Finite Group Databasebeta

← C2×#24913392 #35570841

Subgroups — C2×#24913392 #35570841

Order 21248.

3326 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581768C211yesmaximal, characteristic, complemented
2C22×#14581765C211yesmaximal, characteristic
3#24913392C2116yesmaximal, direct product factor
4C2×#19127642C212yesmaximal, complemented
5C2×#19127628C211yesmaximal, characteristic, complemented
6C2×#19127626C211yesmaximal, characteristic, complemented
7C2×#19127616C212yesmaximal, complemented
8C2×#19127612C211yesmaximal, characteristic, complemented
9C2×#19127579C212yesmaximal, complemented
10C2×#19127577C212yesmaximal, complemented
11C2×#95×D83C211yesmaximal, characteristic, complemented
12C2×#393×C83C211yesmaximal, characteristic, complemented
13C23×D332C2211yescharacteristic
14C23×C22⋊D83C2211yescharacteristic
15C23×C22⋊D83C2211yescharacteristic
16C23×C4×D83C2212yes—
17C23×C4×D83C2211yescharacteristic
18C2×#14581768—28no—
19C2×#14581768C2218yescomplemented
20C2×#14581765—28no—
21C2×#14581765C2218yes—
22C22×C4⋊Dic83C2211yescharacteristic
23C22×Dic83⋊C4C2212yes—
24C22×Dic83⋊C4C2211yescharacteristic
25C22×C22⋊Dic83C2212yes—
26C22×(C2×D83)⋊C4C2212yes—
27C22×(C2×D83)⋊C4C2211yescharacteristic
28C22×(C2×D83)⋊C4C2212yes—
29C22×(C2×D83)⋊C4C2212yes—
30#19127642C22116yescomplemented
31#19127628C2218yescomplemented
32#19127626C2218yescomplemented
33#19127616C22116yescomplemented
34#19127612C2218yescomplemented
35#19127579C22116yescomplemented
36#19127577C22116yescomplemented
37C2×C83⋊#95C2212yes—
38C2×C83⋊#95C2212yes—
39C2×C83⋊#95C2212yes—
40C2×C83⋊#95C2211yescharacteristic
41C2×C83⋊#95C2212yes—
42#95×D83C2218yescomplemented
43C23×Q8×C83C2211yescharacteristic
44C22×C22⋊C4×C83C2211yescharacteristic
45C22×C22⋊C4×C83C2212yes—
46#393×C83C2218yescomplemented
47C2×#95×C83C2212yes—
48C2×#95×C83C2211yescharacteristic
49C24×D83C2311yescharacteristic
50C24×D83C2311yescharacteristic
51C22×D332—24no—
52C22×D332—28no—
53C22×D332C2314yes—
54C22×C22⋊D83—24no—
55C22×C22⋊D83—28no—
56C22×C22⋊D83—24no—
57C22×C22⋊D83—44no—
58C22×C22⋊D83C2314yes—
59C22×C22⋊D83C2314yes—
60C23×Dic83C2312yes—
61C23×Dic83C2312yes—
62C23×Dic83C2311yescharacteristic
63C23×Dic83C2311yescharacteristic
64C22×C4×D83—28no—
65C22×C4×D83—44no—
66C22×C4×D83—44no—
67C22×C4×D83—44no—
68C22×C4×D83D418yes—
69C22×C4×D83C2318yes—
70C22×C4×D83C2314yes—
71#14581768—232no—
72#14581765—232no—
73C2×C4⋊Dic83—24no—
74C2×C4⋊Dic83C2314yes—
75C2×Dic83⋊C4—24no—
76C2×Dic83⋊C4—28no—
77C2×Dic83⋊C4C2318yes—
78C2×Dic83⋊C4C2314yes—
79C2×C22⋊Dic83—44no—
80C2×C22⋊Dic83C2318yes—
81C2×(C2×D83)⋊C4—28no—
82C2×(C2×D83)⋊C4—24no—
83C2×(C2×D83)⋊C4—44no—
84C2×(C2×D83)⋊C4—44no—
85C2×(C2×D83)⋊C4C2318yes—
