, complemented
4#24908239C211yesmaximal, characteristic, complemented
5#24908217C211yesmaximal, characteristic, complemented
6#24908212C211yesmaximal, characteristic, complemented
7#24908176C211yesmaximal, characteristic
8#24908169C211yesmaximal, characteristic
9#24908113C211yesmaximal, characteristic
10#24908113C211yesmaximal, characteristic
11#24908064C211yesmaximal, characteristic, complemented
12#24908064C211yesmaximal, characteristic, complemented
13#24907483C211yesmaximal, characteristic
14#24907340C211yesmaximal, characteristic, complemented
15C83×#3076C211yesmaximal, characteristic
16#19127832—21no—
17#19127832—21no—
18#19127832—21no—
19#19127832—21no—
20#19127762—21no—
21#19127762—21no—
22#19127758—21no—
23#19127758—21no—
24C2×#14581728C2211yescharacteristic
25C2×#14581728C2211yescharacteristic
26#19127728C2211yescharacteristic
27#19127728C2211yescharacteristic
28#19127728C2211yescharacteristic
29#19127728C2211yescharacteristic
30#19127725C2211yescharacteristic
31C2×#14581719C2211yescharacteristic
32C2×#14581719C2211yescharacteristic
33#19127668C2211yescharacteristic
34#19127668C2211yescharacteristic
35#19127657C2211yescharacteristic
36#19127657C2211yescharacteristic
37C4×#13050574C2211yescharacteristic
38C2×#14581703C2211yescharacteristic
39C2×#14581702C2211yescharacteristic
40C2×C8×Dic83C2211yescharacteristic
41C4×C4⋊Dic83C2211yescharacteristic
42#19127466C2211yescharacteristic
43#19127466C2211yescharacteristic
44#19127460C2211yescharacteristic
45#19127460C2211yescharacteristic
46#19127460C2211yescharacteristic
47#19127460C2211yescharacteristic
48#19127460C2211yescharacteristic
49#19127460C2211yescharacteristic
50#19127455C2211yescharacteristic
51#19127455C2211yescharacteristic
52#533×C83C2211yescharacteristic
53C4×#41×C83C2211yescharacteristic
54#479×C83C411yescharacteristic, complemented
55#479×C83C411yescharacteristic, complemented
56#478×C83C411yescharacteristic, complemented
57#478×C83C411yescharacteristic, complemented
58#477×C83C411yescharacteristic, complemented
59#476×C83C411yescharacteristic, complemented
60#475×C83C411yescharacteristic, complemented
61#474×C83C411yescharacteristic, complemented
62#427×C83C2211yescharacteristic
63#427×C83C2211yescharacteristic
64C2×C4⋊C8×C83C2211yescharacteristic
65#416×C83C2211yescharacteristic
66#416×C83C2211yescharacteristic
67C2×#13050574C2311yescharacteristic
68C2×#13050574C2311yescharacteristic
69C2×#13050574C2311yescharacteristic
70C2×#13050574C2311yescharacteristic
71C22×C83⋊C8C2311yescharacteristic
72C22×C83⋊C8C2311yescharacteristic
73C2×C4⋊Dic83—21no—
74C2×C4×Dic83C2311yescharacteristic
75C2×C4×Dic83C2311yescharacteristic
76#14581728—41no—
77#14581728—41no—
78C4⋊(C83⋊C8)—21no—
79C4⋊(C83⋊C8)—21no—
80C4⋊(C83⋊C8)—21no—
81C4⋊(C83⋊C8)—21no—
82C4⋊(C83⋊C8)—21no—
83C4⋊(C83⋊C8)—21no—
84C4⋊(C83⋊C8)—21no—
85C4⋊(C83⋊C8)—21no—
86C4⋊(C83⋊C8)—21no—
87C4⋊(C83⋊C8)—21no—
88#14581719—41no—
89#14581719—41no—
90C22⋊(C83⋊C8)—21no—
91C22⋊(C83⋊C8)—21no—
92C22⋊(C83⋊C8)—21no—
93C22⋊(C83⋊C8)—21no—
94#14581703—21no—
95#14581703—21no—
96#14581703—21no—
97#14581703D411yescharacteristic
98#14581703D411yescharacteristic
99#14581703D411yescharacteristic
