Finite Group Databasebeta

← C2×#99×Dic83 #35402052

Subgroups — C2×#99×Dic83 #35402052

Order 21248.

2242 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic83C211yesmaximal, characteristic
2C22×#14581707C211yesmaximal, characteristic
3C2×C22⋊C4×Dic83C212yesmaximal, complemented
4#99×Dic83C218yesmaximal, direct product factor
5C2×#19127467C212yesmaximal, complemented
6C22×#99×C83C211yesmaximal, characteristic
7C24×Dic83C411yescharacteristic, complemented
8C24×Dic83C2211yescharacteristic
9C2×D4×Dic83—22no—
10C2×D4×Dic83—22no—
11C2×D4×Dic83—24no—
12C2×D4×Dic83C414yescomplemented
13C2×D4×Dic83C2214yes—
14C22×C4⋊Dic83C411yescharacteristic, complemented
15C22×C22⋊Dic83C411yescharacteristic, complemented
16C22×C22⋊Dic83C2212yes—
17C22×C22⋊Dic83C2211yescharacteristic
18C22×C4×Dic83—22no—
19C22×C4×Dic83C411yescharacteristic, complemented
20C2×#14581707C418yescomplemented
21C2×#14581707C2214yes—
22C22⋊C4×Dic83—24no—
23C22⋊C4×Dic83C2218yescomplemented
24C2×C83⋊#95—22no—
25#19127467C2218yescomplemented
26C23×D4×C83C2211yescharacteristic
27C22×C22⋊C4×C83C2212yes—
28C2×#99×C83C418yescomplemented
29C2×#99×C83C2214yes—
30C23×Dic83—22no—
31C23×Dic83—21no—
32C23×Dic83—21no—
33C23×Dic83—22no—
34C23×Dic83—44no—
35C23×Dic83—44no—
36C23×Dic83C2×C411yescharacteristic
37C23×Dic83C2×C411yescharacteristic
38C23×Dic83C2×C411yescharacteristic
39C23×Dic83C2×C411yescharacteristic
40C23×Dic83C2×C412yes—
41C23×Dic83C2×C414yescomplemented
42C23×Dic83D412yes—
43C23×Dic83D412yes—
44C23×Dic83D414yes—
45C23×Dic83C2312yes—
46D4×Dic83—28no—
47D4×Dic83—28no—
48D4×Dic83—28no—
49D4×Dic83—28no—
50C2×C4⋊Dic83—22no—
51C2×C4⋊Dic83—22no—
52C2×C4⋊Dic83C2×C414yescomplemented
53C2×C22⋊Dic83—22no—
54C2×C22⋊Dic83—22no—
55C2×C22⋊Dic83—22no—
56C2×C22⋊Dic83—22no—
57C2×C22⋊Dic83—22no—
58C2×C22⋊Dic83—24no—
59C2×C22⋊Dic83C2×C412yes—
60C2×C22⋊Dic83C2×C414yescomplemented
61C2×C22⋊Dic83C2×C418yescomplemented
62C2×C22⋊Dic83C2312yes—
63C2×C22⋊Dic83C2314yes—
64C2×C4×Dic83—22no—
65C2×C4×Dic83—21no—
66C2×C4×Dic83—21no—
67C2×C4×Dic83—28no—
68C2×C4×Dic83—48no—
69C2×C4×Dic83C2×C414yescomplemented
70#14581707C2×C4116yescomplemented
71C83⋊#95—28no—
72C25×C83C2×C411yescharacteristic
73C25×C83C2311yescharacteristic
74C22×D4×C83—22no—
75C22×D4×C83—22no—
76C22×D4×C83—24no—
77C22×D4×C83C2×C414yes—
78C22×D4×C83C2×C412yes—
79C22×D4×C83C2×C414yes—
80C22×D4×C83C2312yes—
81C23×C4×C83—22no—
82C23×C4×C83C2×C411yescharacteristic
83C2×C22⋊C4×C83—22no—
84C2×C22⋊C4×C83—24no—
