Finite Group Databasebeta

← C2×#24907250 #35402049

Subgroups — C2×#24907250 #35402049

Order 21248.

2242 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D83)⋊C4C211yesmaximal, characteristic
2C22×#14581706C212yesmaximal
3C2×C22⋊C4×Dic83C212yesmaximal, complemented
4#24907250C218yesmaximal, direct product factor
5C2×#19127468C211yesmaximal, characteristic, complemented
6C2×#342×C83C211yesmaximal, characteristic, complemented
7C23×C22⋊D83C2211yescharacteristic
8C24×Dic83C2211yescharacteristic
9C23×C4×D83C411yescharacteristic, complemented
10C2×(C22⋊D83)⋊C4—22no—
11C2×(C22⋊D83)⋊C4—22no—
12C2×(C22⋊D83)⋊C4—24no—
13C2×(C22⋊D83)⋊C4C414yescomplemented
14C2×(C22⋊D83)⋊C4C2214yes—
15C22×Dic83⋊C4C411yescharacteristic, complemented
16C22×C22⋊Dic83C2212yes—
17C22×(C2×D83)⋊C4C411yescharacteristic, complemented
18C22×C4×Dic83—22no—
19C22×C4×Dic83C411yescharacteristic, complemented
20C2×#14581706C4116yescomplemented
21C2×#14581706C2218yes—
22C22⋊C4×Dic83—24no—
23C22⋊C4×Dic83C2218yescomplemented
24C2×C83⋊#95—22no—
25#19127468C2214yescomplemented
26C22×C22⋊C4×C83C2211yescharacteristic
27C22×C22⋊C4×C83C2212yes—
28#342×C83C2214yescomplemented
29C24×D83C2×C411yescharacteristic
30C22×C22⋊D83—22no—
31C22×C22⋊D83—22no—
32C22×C22⋊D83—22no—
33C22×C22⋊D83—22no—
34C22×C22⋊D83C2×C418yes—
35C22×C22⋊D83C2×C412yes—
36C22×C22⋊D83C2312yes—
37C23×Dic83—22no—
38C23×Dic83—44no—
39C23×Dic83C2×C411yescharacteristic
40C23×Dic83C2×C411yescharacteristic
41C23×Dic83C2×C411yescharacteristic
42C23×Dic83C2×C412yes—
43C23×Dic83D412yes—
44C23×Dic83D412yes—
45C23×Dic83D414yes—
46C23×Dic83C2312yes—
47C22×C4×D83—22no—
48C22×C4×D83—21no—
49C22×C4×D83—21no—
50C22×C4×D83—44no—
51C22×C4×D83C2×C414yescomplemented
52(C22⋊D83)⋊C4—28no—
53(C22⋊D83)⋊C4—28no—
54(C22⋊D83)⋊C4—28no—
55(C22⋊D83)⋊C4—28no—
56C2×Dic83⋊C4—22no—
57C2×Dic83⋊C4—22no—
58C2×Dic83⋊C4C2×C414yescomplemented
59C2×C22⋊Dic83—22no—
60C2×C22⋊Dic83—24no—
61C2×C22⋊Dic83C2×C418yescomplemented
62C2×C22⋊Dic83C2314yes—
63C2×(C2×D83)⋊C4—22no—
64C2×(C2×D83)⋊C4—22no—
65C2×(C2×D83)⋊C4C2×C414yescomplemented
66C2×C4×Dic83—22no—
67C2×C4×Dic83—21no—
68C2×C4×Dic83—21no—
69C2×C4×Dic83—28no—
70C2×C4×Dic83—48no—
71C2×C4×Dic83C2×C414yescomplemented
72#14581706C2×C4132yescomplemented
73C83⋊#95—28no—
74C25×C83C2311yescharacteristic
75C23×C4×C83—22no—
76C23×C4×C83C2×C411yescharacteristic
77C23×C4×C83C2×C411yescharacteristic
78C2×C22⋊C4×C83—22no—
79C2×C22⋊C4×C83—22no—
