Finite Group Databasebeta

← C2×#24912411 #35576180

Subgroups — C2×#24912411 #35576180

Order 21248.

4006 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581791C211yesmaximal, characteristic, complemented
2C22×#14581770C212yesmaximal, complemented
3C22×#14581769C212yesmaximal, complemented
4C22×(C22⋊D83)⋊C4C211yesmaximal, characteristic
5#24912411C2116yesmaximal, direct product factor
6C2×#19127638C211yesmaximal, characteristic, complemented
7C2×#19127637C211yesmaximal, characteristic, complemented
8C2×#19127636C211yesmaximal, characteristic, complemented
9C2×#19127601C212yesmaximal
10C2×#19127570C212yesmaximal, complemented
11C2×#19127552C211yesmaximal, characteristic, complemented
12C2×#399×C83C211yesmaximal, characteristic, complemented
13C23×Dic166C2212yes—
14C23×C22⋊D83C2211yescharacteristic
15C24×Dic83C2211yescharacteristic
16C23×C4×D83C2211yescharacteristic
17C2×#14581791—28no—
18C2×#14581791C2218yescomplemented
19C2×#14581770—216no—
20C2×#14581770C22116yescomplemented
21C2×#14581769—216no—
22C2×#14581769C22116yescomplemented
23C2×(C22⋊D83)⋊C4—28no—
24C2×(C22⋊D83)⋊C4C2218yes—
25C22×C4⋊Dic83C2212yes—
26C22×C4⋊Dic83C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×Dic83⋊C4C2212yes—
29C22×Dic83⋊C4C2212yes—
30C22×Dic83⋊C4C2212yes—
31C22×Dic83⋊C4C2212yes—
32C22×C22⋊Dic83C2212yes—
33C22×(C2×D83)⋊C4C2211yescharacteristic
34C22×(C2×D83)⋊C4C2212yes—
35C22×(C2×D83)⋊C4C2212yes—
36C22×C4×Dic83C2212yes—
37C22×C4×Dic83C2211yescharacteristic
38#19127638C2218yescomplemented
39#19127637C2218yescomplemented
40#19127636C2218yescomplemented
41#19127601C22116yes—
42#19127570C22116yescomplemented
43#19127552C2218yescomplemented
44C2×C83⋊#95C2211yescharacteristic
45C22×C4⋊C4×C83C2212yes—
46C22×C4⋊C4×C83C2211yescharacteristic
47C22×C22⋊C4×C83C2211yescharacteristic
48C22×C22⋊C4×C83C2212yes—
49#399×C83C2218yescomplemented
50C2×#95×C83C2211yescharacteristic
51C24×D83C2311yescharacteristic
52C22×Dic166—28no—
53C22×Dic166—28no—
54C22×Dic166—28no—
55C22×Dic166C2318yes—
56C22×C22⋊D83—24no—
57C22×C22⋊D83—24no—
58C22×C22⋊D83Q818yescomplemented
59C22×C22⋊D83C2314yes—
60C23×Dic83—24no—
61C23×Dic83—28no—
62C23×Dic83C2312yes—
63C23×Dic83C2311yescharacteristic
64C23×Dic83C2314yes—
65C23×Dic83C2312yes—
66C23×Dic83C2311yescharacteristic
67C23×Dic83C2311yescharacteristic
68C22×C4×D83—24no—
69C22×C4×D83—28no—
70C22×C4×D83C2314yes—
71#14581791—232no—
72#14581770—264no—
73#14581769—264no—
74(C22⋊D83)⋊C4—232no—
75C2×C4⋊Dic83—28no—
76C2×C4⋊Dic83—24no—
77C2×C4⋊Dic83C2318yes—
78C2×C4⋊Dic83C2314yes—
79C2×Dic83⋊C4—24no—
80C2×Dic83⋊C4—28no—
81C2×Dic83⋊C4—28no—
82C2×Dic83⋊C4—28no—
83C2×Dic83⋊C4D4116yescomplemented
84C2×Dic83⋊C4C2314yes—
85C2×Dic83⋊C4C2318yes—
86C2×Dic83⋊C4C2318yes—
87C2×Dic83⋊C4C2318yes—