85C2×C22⋊C4×C83C2×C418yescomplemented
86C2×C22⋊C4×C83C2314yes—
87#99×C83C2×C4116yescomplemented
88C22×Dic83—24no—
89C22×Dic83—28no—
90C22×Dic83—21no—
91C22×Dic83—21no—
92C22×Dic83—21no—
93C22×Dic83—21no—
94C22×Dic83—28no—
95C22×Dic83—24no—
96C22×Dic83—24no—
97C22×Dic83—24no—
98C22×Dic83—44no—
99C22×Dic83—48no—
100C22×Dic83—44no—
101C22×Dic83—42no—
102C22×Dic83—44no—
103C22×Dic83—44no—
104C22×Dic83—48no—
105C22×Dic83—48no—
106C22×Dic83—44no—
107C22×Dic83—44no—
108C22×Dic83—44no—
109C22×Dic83—42no—
110C22×Dic83—42no—
111C22×Dic83C22⋊C412yes—
112C22×Dic83C22⋊C411yescharacteristic
113C22×Dic83C22⋊C412yes—
114C22×Dic83C22⋊C414yes—
115C22×Dic83C22⋊C412yes—
116C22×Dic83C22⋊C414yes—
117C22×Dic83C22⋊C411yescharacteristic
118C22×Dic83C22×C412yes—
119C22×Dic83C22×C412yes—
120C22×Dic83C22×C412yes—
121C22×Dic83C22×C412yes—
122C22×Dic83C2×D414yes—
123C22×Dic83C2×D414yes—
124C4⋊Dic83—28no—
125C22⋊Dic83—24no—
126C22⋊Dic83—28no—
127C22⋊Dic83—24no—
128C22⋊Dic83—24no—
129C22⋊Dic83—28no—
130C22⋊Dic83C22×C418yescomplemented
131C4×Dic83—24no—
132C4×Dic83—24no—
133C4×Dic83—416no—
134C24×C83—21no—
135C24×C83—21no—
136C24×C83—22no—
137C24×C83—42no—
138C24×C83—42no—
139C24×C83—42no—
140C24×C83—42no—
141C24×C83C4214yescomplemented
142C24×C83C22×C411yescharacteristic
143C24×C83C22×C412yes—
144C24×C83C22×C411yescharacteristic
145C24×C83C22×C412yes—
146C24×C83C22×C412yes—
147C24×C83C2×D412yes—
148C24×C83C2×D412yes—
149C24×C83#4114yes—
150C24×C83C2411yescharacteristic
151C2×D4×C83—24no—
152C2×D4×C83—24no—
153C2×D4×C83—28no—
154C2×D4×C83—28no—
155C2×D4×C83—28no—
156C2×D4×C83—28no—
157C2×D4×C83—24no—
158C2×D4×C83—24no—
159C2×D4×C83C4218yescomplemented
160C2×D4×C83C22×C414yes—
161C2×D4×C83C22×C414yes—
162C22×C4×C83—21no—
163C22×C4×C83—21no—
164C22×C4×C83—22no—
165C22×C4×C83—28no—
166C22×C4×C83—24no—
167C22×C4×C83—44no—
168C22×C4×C83—44no—
169C22×C4×C83C4214yescomplemented
170C22×C4×C83C22×C412yes—
171C22⋊C4×C83—28no—
172C22⋊C4×C83—24no—
173C22⋊C4×C83C22×C418yescomplemented
174C23×C83—24no—
175C23×C83—22no—
176C23×C83—24no—
177C23×C83—22no—
178C23×C83—22no—
179C23×C83—22no—
180C23×C83—24no—
181C23×C83—24no—
182C23×C83—41no—
183C23×C83—44no—
184C23×C83—44no—
185C23×C83—41no—
186C23×C83—42no—
187C23×C83—42no—
188C23×C83—48no—
189C23×C83—41no—
190C23×C83—41no—
191C23×C83—48no—
192C23×C83—42no—
193C23×C83—42no—
194C23×C83—42no—
195C23×C83—48no—
196C23×C83—42no—
197C23×C83—42no—
198C23×C83—42no—
199C23×C83C2×C4212yes—
200C23×C83C2×C4212yes—
201C23×C83C2×C4214yescomplemented
