Finite Group Databasebeta

← C2×#21448441 #29838632

Subgroups — C2×#21448441 #29838632

Order 15616.

3502 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519735C211yesmaximal, characteristic
2C22×#14519734C211yesmaximal, characteristic
3C22×C4⋊C4×D61C211yesmaximal, characteristic
4#21448441C2116yesmaximal, direct product factor
5C2×#16839661C211yesmaximal, characteristic, complemented
6C2×#16839660C211yesmaximal, characteristic, complemented
7C2×#16839658C211yesmaximal, characteristic, complemented
8C2×#16839636C212yesmaximal
9C2×#16839633C212yesmaximal
10C2×#16839631C212yesmaximal, complemented
11C2×#16839626C212yesmaximal, complemented
12C2×C61×#389C211yesmaximal, characteristic, complemented
13C23×C4×D61C2212yes—
14C23×C4×D61C2211yescharacteristic
15C2×#14519735C4116yescomplemented
16C2×#14519735C2218yes—
17C2×#14519734—28no—
18C2×#14519734C2218yes—
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2212yes—
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2212yes—
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2212yes—
26C22×#11758196C2212yes—
27C2×C4⋊C4×D61—28no—
28C2×C4⋊C4×D61C2218yes—
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2212yes—
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2212yes—
34#16839661C2218yescomplemented
35#16839660C2218yescomplemented
36#16839658C2218yescomplemented
37#16839636C22116yes—
38#16839633C22116yes—
39#16839631C22116yescomplemented
40#16839626C22116yescomplemented
41C2×#14519684C2212yes—
42C2×#14519684C2212yes—
43C2×#14519684C2212yes—
44C22×C4⋊C4×C61C2211yescharacteristic
45C22×C4⋊C4×C61C2212yes—
46C22×C4⋊C4×C61C2211yescharacteristic
47C22×C42×C61C2211yescharacteristic
48C61×#389C2218yescomplemented
49C2×#95×C61C2212yes—
50C24×D61C2311yescharacteristic
51C23×Dic61C2311yescharacteristic
52C23×Dic61C2311yescharacteristic
53C23×Dic61C2312yes—
54C23×Dic61C2312yes—
55C23×Dic61C2311yescharacteristic
56C22×C4×D61—28no—
57C22×C4×D61—44no—
58C22×C4×D61—44no—
59C22×C4×D61C2×C418yes—
60C22×C4×D61D418yes—
61C22×C4×D61Q818yes—
62C22×C4×D61C2318yes—
63C22×C4×D61C2314yes—
64#14519735C2×C4164yescomplemented
65#14519734—232no—
66C2×C4⋊Dic61—24no—
67C2×C4⋊Dic61—44no—
68C2×C4⋊Dic61C2×C418yescomplemented
69C2×C4⋊Dic61C2314yes—
70C2×C4⋊Dic61C2318yes—
71C2×C4⋊Dic61C2314yes—
72C2×#11758196—28no—
73C2×#11758196—24no—
74C2×#11758196—24no—
75C2×#11758196—44no—
76C2×#11758196—44no—
77C2×#11758196C2318yes—
78C2×#11758196C2314yes—
79C2×#11758196C2314yes—
80C2×#11758196C2318yes—
81C2×#11758196C2318yes—
82C4⋊C4×D61—232no—
83C2×#11758198—24no—
84C2×#11758198—24no—
85C2×#11758198C2×C4116yes—
86C2×#11758198C2314yes—
87C2×#11758198C2314yes—
88C2×#11758198C2318yes—
89C2×C4×Dic61—24no—
90C2×C4×Dic61C2×C4116yescomplemented
91C2×C4×Dic61C2314yes—
92C2×C4×Dic61C2318yes—
93#14519684C2318yes—
