Finite Group Databasebeta

← C2×#21455764 #30547816

Subgroups — C2×#21455764 #30547816

Order 15616.

2326 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D61C211yesmaximal, characteristic
2C22×#14519735C211yesmaximal, characteristic
3#21455764C2116yesmaximal, direct product factor
4C2×#16840097C211yesmaximal, characteristic, complemented
5C2×#16840105C212yesmaximal, complemented
6C2×#16840101C212yesmaximal, complemented
7C2×#16840093C211yesmaximal, characteristic, complemented
8C2×#16840090C211yesmaximal, characteristic, complemented
9C2×#16839803C212yesmaximal, complemented
10C2×#16839769C212yesmaximal, complemented
11C2×#16839724C211yesmaximal, characteristic
12C2×C61×#484C211yesmaximal, characteristic, complemented
13C22×Q8×D61C2211yescharacteristic
14C23×C4×D61C2211yescharacteristic
15C22×#11758189C2212yes—
16C2×#14519757C2211yescharacteristic
17C2×#14519756C2211yescharacteristic
18C2×#14519755—21no—
19C2×#14519754—21no—
20C2×#14519753C2211yescharacteristic
21C22⋊Q8×D61—24no—
22C22⋊Q8×D61C2218yes—
23C2×#14519735—21no—
24C2×#14519735—24no—
25C2×#14519735—21no—
26C2×#14519735C2212yes—
27C2×#14519735C2212yes—
28C2×#14519735C2218yes—
29C22×C4⋊Dic61C2211yescharacteristic
30C2×C4⋊C4×D61—21no—
31C2×C4⋊C4×D61C2211yescharacteristic
32C22×#11758198—21no—
33C2×C22⋊C4×D61—21no—
34C22×C4×Dic61—21no—
35#16840105C22116yescomplemented
36#16840101C22116yescomplemented
37#16840097C2218yescomplemented
38#16840093C2218yescomplemented
39#16840090C2218yescomplemented
40#16839803C22116yescomplemented
41C2×#14519710C2212yescomplemented
42C2×#14519709C2212yescomplemented
43C2×#14519708C2212yescomplemented
44#16839769C22116yescomplemented
45C2×#14519702C2212yescomplemented
46C2×#14519701C2212yescomplemented
47C2×#14519700C2212yescomplemented
48#16839724C2218yes—
49C2×C22⋊#92418C2211yescharacteristic
50C2×#14519689C2212yes—
51C2×C22⋊Q8×C61C2211yescharacteristic
52C22×C4⋊C4×C61C2211yescharacteristic
53C61×#484C2218yescomplemented
54C2×#107×C61C2212yescomplemented
55C2×#103×C61C2212yescomplemented
56C2×C22⋊C8×C61C2211yescharacteristic
57C24×D61D411yescharacteristic
58C22×Dic122—21no—
59C22×Dic122C2311yescharacteristic
60C2×Q8×D61—22no—
61C2×Q8×D61—28no—
62C2×Q8×D61C2314yes—
63C23×Dic61—21no—
64C23×Dic61D411yescharacteristic
65C22×C4×D61—28no—
66C22×C4×D61—21no—
67C22×C4×D61—21no—
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D414yes—
70C22×C4×D61D411yescharacteristic
71C22×C4×D61C2311yescharacteristic
72C22×C4×D61C2314yes—
73C22×C4×D61C2311yescharacteristic
74C2×#11758189—28no—
75C2×#11758189C2318yes—
76C22×#92418C2312yes—
77#14519757—22no—
78#14519757C2314yes—
79#14519756—22no—
80#14519756C2314yes—
81#14519755—28no—
82#14519754—28no—
83#14519753—22no—
84#14519753C2314yes—
85#14519735—28no—
86#14519735—24no—
87#14519735—28no—
88#14519735—24no—
89#14519735C2318yes—
90#14519735C2318yes—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—22no—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2312yes—
