Finite Group Databasebeta

← #35374496

Subgroups — #35374496

Order 21248.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24916574C211yesmaximal, characteristic, complemented
2#24916539C211yesmaximal, characteristic, complemented
3#24906342C211yesmaximal, characteristic, complemented
4#24906328C211yesmaximal, characteristic, complemented
5#24906307C211yesmaximal, characteristic, complemented
6#24906293C211yesmaximal, characteristic, complemented
7#24906287C211yesmaximal, characteristic, complemented
8SD16⋊(C83⋊C8)C211yesmaximal, characteristic, complemented
9SD16×C83⋊C8C211yesmaximal, characteristic, complemented
10D8×C83⋊C8C211yesmaximal, characteristic, complemented
11#24906248C211yesmaximal, characteristic, complemented
12#24905897C211yesmaximal, characteristic, complemented
13#24905862C211yesmaximal, characteristic, complemented
14#24905763C211yesmaximal, characteristic, complemented
15C83×#3106C211yesmaximal, characteristic
16Q8×C83⋊C8C2211yescharacteristic
17Q8×C83⋊C8C2211yescharacteristic
18#19127779C2211yescharacteristic
19#19127779C2211yescharacteristic
20#19127773—21no—
21#19127773—21no—
22D4×C83⋊C8—21no—
23D4×C83⋊C8—21no—
24D4×C83⋊C8C2211yescharacteristic
25D4×C83⋊C8C2211yescharacteristic
26D4×C83⋊C8C2211yescharacteristic
27D4×C83⋊C8C2211yescharacteristic
28#19127758C2211yescharacteristic
29#19127754—21no—
30#19127754C2211yescharacteristic
31#19127754C2211yescharacteristic
32C2×C4⋊(C83⋊C8)—21no—
33C2×C4⋊(C83⋊C8)C2211yescharacteristic
34#19127668—21no—
35#19127668—21no—
36#19127454C2211yescharacteristic
37#19127454C2211yescharacteristic
38#19127452C2211yescharacteristic
39#19127452C2211yescharacteristic
40Q8⋊(C83⋊C8)C2211yescharacteristic
41Q8⋊(C83⋊C8)C2211yescharacteristic
42D4⋊(C83⋊C8)C2211yescharacteristic
43D4⋊(C83⋊C8)C2211yescharacteristic
44D4⋊(C83⋊C8)C2211yescharacteristic
45D4⋊(C83⋊C8)C2211yescharacteristic
46D4⋊(C83⋊C8)C2211yescharacteristic
47D4⋊(C83⋊C8)C2211yescharacteristic
48#19127423C2211yescharacteristic
49#19127423C2211yescharacteristic
50#19127422C2211yescharacteristic
51C8×C83⋊C8C2211yescharacteristic
52#532×C83C2211yescharacteristic
53C4×#41×C83C2211yescharacteristic
54#482×C83C411yescharacteristic
55#482×C83C411yescharacteristic
56#477×C83C411yescharacteristic
57#476×C83C411yescharacteristic
58#460×C83C411yescharacteristic
59#459×C83C411yescharacteristic
60#449×C83C411yescharacteristic
61#449×C83C411yescharacteristic
62C4×SD16×C83C2211yescharacteristic
63C4×SD16×C83C2211yescharacteristic
64C4×D8×C83C2211yescharacteristic
65C4×D8×C83C2211yescharacteristic
66#431×C83C2211yescharacteristic
67C2×#13050574—21no—
68C2×#13050574—21no—
69C22×C83⋊C8—21no—
70C22×C83⋊C8—21no—
71C22×C83⋊C8—21no—
72C22×C83⋊C8—21no—
73C22×C83⋊C8—21no—
74C4⋊(C83⋊C8)—21no—
75C4⋊(C83⋊C8)—21no—
76C4⋊(C83⋊C8)—21no—
77C4⋊(C83⋊C8)—21no—
78C4⋊(C83⋊C8)D411yescharacteristic
79C4⋊(C83⋊C8)D411yescharacteristic
80C4⋊(C83⋊C8)C2311yescharacteristic
81C4⋊(C83⋊C8)C2311yescharacteristic
82C4⋊(C83⋊C8)C2311yescharacteristic
