Finite Group Databasebeta

← C2×#21446043 #29680865

Subgroups — C2×#21446043 #29680865

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×#16840245C211yesmaximal, characteristic
2C2×#16839802C211yesmaximal, characteristic, complemented
3C22×#14519704C211yesmaximal, characteristic
4C2×#16839631C211yesmaximal, characteristic, complemented
5#21446043C218yesmaximal, direct product factor
6C2×#16839530C211yesmaximal, characteristic, complemented
7C2×#16839523C211yesmaximal, characteristic, complemented
8C2×C61×#417C211yesmaximal, characteristic
9C22×#11758194C2211yescharacteristic
10#16840245—22no—
11#16840245—22no—
12#16840245—22no—
13#16840245C2214yes—
14C2×Q8×Dic61—21no—
15C2×D4×Dic61—21no—
16C2×D4×Dic61—22no—
17C2×#14519736—21no—
18C2×#14519736C2211yescharacteristic
19C22×C4⋊Dic61—21no—
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758196—22no—
22C22×C4×Dic61C2211yescharacteristic
23#16839802—22no—
24#16839802C2214yescomplemented
25C2×#14519710—21no—
26C2×#14519708—21no—
27C2×#14519704C418yescomplemented
28C2×#14519704C2214yes—
29#16839631—22no—
30#16839631C2214yescomplemented
31#16839530C2214yescomplemented
32#16839523C2214yescomplemented
33C22×#41×C61C2211yescharacteristic
34C22×M16×C61C2211yescharacteristic
35C22×C4⋊C4×C61C2211yescharacteristic
36C61×#417—22no—
37C61×#417C2214yes—
38C2×#103×C61—21no—
39C2×#102×C61—21no—
40C23×Dic61—21no—
41C23×Dic61—22no—
42C23×Dic61D412yes—
43C2×#11758194—21no—
44C2×#11758194—22no—
45C2×#11758194C2×C414yescomplemented
46C2×#11758194C2312yes—
47C22×#92418—21no—
48Q8×Dic61—24no—
49Q8×Dic61—24no—
50D4×Dic61—28no—
51D4×Dic61—24no—
52D4×Dic61—24no—
53D4×Dic61—28no—
54#14519736—24no—
55#14519736—21no—
56#14519736—21no—
57#14519736—24no—
58#14519736D412yes—
59#14519736C2312yes—
60C2×C4⋊Dic61—22no—
61C2×C4⋊Dic61—24no—
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—24no—
67C2×C4⋊Dic61D412yes—
68C2×C4⋊Dic61D411yescharacteristic
69C2×C4⋊Dic61D411yescharacteristic
70C2×C4⋊Dic61C2312yes—
71C2×#11758196—28no—
72C2×#11758196—48no—
73C2×C22⋊Dic61—22no—
74C2×C22⋊Dic61—21no—
75C2×C4×Dic61—22no—
76C2×C4×Dic61—21no—
77C2×C4×Dic61—21no—
78C2×C4×Dic61—22no—
79C2×C4×Dic61C2×C414yescomplemented
80C2×C4×Dic61C2312yes—
81#14519710—24no—
82#14519708—24no—
83#14519704C2×C4116yescomplemented
84C2×#41×C61—21no—
85C2×#41×C61—21no—
86C2×#41×C61—22no—
87C2×#41×C61—22no—
88C2×#41×C61C2×C414yes—
89C2×#41×C61D412yes—
90C2×#41×C61Q814yes—
91C2×#41×C61C2312yes—
92C22×Q8×C61D411yescharacteristic
93C22×D4×C61—21no—
94C22×D4×C61D411yescharacteristic
95C23×C4×C61—21no—
96C23×C4×C61—21no—
97C23×C4×C61C2311yescharacteristic
98C2×M16×C61—21no—
99C2×M16×C61—22no—
100C2×M16×C61—22no—
101C2×M16×C61C2312yes—
102C22×C8×C61—21no—
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61C2312yes—
109#103×C61—24no—
110#102×C61—24no—
111C24×C61—21no—
112C24×C61C2×D411yescharacteristic
113#41×C61—24no—
114#41×C61—24no—
115#41×C61—24no—
116#41×C61—24no—
117#41×C61—24no—
118#41×C61—22no—
119#41×C61—22no—
120#41×C61C4⋊C418yescomplemented
121#41×C61C22×C414yes—
122#41×C61C2×Q814yes—
123C2×Q8×C61—21no—
124C2×Q8×C61—22no—
125C2×Q8×C61C4⋊C414yescomplemented
126C2×Q8×C61C2×D412yes—
127C2×D4×C61—24no—
128C2×D4×C61—22no—
129C2×D4×C61—24no—
130C2×D4×C61—22no—
131C2×D4×C61—21no—
132C2×D4×C61—22no—
133C2×D4×C61C4⋊C414yescomplemented
