Finite Group Databasebeta

← C2×#21456983 #30552039

Subgroups — C2×#21456983 #30552039

Order 15616.

1822 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519769C211yesmaximal, characteristic, complemented
2#21456983C2116yesmaximal, direct product factor
3C2×#16840161C212yesmaximal, complemented
4C2×#16840116C212yesmaximal, complemented
5C2×#16840095C211yesmaximal, characteristic, complemented
6C2×#16840078C211yesmaximal, characteristic
7C2×#16840090C211yesmaximal, characteristic, complemented
8C2×#16840073C211yesmaximal, characteristic
9C2×#16840069C212yesmaximal, complemented
10C2×#16840062C212yesmaximal, complemented
11C2×#16839815C211yesmaximal, characteristic, complemented
12C2×C61×#529C211yesmaximal, characteristic
13C2×#14519769—21no—
14C2×#14519769—21no—
15C2×#14519769—24no—
16C2×#14519769C2212yes—
17C2×#14519769C2212yes—
18C2×#14519769C2218yescomplemented
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758196—21no—
22C22×#11758196—21no—
23#16840161C22116yescomplemented
24#16840116C22116yescomplemented
25#16840095C2218yescomplemented
26#16840090C2218yescomplemented
27#16840078C2218yes—
28#16840073C2218yes—
29#16840069C22116yescomplemented
30#16840062C22116yescomplemented
31#16839815C2218yescomplemented
32C2×#14519710C2212yes—
33C2×#14519710C2212yes—
34C2×#14519708C2212yes—
35C2×#14519708C2212yes—
36C2×C4⋊#92418C2212yes—
37C2×#14519701C2212yes—
38C2×#14519701C2212yes—
39C2×#14519698C2212yes—
40C2×#14519698C2212yes—
41C2×C22⋊#92418C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×C4×#92418C2212yes—
44C61×#529—24no—
45C61×#529C2218yes—
46C2×#126×C61—21no—
47C2×#125×C61C2211yescharacteristic
48C2×#124×C61C2211yescharacteristic
49C2×#123×C61—21no—
50C2×C22⋊Q8×C61C2211yescharacteristic
51C2×#121×C61C2211yescharacteristic
52C2×C4×Q8×C61C2211yescharacteristic
53C2×C4×D4×C61—21no—
54C2×C4×D4×C61C2211yescharacteristic
55C2×#117×C61—21no—
56C22×C42×C61C2211yescharacteristic
57C23×Dic61—21no—
58C23×Dic61—21no—
59C22×#92418C2312yes—
60C22×#92418C2312yes—
61#14519769—24no—
62#14519769—24no—
63#14519769—28no—
64#14519769—28no—
65#14519769C2318yes—
66#14519769C2318yes—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—22no—
70C2×C4⋊Dic61—22no—
71C2×C4⋊Dic61C2312yes—
72C2×C4⋊Dic61C2312yes—
73C2×C4⋊Dic61C2314yes—
74C2×C4⋊Dic61C2314yes—
75C2×#11758196—22no—
76C2×#11758196—22no—
77C2×#11758196—22no—
78C2×#11758196—22no—
79C2×#11758196—28no—
80C2×#11758196—28no—
81#14519710C2318yes—
82#14519710C2318yes—
83#14519708C2318yes—
84#14519708C2318yes—
85C4⋊#92418C2318yes—
86#14519701C2318yes—
87#14519701C2318yes—
88#14519698C2318yes—
89#14519698C2318yes—
90C22⋊#92418C2314yes—
91C22⋊#92418C2314yes—
92C4×#92418C2318yes—
93C22×Q8×C61C2311yescharacteristic
94C22×D4×C61—21no—
95C22×D4×C61C2311yescharacteristic
96C23×C4×C61—21no—
97C23×C4×C61D411yescharacteristic
98C23×C4×C61D411yescharacteristic
99C23×C4×C61C2311yescharacteristic
100#126×C61—28no—
101#125×C61—22no—
102#125×C61C2314yes—
103#124×C61—22no—
104#124×C61C2314yes—
105#123×C61—28no—
106C22⋊Q8×C61—22no—
107C22⋊Q8×C61C2314yes—
108#121×C61—22no—
109#121×C61C2314yes—
110C4×Q8×C61—22no—
111C4×Q8×C61C2314yes—