94#14519684C2318yes—
95#14519684C2318yes—
96C23×C4×C61C2311yescharacteristic
97C23×C4×C61C2311yescharacteristic
98C23×C4×C61C2312yes—
99C23×C4×C61C2312yes—
100C23×C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61—24no—
102C2×C4⋊C4×C61—44no—
103C2×C4⋊C4×C61C2×C418yescomplemented
104C2×C4⋊C4×C61C2314yes—
105C2×C4⋊C4×C61C2318yes—
106C2×C4⋊C4×C61C2314yes—
107C2×C42×C61—24no—
108C2×C42×C61C2314yes—
109#95×C61C2318yes—
110C24×C61C2411yescharacteristic
111C23×D61—22no—
112C23×D61—22no—
113C23×D61—22no—
114C23×D61—22no—
115C23×D61C22×C414yes—
116C23×D61C2×D414yes—
117C23×D61C2×Q814yes—
118C23×D61C2412yes—
119C22×C4×C61—24no—
120C22×C4×C61—24no—
121C22×C4×C61—24no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—24no—
125C22×C4×C61—24no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61C22×C418yes—
131C22×C4×C61C22×C414yes—
132C22×C4×C61C2×D414yes—
133C22×C4×C61C2×Q814yes—
134C22×C4×C61C2414yes—
135C22×C4×C61C2412yes—
136C22×C4×C61C2412yes—
137C22×C4×C61C2414yes—
138C22×C4×C61C2412yes—
139C22×Dic61—24no—
140C22×Dic61—24no—
141C22×Dic61—24no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61—24no—
145C22×Dic61—24no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61C22×C418yes—
151C22×Dic61C22×C414yes—
152C22×Dic61C2×D414yes—
153C22×Dic61C2×Q814yes—
154C22×Dic61C2414yes—
155C22×Dic61C2412yes—
156C22×Dic61C2412yes—
157C22×Dic61C2414yes—
158C22×Dic61C2412yes—
159C2×C4×D61—216no—
160C2×C4×D61—48no—
161C2×C4×D61—48no—
162C2×C4×D61—432no—
163C2×C4×D61C4⋊C4164yescomplemented
164C2×C4×D61C22×C4116yes—
165C2×C4×D61C2×D4116yes—
166C2×C4×D61C2×Q8116yes—
167C4⋊C4×C61—28no—
168C4⋊C4×C61—48no—
169C4⋊C4×C61C22×C4116yescomplemented
170C42×C61—28no—
171#11758198—28no—
172#11758198—28no—
173#11758198C22×C4132yes—
174C4⋊Dic61—28no—
175C4⋊Dic61—48no—
176C4⋊Dic61C22×C4116yescomplemented
177#11758196—216no—
178#11758196—28no—
179#11758196—28no—
180#11758196—48no—
181#11758196—48no—
182C4×Dic61—28no—
183C4×Dic61C22×C4132yescomplemented
184C23×C61C23×C412yes—
185C23×C61C22×D412yes—
186C23×C61C22×Q812yes—
187C23×C61H(5,𝔽2)12yes—
188C23×C61H(5,𝔽2)12yes—
189C23×C612−1+412yes—
190C23×C612−1+412yes—
191C23×C61C2511yescharacteristic
192C22×D61—28no—
193C22×D61—28no—
194C22×D61—28no—
195C22×D61—28no—
196C22×D61—28no—
197C22×D61—28no—
198C22×D61—22no—
199C22×D61—22no—
200C22×D61—22no—
201C22×D61—22no—
202C22×D61C2×C4⋊C4116yes—
203C22×D61C23×C414yes—
204C22×D61C22×D414yes—
205C22×D61C22×Q814yes—
206C2×C4×C61—216no—
207C2×C4×C61—24no—
208C2×C4×C61—24no—
209C2×C4×C61—22no—
210C2×C4×C61—22no—
211C2×C4×C61—24no—
212C2×C4×C61—22no—
213C2×C4×C61—24no—
214C2×C4×C61—22no—
215C2×C4×C61—24no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61—48no—
219C2×C4×C61—44no—
220C2×C4×C61—44no—
221C2×C4×C61C2×C4⋊C4116yes—
222C2×C4×C61C23×C418yes—
