Finite Group Databasebeta

← C2×#21455627 #30547537

Subgroups — C2×#21455627 #30547537

Order 15616.

2358 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
2C2×C4×#11758224C211yesmaximal, characteristic
3#21455627C2116yesmaximal, direct product factor
4C2×#16840056C212yesmaximal, complemented
5C2×#16840048C211yesmaximal, characteristic, complemented
6C2×#16840044C211yesmaximal, characteristic, complemented
7C2×#16840050C212yesmaximal, complemented
8C2×#16840042C211yesmaximal, characteristic, complemented
9C2×#16839803C212yesmaximal, complemented
10C2×#16839784C211yesmaximal, characteristic, complemented
11C2×#16839760C212yesmaximal
12C2×C61×#474C211yesmaximal, characteristic, complemented
13C22×#11758224C2211yescharacteristic
14C22×Q8×D61—21no—
15C22×#11758189C2212yes—
16C2×#14519777C2211yescharacteristic
17C2×#14519776—21no—
18C2×#14519776C2212yes—
19C2×#14519775—21no—
20C4⋊Q8×D61—24no—
21C4⋊Q8×D61C2218yescomplemented
22C4×#11758224—24no—
23C4×#11758224C2218yes—
24C2×C4×Dic122C2211yescharacteristic
25C2×#14519742C2211yescharacteristic
26C2×D4×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61—21no—
28C2×#14519737—21no—
29C2×#14519735C2211yescharacteristic
30C2×#14519733—21no—
31C2×C4⋊C4×D61—21no—
32C2×C4⋊C4×D61C2212yes—
33C22×C4×Dic61—21no—
34C2×C42×D61C2211yescharacteristic
35#16840056C22116yescomplemented
36#16840050C22116yescomplemented
37#16840048C2218yescomplemented
38#16840044C2218yescomplemented
39#16840042C2218yescomplemented
40#16839803C22116yescomplemented
41C2×#14519710C2212yes—
42C2×#14519709C2212yes—
43C2×#14519708C2212yes—
44#16839784C2218yescomplemented
45C2×C4⋊#92418C2211yescharacteristic
46C2×#14519706C2212yes—
47#16839760C22116yes—
48C2×#14519702C2212yes—
49C2×#14519700C2212yes—
50C2×#14519698C2212yes—
51C2×C4⋊Q8×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C61×#474C2218yescomplemented
54C2×#107×C61C2212yes—
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#102×C61C2212yes—
57C2×#11758224—22no—
58C2×#11758224—24no—
59C2×#11758224Q818yescomplemented
60C2×#11758224C2314yes—
61C22×Dic122—21no—
62C22×Dic122—22no—
63C22×Dic122C2311yescharacteristic
64C2×Q8×D61—28no—
65C2×Q8×D61—48no—
66C22×C22⋊D61—21no—
67C23×Dic61—21no—
68C23×Dic61—21no—
69C22×C4×D61—22no—
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C2×#11758189—28no—
74C2×#11758189C2318yes—
75C22×#92418C2312yes—
76#14519777—22no—
77#14519777C2314yes—
78#14519776—24no—
79#14519776—28no—
80#14519776C2318yes—
81#14519775—28no—
82C4×Dic122—22no—
83C4×Dic122C2314yes—
84#14519742—22no—
85#14519742C2314yes—
86D4×Dic61—22no—
87D4×Dic61C2314yes—
88C4×C22⋊D61—28no—
89#14519737—28no—
90#14519735—22no—
91#14519735C2314yes—
92#14519733—28no—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61C2312yes—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—22no—
98C2×#11758196—22no—
99C2×#11758196—21no—