88C2×Dic83⋊C4C2318yes—
89C2×C22⋊Dic83—28no—
90C2×C22⋊Dic83C2318yes—
91C2×(C2×D83)⋊C4—28no—
92C2×(C2×D83)⋊C4—24no—
93C2×(C2×D83)⋊C4—28no—
94C2×(C2×D83)⋊C4C2318yes—
95C2×(C2×D83)⋊C4C2318yes—
96C2×(C2×D83)⋊C4C2314yes—
97C2×C4×Dic83—28no—
98C2×C4×Dic83D418yes—
99C2×C4×Dic83C2318yes—
100C2×C4×Dic83C2314yes—
101C83⋊#95C2314yes—
102C25×C83C2311yescharacteristic
103C23×C4×C83C2312yes—
104C23×C4×C83C2311yescharacteristic
105C23×C4×C83C2312yes—
106C23×C4×C83C2311yescharacteristic
107C2×C4⋊C4×C83—28no—
108C2×C4⋊C4×C83—24no—
109C2×C4⋊C4×C83C2318yes—
110C2×C4⋊C4×C83C2314yes—
111C2×C22⋊C4×C83—24no—
112C2×C22⋊C4×C83—28no—
113C2×C22⋊C4×C83C2318yes—
114C2×C22⋊C4×C83C2314yes—
115#95×C83C2314yes—
116C23×D83—22no—
117C23×D83—24no—
118C23×D83—22no—
119C23×D83—24no—
120C23×D83C2×Q814yes—
121C23×D83C2412yes—
122C2×Dic166—216no—
123C2×Dic166—216no—
124C2×Dic166—216no—
125C2×Dic166—432no—
126C2×C22⋊D83—232no—
127C2×C22⋊D83—28no—
128C2×C22⋊D83—28no—
129C2×C22⋊D83C2×Q8116yescomplemented
130C22×Dic83—24no—
131C22×Dic83—24no—
132C22×Dic83—22no—
133C22×Dic83—24no—
134C22×Dic83—24no—
135C22×Dic83—24no—
136C22×Dic83—24no—
137C22×Dic83—216no—
138C22×Dic83—28no—
139C22×Dic83—416no—
140C22×Dic83C2×D418yes—
141C22×Dic83C2×D414yes—
142C22×Dic83C2×D414yes—
143C22×Dic83C2×D418yes—
144C22×Dic83C2×Q814yes—
145C22×Dic83#4114yes—
146C22×Dic83C2412yes—
147C22×Dic83C2414yes—
148C22×Dic83C2414yes—
149C22×Dic83C2412yes—
150C22×Dic83C2412yes—
151C2×C4×D83—216no—
152C2×C4×D83—28no—
153C2×C4×D83—416no—
154C4⋊Dic83—216no—
155C4⋊Dic83—28no—
156Dic83⋊C4—216no—
157Dic83⋊C4—216no—
158Dic83⋊C4—216no—
159Dic83⋊C4—28no—
160Dic83⋊C4C2×D4132yescomplemented
161C22⋊Dic83—216no—
162(C2×D83)⋊C4—216no—
163(C2×D83)⋊C4—28no—
164(C2×D83)⋊C4—216no—
165C4×Dic83—216no—
166C4×Dic83C2×D4116yes—
167C24×C83—22no—
168C24×C83—24no—
169C24×C83—22no—
170C24×C83—24no—
171C24×C83C2×Q814yes—
172C24×C83C2412yes—
173C24×C83C2411yescharacteristic
174C22×C4×C83—24no—
175C22×C4×C83—24no—
176C22×C4×C83—24no—
177C22×C4×C83—22no—
178C22×C4×C83—24no—
179C22×C4×C83—24no—
180C22×C4×C83—24no—
181C22×C4×C83—24no—
182C22×C4×C83C2×D414yes—
183C22×C4×C83C2×D418yes—
184C22×C4×C83C2412yes—
185C22×C4×C83C2414yes—
186C22×C4×C83C2412yes—
187C22×C4×C83C2414yes—
188C4⋊C4×C83—216no—
189C4⋊C4×C83—28no—
190C22⋊C4×C83—216no—
191C22⋊C4×C83—28no—
192C23×C83—28no—
193C23×C83—216no—
194C23×C83—24no—
195C23×C83—22no—
196C23×C83—22no—
197C23×C83—24no—
198C23×C83—44no—
199C23×C83—44no—
200C23×C83—48no—
201C23×C83C22×D412yes—
202C23×C83C22×D414yes—
203C23×C83C22×Q814yes—
204C23×C83C22×Q812yes—
205C23×C83C2×#4112yes—
206C23×C832−1+414yes—
207C23×C83C2511yescharacteristic
208C22×D83—28no—
209C22×D83—216no—
210C22×D83—24no—
211C22×D83—22no—
212C22×D83—22no—
213C22×D83—24no—
214C22×D83—44no—
