Finite Group Databasebeta

← C2×#475×D61 #30547486

Subgroups — C2×#475×D61 #30547486

Order 15616.

2358 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D61C211yesmaximal, characteristic
2C2×C4×Q8×D61C211yesmaximal, characteristic
3C2×#16840048C211yesmaximal, characteristic, complemented
4C2×#16840047C211yesmaximal, characteristic, complemented
5C2×#16840046C212yesmaximal, complemented
6C2×#16840045C212yesmaximal, complemented
7C2×#16840044C211yesmaximal, characteristic, complemented
8#475×D61C2116yesmaximal, direct product factor
9C2×#106×D61C212yesmaximal
10C2×C4⋊C8×D61C211yesmaximal, characteristic
11C2×#103×D61C212yesmaximal
12C2×C61×#475C211yesmaximal, characteristic, complemented
13C22×Q8×D61—21no—
14C22×Q8×D61C2211yescharacteristic
15C22×C8×D61C2212yes—
16C2×#14519777C2211yescharacteristic
17C2×#14519776—21no—
18C2×#14519776C2212yes—
19C2×#14519775—21no—
20C4⋊Q8×D61—24no—
21C4⋊Q8×D61C2218yes—
22C2×Q8×Dic61C2211yescharacteristic
23C2×C4×Dic122—21no—
24C2×C4×Dic122C2211yescharacteristic
25C2×#14519742—21no—
26C2×#14519742C2211yescharacteristic
27C4×Q8×D61—24no—
28C4×Q8×D61C2218yes—
29C2×C4⋊C4×D61—21no—
30C2×C4⋊C4×D61—21no—
31C2×C4⋊C4×D61C2211yescharacteristic
32C2×C4⋊C4×D61C2212yes—
33C2×C42×D61—21no—
34C2×C42×D61C2211yescharacteristic
35#16840048C2218yescomplemented
36#16840047C2218yescomplemented
37#16840046C22116yescomplemented
38#16840045C22116yescomplemented
39#16840044C2218yescomplemented
40C2×#14519709C2212yes—
41C2×#14519708C2212yes—
42C2×#14519708C2212yes—
43#106×D61C22116yes—
44C2×C4⋊#92418C2211yescharacteristic
45C2×#14519706C2212yes—
46C4⋊C8×D61C2218yes—
47C2×#14519702C2212yes—
48C2×#14519701C2212yes—
49C2×#14519700C2212yes—
50#103×D61C22116yes—
51C2×C4⋊Q8×C61C2211yescharacteristic
52C2×C4×Q8×C61C2211yescharacteristic
53C61×#475C2218yescomplemented
54C2×#106×C61C2212yes—
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#103×C61C2212yes—
57C22×Dic122—21no—
58C22×Dic122—21no—
59C22×Dic122—22no—
60C22×Dic122C2311yescharacteristic
61C2×Q8×D61—22no—
62C2×Q8×D61—28no—
63C2×Q8×D61—24no—
64C2×Q8×D61—48no—
65C2×Q8×D61Q818yescomplemented
66C2×Q8×D61C2314yes—
67C22×C4×D61—21no—
68C22×C4×D61—21no—
69C22×C4×D61—22no—
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C22×#92418C2312yes—
74C2×C8×D61—28no—
75C2×C8×D61C2318yes—
76#14519777—22no—
77#14519777C2314yes—
78#14519776—24no—
79#14519776—28no—
80#14519776C2318yes—
81#14519775—28no—
82Q8×Dic61—22no—
83Q8×Dic61C2314yes—
84C4×Dic122—22no—
85C4×Dic122—28no—
86C4×Dic122C2314yes—
87#14519742—22no—
88#14519742—28no—
89#14519742C2314yes—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2312yes—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—22no—
97C2×#11758196—21no—
98C2×#11758196—22no—
99C4⋊C4×D61—28no—
