Finite Group Databasebeta

← C2×#24915791 #35610296

Subgroups — C2×#24915791 #35610296

Order 21248.

4070 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581776C211yesmaximal, characteristic, complemented
2C22×#14581773C211yesmaximal, characteristic, complemented
3C22×#14581764C211yesmaximal, characteristic
4C23×C4×Dic83C211yesmaximal, characteristic, complemented
5#24915791C2116yesmaximal, direct product factor
6C2×#19127601C212yesmaximal, complemented
7C2×#19127598C212yesmaximal, complemented
8C2×#19127594C212yesmaximal, complemented
9C2×#19127590C212yesmaximal, complemented
10C2×#19127580C211yesmaximal, characteristic, complemented
11C2×#19127559C211yesmaximal, characteristic, complemented
12C2×#386×C83C211yesmaximal, characteristic, complemented
13C23×C22⋊D83C2211yescharacteristic
14C23×C22⋊D83C2211yescharacteristic
15C24×Dic83C2211yescharacteristic
16C24×Dic83C2211yescharacteristic
17C2×#14581776—28no—
18C2×#14581776C2218yescomplemented
19C2×#14581773—28no—
20C2×#14581773C2218yescomplemented
21C2×#14581764—28no—
22C2×#14581764C2218yes—
23C22×C4⋊Dic83C2212yes—
24C22×Dic83⋊C4C2212yes—
25C22×Dic83⋊C4C2212yes—
26C22×Dic83⋊C4C2211yescharacteristic
27C22×C22⋊Dic83C2211yescharacteristic
28C22×C22⋊Dic83C2211yescharacteristic
29C22×C22⋊Dic83C2212yes—
30C22×(C2×D83)⋊C4C2212yes—
31C22×(C2×D83)⋊C4C2211yescharacteristic
32C22×(C2×D83)⋊C4C2212yes—
33C22×C4×Dic83—28no—
34C22×C4×Dic83C2212yes—
35C22×C4×Dic83C2212yes—
36C22×C4×Dic83C2218yescomplemented
37#19127601C22116yescomplemented
38#19127598C22116yescomplemented
39#19127594C22116yescomplemented
40#19127590C22116yescomplemented
41#19127580C2218yescomplemented
42#19127559C2218yescomplemented
43C2×C83⋊#95C2212yes—
44C2×C83⋊#95C2212yes—
45C23×D4×C83C2211yescharacteristic
46C24×C4×C83C2211yescharacteristic
47C22×C22⋊C4×C83C2211yescharacteristic
48C22×C22⋊C4×C83C2212yes—
49#386×C83C2218yescomplemented
50C2×#95×C83C2212yes—
51C24×D83C2311yescharacteristic
52C22×C22⋊D83—24no—
53C22×C22⋊D83—28no—
54C22×C22⋊D83—24no—
55C22×C22⋊D83—24no—
56C22×C22⋊D83—24no—
57C22×C22⋊D83C2314yes—
58C22×C22⋊D83C2314yes—
59C23×Dic83—28no—
60C23×Dic83—24no—
61C23×Dic83—24no—
62C23×Dic83D418yes—
63C23×Dic83D418yescomplemented
64C23×Dic83C2312yes—
65C23×Dic83C2311yescharacteristic
66C23×Dic83C2314yes—
67C23×Dic83C2312yes—
68C23×Dic83C2311yescharacteristic
69C23×Dic83C2314yes—
70C23×Dic83C2311yescharacteristic
71#14581776—232no—
72#14581773—232no—
73#14581764—232no—
74C2×C4⋊Dic83—28no—
75C2×C4⋊Dic83C2318yes—
76C2×Dic83⋊C4—24no—
77C2×Dic83⋊C4—28no—
78C2×Dic83⋊C4—28no—
79C2×Dic83⋊C4C2318yes—
80C2×Dic83⋊C4C2318yes—
81C2×Dic83⋊C4C2314yes—
82C2×C22⋊Dic83—24no—
83C2×C22⋊Dic83—28no—
84C2×C22⋊Dic83—24no—
85C2×C22⋊Dic83C2314yes—
86C2×C22⋊Dic83C2314yes—
87C2×C22⋊Dic83C2318yes—
88C2×(C2×D83)⋊C4—24no—
89C2×(C2×D83)⋊C4—28no—
90C2×(C2×D83)⋊C4—28no—
91C2×(C2×D83)⋊C4C2318yes—
92C2×(C2×D83)⋊C4C2314yes—
93C2×(C2×D83)⋊C4C2318yes—
94C2×C4×Dic83—28no—
95C2×C4×Dic83—28no—
