Finite Group Databasebeta

← C2×#21455738 #30547787

Subgroups — C2×#21455738 #30547787

Order 15616.

2650 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840272C211yesmaximal, characteristic
2C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
3#21455738C2116yesmaximal, direct product factor
4C2×#16840099C212yesmaximal, complemented
5C2×#16840079C212yesmaximal, complemented
6C2×#16840093C211yesmaximal, characteristic, complemented
7C2×#16840092C211yesmaximal, characteristic, complemented
8C2×#16840073C211yesmaximal, characteristic, complemented
9C2×#16839803C212yesmaximal, complemented
10C2×#16839760C212yesmaximal, complemented
11C2×#16839724C211yesmaximal, characteristic, complemented
12C2×C61×#480C211yesmaximal, characteristic, complemented
13C22×#11758224C2211yescharacteristic
14C23×C4×D61—21no—
15C23×C4×D61C2211yescharacteristic
16C22×#11758189C2212yes—
17#16840272—24no—
18#16840272C2218yes—
19C2×#14519759—21no—
20C2×#14519757C2211yescharacteristic
21C2×#14519756C2211yescharacteristic
22C2×#14519748C2211yescharacteristic
23C2×#14519745—21no—
24C2×D4×Dic61—21no—
25C2×#14519737—21no—
26C2×#14519735C2211yescharacteristic
27C22×C4⋊Dic61C2211yescharacteristic
28C22×#11758196—21no—
29C2×C4⋊C4×D61—21no—
30C2×C4⋊C4×D61—21no—
31C2×C4⋊C4×D61—24no—
32C2×C4⋊C4×D61C2212yes—
33C2×C4⋊C4×D61C2212yes—
34C2×C4⋊C4×D61C2218yescomplemented
35#16840099C22116yescomplemented
36#16840093C2218yescomplemented
37#16840092C2218yescomplemented
38#16840079C22116yescomplemented
39#16840073C2218yescomplemented
40#16839803C22116yescomplemented
41C2×#14519710C2212yescomplemented
42C2×#14519709C2212yescomplemented
43C2×#14519708C2212yescomplemented
44#16839760C22116yescomplemented
45C2×#14519702C2212yescomplemented
46C2×#14519700C2212yescomplemented
47C2×#14519698C2212yescomplemented
48#16839724C2218yescomplemented
49C2×C22⋊#92418C2211yescharacteristic
50C2×#14519689C2212yes—
51C2×#121×C61C2211yescharacteristic
52C22×C4⋊C4×C61C2211yescharacteristic
53C61×#480C2218yescomplemented
54C2×#107×C61C2212yescomplemented
55C2×#102×C61C2212yescomplemented
56C2×C22⋊C8×C61C2211yescharacteristic
57C24×D61D411yescharacteristic
58C2×#11758224—22no—
59C2×#11758224—28no—
60C2×#11758224C2314yes—
61C22×Dic122C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C22⋊D61—21no—
64C23×Dic61—21no—
65C23×Dic61—21no—
66C23×Dic61D411yescharacteristic
67C22×C4×D61—28no—
68C22×C4×D61—22no—
69C22×C4×D61—22no—
70C22×C4×D61—28no—
71C22×C4×D61—48no—
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D414yes—
75C22×C4×D61C2311yescharacteristic
76C22×C4×D61C2314yes—
77C22×C4×D61C2311yescharacteristic
78C2×#11758189—28no—
79C2×#11758189C2318yes—
80C22×#92418C2312yes—
81#14519759—28no—
82#14519757—22no—
83#14519757C2314yes—
84#14519756—22no—
85#14519756C2314yes—
86#14519748—22no—
87#14519748C2314yes—
88#14519745—28no—
89D4×Dic61—28no—
90#14519737—28no—
91#14519735—22no—
92#14519735C2314yes—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61—22no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61C2312yes—
97C2×C4⋊Dic61C2314yes—
98C2×C4⋊Dic61C2311yescharacteristic
99C2×#11758196—21no—
100C2×#11758196—22no—