223C2×C4×C61C23×C414yes—
224C2×C4×C61C22×D414yes—
225C2×C4×C61C22×Q814yes—
226C2×Dic61—216no—
227C2×Dic61—24no—
228C2×Dic61—24no—
229C2×Dic61—22no—
230C2×Dic61—22no—
231C2×Dic61—24no—
232C2×Dic61—22no—
233C2×Dic61—24no—
234C2×Dic61—22no—
235C2×Dic61—24no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—48no—
239C2×Dic61—44no—
240C2×Dic61—44no—
241C2×Dic61C2×C4⋊C4116yes—
242C2×Dic61C23×C418yes—
243C2×Dic61C23×C414yes—
244C2×Dic61C22×D414yes—
245C2×Dic61C22×Q814yes—
246C4×D61—432no—
247C4×D61C2×C4⋊C4164yescomplemented
248C2×#2317—611nomaximal, Sylow
249C22×C61C22×C4⋊C414yes—
250C22×C61#52014yes—
251C22×C61#52014yes—
252C22×C61#53514yes—
253C22×C61#53614yes—
254C22×C61#54414yes—
255C22×C61#54414yes—
256C22×C61C24×C411yescharacteristic
257C22×C61C23×D411yescharacteristic
258C22×C61C23×Q811yescharacteristic
259C22×C61C2×H(5,𝔽2)11yescharacteristic
260C22×C61C2×H(5,𝔽2)11yescharacteristic
261C22×C61C2×2−1+411yescharacteristic
262C22×C61C2×2−1+411yescharacteristic
263C2×D61—232no—
264C2×D61—24no—
265C2×D61—24no—
266C2×D61—24no—
267C2×D61—24no—
268C2×D61—24no—
269C2×D61—24no—
270C2×D61C22×C4⋊C418yes—
271C4×C61—28no—
272C4×C61—44no—
273C4×C61—42no—
274C4×C61—42no—
275C4×C61C22×C4⋊C418yes—
276Dic61—28no—
277Dic61—44no—
278Dic61—42no—
279Dic61—42no—
280Dic61C22×C4⋊C418yes—
281C22×#117—611no—
282C22×#117—611no—
283C23×C4⋊C4—611no—
284#2317—6116no—
285C2×#389—611no—
286C2×#389—611no—
287C2×#389—611no—
288C2×#389D6111yescharacteristic, complemented
289C2×#385—612no—
290C2×#385—612no—
291C2×#384—612no—
292C2×#382—612no—
293C2×C61#231718yescomplemented
294C2×C61C23×C4⋊C411yescharacteristic
295C2×C61C2×#52011yescharacteristic
296C2×C61C2×#52011yescharacteristic
297C2×C61C2×#53511yescharacteristic
298C2×C61C2×#53611yescharacteristic
299C2×C61C2×#54411yescharacteristic
300C2×C61C2×#54411yescharacteristic
301D61—28no—
302C24×C4—611no—
303C24×C4—612no—
304C2×#117—6116no—
305C2×#117—618no—
306C2×#117—618no—
307C2×#117—1228no—
308C22×C4⋊C4—611no—
309C22×C4⋊C4—612no—
310C22×C4⋊C4—611no—
311C22×C4⋊C4—611no—
312C22×C4⋊C4—611no—
313C22×C4⋊C4—612no—
314C22×C4⋊C4—612no—
315C22×C4⋊C4—612no—
316C22×C4⋊C4—618no—
317C22×C4⋊C4—1228no—
318C22×C4⋊C4C2×D6111yescharacteristic
319C22×C4⋊C4C2×D6112yes—
320C22×C4⋊C4C2×D6111yescharacteristic
321C22×C22⋊C4—612no—
322C22×C22⋊C4—611no—
323C22×C22⋊C4—611no—
324C22×C42—612no—
325C22×C42—611no—
326C22×C42C2×D6111yescharacteristic
327#389—618no—
328#389—618no—
329#389—618no—
330#389C2×D6118yescomplemented
331#385—6116no—
332#385—6116no—
333#384—6116no—
334#382—6116no—
335C2×#95—612no—
336C2×#95—612no—
337C2×#95—612no—
338C2×#95C2×D6112yes—
339C61C2×#231711yescharacteristic, complemented, Sylow
340C25—611no—
341C23×C4—611no—
342C23×C4—618no—
343C23×C4—618no—
344C23×C4—618no—
345C23×C4—614no—
346C23×C4—612no—
