Finite Group Databasebeta

← C2×#21446054 #29680877

Subgroups — C2×#21446054 #29680877

Order 15616.

1478 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840245C211yesmaximal, characteristic
2C2×#16839804C211yesmaximal, characteristic, complemented
3C2×#16839763C211yesmaximal, characteristic
4C2×#16839628C211yesmaximal, characteristic, complemented
5#21446054C218yesmaximal, direct product factor
6C2×#16839530C211yesmaximal, characteristic, complemented
7C2×#16839522C211yesmaximal, characteristic, complemented
8C22×#104×C61C211yesmaximal, 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×C4⋊Dic61C2211yescharacteristic
22#16839804—22no—
23#16839804C2214yescomplemented
24C2×#14519711—21no—
25C2×#14519709—21no—
26#16839763—22no—
27#16839763C2214yes—
28C2×#14519701—21no—
29C2×#14519698—21no—
30#16839628—22no—
31#16839628C2214yescomplemented
32C2×#14519684—22no—
33#16839530C2214yescomplemented
34#16839522C2214yescomplemented
35C22×#41×C61C2211yescharacteristic
36C22×M16×C61C2211yescharacteristic
37C22×C42×C61C2211yescharacteristic
38C2×#104×C61C418yescomplemented
39C2×#104×C61C2214yes—
40C23×Dic61—22no—
41C23×Dic61—21no—
42C23×Dic61D412yes—
43C2×#11758194—21no—
44C2×#11758194—22no—
45C2×#11758194—22no—
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⋊Dic61—21no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61D412yes—
73C2×C4⋊Dic61D411yescharacteristic
74C2×C4⋊Dic61D411yescharacteristic
75C2×C4⋊Dic61C2312yes—
76C2×C4⋊Dic61C2312yes—
77C2×C22⋊Dic61—22no—
78C2×C22⋊Dic61—21no—
79C2×C4×Dic61—22no—
80C2×C4×Dic61—21no—
81#14519711—24no—
82#14519709—24no—
83#14519701—24no—
84#14519698—24no—
85#14519684—28no—
86C2×#41×C61—21no—
87C2×#41×C61—21no—
88C2×#41×C61—22no—
89C2×#41×C61—22no—
90C2×#41×C61C2×C414yes—
91C2×#41×C61D412yes—
92C2×#41×C61Q814yes—
93C2×#41×C61C2312yes—
94C22×Q8×C61D411yescharacteristic
95C22×D4×C61—21no—
96C22×D4×C61D411yescharacteristic
97C23×C4×C61—21no—
98C23×C4×C61—21no—
99C23×C4×C61C2311yescharacteristic
100C2×M16×C61—21no—
101C2×M16×C61—22no—
102C2×M16×C61C2×C414yescomplemented
103C2×M16×C61C2312yes—
104C22×C8×C61—21no—
105C2×C42×C61—21no—
106C2×C42×C61—22no—
107C2×C42×C61C2×C414yescomplemented
108C2×C42×C61C2312yes—
109#104×C61C2×C4116yescomplemented
110C24×C61—21no—
111C24×C61C2×D411yescharacteristic
112#41×C61—24no—
113#41×C61—24no—
114#41×C61—24no—
115#41×C61—24no—
116#41×C61—24no—
117#41×C61—22no—
118#41×C61—22no—
119#41×C61C4⋊C418yes—
120#41×C61C22×C414yes—
121#41×C61C2×Q814yes—
122C2×Q8×C61—21no—
123C2×Q8×C61—22no—
124C2×Q8×C61C4⋊C414yes—
125C2×Q8×C61C2×D412yes—
126C2×D4×C61—24no—
127C2×D4×C61—22no—
128C2×D4×C61—24no—
129C2×D4×C61—22no—
130C2×D4×C61—21no—
131C2×D4×C61—22no—
132C2×D4×C61C4⋊C414yes—
133C2×D4×C61C2×D412yes—
134C22×C4×C61—21no—
135C22×C4×C61—24no—
136C22×C4×C61—22no—
137C22×C4×C61—24no—
138C22×C4×C61—22no—
139C22×C4×C61—24no—
140C22×C4×C61—22no—
141C22×C4×C61—42no—
142C22×C4×C61—42no—
143C22×C4×C61C22×C412yes—
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×Q812yes—
150C22×C4×C61#4112yes—
151C22×C4×C61#4112yes—
152C22×C4×C61C2411yescharacteristic
153C22×Dic61—21no—
154C22×Dic61—22no—
155C22×Dic61—21no—
156C22×Dic61—28no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—44no—
160C22×Dic61—44no—
161C22×Dic61—41no—
162C22×Dic61—41no—