86C2×(C2×D83)⋊C4C2314yes—
87C2×(C2×D83)⋊C4C2318yes—
88C2×(C2×D83)⋊C4C2318yes—
89C83⋊#95C2318yes—
90C83⋊#95C2318yes—
91C83⋊#95C2318yes—
92C83⋊#95C2314yes—
93C83⋊#95C2318yes—
94C25×C83C2311yescharacteristic
95C22×Q8×C83—24no—
96C22×Q8×C83—44no—
97C22×Q8×C83C2314yes—
98C23×C4×C83C2312yes—
99C23×C4×C83C2312yes—
100C23×C4×C83C2311yescharacteristic
101C23×C4×C83C2311yescharacteristic
102C2×C22⋊C4×C83—24no—
103C2×C22⋊C4×C83—44no—
104C2×C22⋊C4×C83C2314yes—
105C2×C22⋊C4×C83C2318yes—
106#95×C83C2318yes—
107#95×C83C2314yes—
108C23×D83—24no—
109C23×D83—22no—
110C23×D83—22no—
111C23×D83—22no—
112C23×D83—24no—
113C23×D83—24no—
114C23×D83—22no—
115C23×D83—22no—
116C23×D83C2×D414yes—
117C23×D83#4118yes—
118C23×D83C2412yes—
119C23×D83C2412yes—
120C2×D332—28no—
121C2×D332—216no—
122C2×D332—416no—
123C2×C22⋊D83—28no—
124C2×C22⋊D83—216no—
125C2×C22⋊D83—28no—
126C2×C22⋊D83—48no—
127C2×C22⋊D83—416no—
128C2×C22⋊D83—416no—
129C22×Dic83—24no—
130C22×Dic83—22no—
131C22×Dic83—24no—
132C22×Dic83—24no—
133C22×Dic83—24no—
134C22×Dic83—24no—
135C22×Dic83—24no—
136C22×Dic83—24no—
137C22×Dic83—24no—
138C22×Dic83C2×D414yes—
139C22×Dic83C2414yes—
140C22×Dic83C2412yes—
141C22×Dic83C2414yes—
142C22×Dic83C2412yes—
143C2×C4×D83—216no—
144C2×C4×D83—416no—
145C2×C4×D83—48no—
146C2×C4×D83—48no—
147C2×C4×D83—48no—
148C2×C4×D83—432no—
149C2×C4×D83C2×D4116yes—
150C4⋊Dic83—28no—
151Dic83⋊C4—28no—
152Dic83⋊C4—216no—
153C22⋊Dic83—48no—
154(C2×D83)⋊C4—216no—
155(C2×D83)⋊C4—28no—
156(C2×D83)⋊C4—48no—
157(C2×D83)⋊C4—48no—
158C24×C83—22no—
159C24×C83—24no—
160C24×C83—24no—
161C24×C83—22no—
162C24×C83—22no—
163C24×C83C2412yes—
164C24×C83C2411yescharacteristic
165C2×Q8×C83—28no—
166C2×Q8×C83—48no—
167C2×Q8×C83—416no—
168C22×C4×C83—24no—
169C22×C4×C83—22no—
170C22×C4×C83—24no—
171C22×C4×C83—24no—
172C22×C4×C83—24no—
173C22×C4×C83—24no—
174C22×C4×C83—24no—
175C22×C4×C83—24no—
176C22×C4×C83—24no—
177C22×C4×C83C2×D414yes—
178C22×C4×C83C2414yes—
179C22×C4×C83C2412yes—
180C22×C4×C83C2414yes—
181C22×C4×C83C2412yes—
182C22⋊C4×C83—28no—
183C22⋊C4×C83—48no—
184C23×C83—22no—
185C23×C83—24no—
186C23×C83—24no—
187C23×C83—22no—
188C23×C83—22no—
189C23×C83—44no—
190C23×C83—44no—
191C23×C83—44no—
192C23×C83—48no—
193C23×C83—48no—
194C23×C83C22×D412yes—
195C23×C83C2×#4114yes—
196C23×C83H(5,𝔽2)14yes—
197C23×C83H(5,𝔽2)12yes—
198C23×C832−1+412yes—
199C23×C83C2511yescharacteristic
200C22×D83—28no—
201C22×D83—28no—
202C22×D83—216no—
203C22×D83—216no—
204C22×D83—24no—
205C22×D83—22no—
206C22×D83—22no—
207C22×D83—22no—
208C22×D83—24no—
209C22×D83—22no—
210C22×D83—24no—
211C22×D83—22no—
212C22×D83—44no—
213C22×D83—44no—
214C22×D83—44no—
215C22×D83—48no—
216C22×D83—48no—
217C22×D83#124116yes—
218C22×D83C22×D414yes—
