Finite Group Databasebeta

← C2×#21444216 #29646506

Subgroups — C2×#21444216 #29646506

Order 15616.

1346 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840309C211yesmaximal, characteristic
2C2×#16839813C211yesmaximal, characteristic, complemented
3C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
4#21444216C218yesmaximal, direct product factor
5C2×#16839491C211yesmaximal, characteristic, complemented
6C2×D4⋊#92418C211yesmaximal, characteristic, complemented
7C2×#16839489C211yesmaximal, characteristic, complemented
8C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
9C22×#11758222—21no—
10C22×C8×D61—21no—
11#16840309—22no—
12#16840309—22no—
13#16840309C414yes—
14#16840309C2214yes—
15C2×#14519776C411yescharacteristic
16C2×#14519773C411yescharacteristic
17C2×#14519763—21no—
18C2×#14519752C411yescharacteristic
19C2×#14519750—21no—
20C2×#14519748C411yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C4×C22⋊D61—21no—
23C2×C42×D61C2211yescharacteristic
24#16839813—22no—
25#16839813C2214yescomplemented
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519706—21no—
28C2×#14519706—21no—
29C4⋊C8×D61—22no—
30C4⋊C8×D61C2214yescomplemented
31C2×#14519689—21no—
32C2×C4×#92418C2211yescharacteristic
33#16839491C2214yescomplemented
34D4⋊#92418C2214yescomplemented
35#16839489C2214yescomplemented
36C2×C4×D4×C61C2211yescharacteristic
37C2×C4⋊C8×C61C2211yescharacteristic
38C2×C4×C8×C61C2211yescharacteristic
39C61×D4⋊C8C2214yescomplemented
40C2×#11758222—24no—
41C2×#11758222—24no—
42C2×#11758222—44no—
43C2×#11758222—44no—
44C22×Dic122—21no—
45C22×D244—21no—
46C22×D244C2×C411yescharacteristic
47C22×C22⋊D61—21no—
48C22×C22⋊D61—21no—
49C22×C22⋊D61—21no—
50C22×C4×D61—21no—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×#92418—21no—
55C22×#92418—21no—
56C2×C8×D61—24no—
57C2×C8×D61—44no—
58#14519776—22no—
59#14519776C2×C414yes—
60#14519773—22no—
61#14519773C2×C414yes—
62#14519763—24no—
63#14519763—24no—
64#14519752—22no—
65#14519752C2×C414yes—
66#14519750—24no—
67#14519750—24no—
68#14519748—22no—
69#14519748C2×C414yes—
70C4×D244—21no—
71C4×D244—21no—
72C4×D244C2×C412yes—
73C4×D244C2312yes—
74C4×C22⋊D61—24no—
75C4×C22⋊D61—24no—
76C2×C4⋊Dic61C2×C411yescharacteristic
77C2×#11758196—21no—
78C2×C22⋊Dic61—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×C4×Dic61C2×C411yescharacteristic
82C2×C4×Dic61D411yescharacteristic
83C2×C4×Dic61D411yescharacteristic
84C42×D61C2×C412yes—
85C42×D61D412yes—
86C42×D61D412yes—
87C42×D61C2312yes—
88C4⋊#92418—21no—
89C4⋊#92418C2312yes—
90#14519706—24no—
91#14519706—24no—
92#14519689—24no—
93C4×#92418—21no—
94C4×#92418C2312yes—
95C22×D4×C61C2×C411yescharacteristic
96C23×C4×C61—21no—
97C22×C8×C61—21no—
98C22×C8×C61—21no—
99C4×D4×C61—21no—
100C4×D4×C61—21no—
101C4×D4×C61C2×C412yes—
102C4×D4×C61C2312yes—
103C2×C4⋊C4×C61C2×C411yescharacteristic
104C2×C22⋊C4×C61—21no—
105C2×C42×C61C2311yescharacteristic
106C4⋊C8×C61—21no—
107C4⋊C8×C61C2312yes—
108C4×C8×C61—21no—
109C4×C8×C61C2312yes—
110C24×C61—21no—
111C23×D61—21no—
112C23×D61C22⋊C411yescharacteristic
113C2×D4×C61—21no—
114C2×D4×C61—22no—
115C2×D4×C61—22no—
116C2×D4×C61C22×C412yes—
117C22×C4×C61—21no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—42no—
121C22×C4×C61—42no—
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C2×C22⋊D61—24no—