215C22×D83—44no—
216C22×D83—48no—
217C22×D83C22×Q814yes—
218C2×C4×C83—28no—
219C2×C4×C83—216no—
220C2×C4×C83—24no—
221C2×C4×C83—24no—
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—44no—
229C2×C4×C83—48no—
230C2×C4×C83C22×D414yes—
231C2×C4×C83C22×D418yes—
232C22⋊D83—232no—
233C2×Dic83—216no—
234C2×Dic83—24no—
235C2×Dic83—24no—
236C2×Dic83—22no—
237C2×Dic83—24no—
238C2×Dic83—24no—
239C2×Dic83—24no—
240C2×Dic83—24no—
241C2×Dic83—44no—
242C2×Dic83—48no—
243C2×Dic83—416no—
244C2×Dic83C22⋊Q8116yescomplemented
245C2×Dic83#127116yes—
246C2×Dic83C22×D418yes—
247C2×Dic83C22×D414yes—
248C2×Dic83C22×D414yes—
249C2×Dic83C22×D418yes—
250C2×Dic83C22×Q814yes—
251C2×Dic83C2×#4114yes—
252C4×D83—416no—
253Dic166—432no—
254C22×C83—24no—
255C22×C83—28no—
256C22×C83—42no—
257C22×C83—42no—
258C22×C83—44no—
259C22×C83—416no—
260C22×C83C2×C22⋊Q814yes—
261C22×C83C2×#12714yes—
262C22×C83#53614yes—
263C22×C83#54718yes—
264C22×C83D4×Q818yes—
265C22×C83C23×D411yescharacteristic
266C22×C83C23×D412yes—
267C22×C83C23×Q811yescharacteristic
268C22×C83C22×#4111yescharacteristic
269C22×C83C2×2−1+412yes—
270C2×D83—24no—
271C2×D83—28no—
272C2×D83—42no—
273C2×D83—42no—
274C2×D83—44no—
275C2×D83—416no—
276C4×C83—24no—
277C4×C83—28no—
278C4×C83—44no—
279C4×C83—42no—
280Dic83—28no—
281Dic83—44no—
282Dic83—42no—
283Dic83C2×C22⋊Q818yescomplemented
284Dic83C2×#12718yes—
285C2×#2542—831nomaximal, Sylow
286C2×C83—44no—
287C2×C83#254218yescomplemented
288C2×C83C22×C22⋊Q811yescharacteristic
289C2×C83C22×#12711yescharacteristic
290C2×C83C2×#53611yescharacteristic
291C2×C83C2×#54712yes—
292C2×C83C2×D4×Q812yes—
293D83—44no—
294C22×C4⋊Q8—831no—
295C22×C22⋊Q8—832no—
296C22×C22⋊Q8—832no—
297C22×C4×D4—831no—
298#2542—8316no—
299C2×#399—831no—
300C2×#399—831no—
301C2×#399—831no—
302C2×#399D8311yescharacteristic, complemented
303C2×#390—832no—
304C2×#384—832no—
305C2×C4×C4⋊C4—831no—
306C83C2×#254211yescharacteristic, complemented, Sylow
307C23×Q8—832no—
308C23×D4—831no—
309C24×C4—831no—
310C24×C4—831no—
311C2×C4⋊Q8—838no—
312C2×C4⋊Q8—1668no—
313C2×C22⋊Q8—8316no—
314C2×C22⋊Q8—8316no—
315C2×C22⋊Q8—16616no—
316C2×C22⋊Q8—16616no—
317C2×C4×D4—838no—
318C2×C4×D4—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⋊C4C2×D8311yescharacteristic
327C22×C4⋊C4C2×D8312yes—
328C22×C22⋊C4—832no—
329C22×C22⋊C4—831no—
330C22×C22⋊C4—832no—
331C22×C22⋊C4—832no—
332C22×C22⋊C4C2×D8311yescharacteristic
333C22×C22⋊C4C2×D8312yes—
334C22×C42—831no—
335C22×C42—832no—
336#399—838no—
337#399—838no—
338#399—838no—
339#399C2×D8318yescomplemented
340#390—8316no—
341#384—8316no—
342C4×C4⋊C4—838no—
343C2×#95—831no—
344C2×#95C2×D8311yescharacteristic
345C25—831no—
346C25C22×D8311yescharacteristic
347C22×Q8—838no—
348C22×Q8—1668no—
349C22×Q8—1668no—
350C22×Q8—1668no—