219C22×D83C2×#4118yes—
220Q8×C83—416no—
221C2×C4×C83—28no—
222C2×C4×C83—24no—
223C2×C4×C83—22no—
224C2×C4×C83—24no—
225C2×C4×C83—24no—
226C2×C4×C83—24no—
227C2×C4×C83—24no—
228C2×C4×C83—24no—
229C2×C4×C83—24no—
230C2×C4×C83—24no—
231C2×C4×C83—44no—
232C2×C4×C83—48no—
233C2×C4×C83—48no—
234C2×C4×C83C22×D414yes—
235C22⋊D83—416no—
236C22⋊D83—416no—
237C2×Dic83—28no—
238C2×Dic83—24no—
239C2×Dic83—24no—
240C2×Dic83—22no—
241C2×Dic83—24no—
242C2×Dic83—24no—
243C2×Dic83—24no—
244C2×Dic83—24no—
245C2×Dic83—24no—
246C2×Dic83—24no—
247C2×Dic83—44no—
248C2×Dic83—48no—
249C2×Dic83—48no—
250C2×Dic83C22×D414yes—
251D332—416no—
252C4×D83—416no—
253C4×D83—432no—
254C22×C83—42no—
255C22×C83—42no—
256C22×C83—42no—
257C22×C83—44no—
258C22×C83—44no—
259C22×C83—88no—
260C22×C83C2×#12414yes—
261C22×C83#53414yes—
262C22×C83#53714yes—
263C22×C83#53818yes—
264C22×C83#53918yes—
265C22×C83C23×D411yescharacteristic
266C22×C83C22×#4112yes—
267C22×C83C2×H(5,𝔽2)12yes—
268C22×C83C2×H(5,𝔽2)11yescharacteristic
269C22×C83C2×2−1+411yescharacteristic
270C2×D83—232no—
271C2×D83—24no—
272C2×D83—24no—
273C2×D83—28no—
274C2×D83—28no—
275C2×D83—42no—
276C2×D83—42no—
277C2×D83—42no—
278C2×D83—44no—
279C2×D83—44no—
280C2×D83—88no—
281C2×D83C2×#12418yes—
282C4×C83—24no—
283C4×C83—42no—
284C4×C83—44no—
285C4×C83—44no—
286Dic83—24no—
287Dic83—42no—
288Dic83—44no—
289Dic83—44no—
290C2×#2639—831nomaximal, Sylow
291C2×C83—82no—
292C2×C83#263918yescomplemented
293C2×C83C22×#12411yescharacteristic
294C2×C83C2×#53411yescharacteristic
295C2×C83C2×#53711yescharacteristic
296C2×C83C2×#53812yes—
297C2×C83C2×#53912yes—
298D83—28no—
299D83—82no—
300C22×C22⋊Q8—831no—
301C22×#121—831no—
302#2639—8316no—
303C2×#400—832no—
304C2×#397—831no—
305C2×#397—831no—
306C2×#394—832no—
307C2×#393—831no—
308C2×#393D8311yescharacteristic, complemented
309C2×#386—832no—
310C2×#386—832no—
311C22×#95—831no—
312C83C2×#263911yescharacteristic, complemented, Sylow
313C23×Q8C2×D8311yescharacteristic
314C23×D4—831no—
315C23×D4—831no—
316C23×D4—831no—
317C24×C4—831no—
318C24×C4—832no—
319C2×C22⋊Q8—838no—
320C2×C22⋊Q8—1668no—
321C2×#121—838no—
322C2×#121—1668no—
323C22×C4⋊C4—832no—
324C22×C4⋊C4—831no—
325C22×C4⋊C4—831no—
326C22×C22⋊C4—832no—
327C22×C22⋊C4—832no—
328C22×C22⋊C4—832no—
329C22×C22⋊C4—831no—
330C22×C22⋊C4—832no—
331C22×C22⋊C4C2×D8311yescharacteristic
332C22×C22⋊C4C2×D8312yes—
333#400—8316no—
334#397—838no—
335#397—838no—
336#394—8316no—
337#393—838no—
338#393C2×D8318yescomplemented
339#386—8316no—
340#386—8316no—
341C2×#95—831no—
342C2×#95—832no—
343C2×#95—832no—
344C2×#95—832no—
345C2×#95—832no—
346C2×#95—838no—
347C2×#95C2×D8311yescharacteristic
348C2×#95C2×D8312yes—
349C25—831no—
350C25—831no—