126C2×C22⋊D61—24no—
127C2×C22⋊D61—24no—
128C2×C22⋊D61—44no—
129C2×C22⋊D61—44no—
130C2×C22⋊D61—44no—
131C22×Dic61—21no—
132C22×Dic61C22⋊C411yescharacteristic
133C22×Dic61C22⋊C411yescharacteristic
134C22×Dic61C22⋊C411yescharacteristic
135#11758222—416no—
136#11758222—48no—
137#11758222—48no—
138C2×D244—22no—
139C2×D244—22no—
140C2×D244—24no—
141C2×D244—21no—
142C2×D244—44no—
143C2×D244C22×C412yes—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—42no—
149C2×C4×D61—42no—
150C2×C4×D61—42no—
151C2×C4×D61C22⋊C412yes—
152C2×C4×D61C22⋊C412yes—
153C2×C4×D61C22⋊C412yes—
154C2×C4×D61D814yes—
155C2×C4×D61SD1614yes—
156C2×C4×D61C22×C412yes—
157C2×C4×D61C2×D412yes—
158C2×C4×D61C2×D412yes—
159C2×Dic122—24no—
160C2×Dic122—44no—
161C2×C8×C61—22no—
162C2×C8×C61—22no—
163C2×C8×C61—42no—
164C2×C8×C61—42no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61C22×C412yes—
167C22⋊C4×C61—22no—
168C22⋊C4×C61—22no—
169C42×C61C22×C411yescharacteristic
170C42×C61C2×D411yescharacteristic
171C42×C61C2×D411yescharacteristic
172C42×C61C2411yescharacteristic
173C22⋊Dic61—24no—
174#11758198—22no—
175#11758198—22no—
176#11758198—24no—
177C4⋊Dic61—21no—
178C4⋊Dic61C22×C412yes—
179#11758196—24no—
180C4×Dic61C22⋊C412yes—
181C4×Dic61C22⋊C412yes—
182C4×Dic61C22⋊C412yes—
183C4×Dic61C22×C412yes—
184C4×Dic61C2×D412yes—
185C4×Dic61C2×D412yes—
186C2×#92418—22no—
187C2×#92418—22no—
188C2×#92418—42no—
189C2×#92418—42no—
190C8×D61—48no—
191C23×C61—22no—
192C23×C61—42no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61C2×C22⋊C411yescharacteristic
196C22×D61—22no—
197C22×D61—22no—
198C22×D61—22no—
199C22×D61—42no—
200C22×D61—42no—
201C22×D61—42no—
202C22×D61#10214yes—
203C22×D61C2×C22⋊C412yes—
204D4×C61—22no—
205D4×C61—22no—
206D4×C61—42no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61—42no—
212C2×C4×C61—44no—
213C2×C4×C61C2×C22⋊C411yescharacteristic
214C2×C4×C61C2×C22⋊C411yescharacteristic
215C2×C4×C61C2×C22⋊C411yescharacteristic
216C2×C4×C61#13112yes—
217C2×C4×C61#13112yes—
218C2×C4×C61C2×D812yes—
219C2×C4×C61C2×SD1612yes—
220C2×C4×C61C23×C411yescharacteristic
221C2×C4×C61C22×D411yescharacteristic
222C2×C4×C61C22×D411yescharacteristic
223C22⋊D61—48no—
224C22⋊D61—48no—
225C22⋊D61—48no—
226C2×Dic61—22no—
227C2×Dic61—22no—
228C2×Dic61—22no—
229C2×Dic61—42no—
230C2×Dic61#10214yes—
231C2×Dic61C2×C22⋊C412yes—
232C2×Dic61C2×C22⋊C412yes—
233C2×Dic61C2×C22⋊C412yes—
234D244—22no—
235D244—22no—
236D244—48no—
237D244—42no—
238C4×D61—22no—
239C4×D61—22no—
240C4×D61—24no—
241C4×D61—42no—
242C4×D61—42no—
243C4×D61—42no—
244C4×D61—42no—
245C4×D61—44no—
246C4×D61#10218yes—
247C4×D61C2×D814yes—
248C4×D61C2×SD1614yes—
249Dic122—48no—
250C8×C61—42no—
251C8×C61—42no—
252#92418—42no—
253#92418—42no—
254C2×#1480—611nomaximal, Sylow
255C22×C61—42no—
256C22×C61—42no—
257C22×C61—42no—
258C22×C61—84no—
259C22×C61#40812yes—
260C22×C61C2×#10212yes—
261C22×C61#42112yes—
262C22×C61C22×C22⋊C411yescharacteristic
263C2×D61—22no—
264C2×D61—22no—
265C2×D61—28no—
266C2×D61—42no—
267C2×D61—42no—
268C2×D61—42no—
269C2×D61—84no—
270C2×D61C2×#10214yes—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—42no—
274C4×C61#40812yes—
275C4×C61C2×#10212yes—
276C4×C61C2×#13111yescharacteristic
277C4×C61C2×#13111yescharacteristic
278C4×C61C22×D811yescharacteristic
279C4×C61C22×SD1611yescharacteristic
280Dic61—22no—