100#14581703D411yescharacteristic
101#14581702—41no—
102C4×C83⋊C8—21no—
103C4×C83⋊C8—21no—
104C4×C83⋊C8—21no—
105C8×Dic83—41no—
106C83⋊#95—21no—
107C2×#41×C83C2311yescharacteristic
108C22×C8×C83C2311yescharacteristic
109C22×C8×C83C2311yescharacteristic
110C4⋊Q8×C83C2×C411yescharacteristic
111C4⋊Q8×C83C2×C411yescharacteristic
112#125×C83C2×C411yescharacteristic
113#125×C83C2×C411yescharacteristic
114C22⋊Q8×C83—21no—
115C22⋊Q8×C83—21no—
116C4×Q8×C83—21no—
117C4×Q8×C83—21no—
118C4×Q8×C83C2×C411yescharacteristic
119C4×Q8×C83C2×C411yescharacteristic
120C4×D4×C83—21no—
121C4×D4×C83—21no—
122C4×D4×C83C2×C411yescharacteristic
123C4×D4×C83C2×C411yescharacteristic
124#117×C83—21no—
125#117×C83C2311yescharacteristic
126#117×C83C2311yescharacteristic
127#117×C83C2311yescharacteristic
128C2×C42×C83—21no—
129C2×C42×C83C2311yescharacteristic
130#107×C83C2×C411yescharacteristic
131#107×C83C2×C411yescharacteristic
132#107×C83C2×C411yescharacteristic
133#107×C83C2×C411yescharacteristic
134#106×C83C2×C411yescharacteristic
135#106×C83C2×C411yescharacteristic
136#106×C83C2×C411yescharacteristic
137#106×C83C2×C411yescharacteristic
138C4⋊C8×C83C2×C411yescharacteristic
139C4⋊C8×C83C2×C411yescharacteristic
140C4⋊C8×C83C2×C411yescharacteristic
141C4⋊C8×C83C2×C411yescharacteristic
142#103×C83C2×C411yescharacteristic
143#103×C83C2×C411yescharacteristic
144#103×C83C2×C411yescharacteristic
145#103×C83C2×C411yescharacteristic
146#102×C83C2×C411yescharacteristic
147#102×C83C2×C411yescharacteristic
148#102×C83C2×C411yescharacteristic
149#102×C83C2×C411yescharacteristic
150C22×Dic83—21no—
151C22×Dic83—21no—
152#13050574—21no—
153#13050574—21no—
154#13050574—21no—
155#13050574—21no—
156#13050574—21no—
157#13050574—21no—
158#13050574—21no—
159#13050574—21no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—21no—
163C2×C83⋊C8—21no—
164C2×C83⋊C8—21no—
165C2×C83⋊C8—21no—
166C2×C83⋊C8—21no—
167C2×C83⋊C8—21no—
168C2×C83⋊C8C2×D411yescharacteristic
169C2×C83⋊C8C2×D411yescharacteristic
170C2×C83⋊C8C2×D411yescharacteristic
171C2×C83⋊C8C2×D411yescharacteristic
172C4⋊Dic83—42no—
173C4×Dic83—21no—
174C4×Dic83—21no—
175C4×Dic83—21no—
176C4×Dic83—21no—
177#41×C83—21no—
178#41×C83—21no—
179#41×C83—21no—
180#41×C83—21no—
181C2×Q8×C83—21no—
182C2×Q8×C83—21no—
183C2×Q8×C83C22×C411yescharacteristic
184C2×D4×C83—21no—
185C2×D4×C83C22×C411yescharacteristic
186C22×C4×C83—21no—
187C22×C4×C83—21no—
188C22×C4×C83—21no—
189C22×C4×C83#4111yescharacteristic
190C22×C4×C83#4111yescharacteristic
191C22×C4×C83C2411yescharacteristic
192C2×C8×C83—21no—
193C2×C8×C83—21no—
194C2×C8×C83—21no—
195C2×C8×C83—21no—
196C2×C8×C83C22×C411yescharacteristic
197C2×C8×C83C22×C411yescharacteristic
198C2×C8×C83C22×C411yescharacteristic
199C2×C8×C83C22×C411yescharacteristic
200C4⋊C4×C83—21no—
201C4⋊C4×C83—21no—
202C4⋊C4×C83—21no—
203C4⋊C4×C83—21no—
204C4⋊C4×C83—21no—
205C4⋊C4×C83—21no—
206C4⋊C4×C83—21no—
207C4⋊C4×C83—21no—
208C4⋊C4×C83C22×C411yescharacteristic
209C4⋊C4×C83C22×C411yescharacteristic
210C4⋊C4×C83C22×C411yescharacteristic
211C4⋊C4×C83C22×C411yescharacteristic
212C4⋊C4×C83C22×C411yescharacteristic
213C4⋊C4×C83C22×C411yescharacteristic