101C2×#11758196—22no—
102C2×#11758196—28no—
103C4⋊C4×D61—24no—
104C4⋊C4×D61—24no—
105C4⋊C4×D61—28no—
106C4⋊C4×D61—28no—
107C4⋊C4×D61C2318yes—
108C4⋊C4×D61C2318yes—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×C4×Dic61—21no—
114#14519710C2318yescomplemented
115#14519709C2318yescomplemented
116#14519708C2318yescomplemented
117#14519702C2318yescomplemented
118#14519700C2318yescomplemented
119#14519698C2318yescomplemented
120C22⋊#92418C2314yes—
121#14519689C2318yes—
122C22×D4×C61—21no—
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61—21no—
125C23×C4×C61C2311yescharacteristic
126C22×C8×C61C2312yes—
127#121×C61—22no—
128#121×C61C2314yes—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—22no—
131C2×C4⋊C4×C61C2312yes—
132C2×C4⋊C4×C61C2314yes—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—21no—
135#107×C61C2318yescomplemented
136#102×C61C2318yescomplemented
137C22⋊C8×C61C2314yes—
138C24×C61—21no—
139C24×C61C2×D411yescharacteristic
140C23×D61—24no—
141C23×D61—24no—
142C23×D61—24no—
143C23×D61C2×D414yes—
144C23×D61C2×D411yescharacteristic
145C23×D61C2×D411yescharacteristic
146C2×D4×C61—24no—
147C2×D4×C61—21no—
148C2×D4×C61—24no—
149C2×D4×C61—44no—
150C2×D4×C61C2412yes—
151C22×C4×C61—24no—
152C22×C4×C61—24no—
153C22×C4×C61—22no—
154C22×C4×C61—21no—
155C22×C4×C61—44no—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2412yes—
159C22×C4×C61C2411yescharacteristic
160C2×C22⋊D61—24no—
161C2×C22⋊D61—24no—
162C2×C22⋊D61—44no—
163C2×C22⋊D61—44no—
164C22×Dic61—24no—
165C22×Dic61—24no—
166C22×Dic61—22no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—24no—
170C22×Dic61—44no—
171C22×Dic61—44no—
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D414yes—
174C22×Dic61C2×D411yescharacteristic
175#11758224—216no—
176#11758224—48no—
177C2×C4×D61—24no—
178C2×C4×D61—24no—
179C2×C4×D61—24no—
180C2×C4×D61—216no—
181C2×C4×D61—216no—
182C2×C4×D61—28no—
183C2×C4×D61—28no—
184C2×C4×D61—48no—
185C2×C4×D61—48no—
186C2×C4×D61—432no—
187C2×C4×D61C2×D414yes—
188C2×C4×D61C2×D412yes—
189C2×C4×D61C2×D414yes—
190C2×C4×D61C2×D412yes—
191C2×C4×D61#4118yes—
192C2×C4×D61C2412yes—
193C2×C4×D61C2412yes—
194C2×Dic122—24no—
195C2×Dic122—21no—
196C2×Dic122C2412yes—
197C2×C8×C61—24no—
198C2×C8×C61C2414yes—
199C4⋊C4×C61—24no—
200C4⋊C4×C61—22no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61C2414yes—
203C4⋊C4×C61C2412yes—
204C22⋊C4×C61—24no—
205C22⋊Dic61—24no—
206C22⋊Dic61—24no—
207#11758198—24no—
208#11758198—24no—
209C4⋊Dic61—24no—
210C4⋊Dic61—22no—
211C4⋊Dic61—21no—
212C4⋊Dic61—24no—
213C4⋊Dic61C2414yes—
214C4⋊Dic61C2412yes—
215#11758196—24no—
216#11758196—28no—
217#11758196—28no—
218C4×Dic61—24no—
219C2×#92418—24no—
220C2×#92418C2414yes—
221#11758189—216no—
222C23×C61—22no—
223C23×C61—22no—
224C23×C61—22no—
225C23×C61—42no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61AGL(1,ℤ/8)14yes—
229C23×C61C22×D412yes—
230C23×C61C22×D411yescharacteristic
231C22×D61—232no—
232C22×D61—22no—
233C22×D61—28no—
234C22×D61—22no—
235C22×D61—22no—
236C22×D61—22no—
237C22×D61—28no—
238C22×D61—28no—
239C22×D61#12314yes—
240C22×D61#13714yes—
241C22×D61C22×D412yes—