202C23×C83C2×C22⋊C411yescharacteristic
203C23×C83C2×C22⋊C412yes—
204C23×C83C2×C22⋊C411yescharacteristic
205C23×C83#11712yes—
206C23×C83#11712yes—
207C23×C83C4×D414yes—
208C23×C83C4×D414yes—
209C23×C83C4×D414yes—
210C23×C83C4×D414yes—
211C23×C83C23×C411yescharacteristic
212C23×C83C23×C411yescharacteristic
213C23×C83C23×C411yescharacteristic
214C23×C83C22×D412yes—
215C23×C83C2×#4112yes—
216D4×C83—28no—
217D4×C83—28no—
218D4×C83—216no—
219C2×C4×C83—22no—
220C2×C4×C83—22no—
221C2×C4×C83—24no—
222C2×C4×C83—24no—
223C2×C4×C83—28no—
224C2×C4×C83—44no—
225C2×C4×C83—416no—
226C2×C4×C83—44no—
227C2×C4×C83C2×C4214yescomplemented
228C2×Dic83—22no—
229C2×Dic83—24no—
230C2×Dic83—28no—
231C2×Dic83—24no—
232C2×Dic83—24no—
233C2×Dic83—28no—
234C2×Dic83—22no—
235C2×Dic83—22no—
236C2×Dic83—28no—
237C2×Dic83—44no—
238C2×Dic83—42no—
239C2×Dic83—42no—
240C2×Dic83—44no—
241C2×Dic83—48no—
242C2×Dic83—44no—
243C2×Dic83—44no—
244C2×Dic83—416no—
245C2×Dic83—42no—
246C2×Dic83—42no—
247C2×Dic83—42no—
248C2×Dic83—42no—
249C2×Dic83—48no—
250C2×Dic83—42no—
251C2×Dic83—42no—
252C2×Dic83#9914yesdirect product factor
253C2×Dic83C2×C22⋊C412yes—
254C2×Dic83C2×C22⋊C414yes—
255C2×Dic83C2×C22⋊C412yes—
256C22×C83—22no—
257C22×C83—21no—
258C22×C83—21no—
259C22×C83—22no—
260C22×C83—22no—
261C22×C83—21no—
262C22×C83—21no—
263C22×C83—22no—
264C22×C83—28no—
265C22×C83—28no—
266C22×C83—24no—
267C22×C83—24no—
268C22×C83—24no—
269C22×C83—42no—
270C22×C83—42no—
271C22×C83—44no—
272C22×C83—44no—
273C22×C83—41no—
274C22×C83—41no—
275C22×C83—42no—
276C22×C83—44no—
277C22×C83—44no—
278C22×C83—48no—
279C22×C83—42no—
280C22×C83—42no—
281C22×C83—48no—
282C22×C83C4×C22⋊C412yes—
283C22×C83C4×C22⋊C414yes—
284C22×C83C4×C22⋊C412yes—
285C22×C83C2×#9912yes—
286C22×C83#41012yes—
287C22×C83C22×C4211yescharacteristic
288C22×C83C22×C22⋊C411yescharacteristic
289C22×C83C2×#11711yescharacteristic
290C22×C83C2×C4×D412yes—
291C22×C83C2×C4×D412yes—
292C4×C83—24no—
293C4×C83—48no—
294Dic83—22no—
295Dic83—24no—
296Dic83—48no—
297Dic83—42no—
298Dic83—42no—
299Dic83C2×#9914yesdirect product factor
300C2×C4×#99—831nomaximal, Sylow
301C2×C83—22no—
302C2×C83—22no—
303C2×C83—21no—
304C2×C83—22no—
305C2×C83—21no—
306C2×C83—24no—
307C2×C83—44no—
308C2×C83C4×#9914yescomplemented
309C2×C83C2×C4×C22⋊C411yescharacteristic
310C2×C83C22×#9911yescharacteristic
311C2×C83C2×#41011yescharacteristic
312C22×C4×D4—831no—
313C22×#99—831no—
314C22×#99D8311yescharacteristic
315C2×C4×C22⋊C4—832no—