96C2×C4×Dic83—232no—
97C2×C4×Dic83C2318yes—
98C2×C4×Dic83C2318yes—
99C83⋊#95C2318yes—
100C83⋊#95C2318yes—
101C25×C83C2311yescharacteristic
102C25×C83C2311yescharacteristic
103C22×D4×C83—24no—
104C22×D4×C83—24no—
105C22×D4×C83—24no—
106C22×D4×C83C2314yes—
107C23×C4×C83—24no—
108C23×C4×C83—28no—
109C23×C4×C83C2314yes—
110C23×C4×C83C2312yes—
111C23×C4×C83C2311yescharacteristic
112C23×C4×C83C2312yes—
113C2×C22⋊C4×C83—24no—
114C2×C22⋊C4×C83—28no—
115C2×C22⋊C4×C83C2314yes—
116C2×C22⋊C4×C83C2318yes—
117#95×C83C2318yes—
118C23×D83—22no—
119C23×D83—22no—
120C23×D83—24no—
121C23×D83—22no—
122C23×D83—24no—
123C23×D83C2412yes—
124C2×C22⋊D83—28no—
125C2×C22⋊D83—28no—
126C2×C22⋊D83—28no—
127C2×C22⋊D83—28no—
128C2×C22⋊D83—216no—
129C2×C22⋊D83—416no—
130C2×C22⋊D83—416no—
131C22×Dic83—232no—
132C22×Dic83—24no—
133C22×Dic83—28no—
134C22×Dic83—24no—
135C22×Dic83—24no—
136C22×Dic83—28no—
137C22×Dic83—232no—
138C22×Dic83—216no—
139C22×Dic83—22no—
140C22×Dic83—22no—
141C22×Dic83—24no—
142C22×Dic83—22no—
143C22×Dic83—24no—
144C22×Dic83—24no—
145C22×Dic83C2×D4116yes—
146C22×Dic83C2×D414yes—
147C22×Dic83C2×D418yes—
148C22×Dic83C2×D414yes—
149C22×Dic83C2×D4116yescomplemented
150C22×Dic83#4118yes—
151C22×Dic83C2412yes—
152C22×Dic83C2414yes—
153C22×Dic83C2412yes—
154C22×Dic83C2414yes—
155C22×Dic83C2412yes—
156C4⋊Dic83—216no—
157Dic83⋊C4—28no—
158Dic83⋊C4—216no—
159Dic83⋊C4—216no—
160C22⋊Dic83—28no—
161C22⋊Dic83—28no—
162C22⋊Dic83—216no—
163(C2×D83)⋊C4—216no—
164(C2×D83)⋊C4—28no—
165(C2×D83)⋊C4—216no—
166C4×Dic83—216no—
167C4×Dic83—216no—
168C24×C83—24no—
169C24×C83—24no—
170C24×C83—22no—
171C24×C83—22no—
172C24×C83—24no—
173C24×C83—24no—
174C24×C83—22no—
175C24×C83C2×D414yes—
176C24×C83C2×D414yes—
177C24×C83#4114yes—
178C24×C83C2412yes—
179C24×C83C2412yes—
180C24×C83C2411yescharacteristic
181C2×D4×C83—28no—
182C2×D4×C83—28no—
183C2×D4×C83—28no—
184C2×D4×C83—416no—
185C22×C4×C83—232no—
186C22×C4×C83—28no—
187C22×C4×C83—24no—
188C22×C4×C83—24no—
189C22×C4×C83—216no—
190C22×C4×C83—24no—
191C22×C4×C83—22no—
192C22×C4×C83—22no—
193C22×C4×C83—24no—
194C22×C4×C83—22no—
195C22×C4×C83—24no—
196C22×C4×C83#4118yes—
197C22×C4×C83C2412yes—
198C22×C4×C83C2414yes—
199C22×C4×C83C2414yes—
200C22⋊C4×C83—28no—
201C22⋊C4×C83—216no—
202C23×C83—28no—
203C23×C83—28no—
204C23×C83—216no—
205C23×C83—216no—
206C23×C83—24no—
207C23×C83—24no—
208C23×C83—22no—
209C23×C83—22no—
210C23×C83—24no—
211C23×C83—22no—
212C23×C83—24no—
213C23×C83—44no—
214C23×C83—44no—
215C23×C83—44no—
216C23×C83—48no—
217C23×C83—48no—
218C23×C83#121116yes—
219C23×C83C22×D414yes—
220C23×C83C22×D414yes—
221C23×C83C22×D412yes—
222C23×C83C22×D412yes—
223C23×C83C2×#4114yes—
224C23×C83C2×#4114yes—
225C23×C83C2×#4114yes—
226C23×C83C2×#4112yes—
227C23×C83C2511yescharacteristic
228C22×D83—22no—
229C22×D83—22no—
230C22×D83—24no—
231C22×D83—24no—
232C22×D83—22no—
233C22×D83—44no—
234C22×D83—44no—
235C22×D83—44no—
236C22×D83—48no—
237C22×D83—48no—
238D4×C83—416no—