242C22×D61C22×D412yes—
243D4×C61—24no—
244D4×C61—48no—
245D4×C61—42no—
246C2×C4×C61—22no—
247C2×C4×C61—24no—
248C2×C4×C61—24no—
249C2×C4×C61—22no—
250C2×C4×C61—24no—
251C2×C4×C61—48no—
252C2×C4×C61—44no—
253C2×C4×C61—42no—
254C2×C4×C61C22×D412yes—
255C2×C4×C61C22×D411yescharacteristic
256C2×C4×C61C2×#4114yes—
257C2×C4×C61C2511yescharacteristic
258C22⋊D61—48no—
259C22⋊D61—48no—
260C2×Dic61—22no—
261C2×Dic61—28no—
262C2×Dic61—22no—
263C2×Dic61—24no—
264C2×Dic61—22no—
265C2×Dic61—42no—
266C2×Dic61—48no—
267C2×Dic61—44no—
268C2×Dic61—42no—
269C2×Dic61—48no—
270C2×Dic61#12314yes—
271C2×Dic61C22×D412yes—
272C2×Dic61C22×D412yes—
273C4×D61—28no—
274C4×D61—24no—
275C4×D61—24no—
276C4×D61—28no—
277C4×D61—416no—
278C4×D61—416no—
279C4×D61#12318yes—
280C4×D61C2×#4118yes—
281Dic122—24no—
282Dic122—42no—
283C8×C61—24no—
284#92418—24no—
285C2×#3092—611nomaximal, Sylow
286C22×C61—28no—
287C22×C61—22no—
288C22×C61—22no—
289C22×C61—42no—
290C22×C61—42no—
291C22×C61—42no—
292C22×C61—84no—
293C22×C61C2×#12312yes—
294C22×C61C2×AGL(1,ℤ/8)14yes—
295C22×C61C2×AGL(1,ℤ/8)12yes—
296C22×C61C2×#13712yes—
297C22×C61C23×D411yescharacteristic
298C2×D61—232no—
299C2×D61—28no—
300C2×D61—28no—
301C2×D61—22no—
302C2×D61—22no—
303C2×D61—22no—
304C2×D61—22no—
305C2×D61C2×#12314yes—
306C2×D61C2×#13714yes—
307C4×C61—22no—
308C4×C61—44no—
309C4×C61—42no—
310C4×C61C2×#12312yes—
311C4×C61C22×#4112yes—
312Dic61—22no—
313Dic61—42no—
314Dic61—44no—
315Dic61—42no—
316Dic61C2×#12314yes—
317C2×#525—611no—
318C23×C4⋊C4—611no—
319#3092—6116no—
320C2×#484—612no—
321C2×#481—612no—
322C2×#483—611no—
323C2×#483—611no—
324C2×#480—611no—
325C2×#480D6111yescharacteristic, complemented
326C2×#428—612no—
327C2×#417—612no—
328C2×#407—611no—
329C2×C61—24no—
330C2×C61—82no—
331C2×C61#309214yescomplemented
332C2×C61C22×#12311yescharacteristic
333C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
334C2×C61C22×#13711yescharacteristic
335D61—24no—
336D61—24no—
337C22×#41—611no—
338C24×C4—611no—
339C24×C4—1221no—
340C22×M16—612no—
341#525—618no—
342#525—1224no—
343C2×#123—1221no—
344C2×C22⋊Q8—611no—
345C2×C22⋊Q8—611no—
346C2×#121—611no—
347C2×#121C2×D6111yescharacteristic
348C2×#120—1221no—
349C2×C4×D4—1221no—
350C2×C4×D4—1221no—
351C2×#117—611no—
352C22×C4⋊C4—611no—
353C22×C4⋊C4—612no—
354C22×C4⋊C4—612no—
355C22×C4⋊C4—618no—
356C22×C4⋊C4—1221no—
357C22×C4⋊C4—1221no—
358C22×C4⋊C4—1224no—
359C22×C4⋊C4—1221no—
360C22×C4⋊C4C2×D6111yescharacteristic
361#484—6116no—
362#483—618no—
363#483—618no—
364#481—6116no—
365#480—618no—
366#480C2×D6118yescomplemented
367#428—6116no—
368C2×#107—612no—
369C2×#107C2×D6112yescomplemented
370C2×#106—612no—
371C2×#106—612no—
372#417—6116no—
373C2×#103—612no—
374C2×#103—612no—
375C2×#102—612no—
376C2×#102C2×D6112yescomplemented
377#407—618no—
378C2×C22⋊C8—611no—
379C2×C22⋊C8—612no—
380C2×C22⋊C8C2×D6111yescharacteristic
381C61C2×#309211yescharacteristic, complemented, Sylow
382C25—611no—
383C2×#41—614no—
384C2×#41—1222no—
385C2×#41—1228no—
386C22×Q8—611no—
387C22×D4—21no—
388C22×D4—1221no—
389C22×D4—1221no—
390C22×D4C22×D6111yescharacteristic
391C23×C4—21no—
392C23×C4—611no—