112C4×D4×C61—28no—
113C4×D4×C61—22no—
114C4×D4×C61C2314yes—
115#117×C61—28no—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C42×C61—21no—
128C2×C42×C61D411yescharacteristic
129C2×C42×C61D411yescharacteristic
130C2×C42×C61D414yes—
131C2×C42×C61C2311yescharacteristic
132C2×C42×C61C2311yescharacteristic
133C2×C42×C61C2314yes—
134C24×C61—21no—
135C24×C61C2×D411yescharacteristic
136C2×Q8×C61—21no—
137C2×Q8×C61—24no—
138C2×Q8×C61C2412yes—
139C2×D4×C61—24no—
140C2×D4×C61—21no—
141C2×D4×C61—24no—
142C2×D4×C61—44no—
143C2×D4×C61C2412yes—
144C22×C4×C61—24no—
145C22×C4×C61—24no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—24no—
150C22×C4×C61—42no—
151C22×C4×C61—44no—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D412yes—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D414yes—
159C22×C4×C61C2×D414yes—
160C22×C4×C61C2412yes—
161C22×C4×C61C2411yescharacteristic
162C22×Dic61—24no—
163C22×Dic61—24no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—44no—
167C22×Dic61—44no—
168C4⋊C4×C61—24no—
169C4⋊C4×C61—24no—
170C4⋊C4×C61—24no—
171C4⋊C4×C61—24no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61C2412yes—
175C4⋊C4×C61C2412yes—
176C22⋊C4×C61—24no—
177C22⋊C4×C61—24no—
178C22⋊C4×C61—24no—
179C22⋊C4×C61—24no—
180C22⋊C4×C61—24no—
181C42×C61—24no—
182C42×C61C2×D414yes—
183C42×C61C2×D412yes—
184C42×C61C2×D412yes—
185C42×C61C2×D414yes—
186C42×C61C2412yes—
187C42×C61C2412yes—
188C4⋊Dic61—24no—
189C4⋊Dic61—24no—
190C4⋊Dic61—22no—
191C4⋊Dic61—22no—
192C4⋊Dic61C2414yes—
193C4⋊Dic61C2414yes—
194#11758196—28no—
195#11758196—28no—
196#11758196—28no—
197#11758196—28no—
198C2×#92418—24no—
199C2×#92418—24no—
200C2×#92418C2414yes—
201C2×#92418C2414yes—
202C23×C61—22no—
203C23×C61—22no—
204C23×C61—22no—
205C23×C61—42no—
206C23×C61—42no—
207C23×C61—42no—
208C23×C61#13514yes—
209C23×C61C22×D412yes—
210C23×C61C22×D411yescharacteristic
211Q8×C61—24no—
212Q8×C61—42no—
213D4×C61—24no—
214D4×C61—48no—
215D4×C61—42no—
216C2×C4×C61—22no—
217C2×C4×C61—28no—
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—24no—
223C2×C4×C61—24no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—44no—
228C2×C4×C61—48no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61C22×D412yes—
233C2×C4×C61C22×D412yes—
234C2×C4×C61C22×D412yes—
235C2×C4×C61C22×D412yes—
236C2×C4×C61C22×D412yes—
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C612−1+414yes—
239C2×C4×C61C2511yescharacteristic
240C2×Dic61—24no—
241C2×Dic61—24no—
242C2×Dic61—48no—
243C2×Dic61—48no—
244C2×Dic61—44no—
245C2×Dic61—44no—
246#92418—24no—
247#92418—24no—
248C2×#3232—611nomaximal, Sylow
249C22×C61—22no—
250C22×C61—28no—
251C22×C61—22no—
252C22×C61—42no—
253C22×C61—42no—
254C22×C61—42no—
255C22×C61—84no—
256C22×C61#53612yes—
257C22×C61C2×#13514yes—
258C22×C61C2×#13512yes—
259C22×C61#57512yes—
260C22×C61C23×D411yescharacteristic
261C4×C61—22no—
262C4×C61—22no—
263C4×C61—22no—
264C4×C61—22no—
265C4×C61—22no—
266C4×C61—42no—
267C4×C61—42no—
268C4×C61—42no—
269C4×C61#53612yes—
270C4×C61C2×2−1+412yes—
271Dic61—44no—
272Dic61—44no—
273C2×#529D6111yescharacteristic
274C22×#125—611no—
275#3232—6116no—
276C2×#499—612no—
277C2×#488—612no—