239C2×C4×C83—232no—
240C2×C4×C83—216no—
241C2×C4×C83—24no—
242C2×C4×C83—24no—
243C2×C4×C83—24no—
244C2×C4×C83—22no—
245C2×C4×C83—22no—
246C2×C4×C83—24no—
247C2×C4×C83—22no—
248C2×C4×C83—24no—
249C2×C4×C83—44no—
250C2×C4×C83—48no—
251C2×C4×C83C2×#4118yes—
252C22⋊D83—416no—
253C22⋊D83—416no—
254C2×Dic83—216no—
255C2×Dic83—232no—
256C2×Dic83—28no—
257C2×Dic83—24no—
258C2×Dic83—24no—
259C2×Dic83—24no—
260C2×Dic83—232no—
261C2×Dic83—24no—
262C2×Dic83—22no—
263C2×Dic83—22no—
264C2×Dic83—24no—
265C2×Dic83—24no—
266C2×Dic83—22no—
267C2×Dic83—44no—
268C2×Dic83—48no—
269C2×Dic83#123116yescomplemented
270C2×Dic83C22×D414yes—
271C2×Dic83C22×D418yes—
272C2×Dic83C22×D414yes—
273C2×Dic83C2×#4118yes—
274C22×C83—232no—
275C22×C83—24no—
276C22×C83—24no—
277C22×C83—28no—
278C22×C83—28no—
279C22×C83—42no—
280C22×C83—42no—
281C22×C83—42no—
282C22×C83—44no—
283C22×C83—44no—
284C22×C83—88no—
285C22×C83C2×#12118yes—
286C22×C83C2×#12114yes—
287C22×C83C2×#12314yes—
288C22×C83#52514yes—
289C22×C83#52918yes—
290C22×C83#53218yes—
291C22×C83C23×D411yescharacteristic
292C22×C83C23×D411yescharacteristic
293C22×C83C22×#4112yes—
294C22×C83C22×#4112yes—
295C22×C83C22×#4111yescharacteristic
296C2×D83—42no—
297C2×D83—42no—
298C2×D83—42no—
299C2×D83—44no—
300C2×D83—44no—
301C2×D83—88no—
302C4×C83—28no—
303C4×C83—42no—
304C4×C83—44no—
305Dic83—28no—
306Dic83—24no—
307Dic83—42no—
308Dic83—44no—
309Dic83C2×#12318yescomplemented
310C2×#2854—831nomaximal, Sylow
311C2×C83—28no—
312C2×C83—82no—
313C2×C83#285418yescomplemented
314C2×C83C22×#12111yescharacteristic
315C2×C83C22×#12311yescharacteristic
316C2×C83C2×#52511yescharacteristic
317C2×C83C2×#52912yes—
318C2×C83C2×#53212yes—
319D83—82no—
320C22×#123—831no—
321C22×#123—831no—
322C22×#121—831no—
323C23×C42—831no—
324#2854—8316no—
325C2×#390—832no—
326C2×#389—832no—
327C2×#388—832no—
328C2×#388—832no—
329C2×#386—831no—
330C2×#386D8311yescharacteristic, complemented
331C2×#380—831no—
332C83C2×#285411yescharacteristic, complemented, Sylow
333C23×D4—831no—
334C23×D4—831no—
335C23×D4C2×D8311yescharacteristic
336C24×C4—831no—
337C24×C4—831no—
338C24×C4C2×D8311yescharacteristic
339C2×#123—838no—
340C2×#123—838no—
341C2×#123—1668no—
342C2×#123—1668no—
343C2×#121—838no—
344C2×#121—1668no—
345C22×C4⋊C4—831no—
346C22×C4⋊C4—832no—
347C22×C4⋊C4—832no—
348C22×C4⋊C4—832no—
349C22×C22⋊C4—831no—
350C22×C22⋊C4—831no—
351C22×C22⋊C4—832no—
352C22×C22⋊C4—831no—
353C22×C22⋊C4—832no—
354C22×C22⋊C4—832no—
355C22×C22⋊C4C2×D8311yescharacteristic
356C22×C22⋊C4C2×D8312yes—
357C22×C42—838no—
358C22×C42—832no—
359C22×C42—832no—
360C22×C42—1668no—
361#390—8316no—
362#389—8316no—
363#388—8316no—
364#388—8316no—
365#386—838no—
366#386C2×D8318yescomplemented
367#380—838no—
368C2×#95—832no—
369C2×#95—832no—
370C2×#95C2×D8312yes—
371C25—831no—
372C25C22×D8311yescharacteristic
373C25C22×D8311yescharacteristic
374C22×D4—24no—
375C22×D4—24no—
376C22×D4—24no—
377C22×D4—834no—
378C22×D4—834no—