163C22×Dic61—84no—
164C22×Dic61C2×D414yes—
165M16×C61—24no—
166M16×C61—22no—
167M16×C61C22×C414yescomplemented
168C2×C8×C61—24no—
169C2×C8×C61—22no—
170C42×C61—24no—
171C42×C61—22no—
172C42×C61C22×C414yescomplemented
173C22⋊Dic61—28no—
174C22⋊Dic61—22no—
175C22⋊Dic61—22no—
176C4⋊Dic61—28no—
177C4⋊Dic61—22no—
178C4⋊Dic61—21no—
179C4⋊Dic61—22no—
180C4⋊Dic61—21no—
181C4⋊Dic61—22no—
182C4⋊Dic61—22no—
183C4⋊Dic61—22no—
184C4⋊Dic61—22no—
185C4⋊Dic61—41no—
186C4⋊Dic61—41no—
187C4⋊Dic61C2×D412yes—
188C4⋊Dic61C2×D412yes—
189C4×Dic61—28no—
190C4×Dic61—22no—
191C4×Dic61—22no—
192#11758194—22no—
193#11758194—22no—
194#11758194—42no—
195C2×#92418—22no—
196C2×#92418—42no—
197C23×C61—22no—
198C23×C61—22no—
199C23×C61—22no—
200C23×C61—24no—
201C23×C61—42no—
202C23×C61—42no—
203C23×C61C4×D412yes—
204C23×C61#12011yescharacteristic
205C23×C61#12011yescharacteristic
206C23×C61C22⋊Q812yes—
207C23×C61C22×D411yescharacteristic
208Q8×C61—22no—
209Q8×C61—24no—
210Q8×C61C2×C4⋊C414yes—
211D4×C61—24no—
212D4×C61—24no—
213D4×C61—28no—
214D4×C61—22no—
215D4×C61—24no—
216D4×C61C2×C4⋊C414yes—
217C2×C4×C61—22no—
218C2×C4×C61—24no—
219C2×C4×C61—24no—
220C2×C4×C61—24no—
221C2×C4×C61—28no—
222C2×C4×C61—24no—
223C2×C4×C61—48no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61C2×C4⋊C412yes—
227C2×C4×C61C2×C4⋊C412yes—
228C2×C4×C61C4×D412yes—
229C2×C4×C61C4×D412yes—
230C2×C4×C61C4×D412yes—
231C2×C4×C61#12011yescharacteristic
232C2×C4×C61#12011yescharacteristic
233C2×C4×C61C22⋊Q812yes—
234C2×C4×C61C22⋊Q812yes—
235C2×C4×C61C22⋊Q812yes—
236C2×C4×C61#12312yes—
237C2×C4×C61#12312yes—
238C2×C4×C61C23×C411yescharacteristic
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C22×D411yescharacteristic
241C2×C4×C61C22×Q811yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×Dic61—22no—
245C2×Dic61—24no—
246C2×Dic61—22no—
247C2×Dic61—42no—
248C2×Dic61—44no—
249C2×Dic61—42no—
250C2×Dic61—44no—
251C2×Dic61—44no—
252C2×Dic61—42no—
253C2×Dic61—82no—
254C2×Dic61—88no—
255C2×Dic61—82no—
256C2×Dic61—82no—
257C8×C61—24no—
258#92418—42no—
259C2×#1860—611nomaximal, Sylow
260C22×C61—24no—
261C22×C61—24no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—21no—
266C22×C61—24no—
267C22×C61—48no—
268C22×C61—42no—
269C22×C61—42no—
270C22×C61#38512yes—
271C22×C61#38512yes—
272C22×C61#45412yes—
273C22×C61#45512yes—
274C22×C61C2×C4×D411yescharacteristic
275C22×C61C2×#12011yescharacteristic
276C22×C61C2×C22⋊Q811yescharacteristic
277C4×C61—24no—
278C4×C61—44no—
279C4×C61#38512yes—
280C4×C61#38512yes—
281C4×C61C22×C4⋊C411yescharacteristic
282C4×C61C2×C4×D411yescharacteristic
283C4×C61C2×C22⋊Q811yescharacteristic
284C4×C61C2×#12311yescharacteristic
285Dic61—44no—
286Dic61—42no—
287Dic61—42no—
288Dic61—82no—
289C2×#520—611no—
290C2×#428—611no—
291C22×#104D6111yescharacteristic
292C2×#417—611no—
293C2×#382—611no—
294#1860—618no—
295C2×#343—611no—
296C2×#339—611no—
297C2×C61—21no—
298C2×C61—21no—
299C2×C61—22no—
300C2×C61—44no—
301C2×C61#186014yescomplemented
302C2×C61C2×#38511yescharacteristic
303C2×C61C2×#45511yescharacteristic
304C2×C61C2×#45411yescharacteristic
305C22×#41C2×D6111yescharacteristic
306C22×M16—611no—
307C22×M16C2×D6111yescharacteristic
308#520—614no—
309#520—1222no—
310#520—1222no—
311#520—1222no—
312C2×C4×Q8—1221no—
313C2×C4×D4—1222no—