80C2×C22⋊C4×C83—22no—
81C2×C22⋊C4×C83—24no—
82C2×C22⋊C4×C83C2×C412yes—
83C2×C22⋊C4×C83C2×C418yescomplemented
84C2×C22⋊C4×C83C2312yes—
85C2×C22⋊C4×C83C2314yes—
86C23×D83—21no—
87C23×D83—21no—
88C23×D83—22no—
89C23×D83—42no—
90C23×D83—42no—
91C23×D83C4214yescomplemented
92C23×D83C22×C412yes—
93C2×C22⋊D83—24no—
94C2×C22⋊D83—24no—
95C2×C22⋊D83—28no—
96C2×C22⋊D83—28no—
97C2×C22⋊D83—28no—
98C2×C22⋊D83—28no—
99C2×C22⋊D83—24no—
100C2×C22⋊D83—22no—
101C2×C22⋊D83—22no—
102C2×C22⋊D83C4218yescomplemented
103C2×C22⋊D83C22×C418yes—
104C22×Dic83—21no—
105C22×Dic83—21no—
106C22×Dic83—22no—
107C22×Dic83—24no—
108C22×Dic83—28no—
109C22×Dic83—28no—
110C22×Dic83—24no—
111C22×Dic83—44no—
112C22×Dic83—48no—
113C22×Dic83—44no—
114C22×Dic83—42no—
115C22×Dic83—44no—
116C22×Dic83—44no—
117C22×Dic83—44no—
118C22×Dic83C4214yescomplemented
119C22×Dic83C22⋊C412yes—
120C22×Dic83C22⋊C411yescharacteristic
121C22×Dic83C22⋊C412yes—
122C22×Dic83C22⋊C414yes—
123C22×Dic83C22⋊C412yes—
124C22×Dic83C22⋊C414yes—
125C22×Dic83C22⋊C411yescharacteristic
126C22×Dic83C22×C412yes—
127C22×Dic83C22×C412yes—
128C22×Dic83C22×C412yes—
129C22×Dic83C2×D414yes—
130C22×Dic83C2×D414yes—
131C2×C4×D83—24no—
132C2×C4×D83—24no—
133C2×C4×D83—44no—
134C2×C4×D83—48no—
135C2×C4×D83—44no—
136C2×C4×D83—48no—
137Dic83⋊C4—28no—
138C22⋊Dic83—28no—
139C22⋊Dic83—24no—
140C22⋊Dic83C22×C418yescomplemented
141(C2×D83)⋊C4—28no—
142C4×Dic83—24no—
143C4×Dic83—24no—
144C4×Dic83—416no—
145C24×C83—42no—
146C24×C83—42no—
147C24×C83C22×C411yescharacteristic
148C24×C83C22×C411yescharacteristic
149C24×C83C22×C414yes—
150C24×C83C2×D412yes—
151C24×C83C2×D412yes—
152C24×C83#4112yes—
153C24×C83#4112yes—
154C24×C83C2411yescharacteristic
155C22×C4×C83—21no—
156C22×C4×C83—21no—
157C22×C4×C83—21no—
158C22×C4×C83—21no—
159C22×C4×C83—28no—
160C22×C4×C83—24no—
161C22×C4×C83—44no—
162C22×C4×C83—44no—
163C22×C4×C83—42no—
164C22×C4×C83—42no—
165C22×C4×C83C22×C412yes—
166C22×C4×C83C22×C412yes—
167C22⋊C4×C83—24no—
168C22⋊C4×C83—28no—
169C22⋊C4×C83—24no—
170C22⋊C4×C83—24no—
171C22⋊C4×C83C22×C418yescomplemented
172C23×C83—22no—
173C23×C83—24no—
174C23×C83—22no—
175C23×C83—24no—
176C23×C83—41no—
177C23×C83—48no—
178C23×C83—41no—
179C23×C83—42no—
180C23×C83—42no—
181C23×C83—44no—
182C23×C83—44no—
183C23×C83—41no—
184C23×C83—41no—
185C23×C83C2×C4212yes—
186C23×C83C2×C4212yes—
187C23×C83C2×C22⋊C412yes—
188C23×C83C2×C22⋊C411yescharacteristic
189C23×C83C2×C22⋊C411yescharacteristic