83C4⋊(C83⋊C8)C2311yescharacteristic
84C22⋊(C83⋊C8)—21no—
85C22⋊(C83⋊C8)—21no—
86C22⋊(C83⋊C8)—21no—
87C22⋊(C83⋊C8)—21no—
88C22⋊(C83⋊C8)—21no—
89C22⋊(C83⋊C8)—21no—
90C22⋊(C83⋊C8)—21no—
91C22⋊(C83⋊C8)—21no—
92C22⋊(C83⋊C8)D411yescharacteristic
93C22⋊(C83⋊C8)D411yescharacteristic
94#14581703—21no—
95C4×C83⋊C8—21no—
96C4×C83⋊C8—21no—
97C4×C83⋊C8C2311yescharacteristic
98C4×C83⋊C8C2311yescharacteristic
99C4×C83⋊C8C2311yescharacteristic
100C4×C83⋊C8C2311yescharacteristic
101C2×#41×C83—21no—
102C2×#41×C83C2×C411yescharacteristic
103C2×SD16×C83C2×C411yescharacteristic
104C2×SD16×C83C2×C411yescharacteristic
105C2×D8×C83C2×C411yescharacteristic
106C2×D8×C83C2×C411yescharacteristic
107C4⋊Q8×C83C2×C411yescharacteristic
108#127×C83C2×C411yescharacteristic
109#124×C83—21no—
110#121×C83—21no—
111#121×C83C2×C411yescharacteristic
112#121×C83C2×C411yescharacteristic
113C4×Q8×C83C2×C411yescharacteristic
114C4×Q8×C83C2311yescharacteristic
115C4×D4×C83—21no—
116C4×D4×C83—21no—
117C4×D4×C83—21no—
118C4×D4×C83C2×C411yescharacteristic
119C4×D4×C83C2311yescharacteristic
120C4×D4×C83C2311yescharacteristic
121C4×D4×C83C2311yescharacteristic
122#117×C83—21no—
123#117×C83C2×C411yescharacteristic
124C2×C42×C83—21no—
125C2×C42×C83C2311yescharacteristic
126#107×C83C2×C411yescharacteristic
127#107×C83C2×C411yescharacteristic
128#106×C83C2×C411yescharacteristic
129#106×C83C2×C411yescharacteristic
130C4⋊C8×C83C2×C411yescharacteristic
131C4⋊C8×C83C2×C411yescharacteristic
132#103×C83C2×C411yescharacteristic
133#103×C83C2×C411yescharacteristic
134#102×C83C2×C411yescharacteristic
135#102×C83C2×C411yescharacteristic
136#102×C83C2×C411yescharacteristic
137#102×C83C2×C411yescharacteristic
138#102×C83C2×C411yescharacteristic
139#102×C83C2×C411yescharacteristic
140C22⋊C8×C83C2×C411yescharacteristic
141C22⋊C8×C83C2×C411yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#13050574—81no—
145#13050574—81no—
146C2×C83⋊C8—21no—
147C2×C83⋊C8—21no—
148C2×C83⋊C8—21no—
149C2×C83⋊C8—21no—
150C2×C83⋊C8—21no—
151C2×C83⋊C8—21no—
152C2×C83⋊C8—81no—
153C2×C83⋊C8—81no—
154C2×C83⋊C8—81no—
155C2×C83⋊C8—81no—
156C2×C83⋊C8—81no—
157C2×C83⋊C8C2×D411yescharacteristic
158C2×C83⋊C8C2×D411yescharacteristic
159C2×C83⋊C8C2×D411yescharacteristic
160C2×C83⋊C8C2×D411yescharacteristic
161#41×C83—22no—
162#41×C83—22no—
163#41×C83—81no—
164#41×C83—81no—
165C2×Q8×C83—21no—
166C2×Q8×C83C22×C411yescharacteristic
167C2×D4×C83—21no—
168C2×D4×C83—21no—
169C2×D4×C83—21no—
170C2×D4×C83—21no—
171C2×D4×C83—21no—
172C2×D4×C83C22×C411yescharacteristic
173C2×D4×C83C22×C411yescharacteristic
174C2×D4×C83C22×C411yescharacteristic
175C22×C4×C83—21no—
176C22×C4×C83—21no—
177C22×C4×C83—21no—
178C22×C4×C83—21no—
179C22×C4×C83—21no—
180C22×C4×C83C22×C411yescharacteristic
181C22×C4×C83C2×D411yescharacteristic
182C22×C4×C83#4111yescharacteristic
183SD16×C83—22no—
184SD16×C83—22no—
185D8×C83—22no—
186D8×C83—22no—
187C2×C8×C83C22×C411yescharacteristic
188C2×C8×C83C22×C411yescharacteristic
