Finite Group Databasebeta

← C2×#21446048 #29680870

Subgroups — C2×#21446048 #29680870

Order 15616.

1566 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840243C211yesmaximal, characteristic
2C2×#16839804C211yesmaximal, characteristic, complemented
3C22×#14519703C211yesmaximal, characteristic
4C2×#16839764C211yesmaximal, characteristic
5C2×#16839631C211yesmaximal, characteristic, complemented
6#21446048C218yesmaximal, direct product factor
7C2×#16839523C211yesmaximal, characteristic, complemented
8C2×C61×#343C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10#16840243—22no—
11#16840243—22no—
12#16840243—22no—
13#16840243C2214yes—
14C2×#14519742—21no—
15C2×#14519739—21no—
16C2×C4×C22⋊D61—22no—
17C2×#14519736C2211yescharacteristic
18C2×#14519735—21no—
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758196—22no—
21C2×C4⋊C4×D61—21no—
22C22×C4×Dic61C2211yescharacteristic
23#16839804—22no—
24#16839804C2214yescomplemented
25C2×#14519711—21no—
26C2×#14519709—21no—
27C2×#14519703C418yescomplemented
28C2×#14519703C2214yes—
29#16839764—22no—
30#16839764C2214yes—
31C2×#14519702—21no—
32C2×#14519699—21no—
33#16839631—22no—
34#16839631C2214yescomplemented
35#16839523C2214yescomplemented
36C22×M16×C61C2211yescharacteristic
37C22×M16×C61C2211yescharacteristic
38C22×C4⋊C4×C61C2211yescharacteristic
39C61×#343C2214yescomplemented
40C2×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222—22no—
43C2×#11758222—22no—
44C2×#11758222C2×C414yes—
45C2×#11758222D412yes—
46C2×#11758222Q814yes—
47C2×#11758222C2312yes—
48C22×Dic122D411yescharacteristic
49C22×D244D411yescharacteristic
50C22×C22⋊D61—21no—
51C23×Dic61—21no—
52C23×Dic61—21no—
53C22×C4×D61—21no—
54C22×C4×D61—22no—
55#14519742—24no—
56#14519742—24no—
57#14519739—24no—
58#14519739—24no—
59C4×C22⋊D61—28no—
60C4×C22⋊D61—28no—
61#14519736—21no—
62#14519736—21no—
63#14519736D412yes—
64#14519736C2312yes—
65#14519735—24no—
66#14519735—24no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61D411yescharacteristic
73C2×C4⋊Dic61D411yescharacteristic
74C2×C4⋊Dic61C2312yes—
75C2×#11758196—22no—
76C2×#11758196—28no—
77C2×#11758196—48no—
78C4⋊C4×D61—24no—
79C4⋊C4×D61—24no—
80C2×C22⋊Dic61—21no—
81C2×#11758198—22no—
82C2×C4×Dic61—22no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—22no—
86C2×C4×Dic61C2×C414yescomplemented
87C2×C4×Dic61C2312yes—
88#14519711—24no—
89#14519709—24no—
90#14519703C2×C4116yescomplemented
91#14519702—24no—
92#14519699—24no—
93C23×C4×C61D412yes—
94C23×C4×C61C2311yescharacteristic
95C2×M16×C61—21no—
96C2×M16×C61—22no—
97C2×M16×C61—21no—
98C2×M16×C61—22no—
99C2×M16×C61—22no—
100C2×M16×C61C2×C414yescomplemented
101C2×M16×C61C2312yes—
102C2×M16×C61C2312yes—
103C22×C8×C61—21no—
104C22×C8×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61D412yes—