96C2×C4⋊Dic61C2314yes—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C4⋊C4×D61—28no—
101C4⋊C4×D61—22no—
102C4⋊C4×D61C2314yes—
103C2×C22⋊Dic61—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—22no—
107C2×#11758198—28no—
108C2×#11758198—22no—
109C22⋊C4×D61—28no—
110C2×C4×Dic61—22no—
111C2×C4×Dic61—28no—
112C2×C4×Dic61—22no—
113#14519710C2318yescomplemented
114#14519709C2318yescomplemented
115#14519708C2318yescomplemented
116#14519702C2318yescomplemented
117#14519701C2318yescomplemented
118#14519700C2318yescomplemented
119C22⋊#92418C2314yes—
120#14519689C2318yes—
121C22×Q8×C61C2311yescharacteristic
122C23×C4×C61—21no—
123C23×C4×C61C2311yescharacteristic
124C22×C8×C61C2312yes—
125C22⋊Q8×C61—22no—
126C22⋊Q8×C61C2314yes—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—22no—
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2312yes—
132C2×C4⋊C4×C61C2314yes—
133C2×C22⋊C4×C61—21no—
134#107×C61C2318yescomplemented
135#103×C61C2318yescomplemented
136C22⋊C8×C61C2314yes—
137C24×C61C2×D411yescharacteristic
138C23×D61—24no—
139C23×D61—24no—
140C23×D61—42no—
141C23×D61C2×D411yescharacteristic
142C23×D61C2×D414yes—
143C23×D61C2×D411yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—24no—
146C2×Q8×C61C2412yes—
147C22×C4×C61—24no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—24no—
151C22×C4×C61—22no—
152C22×C4×C61—44no—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D412yes—
155C22×C4×C61C2412yes—
156C22×C4×C61C2411yescharacteristic
157C22×Dic61—24no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—24no—
161C22×Dic61—22no—
162C22×Dic61—44no—
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D414yes—
165C22×Dic61C2×D411yescharacteristic
166Q8×D61—216no—
167Q8×D61—48no—
168C2×C4×D61—24no—
169C2×C4×D61—24no—
170C2×C4×D61—24no—
171C2×C4×D61—216no—
172C2×C4×D61—216no—
173C2×C4×D61—24no—
174C2×C4×D61—24no—
175C2×C4×D61—44no—
176C2×C4×D61—44no—
177C2×C4×D61C2×D414yes—
178C2×C4×D61C2×D412yes—
179C2×C4×D61C2×D414yes—
180C2×C4×D61C2×D412yes—
181C2×C4×D61#4118yes—
182C2×C4×D61C2412yes—
183C2×C4×D61C2412yes—
184C2×Dic122—24no—
185C2×Dic122—21no—
186C2×Dic122—24no—
187C2×Dic122—44no—
188C2×Dic122C2412yes—
189C2×C8×C61—24no—
190C2×C8×C61C2414yes—
191C4⋊C4×C61—24no—
192C4⋊C4×C61—22no—
193C4⋊C4×C61—24no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61C2414yes—
196C4⋊C4×C61C2412yes—
197C22⋊C4×C61—24no—
198C22⋊Dic61—24no—
199#11758198—24no—
200#11758198—24no—
201#11758198—28no—
202#11758198—28no—
203C4⋊Dic61—21no—
204C4⋊Dic61—24no—
205C4⋊Dic61—22no—
206C4⋊Dic61—24no—
207C4⋊Dic61C2414yes—
208C4⋊Dic61C2412yes—
209#11758196—24no—
210#11758196—24no—
211#11758196—24no—
212C4×Dic61—28no—
213C4×Dic61—28no—
214C2×#92418—24no—
215C2×#92418C2414yes—
216#11758189—216no—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61#13714yes—
220C23×C61C22×D412yes—
221C23×C61C22×D411yescharacteristic
222C22×D61—22no—
223C22×D61—22no—
224C22×D61—22no—
225C22×D61—28no—
226C22×D61—22no—
227C22×D61—22no—
228C22×D61—28no—
229C22×D61—44no—
230C22×D61—416no—
231C22×D61#12314yes—