100C4⋊C4×D61—28no—
101C4⋊C4×D61—24no—
102C4⋊C4×D61C2318yes—
103C2×C22⋊Dic61—21no—
104C2×#11758198—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—28no—
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C42×D61D414yes—
113C42×D61C2314yes—
114#14519710C2318yes—
115#14519709C2318yes—
116#14519708C2318yes—
117C4⋊#92418C2314yes—
118#14519706C2318yes—
119#14519702C2318yes—
120#14519700C2318yes—
121#14519698C2318yes—
122C22×Q8×C61—21no—
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61—21no—
125C22×C8×C61C2312yes—
126C4⋊Q8×C61—22no—
127C4⋊Q8×C61C2314yes—
128C4×D4×C61—22no—
129C4×D4×C61C2314yes—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61C2312yes—
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C22⋊C4×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#107×C61C2318yes—
136C4⋊C8×C61C2314yes—
137#102×C61C2318yes—
138C24×C61—21no—
139C23×D61C2×D411yescharacteristic
140C2×Q8×C61—24no—
141C2×Q8×C61—44no—
142C2×D4×C61—21no—
143C2×D4×C61—22no—
144C2×D4×C61C2×Q814yescomplemented
145C2×D4×C61C2412yes—
146C22×C4×C61—22no—
147C22×C4×C61—21no—
148C22×C4×C61—24no—
149C22×C4×C61—44no—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2411yescharacteristic
153C2×C22⋊D61—28no—
154C2×C22⋊D61—24no—
155C22×Dic61—21no—
156C22×Dic61—28no—
157C22×Dic61—24no—
158C22×Dic61—22no—
159C22×Dic61—21no—
160C22×Dic61—24no—
161C22×Dic61—44no—
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165Q8×D61—432no—
166#11758224—216no—
167#11758224—28no—
168#11758224C2×Q8116yescomplemented
169C2×C4×D61—24no—
170C2×C4×D61—24no—
171C2×C4×D61—28no—
172C2×C4×D61—48no—
173C2×C4×D61C2×D414yes—
174C2×C4×D61C2×D414yes—
175C2×C4×D61C2×D412yes—
176C2×C4×D61C2×Q814yes—
177C2×C4×D61#4114yes—
178C2×C4×D61C2412yes—
179C2×Dic122—21no—
180C2×Dic122—22no—
181C2×Dic122—24no—
182C2×Dic122—28no—
183C2×Dic122—48no—
184C2×Dic122—44no—
185C2×Dic122C2×Q814yescomplemented
186C2×Dic122C2412yes—
187C2×C8×C61—24no—
188C2×C8×C61C2414yes—
189C4⋊C4×C61—24no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—22no—
192C4⋊C4×C61C2414yes—
193C4⋊C4×C61C2412yes—
194C22⋊C4×C61—24no—
195C42×C61C2×D412yes—
196C42×C61C2412yes—
197C22⋊Dic61—24no—
198#11758198—24no—
199C4⋊Dic61—24no—
200C4⋊Dic61—22no—
201C4⋊Dic61—21no—
202C4⋊Dic61C2414yes—
203C4⋊Dic61C2412yes—
204#11758196—24no—
205#11758196—28no—
206#11758196—28no—
207#11758196—24no—
208C4×Dic61—24no—
209C4×Dic61—24no—
210C4×Dic61—24no—
211C4×Dic61C2×D412yes—
212C4×Dic61C2×D414yes—
213C4×Dic61C2×D414yes—
214C4×Dic61C2412yes—
215C2×#92418—24no—
216C2×#92418C2414yes—
217#11758189—216no—
218C23×C61—24no—
219C23×C61—22no—
220C23×C61—42no—
221C23×C61—42no—
222C23×C61C22×D411yescharacteristic
223C22×D61—22no—
224C22×D61—22no—
225C22×D61C22⋊Q814yes—
226C22×D61C22×D412yes—
227Q8×C61—48no—
228D4×C61—24no—
229D4×C61—22no—
230D4×C61C22×Q814yescomplemented
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—24no—