189C2×C8×C83C22×C411yescharacteristic
190C2×C8×C83C22×C411yescharacteristic
191C4⋊C4×C83—21no—
192C4⋊C4×C83—21no—
193C4⋊C4×C83—21no—
194C4⋊C4×C83C22×C411yescharacteristic
195C4⋊C4×C83C22×C411yescharacteristic
196C4⋊C4×C83C22×C411yescharacteristic
197C4⋊C4×C83C22×C411yescharacteristic
198C22⋊C4×C83—21no—
199C22⋊C4×C83—21no—
200C22⋊C4×C83—21no—
201C22⋊C4×C83—21no—
202C22⋊C4×C83—21no—
203C22⋊C4×C83—21no—
204C22⋊C4×C83—21no—
205C42×C83—21no—
206C42×C83—21no—
207C42×C83—21no—
208C42×C83C22×C411yescharacteristic
209C42×C83C2×D411yescharacteristic
210C42×C83#4111yescharacteristic
211C42×C83C2411yescharacteristic
212C23×C83—21no—
213C23×C83—21no—
214C23×C83—21no—
215C23×C83C4×D411yescharacteristic
216Q8×C83—21no—
217Q8×C83—81no—
218Q8×C83#13112yes—
219D4×C83—24no—
220D4×C83—21no—
221D4×C83—21no—
222D4×C83—21no—
223D4×C83—21no—
224D4×C83—21no—
225D4×C83—81no—
226D4×C83—81no—
227D4×C83—81no—
228D4×C83—81no—
229D4×C83#13112yes—
230C2×C4×C83—24no—
231C2×C4×C83—21no—
232C2×C4×C83—21no—
233C2×C4×C83—21no—
234C2×C4×C83—21no—
235C2×C4×C83—21no—
236C2×C4×C83—21no—
237C2×C4×C83—21no—
238C2×C4×C83—21no—
239C2×C4×C83—21no—
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×C83—81no—
248C2×C4×C83C4×D411yescharacteristic
249C2×C4×C83C4×D411yescharacteristic
250C2×C4×C83C4×D411yescharacteristic
251C2×C4×C83C23×C411yescharacteristic
252C2×C4×C83C22×D411yescharacteristic
253C2×C4×C83C2×#4111yescharacteristic
254C8×C83—21no—
255C8×C83—21no—
256C8×C83—21no—
257C8×C83—21no—
258C83⋊C8—21no—
259C83⋊C8—21no—
260C83⋊C8—21no—
261C83⋊C8—21no—
262C83⋊C8—41no—
263C83⋊C8—41no—
264C83⋊C8—41no—
265C83⋊C8—41no—
266C83⋊C8—41no—
267C83⋊C8—41no—
268C22×C83—21no—
269C22×C83—22no—
270C22×C83—21no—
271C22×C83—21no—
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×C83C2×C4×D411yescharacteristic
281C4×C83—21no—
282C4×C83—22no—
283C4×C83—21no—
284C4×C83—21no—
285C4×C83—21no—
286C4×C83—41no—
287C4×C83—41no—
288C4×C83—41no—
289C4×C83—41no—
290C4×C83C2×#13111yescharacteristic
291C4×C83C2×#13111yescharacteristic
292C4×C83#57611yescharacteristic
293C4×C83#57711yescharacteristic
294#17920—831nomaximal, Sylow
295C2×C83—41no—
296C2×C83—42no—
297C2×C83—81no—
298C2×C83—81no—
299C2×C83#292911yescharacteristic
300C2×C83#294611yescharacteristic
301C2×C83#295711yescharacteristic
302#3106D8311yescharacteristic
303#2988—831no—
304#2981—831no—
305#1588—831no—
306#1586—831no—
307#1583—831no—
308#1581—831no—
309#1580—831no—
310SD16⋊C8—831no—
311C8×SD16—831no—
312C8×D8—831no—
313#1573—831no—
314#1488—831no—
315#1480—831no—
316#1454—831no—
317C83#1792011yescharacteristic, complemented, Sylow
318#532C2×D8311yescharacteristic
319C4×#41C2×D8311yescharacteristic
320#482Dic8311yescharacteristic
321#482Dic8311yescharacteristic
322#477Dic8311yescharacteristic
323#476Dic8311yescharacteristic
324#460Dic8311yescharacteristic
325#459Dic8311yescharacteristic
326#449Dic8311yescharacteristic
327#449Dic8311yescharacteristic
328C8×Q8—831no—
329C8×Q8—831no—