232C22×D61C22×D412yes—
233C22×D61C22×D412yes—
234Q8×C61—24no—
235Q8×C61—42no—
236C2×C4×C61—22no—
237C2×C4×C61—24no—
238C2×C4×C61—24no—
239C2×C4×C61—24no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—48no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—44no—
246C2×C4×C61C22×D412yes—
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C2×#4114yes—
249C2×C4×C61C2511yescharacteristic
250C2×Dic61—22no—
251C2×Dic61—28no—
252C2×Dic61—24no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—42no—
256C2×Dic61—48no—
257C2×Dic61—44no—
258C2×Dic61—42no—
259C2×Dic61#12314yes—
260C2×Dic61C22×D412yes—
261C2×Dic61C22×D412yes—
262C4×D61—28no—
263C4×D61—24no—
264C4×D61—24no—
265C4×D61—28no—
266C4×D61—48no—
267C4×D61—48no—
268C4×D61#12318yes—
269C4×D61C2×#4118yes—
270Dic122—24no—
271Dic122—42no—
272Dic122—48no—
273C8×C61—24no—
274#92418—24no—
275C2×#3095—611nomaximal, Sylow
276C22×C61—28no—
277C22×C61—22no—
278C22×C61—22no—
279C22×C61C2×#12312yes—
280C22×C61C2×#13714yes—
281C22×C61C2×#13712yes—
282C22×C61#57512yes—
283C22×C61C23×D411yescharacteristic
284C2×D61—28no—
285C2×D61—22no—
286C2×D61—22no—
287C2×D61—22no—
288C2×D61—22no—
289C2×D61—22no—
290C2×D61—416no—
291C2×D61—44no—
292C2×D61C2×#12314yes—
293C4×C61—22no—
294C4×C61—42no—
295C4×C61—42no—
296C4×C61—44no—
297C4×C61C2×#12312yes—
298C4×C61C22×#4112yes—
299Dic61—22no—
300Dic61—42no—
301Dic61—44no—
302Dic61—42no—
303Dic61C2×#12314yes—
304C22×C22⋊Q8—611no—
305C22×#117—611no—
306#3095—6116no—
307C2×#484—611no—
308C2×#484D6111yescharacteristic, complemented
309C2×#485—612no—
310C2×#485—612no—
311C2×#483—611no—
312C2×#483—611no—
313C2×#428—612no—
314C2×#419—612no—
315C2×#407—611no—
316C2×C61—24no—
317C2×C61#309514yescomplemented
318C2×C61C22×#12311yescharacteristic
319C2×C61C22×#13711yescharacteristic
320C2×C61C2×#57511yescharacteristic
321D61—24no—
322D61—42no—
323C23×Q8—611no—
324C24×C4—611no—
325C22×M16—612no—
326C2×C22⋊Q8—611no—
327C2×C22⋊Q8—611no—
328C2×C22⋊Q8—618no—
329C2×C22⋊Q8—611no—
330C2×C22⋊Q8—1221no—
331C2×C22⋊Q8—1221no—
332C2×C22⋊Q8—1224no—
333C2×C22⋊Q8C2×D6111yescharacteristic
334C2×#117—612no—
335C2×#117—618no—
336C2×#117—612no—
337C2×#117—1221no—
338C2×#117—1224no—
339C2×#117—1221no—
340C22×C4⋊C4—611no—
341C22×C4⋊C4—611no—
342C22×C4⋊C4—1221no—
343C22×C4⋊C4C2×D6111yescharacteristic
344C22×C22⋊C4—1221no—
345C22×C22⋊C4—1221no—
346C22×C42—1221no—
347#485—6116no—
348#485—6116no—
349#484—618no—
350#484C2×D6118yescomplemented
351#483—618no—
352#483—618no—
353#428—6116no—
354C2×#107—612no—
355C2×#107C2×D6112yescomplemented
356C2×#106—612no—
357C2×#106—612no—
358#419—6116no—
359C2×#103—612no—
360C2×#103—612no—
361C2×#103—612no—
362C2×#103C2×D6112yescomplemented
363#407—618no—
364C2×C22⋊C8—611no—
365C2×C22⋊C8—612no—
366C2×C22⋊C8C2×D6111yescharacteristic
367C61C2×#309511yescharacteristic, complemented, Sylow
368C25—611no—
369C22×Q8—614no—
370C22×Q8—611no—
371C22×Q8—1221no—
372C22×Q8—1222no—
373C22×Q8—1228no—
374C22×Q8C22×D6111yescharacteristic
375C23×C4—21no—
376C23×C4—611no—