190C23×C83#11712yes—
191C23×C83#11712yes—
192C23×C83C4×D414yes—
193C23×C83C4×D414yes—
194C23×C83C4×D414yes—
195C23×C83C4×D414yes—
196C23×C83C23×C411yescharacteristic
197C23×C83C23×C412yes—
198C23×C83C22×D412yes—
199C23×C83C2×#4111yescharacteristic
200C23×C83C2×#4111yescharacteristic
201C22×D83—22no—
202C22×D83—22no—
203C22×D83—24no—
204C22×D83—24no—
205C22×D83—42no—
206C22×D83—42no—
207C22×D83—48no—
208C22×D83—42no—
209C22×D83—42no—
210C22×D83—42no—
211C22×D83—48no—
212C22×D83—42no—
213C22×D83C2×C4214yescomplemented
214C2×C4×C83—22no—
215C2×C4×C83—22no—
216C2×C4×C83—28no—
217C2×C4×C83—44no—
218C2×C4×C83—416no—
219C2×C4×C83—42no—
220C2×C4×C83—44no—
221C2×C4×C83—42no—
222C2×C4×C83—42no—
223C2×C4×C83—42no—
224C2×C4×C83—42no—
225C2×C4×C83—42no—
226C22⋊D83—28no—
227C22⋊D83—28no—
228C22⋊D83—216no—
229C2×Dic83—22no—
230C2×Dic83—22no—
231C2×Dic83—24no—
232C2×Dic83—24no—
233C2×Dic83—22no—
234C2×Dic83—24no—
235C2×Dic83—28no—
236C2×Dic83—24no—
237C2×Dic83—24no—
238C2×Dic83—28no—
239C2×Dic83—28no—
240C2×Dic83—44no—
241C2×Dic83—42no—
242C2×Dic83—42no—
243C2×Dic83—44no—
244C2×Dic83—44no—
245C2×Dic83—44no—
246C2×Dic83—416no—
247C2×Dic83#9914yescomplemented
248C2×Dic83C2×C4214yescomplemented
249C2×Dic83C2×C22⋊C412yes—
250C2×Dic83C2×C22⋊C414yes—
251C2×Dic83C2×C22⋊C412yes—
252C4×D83—48no—
253C4×D83—48no—
254C22×C83—22no—
255C22×C83—21no—
256C22×C83—21no—
257C22×C83—22no—
258C22×C83—22no—
259C22×C83—21no—
260C22×C83—21no—
261C22×C83—22no—
262C22×C83—28no—
263C22×C83—28no—
264C22×C83—24no—
265C22×C83—24no—
266C22×C83—42no—
267C22×C83—42no—
268C22×C83—44no—
269C22×C83—44no—
270C22×C83—42no—
271C22×C83—41no—
272C22×C83—41no—
273C22×C83C4×C22⋊C412yes—
274C22×C83C4×C22⋊C414yes—
275C22×C83C4×C22⋊C412yes—
276C22×C83C2×#9912yes—
277C22×C83#41012yes—
278C22×C83C22×C4211yescharacteristic
279C22×C83C22×C22⋊C411yescharacteristic
280C22×C83C2×#11711yescharacteristic
281C22×C83C2×C4×D412yes—
282C22×C83C2×C4×D412yes—
283C2×D83—24no—
284C2×D83—44no—
285C2×D83—48no—
286C2×D83—42no—
287C2×D83—42no—
288C2×D83—48no—
289C2×D83—44no—
290C4×C83—48no—
291C4×C83—42no—
292C4×C83—42no—
293Dic83—22no—
294Dic83—24no—
295Dic83—24no—
296Dic83—48no—
297Dic83C2×#9914yescomplemented
298C2×C4×#99—831nomaximal, Sylow
299C2×C83—22no—
300C2×C83—22no—
301C2×C83—21no—
302C2×C83—22no—
303C2×C83—21no—
304C2×C83—24no—
305C2×C83C4×#9914yescomplemented
306C2×C83C2×C4×C22⋊C411yescharacteristic
307C2×C83C22×#9911yescharacteristic