100C4⋊C4×D61—28no—
101C4⋊C4×D61—22no—
102C4⋊C4×D61—24no—
103C4⋊C4×D61C2314yes—
104C4⋊C4×D61C2318yes—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C42×D61—28no—
112C42×D61D414yes—
113C42×D61C2314yes—
114#14519709C2318yes—
115#14519708C2318yes—
116#14519708C2318yes—
117C4⋊#92418C2314yes—
118#14519706C2318yes—
119#14519702C2318yes—
120#14519701C2318yes—
121#14519700C2318yes—
122C22×Q8×C61—21no—
123C22×Q8×C61C2311yescharacteristic
124C22×C8×C61C2312yes—
125C4⋊Q8×C61—22no—
126C4⋊Q8×C61C2314yes—
127C4×Q8×C61—22no—
128C4×Q8×C61C2314yes—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61C2312yes—
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C42×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#106×C61C2318yes—
136C4⋊C8×C61C2314yes—
137#103×C61C2318yes—
138C23×D61C2×D411yescharacteristic
139C2×Q8×C61—21no—
140C2×Q8×C61—24no—
141C2×Q8×C61—22no—
142C2×Q8×C61—44no—
143C2×Q8×C61C2×Q814yescomplemented
144C2×Q8×C61C2412yes—
145C22×C4×C61—21no—
146C22×C4×C61—22no—
147C22×C4×C61—21no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2411yescharacteristic
151C22×Dic61—21no—
152C22×Dic61—22no—
153C22×Dic61—21no—
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157Q8×D61—216no—
158Q8×D61—28no—
159Q8×D61—432no—
160Q8×D61C2×Q8116yescomplemented
161C2×C4×D61—28no—
162C2×C4×D61—24no—
163C2×C4×D61—24no—
164C2×C4×D61—28no—
165C2×C4×D61—24no—
166C2×C4×D61—48no—
167C2×C4×D61—44no—
168C2×C4×D61SD1618yes—
169C2×C4×D61C2×D414yes—
170C2×C4×D61C2×D412yes—
171C2×C4×D61C2×D414yes—
172C2×C4×D61C2×Q814yes—
173C2×C4×D61#4114yes—
174C2×C4×D61C2412yes—
175C2×Dic122—21no—
176C2×Dic122—22no—
177C2×Dic122—28no—
178C2×Dic122—24no—
179C2×Dic122—24no—
180C2×Dic122—28no—
181C2×Dic122—44no—
182C2×Dic122—48no—
183C2×Dic122C2×Q814yescomplemented
184C2×Dic122C2412yes—
185C2×C8×C61—24no—
186C2×C8×C61C2414yes—
187C4⋊C4×C61—24no—
188C4⋊C4×C61—24no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—22no—
191C4⋊C4×C61C2414yes—
192C4⋊C4×C61C2412yes—
193C42×C61—24no—
194C42×C61C2×D412yes—
195C42×C61C2412yes—
196C4⋊Dic61—24no—
197C4⋊Dic61—21no—
198C4⋊Dic61—22no—
199C4⋊Dic61—24no—
200C4⋊Dic61C2414yes—
201C4⋊Dic61C2412yes—
202#11758196—24no—
203#11758196—24no—
204#11758196—28no—
205#11758196—24no—
206#11758196—28no—
207C4×Dic61—24no—
208C4×Dic61—24no—
209C4×Dic61—24no—
210C4×Dic61C2×D412yes—
211C4×Dic61C2×D414yes—
212C4×Dic61C2×D414yes—
213C4×Dic61C2412yes—
214C2×#92418—24no—
215C2×#92418C2414yes—
216C8×D61—216no—
217C23×C61C22×D411yescharacteristic
218C22×D61C22⋊Q814yes—
219C22×D61C2×SD1614yes—
220C22×D61#13714yes—
221C22×D61C22×D412yes—
222Q8×C61—24no—
223Q8×C61—22no—
224Q8×C61—48no—
225Q8×C61C22×Q814yescomplemented
226C2×C4×C61—24no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—24no—
231C2×C4×C61—44no—