234C2×C4×C61—44no—
235C2×C4×C61—42no—
236C2×C4×C61—48no—
237C2×C4×C61AGL(1,ℤ/8)14yes—
238C2×C4×C61C22×D412yes—
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C22×D412yes—
241C2×C4×C61C22×Q812yes—
242C2×C4×C61C2×#4112yes—
243C2×C4×C61C2511yescharacteristic
244C22⋊D61—216no—
245C2×Dic61—24no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—216no—
249C2×Dic61—22no—
250C2×Dic61—24no—
251C2×Dic61—44no—
252C2×Dic61—42no—
253C2×Dic61—48no—
254C2×Dic61C22⋊Q814yes—
255C2×Dic61#13714yes—
256C2×Dic61C22×D412yes—
257C2×Dic61C22×D412yes—
258C2×Dic61C22×D412yes—
259C4×D61—28no—
260C4×D61—28no—
261C4×D61—416no—
262C4×D61C22⋊Q818yes—
263C4×D61C22×Q814yes—
264C4×D61C2×#4114yes—
265Dic122—24no—
266Dic122—22no—
267Dic122—416no—
268Dic122—48no—
269Dic122C22×Q814yescomplemented
270C8×C61—24no—
271#92418—24no—
272C2×#3079—611nomaximal, Sylow
273C22×C61—24no—
274C22×C61—48no—
275C22×C61—42no—
276C22×C61—42no—
277C22×C61C2×C22⋊Q812yes—
278C22×C61C2×AGL(1,ℤ/8)12yes—
279C22×C61C2×#13712yes—
280C22×C61C23×D411yescharacteristic
281C2×D61—28no—
282C2×D61—22no—
283C2×D61—22no—
284C2×D61C2×C22⋊Q814yes—
285C4×C61—22no—
286C4×C61—44no—
287C4×C61—42no—
288C4×C61C2×C22⋊Q812yes—
289C4×C61C2×AGL(1,ℤ/8)14yes—
290C4×C61C23×Q811yescharacteristic
291C4×C61C22×#4111yescharacteristic
292Dic61—24no—
293Dic61—22no—
294Dic61—44no—
295Dic61—42no—
296Dic61C2×C22⋊Q814yes—
297Dic61C2×#13714yes—
298C22×C4⋊Q8—611no—
299C2×C4×#41—611no—
300#3079—6116no—
301C2×#477—612no—
302C2×#475—611no—
303C2×#475—611no—
304C2×#476—612no—
305C2×#474—611no—
306C2×#474D6111yescharacteristic, complemented
307C2×#428—612no—
308C2×#423—611no—
309C2×#417—612no—
310C2×C61—44no—
311C2×C61#307914yescomplemented
312C2×C61C22×C22⋊Q811yescharacteristic
313C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
314C2×C61C22×#13711yescharacteristic
315D61—24no—
316C22×#41—611no—
317C23×Q8—1221no—
318C22×M16—612no—
319C2×C4⋊Q8—618no—
320C2×C4⋊Q8—612no—
321C2×C4⋊Q8—611no—
322C2×C4⋊Q8—1221no—
323C2×C4⋊Q8—1224no—
324C2×C4⋊Q8—1221no—
325C2×C4⋊Q8C2×D6111yescharacteristic
326C4×#41—618no—
327C4×#41—1224no—
328C2×C4×Q8—611no—
329C2×C4×Q8—611no—
330C2×C4×D4—611no—
331C2×C4×D4—1221no—
332C2×C4×D4—1221no—
333C2×C4×D4C2×D6111yescharacteristic
334C2×#117—611no—
335C2×#117—1221no—
336C22×C4⋊C4—612no—
337C22×C4⋊C4—1221no—
338C22×C42—611no—
339C22×C42—1221no—
340#477—6116no—
341#476—6116no—
342#475—618no—
343#475—618no—
344#474—618no—
345#474C2×D6118yescomplemented
346#428—6116no—
347C2×#107—612no—
348C2×#107C2×D6112yes—
349C2×#106—612no—
350C2×#106—612no—
351#423—618no—
352C2×C4⋊C8—612no—
353C2×C4⋊C8—611no—
354C2×C4⋊C8C2×D6111yescharacteristic
355#417—6116no—
356C2×#103—612no—
357C2×#103—612no—
358C2×#102—612no—
359C2×#102C2×D6112yes—
360C61C2×#307911yescharacteristic, complemented, Sylow
361C2×#41—618no—
362C2×#41—614no—
363C2×#41—1222no—
364C2×#41—1224no—