110C2×C4⋊C4×C61C2312yes—
111C24×C61C2×D411yescharacteristic
112C23×D61—21no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—44no—
116C22×C4×C61C22×C412yes—
117C22×C4×C61C2×D414yes—
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×Q812yes—
124C22×C4×C61#4112yes—
125C22×C4×C61#4112yes—
126C22×C4×C61C2411yescharacteristic
127C2×C22⋊D61—24no—
128C2×C22⋊D61—22no—
129C2×C22⋊D61—24no—
130C2×C22⋊D61—22no—
131C22×Dic61—24no—
132C22×Dic61—24no—
133C22×Dic61—24no—
134C22×Dic61—21no—
135C22×Dic61—22no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—22no—
139C22×Dic61—44no—
140C22×Dic61—41no—
141C22×Dic61—41no—
142#11758222—24no—
143#11758222—24no—
144#11758222—24no—
145#11758222—24no—
146#11758222—24no—
147#11758222—22no—
148#11758222—22no—
149#11758222C4⋊C418yescomplemented
150#11758222C22×C414yes—
151#11758222C2×Q814yes—
152C2×D244—21no—
153C2×D244—22no—
154C2×D244C4⋊C414yescomplemented
155C2×D244C2×D412yes—
156C2×C4×D61—24no—
157C2×C4×D61—22no—
158C2×C4×D61—24no—
159C2×C4×D61—22no—
160C2×C4×D61—28no—
161C2×C4×D61—84no—
162C2×Dic122—21no—
163C2×Dic122—22no—
164C2×Dic122C4⋊C414yescomplemented
165C2×Dic122C2×D412yes—
166M16×C61—24no—
167M16×C61—22no—
168M16×C61—22no—
169M16×C61—22no—
170M16×C61—42no—
171M16×C61C22×C414yescomplemented
172C2×C8×C61—24no—
173C2×C8×C61—22no—
174C2×C8×C61—22no—
175C2×C8×C61—42no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61—22no—
178C4⋊C4×C61—22no—
179C4⋊C4×C61—22no—
180C22⋊Dic61—22no—
181C22⋊Dic61—22no—
182#11758198—28no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—22no—
186C4⋊Dic61—22no—
187C4⋊Dic61—41no—
188C4⋊Dic61—41no—
189C4⋊Dic61C2×D412yes—
190C4⋊Dic61C2×D412yes—
191#11758196—28no—
192#11758196—416no—
193C4×Dic61—28no—
194C4×Dic61—24no—
195C4×Dic61—22no—
196C4×Dic61—22no—
197C4×Dic61—22no—
198C4×Dic61C22×C414yescomplemented
199C23×C61—22no—
200C23×C61—22no—
201C23×C61C4×D412yes—
202C23×C61#12011yescharacteristic
203C23×C61#12011yescharacteristic
204C23×C61C22⋊Q812yes—
205C23×C61C22×D411yescharacteristic
206C22×D61—22no—
207C22×D61—24no—
208C22×D61—42no—
209C22×D61—42no—
210C2×C4×C61—24no—
211C2×C4×C61—44no—
212C2×C4×C61—44no—
213C2×C4×C61—82no—
214C2×C4×C61C2×C4⋊C412yes—
215C2×C4×C61C2×C4⋊C412yes—
216C2×C4×C61C4×D412yes—
217C2×C4×C61C4×D412yes—
218C2×C4×C61C4×D412yes—
219C2×C4×C61#12011yescharacteristic
220C2×C4×C61#12011yescharacteristic
221C2×C4×C61C22⋊Q812yes—
222C2×C4×C61C22⋊Q812yes—
223C2×C4×C61C22⋊Q812yes—
224C2×C4×C61#12312yes—
225C2×C4×C61#12312yes—
226C2×C4×C61C23×C411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C22×Q811yescharacteristic
230C2×C4×C61C2×#4111yescharacteristic
231C2×C4×C61C2×#4111yescharacteristic
232C22⋊D61—24no—
233C22⋊D61—24no—
234C22⋊D61—28no—
235C2×Dic61—24no—
236C2×Dic61—216no—