351C25C22×D8311yescharacteristic
352C22×Q8—24no—
353C22×Q8—44no—
354C22×Q8C22×D8314yes—
355C22×D4—3324no—
356C22×D4—834no—
357C22×D4—834no—
358C22×D4—834no—
359C22×D4—1664no—
360C22×D4—1668no—
361C22×D4—1664no—
362C22×D4—1664no—
363C22×D4—1668no—
364C23×C4—3324no—
365C23×C4—3324no—
366C23×C4—3324no—
367C23×C4—838no—
368C23×C4—834no—
369C23×C4—838no—
370C23×C4—831no—
371C23×C4—832no—
372C23×C4—832no—
373C23×C4—831no—
374C23×C4—1668no—
375C23×C4C22×D8312yes—
376C23×C4C22×D8312yes—
377C23×C4C22×D8311yescharacteristic
378C23×C4C22×D8311yescharacteristic
379C22⋊Q8—16632no—
380#121—16632no—
381C2×C4⋊C4—834no—
382C2×C4⋊C4—838no—
383C2×C4⋊C4—834no—
384C2×C4⋊C4—1664no—
385C2×C4⋊C4—1668no—
386C2×C4⋊C4—1664no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—3324no—
390C2×C22⋊C4—3324no—
391C2×C22⋊C4—3324no—
392C2×C22⋊C4—838no—
393C2×C22⋊C4—838no—
394C2×C22⋊C4—838no—
395C2×C22⋊C4—834no—
396C2×C22⋊C4—838no—
397C2×C22⋊C4—1668no—
398C2×C22⋊C4—1664no—
399C2×C22⋊C4C22×D8314yes—
400C2×C22⋊C4C22×D8318yes—
401#95—834no—
402#95—838no—
403#95—838no—
404#95—838no—
405#95—838no—
406#95C22×D8314yes—
407#95C22×D8318yes—
408C24—22no—
409C24—24no—
410C24—24no—
411C24—22no—
412C24—22no—
413C24—834no—
414C24—838no—
415C24—832no—
416C24—832no—
417C24—1662no—
418C24—1664no—
419C24—1664no—
420C24—1662no—
421C24—1662no—
422C24—1664no—
423C24—1662no—
424C24—1662no—
425C24C23×D8312yes—
426C24C23×D8311yescharacteristic
427C2×Q8—28no—
428C2×Q8—48no—
429C2×Q8—416no—
430C2×D4—33216no—
431C2×D4—33216no—
432C2×D4—3328no—
433C2×D4—33216no—
434C2×D4—1668no—
435C2×D4—16616no—
436C2×D4—1668no—
437C2×D4—1668no—
438C2×D4—16616no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—33216no—
449C22×C4—3328no—
450C22×C4—3328no—
451C22×C4—3328no—
452C22×C4—33232no—
453C22×C4—8316no—
454C22×C4—834no—
455C22×C4—832no—
456C22×C4—834no—
457C22×C4—832no—
458C22×C4—834no—
459C22×C4—16616no—
460C22×C4—1664no—
461C22×C4—1662no—
462C22×C4—1664no—
463C22×C4—1664no—
464C22×C4—1664no—
465C22×C4—1664no—
466C22×C4—1664no—
467C22×C4—1664no—
468C22×C4—1664no—
469C22×C4D4×D8314yes—
470C22×C4C23×D8314yes—
471C22×C4C23×D8312yes—
472C22×C4C23×D8314yes—
473C22×C4C23×D8312yes—
474C4⋊C4—1668no—
475C4⋊C4—16616no—
476C4⋊C4—1668no—
477C22⋊C4—28no—
478C22⋊C4—48no—
479C22⋊C4—3328no—
480C22⋊C4—3328no—
481C22⋊C4—3328no—
482C22⋊C4—16616no—
483C22⋊C4—1668no—
484C23—22no—
485C23—24no—
486C23—24no—
487C23—22no—
488C23—22no—
489C23—44no—
490C23—44no—
491C23—44no—
492C23—48no—
493C23—48no—
494C23—3324no—
495C23—3324no—
496C23—3324no—
497C23—3328no—
498C23—3328no—
499C23—8316no—
500C23—834no—
501C23—838no—
502C23—1662no—
503C23—1664no—
504C23—1664no—
505C23—1662no—
506C23—1662no—
507C23—1668no—
508C23—1664no—