314C2×C4×D4—1221no—
315C2×#117—611no—
316C2×#117—1221no—
317C22×C4⋊C4—611no—
318C22×C4⋊C4—611no—
319C22×C4⋊C4—1221no—
320C22×C42C2×D6111yescharacteristic
321#428—614no—
322#428—1222no—
323C2×#107—1221no—
324C2×#106—1221no—
325C2×#104Dic6118yescomplemented
326C2×#104C2×D6114yes—
327#417—614no—
328#417—1222no—
329C2×#103—1221no—
330C2×#102—1221no—
331#382—614no—
332#382—1222no—
333C2×#95—1222no—
334#343—614no—
335#339—614no—
336C61C2×#186011yescharacteristic, complemented, Sylow
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41Dic12214yes—
342C2×#41D24412yes—
343C2×#41C2×Dic6114yes—
344C2×#41C22×D6112yes—
345C22×Q8D24411yescharacteristic
346C22×D4—21no—
347C22×D4D24411yescharacteristic
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—612no—
351C23×C4—1222no—
352C23×C4—1221no—
353C23×C4C22×D6111yescharacteristic
354C2×M16—21no—
355C2×M16—22no—
356C2×M16—612no—
357C2×M16—1221no—
358C2×M16—1222no—
359C2×M16—1222no—
360C2×M16C2×Dic6114yescomplemented
361C2×M16C22×D6112yes—
362C22×C8—21no—
363C22×C8—1221no—
364C4×Q8—1224no—
365C4×Q8—1224no—
366C4×D4—1228no—
367C4×D4—1228no—
368C4×D4—1224no—
369C4×D4—1224no—
370#117—612no—
371#117—612no—
372#117—1224no—
373#117—1224no—
374#117—1221no—
375#117—1221no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—612no—
379C2×C4⋊C4—612no—
380C2×C4⋊C4—612no—
381C2×C4⋊C4—1224no—
382C2×C4⋊C4—1222no—
383C2×C4⋊C4—1224no—
384C2×C4⋊C4—1221no—
385C2×C4⋊C4—1221no—
386C2×C4⋊C4—1221no—
387C2×C4⋊C4—1221no—
388C2×C4⋊C4—1221no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4—1221no—
393C2×C22⋊C4—1222no—
394C2×C22⋊C4—1221no—
395C2×C42—21no—
396C2×C42—22no—
397C2×C42—1222no—
398C2×C42—1221no—
399C2×C42C2×Dic6114yescomplemented
400C2×C42C22×D6112yes—
401#107—1224no—
402#106—1224no—
403#104C2×Dic61116yescomplemented
404#103—1224no—
405#102—1224no—
406#95—1228no—
407C24—21no—
408C24D4×D6111yescharacteristic
409#41—22no—
410#41—22no—
411#41—24no—
412#41—24no—
413#41—24no—
414#41—24no—
415#41—24no—
416#41C4⋊Dic6118yes—
417#41C2×Dic12214yes—
418#41C22×Dic6114yes—
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8C4⋊Dic6114yes—
422C2×Q8C2×D24412yes—
423C2×D4—22no—
424C2×D4—24no—
425C2×D4—22no—
426C2×D4—24no—
427C2×D4—21no—
428C2×D4—22no—
429C2×D4C4⋊Dic6114yes—
430C2×D4C2×D24412yes—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—614no—
441C22×C4—1228no—
442C22×C4—1222no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1222no—
446C22×C4—1222no—
447C22×C4—4884no—
448C22×C4—2444no—
449C22×C4—2441no—
450C22×C4—2441no—
451C22×C4—2444no—
452C22×C4C2×Dic12212yes—
453C22×C4C2×D24411yescharacteristic
454C22×C4C2×D24411yescharacteristic
455C22×C4D4×D6111yescharacteristic
456C22×C4D4×D6111yescharacteristic
457C22×C4D4×D6111yescharacteristic
458C22×C4#1175822412yes—
459C22×C4#1175822412yes—
460C22×C4C22×Dic6112yes—
461C22×C4C23×D6111yescharacteristic
462M16—22no—
463M16—24no—
464M16—1222no—
465M16—1222no—
466M16—2442no—
467M16C22×Dic6114yescomplemented
468C2×C8—22no—
469C2×C8—24no—
470C2×C8—1222no—
471C2×C8—2442no—
472C4⋊C4—612no—
473C4⋊C4—612no—
474C4⋊C4—1228no—
475C4⋊C4—1222no—
476C4⋊C4—1222no—
477C4⋊C4—1221no—
478C4⋊C4—1222no—
479C4⋊C4—1222no—
480C4⋊C4—1221no—
481C4⋊C4—1222no—
482C4⋊C4—1222no—
483C4⋊C4—2441no—
484C4⋊C4—2441no—
485C22⋊C4—1228no—