308C2×C83C2×#41011yescharacteristic
309D83—44no—
310C22×C4×D4—831no—
311C22×#99—832no—
312C2×C4×C22⋊C4—832no—
313C4×#99—838no—
314C2×#342—831no—
315C2×#342D8311yescharacteristic, complemented
316C83C2×C4×#9911yescharacteristic, complemented, Sylow
317C23×D4—831no—
318C24×C4—831no—
319C24×C4—831no—
320C2×C4×D4—834no—
321C2×C4×D4—834no—
322C2×C4×D4—1662no—
323C2×C4×D4—1664no—
324C2×C4×D4—1662no—
325C22×C4⋊C4—831no—
326C22×C22⋊C4—832no—
327C22×C22⋊C4—831no—
328C22×C22⋊C4C2×D8311yescharacteristic
329C22×C22⋊C4C2×D8312yes—
330C22×C42—831no—
331C22×C42—1662no—
332C2×#99—8316no—
333C2×#99—838no—
334C4×C22⋊C4—838no—
335C4×C22⋊C4—1664no—
336C2×#95—1662no—
337#342—834no—
338#342C2×D8314yescomplemented
339C25—831no—
340C25C22×D8311yescharacteristic
341C22×D4—832no—
342C22×D4—838no—
343C22×D4—832no—
344C22×D4—1662no—
345C22×D4—1662no—
346C22×D4—1662no—
347C22×D4—1662no—
348C23×C4—22no—
349C23×C4—3324no—
350C23×C4—3324no—
351C23×C4—831no—
352C23×C4—832no—
353C23×C4—832no—
354C23×C4—834no—
355C23×C4—832no—
356C23×C4—834no—
357C23×C4—831no—
358C23×C4—831no—
359C23×C4—832no—
360C23×C4—1662no—
361C23×C4—1661no—
362C23×C4—1661no—
363C23×C4—1662no—
364C23×C4C4×D8311yescharacteristic
365C23×C4C4×D8311yescharacteristic
366C4×D4—1668no—
367C4×D4—1668no—
368C4×D4—1668no—
369C4×D4—1668no—
370C2×C4⋊C4—834no—
371C2×C4⋊C4—1662no—
372C2×C4⋊C4—1662no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—838no—
378C2×C22⋊C4—834no—
379C2×C22⋊C4—834no—
380C2×C22⋊C4—1662no—
381C2×C22⋊C4—1662no—
382C2×C22⋊C4—1662no—
383C2×C22⋊C4—1664no—
384C2×C22⋊C4C4×D8312yes—
385C2×C22⋊C4C4×D8318yescomplemented
386C2×C22⋊C4C22×D8312yes—
387C2×C22⋊C4C22×D8314yes—
388C2×C42—3328no—
389C2×C42—834no—
390C2×C42—1668no—
391C2×C42—1662no—
392C2×C42—1661no—
393C2×C42—1661no—
394#99—8332no—
395#95—1668no—
396C24—42no—
397C24—42no—
398C24—3322no—
399C24—3322no—
400C24—832no—
401C24—834no—
402C24—1661no—
403C24—1661no—
404C24—1662no—
405C24C2×C4×D8311yescharacteristic
406C24C2×C4×D8311yescharacteristic
407C24C2×C4×D8314yes—
408C24D4×D8312yes—
409C24D4×D8312yes—
410C24#1305058912yes—
411C24#1305059112yes—
412C24C23×D8311yescharacteristic
413C2×D4—838no—
414C2×D4—838no—
415C2×D4—1664no—
416C2×D4—1662no—
417C2×D4—1662no—
418C2×D4—1664no—
419C2×D4—1664no—
420C2×D4—1668no—
421C2×D4—1668no—
422C2×D4—1668no—
423C2×D4—1668no—
424C22×C4—24no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—28no—
430C22×C4—44no—
