Finite Group Databasebeta

← C2×#21450330 #29849133

Subgroups — C2×#21450330 #29849133

Order 15616.

2358 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519768C211yesmaximal, characteristic
2C22×#14519767C211yesmaximal, characteristic
3#21450330C2116yesmaximal, direct product factor
4C2×#16839702C211yesmaximal, characteristic
5C2×#16839696C211yesmaximal, characteristic
6C2×#16839696C211yesmaximal, characteristic
7C2×#16839659C211yesmaximal, characteristic
8C2×#16839659C211yesmaximal, characteristic
9C2×#16839659C211yesmaximal, characteristic
10C2×#16839657C211yesmaximal, characteristic
11C2×#16839649C211yesmaximal, characteristic
12C2×#16839644C211yesmaximal, characteristic
13C2×#16839631C211yesmaximal, characteristic
14C2×#16839613C211yesmaximal, characteristic
15C2×#16839613C211yesmaximal, characteristic
16C2×C61×#400C211yesmaximal, characteristic
17C2×#14519768—28no—
18C2×#14519768C2218yes—
19C2×#14519767—28no—
20C2×#14519767C2218yes—
21C22×C4⋊Dic61C2211yescharacteristic
22C22×C4⋊Dic61C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24C22×C4⋊Dic61C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×#11758196C2211yescharacteristic
33C22×#11758196C2211yescharacteristic
34C22×#11758196C2211yescharacteristic
35C22×#11758196C2211yescharacteristic
36C22×#11758196C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41C22×C4×Dic61C2211yescharacteristic
42#16839702C2218yes—
43#16839696C2218yes—
44#16839696C2218yes—
45#16839659C2218yes—
46#16839659C2218yes—
47#16839659C2218yes—
48#16839657C2218yes—
49#16839649C2218yes—
50#16839644C2218yes—
51#16839631C2218yes—
52#16839613C2218yes—
53#16839613C2218yes—
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C61×#400C2218yes—
64C2×#95×C61C2211yescharacteristic
65C2×#95×C61C2211yescharacteristic
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C2×#95×C61C2211yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77#14519768—232no—
78#14519767—232no—
79C2×C4⋊Dic61—24no—
80C2×C4⋊Dic61—24no—
81C2×C4⋊Dic61—24no—
82C2×C4⋊Dic61—24no—
83C2×C4⋊Dic61C2314yes—
84C2×C4⋊Dic61C2314yes—
85C2×C4⋊Dic61C2314yes—
86C2×C4⋊Dic61C2314yes—
87C2×#11758196—24no—
88C2×#11758196—24no—
89C2×#11758196—24no—
90C2×#11758196—24no—
91C2×#11758196—24no—
92C2×#11758196—24no—
93C2×#11758196—24no—
94C2×#11758196—24no—
95C2×#11758196—24no—
96C2×#11758196—24no—
97C2×#11758196D418yes—
98C2×#11758196Q818yes—
99C2×#11758196C2314yes—
100C2×#11758196C2314yes—
101C2×#11758196C2314yes—
102C2×#11758196C2314yes—
103C2×#11758196C2314yes—
104C2×#11758196C2314yes—
105C2×#11758196C2314yes—
106C2×#11758196C2314yes—
107C2×#11758196C2314yes—
108C2×#11758196C2314yes—
109C2×#11758196C2314yes—
110C2×#11758196C2314yes—
111C2×C4×Dic61—24no—
112C2×C4×Dic61—24no—
113C2×C4×Dic61—24no—
114C2×C4×Dic61—24no—
115C2×C4×Dic61—24no—
116C2×C4×Dic61C2314yes—
117C2×C4×Dic61C2314yes—
118C2×C4×Dic61C2314yes—
119C2×C4×Dic61C2314yes—
120C2×C4×Dic61C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61—24no—
136C2×C4⋊C4×C61—24no—
137C2×C4⋊C4×C61C2314yes—
138C2×C4⋊C4×C61C2314yes—
139#95×C61C2314yes—
140#95×C61C2314yes—
141#95×C61C2314yes—
142#95×C61C2314yes—
143#95×C61C2314yes—
144C24×C61C2411yescharacteristic
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61C2×D414yes—