509C23—1662no—
510C23—1662no—
511C23—1668no—
512C23—16616no—
513C23—16616no—
514C23C2×D4×D8312yes—
515C23#41×D8314yes—
516C23#1458183714yes—
517C23#1458183812yes—
518C23#1458184012yes—
519C23C24×D8311yescharacteristic
520Q8—416no—
521D4—33216no—
522D4—33216no—
523D4—33216no—
524C2×C4—28no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—44no—
535C2×C4—48no—
536C2×C4—48no—
537C2×C4—33216no—
538C2×C4—33232no—
539C2×C4—3324no—
540C2×C4—3328no—
541C2×C4—3328no—
542C2×C4—834no—
543C2×C4—1664no—
544C2×C4—1662no—
545C2×C4—1664no—
546C2×C4—1664no—
547C2×C4—1664no—
548C2×C4—1664no—
549C2×C4—1664no—
550C2×C4—1664no—
551C2×C4—1668no—
552C2×C4—1664no—
553C2×C4C2×D4×D8314yes—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—44no—
558C22—44no—
559C22—88no—
560C22—3322no—
561C22—3322no—
562C22—3322no—
563C22—3324no—
564C22—3324no—
565C22—838no—
566C22—6648no—
567C22—1664no—
568C22—1664no—
569C22—1668no—
570C22—1668no—
571C22—16632no—
572C22#124×D8314yes—
573C22#1912826114yes—
574C22#1912828114yes—
575C22#1912828518yes—
576C22#1912829718yes—
577C22C22×D4×D8311yescharacteristic
578C22C2×#41×D8312yes—
579C22C2×#1458183712yes—
580C22C2×#1458183811yescharacteristic
581C22C2×#1458184011yescharacteristic
582C4—24no—
583C4—42no—
584C4—44no—
585C4—44no—
586C4—3322no—
587C4—3324no—
588C4—3324no—
589C4—1664no—
590C2—82no—
591C2—6642no—
592C2—1668no—
593C2#2491339218yesdirect product factor
594C2C2×#124×D8311yescharacteristic
595C2C2×#1912826111yescharacteristic
596C2C2×#1912828111yescharacteristic
597C2C2×#1912828512yes—
598C2C2×#1912829712yes—
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#393×C83C2
socleC24×C83C24
prime radicalC22×#14581765C2
hypercenterC2×#393D83
hypocenterC83C2×#2639
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#14581768C2semidirect
3. #24913392C2direct (N × H)
4. C2×#19127642C2semidirect
5. C2×#19127628C2semidirect
6. C2×#19127626C2semidirect
7. C2×#19127616C2semidirect
8. C2×#19127612C2semidirect
9. C2×#19127579C2semidirect
10. C2×#19127577C2semidirect
11. C2×#95×D83C2semidirect
12. C2×#393×C83C2semidirect
19. C2×#14581768C22semidirect
30. #19127642C22semidirect
31. #19127628C22semidirect
32. #19127626C22semidirect
33. #19127616C22semidirect
34. #19127612C22semidirect
35. #19127579C22semidirect
36. #19127577C22semidirect
42. #95×D83C22semidirect
46. #393×C83C22semidirect
292. C2×C83#2639semidirect
308. C2×#393D83semidirect
312. C83C2×#2639semidirect
338. #393C2×D83semidirect
593. C2#24913392direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817682
C22×#145817652
#249133922
C2×#191276422
C2×#191276282
C2×#191276262
C2×#191276162
C2×#191276122
C2×#191275792
C2×#191275772
C2×#95×D832
C2×#393×C832
C2×#263983