232C2×C4×C61—42no—
233C2×C4×C61C2×SD1614yes—
234C2×C4×C61C22×D412yes—
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61C22×D412yes—
237C2×C4×C61C22×Q812yes—
238C2×C4×C61C2×#4112yes—
239C2×C4×C61C2511yescharacteristic
240C2×Dic61—24no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—24no—
245C2×Dic61—44no—
246C2×Dic61—42no—
247C2×Dic61C22⋊Q814yes—
248C2×Dic61C2×SD1614yes—
249C2×Dic61C22×D412yes—
250C2×Dic61C22×D412yes—
251C2×Dic61C22×D412yes—
252C4×D61—216no—
253C4×D61—28no—
254C4×D61—416no—
255C4×D61—48no—
256C4×D61C22⋊Q818yes—
257C4×D61C2×SD16116yes—
258C4×D61C22×Q814yes—
259C4×D61C2×#4114yes—
260Dic122—24no—
261Dic122—22no—
262Dic122—216no—
263Dic122—48no—
264Dic122—416no—
265Dic122C22×Q814yescomplemented
266C8×C61—24no—
267#92418—24no—
268C22×#475—611nomaximal, Sylow
269C22×C61C2×C22⋊Q812yes—
270C22×C61C22×SD1612yes—
271C22×C61C2×#13712yes—
272C22×C61C23×D411yescharacteristic
273C2×D61#475116yesdirect product factor
274C2×D61C2×C22⋊Q814yes—
275C2×D61C22×SD1614yes—
276C2×D61C2×#13714yes—
277C4×C61—24no—
278C4×C61—22no—
279C4×C61—44no—
280C4×C61—42no—
281C4×C61C2×C22⋊Q812yes—
282C4×C61C22×SD1614yes—
283C4×C61C23×Q811yescharacteristic
284C4×C61C22×#4111yescharacteristic
285Dic61—24no—
286Dic61—22no—
287Dic61—44no—
288Dic61—42no—
289Dic61C2×C22⋊Q814yes—
290Dic61C22×SD1614yes—
291C22×C4⋊Q8—611no—
292C22×C4×Q8—611no—
293C2×#475—6116no—
294C2×#475—612no—
295C2×#475—611no—
296C2×#475—612no—
297C2×#475—611no—
298C2×#475—611no—
299C2×#475D6111yescharacteristic, direct product factor
300C22×#106—612no—
301C22×C4⋊C8—611no—
302C22×#103—612no—
303C2×C61C2×#47514yescomplemented
304C2×C61C22×C22⋊Q811yescharacteristic
305C2×C61C23×SD1611yescharacteristic
306C2×C61C22×#13711yescharacteristic
307D61C2×#47518yesdirect product factor
308C23×Q8—611no—
309C23×Q8—1221no—
310C23×C8—612no—
311C2×C4⋊Q8—618no—
312C2×C4⋊Q8—612no—
313C2×C4⋊Q8—611no—
314C2×C4⋊Q8—1221no—
315C2×C4⋊Q8—1224no—
316C2×C4⋊Q8—1221no—
317C2×C4⋊Q8C2×D6111yescharacteristic
318C2×C4×Q8—611no—
319C2×C4×Q8—618no—
320C2×C4×Q8—611no—
321C2×C4×Q8—611no—
322C2×C4×Q8—1221no—
323C2×C4×Q8—1221no—
324C2×C4×Q8—1224no—
325C2×C4×Q8C2×D6111yescharacteristic
326C22×C4⋊C4—612no—
327C22×C4⋊C4—611no—
328C22×C4⋊C4—1221no—
329C22×C4⋊C4—1221no—
330C22×C42—611no—
331C22×C42—1221no—
332#475—618no—
333#475—618no—
334#475—6116no—
335#475—618no—
336#475—6116no—
337#475C2×D6118yesdirect product factor
338C2×#106—612no—
339C2×#106—612no—
340C2×#106—612no—
341C2×#106—6116no—
342C2×#106C2×D6112yes—
343C2×C4⋊C8—612no—
344C2×C4⋊C8—611no—
345C2×C4⋊C8—618no—
346C2×C4⋊C8C2×D6111yescharacteristic
347C2×#103—612no—
348C2×#103—612no—
349C2×#103—612no—
350C2×#103—6116no—
351C2×#103C2×D6112yes—
352C61C22×#47511yescharacteristic, complemented, Sylow
353C22×Q8—21no—