486C22⋊C4—1222no—
487C22⋊C4—1222no—
488C42—22no—
489C42—24no—
490C42—1228no—
491C42—1222no—
492C42—1222no—
493C42C22×Dic6114yescomplemented
494C23—22no—
495C23—22no—
496C23—22no—
497C23—24no—
498C23—42no—
499C23—42no—
500C23D4×Dic6112yes—
501C23#1451974711yescharacteristic
502C23#1451974711yescharacteristic
503C23#1451975412yes—
504C23C2×D4×D6111yescharacteristic
505Q8—22no—
506Q8—24no—
507Q8C2×C4⋊Dic6114yes—
508D4—24no—
509D4—24no—
510D4—28no—
511D4—22no—
512D4—24no—
513D4C2×C4⋊Dic6114yes—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—28no—
519C2×C4—24no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—48no—
523C2×C4—1222no—
524C2×C4—1222no—
525C2×C4—1224no—
526C2×C4—4882no—
527C2×C4—4882no—
528C2×C4—4882no—
529C2×C4—4888no—
530C2×C4—2444no—
531C2×C4—2442no—
532C2×C4—2442no—
533C2×C4—2442no—
534C2×C4—2444no—
535C2×C4—2444no—
536C2×C4C2×C4⋊Dic6112yes—
537C2×C4C2×C4⋊Dic6112yes—
538C2×C4D4×Dic6112yes—
539C2×C4D4×Dic6112yes—
540C2×C4D4×Dic6112yes—
541C2×C4#1451974711yescharacteristic
542C2×C4#1451974711yescharacteristic
543C2×C4#1451975412yes—
544C2×C4#1451975412yes—
545C2×C4#1451975412yes—
546C2×C4#1451976112yes—
547C2×C4#1451976112yes—
548C2×C4C23×Dic6111yescharacteristic
549C2×C4C2×D4×D6111yescharacteristic
550C2×C4C22×D24411yescharacteristic
551C2×C4C22×Dic12211yescharacteristic
552C2×C4C2×#1175822411yescharacteristic
553C2×C4C2×#1175822411yescharacteristic
554C8—24no—
555C8—2442no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—24no—
561C22—24no—
562C22—24no—
563C22—42no—
564C22—42no—
565C22—48no—
566C22#1683963712yes—
567C22#1683963712yes—
568C22#1683993612yes—
569C22#1683994112yes—
570C22C2×D4×Dic6111yescharacteristic
571C22C2×#1451974711yescharacteristic
572C22C2×#1451975411yescharacteristic
573C4—24no—
574C4—44no—
575C4—4882no—
576C4—2442no—
577C4—2444no—
578C4—2442no—
579C4#1683963712yes—
580C4#1683963712yes—
581C4C22×C4⋊Dic6111yescharacteristic
582C4C2×D4×Dic6111yescharacteristic
583C4C2×#1451975411yescharacteristic
584C4C2×#1451976111yescharacteristic
585C2—21no—
586C2—21no—
587C2—22no—
588C2—44no—
589C2#2144605414yesdirect product factor
590C2C2×#1683963711yescharacteristic
591C2C2×#1683994111yescharacteristic
592C2C2×#1683993611yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×#104×C61C2
socleC23×C61#120
prime radicalC22×#41×C61C22
cosocleC22×C4×C61C24
hypercenterC22×#104D61
hypocenterC61C2×#1860
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C2×#16839804C2semidirect
4. C2×#16839628C2semidirect
5. #21446054C2direct (N × H)
6. C2×#16839530C2semidirect
7. C2×#16839522C2semidirect
23. #16839804C22semidirect
31. #16839628C22semidirect
33. #16839530C22semidirect
34. #16839522C22semidirect
38. C2×#104×C61C4semidirect
102. C2×M16×C61C2×C4semidirect
107. C2×C42×C61C2×C4semidirect
109. #104×C61C2×C4semidirect
167. M16×C61C22×C4semidirect
172. C42×C61C22×C4semidirect
301. C2×C61#1860semidirect
325. C2×#104Dic61semidirect
336. C61C2×#1860semidirect
360. C2×M16C2×Dic61semidirect
399. C2×C42C2×Dic61semidirect
403. #104C2×Dic61semidirect
467. M16C22×Dic61semidirect
493. C42C22×Dic61semidirect
589. C2#21446054direct (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×#168398042
C2×#168397632
C2×#168396282
#214460542
C2×#168395302
C2×#168395222
C22×#104×C612
C2×#186061