281Dic61—22no—
282Dic61—42no—
283Dic61C2×#10214yes—
284C2×#532—611no—
285C2×#431—611no—
286C22×C4⋊C8—611no—
287#1480—618no—
288C2×D4⋊C8—611no—
289C2×D4⋊C8—611no—
290C2×D4⋊C8—611no—
291C2×D4⋊C8D6111yescharacteristic, complemented
292C2×C61—82no—
293C2×C61#148014yescomplemented
294C2×C61C2×#40811yescharacteristic
295C2×C61C22×#10211yescharacteristic
296C2×C61C2×#42111yescharacteristic
297D61—24no—
298D61—82no—
299C22×#41—1221no—
300C23×C8—1221no—
301#532—614no—
302#532—614no—
303#532—1222no—
304#532—1222no—
305C2×C4⋊Q8—611no—
306C2×#127—611no—
307C2×#124—1221no—
308C2×#121—611no—
309C2×#121—611no—
310C2×#121—1221no—
311C2×C4×D4—611no—
312C2×C4×D4—1221no—
313C2×C4×D4C2×D6111yescharacteristic
314C22×C42—611no—
315#431—614no—
316#431—1222no—
317C2×C4⋊C8—611no—
318C2×C4⋊C8—614no—
319C2×C4⋊C8—1222no—
320C2×C4⋊C8—1221no—
321C2×C4⋊C8—1221no—
322C2×C4⋊C8C2×D6111yescharacteristic
323C2×C22⋊C8—1221no—
324C2×C4×C8—611no—
325C2×C4×C8C2×D6111yescharacteristic
326D4⋊C8—614no—
327D4⋊C8—614no—
328D4⋊C8—614no—
329D4⋊C8C2×D6114yescomplemented
330C61C2×#148011yescharacteristic, complemented, Sylow
331C2×#41—1224no—
332C2×#41—1224no—
333C2×#41—2444no—
334C2×#41—2444no—
335C22×Q8—1221no—
336C22×D4—611no—
337C22×D4—1221no—
338C22×D4—1221no—
339C22×D4—1221no—
340C22×D4—1221no—
341C22×D4C4×D6111yescharacteristic
342C23×C4—21no—
343C23×C4—611no—
344C23×C4—611no—
345C23×C4—611no—
346C23×C4—1221no—
347C22×C8—21no—
348C22×C8—21no—
349C22×C8—1224no—
350C22×C8—1221no—
351C22×C8—1221no—
352C22×C8—2444no—
353C4⋊Q8—614no—
354C4⋊Q8—1222no—
355#127—614no—
356#127—1222no—
357#124—1224no—
358#124—1224no—
359#121—614no—
360#121—614no—
361#121—1224no—
362#121—1224no—
363#121—1222no—
364#121—1222no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4—612no—
368C4×D4—612no—
369C4×D4—1224no—
370C4×D4—1224no—
371C4×D4—1221no—
372C4×D4—1221no—
373C4×D4C4×D6112yes—
374C4×D4C22×D6112yes—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4C4×D6111yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—1221no—
380C2×C22⋊C4—1221no—
381C2×C22⋊C4—1221no—
382C2×C42—611no—
383C2×C42—611no—
384C2×C42—611no—
385C2×C42—612no—
386C2×C42—612no—
387C2×C42—612no—
388C2×C42—612no—
389C2×C42C22×D6111yescharacteristic
390C4⋊C8—21no—
391C4⋊C8—612no—
392C4⋊C8—1224no—
393C4⋊C8—1224no—
394C4⋊C8—1221no—
395C4⋊C8C22×D6112yes—
396C22⋊C8—1224no—
397C4×C8—21no—
398C4×C8—612no—
399C4×C8—1221no—
400C4×C8C22×D6112yes—
401C24—21no—
402C24—611no—
403C24—1221no—
404#41—24416no—
405#41—2448no—
406#41—2448no—
407C2×Q8—1224no—
408C2×Q8—2444no—
409C2×D4—21no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—612no—
413C2×D4—1224no—
414C2×D4—1224no—
415C2×D4—1224no—
416C2×D4—1224no—
417C2×D4—1221no—
418C2×D4—1222no—
419C2×D4—1222no—
420C2×D4—2444no—
421C2×D4—2444no—
422C2×D4—2444no—
423C2×D4—2444no—
424C2×D4C2×C4×D6112yes—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—611no—
431C22×C4—612no—
432C22×C4—612no—
433C22×C4—614no—
434C22×C4—614no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—612no—
438C22×C4—612no—
439C22×C4—612no—
440C22×C4—612no—
441C22×C4—1222no—
442C22×C4—1222no—
443C22×C4—1221no—
444C22×C4—1222no—
445C22×C4—1222no—
446C22×C4—2442no—
447C22×C4—2442no—
448C22×C4—2442no—
449C22×C4C2×C4×D6111yescharacteristic
450C22×C4D4×D6111yescharacteristic
451C22×C4D4×D6111yescharacteristic