237C2×Dic61—24no—
238C2×Dic61—24no—
239C2×Dic61—22no—
240C2×Dic61—24no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—42no—
244C2×Dic61—42no—
245C2×Dic61—44no—
246C2×Dic61—42no—
247C2×Dic61—82no—
248C2×Dic61—82no—
249D244—22no—
250D244—24no—
251D244C2×C4⋊C414yescomplemented
252C4×D61—24no—
253C4×D61—24no—
254C4×D61—28no—
255C4×D61—88no—
256Dic122—22no—
257Dic122—24no—
258Dic122C2×C4⋊C414yescomplemented
259C8×C61—24no—
260C8×C61—42no—
261C2×#1859—611nomaximal, Sylow
262C22×C61—24no—
263C22×C61—24no—
264C22×C61—21no—
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—21no—
268C22×C61#38512yes—
269C22×C61#38512yes—
270C22×C61#45312yes—
271C22×C61#45612yes—
272C22×C61C2×C4×D411yescharacteristic
273C22×C61C2×#12011yescharacteristic
274C22×C61C2×C22⋊Q811yescharacteristic
275C2×D61—24no—
276C2×D61—48no—
277C2×D61—42no—
278C2×D61—42no—
279C4×C61—44no—
280C4×C61#38512yes—
281C4×C61#38512yes—
282C4×C61C22×C4⋊C411yescharacteristic
283C4×C61C2×C4×D411yescharacteristic
284C4×C61C2×C22⋊Q811yescharacteristic
285C4×C61C2×#12311yescharacteristic
286Dic61—28no—
287Dic61—24no—
288Dic61—42no—
289Dic61—42no—
290Dic61—82no—
291C2×#520—611no—
292C2×#428—611no—
293C22×#104—611no—
294C2×#417—611no—
295C2×#384—611no—
296#1859—618no—
297C2×#343D6111yescharacteristic, complemented
298C2×#339—611no—
299C2×C61—21no—
300C2×C61—21no—
301C2×C61—22no—
302C2×C61#185914yescomplemented
303C2×C61C2×#38511yescharacteristic
304C2×C61C2×#45311yescharacteristic
305C2×C61C2×#45611yescharacteristic
306D61—44no—
307C22×#41—611no—
308C22×M16C2×D6111yescharacteristic
309C22×M16C2×D6111yescharacteristic
310#520—614no—
311#520—1222no—
312#520—1222no—
313#520—1222no—
314C2×C4×Q8—1221no—
315C2×C4×D4—1221no—
316C2×C4×D4—1222no—
317C2×#117—611no—
318C2×#117—1221no—
319C22×C4⋊C4—611no—
320C22×C4⋊C4—1221no—
321C22×C4⋊C4—1222no—
322C22×C4⋊C4C2×D6111yescharacteristic
323C22×C42—611no—
324#428—614no—
325#428—1222no—
326C2×#107—1221no—
327C2×#106—1221no—
328C2×#104—618no—
329C2×#104—614no—
330#417—614no—
331#417—1222no—
332C2×#103—1221no—
333C2×#102—1221no—
334#384—614no—
335#384—1222no—
336#343C2×D6114yescomplemented
337#339—614no—
338C61C2×#185911yescharacteristic, complemented, Sylow
339C2×#41—614no—
340C2×#41—612no—
341C2×#41—614no—
342C2×#41—612no—
343C2×#41—1221no—
344C2×#41—1222no—
345C2×#41—1221no—
346C2×#41—1222no—
347C22×Q8—611no—
348C22×D4—611no—
349C22×D4—1221no—
350C23×C4—1222no—
351C23×C4—1221no—
352C23×C4—1221no—
353C23×C4—1221no—
354C23×C4D24412yes—
355C23×C4C22×D6111yescharacteristic
356C2×M16—21no—
357C2×M16—22no—
358C2×M16—21no—
359C2×M16—22no—
360C2×M16—22no—
361C2×M16C4×D6114yescomplemented
362C2×M16C22×D6112yes—
363C2×M16C22×D6112yes—
364C22×C8—21no—
365C22×C8—21no—
366C4×Q8—1224no—
367C4×Q8—1224no—
368C4×D4—1224no—
369C4×D4—1224no—