365C22×Q8—21no—
366C22×Q8—611no—
367C22×Q8—1222no—
368C22×Q8—1228no—
369C22×Q8—1221no—
370C22×Q8—2448no—
371C22×D4—1221no—
372C22×D4C22×D6111yescharacteristic
373C23×C4—21no—
374C23×C4—611no—
375C23×C4—611no—
376C23×C4—611no—
377C23×C4—1222no—
378C23×C4—1221no—
379C23×C4—1221no—
380C2×M16—618no—
381C2×M16—1228no—
382C22×C8—612no—
383C22×C8C22×D6112yes—
384C4⋊Q8—22no—
385C4⋊Q8—618no—
386C4⋊Q8—614no—
387C4⋊Q8—1228no—
388C4⋊Q8—1224no—
389C4⋊Q8—1228no—
390C4⋊Q8—1222no—
391C4⋊Q8C22×D6114yes—
392C4×Q8—614no—
393C4×Q8—614no—
394C4×Q8—1222no—
395C4×Q8—1222no—
396C4×D4—22no—
397C4×D4—614no—
398C4×D4—1222no—
399C4×D4—1228no—
400C4×D4—1228no—
401C4×D4C22×D6114yes—
402#117—614no—
403#117—1228no—
404#117—1222no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—612no—
407C2×C4⋊C4—611no—
408C2×C4⋊C4—618no—
409C2×C4⋊C4—1224no—
410C2×C4⋊C4—1228no—
411C2×C4⋊C4—1222no—
412C2×C4⋊C4—1222no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4C22×D6112yes—
417C2×C4⋊C4C22×D6111yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—1221no—
420C2×C22⋊C4—1221no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—614no—
425C2×C42—614no—
426C2×C42—1228no—
427C2×C42—1221no—
428C2×C42—1221no—
429C2×C42—1221no—
430C2×C42C22×D6111yescharacteristic
431#107—618no—
432#107C22×D6118yes—
433#106—618no—
434#106—618no—
435C4⋊C8—618no—
436C4⋊C8—614no—
437C4⋊C8C22×D6114yes—
438#103—618no—
439#103—618no—
440#102—618no—
441#102C22×D6118yes—
442C24—21no—
443C24—611no—
444#41—6116no—
445#41—12216no—
446#41—1228no—
447C2×Q8—24no—
448C2×Q8—44no—
449C2×Q8—614no—
450C2×Q8—612no—
451C2×Q8—1228no—
452C2×Q8—1221no—
453C2×Q8—1224no—
454C2×Q8—1222no—
455C2×Q8—2448no—
456C2×Q8—24432no—
457C2×Q8—2444no—
458C2×D4—21no—
459C2×D4—22no—
460C2×D4—1224no—
461C2×D4—1228no—
462C2×D4Q8×D6114yescomplemented
463C2×D4C23×D6112yes—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—44no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—612no—
471C22×C4—614no—
472C22×C4—614no—
473C22×C4—612no—
474C22×C4—611no—
475C22×C4—614no—
476C22×C4—614no—
477C22×C4—1224no—
478C22×C4—1228no—
479C22×C4—1224no—
480C22×C4—1228no—
481C22×C4—1224no—
482C22×C4—1221no—
483C22×C4—1224no—
484C22×C4—1221no—
485C22×C4—1222no—
486C22×C4—2448no—
487C22×C4—2444no—
488C22×C4D4×D6111yescharacteristic
489C22×C4D4×D6111yescharacteristic
490C22×C4C23×D6111yescharacteristic
491M16—12216no—
492C2×C8—24no—
493C2×C8—614no—
494C2×C8—1224no—
495C2×C8C23×D6114yes—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—614no—
500C4⋊C4—612no—
501C4⋊C4—1228no—
502C4⋊C4—1228no—
503C4⋊C4—1224no—
504C4⋊C4—1222no—
505C4⋊C4—1221no—
506C4⋊C4—1224no—
507C4⋊C4—1224no—
508C4⋊C4C23×D6114yes—
509C4⋊C4C23×D6112yes—
510C22⋊C4—24no—
511C22⋊C4—1224no—
512C22⋊C4—1224no—
513C42—614no—
514C42—614no—
515C42—612no—
516C42—612no—
517C42—1224no—
518C42—1224no—
519C42—1224no—
520C42D4×D6112yes—
521C42C23×D6112yes—