134C2×D4×C61C2×D412yes—
135C22×C4×C61—21no—
136C22×C4×C61—24no—
137C22×C4×C61—22no—
138C22×C4×C61—24no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—44no—
142C22×C4×C61—41no—
143C22×C4×C61—41no—
144C22×C4×C61C22×C412yes—
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×Q812yes—
151C22×C4×C61#4112yes—
152C22×C4×C61#4112yes—
153C22×C4×C61C2411yescharacteristic
154C22×Dic61—24no—
155C22×Dic61—24no—
156C22×Dic61—24no—
157C22×Dic61—22no—
158C22×Dic61—21no—
159C22×Dic61—22no—
160C22×Dic61—21no—
161C22×Dic61—28no—
162C22×Dic61—22no—
163C22×Dic61—44no—
164C22×Dic61—84no—
165C22×Dic61C2×D414yes—
166M16×C61—22no—
167M16×C61—22no—
168M16×C61—42no—
169C2×C8×C61—22no—
170C2×C8×C61—42no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61—22no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61—41no—
175C22⋊Dic61—28no—
176C22⋊Dic61—22no—
177C22⋊Dic61—22no—
178C4⋊Dic61—28no—
179C4⋊Dic61—22no—
180C4⋊Dic61—21no—
181C4⋊Dic61—22no—
182C4⋊Dic61—21no—
183C4⋊Dic61—22no—
184C4⋊Dic61—22no—
185C4⋊Dic61C2×D412yes—
186C4⋊Dic61C2×D412yes—
187#11758196—416no—
188C4×Dic61—28no—
189C4×Dic61—24no—
190C4×Dic61—22no—
191C4×Dic61—22no—
192C4×Dic61—22no—
193C4×Dic61C22×C414yescomplemented
194#11758194—24no—
195#11758194—22no—
196#11758194C22×C414yescomplemented
197C2×#92418—24no—
198C2×#92418—22no—
199C23×C61—22no—
200C23×C61—22no—
201C23×C61—22no—
202C23×C61—24no—
203C23×C61—42no—
204C23×C61—42no—
205C23×C61C4×D412yes—
206C23×C61#12011yescharacteristic
207C23×C61#12011yescharacteristic
208C23×C61C22⋊Q812yes—
209C23×C61C22×D411yescharacteristic
210Q8×C61—22no—
211Q8×C61—24no—
212Q8×C61C2×C4⋊C414yescomplemented
213D4×C61—24no—
214D4×C61—24no—
215D4×C61—28no—
216D4×C61—22no—
217D4×C61—24no—
218D4×C61C2×C4⋊C414yescomplemented
219C2×C4×C61—22no—
220C2×C4×C61—24no—
221C2×C4×C61—24no—
222C2×C4×C61—24no—
223C2×C4×C61—28no—
224C2×C4×C61—44no—
225C2×C4×C61—42no—
226C2×C4×C61—82no—
227C2×C4×C61—82no—
228C2×C4×C61C2×C4⋊C412yes—
229C2×C4×C61C2×C4⋊C412yes—
230C2×C4×C61C4×D412yes—
231C2×C4×C61C4×D412yes—
232C2×C4×C61C4×D412yes—
233C2×C4×C61#12011yescharacteristic
234C2×C4×C61#12011yescharacteristic
235C2×C4×C61C22⋊Q812yes—
236C2×C4×C61C22⋊Q812yes—
237C2×C4×C61C22⋊Q812yes—
238C2×C4×C61#12312yes—
239C2×C4×C61#12312yes—
240C2×C4×C61C23×C411yescharacteristic
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C22×Q811yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×Dic61—24no—
247C2×Dic61—216no—
248C2×Dic61—24no—
249C2×Dic61—24no—
250C2×Dic61—22no—
251C2×Dic61—24no—
252C2×Dic61—22no—
253C2×Dic61—44no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61—44no—
257C2×Dic61—82no—
258C2×Dic61—88no—
259C8×C61—42no—
260#92418—24no—
261C2×#1859—611nomaximal, Sylow
262C22×C61—24no—
263C22×C61—24no—
264C22×C61—21no—
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—24no—
269C22×C61—48no—
270C22×C61—42no—
271C22×C61—42no—
272C22×C61#38512yes—
273C22×C61#38512yes—
274C22×C61#45312yes—
275C22×C61#45612yes—
276C22×C61C2×C4×D411yescharacteristic
277C22×C61C2×#12011yescharacteristic
278C22×C61C2×C22⋊Q811yescharacteristic
279C4×C61—24no—
280C4×C61—82no—
281C4×C61#38512yes—
282C4×C61#38512yes—
283C4×C61C22×C4⋊C411yescharacteristic
284C4×C61C2×C4×D411yescharacteristic
285C4×C61C2×C22⋊Q811yescharacteristic
286C4×C61C2×#12311yescharacteristic
287Dic61—28no—
288Dic61—44no—
