Finite Group Databasebeta

← C2×#24910873 #35573109

Subgroups — C2×#24910873 #35573109

Order 21248.

3570 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581773C211yesmaximal, characteristic
2C22×#14581773C211yesmaximal, characteristic
3C22×#14581748C211yesmaximal, characteristic, complemented
4C23×C4⋊Dic83C211yesmaximal, characteristic, complemented
5#24910873C2116yesmaximal, direct product factor
6C2×#19127635C212yesmaximal, complemented
7C2×#19127624C212yesmaximal, complemented
8C2×#19127598C212yesmaximal, complemented
9C2×#19127594C212yesmaximal, complemented
10C2×#19127574C211yesmaximal, characteristic, complemented
11C2×#19127562C211yesmaximal, characteristic, complemented
12C2×#386×C83C211yesmaximal, characteristic
13C24×Dic83C2211yescharacteristic
14C24×Dic83C2211yescharacteristic
15C2×#14581773—28no—
16C2×#14581773—28no—
17C2×#14581773C2218yes—
18C2×#14581773C2218yes—
19C2×#14581748—28no—
20C2×#14581748C2218yescomplemented
21C22×C4⋊Dic83—28no—
22C22×C4⋊Dic83C2212yes—
23C22×C4⋊Dic83C2212yes—
24C22×C4⋊Dic83C2218yescomplemented
25C22×Dic83⋊C4C2212yes—
26C22×Dic83⋊C4C2212yes—
27C22×Dic83⋊C4C2211yescharacteristic
28C22×Dic83⋊C4C2212yes—
29C22×Dic83⋊C4C2211yescharacteristic
30C22×C22⋊Dic83C2211yescharacteristic
31C22×C22⋊Dic83C2211yescharacteristic
32C22×C22⋊Dic83C2212yes—
33C22×C22⋊Dic83C2211yescharacteristic
34C22×C22⋊Dic83C2211yescharacteristic
35C22×C4×Dic83C2212yes—
36#19127635C22116yescomplemented
37#19127624C22116yescomplemented
38#19127598C22116yescomplemented
39#19127594C22116yescomplemented
40#19127574C2218yescomplemented
41#19127562C2218yescomplemented
42C2×C83⋊#95C2212yes—
43C2×C83⋊#95C2212yes—
44C2×C83⋊#95C2212yes—
45C23×D4×C83C2211yescharacteristic
46C24×C4×C83C2211yescharacteristic
47C22×C22⋊C4×C83C2211yescharacteristic
48C22×C22⋊C4×C83C2212yes—
49#386×C83C2218yes—
50C2×#95×C83C2212yes—
51C23×Dic83—24no—
52C23×Dic83—24no—
53C23×Dic83—24no—
54C23×Dic83—24no—
55C23×Dic83—24no—
56C23×Dic83D418yes—
57C23×Dic83C2314yes—
58C23×Dic83C2311yescharacteristic
59C23×Dic83C2311yescharacteristic
60C23×Dic83C2312yes—
61C23×Dic83C2311yescharacteristic
62C23×Dic83C2312yes—
63C23×Dic83C2311yescharacteristic
64C23×Dic83C2314yes—
65#14581773—232no—
66#14581773—232no—
67#14581748—232no—
68C2×C4⋊Dic83—28no—
69C2×C4⋊Dic83—28no—
70C2×C4⋊Dic83—232no—
71C2×C4⋊Dic83C2318yes—
72C2×C4⋊Dic83C2318yes—
73C2×Dic83⋊C4—28no—
74C2×Dic83⋊C4—28no—
75C2×Dic83⋊C4—24no—
76C2×Dic83⋊C4—24no—
77C2×Dic83⋊C4—28no—
78C2×Dic83⋊C4C2318yes—
79C2×Dic83⋊C4C2314yes—
80C2×Dic83⋊C4C2318yes—
81C2×Dic83⋊C4C2318yes—
82C2×Dic83⋊C4C2314yes—
83C2×C22⋊Dic83—28no—
84C2×C22⋊Dic83—24no—
85C2×C22⋊Dic83—24no—
86C2×C22⋊Dic83—24no—
87C2×C22⋊Dic83D418yes—