330C4×SD16C2×D8311yescharacteristic
331C4×SD16C2×D8311yescharacteristic
332C4×D8C2×D8311yescharacteristic
333C4×D8C2×D8311yescharacteristic
334#436—831no—
335#436—831no—
336#435—1661no—
337#435—1661no—
338C8×D4—831no—
339C8×D4—831no—
340C8×D4—831no—
341C8×D4—831no—
342C8×D4—1661no—
343C8×D4—1661no—
344#432—831no—
345#431—831no—
346#431—831no—
347#431—1661no—
348#431C2×D8311yescharacteristic
349C2×C4⋊C8—831no—
350C2×C4⋊C8—1661no—
351#408—1661no—
352#408—1661no—
353#335—831no—
354#335—831no—
355#334—831no—
356#334—831no—
357Q8⋊C8—831no—
358Q8⋊C8—831no—
359D4⋊C8—831no—
360D4⋊C8—831no—
361D4⋊C8—831no—
362D4⋊C8—831no—
363D4⋊C8—831no—
364D4⋊C8—831no—
365#322—831no—
366#322—831no—
367#322—831no—
368C82—831no—
369C2×#41—21no—
370C2×#41C2×Dic8311yescharacteristic
371C2×SD16C2×Dic8311yescharacteristic
372C2×SD16C2×Dic8311yescharacteristic
373C2×D8C2×Dic8311yescharacteristic
374C2×D8C2×Dic8311yescharacteristic
375C2×M16—1661no—
376C2×M16—1661no—
377C22×C8—1661no—
378C22×C8—1661no—
379C22×C8—1661no—
380C22×C8—1661no—
381C22×C8—1661no—
382C4⋊Q8C2×Dic8311yescharacteristic
383#127C2×Dic8311yescharacteristic
384#124—21no—
385#121—21no—
386#121C2×Dic8311yescharacteristic
387#121C2×Dic8311yescharacteristic
388C4×Q8C2×Dic8311yescharacteristic
389C4×Q8C22×D8311yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4C2×Dic8311yescharacteristic
394C4×D4C22×D8311yescharacteristic
395C4×D4C22×D8311yescharacteristic
396C4×D4C22×D8311yescharacteristic
397#117—21no—
398#117C2×Dic8311yescharacteristic
399C2×C42—21no—
400C2×C42C22×D8311yescharacteristic
401#107C2×Dic8311yescharacteristic
402#107C2×Dic8311yescharacteristic
403#106C2×Dic8311yescharacteristic
404#106C2×Dic8311yescharacteristic
405C4⋊C8—831no—
406C4⋊C8—831no—
407C4⋊C8—831no—
408C4⋊C8—831no—
409C4⋊C8—831no—
410C4⋊C8—831no—
411C4⋊C8—1661no—
412C4⋊C8—1661no—
413C4⋊C8—1661no—
414C4⋊C8—1661no—
415C4⋊C8C2×Dic8311yescharacteristic
416C4⋊C8C2×Dic8311yescharacteristic
417#103C2×Dic8311yescharacteristic
418#103C2×Dic8311yescharacteristic
419#102C2×Dic8311yescharacteristic
420#102C2×Dic8311yescharacteristic
421#102C2×Dic8311yescharacteristic
422#102C2×Dic8311yescharacteristic
423#102C2×Dic8311yescharacteristic
424#102C2×Dic8311yescharacteristic
425C22⋊C8—831no—
426C22⋊C8—831no—
427C22⋊C8—1661no—
428C22⋊C8—1661no—
429C22⋊C8—1661no—
430C22⋊C8—1661no—
431C22⋊C8—1661no—
432C22⋊C8—1661no—
433C22⋊C8—1661no—
434C22⋊C8—1661no—
435C22⋊C8C2×Dic8311yescharacteristic
436C22⋊C8C2×Dic8311yescharacteristic
437#97—1661no—
438C4×C8—831no—
439C4×C8—831no—
440C4×C8—831no—
441C4×C8—831no—
442C4×C8—1661no—
443C4×C8—1661no—
444C4×C8C22×D8311yescharacteristic
445C4×C8C22×D8311yescharacteristic
446#41—22no—
447#41—22no—
448#41—81no—
449#41—81no—
450C2×Q8—21no—
451C2×Q8C22×Dic8311yescharacteristic
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4C22×Dic8311yescharacteristic
458C2×D4C22×Dic8311yescharacteristic
459C2×D4C22×Dic8311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4C22×Dic8311yescharacteristic