289Dic61—42no—
290Dic61—42no—
291C2×#520—611no—
292C2×#428—611no—
293C22×#104—611no—
294C2×#417D6111yescharacteristic
295C2×#384—611no—
296#1859—618no—
297C2×#343—611no—
298C2×#339—611no—
299C2×C61—21no—
300C2×C61—21no—
301C2×C61—22no—
302C2×C61—44no—
303C2×C61#185914yescomplemented
304C2×C61C2×#38511yescharacteristic
305C2×C61C2×#45311yescharacteristic
306C2×C61C2×#45611yescharacteristic
307C22×#41C2×D6111yescharacteristic
308C22×M16—611no—
309C22×M16C2×D6111yescharacteristic
310#520—614no—
311#520—1222no—
312#520—1222no—
313#520—1222no—
314C2×C4×Q8—1221no—
315C2×C4×D4—1222no—
316C2×C4×D4—1221no—
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—22no—
331#417C2×D6114yes—
332C2×#103—21no—
333C2×#102—21no—
334#384—614no—
335#384—1222no—
336#343—614no—
337#339—614no—
338C61C2×#185911yescharacteristic, complemented, Sylow
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41Dic12214yes—
344C2×#41C4×D6114yes—
345C2×#41C22⋊D6112yes—
346C2×#41C22×D6112yes—
347C22×Q8C22⋊D6111yescharacteristic
348C22×D4—21no—
349C22×D4C22⋊D6111yescharacteristic
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—612no—
353C23×C4—1221no—
354C23×C4—1222no—
355C23×C4C22×D6111yescharacteristic
356C2×M16—21no—
357C2×M16—22no—
358C2×M16—22no—
359C2×M16—614no—
360C2×M16—612no—
361C2×M16—1221no—
362C2×M16—1222no—
363C2×M16C22×D6112yes—
364C22×C8—21no—
365C22×C8—1221no—
366C4×Q8—1224no—
367C4×Q8—1224no—
368C4×D4—1228no—
369C4×D4—1228no—
370C4×D4—1224no—
371C4×D4—1224no—
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—21no—
383C2×C4⋊C4—611no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—612no—
386C2×C4⋊C4—612no—
387C2×C4⋊C4—1224no—
388C2×C4⋊C4—1222no—
389C2×C4⋊C4—1224no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4—1228no—
395C2×C4⋊C4—2448no—
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—24no—
409#102—24no—
410C24—21no—
411C24D4×D6111yescharacteristic
412#41—22no—
413#41—22no—
414#41—24no—
415#41—24no—
416#41—24no—
417#41—24no—
418#41—24no—
419#41#1175819618yescomplemented
420#41C2×Dic12214yes—
421#41C2×C4×D6114yes—
422C2×Q8—21no—
423C2×Q8—22no—
424C2×Q8#1175819614yescomplemented
425C2×Q8C2×C22⋊D6112yes—
426C2×D4—22no—
427C2×D4—24no—
428C2×D4—22no—
429C2×D4—24no—
430C2×D4—21no—
431C2×D4—22no—
432C2×D4#1175819614yescomplemented
433C2×D4C2×C22⋊D6112yes—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—44no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—614no—
444C22×C4—1224no—
445C22×C4—1224no—
446C22×C4—1222no—
447C22×C4—1224no—
448C22×C4—1228no—
449C22×C4—1222no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1222no—
453C22×C4—4884no—
454C22×C4—2444no—
455C22×C4C2×Dic12212yes—
456C22×C4C2×C4×D6112yes—
457C22×C4D4×D6111yescharacteristic
458C22×C4D4×D6111yescharacteristic
459C22×C4D4×D6111yescharacteristic
460C22×C4#1175822412yes—
461C22×C4#1175822412yes—
462C22×C4C2×C22⋊D6111yescharacteristic
463C22×C4C2×C22⋊D6111yescharacteristic
464C22×C4C23×D6111yescharacteristic
465M16—22no—
466M16—22no—
467M16—42no—
468M16—614no—
469M16—1222no—
470M16—1224no—
471C2×C8—22no—
472C2×C8—42no—
473C2×C8—1222no—
474C2×C8—1224no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—612no—
480C4⋊C4—612no—
481C4⋊C4—1228no—
482C4⋊C4—1222no—
483C4⋊C4—1222no—
484C4⋊C4—1221no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—1221no—