88C2×C22⋊Dic83C2314yes—
89C2×C22⋊Dic83C2314yes—
90C2×C22⋊Dic83C2318yes—
91C2×C22⋊Dic83C2314yes—
92C2×C22⋊Dic83C2314yes—
93C2×C4×Dic83—28no—
94C2×C4×Dic83C2318yes—
95C83⋊#95C2318yes—
96C83⋊#95C2318yes—
97C83⋊#95C2318yes—
98C25×C83C2311yescharacteristic
99C25×C83C2311yescharacteristic
100C22×D4×C83—24no—
101C22×D4×C83—24no—
102C22×D4×C83—24no—
103C22×D4×C83C2314yes—
104C23×C4×C83—24no—
105C23×C4×C83—28no—
106C23×C4×C83C2314yes—
107C23×C4×C83C2312yes—
108C23×C4×C83C2311yescharacteristic
109C23×C4×C83C2312yes—
110C2×C22⋊C4×C83—24no—
111C2×C22⋊C4×C83—28no—
112C2×C22⋊C4×C83C2314yes—
113C2×C22⋊C4×C83C2318yes—
114#95×C83C2318yes—
115C22×Dic83—232no—
116C22×Dic83—22no—
117C22×Dic83—22no—
118C22×Dic83—28no—
119C22×Dic83—28no—
120C22×Dic83—22no—
121C22×Dic83—22no—
122C22×Dic83—24no—
123C22×Dic83—24no—
124C22×Dic83—28no—
125C22×Dic83—24no—
126C22×Dic83—28no—
127C22×Dic83—24no—
128C22×Dic83—22no—
129C22×Dic83—22no—
130C22×Dic83—28no—
131C22×Dic83—24no—
132C22×Dic83—24no—
133C22×Dic83—24no—
134C22×Dic83—416no—
135C22×Dic83C2×D4116yes—
136C22×Dic83C2×D414yes—
137C22×Dic83C2×D414yes—
138C22×Dic83C2×D418yes—
139C22×Dic83C2414yes—
140C22×Dic83C2412yes—
141C22×Dic83C2412yes—
142C22×Dic83C2412yes—
143C22×Dic83C2412yes—
144C22×Dic83C2414yes—
145C4⋊Dic83—216no—
146C4⋊Dic83—216no—
147Dic83⋊C4—216no—
148Dic83⋊C4—28no—
149Dic83⋊C4—28no—
150Dic83⋊C4—216no—
151Dic83⋊C4—216no—
152C22⋊Dic83—28no—
153C22⋊Dic83—28no—
154C22⋊Dic83—28no—
155C22⋊Dic83—216no—
156C22⋊Dic83C2×D4116yes—
157C4×Dic83—216no—
158C24×C83—24no—
159C24×C83—24no—
160C24×C83—22no—
161C24×C83—22no—
162C24×C83—24no—
163C24×C83—22no—
164C24×C83—24no—
165C24×C83C2×D414yes—
166C24×C83C2×D414yes—
167C24×C83#4114yes—
168C24×C83C2412yes—
169C24×C83C2412yes—
170C24×C83C2411yescharacteristic
171C2×D4×C83—28no—
172C2×D4×C83—28no—
173C2×D4×C83—28no—
174C2×D4×C83—416no—
175C22×C4×C83—232no—
176C22×C4×C83—28no—
177C22×C4×C83—24no—
178C22×C4×C83—24no—
179C22×C4×C83—216no—
180C22×C4×C83—24no—
181C22×C4×C83—22no—
182C22×C4×C83—22no—
183C22×C4×C83—24no—
184C22×C4×C83—22no—
185C22×C4×C83—24no—
186C22×C4×C83#4118yes—
187C22×C4×C83C2412yes—
188C22×C4×C83C2414yes—
189C22×C4×C83C2414yes—
190C22⋊C4×C83—28no—
191C22⋊C4×C83—216no—
192C23×C83—28no—
193C23×C83—28no—
194C23×C83—216no—
195C23×C83—216no—
196C23×C83—24no—
197C23×C83—24no—
198C23×C83—22no—
199C23×C83—22no—
200C23×C83—24no—
201C23×C83—22no—
202C23×C83—24no—
203C23×C83—44no—
204C23×C83—44no—
205C23×C83—44no—
206C23×C83—48no—
207C23×C83—48no—
208C23×C83#121116yes—
209C23×C83C22×D414yes—
210C23×C83C22×D414yes—
211C23×C83C22×D412yes—
212C23×C83C22×D412yes—
213C23×C83C2×#4114yes—
214C23×C83C2×#4114yes—
215C23×C83C2×#4112yes—
216C23×C832−1+414yes—