354C22×Q8—618no—
355C22×Q8—614no—
356C22×Q8—611no—
357C22×Q8—1221no—
358C22×Q8—1222no—
359C22×Q8—1222no—
360C22×Q8—1224no—
361C22×Q8—1228no—
362C22×Q8—1221no—
363C22×Q8—2448no—
364C22×Q8C22×D6111yescharacteristic
365C23×C4—611no—
366C23×C4—611no—
367C23×C4—611no—
368C23×C4—1221no—
369C23×C4—1222no—
370C23×C4—1221no—
371C22×C8—612no—
372C22×C8—618no—
373C22×C8—1228no—
374C22×C8C22×D6112yes—
375C4⋊Q8—22no—
376C4⋊Q8—618no—
377C4⋊Q8—614no—
378C4⋊Q8—1228no—
379C4⋊Q8—1224no—
380C4⋊Q8—1228no—
381C4⋊Q8—1222no—
382C4⋊Q8C22×D6114yes—
383C4×Q8—22no—
384C4×Q8—614no—
385C4×Q8—614no—
386C4×Q8—614no—
387C4×Q8—1228no—
388C4×Q8—1228no—
389C4×Q8—1222no—
390C4×Q8—1222no—
391C4×Q8—1222no—
392C4×Q8C22×D6114yes—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—612no—
397C2×C4⋊C4—614no—
398C2×C4⋊C4—618no—
399C2×C4⋊C4—1222no—
400C2×C4⋊C4—1224no—
401C2×C4⋊C4—1228no—
402C2×C4⋊C4—1228no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1222no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1222no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4C22×D6111yescharacteristic
411C2×C4⋊C4C22×D6112yes—
412C2×C42—21no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—614no—
417C2×C42—614no—
418C2×C42—1228no—
419C2×C42—1221no—
420C2×C42—1221no—
421C2×C42—1221no—
422C2×C42C22×D6111yescharacteristic
423#106—618no—
424#106—618no—
425#106—618no—
426#106C22×D6118yes—
427C4⋊C8—618no—
428C4⋊C8—614no—
429C4⋊C8C22×D6114yes—
430#103—618no—
431#103—618no—
432#103—618no—
433#103C22×D6118yes—
434C24—611no—
435C2×Q8—21no—
436C2×Q8—24no—
437C2×Q8—22no—
438C2×Q8—44no—
439C2×Q8—6116no—
440C2×Q8—614no—
441C2×Q8—612no—
442C2×Q8—1224no—
443C2×Q8—1228no—
444C2×Q8—1228no—
445C2×Q8—12216no—
446C2×Q8—1228no—
447C2×Q8—1221no—
448C2×Q8—1224no—
449C2×Q8—1222no—
450C2×Q8—2448no—
451C2×Q8—24432no—
452C2×Q8—2444no—
453C2×Q8Q8×D6114yescomplemented
454C2×Q8C23×D6112yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—614no—
461C22×C4—612no—
462C22×C4—614no—
463C22×C4—614no—
464C22×C4—612no—
465C22×C4—618no—
466C22×C4—611no—
467C22×C4—614no—
468C22×C4—1224no—
469C22×C4—1224no—
470C22×C4—1228no—
471C22×C4—1224no—
472C22×C4—1228no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1222no—
476C22×C4—2448no—
477C22×C4—2444no—
478C22×C4D4×D6111yescharacteristic
479C22×C4D4×D6111yescharacteristic
480C22×C4C23×D6111yescharacteristic
481C2×C8—24no—
482C2×C8—614no—
483C2×C8—12216no—
484C2×C8—1224no—
485C2×C8C23×D6114yes—
486C4⋊C4—24no—
487C4⋊C4—24no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—614no—
491C4⋊C4—612no—
492C4⋊C4—1224no—
493C4⋊C4—1228no—
494C4⋊C4—1224no—
495C4⋊C4—1228no—
496C4⋊C4—1224no—
497C4⋊C4—1221no—
498C4⋊C4—1222no—
499C4⋊C4—1224no—
500C4⋊C4—1224no—
501C4⋊C4C23×D6114yes—
502C4⋊C4C23×D6112yes—
503C42—24no—
504C42—614no—