347C23×C4—611no—
348C23×C4—611no—
349C23×C4—612no—
350C23×C4—618no—
351C23×C4—1228no—
352C23×C4—2444no—
353C23×C4—2444no—
354C23×C4C22×D6111yescharacteristic
355C23×C4C22×D6111yescharacteristic
356C23×C4C22×D6112yes—
357C23×C4C22×D6112yes—
358C23×C4C22×D6111yescharacteristic
359#117—6164no—
360#117—12232no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—618no—
364C2×C4⋊C4—614no—
365C2×C4⋊C4—618no—
366C2×C4⋊C4—614no—
367C2×C4⋊C4—614no—
368C2×C4⋊C4—614no—
369C2×C4⋊C4—618no—
370C2×C4⋊C4—618no—
371C2×C4⋊C4—618no—
372C2×C4⋊C4—12232no—
373C2×C4⋊C4—1228no—
374C2×C4⋊C4—1224no—
375C2×C4⋊C4—1224no—
376C2×C4⋊C4—1224no—
377C2×C4⋊C4—2444no—
378C2×C4⋊C4—2444no—
379C2×C4⋊C4—2444no—
380C2×C4⋊C4C4×D6118yescomplemented
381C2×C4⋊C4C22×D6114yes—
382C2×C4⋊C4C22×D6118yes—
383C2×C4⋊C4C22×D6114yes—
384C2×C22⋊C4—6116no—
385C2×C22⋊C4—618no—
386C2×C22⋊C4—614no—
387C2×C22⋊C4—614no—
388C2×C22⋊C4—1224no—
389C2×C22⋊C4—1224no—
390C2×C42—24no—
391C2×C42—6116no—
392C2×C42—618no—
393C2×C42—614no—
394C2×C42—1224no—
395C2×C42C22×D6114yes—
396#95—618no—
397#95—618no—
398#95—618no—
399#95C22×D6118yes—
400C24—614no—
401C24—614no—
402C24—614no—
403C24—612no—
404C24—1222no—
405C24—1222no—
406C24—1222no—
407C24—1222no—
408C24C23×D6111yescharacteristic
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—614no—
421C22×C4—614no—
422C22×C4—614no—
423C22×C4—612no—
424C22×C4—6116no—
425C22×C4—6116no—
426C22×C4—6116no—
427C22×C4—6164no—
428C22×C4—618no—
429C22×C4—614no—
430C22×C4—612no—
431C22×C4—614no—
432C22×C4—612no—
433C22×C4—12216no—
434C22×C4—1224no—
435C22×C4—1224no—
436C22×C4—1222no—
437C22×C4—1222no—
438C22×C4—1224no—
439C22×C4—1222no—
440C22×C4—1224no—
441C22×C4—1222no—
442C22×C4—1224no—
443C22×C4—1222no—
444C22×C4—1222no—
445C22×C4—2448no—
446C22×C4—2448no—
447C22×C4—24432no—
448C22×C4C2×C4×D6118yes—
449C22×C4C2×C4×D6114yes—
450C22×C4D4×D6114yes—
451C22×C4Q8×D6114yes—
452C22×C4C23×D6112yes—
453C22×C4C23×D6114yes—
454C22×C4C23×D6112yes—
455C22×C4C23×D6114yes—
456C22×C4C23×D6112yes—
457C4⋊C4—28no—
458C4⋊C4—48no—
459C4⋊C4—6116no—
460C4⋊C4—12216no—
461C4⋊C4—1228no—
462C4⋊C4—1228no—
463C4⋊C4—1228no—
464C4⋊C4—2448no—
465C4⋊C4—2448no—
466C4⋊C4—2448no—
467C4⋊C4C2×C4×D61116yescomplemented
468C22⋊C4—6132no—
469C22⋊C4—1228no—
470C22⋊C4—1228no—
471C42—28no—
472C42—6132no—
473C42—1228no—
474C23—6116no—
475C23—614no—
476C23—614no—
477C23—614no—
478C23—1228no—
479C23—1228no—
480C23—1228no—
481C23—1228no—
482C23—1222no—
483C23—1222no—
484C23—1222no—
485C23—1222no—
486C23—1228no—
487C23—1228no—
488C23C22×C4×D6112yes—
489C23C2×D4×D6112yes—
490C23C2×Q8×D6112yes—
491C23#1451982212yes—
492C23#1451982312yes—
493C23#1451982412yes—
494C23#1451982512yes—
495C23C24×D6111yescharacteristic
496C2×C4—216no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—44no—
509C2×C4—48no—