316C4×#99—838no—
317C2×#342—832no—
318C83C2×C4×#9911yescharacteristic, complemented, Sylow
319C23×D4C2×D8311yescharacteristic
320C24×C4—831no—
321C24×C4—831no—
322C2×C4×D4—834no—
323C2×C4×D4—834no—
324C2×C4×D4—1662no—
325C2×C4×D4—1664no—
326C2×C4×D4—1662no—
327C22×C4⋊C4—831no—
328C22×C22⋊C4—832no—
329C22×C22⋊C4—831no—
330C22×C22⋊C4—831no—
331C22×C22⋊C4C2×D8312yes—
332C22×C42—831no—
333C22×C42—1662no—
334C2×#99—838no—
335C2×#99—834no—
336C2×#99Dic8318yesdirect product factor
337C2×#99C2×D8314yes—
338C4×C22⋊C4—838no—
339C4×C22⋊C4—1664no—
340C2×#95—1662no—
341#342—838no—
342C25C4×D8311yescharacteristic
343C25C22×D8311yescharacteristic
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—24no—
347C22×D4C4×D8314yes—
348C22×D4C4×D8312yes—
349C22×D4C2×Dic8314yes—
350C22×D4C22×D8312yes—
351C23×C4—22no—
352C23×C4—3324no—
353C23×C4—3324no—
354C23×C4—831no—
355C23×C4—832no—
356C23×C4—832no—
357C23×C4—834no—
358C23×C4—832no—
359C23×C4—831no—
360C23×C4—831no—
361C23×C4—834no—
362C23×C4—831no—
363C23×C4—832no—
364C23×C4—1661no—
365C23×C4—1662no—
366C23×C4—1661no—
367C23×C4—1662no—
368C23×C4C4×D8311yescharacteristic
369C4×D4—1668no—
370C4×D4—1668no—
371C4×D4—1668no—
372C4×D4—1668no—
373C2×C4⋊C4—834no—
374C2×C4⋊C4—1662no—
375C2×C4⋊C4—1662no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—838no—
379C2×C22⋊C4—834no—
380C2×C22⋊C4—832no—
381C2×C22⋊C4—834no—
382C2×C22⋊C4—832no—
383C2×C22⋊C4—1662no—
384C2×C22⋊C4—1662no—
385C2×C22⋊C4—1662no—
386C2×C22⋊C4—1662no—
387C2×C22⋊C4—1662no—
388C2×C22⋊C4—1664no—
389C2×C22⋊C4C2×Dic8318yescomplemented
390C2×C22⋊C4C22×D8314yes—
391C2×C42—3328no—
392C2×C42—834no—
393C2×C42—1668no—
394C2×C42—1662no—
395C2×C42—1661no—
396C2×C42—1661no—
397#99—8316no—
398#99C2×Dic83116yesdirect product factor
399#95—1668no—
400C24—21no—
401C24—21no—
402C24—22no—
403C24—42no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24C4×Dic8314yescomplemented
408C24C2×C4×D8311yescharacteristic
409C24C2×C4×D8312yes—
410C24C2×C4×D8311yescharacteristic
411C24C2×C4×D8312yes—
412C24C22×Dic8312yes—
413C24D4×D8312yes—
414C24D4×D8312yes—
415C24#1305058914yes—
416C24C23×D8311yescharacteristic
417C2×D4—24no—
418C2×D4—24no—
419C2×D4—24no—
420C2×D4—24no—
421C2×D4—28no—
422C2×D4—28no—
423C2×D4—28no—
424C2×D4—28no—
425C2×D4C4×Dic8318yescomplemented
426C2×D4C2×C4×D8314yes—
427C2×D4C22×Dic8314yes—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—28no—
433C22×C4—44no—
434C22×C4—44no—
435C22×C4—3324no—
436C22×C4—3324no—
437C22×C4—3324no—