165C22×C4×C61C2×Q814yes—
166C22×C4×C61C2412yes—
167C22×C4×C61C2412yes—
168C22×C4×C61C2412yes—
169C22×C4×C61C2412yes—
170C22×C4×C61C2412yes—
171C22×C4×C61C2412yes—
172C22×C4×C61C2412yes—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61C2×D414yes—
191C22×Dic61C2×D414yes—
192C22×Dic61C2×Q814yes—
193C22×Dic61C2×Q814yes—
194C22×Dic61#4114yes—
195C22×Dic61#4114yes—
196C22×Dic61#4114yes—
197C22×Dic61C2412yes—
198C22×Dic61C2412yes—
199C22×Dic61C2412yes—
200C22×Dic61C2412yes—
201C22×Dic61C2412yes—
202C22×Dic61C2412yes—
203C22×Dic61C2412yes—
204C22×Dic61C2412yes—
205C4⋊C4×C61—28no—
206C4⋊C4×C61—28no—
207C4⋊Dic61—28no—
208C4⋊Dic61—28no—
209C4⋊Dic61—28no—
210C4⋊Dic61—28no—
211#11758196—28no—
212#11758196—28no—
213#11758196—28no—
214#11758196—28no—
215#11758196—28no—
216#11758196—28no—
217#11758196—28no—
218#11758196—28no—
219#11758196—28no—
220#11758196—28no—
221#11758196C2×D4116yes—
222#11758196C2×Q8116yes—
223C4×Dic61—28no—
224C4×Dic61—28no—
225C4×Dic61—28no—
226C4×Dic61—28no—
227C4×Dic61—28no—
228C23×C61C22×D412yes—
229C23×C61C22×Q812yes—
230C23×C61C2×#4112yes—
231C23×C61C2×#4112yes—
232C23×C61C2×#4112yes—
233C23×C612−1+412yes—
234C23×C612−1+412yes—
235C23×C61C2511yescharacteristic
236C2×C4×C61—28no—
237C2×C4×C61—28no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—22no—
248C2×C4×C61—22no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—44no—
258C2×C4×C61—44no—
259C2×C4×C61—44no—
260C2×C4×C61—44no—
261C2×C4×C61—44no—
262C2×C4×C61C22×D414yes—
263C2×C4×C61C22×Q814yes—
264C2×Dic61—28no—
265C2×Dic61—28no—
266C2×Dic61—28no—
267C2×Dic61—28no—
268C2×Dic61—22no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—22no—
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—22no—
278C2×Dic61—22no—
279C2×Dic61—22no—
280C2×Dic61—22no—
281C2×Dic61—22no—
282C2×Dic61—22no—
283C2×Dic61—22no—
284C2×Dic61—22no—
285C2×Dic61—44no—
286C2×Dic61—44no—
287C2×Dic61—44no—
288C2×Dic61#125116yescomplemented
289C2×Dic61C22×D414yes—
290C2×Dic61C22×D414yes—
291C2×Dic61C22×Q814yes—
292C2×Dic61C22×Q814yes—
293C2×Dic61C2×#4114yes—
294C2×Dic61C2×#4114yes—
295C2×Dic61C2×#4114yes—
296C2×#2506—611nomaximal, Sylow
297C22×C61C2×#12514yes—
298C22×C61#53214yes—
299C22×C61#54114yes—
300C22×C61#54714yes—
301C22×C61D4×Q814yes—
302C22×C61#55214yes—
303C22×C61#55714yes—
304C22×C61C23×D411yescharacteristic
305C22×C61C23×Q811yescharacteristic
306C22×C61C22×#4111yescharacteristic
307C22×C61C22×#4111yescharacteristic
308C22×C61C22×#4111yescharacteristic
309C22×C61C2×2−1+411yescharacteristic
310C22×C61C2×2−1+411yescharacteristic
311C4×C61—24no—
312C4×C61—24no—
313C4×C61—42no—
314C4×C61—42no—
315C4×C61—42no—
316C4×C61—42no—
317C4×C61—42no—
318Dic61—24no—
319Dic61—24no—
320Dic61—24no—
321Dic61—24no—
322Dic61—42no—
323Dic61—42no—
324Dic61—42no—
325Dic61C2×#12518yescomplemented
326C22×#125—611no—
327C22×#125—611no—
328#2506—6116no—
329C2×#400—611no—
330C2×#400D6111yescharacteristic
331C2×#398—611no—
332C2×#398—611no—
333C2×#389—611no—
334C2×#389—611no—
335C2×#389—611no—
336C2×#389—611no—
337C2×#387—611no—
338C2×#387—611no—
339C2×#384—611no—
340C2×C4×C4⋊C4—611no—
341C2×C4×C4⋊C4—611no—
342C2×C61#250618yescomplemented
343C2×C61C22×#12511yescharacteristic
344C2×C61C2×#53211yescharacteristic