351C22×D4—838no—
352C22×D4—834no—
353C22×D4—1664no—
354C22×D4—1664no—
355C23×C4—831no—
356C23×C4—831no—
357C23×C4—832no—
358C23×C4—834no—
359C23×C4—832no—
360C23×C4—831no—
361C23×C4—834no—
362C23×C4—1664no—
363C23×C4—1668no—
364C23×C4—1664no—
365C23×C4—1668no—
366C23×C4C22×D8312yes—
367C23×C4C22×D8311yescharacteristic
368C23×C4C22×D8312yes—
369C23×C4C22×D8311yescharacteristic
370C4⋊Q8—16632no—
371C22⋊Q8—16664no—
372C22⋊Q8—16664no—
373C4×D4—16632no—
374C2×C4⋊C4—28no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—8316no—
377C2×C4⋊C4—838no—
378C2×C4⋊C4—834no—
379C2×C4⋊C4—838no—
380C2×C4⋊C4—838no—
381C2×C4⋊C4—838no—
382C2×C4⋊C4—838no—
383C2×C4⋊C4—834no—
384C2×C4⋊C4—1664no—
385C2×C4⋊C4—1668no—
386C2×C4⋊C4—1668no—
387C2×C4⋊C4—1668no—
388C2×C4⋊C4—1668no—
389C2×C4⋊C4—1664no—
390C2×C4⋊C4C22×D8318yes—
391C2×C4⋊C4C22×D8314yes—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—838no—
395C2×C22⋊C4—834no—
396C2×C22⋊C4—838no—
397C2×C22⋊C4—838no—
398C2×C22⋊C4—1668no—
399C2×C22⋊C4—1668no—
400C2×C22⋊C4—1664no—
401C2×C22⋊C4—1668no—
402C2×C22⋊C4C22×D8314yes—
403C2×C22⋊C4C22×D8318yes—
404C2×C42—838no—
405C2×C42—834no—
406C2×C42—838no—
407C2×C42—1668no—
408#95—834no—
409#95C22×D8314yes—
410C24—24no—
411C24—22no—
412C24—22no—
413C24—24no—
414C24—834no—
415C24—832no—
416C24—1664no—
417C24—1662no—
418C24—1662no—
419C24—1664no—
420C24Q8×D8314yes—
421C24C23×D8312yes—
422C24C23×D8311yescharacteristic
423C2×Q8—33232no—
424C2×Q8—16616no—
425C2×Q8—16616no—
426C2×Q8—16616no—
427C2×D4—8316no—
428C2×D4—1668no—
429C2×D4—16632no—
430C2×D4—1668no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—33216no—
440C22×C4—33216no—
441C22×C4—834no—
442C22×C4—834no—
443C22×C4—838no—
444C22×C4—834no—
445C22×C4—834no—
446C22×C4—832no—
447C22×C4—832no—
448C22×C4—838no—
449C22×C4—834no—
450C22×C4—834no—
451C22×C4—832no—
452C22×C4—1668no—
453C22×C4—16616no—
454C22×C4—1668no—
455C22×C4—16616no—
456C22×C4—1662no—
457C22×C4—1664no—
458C22×C4—1664no—
459C22×C4—1664no—
460C22×C4—1664no—
461C22×C4—1664no—
462C22×C4—1664no—
463C22×C4D4×D8314yes—
464C22×C4D4×D8318yes—
465C22×C4C23×D8314yes—
466C22×C4C23×D8312yes—
467C22×C4C23×D8312yes—
468C22×C4C23×D8314yes—
469C4⋊C4—216no—
470C4⋊C4—28no—
471C4⋊C4—8332no—
472C4⋊C4—1668no—
473C4⋊C4—16616no—
474C4⋊C4—16616no—
475C4⋊C4—16616no—
476C4⋊C4—16616no—
477C4⋊C4—1668no—
478C22⋊C4—28no—
479C22⋊C4—216no—
480C22⋊C4—16616no—
481C22⋊C4—16616no—
482C22⋊C4—1668no—
483C22⋊C4—16616no—
484C42—8316no—
485C42—16616no—
486C23—216no—
487C23—28no—
488C23—24no—
489C23—22no—
490C23—22no—
491C23—24no—
492C23—48no—
493C23—44no—
494C23—44no—
495C23—3328no—
496C23—3324no—
497C23—3324no—
498C23—834no—
499C23—16616no—
500C23—1668no—
501C23—1664no—
502C23—1662no—
503C23—1662no—
504C23—1664no—