214C22⋊C4×C83—21no—
215C22⋊C4×C83—21no—
216C22⋊C4×C83—21no—
217C22⋊C4×C83—21no—
218C22⋊C4×C83—21no—
219C42×C83—21no—
220C42×C83—21no—
221C42×C83—21no—
222C42×C83—21no—
223C42×C83—21no—
224C42×C83C22×C411yescharacteristic
225C42×C83C22×C411yescharacteristic
226C42×C83C2×D411yescharacteristic
227C42×C83C2×D411yescharacteristic
228C23×C83—21no—
229C23×C83C2×#4111yescharacteristic
230Q8×C83—21no—
231Q8×C83—21no—
232Q8×C83—81no—
233Q8×C83—81no—
234D4×C83—21no—
235D4×C83—21no—
236D4×C83—41no—
237D4×C83—41no—
238C2×C4×C83—21no—
239C2×C4×C83—21no—
240C2×C4×C83—21no—
241C2×C4×C83—21no—
242C2×C4×C83—21no—
243C2×C4×C83—21no—
244C2×C4×C83—21no—
245C2×C4×C83—41no—
246C2×C4×C83—41no—
247C2×C4×C83—41no—
248C2×C4×C83—41no—
249C2×C4×C83—81no—
250C2×C4×C83—81no—
251C2×C4×C83C4×D411yescharacteristic
252C2×C4×C83C4×D411yescharacteristic
253C2×C4×C83C4×D411yescharacteristic
254C2×C4×C83C4×D411yescharacteristic
255C2×C4×C83C23×C411yescharacteristic
256C2×C4×C83C22×D411yescharacteristic
257C2×C4×C83H(5,𝔽2)11yescharacteristic
258C2×C4×C832−1+411yescharacteristic
259C2×C4×C832−1+411yescharacteristic
260C2×C4×C832−1+411yescharacteristic
261C2×Dic83—22no—
262C2×Dic83—41no—
263C2×Dic83—41no—
264C2×Dic83—41no—
265C2×Dic83—41no—
266C2×Dic83—41no—
267C8×C83—21no—
268C8×C83—21no—
269C8×C83—21no—
270C8×C83—21no—
271C83⋊C8—21no—
272C83⋊C8—21no—
273C83⋊C8—21no—
274C83⋊C8—21no—
275C83⋊C8—41no—
276C83⋊C8—41no—
277C83⋊C8—41no—
278C83⋊C8—41no—
279C22×C83—21no—
280C22×C83—21no—
281C22×C83—41no—
282C22×C83—41no—
283C22×C83—41no—
284C22×C83C2×C4×D411yescharacteristic
285C22×C83#54111yescharacteristic
286C22×C83#54211yescharacteristic
287C4×C83—21no—
288C4×C83—21no—
289C4×C83—21no—
290C4×C83—21no—
291C4×C83—41no—
292C4×C83—41no—
293C4×C83—41no—
294C4×C83—41no—
295C4×C83—41no—
296C4×C83—41no—
297C4×C83—41no—
298C4×C83#51911yescharacteristic
299C4×C83#52011yescharacteristic
300C4×C83#53611yescharacteristic
301C4×C83#53711yescharacteristic
302Dic83—42no—
303Dic83—81no—
304#22132—831nomaximal, Sylow
305C2×C83—21no—
306C2×C83—21no—
307C2×C83—81no—
308C2×C83#232311yescharacteristic
309C2×C83#295611yescharacteristic
310C2×C83#295711yescharacteristic
311#3076D8311yescharacteristic
312#2961—831no—
313#2923—831no—
314#1986—831no—
315#1950—831no—
316#1946—831no—
317#1945—831no—
318#1938—831no—
319#1937—831no—
320#1929—831no—
321#1929—831no—
322#1922—831no—
323#1922—831no—
324#1806—831no—
325#1771—831no—
326C83#2213211yescharacteristic, complemented, Sylow
327#533C2×D8311yescharacteristic
328C4×#41C2×D8311yescharacteristic
329#479Dic8311yescharacteristic, complemented
330#479Dic8311yescharacteristic, complemented
331#478Dic8311yescharacteristic, complemented
332#478Dic8311yescharacteristic, complemented
333#477Dic8311yescharacteristic, complemented
334#476Dic8311yescharacteristic, complemented
335#475Dic8311yescharacteristic, complemented
336#474Dic8311yescharacteristic, complemented
337#446—1661no—
338#446—1661no—
339#446—1661no—
340#446—1661no—
341#433—1661no—
342#433—1661no—
343#432—1661no—
344#432—1661no—
345C2×#108—831no—
346C2×#108—831no—
347#427C2×D8311yescharacteristic
348#427C2×D8311yescharacteristic
349#424—831no—
350#424—831no—