379C22×D4—1664no—
380C22×D4—1668no—
381C22×D4—1664no—
382C22×D4—1664no—
383C22×D4—1664no—
384C22×D4C22×D8314yes—
385C23×C4—24no—
386C23×C4—28no—
387C23×C4—831no—
388C23×C4—838no—
389C23×C4—838no—
390C23×C4—834no—
391C23×C4—834no—
392C23×C4—832no—
393C23×C4—831no—
394C23×C4—832no—
395C23×C4—831no—
396C23×C4—1668no—
397C23×C4—1664no—
398C23×C4—1664no—
399C23×C4C22×D8314yes—
400C23×C4C22×D8312yes—
401C23×C4C22×D8311yescharacteristic
402C23×C4C22×D8312yes—
403#123—16632no—
404#123—16632no—
405#121—16632no—
406C2×C4⋊C4—834no—
407C2×C4⋊C4—838no—
408C2×C4⋊C4—838no—
409C2×C4⋊C4—838no—
410C2×C4⋊C4—1664no—
411C2×C4⋊C4—1668no—
412C2×C4⋊C4—1668no—
413C2×C4⋊C4—1668no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—28no—
416C2×C22⋊C4—834no—
417C2×C22⋊C4—834no—
418C2×C22⋊C4—838no—
419C2×C22⋊C4—834no—
420C2×C22⋊C4—838no—
421C2×C22⋊C4—838no—
422C2×C22⋊C4—1664no—
423C2×C22⋊C4—1668no—
424C2×C22⋊C4—1664no—
425C2×C22⋊C4—1668no—
426C2×C22⋊C4—1664no—
427C2×C22⋊C4—1668no—
428C2×C22⋊C4C22×D8314yes—
429C2×C22⋊C4C22×D8318yes—
430C2×C42—838no—
431C2×C42—838no—
432C2×C42—1668no—
433C2×C42—1668no—
434C2×C42—16632no—
435#95—838no—
436#95—838no—
437#95C22×D8318yes—
438C24—24no—
439C24—24no—
440C24—22no—
441C24—22no—
442C24—24no—
443C24—24no—
444C24—22no—
445C24—832no—
446C24—1662no—
447C24—1662no—
448C24—1664no—
449C24—1664no—
450C24—1662no—
451C24D4×D8314yes—
452C24D4×D8314yes—
453C24#1305059014yes—
454C24C23×D8312yes—
455C24C23×D8312yes—
456C24C23×D8311yescharacteristic
457C2×D4—28no—
458C2×D4—28no—
459C2×D4—28no—
460C2×D4—416no—
461C2×D4—33216no—
462C2×D4—33216no—
463C2×D4—1668no—
464C2×D4—16616no—
465C2×D4—1668no—
466C2×D4—1668no—
467C2×D4—1668no—
468C22×C4—232no—
469C22×C4—28no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—216no—
473C22×C4—24no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—834no—
480C22×C4—838no—
481C22×C4—832no—
482C22×C4—834no—
483C22×C4—8316no—
484C22×C4—838no—
485C22×C4—8316no—
486C22×C4—832no—
487C22×C4—834no—
488C22×C4—834no—
489C22×C4—832no—
490C22×C4—1664no—
491C22×C4—1662no—
492C22×C4—1662no—
493C22×C4—1664no—
494C22×C4—1664no—
495C22×C4—1662no—
496C22×C4—16632no—
497C22×C4—16616no—
498C22×C4—16632no—
499C22×C4—1668no—
500C22×C4—1664no—
501C22×C4—1664no—
502C22×C4—1668no—
503C22×C4—1664no—
504C22×C4#1305058918yes—
505C22×C4C23×D8314yes—
506C22×C4C23×D8312yes—
507C22×C4C23×D8314yes—
508C4⋊C4—1668no—
509C4⋊C4—16616no—
510C4⋊C4—16616no—
511C4⋊C4—16616no—
512C22⋊C4—28no—
513C22⋊C4—216no—
514C22⋊C4—1668no—
515C22⋊C4—16616no—
516C22⋊C4—1668no—
517C22⋊C4—16616no—
518C22⋊C4—1668no—
519C22⋊C4—16616no—
520C42—16616no—
521C42—16616no—
522C23—28no—
523C23—28no—
524C23—216no—
525C23—216no—
526C23—24no—
527C23—24no—
528C23—22no—
529C23—22no—
530C23—24no—
531C23—24no—
532C23—22no—
533C23—44no—
534C23—44no—
535C23—44no—
536C23—48no—
537C23—48no—
538C23—3324no—
539C23—3324no—
540C23—3324no—
541C23—3328no—
542C23—3328no—
543C23—1662no—
544C23—1662no—
545C23—1664no—