505C42—612no—
506C42—614no—
507C42—612no—
508C42—1224no—
509C42—1224no—
510C42—1224no—
511C42D4×D6112yes—
512C42C23×D6112yes—
513C23—614no—
514C23—614no—
515C23—614no—
516C23—612no—
517C23C2×D4×D6111yescharacteristic
518Q8—24no—
519Q8—22no—
520Q8—48no—
521Q8—614no—
522Q8—12216no—
523Q8—1224no—
524Q8—1222no—
525Q8—24416no—
526Q8—2448no—
527Q8C2×Q8×D6114yescomplemented
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—44no—
534C2×C4—42no—
535C2×C4—614no—
536C2×C4—614no—
537C2×C4—612no—
538C2×C4—612no—
539C2×C4—618no—
540C2×C4—6116no—
541C2×C4—614no—
542C2×C4—614no—
543C2×C4—612no—
544C2×C4—1228no—
545C2×C4—12216no—
546C2×C4—1224no—
547C2×C4—1222no—
548C2×C4—1222no—
549C2×C4—1222no—
550C2×C4—1224no—
551C2×C4—2448no—
552C2×C4—24416no—
553C2×C4—2444no—
554C2×C4—2442no—
555C2×C4SD16×D6114yes—
556C2×C4C2×D4×D6112yes—
557C2×C4C2×D4×D6111yescharacteristic
558C2×C4C2×D4×D6112yes—
559C2×C4C2×Q8×D6112yes—
560C2×C4#41×D6112yes—
561C2×C4C24×D6111yescharacteristic
562C8—24no—
563C8—1224no—
564C22—614no—
565C22—614no—
566C22—614no—
567C22—6116no—
568C22C22⋊Q8×D6112yes—
569C22C2×SD16×D6112yes—
570C22#137×D6112yes—
571C22C22×D4×D6111yescharacteristic
572C4—22no—
573C4—24no—
574C4—44no—
575C4—42no—
576C4—614no—
577C4—614no—
578C4—1222no—
579C4—1224no—
580C4—2444no—
581C4—2442no—
582C4C22⋊Q8×D6112yes—
583C4C2×SD16×D6114yes—
584C4C22×Q8×D6111yescharacteristic
585C4C2×#41×D6111yescharacteristic
586C2—618no—
587C2#475×D6114yesdirect product factor
588C2C2×C22⋊Q8×D6111yescharacteristic
589C2C22×SD16×D6111yescharacteristic
590C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#475C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenterC2×#475D61
hypocenterC61C22×#475
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. C2×#16840048C2semidirect
4. C2×#16840047C2semidirect
5. C2×#16840046C2semidirect
6. C2×#16840045C2semidirect
7. C2×#16840044C2semidirect
8. #475×D61C2direct (N × H)
12. C2×C61×#475C2semidirect
35. #16840048C22semidirect
36. #16840047C22semidirect
37. #16840046C22semidirect
38. #16840045C22semidirect
39. #16840044C22semidirect
53. C61×#475C22semidirect
65. C2×Q8×D61Q8semidirect
143. C2×Q8×C61C2×Q8semidirect
160. Q8×D61C2×Q8semidirect
183. C2×Dic122C2×Q8semidirect
225. Q8×C61C22×Q8semidirect
265. Dic122C22×Q8semidirect
273. C2×D61#475direct (N × H)
299. C2×#475D61direct (N × H)
303. C2×C61C2×#475semidirect
307. D61C2×#475direct (N × H)
337. #475C2×D61direct (N × H)
352. C61C22×#475semidirect
453. C2×Q8Q8×D61semidirect
527. Q8C2×Q8×D61semidirect
587. C2#475×D61direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D612
C2×C4×Q8×D612
C2×#168400482
C2×#168400472
C2×#168400462
C2×#168400452
C2×#168400442
#475×D612
C2×#106×D612
C2×C4⋊C8×D612
C2×#103×D612
C2×C61×#4752
C22×#47561