393C23×C4—611no—
394C23×C4—611no—
395C23×C4—611no—
396C23×C4—614no—
397C23×C4—611no—
398C23×C4—614no—
399C23×C4—1228no—
400C23×C4—1228no—
401C23×C4—1222no—
402C23×C4—1222no—
403C23×C4—1221no—
404C23×C4—1221no—
405C23×C4—2448no—
406C23×C4C22×D6111yescharacteristic
407C2×M16—618no—
408C2×M16—1228no—
409C22×C8—612no—
410C22×C8C22×D6112yes—
411#123—1228no—
412C22⋊Q8—614no—
413C22⋊Q8—614no—
414C22⋊Q8—1222no—
415C22⋊Q8—1222no—
416#121—22no—
417#121—614no—
418#121—1222no—
419#121C22×D6114yes—
420#120—1228no—
421C4×D4—1228no—
422C4×D4—1228no—
423#117—614no—
424#117—1222no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—612no—
428C2×C4⋊C4—614no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—618no—
431C2×C4⋊C4—618no—
432C2×C4⋊C4—1224no—
433C2×C4⋊C4—1228no—
434C2×C4⋊C4—1224no—
435C2×C4⋊C4—1228no—
436C2×C4⋊C4—1228no—
437C2×C4⋊C4—1222no—
438C2×C4⋊C4—1222no—
439C2×C4⋊C4—1221no—
440C2×C4⋊C4—1222no—
441C2×C4⋊C4—1221no—
442C2×C4⋊C4—1221no—
443C2×C4⋊C4C22×D6112yes—
444C2×C4⋊C4C22×D6114yes—
445C2×C4⋊C4C22×D6111yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—1221no—
448C2×C22⋊C4—1221no—
449C2×C22⋊C4—1221no—
450C2×C22⋊C4—1221no—
451C2×C42—1221no—
452#107—618no—
453#107C22×D6118yescomplemented
454#106—618no—
455#106—618no—
456#103—618no—
457#103—618no—
458#102—618no—
459#102C22×D6118yescomplemented
460C22⋊C8—614no—
461C22⋊C8—618no—
462C22⋊C8C22×D6114yes—
463C24—21no—
464C24—611no—
465C24—611no—
466C24—614no—
467C24—1224no—
468C24—1224no—
469C24—1224no—
470C24D4×D6111yescharacteristic
471#41—12216no—
472#41—2448no—
473C2×Q8—612no—
474C2×Q8—1221no—
475C2×Q8—1224no—
476C2×D4—24no—
477C2×D4—21no—
478C2×D4—24no—
479C2×D4—44no—
480C2×D4—1224no—
481C2×D4—1224no—
482C2×D4—2444no—
483C2×D4—2444no—
484C2×D4C23×D6112yes—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—611no—
491C22×C4—612no—
492C22×C4—618no—
493C22×C4—612no—
494C22×C4—614no—
495C22×C4—611no—
496C22×C4—614no—
497C22×C4—612no—
498C22×C4—614no—
499C22×C4—612no—
500C22×C4—1224no—
501C22×C4—12216no—
502C22×C4—12216no—
503C22×C4—1224no—
504C22×C4—1228no—
505C22×C4—1228no—
506C22×C4—1224no—
507C22×C4—1224no—
508C22×C4—1224no—
509C22×C4—1224no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1222no—
513C22×C4—24432no—
514C22×C4—2448no—
515C22×C4—2448no—
516C22×C4—2444no—
517C22×C4—2444no—
518C22×C4D4×D6112yes—
519C22×C4D4×D6111yescharacteristic
520C22×C4C23×D6112yes—
521C22×C4C23×D6111yescharacteristic
522M16—12216no—
523C2×C8—24no—
524C2×C8—614no—
525C2×C8—1224no—
526C2×C8C23×D6114yes—
527C4⋊C4—24no—
528C4⋊C4—22no—
529C4⋊C4—21no—
530C4⋊C4—614no—
531C4⋊C4—612no—
532C4⋊C4—1228no—
533C4⋊C4—1228no—
534C4⋊C4—1224no—
535C4⋊C4—1224no—
536C4⋊C4—1222no—
537C4⋊C4—1221no—
538C4⋊C4—1224no—
539C4⋊C4C23×D6114yes—
540C4⋊C4C23×D6112yes—
541C22⋊C4—24no—
542C22⋊C4—1224no—
543C22⋊C4—1224no—
544C22⋊C4—1224no—
545C22⋊C4—1224no—
546C42—1224no—
547C23—22no—
548C23—22no—
549C23—22no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—614no—
554C23—614no—
555C23—612no—
556C23—612no—
557C23—1228no—
558C23—1228no—
559C23—12232no—
560C23—1222no—
561C23—1228no—
562C23—1222no—
563C23—1222no—
564C23—1222no—
565C23#1451980114yes—