377C23×C4—611no—
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—614no—
381C23×C4—611no—
382C23×C4—614no—
383C23×C4—1228no—
384C23×C4—1221no—
385C23×C4—1221no—
386C23×C4—1221no—
387C23×C4C22×D6111yescharacteristic
388C2×M16—618no—
389C2×M16—1228no—
390C22×C8—612no—
391C22×C8C22×D6112yes—
392C22⋊Q8—22no—
393C22⋊Q8—614no—
394C22⋊Q8—614no—
395C22⋊Q8—614no—
396C22⋊Q8—1228no—
397C22⋊Q8—1228no—
398C22⋊Q8—1222no—
399C22⋊Q8—1222no—
400C22⋊Q8—1222no—
401C22⋊Q8C22×D6114yes—
402#117—618no—
403#117—618no—
404#117—1224no—
405#117—1228no—
406#117—1224no—
407#117—1228no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—612no—
412C2×C4⋊C4—614no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4—614no—
415C2×C4⋊C4—1222no—
416C2×C4⋊C4—1228no—
417C2×C4⋊C4—1221no—
418C2×C4⋊C4—1221no—
419C2×C4⋊C4—1221no—
420C2×C4⋊C4—1222no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4C22×D6111yescharacteristic
424C2×C4⋊C4C22×D6112yes—
425C2×C4⋊C4C22×D6114yes—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—1228no—
428C2×C22⋊C4—1228no—
429C2×C22⋊C4—1222no—
430C2×C22⋊C4—1222no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—1221no—
433C2×C22⋊C4—1221no—
434C2×C42—1228no—
435C2×C42—1222no—
436C2×C42—1222no—
437#107—618no—
438#107C22×D6118yescomplemented
439#106—618no—
440#106—618no—
441#103—618no—
442#103—618no—
443#103—618no—
444#103C22×D6118yescomplemented
445C22⋊C8—614no—
446C22⋊C8—618no—
447C22⋊C8C22×D6114yes—
448C24—611no—
449C24—611no—
450C24—614no—
451C24—1224no—
452C24—1224no—
453C24—2442no—
454C24D4×D6111yescharacteristic
455C2×Q8—21no—
456C2×Q8—24no—
457C2×Q8—612no—
458C2×Q8—1224no—
459C2×Q8—12216no—
460C2×Q8—1221no—
461C2×Q8—1224no—
462C2×Q8—2444no—
463C2×Q8—2448no—
464C2×Q8C23×D6112yes—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—44no—
471C22×C4—611no—
472C22×C4—612no—
473C22×C4—618no—
474C22×C4—612no—
475C22×C4—614no—
476C22×C4—611no—
477C22×C4—614no—
478C22×C4—614no—
479C22×C4—612no—
480C22×C4—612no—
481C22×C4—1224no—
482C22×C4—12216no—
483C22×C4—12216no—
484C22×C4—1224no—
485C22×C4—1224no—
486C22×C4—1224no—
487C22×C4—1224no—
488C22×C4—1224no—
489C22×C4—1224no—
490C22×C4—1222no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—2444no—
494C22×C4—2444no—
495C22×C4—2444no—
496C22×C4D4×D6112yes—
497C22×C4D4×D6111yescharacteristic
498C22×C4C23×D6112yes—
499C22×C4C23×D6111yescharacteristic
500M16—12216no—
501C2×C8—24no—
502C2×C8—614no—
503C2×C8—1224no—
504C2×C8C23×D6114yes—
505C4⋊C4—24no—
506C4⋊C4—22no—
507C4⋊C4—24no—
508C4⋊C4—21no—
509C4⋊C4—614no—
510C4⋊C4—612no—
511C4⋊C4—1224no—
512C4⋊C4—1224no—
513C4⋊C4—1224no—
514C4⋊C4—1224no—
515C4⋊C4—1222no—
516C4⋊C4—1221no—
517C4⋊C4—1224no—
518C4⋊C4C23×D6114yes—
519C4⋊C4C23×D6112yes—
520C22⋊C4—24no—
521C22⋊C4—1228no—
522C22⋊C4—1228no—
523C22⋊C4—1224no—
524C22⋊C4—1224no—
525C22⋊C4—1224no—
526C42—1228no—
527C42—1228no—
528C23—22no—
529C23—22no—
530C23—614no—
531C23—612no—
532C23—612no—
533C23—1228no—
534C23—1222no—
535C23—1222no—
536C23—1222no—
537C23—1228no—
538C23—1222no—
539C23—1222no—