278C2×#484—611no—
279C2×#481—611no—
280C2×#483—611no—
281C2×#480—611no—
282C2×#479—612no—
283C2×#478—612no—
284C2×#431—611no—
285C2×C61—24no—
286C2×C61—82no—
287C2×C61#323214yescomplemented
288C2×C61C2×#53611yescharacteristic
289C2×C61C22×#13511yescharacteristic
290C2×C61C2×#57511yescharacteristic
291#529—24no—
292#529C2×D6118yes—
293C2×#126—21no—
294C2×#125—612no—
295C2×#125—612no—
296C2×#125—618no—
297C2×#125—1221no—
298C2×#125—1221no—
299C2×#125—1224no—
300C2×#125C2×D6111yescharacteristic
301C2×#124C2×D6111yescharacteristic
302C2×#123—21no—
303C2×C22⋊Q8C2×D6111yescharacteristic
304C2×#121C2×D6111yescharacteristic
305C2×C4×Q8C2×D6111yescharacteristic
306C2×C4×D4—21no—
307C2×C4×D4C2×D6111yescharacteristic
308C2×#117—21no—
309C22×C4⋊C4—611no—
310C22×C4⋊C4—611no—
311C22×C4⋊C4—1221no—
312C22×C4⋊C4—1221no—
313C22×C42C2×D6111yescharacteristic
314#499—6116no—
315#488—6116no—
316#484—618no—
317#483—618no—
318#481—618no—
319#480—618no—
320#479—6116no—
321#478—6116no—
322#431—618no—
323C2×#107—612no—
324C2×#107—612no—
325C2×#106—612no—
326C2×#106—612no—
327C2×C4⋊C8—612no—
328C2×#103—612no—
329C2×#103—612no—
330C2×#102—612no—
331C2×#102—612no—
332C2×C22⋊C8—611no—
333C2×C22⋊C8—611no—
334C2×C4×C8—612no—
335C61C2×#323211yescharacteristic, complemented, Sylow
336C22×Q8C22×D6111yescharacteristic
337C22×D4—21no—
338C22×D4C22×D6111yescharacteristic
339C23×C4—21no—
340C23×C4—1221no—
341C23×C4—1221no—
342C23×C4C22⋊D6111yescharacteristic
343C23×C4C22⋊D6111yescharacteristic
344C23×C4C22×D6111yescharacteristic
345C22×C8—612no—
346C22×C8—612no—
347#126—28no—
348#125—22no—
349#125—618no—
350#125—618no—
351#125—1228no—
352#125—1224no—
353#125—1224no—
354#125—1228no—
355#125C22×D6114yes—
356#124—22no—
357#124C22×D6114yes—
358#123—28no—
359C22⋊Q8—22no—
360C22⋊Q8C22×D6114yes—
361#121—22no—
362#121C22×D6114yes—
363C4×Q8—22no—
364C4×Q8C22×D6114yes—
365C4×D4—28no—
366C4×D4—22no—
367C4×D4C22×D6114yes—
368#117—28no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—612no—
374C2×C4⋊C4—612no—
375C2×C4⋊C4—614no—
376C2×C4⋊C4—614no—
377C2×C4⋊C4—1222no—
378C2×C4⋊C4—1222no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1228no—
382C2×C4⋊C4—1228no—
383C2×C4⋊C4—1222no—
384C2×C4⋊C4—1222no—
385C2×C4⋊C4—1222no—
386C2×C4⋊C4—1222no—
387C2×C4⋊C4C22×D6111yescharacteristic
388C2×C4⋊C4C22×D6111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C42—21no—
395C2×C42C22⋊D6111yescharacteristic
396C2×C42C22⋊D6111yescharacteristic
397C2×C42C22⋊D6114yes—
398C2×C42C22×D6111yescharacteristic
399C2×C42C22×D6111yescharacteristic
400C2×C42C22×D6114yes—
401#107—618no—
402#107—618no—
403#106—618no—
404#106—618no—
405C4⋊C8—618no—
406#103—618no—
407#103—618no—
408#102—618no—
409#102—618no—
410C22⋊C8—614no—
411C22⋊C8—614no—
412C4×C8—618no—
413C24—21no—
414C24C2×C22⋊D6111yescharacteristic
415C2×Q8—21no—
416C2×Q8—24no—
417C2×Q8C23×D6112yes—
418C2×D4—24no—
419C2×D4—21no—
420C2×D4—24no—
421C2×D4—44no—
422C2×D4C23×D6112yes—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—42no—
430C22×C4—44no—
431C22×C4—1224no—
432C22×C4—1224no—
433C22×C4—1222no—
434C22×C4—1222no—
435C22×C4—2444no—
436C22×C4—2444no—
437C22×C4C2×C22⋊D6112yes—