351#424—831no—
352#424—831no—
353#423—831no—
354C2×C4⋊C8C2×D8311yescharacteristic
355C2×#104—831no—
356C2×#104—831no—
357#416C2×D8311yescharacteristic
358#416C2×D8311yescharacteristic
359#408—831no—
360#408—831no—
361#405—831no—
362#405—831no—
363C4×M16—831no—
364C2×#97—831no—
365C2×#97—831no—
366C2×C4×C8—831no—
367C4×C4⋊C4—831no—
368#341—831no—
369#341—831no—
370#339—831no—
371#339—831no—
372#339—831no—
373#339—831no—
374#339—831no—
375#339—831no—
376#336—831no—
377#336—831no—
378C2×#41C22×D8311yescharacteristic
379C2×M16—831no—
380C2×M16—831no—
381C2×M16—831no—
382C2×M16—831no—
383C22×C8—831no—
384C22×C8—831no—
385C22×C8C22×D8311yescharacteristic
386C22×C8C22×D8311yescharacteristic
387C4⋊Q8C2×Dic8311yescharacteristic
388C4⋊Q8C2×Dic8311yescharacteristic
389#125C2×Dic8311yescharacteristic
390#125C2×Dic8311yescharacteristic
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8C2×Dic8311yescharacteristic
396C4×Q8C2×Dic8311yescharacteristic
397C4×D4—21no—
398C4×D4—21no—
399C4×D4C2×Dic8311yescharacteristic
400C4×D4C2×Dic8311yescharacteristic
401#117—21no—
402#117C22×D8311yescharacteristic
403#117C22×D8311yescharacteristic
404#117C22×D8311yescharacteristic
405C2×C4⋊C4—1661no—
406C2×C42—21no—
407C2×C42—831no—
408C2×C42—831no—
409C2×C42C22×D8311yescharacteristic
410#108—3321no—
411#108—3321no—
412#107C2×Dic8311yescharacteristic
413#107C2×Dic8311yescharacteristic
414#107C2×Dic8311yescharacteristic
415#107C2×Dic8311yescharacteristic
416#106C2×Dic8311yescharacteristic
417#106C2×Dic8311yescharacteristic
418#106C2×Dic8311yescharacteristic
419#106C2×Dic8311yescharacteristic
420C4⋊C8—1661no—
421C4⋊C8—1661no—
422C4⋊C8—1661no—
423C4⋊C8—1661no—
424C4⋊C8—1661no—
425C4⋊C8—1661no—
426C4⋊C8—1661no—
427C4⋊C8—1661no—
428C4⋊C8—1661no—
429C4⋊C8—1661no—
430C4⋊C8C2×Dic8311yescharacteristic
431C4⋊C8C2×Dic8311yescharacteristic
432C4⋊C8C2×Dic8311yescharacteristic
433C4⋊C8C2×Dic8311yescharacteristic
434#104—3321no—
435#104—3321no—
436#103C2×Dic8311yescharacteristic
437#103C2×Dic8311yescharacteristic
438#103C2×Dic8311yescharacteristic
439#103C2×Dic8311yescharacteristic
440#102C2×Dic8311yescharacteristic
441#102C2×Dic8311yescharacteristic
442#102C2×Dic8311yescharacteristic
443#102C2×Dic8311yescharacteristic
444C22⋊C8—1661no—
445C22⋊C8—1661no—
446C22⋊C8—1661no—
447C22⋊C8—1661no—
448#97—3321no—
449#97—831no—
450#97—831no—
451#97—831no—
452#97—831no—
453#97—1661no—
454#97—1661no—
455#97—1661no—
456C4×C8—3321no—
457C4×C8—1661no—
458C4×C8—1661no—
459C4×C8—1661no—
460#95—1661no—
461#41—21no—
462#41—21no—
463#41—21no—
464#41—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8C22×Dic8311yescharacteristic
468C2×D4—21no—
469C2×D4C22×Dic8311yescharacteristic
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—1661no—
474C22×C4—1661no—
475C22×C4#1305058911yescharacteristic
476C22×C4#1305058911yescharacteristic
477C22×C4C23×D8311yescharacteristic
478M16—1661no—
479M16—1661no—
480M16—1661no—
481M16—1661no—
482M16—1661no—
483M16—1661no—
484M16—1661no—
485M16—1661no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—831no—
491C2×C8—831no—
492C2×C8—831no—
493C2×C8—831no—
494C2×C8—1661no—
495C2×C8—1661no—
496C2×C8—1661no—