217C23×C83C2511yescharacteristic
218D4×C83—416no—
219C2×C4×C83—232no—
220C2×C4×C83—216no—
221C2×C4×C83—24no—
222C2×C4×C83—24no—
223C2×C4×C83—24no—
224C2×C4×C83—22no—
225C2×C4×C83—22no—
226C2×C4×C83—24no—
227C2×C4×C83—22no—
228C2×C4×C83—24no—
229C2×C4×C83—44no—
230C2×C4×C83—48no—
231C2×C4×C83C2×#4118yes—
232C2×Dic83—232no—
233C2×Dic83—28no—
234C2×Dic83—28no—
235C2×Dic83—216no—
236C2×Dic83—22no—
237C2×Dic83—22no—
238C2×Dic83—24no—
239C2×Dic83—22no—
240C2×Dic83—22no—
241C2×Dic83—24no—
242C2×Dic83—22no—
243C2×Dic83—22no—
244C2×Dic83—24no—
245C2×Dic83—24no—
246C2×Dic83—24no—
247C2×Dic83—24no—
248C2×Dic83—24no—
249C2×Dic83—416no—
250C2×Dic83—48no—
251C2×Dic83—44no—
252C2×Dic83—44no—
253C2×Dic83C22×D418yes—
254C2×Dic83C22×D414yes—
255C2×Dic83C22×D414yes—
256C22×C83—24no—
257C22×C83—232no—
258C22×C83—24no—
259C22×C83—28no—
260C22×C83—28no—
261C22×C83—42no—
262C22×C83—42no—
263C22×C83—42no—
264C22×C83—44no—
265C22×C83—44no—
266C22×C83—88no—
267C22×C83C2×#12118yes—
268C22×C83C2×#12114yes—
269C22×C83#52514yes—
270C22×C83#53614yes—
271C22×C83#54718yes—
272C22×C83#55218yes—
273C22×C83C23×D411yescharacteristic
274C22×C83C23×D411yescharacteristic
275C22×C83C22×#4112yes—
276C22×C83C22×#4111yescharacteristic
277C22×C83C2×2−1+412yes—
278C4×C83—28no—
279C4×C83—42no—
280C4×C83—44no—
281Dic83—24no—
282Dic83—24no—
283Dic83—28no—
284Dic83—44no—
285Dic83—42no—
286Dic83—42no—
287C2×#2413—831nomaximal, Sylow
288C2×C83—28no—
289C2×C83—82no—
290C2×C83#241318yescomplemented
291C2×C83C22×#12111yescharacteristic
292C2×C83C2×#52511yescharacteristic
293C2×C83C2×#53611yescharacteristic
294C2×C83C2×#54712yes—
295C2×C83C2×#55212yes—
296C22×#123—831no—
297C22×#123—831no—
298C22×#117—831no—
299C23×C4⋊C4—831no—
300#2413—8316no—
301C2×#398—832no—
302C2×#396—832no—
303C2×#389—832no—
304C2×#388—832no—
305C2×#386D8311yescharacteristic
306C2×#385—831no—
307C2×#381—831no—
308C83C2×#241311yescharacteristic, complemented, Sylow
309C23×D4C2×D8311yescharacteristic
310C24×C4—831no—
311C24×C4—831no—
312C24×C4C2×D8311yescharacteristic
313C2×#123—838no—
314C2×#123—838no—
315C2×#123—1668no—
316C2×#123—1668no—
317C2×#117—838no—
318C2×#117—1668no—
319C22×C4⋊C4—832no—
320C22×C4⋊C4—832no—
321C22×C4⋊C4—832no—
322C22×C4⋊C4—831no—
323C22×C4⋊C4—832no—
324C22×C4⋊C4—831no—
325C22×C4⋊C4—832no—
326C22×C4⋊C4—838no—
327C22×C4⋊C4—1668no—
328C22×C22⋊C4—831no—
329C22×C22⋊C4—831no—
330C22×C22⋊C4—832no—
331C22×C22⋊C4—831no—
332C22×C22⋊C4—831no—
333C22×C22⋊C4C2×D8312yes—
334C22×C22⋊C4C2×D8311yescharacteristic
335C22×C42—832no—
336#398—8316no—
337#396—8316no—
338#389—8316no—
339#388—8316no—
340#386C2×D8318yes—
341#385—838no—
342#381—838no—
343C2×#95—832no—
344C2×#95—832no—
345C2×#95—832no—