438C22×C4C2×C22⋊D6114yes—
439C22×C4C2×C22⋊D6111yescharacteristic
440C22×C4C2×C22⋊D6111yescharacteristic
441C22×C4C2×C22⋊D6111yescharacteristic
442C22×C4C2×C22⋊D6111yescharacteristic
443C22×C4C2×C22⋊D6111yescharacteristic
444C22×C4C2×C22⋊D6114yes—
445C22×C4C23×D6112yes—
446C22×C4C23×D6111yescharacteristic
447C2×C8—614no—
448C2×C8—614no—
449C2×C8—1224no—
450C2×C8—1224no—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—24no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—614no—
458C4⋊C4—614no—
459C4⋊C4—1224no—
460C4⋊C4—1224no—
461C4⋊C4—1222no—
462C4⋊C4—1222no—
463C4⋊C4—1228no—
464C4⋊C4—1228no—
465C4⋊C4—1228no—
466C4⋊C4—1228no—
467C4⋊C4C23×D6112yes—
468C4⋊C4C23×D6112yes—
469C22⋊C4—24no—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C42—24no—
475C42C2×C22⋊D6114yes—
476C42C2×C22⋊D6112yes—
477C42C2×C22⋊D6112yes—
478C42C2×C22⋊D6114yes—
479C42C23×D6112yes—
480C42C23×D6112yes—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23#1451979714yes—
488C23C22×C22⋊D6112yes—
489C23C22×C22⋊D6111yescharacteristic
490Q8—24no—
491Q8—42no—
492D4—24no—
493D4—48no—
494D4—42no—
495C2×C4—28no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—44no—
507C2×C4—48no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—1224no—
512C2×C4—1224no—
513C2×C4—2448no—
514C2×C4—2448no—
515C2×C4—2444no—
516C2×C4—2444no—
517C2×C4C22×C22⋊D6112yes—
518C2×C4C22×C22⋊D6112yes—
519C2×C4C22×C22⋊D6112yes—
520C2×C4C22×C22⋊D6112yes—
521C2×C4C22×C22⋊D6112yes—
522C2×C4C22×C22⋊D6111yescharacteristic
523C2×C4#1451982414yes—
524C2×C4C24×D6111yescharacteristic
525C8—1224no—
526C8—1224no—
527C22—22no—
528C22—28no—
529C22—22no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—84no—
534C22#1684033312yes—
535C22C2×#1451979714yes—
536C22C2×#1451979712yes—
537C22#1684056012yes—
538C22C23×C22⋊D6111yescharacteristic
539C4—22no—
540C4—22no—
541C4—22no—
542C4—22no—
543C4—22no—
544C4—42no—
545C4—42no—
546C4—42no—
547C4—2444no—
548C4—2444no—
549C4#1684033312yes—
550C4C2×#1451982412yes—
551C2—24no—
552C2—82no—
553C2#2145698314yesdirect product factor
554C2C2×#1684033311yescharacteristic
555C2C22×#1451979711yescharacteristic
556C2C2×#1684056011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#529C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
hypercenterC2×#529D61
hypocenterC61C2×#3232
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C22×#14519769C2semidirect
2. #21456983C2direct (N × H)
3. C2×#16840161C2semidirect
4. C2×#16840116C2semidirect
5. C2×#16840095C2semidirect
7. C2×#16840090C2semidirect
9. C2×#16840069C2semidirect
10. C2×#16840062C2semidirect
11. C2×#16839815C2semidirect
18. C2×#14519769C22semidirect
23. #16840161C22semidirect
24. #16840116C22semidirect
25. #16840095C22semidirect
26. #16840090C22semidirect
29. #16840069C22semidirect
30. #16840062C22semidirect
31. #16839815C22semidirect
287. C2×C61#3232semidirect
335. C61C2×#3232semidirect
553. C2#21456983direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197692
#214569832
C2×#168401612
C2×#168401162
C2×#168400952
C2×#168400782
C2×#168400902
C2×#168400732
C2×#168400692
C2×#168400622
C2×#168398152
C2×C61×#5292
C2×#323261