438C22×C4—3328no—
439C22×C4—3324no—
440C22×C4—3322no—
441C22×C4—3322no—
442C22×C4—3324no—
443C22×C4—3322no—
444C22×C4—3328no—
445C22×C4—3324no—
446C22×C4—3328no—
447C22×C4—3324no—
448C22×C4—832no—
449C22×C4—834no—
450C22×C4—832no—
451C22×C4—834no—
452C22×C4—832no—
453C22×C4—832no—
454C22×C4—831no—
455C22×C4—832no—
456C22×C4—834no—
457C22×C4—832no—
458C22×C4—834no—
459C22×C4—831no—
460C22×C4—832no—
461C22×C4—1664no—
462C22×C4—1664no—
463C22×C4—1664no—
464C22×C4—1661no—
465C22×C4—1661no—
466C22×C4—1661no—
467C22×C4—1661no—
468C22×C4—1668no—
469C22×C4—1668no—
470C22×C4—1664no—
471C22×C4C4×Dic8314yescomplemented
472C22×C4C2×C4×D8312yes—
473C4⋊C4—1668no—
474C22⋊C4—24no—
475C22⋊C4—28no—
476C22⋊C4—838no—
477C22⋊C4—1668no—
478C22⋊C4—1664no—
479C22⋊C4—1664no—
480C22⋊C4—1664no—
481C22⋊C4—1668no—
482C22⋊C4C22×Dic8318yescomplemented
483C42—33216no—
484C42—1664no—
485C42—1664no—
486C23—24no—
487C23—22no—
488C23—24no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—24no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23—41no—
498C23—44no—
499C23—44no—
500C23—42no—
501C23—48no—
502C23—41no—
503C23—42no—
504C23—48no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—48no—
509C23—42no—
510C23—42no—
511C23C2×C4×Dic8312yes—
512C23C2×C4×Dic8312yes—
513C23C2×C4×Dic8314yescomplemented
514C23C22⋊C4×D8312yes—
515C23C22⋊C4×D8311yescharacteristic
516C23C22⋊C4×D8311yescharacteristic
517C23#1458174812yes—
518C23#1458174812yes—
519C23(C22⋊D83)⋊C414yes—
520C23(C22⋊D83)⋊C414yes—
521C23D4×Dic8314yes—
522C23D4×Dic8314yes—
523C23C22×C4×D8311yescharacteristic
524C23C22×C4×D8311yescharacteristic
525C23C23×Dic8311yescharacteristic
526C23C2×D4×D8312yes—
527C23C2×#1305058912yes—
528D4—28no—
529D4—28no—
530D4—216no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—28no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—416no—
539C2×C4—3324no—
540C2×C4—3322no—
541C2×C4—3324no—
542C2×C4—33216no—
543C2×C4—3322no—
544C2×C4—3322no—
545C2×C4—3322no—
546C2×C4—3328no—
547C2×C4—3328no—
548C2×C4—3322no—
549C2×C4—3322no—
550C2×C4—3324no—
551C2×C4—3324no—
552C2×C4—3322no—
553C2×C4—3322no—
554C2×C4—832no—
555C2×C4—834no—
556C2×C4—832no—
557C2×C4—834no—
558C2×C4—1662no—
559C2×C4—1662no—
560C2×C4—1668no—
561C2×C4—1668no—
562C2×C4—1664no—
563C2×C4—1664no—
564C2×C4—1668no—
565C2×C4—1662no—
566C2×C4—1664no—
567C2×C4C2×C4×Dic8314yescomplemented
568C22—22no—
569C22—21no—
570C22—21no—
571C22—22no—
572C22—22no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—28no—