370C4×D4—1228no—
371C4×D4—1228no—
372#117—612no—
373#117—612no—
374#117—1224no—
375#117—1224no—
376#117—1221no—
377#117—1221no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—611no—
383C2×C4⋊C4—611no—
384C2×C4⋊C4—612no—
385C2×C4⋊C4—1224no—
386C2×C4⋊C4—1224no—
387C2×C4⋊C4—1222no—
388C2×C4⋊C4—1221no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1228no—
394C2×C4⋊C4—2448no—
395C2×C4⋊C4D24412yes—
396C2×C4⋊C4C22×D6112yes—
397C2×C22⋊C4—1222no—
398C2×C22⋊C4—1221no—
399C2×C42—614no—
400C2×C42—612no—
401C2×C42—1222no—
402C2×C42—1221no—
403C2×C42—1222no—
404C2×C42—1221no—
405#107—1224no—
406#106—1224no—
407#104—6116no—
408#103—1224no—
409#102—1224no—
410C24—1221no—
411C24C2×D24411yescharacteristic
412#41—614no—
413#41—614no—
414#41—618no—
415#41—1222no—
416#41—1222no—
417#41—1224no—
418#41—1224no—
419#41—1224no—
420#41—1224no—
421#41—1224no—
422C2×Q8—612no—
423C2×Q8—614no—
424C2×Q8—1221no—
425C2×Q8—1222no—
426C2×D4—612no—
427C2×D4—614no—
428C2×D4—1222no—
429C2×D4—1224no—
430C2×D4—1222no—
431C2×D4—1224no—
432C2×D4—1221no—
433C2×D4—1222no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—44no—
437C22×C4—1228no—
438C22×C4—1224no—
439C22×C4—1224no—
440C22×C4—1222no—
441C22×C4—1224no—
442C22×C4—1221no—
443C22×C4—1222no—
444C22×C4—1224no—
445C22×C4—1222no—
446C22×C4—1224no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1222no—
450C22×C4—4884no—
451C22×C4—2444no—
452C22×C4—2441no—
453C22×C4—2441no—
454C22×C4C2×C4×D6112yes—
455C22×C4C2×D24414yes—
456C22×C4C2×D24411yescharacteristic
457C22×C4#1175822212yes—
458C22×C4D4×D6111yescharacteristic
459C22×C4D4×D6111yescharacteristic
460C22×C4D4×D6111yescharacteristic
461C22×C4D4×D6111yescharacteristic
462C22×C4#1175822412yes—
463C22×C4Q8×D6112yes—
464C22×C4C23×D6111yescharacteristic
465M16—22no—
466M16—24no—
467M16—22no—
468M16—22no—
469M16—42no—
470M16C2×C4×D6114yescomplemented
471C2×C8—22no—
472C2×C8—24no—
473C2×C8—22no—
474C2×C8—42no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—612no—
480C4⋊C4—612no—
481C4⋊C4—1228no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4—24416no—
487C4⋊C4—2441no—
488C4⋊C4—2441no—
489C22⋊C4—1228no—
490C22⋊C4—1222no—
491C22⋊C4—1222no—
492C42—614no—
493C42—1228no—
494C42—1222no—
495C42—1222no—
496C42—1224no—
497C42—1222no—
498C23—22no—
499C23—22no—
500C23—1222no—
501C23—1224no—
502C23—2442no—
503C23—2442no—
504C23C4×D24412yes—
505C23#1451974711yescharacteristic
506C23#1451974711yescharacteristic
507C23#1451975712yes—
508C23C22×D24411yescharacteristic
509Q8—614no—
510Q8—1222no—
511Q8—1224no—
512D4—614no—
513D4—1224no—
514D4—1224no—
515D4—1228no—
516D4—1222no—
517D4—1224no—
518C2×C4—24no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—82no—
522C2×C4—1224no—
523C2×C4—1224no—
524C2×C4—12216no—
525C2×C4—1224no—