488C4⋊C4—24416no—
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—22no—
501C23—24no—
502C23—42no—
503C23—42no—
504C23#1451973712yes—
505C23#1451974511yescharacteristic
506C23#1451974511yescharacteristic
507C23#1451975412yes—
508C23C2×D4×D6111yescharacteristic
509Q8—22no—
510Q8—24no—
511Q8C2×#1175819614yescomplemented
512D4—24no—
513D4—24no—
514D4—28no—
515D4—22no—
516D4—24no—
517D4C2×#1175819614yescomplemented
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—28no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—1224no—
528C2×C4—1224no—
529C2×C4—12216no—
530C2×C4—1224no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1224no—
534C2×C4—4882no—
535C2×C4—4888no—
536C2×C4—2442no—
537C2×C4—2442no—
538C2×C4—2444no—
539C2×C4—2444no—
540C2×C4C2×#1175819612yes—
541C2×C4C2×#1175819612yes—
542C2×C4#1451973712yes—
543C2×C4#1451973712yes—
544C2×C4#1451973712yes—
545C2×C4#1451974511yescharacteristic
546C2×C4#1451974511yescharacteristic
547C2×C4#1451975412yes—
548C2×C4#1451975412yes—
549C2×C4#1451975412yes—
550C2×C4#1451975812yes—
551C2×C4#1451975812yes—
552C2×C4C22×C4×D6111yescharacteristic
553C2×C4C2×D4×D6111yescharacteristic
554C2×C4C22×C22⋊D6111yescharacteristic
555C2×C4C22×Dic12211yescharacteristic
556C2×C4C2×#1175822411yescharacteristic
557C2×C4C2×#1175822411yescharacteristic
558C8—42no—
559C8—1224no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—24no—
565C22—24no—
566C22—24no—
567C22—42no—
568C22—42no—
569C22—48no—
570C22#1683963412yes—
571C22#1683963412yes—
572C22#1683992812yes—
573C22#1683994312yes—
574C22C2×#1451973711yescharacteristic
575C22C2×#1451974511yescharacteristic
576C22C2×#1451975411yescharacteristic
577C4—24no—
578C4—82no—
579C4—1228no—
580C4—2442no—
581C4—2444no—
582C4—2442no—
583C4#1683963412yes—
584C4#1683963412yes—
585C4C22×#1175819611yescharacteristic
586C4C2×#1451973711yescharacteristic
587C4C2×#1451975411yescharacteristic
588C4C2×#1451975811yescharacteristic
589C2—21no—
590C2—21no—
591C2—22no—
592C2—44no—
593C2#2144604314yesdirect product factor
594C2C2×#1683963411yescharacteristic
595C2C2×#1683992811yescharacteristic
596C2C2×#1683994311yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#417C2
socleC23×C61#120
prime radicalC22×#41×C61C22
cosocleC22×C4×C61C24
hypercenterC2×#417D61
hypocenterC61C2×#1859
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#16839802C2semidirect
4. C2×#16839631C2semidirect
5. #21446043C2direct (N × H)
6. C2×#16839530C2semidirect
7. C2×#16839523C2semidirect
24. #16839802C22semidirect
27. C2×#14519704C4semidirect
30. #16839631C22semidirect
31. #16839530C22semidirect
32. #16839523C22semidirect
45. C2×#11758194C2×C4semidirect
79. C2×C4×Dic61C2×C4semidirect
83. #14519704C2×C4semidirect
120. #41×C61C4⋊C4semidirect
125. C2×Q8×C61C4⋊C4semidirect
133. C2×D4×C61C4⋊C4semidirect
193. C4×Dic61C22×C4semidirect
196. #11758194C22×C4semidirect
212. Q8×C61C2×C4⋊C4semidirect
218. D4×C61C2×C4⋊C4semidirect
303. C2×C61#1859semidirect
338. C61C2×#1859semidirect
419. #41#11758196semidirect
424. C2×Q8#11758196semidirect
432. C2×D4#11758196semidirect
511. Q8C2×#11758196semidirect
517. D4C2×#11758196semidirect
593. C2#21446043direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402452
C2×#168398022
C22×#145197042
C2×#168396312
#214460432
C2×#168395302
C2×#168395232
C2×C61×#4172
C2×#185961