577C22—28no—
578C22—24no—
579C22—24no—
580C22—24no—
581C22—41no—
582C22—41no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—44no—
590C22—48no—
591C22—42no—
592C22—42no—
593C22—48no—
594C22C22⋊C4×Dic8312yes—
595C22C22⋊C4×Dic8314yes—
596C22C22⋊C4×Dic8312yes—
597C22#99×D8312yes—
598C22#1912767312yes—
599C22C22×C4×Dic8311yescharacteristic
600C22C2×C22⋊C4×D8311yescharacteristic
601C22C2×#1458174811yescharacteristic
602C22C2×(C22⋊D83)⋊C412yes—
603C22C2×D4×Dic8312yes—
604C4—24no—
605C4—48no—
606C4—3328no—
607C4—3322no—
608C4—3322no—
609C4—834no—
610C4—1662no—
611C4—1664no—
612C2—22no—
613C2—22no—
614C2—21no—
615C2—21no—
616C2—22no—
617C2—24no—
618C2—44no—
619C2#99×Dic8314yesdirect product factor
620C2C2×C22⋊C4×Dic8311yescharacteristic
621C2C2×#99×D8311yescharacteristic
622C2C2×#1912767311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D83
commutatorC22×C83C22×C42
FrattiniC24C23×D83
FittingC22×#99×C83C2
socleC23×C83C2×C22⋊C4
prime radicalC23×D4×C83C22
cosocleC24×C83C24
hypercenterC22×#99D83
hypocenterC83C2×C4×#99
LCSG ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
3. C2×C22⋊C4×Dic83C2semidirect
4. #99×Dic83C2direct (N × H)
5. C2×#19127467C2semidirect
7. C24×Dic83C4semidirect
12. C2×D4×Dic83C4semidirect
14. C22×C4⋊Dic83C4semidirect
15. C22×C22⋊Dic83C4semidirect
19. C22×C4×Dic83C4semidirect
20. C2×#14581707C4semidirect
23. C22⋊C4×Dic83C22semidirect
25. #19127467C22semidirect
28. C2×#99×C83C4semidirect
41. C23×Dic83C2×C4semidirect
52. C2×C4⋊Dic83C2×C4semidirect
60. C2×C22⋊Dic83C2×C4semidirect
61. C2×C22⋊Dic83C2×C4semidirect
69. C2×C4×Dic83C2×C4semidirect
70. #14581707C2×C4semidirect
85. C2×C22⋊C4×C83C2×C4semidirect
87. #99×C83C2×C4semidirect
130. C22⋊Dic83C22×C4semidirect
141. C24×C83C42semidirect
159. C2×D4×C83C42semidirect
169. C22×C4×C83C42semidirect
173. C22⋊C4×C83C22×C4semidirect
201. C23×C83C2×C42semidirect
227. C2×C4×C83C2×C42semidirect
252. C2×Dic83#99direct (N × H)
299. Dic83C2×#99direct (N × H)
308. C2×C83C4×#99semidirect
318. C83C2×C4×#99semidirect
336. C2×#99Dic83direct (N × H)
389. C2×C22⋊C4C2×Dic83semidirect
398. #99C2×Dic83direct (N × H)
407. C24C4×Dic83semidirect
425. C2×D4C4×Dic83semidirect
471. C22×C4C4×Dic83semidirect
482. C22⋊C4C22×Dic83semidirect
513. C23C2×C4×Dic83semidirect
567. C2×C4C2×C4×Dic83semidirect
619. C2#99×Dic83direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×Dic832
C22×#145817072
C2×C22⋊C4×Dic832
#99×Dic832
C2×#191274672
C22×#99×C832
C2×C4×#9983