526C2×C4—1222no—
527C2×C4—1224no—
528C2×C4—1224no—
529C2×C4—1224no—
530C2×C4—1228no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—4888no—
534C2×C4—4882no—
535C2×C4—4882no—
536C2×C4—2444no—
537C2×C4—2442no—
538C2×C4—2442no—
539C2×C4—2442no—
540C2×C4C4⋊C4×D6112yes—
541C2×C4C4⋊C4×D6112yes—
542C2×C4#1451973712yes—
543C2×C4#1451973712yes—
544C2×C4C4×D24412yes—
545C2×C4#1451974711yescharacteristic
546C2×C4#1451974711yescharacteristic
547C2×C4#1451975512yes—
548C2×C4#1451975512yes—
549C2×C4#1451975712yes—
550C2×C4#1451975912yes—
551C2×C4#1451975912yes—
552C2×C4C22×C4×D6111yescharacteristic
553C2×C4C2×D4×D6111yescharacteristic
554C2×C4C2×D4×D6111yescharacteristic
555C2×C4C2×Q8×D6111yescharacteristic
556C2×C4C2×#1175822411yescharacteristic
557C2×C4C2×#1175822211yescharacteristic
558C8—24no—
559C8—42no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—24no—
565C22—24no—
566C22—1224no—
567C22—2442no—
568C22—2442no—
569C22—2448no—
570C22#1683963612yes—
571C22#1683963612yes—
572C22#1683993212yes—
573C22#1683994712yes—
574C22C2×C4×D24411yescharacteristic
575C22C2×#1451974711yescharacteristic
576C22C2×#1451975711yescharacteristic
577C4—44no—
578C4—1228no—
579C4—1224no—
580C4—4882no—
581C4—2442no—
582C4—2442no—
583C4#1683963612yes—
584C4#1683963612yes—
585C4C2×C4⋊C4×D6111yescharacteristic
586C4C2×#1451973711yescharacteristic
587C4C2×#1451975511yescharacteristic
588C4C2×#1451975911yescharacteristic
589C2—21no—
590C2—21no—
591C2—22no—
592C2—2444no—
593C2#2144604814yesdirect product factor
594C2C2×#1683963611yescharacteristic
595C2C2×#1683993211yescharacteristic
596C2C2×#1683994711yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#343C2
socleC23×C61#120
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenterC2×#343D61
hypocenterC61C2×#1859
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
2. C2×#16839804C2semidirect
5. C2×#16839631C2semidirect
6. #21446048C2direct (N × H)
7. C2×#16839523C2semidirect
8. C2×C61×#343C2semidirect
24. #16839804C22semidirect
27. C2×#14519703C4semidirect
34. #16839631C22semidirect
35. #16839523C22semidirect
39. C61×#343C22semidirect
86. C2×C4×Dic61C2×C4semidirect
90. #14519703C2×C4semidirect
100. C2×M16×C61C2×C4semidirect
149. #11758222C4⋊C4semidirect
154. C2×D244C4⋊C4semidirect
164. C2×Dic122C4⋊C4semidirect
171. M16×C61C22×C4semidirect
198. C4×Dic61C22×C4semidirect
251. D244C2×C4⋊C4semidirect
258. Dic122C2×C4⋊C4semidirect
297. C2×#343D61semidirect
302. C2×C61#1859semidirect
336. #343C2×D61semidirect
338. C61C2×#1859semidirect
361. C2×M16C4×D61semidirect
470. M16C2×C4×D61semidirect
593. C2#21446048direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402432
C2×#168398042
C22×#145197032
C2×#168397642
C2×#168396312
#214460482
C2×#168395232
C2×C61×#3432
C2×#185961