566C23C2×D4×D6112yes—
567C23C2×D4×D6111yescharacteristic
568Q8—1224no—
569Q8—2442no—
570D4—24no—
571D4—48no—
572D4—42no—
573D4—2448no—
574D4—2448no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—48no—
581C2×C4—44no—
582C2×C4—42no—
583C2×C4—614no—
584C2×C4—612no—
585C2×C4—618no—
586C2×C4—618no—
587C2×C4—612no—
588C2×C4—1228no—
589C2×C4—1228no—
590C2×C4—1228no—
591C2×C4—1222no—
592C2×C4—1224no—
593C2×C4—1224no—
594C2×C4—1222no—
595C2×C4—1222no—
596C2×C4—1224no—
597C2×C4—24416no—
598C2×C4—24416no—
599C2×C4—2448no—
600C2×C4—2442no—
601C2×C4—2448no—
602C2×C4—2444no—
603C2×C4—2442no—
604C2×C4C2×D4×D6112yes—
605C2×C4C2×D4×D6111yescharacteristic
606C2×C4#41×D6114yes—
607C2×C4C24×D6111yescharacteristic
608C8—24no—
609C8—1224no—
610C22—22no—
611C22—22no—
612C22—28no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—84no—
617C22—614no—
618C22—614no—
619C22—12232no—
620C22—1222no—
621C22—1222no—
622C22—1222no—
623C22—1222no—
624C22—1228no—
625C22—1228no—
626C22#123×D6112yes—
627C22C2×#1451980114yes—
628C22C2×#1451980112yes—
629C22#137×D6112yes—
630C22C22×D4×D6111yescharacteristic
631C4—22no—
632C4—44no—
633C4—42no—
634C4—614no—
635C4—1222no—
636C4—2444no—
637C4—2442no—
638C4—2442no—
639C4#123×D6112yes—
640C4C2×#41×D6112yes—
641C2—24no—
642C2—82no—
643C2—1224no—
644C2—1224no—
645C2#2145573814yesdirect product factor
646C2C2×#123×D6111yescharacteristic
647C2C22×#1451980111yescharacteristic
648C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#480C2
socleC23×C61C22×D4
prime radicalC2×#16840272C2
hypercenterC2×#480D61
hypocenterC61C2×#3092
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D61C2semidirect
3. #21455738C2direct (N × H)
4. C2×#16840099C2semidirect
5. C2×#16840079C2semidirect
6. C2×#16840093C2semidirect
7. C2×#16840092C2semidirect
8. C2×#16840073C2semidirect
9. C2×#16839803C2semidirect
10. C2×#16839760C2semidirect
11. C2×#16839724C2semidirect
12. C2×C61×#480C2semidirect
34. C2×C4⋊C4×D61C22semidirect
35. #16840099C22semidirect
36. #16840093C22semidirect
37. #16840092C22semidirect
38. #16840079C22semidirect
39. #16840073C22semidirect
40. #16839803C22semidirect
41. C2×#14519710C22semidirect
42. C2×#14519709C22semidirect
43. C2×#14519708C22semidirect
44. #16839760C22semidirect
45. C2×#14519702C22semidirect
46. C2×#14519700C22semidirect
47. C2×#14519698C22semidirect
48. #16839724C22semidirect
53. C61×#480C22semidirect
54. C2×#107×C61C22semidirect
55. C2×#102×C61C22semidirect
114. #14519710C23semidirect
115. #14519709C23semidirect
116. #14519708C23semidirect
117. #14519702C23semidirect
118. #14519700C23semidirect
119. #14519698C23semidirect
135. #107×C61C23semidirect
136. #102×C61C23semidirect
325. C2×#480D61semidirect
331. C2×C61#3092semidirect
366. #480C2×D61semidirect
369. C2×#107C2×D61semidirect
376. C2×#102C2×D61semidirect
381. C61C2×#3092semidirect
453. #107C22×D61semidirect
459. #102C22×D61semidirect
645. C2#21455738direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402722
C22×C4⋊C4×D612
#214557382
C2×#168400992
C2×#168400792
C2×#168400932
C2×#168400922
C2×#168400732
C2×#168398032
C2×#168397602
C2×#168397242
C2×C61×#4802
C2×#309261