345C2×C61C2×#54111yescharacteristic
346C2×C61C2×#54711yescharacteristic
347C2×C61C2×D4×Q811yescharacteristic
348C2×C61C2×#55211yescharacteristic
349C2×C61C2×#55711yescharacteristic
350C2×#125—618no—
351C2×#125—618no—
352C2×#125—1228no—
353C2×#125—1228no—
354C22×C4⋊C4—611no—
355C22×C4⋊C4—611no—
356C22×C4⋊C4—611no—
357C22×C4⋊C4—611no—
358C22×C4⋊C4—611no—
359C22×C4⋊C4—611no—
360C22×C4⋊C4—611no—
361C22×C4⋊C4—611no—
362C22×C4⋊C4—611no—
363C22×C4⋊C4—611no—
364C22×C4⋊C4—611no—
365C22×C4⋊C4—611no—
366C22×C4⋊C4—611no—
367C22×C4⋊C4—611no—
368C22×C4⋊C4—611no—
369C22×C4⋊C4—611no—
370C22×C4⋊C4C2×D6111yescharacteristic
371C22×C4⋊C4C2×D6111yescharacteristic
372C22×C42—611no—
373C22×C42—611no—
374C22×C42—611no—
375C22×C42—611no—
376C22×C42—611no—
377#400—618no—
378#400C2×D6118yes—
379#398—618no—
380#398—618no—
381#389—618no—
382#389—618no—
383#389—618no—
384#389—618no—
385#387—618no—
386#387—618no—
387#384—618no—
388C4×C4⋊C4—618no—
389C4×C4⋊C4—618no—
390C2×#95—611no—
391C2×#95—611no—
392C2×#95—611no—
393C2×#95—611no—
394C2×#95—611no—
395C2×#95—611no—
396C2×#95—611no—
397C2×#95C2×D6111yescharacteristic
398C2×#95C2×D6111yescharacteristic
399C2×#95C2×D6111yescharacteristic
400C2×#95C2×D6111yescharacteristic
401C2×#95C2×D6111yescharacteristic
402C61C2×#250611yescharacteristic, complemented, Sylow
403C23×C4—611no—
404C23×C4—611no—
405C23×C4—611no—
406C23×C4—611no—
407C23×C4—611no—
408C23×C4—611no—
409C23×C4—611no—
410C23×C4—611no—
411C23×C4C22×D6111yescharacteristic
412C23×C4C22×D6111yescharacteristic
413C23×C4C22×D6111yescharacteristic
414C23×C4C22×D6111yescharacteristic
415C23×C4C22×D6111yescharacteristic
416C23×C4C22×D6111yescharacteristic
417C23×C4C22×D6111yescharacteristic
418#125—12232no—
419#125—12232no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—618no—
423C2×C4⋊C4—618no—
424C2×C4⋊C4—614no—
425C2×C4⋊C4—614no—
426C2×C4⋊C4—614no—
427C2×C4⋊C4—614no—
428C2×C4⋊C4—614no—
429C2×C4⋊C4—614no—
430C2×C4⋊C4—614no—
431C2×C4⋊C4—614no—
432C2×C4⋊C4—614no—
433C2×C4⋊C4—614no—
434C2×C4⋊C4—614no—
435C2×C4⋊C4—614no—
436C2×C4⋊C4—614no—
437C2×C4⋊C4—614no—
438C2×C4⋊C4—614no—
439C2×C4⋊C4—614no—
440C2×C4⋊C4—1224no—
441C2×C4⋊C4—1224no—
442C2×C4⋊C4—1224no—
443C2×C4⋊C4—1224no—
444C2×C4⋊C4—1224no—
445C2×C4⋊C4—1224no—
446C2×C4⋊C4—1224no—
447C2×C4⋊C4—1224no—
448C2×C4⋊C4—1224no—
449C2×C4⋊C4—1224no—
450C2×C4⋊C4—1224no—
451C2×C4⋊C4—1224no—
452C2×C4⋊C4—1224no—
453C2×C4⋊C4—1224no—
454C2×C4⋊C4C22×D6114yes—
455C2×C4⋊C4C22×D6114yes—
456C2×C42—614no—
457C2×C42—614no—
458C2×C42—614no—
459C2×C42—614no—
460C2×C42—614no—
461C2×C42—1224no—
462C2×C42—1224no—
463C2×C42—1224no—
464C2×C42—1224no—
465C2×C42—1224no—
466#95—614no—
467#95—614no—
468#95—614no—
469#95—614no—
470#95—614no—
471#95—614no—
472#95—614no—
473#95C22×D6114yes—
474#95C22×D6114yes—
475#95C22×D6114yes—
476#95C22×D6114yes—
477#95C22×D6114yes—
478C24C23×D6111yescharacteristic
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—614no—
499C22×C4—614no—
500C22×C4—614no—
501C22×C4—612no—
502C22×C4—614no—
503C22×C4—614no—
504C22×C4—614no—
505C22×C4—614no—
506C22×C4—612no—
507C22×C4—612no—
508C22×C4—612no—
509C22×C4—612no—
510C22×C4—612no—
511C22×C4—612no—
512C22×C4—612no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4—1222no—