431C22×C4—44no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—3324no—
435C22×C4—3328no—
436C22×C4—3324no—
437C22×C4—3328no—
438C22×C4—3324no—
439C22×C4—3324no—
440C22×C4—3324no—
441C22×C4—3322no—
442C22×C4—3324no—
443C22×C4—3328no—
444C22×C4—3324no—
445C22×C4—832no—
446C22×C4—834no—
447C22×C4—832no—
448C22×C4—834no—
449C22×C4—831no—
450C22×C4—832no—
451C22×C4—832no—
452C22×C4—834no—
453C22×C4—834no—
454C22×C4—832no—
455C22×C4—834no—
456C22×C4—831no—
457C22×C4—832no—
458C22×C4—1664no—
459C22×C4—1664no—
460C22×C4—1664no—
461C22×C4—1668no—
462C22×C4—1668no—
463C22×C4—1664no—
464C22×C4—1661no—
465C22×C4—1661no—
466C22×C4—1662no—
467C22×C4C2×C4×D8312yes—
468C22×C4C2×C4×D8312yes—
469C4⋊C4—1668no—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—28no—
474C22⋊C4—838no—
475C22⋊C4—1668no—
476C22⋊C4—1664no—
477C22⋊C4—1668no—
478C22⋊C4C2×C4×D8318yescomplemented
479C42—33216no—
480C42—1664no—
481C42—1664no—
482C23—24no—
483C23—22no—
484C23—24no—
485C23—22no—
486C23—41no—
487C23—42no—
488C23—41no—
489C23—41no—
490C23—48no—
491C23—42no—
492C23—44no—
493C23—44no—
494C23—41no—
495C23—3322no—
496C23—3322no—
497C23—3328no—
498C23—3322no—
499C23—3322no—
500C23—3328no—
501C23—3322no—
502C23—3322no—
503C23—834no—
504C23—1662no—
505C23—1662no—
506C23—1664no—
507C23—1664no—
508C23C42×D8312yes—
509C23C42×D8312yes—
510C23C22⋊C4×D8312yes—
511C23C22⋊C4×D8311yescharacteristic
512C23C22⋊C4×D8311yescharacteristic
513C23#1458175012yes—
514C23#1458175012yes—
515C23(C22⋊D83)⋊C414yes—
516C23(C22⋊D83)⋊C414yes—
517C23#1458175414yes—
518C23#1458175414yes—
519C23C22×C4×D8311yescharacteristic
520C23C22×C4×D8312yes—
521C23C2×D4×D8312yes—
522C23C2×#1305058911yescharacteristic
523C23C2×#1305059111yescharacteristic
524D4—1668no—
525D4—1668no—
526D4—16616no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—28no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—416no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—3328no—
540C2×C4—3328no—
541C2×C4—3324no—
542C2×C4—3324no—
543C2×C4—33216no—
544C2×C4—3324no—
545C2×C4—3324no—
546C2×C4—3322no—
547C2×C4—3322no—
548C2×C4—832no—
549C2×C4—834no—
550C2×C4—834no—
551C2×C4—832no—
552C2×C4—834no—
553C2×C4—1668no—
554C2×C4—1668no—
555C2×C4—1664no—
556C2×C4—1664no—
557C2×C4—1668no—
558C2×C4—1662no—
559C2×C4—1662no—
560C2×C4—1662no—
561C2×C4—1664no—
562C2×C4—1664no—
563C2×C4—1664no—
564C22—22no—
565C22—21no—
566C22—21no—
567C22—22no—
568C22—22no—
569C22—21no—