497C2×C8—1661no—
498C2×C8—1661no—
499C2×C8—1661no—
500C2×C8—1661no—
501C2×C8—1661no—
502C2×C8C22×Dic8311yescharacteristic
503C2×C8C22×Dic8311yescharacteristic
504C2×C8C22×Dic8311yescharacteristic
505C2×C8C22×Dic8311yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—3322no—
515C4⋊C4C22×Dic8311yescharacteristic
516C4⋊C4C22×Dic8311yescharacteristic
517C4⋊C4C22×Dic8311yescharacteristic
518C4⋊C4C22×Dic8311yescharacteristic
519C4⋊C4C22×Dic8311yescharacteristic
520C4⋊C4C22×Dic8311yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—1661no—
532C42—1661no—
533C42—1661no—
534C42—1661no—
535C42C22×Dic8311yescharacteristic
536C42C22×Dic8311yescharacteristic
537C42D4×D8311yescharacteristic
538C42D4×D8311yescharacteristic
539C23—21no—
540C23C2×#1305058911yescharacteristic
541Q8—21no—
542Q8—21no—
543Q8—81no—
544Q8—81no—
545D4—21no—
546D4—21no—
547D4—41no—
548D4—41no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—3321no—
563C2×C4—3321no—
564C2×C4—3321no—
565C2×C4—3321no—
566C2×C4—3321no—
567C2×C4—1662no—
568C2×C4D4×Dic8311yescharacteristic
569C2×C4D4×Dic8311yescharacteristic
570C2×C4D4×Dic8311yescharacteristic
571C2×C4D4×Dic8311yescharacteristic
572C2×C4C23×Dic8311yescharacteristic
573C2×C4C2×D4×D8311yescharacteristic
574C2×C4#1458183811yescharacteristic
575C2×C4#1458183911yescharacteristic
576C2×C4#1458184011yescharacteristic
577C2×C4#1458184011yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—3321no—
583C8—3321no—
584C8—3321no—
585C8—3321no—
586C8—1661no—
587C8—1661no—
588C8—1661no—
589C8—1661no—
590C22—21no—
591C22—21no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22C2×D4×Dic8311yescharacteristic
596C22#1912831111yescharacteristic
597C22#1912832411yescharacteristic
598C4—21no—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—3322no—
610C4—6641no—
611C4#1912817911yescharacteristic
612C4#1912818411yescharacteristic
613C4#1912827411yescharacteristic
614C4#1912828111yescharacteristic
615C2—21no—
616C2—21no—
617C2—81no—
618C2#2491014711yescharacteristic
619C2#2491637311yescharacteristic
620C2#2491638011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#3076C2
socleC22×C83C2×C4×D4
prime radicalC2×#41×C83C23
cosocleC22×C4×C83C24
hypercenter#3076D83
hypocenterC83#22132
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #24916404C2semidirect
3. #24908408C2semidirect
4. #24908239C2semidirect
5. #24908217C2semidirect
6. #24908212C2semidirect
11. #24908064C2semidirect
12. #24908064C2semidirect
14. #24907340C2semidirect
54. #479×C83C4semidirect
55. #479×C83C4semidirect
56. #478×C83C4semidirect
57. #478×C83C4semidirect
58. #477×C83C4semidirect
59. #476×C83C4semidirect
60. #475×C83C4semidirect
61. #474×C83C4semidirect
326. C83#22132semidirect
329. #479Dic83semidirect
330. #479Dic83semidirect
331. #478Dic83semidirect
332. #478Dic83semidirect
333. #477Dic83semidirect
334. #476Dic83semidirect
335. #475Dic83semidirect
336. #474Dic83semidirect

Maximal subgroups

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

subgroupindex
#249164042
#249161142
#249084082
#249082392
#249082172
#249082122
#249081762
#249081692
#249081132
#249080642
#249074832
#249073402
C83×#30762
#2213283