540C23—2444no—
541C23—24416no—
542C23#1451980914yes—
543C23C2×D4×D6112yes—
544C23C2×D4×D6111yescharacteristic
545Q8—24no—
546Q8—42no—
547Q8—1224no—
548Q8—2448no—
549Q8—2442no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—48no—
557C2×C4—42no—
558C2×C4—44no—
559C2×C4—42no—
560C2×C4—614no—
561C2×C4—612no—
562C2×C4—618no—
563C2×C4—618no—
564C2×C4—612no—
565C2×C4—1228no—
566C2×C4—1228no—
567C2×C4—1228no—
568C2×C4—1222no—
569C2×C4—1224no—
570C2×C4—1224no—
571C2×C4—1224no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—2448no—
575C2×C4—2448no—
576C2×C4—2442no—
577C2×C4—2448no—
578C2×C4—2444no—
579C2×C4—2442no—
580C2×C4C2×D4×D6112yes—
581C2×C4C2×D4×D6111yescharacteristic
582C2×C4#41×D6114yes—
583C2×C4C24×D6111yescharacteristic
584C8—24no—
585C8—1224no—
586C22—22no—
587C22—22no—
588C22—28no—
589C22—614no—
590C22—1222no—
591C22—1222no—
592C22—1228no—
593C22—1222no—
594C22—1222no—
595C22—1222no—
596C22—24416no—
597C22—2444no—
598C22#123×D6112yes—
599C22C2×#1451980914yes—
600C22C2×#1451980912yes—
601C22#1684055812yes—
602C22C22×D4×D6111yescharacteristic
603C4—22no—
604C4—44no—
605C4—42no—
606C4—42no—
607C4—614no—
608C4—1222no—
609C4—2444no—
610C4—2442no—
611C4—2442no—
612C4#123×D6112yes—
613C4C2×#41×D6112yes—
614C2—24no—
615C2—1224no—
616C2—2442no—
617C2#2145576414yesdirect product factor
618C2C2×#123×D6111yescharacteristic
619C2C22×#1451980911yescharacteristic
620C2C2×#1684055811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#484C2
socleC23×C61C22×D4
prime radicalC24×D61D4
hypercenterC2×#484D61
hypocenterC61C2×#3095
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #21455764C2direct (N × H)
4. C2×#16840097C2semidirect
5. C2×#16840105C2semidirect
6. C2×#16840101C2semidirect
7. C2×#16840093C2semidirect
8. C2×#16840090C2semidirect
9. C2×#16839803C2semidirect
10. C2×#16839769C2semidirect
12. C2×C61×#484C2semidirect
35. #16840105C22semidirect
36. #16840101C22semidirect
37. #16840097C22semidirect
38. #16840093C22semidirect
39. #16840090C22semidirect
40. #16839803C22semidirect
41. C2×#14519710C22semidirect
42. C2×#14519709C22semidirect
43. C2×#14519708C22semidirect
44. #16839769C22semidirect
45. C2×#14519702C22semidirect
46. C2×#14519701C22semidirect
47. C2×#14519700C22semidirect
53. C61×#484C22semidirect
54. C2×#107×C61C22semidirect
55. C2×#103×C61C22semidirect
113. #14519710C23semidirect
114. #14519709C23semidirect
115. #14519708C23semidirect
116. #14519702C23semidirect
117. #14519701C23semidirect
118. #14519700C23semidirect
134. #107×C61C23semidirect
135. #103×C61C23semidirect
308. C2×#484D61semidirect
317. C2×C61#3095semidirect
350. #484C2×D61semidirect
355. C2×#107C2×D61semidirect
362. C2×#103C2×D61semidirect
367. C61C2×#3095semidirect
438. #107C22×D61semidirect
444. #103C22×D61semidirect
617. C2#21455764direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D612
C22×#145197352
#214557642
C2×#168400972
C2×#168401052
C2×#168401012
C2×#168400932
C2×#168400902
C2×#168398032
C2×#168397692
C2×#168397242
C2×C61×#4842
C2×#309561