518C22×C4—1222no—
519C22×C4—1222no—
520C22×C4—1222no—
521C22×C4—1222no—
522C22×C4—1222no—
523C22×C4—1222no—
524C22×C4—1222no—
525C22×C4—1222no—
526C22×C4—1222no—
527C22×C4—1222no—
528C22×C4—1222no—
529C22×C4—1222no—
530C22×C4D4×D6114yes—
531C22×C4Q8×D6114yes—
532C22×C4C23×D6112yes—
533C22×C4C23×D6112yes—
534C22×C4C23×D6112yes—
535C22×C4C23×D6112yes—
536C22×C4C23×D6112yes—
537C22×C4C23×D6112yes—
538C22×C4C23×D6112yes—
539C4⋊C4—28no—
540C4⋊C4—28no—
541C4⋊C4—6116no—
542C4⋊C4—6116no—
543C4⋊C4—1228no—
544C4⋊C4—1228no—
545C4⋊C4—1228no—
546C4⋊C4—1228no—
547C4⋊C4—1228no—
548C4⋊C4—1228no—
549C4⋊C4—1228no—
550C4⋊C4—1228no—
551C4⋊C4—1228no—
552C4⋊C4—1228no—
553C4⋊C4—1228no—
554C4⋊C4—1228no—
555C4⋊C4—1228no—
556C4⋊C4—1228no—
557C42—1228no—
558C42—1228no—
559C42—1228no—
560C42—1228no—
561C42—1228no—
562C23C2×D4×D6112yes—
563C23C2×Q8×D6112yes—
564C23#41×D6112yes—
565C23#41×D6112yes—
566C23#41×D6112yes—
567C23#1451982412yes—
568C23#1451982412yes—
569C23C24×D6111yescharacteristic
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—28no—
575C2×C4—28no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—44no—
594C2×C4—44no—
595C2×C4—44no—
596C2×C4—6116no—
597C2×C4—614no—
598C2×C4—614no—
599C2×C4—614no—
600C2×C4—614no—
601C2×C4—614no—
602C2×C4—614no—
603C2×C4—614no—
604C2×C4—1228no—
605C2×C4—1228no—
606C2×C4—1222no—
607C2×C4—1222no—
608C2×C4—1222no—
609C2×C4—1222no—
610C2×C4—1222no—
611C2×C4—1222no—
612C2×C4—1222no—
613C2×C4—1222no—
614C2×C4—1228no—
615C2×C4—1228no—
616C2×C4—1222no—
617C2×C4—1222no—
618C2×C4—1222no—
619C2×C4—1222no—
620C2×C4—1222no—
621C2×C4—1222no—
622C2×C4—1222no—
623C2×C4—1222no—
624C2×C4—1222no—
625C2×C4—2444no—
626C2×C4—2444no—
627C2×C4—2444no—
628C2×C4C2×D4×D6114yes—
629C2×C4C2×Q8×D6114yes—
630C22#125×D6114yes—
631C22#1684031114yes—
632C22#1684036914yes—
633C22#1684041014yes—
634C22#1684042514yes—
635C22#1684044814yes—
636C22#1684048914yes—
637C22C22×D4×D6111yescharacteristic
638C22C22×Q8×D6111yescharacteristic
639C22C2×#41×D6111yescharacteristic
640C22C2×#41×D6111yescharacteristic
641C22C2×#41×D6111yescharacteristic
642C22C2×#1451982411yescharacteristic
643C22C2×#1451982411yescharacteristic
644C4—24no—
645C4—24no—
646C4—42no—
647C4—42no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—618no—
652C4—1224no—
653C4—1224no—
654C4—1224no—
655C4—1224no—
656C4—2442no—
657C4—2442no—
658C4—2442no—
659C2#2145033018yesdirect product factor
660C2C2×#125×D6111yescharacteristic
661C2C2×#1684031111yescharacteristic
662C2C2×#1684036911yescharacteristic
663C2C2×#1684041011yescharacteristic
664C2C2×#1684042511yescharacteristic
665C2C2×#1684044811yescharacteristic
666C2C2×#1684048911yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#400C2
socle, prime radicalC24×C61C24
hypercenterC2×#400D61
hypocenterC61C2×#2506
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
3. #21450330C2direct (N × H)
288. C2×Dic61#125semidirect
325. Dic61C2×#125semidirect
342. C2×C61#2506semidirect
402. C61C2×#2506semidirect
659. C2#21450330direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197682
C22×#145197672
#214503302
C2×#168397022
C2×#168396962
C2×#168396592
C2×#168396572
C2×#168396492
C2×#168396442
C2×#168396312
C2×#168396132
C2×C61×#4002
C2×#250661