466C22×C4D4×D8311yescharacteristic
467C22×C4#1305058911yescharacteristic
468SD16—22no—
469SD16—22no—
470D8—22no—
471D8—22no—
472M16—6641no—
473M16—6641no—
474C2×C8—831no—
475C2×C8—831no—
476C2×C8—831no—
477C2×C8—831no—
478C2×C8—6641no—
479C2×C8—6641no—
480C2×C8—6641no—
481C2×C8—6641no—
482C2×C8—6641no—
483C2×C8—1661no—
484C2×C8—1661no—
485C2×C8—1661no—
486C2×C8—1661no—
487C2×C8—1661no—
488C2×C8—1661no—
489C2×C8C22×Dic8311yescharacteristic
490C2×C8C22×Dic8311yescharacteristic
491C2×C8C22×Dic8311yescharacteristic
492C2×C8C22×Dic8311yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4C22×Dic8311yescharacteristic
497C4⋊C4C22×Dic8311yescharacteristic
498C4⋊C4C22×Dic8311yescharacteristic
499C4⋊C4C22×Dic8311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42C22×Dic8311yescharacteristic
511C42D4×D8311yescharacteristic
512C42#1305058911yescharacteristic
513C42C23×D8311yescharacteristic
514C23—21no—
515C23—21no—
516C23—21no—
517C23D4×Dic8311yescharacteristic
518Q8—21no—
519Q8—81no—
520Q8#1458179912yes—
521D4—24no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531D4#1458179912yes—
532C2×C4—24no—
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—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—81no—
550C2×C4D4×Dic8311yescharacteristic
551C2×C4D4×Dic8311yescharacteristic
552C2×C4D4×Dic8311yescharacteristic
553C2×C4C23×Dic8311yescharacteristic
554C2×C4C2×D4×D8311yescharacteristic
555C2×C4C2×#1305058911yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—3321no—
561C8—3321no—
562C8—3321no—
563C8—3321no—
564C8—3321no—
565C8—3321no—
566C8—1661no—
567C8—1661no—
568C8—1661no—
569C8—1661no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22C2×D4×Dic8311yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—22no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4C2×#1458179911yescharacteristic
593C4C2×#1458179911yescharacteristic
594C4#1912850511yescharacteristic
595C4#1912851111yescharacteristic
596C2—41no—
597C2—42no—
598C2—81no—
599C2—81no—
600C2#2491615811yescharacteristic
601C2#2491629611yescharacteristic
602C2#2491638011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
Fitting, prime radicalC83×#3106C2
socleC22×C83C2×C4×D4
cosocleC42×C83C24
hypercenter#3106D83
hypocenterC83#17920
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #24916574C2semidirect
2. #24916539C2semidirect
3. #24906342C2semidirect
4. #24906328C2semidirect
5. #24906307C2semidirect
6. #24906293C2semidirect
7. #24906287C2semidirect
8. SD16⋊(C83⋊C8)C2semidirect
9. SD16×C83⋊C8C2semidirect
10. D8×C83⋊C8C2semidirect
11. #24906248C2semidirect
12. #24905897C2semidirect
13. #24905862C2semidirect
14. #24905763C2semidirect
317. C83#17920semidirect

Maximal subgroups

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

subgroupindex
#249165742
#249165392
#249063422
#249063282
#249063072
#249062932
#249062872
SD16⋊(C83⋊C8)2
SD16×C83⋊C82
D8×C83⋊C82
#249062482
#249058972
#249058622
#249057632
C83×#31062
#1792083