346C2×#95C2×D8312yes—
347C25C22×D8311yescharacteristic
348C25C22×D8311yescharacteristic
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4C22×D8314yes—
353C23×C4—24no—
354C23×C4—28no—
355C23×C4—838no—
356C23×C4—834no—
357C23×C4—832no—
358C23×C4—831no—
359C23×C4—831no—
360C23×C4—834no—
361C23×C4—831no—
362C23×C4—831no—
363C23×C4—832no—
364C23×C4—1664no—
365C23×C4—1664no—
366C23×C4—1664no—
367C23×C4—1664no—
368C23×C4—1664no—
369C23×C4C22×D8314yes—
370C23×C4C22×D8312yes—
371C23×C4C22×D8311yescharacteristic
372C23×C4C22×D8312yes—
373#123—16632no—
374#123—16632no—
375#117—16632no—
376C2×C4⋊C4—838no—
377C2×C4⋊C4—838no—
378C2×C4⋊C4—838no—
379C2×C4⋊C4—834no—
380C2×C4⋊C4—838no—
381C2×C4⋊C4—834no—
382C2×C4⋊C4—838no—
383C2×C4⋊C4—1668no—
384C2×C4⋊C4—1668no—
385C2×C4⋊C4—16632no—
386C2×C4⋊C4—1668no—
387C2×C4⋊C4—1668no—
388C2×C4⋊C4—1664no—
389C2×C4⋊C4—1664no—
390C2×C4⋊C4—1668no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—838no—
394C2×C22⋊C4—834no—
395C2×C22⋊C4—834no—
396C2×C22⋊C4—834no—
397C2×C22⋊C4—838no—
398C2×C22⋊C4—834no—
399C2×C22⋊C4—1668no—
400C2×C22⋊C4—1664no—
401C2×C22⋊C4—1664no—
402C2×C22⋊C4—1664no—
403C2×C22⋊C4C22×D8314yes—
404C2×C22⋊C4C22×D8318yes—
405C2×C42—838no—
406C2×C42—1668no—
407#95—838no—
408#95—838no—
409#95—838no—
410#95C22×D8318yes—
411C24—24no—
412C24—24no—
413C24—22no—
414C24—22no—
415C24—24no—
416C24—22no—
417C24—24no—
418C24D4×D8314yes—
419C24D4×D8314yes—
420C24#1305059014yes—
421C24C23×D8312yes—
422C24C23×D8312yes—
423C24C23×D8311yescharacteristic
424C2×D4—28no—
425C2×D4—28no—
426C2×D4—28no—
427C2×D4—416no—
428C22×C4—232no—
429C22×C4—28no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—216no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—33216no—
440C22×C4—838no—
441C22×C4—834no—
442C22×C4—834no—
443C22×C4—8316no—
444C22×C4—834no—
445C22×C4—832no—
446C22×C4—832no—
447C22×C4—832no—
448C22×C4—832no—
449C22×C4—834no—
450C22×C4—1662no—
451C22×C4—1662no—
452C22×C4—1664no—
453C22×C4—1668no—
454C22×C4—1664no—
455C22×C4—1668no—
456C22×C4—1664no—
457C22×C4—1668no—
458C22×C4—1664no—
459C22×C4—1664no—
460C22×C4—16632no—
461C22×C4—1662no—
462C22×C4—1662no—
463C22×C4—1668no—
464C22×C4—1664no—
465C22×C4—1668no—
466C22×C4—1662no—
467C22×C4—1662no—
468C22×C4—1664no—
469C22×C4#1305058918yes—
470C22×C4C23×D8314yes—
471C22×C4C23×D8312yes—
472C22×C4C23×D8314yes—
473C4⋊C4—16616no—
474C4⋊C4—16616no—
475C4⋊C4—16616no—
476C4⋊C4—16616no—
477C4⋊C4—1668no—
478C4⋊C4—1668no—
479C4⋊C4—16616no—
480C22⋊C4—28no—
481C22⋊C4—216no—
482C22⋊C4—8316no—
483C22⋊C4—16616no—
484C22⋊C4—1668no—
485C22⋊C4—1668no—
486C22⋊C4—1668no—
487C42—16616no—
488C23—216no—
489C23—216no—
490C23—28no—
491C23—24no—
492C23—28no—
493C23—24no—
494C23—22no—