522C23—24no—
523C23—22no—
524C23—42no—
525C23—42no—
526C23—614no—
527C23—612no—
528C23—1222no—
529C23—1222no—
530C23C2×D4×D6111yescharacteristic
531Q8—48no—
532Q8—614no—
533Q8—1224no—
534Q8—1222no—
535Q8—24416no—
536Q8—2448no—
537D4—24no—
538D4—22no—
539D4—12216no—
540D4C2×Q8×D6114yescomplemented
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—42no—
545C2×C4—44no—
546C2×C4—48no—
547C2×C4—614no—
548C2×C4—614no—
549C2×C4—612no—
550C2×C4—612no—
551C2×C4—618no—
552C2×C4—614no—
553C2×C4—614no—
554C2×C4—612no—
555C2×C4—1228no—
556C2×C4—12216no—
557C2×C4—1224no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—1228no—
561C2×C4—1222no—
562C2×C4—1224no—
563C2×C4—24416no—
564C2×C4—2448no—
565C2×C4—2444no—
566C2×C4—2442no—
567C2×C4#1451980114yes—
568C2×C4C2×D4×D6112yes—
569C2×C4C2×D4×D6111yescharacteristic
570C2×C4C2×D4×D6112yes—
571C2×C4C2×Q8×D6112yes—
572C2×C4#41×D6112yes—
573C2×C4C24×D6111yescharacteristic
574C8—24no—
575C8—1224no—
576C22—24no—
577C22—48no—
578C22—42no—
579C22—42no—
580C22—614no—
581C22—1228no—
582C22—1222no—
583C22—1222no—
584C22C22⋊Q8×D6112yes—
585C22C2×#1451980112yes—
586C22#137×D6112yes—
587C22C22×D4×D6111yescharacteristic
588C4—22no—
589C4—42no—
590C4—44no—
591C4—614no—
592C4—614no—
593C4—1222no—
594C4—1224no—
595C4—2444no—
596C4—2442no—
597C4C22⋊Q8×D6112yes—
598C4C2×#1451980114yes—
599C4C22×Q8×D6111yescharacteristic
600C4C2×#41×D6111yescharacteristic
601C2—44no—
602C2—1224no—
603C2#2145562714yesdirect product factor
604C2C2×C22⋊Q8×D6111yescharacteristic
605C2C22×#1451980111yescharacteristic
606C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#474C2
socleC23×C61C22×D4
prime radicalC22×#11758224C22
hypercenterC2×#474D61
hypocenterC61C2×#3079
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Q8×D61C2semidirect
3. #21455627C2direct (N × H)
4. C2×#16840056C2semidirect
5. C2×#16840048C2semidirect
6. C2×#16840044C2semidirect
7. C2×#16840050C2semidirect
8. C2×#16840042C2semidirect
9. C2×#16839803C2semidirect
10. C2×#16839784C2semidirect
12. C2×C61×#474C2semidirect
21. C4⋊Q8×D61C22semidirect
35. #16840056C22semidirect
36. #16840050C22semidirect
37. #16840048C22semidirect
38. #16840044C22semidirect
39. #16840042C22semidirect
40. #16839803C22semidirect
44. #16839784C22semidirect
53. C61×#474C22semidirect
59. C2×#11758224Q8semidirect
144. C2×D4×C61C2×Q8semidirect
168. #11758224C2×Q8semidirect
185. C2×Dic122C2×Q8semidirect
230. D4×C61C22×Q8semidirect
269. Dic122C22×Q8semidirect
306. C2×#474D61semidirect
311. C2×C61#3079semidirect
345. #474C2×D61semidirect
360. C61C2×#3079semidirect
462. C2×D4Q8×D61semidirect
540. D4C2×Q8×D61semidirect
603. C2#21455627direct (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×#117582242
#214556272
C2×#168400562
C2×#168400482
C2×#168400442
C2×#168400502
C2×#168400422
C2×#168398032
C2×#168397842
C2×#168397602
C2×C61×#4742
C2×#307961