510C2×C4—44no—
511C2×C4—6116no—
512C2×C4—614no—
513C2×C4—614no—
514C2×C4—614no—
515C2×C4—6164no—
516C2×C4—618no—
517C2×C4—12216no—
518C2×C4—1224no—
519C2×C4—1224no—
520C2×C4—1222no—
521C2×C4—1222no—
522C2×C4—1224no—
523C2×C4—1222no—
524C2×C4—1224no—
525C2×C4—1222no—
526C2×C4—1224no—
527C2×C4—1222no—
528C2×C4—1222no—
529C2×C4—24432no—
530C2×C4—2444no—
531C2×C4—2448no—
532C2×C4—2444no—
533C2×C4C4⋊C4×D61116yes—
534C2×C4C22×C4×D6118yes—
535C2×C4C22×C4×D6114yes—
536C2×C4C2×D4×D6114yes—
537C2×C4C2×Q8×D6114yes—
538C22—618no—
539C22—1224no—
540C22—1224no—
541C22—1224no—
542C22—1224no—
543C22—1224no—
544C22—1224no—
545C22—12232no—
546C22C2×C4⋊C4×D6114yes—
547C22#1684024114yes—
548C22#1684024414yes—
549C22#1684032814yes—
550C22#1684033514yes—
551C22#1684038914yes—
552C22#1684039214yes—
553C22C23×C4×D6111yescharacteristic
554C22C22×D4×D6111yescharacteristic
555C22C22×Q8×D6111yescharacteristic
556C22C2×#1451982211yescharacteristic
557C22C2×#1451982311yescharacteristic
558C22C2×#1451982411yescharacteristic
559C22C2×#1451982511yescharacteristic
560C4—28no—
561C4—42no—
562C4—44no—
563C4—42no—
564C4—618no—
565C4—1228no—
566C4—2442no—
567C4—2444no—
568C4—2442no—
569C4C2×C4⋊C4×D6118yes—
570C2—1228no—
571C2#2144844118yesdirect product factor
572C2C22×C4⋊C4×D6111yescharacteristic
573C2C2×#1684024111yescharacteristic
574C2C2×#1684024411yescharacteristic
575C2C2×#1684032811yescharacteristic
576C2C2×#1684033511yescharacteristic
577C2C2×#1684038911yescharacteristic
578C2C2×#1684039211yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#389C2
socleC24×C61C24
prime radicalC24×D61C23
cosocleC23×C61C25
hypercenterC2×#389D61
hypocenterC61C2×#2317
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
4. #21448441C2direct (N × H)
5. C2×#16839661C2semidirect
6. C2×#16839660C2semidirect
7. C2×#16839658C2semidirect
10. C2×#16839631C2semidirect
11. C2×#16839626C2semidirect
12. C2×C61×#389C2semidirect
15. C2×#14519735C4semidirect
34. #16839661C22semidirect
35. #16839660C22semidirect
36. #16839658C22semidirect
39. #16839631C22semidirect
40. #16839626C22semidirect
48. C61×#389C22semidirect
64. #14519735C2×C4semidirect
68. C2×C4⋊Dic61C2×C4semidirect
90. C2×C4×Dic61C2×C4semidirect
103. C2×C4⋊C4×C61C2×C4semidirect
163. C2×C4×D61C4⋊C4semidirect
169. C4⋊C4×C61C22×C4semidirect
176. C4⋊Dic61C22×C4semidirect
183. C4×Dic61C22×C4semidirect
247. C4×D61C2×C4⋊C4semidirect
288. C2×#389D61semidirect
293. C2×C61#2317semidirect
330. #389C2×D61semidirect
339. C61C2×#2317semidirect
380. C2×C4⋊C4C4×D61semidirect
467. C4⋊C4C2×C4×D61semidirect
571. C2#21448441direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197352
C22×#145197342
C22×C4⋊C4×D612
#214484412
C2×#168396612
C2×#168396602
C2×#168396582
C2×#168396362
C2×#168396332
C2×#168396312
C2×#168396262
C2×C61×#3892
C2×#231761