505C23C2×D4×D8314yes—
506C23C2×D4×D8312yes—
507C23C2×Q8×D8314yes—
508C23C2×Q8×D8312yes—
509C23#41×D8312yes—
510C23#1458183914yes—
511C23C24×D8311yescharacteristic
512Q8—33232no—
513D4—16632no—
514C2×C4—216no—
515C2×C4—24no—
516C2×C4—28no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—44no—
525C2×C4—48no—
526C2×C4—33216no—
527C2×C4—3324no—
528C2×C4—3328no—
529C2×C4—33216no—
530C2×C4—8316no—
531C2×C4—8316no—
532C2×C4—834no—
533C2×C4—834no—
534C2×C4—838no—
535C2×C4—834no—
536C2×C4—834no—
537C2×C4—838no—
538C2×C4—1662no—
539C2×C4—1664no—
540C2×C4—1664no—
541C2×C4—1664no—
542C2×C4—1664no—
543C2×C4—16616no—
544C2×C4—1664no—
545C2×C4—1664no—
546C2×C4C2×D4×D8314yes—
547C2×C4C2×D4×D8318yes—
548C22—28no—
549C22—24no—
550C22—416no—
551C22—44no—
552C22—42no—
553C22—42no—
554C22—33216no—
555C22—3324no—
556C22—3322no—
557C22—3322no—
558C22—1668no—
559C22—1664no—
560C22C22⋊Q8×D8314yes—
561C22#127×D8314yes—
562C22#1912827314yes—
563C22#1912834918yes—
564C22#1912836418yes—
565C22C22×D4×D8312yes—
566C22C22×D4×D8311yescharacteristic
567C22C22×Q8×D8311yescharacteristic
568C22C2×#41×D8311yescharacteristic
569C22C2×#1458183912yes—
570C4—28no—
571C4—24no—
572C4—42no—
573C4—44no—
574C4—3322no—
575C4—3324no—
576C4—838no—
577C4—838no—
578C4—1668no—
579C2—44no—
580C2—3324no—
581C2#2491241118yesdirect product factor
582C2C2×C22⋊Q8×D8311yescharacteristic
583C2C2×#127×D8311yescharacteristic
584C2C2×#1912827311yescharacteristic
585C2C2×#1912834912yes—
586C2C2×#1912836412yes—
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#399×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC2×#399D83
hypocenterC83C2×#2542
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#14581791C2semidirect
2. C22×#14581770C2semidirect
3. C22×#14581769C2semidirect
5. #24912411C2direct (N × H)
6. C2×#19127638C2semidirect
7. C2×#19127637C2semidirect
8. C2×#19127636C2semidirect
10. C2×#19127570C2semidirect
11. C2×#19127552C2semidirect
12. C2×#399×C83C2semidirect
18. C2×#14581791C22semidirect
20. C2×#14581770C22semidirect
22. C2×#14581769C22semidirect
38. #19127638C22semidirect
39. #19127637C22semidirect
40. #19127636C22semidirect
42. #19127570C22semidirect
43. #19127552C22semidirect
49. #399×C83C22semidirect
58. C22×C22⋊D83Q8semidirect
83. C2×Dic83⋊C4D4semidirect
129. C2×C22⋊D83C2×Q8semidirect
160. Dic83⋊C4C2×D4semidirect
244. C2×Dic83C22⋊Q8semidirect
283. Dic83C2×C22⋊Q8semidirect
287. C2×C83#2542semidirect
302. C2×#399D83semidirect
306. C83C2×#2542semidirect
339. #399C2×D83semidirect
581. C2#24912411direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817912
C22×#145817702
C22×#145817692
C22×(C22⋊D83)⋊C42
#249124112
C2×#191276382
C2×#191276372
C2×#191276362
C2×#191276012
C2×#191275702
C2×#191275522
C2×#399×C832
C2×#254283