495C23—22no—
496C23—24no—
497C23—22no—
498C23—24no—
499C23—48no—
500C23—48no—
501C23—44no—
502C23—44no—
503C23—44no—
504C23#14581765116yes—
505C23C2×D4×D8314yes—
506C23C2×D4×D8314yes—
507C23C2×D4×D8312yes—
508C23C2×D4×D8312yes—
509C23C2×#1305058914yes—
510C23C2×#1305059014yes—
511C23C2×#1305059012yes—
512C23#1458183914yes—
513C23C24×D8311yescharacteristic
514D4—416no—
515C2×C4—232no—
516C2×C4—216no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—48no—
526C2×C4—44no—
527C2×C4—33216no—
528C2×C4—3328no—
529C2×C4—3324no—
530C2×C4—3324no—
531C2×C4—838no—
532C2×C4—834no—
533C2×C4—834no—
534C2×C4—1662no—
535C2×C4—1662no—
536C2×C4—1664no—
537C2×C4—1664no—
538C2×C4—1664no—
539C2×C4—1664no—
540C2×C4—1664no—
541C2×C4—16616no—
542C2×C4—16632no—
543C2×C4—1668no—
544C2×C4—1668no—
545C2×C4—1662no—
546C2×C4—1662no—
547C2×C4—1664no—
548C2×C4—1662no—
549C2×C4—1662no—
550C2×C4—1664no—
551C2×C4C2×#1305058918yes—
552C22—232no—
553C22—28no—
554C22—24no—
555C22—28no—
556C22—24no—
557C22—44no—
558C22—42no—
559C22—42no—
560C22—44no—
561C22—42no—
562C22—88no—
563C22C2×#1458176518yes—
564C22C2×#1458176514yes—
565C22#1912820714yes—
566C22#1912827314yes—
567C22#1912835118yes—
568C22#1912839118yes—
569C22C22×D4×D8311yescharacteristic
570C22C22×D4×D8311yescharacteristic
571C22C22×#1305058912yes—
572C22C22×#1305059011yescharacteristic
573C22C2×#1458183912yes—
574C4—28no—
575C4—44no—
576C4—42no—
577C4—3324no—
578C4—3322no—
579C4—3322no—
580C4—1668no—
581C4—1664no—
582C4—1664no—
583C2—28no—
584C2—82no—
585C2#2491087318yesdirect product factor
586C2C22×#1458176511yescharacteristic
587C2C2×#1912820711yescharacteristic
588C2C2×#1912827311yescharacteristic
589C2C2×#1912835112yes—
590C2C2×#1912839112yes—
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#386×C83C2
socleC24×C83C24
prime radicalC23×D4×C83C22
hypercenterC2×#386D83
hypocenterC83C2×#2413
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C22×#14581748C2semidirect
4. C23×C4⋊Dic83C2semidirect
5. #24910873C2direct (N × H)
6. C2×#19127635C2semidirect
7. C2×#19127624C2semidirect
8. C2×#19127598C2semidirect
9. C2×#19127594C2semidirect
10. C2×#19127574C2semidirect
11. C2×#19127562C2semidirect
20. C2×#14581748C22semidirect
24. C22×C4⋊Dic83C22semidirect
36. #19127635C22semidirect
37. #19127624C22semidirect
38. #19127598C22semidirect
39. #19127594C22semidirect
40. #19127574C22semidirect
41. #19127562C22semidirect
290. C2×C83#2413semidirect
308. C83C2×#2413semidirect
585. C2#24910873direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817732
C22×#145817482
C23×C4⋊Dic832
#249108732
C2×#191276352
C2×#191276242
C2×#191275982
C2×#191275942
C2×#191275742
C2×#191275622
C2×#386×C832
C2×#241383