570C22—21no—
571C22—22no—
572C22—28no—
573C22—28no—
574C22—24no—
575C22—24no—
576C22—42no—
577C22—41no—
578C22—41no—
579C22—42no—
580C22—42no—
581C22—44no—
582C22—44no—
583C22—3324no—
584C22—3324no—
585C22—3328no—
586C22—3322no—
587C22—3322no—
588C22—3328no—
589C22—1664no—
590C22#1912754812yes—
591C22#1912754814yes—
592C22#1912754812yes—
593C22#99×D8312yes—
594C22#1912767312yes—
595C22C2×C42×D8311yescharacteristic
596C22C2×C22⋊C4×D8311yescharacteristic
597C22C2×#1458175011yescharacteristic
598C22C2×(C22⋊D83)⋊C412yes—
599C22C2×#1458175412yes—
600C4—48no—
601C4—42no—
602C4—42no—
603C4—3328no—
604C4—834no—
605C4—1662no—
606C4—1664no—
607C4—1664no—
608C2—22no—
609C2—22no—
610C2—21no—
611C2—21no—
612C2—22no—
613C2—24no—
614C2—3324no—
615C2#2490725014yesdirect product factor
616C2C2×#1912754811yescharacteristic
617C2C2×#99×D8311yescharacteristic
618C2C2×#1912767311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D83
commutatorC22×C83C22×C42
FrattiniC24C23×D83
FittingC2×#342×C83C2
socleC23×C83C2×C22⋊C4
prime radicalC23×C22⋊D83C22
cosocleC24×C83C24
hypercenterC2×#342D83
hypocenterC83C2×C4×#99
LCSG ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
3. C2×C22⋊C4×Dic83C2semidirect
4. #24907250C2direct (N × H)
5. C2×#19127468C2semidirect
6. C2×#342×C83C2semidirect
9. C23×C4×D83C4semidirect
13. C2×(C22⋊D83)⋊C4C4semidirect
15. C22×Dic83⋊C4C4semidirect
17. C22×(C2×D83)⋊C4C4semidirect
19. C22×C4×Dic83C4semidirect
20. C2×#14581706C4semidirect
23. C22⋊C4×Dic83C22semidirect
25. #19127468C22semidirect
28. #342×C83C22semidirect
51. C22×C4×D83C2×C4semidirect
58. C2×Dic83⋊C4C2×C4semidirect
61. C2×C22⋊Dic83C2×C4semidirect
65. C2×(C2×D83)⋊C4C2×C4semidirect
71. C2×C4×Dic83C2×C4semidirect
72. #14581706C2×C4semidirect
83. C2×C22⋊C4×C83C2×C4semidirect
91. C23×D83C42semidirect
102. C2×C22⋊D83C42semidirect
118. C22×Dic83C42semidirect
140. C22⋊Dic83C22×C4semidirect
171. C22⋊C4×C83C22×C4semidirect
213. C22×D83C2×C42semidirect
247. C2×Dic83#99semidirect
248. C2×Dic83C2×C42semidirect
297. Dic83C2×#99semidirect
305. C2×C83C4×#99semidirect
315. C2×#342D83semidirect
316. C83C2×C4×#99semidirect
338. #342C2×D83semidirect
385. C2×C22⋊C4C4×D83semidirect
478. C22⋊C4C2×C4×D83semidirect
615. C2#24907250direct (N × H)

Maximal subgroups

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

subgroupindex
C22×(C22⋊D83)⋊C42
C22×#145817062
C2×C22⋊C4×Dic832
#249072502
C2×#191274682
C2×#342×C832
C2×C4×#9983