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—42no—
455C2×C8—42no—
456C2×C8—1222no—
457C2×C8—1222no—
458C2×C8—2448no—
459C2×C8—2442no—
460C2×C8—2442no—
461C4⋊C4—21no—
462C4⋊C4—612no—
463C4⋊C4—1224no—
464C4⋊C4—1221no—
465C4⋊C4C2×C4×D6112yes—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—1224no—
469C22⋊C4—1224no—
470C22⋊C4—1222no—
471C22⋊C4—1222no—
472C42—612no—
473C42—612no—
474C42—612no—
475C42—612no—
476C42—612no—
477C42—612no—
478C42C2×C4×D6111yescharacteristic
479C42D4×D6111yescharacteristic
480C42D4×D6111yescharacteristic
481C42C23×D6111yescharacteristic
482C23—22no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—612no—
487C23—614no—
488C23—1222no—
489C23—1222no—
490C23—1222no—
491C23—2442no—
492C23—2442no—
493C23—2442no—
494C23C22⋊C4×D6111yescharacteristic
495Q8—2448no—
496D4—22no—
497D4—22no—
498D4—42no—
499D4—1222no—
500D4—1222no—
501D4—2448no—
502D4—2448no—
503D4—2448no—
504D4—2448no—
505D4—2442no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—42no—
509C2×C4—44no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—612no—
513C2×C4—614no—
514C2×C4—618no—
515C2×C4—614no—
516C2×C4—614no—
517C2×C4—612no—
518C2×C4—612no—
519C2×C4—1222no—
520C2×C4—1222no—
521C2×C4—1224no—
522C2×C4—1222no—
523C2×C4—1222no—
524C2×C4—1222no—
525C2×C4—2442no—
526C2×C4—2442no—
527C2×C4—2442no—
528C2×C4—2444no—
529C2×C4—2442no—
530C2×C4—2442no—
531C2×C4C22⋊C4×D6111yescharacteristic
532C2×C4C22⋊C4×D6111yescharacteristic
533C2×C4C22⋊C4×D6111yescharacteristic
534C2×C4#1451978312yes—
535C2×C4#1451978512yes—
536C2×C4D8×D6112yes—
537C2×C4SD16×D6112yes—
538C2×C4C22×C4×D6111yescharacteristic
539C2×C4C2×D4×D6111yescharacteristic
540C2×C4C2×D4×D6111yescharacteristic
541C8—42no—
542C8—42no—
543C8—2442no—
544C8—2442no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—84no—
549C22—614no—
550C22—1222no—
551C22—1228no—
552C22—1222no—
553C22—4884no—
554C22—2442no—
555C22—2442no—
556C22—2442no—
557C22#1683972712yes—
558C22#102×D6112yes—
559C22#1683977712yes—
560C22C2×C22⋊C4×D6111yescharacteristic
561C4—21no—
562C4—21no—
563C4—42no—
564C4—614no—
565C4—1222no—
566C4—1222no—
567C4—2442no—
568C4#1683972712yes—
569C4#102×D6112yes—
570C4C2×#1451978311yescharacteristic
571C4C2×#1451978511yescharacteristic
572C4C2×D8×D6111yescharacteristic
573C4C2×SD16×D6111yescharacteristic
574C2—82no—
575C2—1224no—
576C2—4882no—
577C2#2144421614yesdirect product factor
578C2C2×#1683972711yescharacteristic
579C2C2×#102×D6111yescharacteristic
580C2C2×#1683977711yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840309C2
cosocleC42×C61C24
hypercenterC2×D4⋊C8D61
hypocenterC61C2×#1480
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#16839813C2semidirect
3. C2×C4⋊C8×D61C2semidirect
4. #21444216C2direct (N × H)
5. C2×#16839491C2semidirect
6. C2×D4⋊#92418C2semidirect
7. C2×#16839489C2semidirect
8. C2×C61×D4⋊C8C2semidirect
25. #16839813C22semidirect
30. C4⋊C8×D61C22semidirect
33. #16839491C22semidirect
34. D4⋊#92418C22semidirect
35. #16839489C22semidirect
39. C61×D4⋊C8C22semidirect
291. C2×D4⋊C8D61semidirect
293. C2×C61#1480semidirect
329. D4⋊C8C2×D61semidirect
330. C61C2×#1480semidirect
577. C2#21444216direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403092
C2×#168398132
C2×C4⋊C8×D612
#214442162
C2×#168394912
C2×D4⋊#924182
C2×#168394892
C2×C61×D4⋊C82
C2×#148061