546C23—1664no—
547C23—1662no—
548C23#14581765116yes—
549C23C2×D4×D8314yes—
550C23C2×D4×D8314yes—
551C23C2×D4×D8312yes—
552C23C2×D4×D8312yes—
553C23#41×D8314yes—
554C23C2×#1305058914yes—
555C23C2×#1305059014yes—
556C23C2×#1305059012yes—
557C23C24×D8311yescharacteristic
558D4—416no—
559D4—33216no—
560D4—33216no—
561C2×C4—232no—
562C2×C4—216no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—44no—
572C2×C4—48no—
573C2×C4—3324no—
574C2×C4—3328no—
575C2×C4—8316no—
576C2×C4—834no—
577C2×C4—838no—
578C2×C4—834no—
579C2×C4—838no—
580C2×C4—1664no—
581C2×C4—1662no—
582C2×C4—1662no—
583C2×C4—1664no—
584C2×C4—1664no—
585C2×C4—1662no—
586C2×C4—16632no—
587C2×C4—16632no—
588C2×C4—16616no—
589C2×C4—1668no—
590C2×C4—1664no—
591C2×C4—1664no—
592C2×C4—1664no—
593C2×C4C2×#1305058918yes—
594C22—232no—
595C22—24no—
596C22—24no—
597C22—28no—
598C22—28no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—44no—
603C22—44no—
604C22—88no—
605C22—3322no—
606C22—3322no—
607C22—3322no—
608C22—3324no—
609C22—3324no—
610C22—6648no—
611C22C2×#1458176518yes—
612C22C2×#1458176514yes—
613C22#123×D8314yes—
614C22#1912820714yes—
615C22#1912823118yes—
616C22#1912824618yes—
617C22C22×D4×D8311yescharacteristic
618C22C22×D4×D8311yescharacteristic
619C22C2×#41×D8312yes—
620C22C22×#1305058912yes—
621C22C22×#1305059011yescharacteristic
622C4—28no—
623C4—42no—
624C4—44no—
625C4—3322no—
626C4—3324no—
627C4—838no—
628C4—1668no—
629C4—1664no—
630C2—28no—
631C2—82no—
632C2—6642no—
633C2#2491579118yesdirect product factor
634C2C22×#1458176511yescharacteristic
635C2C2×#123×D8311yescharacteristic
636C2C2×#1912820711yescharacteristic
637C2C2×#1912823112yes—
638C2C2×#1912824612yes—
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#386×C83C2
socleC24×C83C24
prime radicalC22×#14581764C2
hypercenterC2×#386D83
hypocenterC83C2×#2854
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#14581776C2semidirect
2. C22×#14581773C2semidirect
4. C23×C4×Dic83C2semidirect
5. #24915791C2direct (N × H)
6. C2×#19127601C2semidirect
7. C2×#19127598C2semidirect
8. C2×#19127594C2semidirect
9. C2×#19127590C2semidirect
10. C2×#19127580C2semidirect
11. C2×#19127559C2semidirect
12. C2×#386×C83C2semidirect
18. C2×#14581776C22semidirect
20. C2×#14581773C22semidirect
36. C22×C4×Dic83C22semidirect
37. #19127601C22semidirect
38. #19127598C22semidirect
39. #19127594C22semidirect
40. #19127590C22semidirect
41. #19127580C22semidirect
42. #19127559C22semidirect
49. #386×C83C22semidirect
63. C23×Dic83D4semidirect
149. C22×Dic83C2×D4semidirect
269. C2×Dic83#123semidirect
309. Dic83C2×#123semidirect
313. C2×C83#2854semidirect
330. C2×#386D83semidirect
332. C83C2×#2854semidirect
366. #386C2×D83semidirect
633. C2#24915791direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817762
C22×#145817732
C22×#145817642
C23×C4×Dic832
#249157912
C2×#191276012
C2×#191275982
C2×#191275942
C2×#191275902
C2×#191275802
C2×#191275592
C2×#386×C832
C2×#285483