Finite Group Databasebeta

← C2×#21456850 #30551291

Subgroups — C2×#21456850 #30551291

Order 15616.

2146 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
2C2×#16840299C211yesmaximal, characteristic
3#21456850C2116yesmaximal, direct product factor
4C2×#16840155C212yesmaximal, complemented
5C2×#16840129C212yesmaximal, complemented
6C2×#16839972C211yesmaximal, characteristic, complemented
7C2×#16839968C211yesmaximal, characteristic, complemented
8C2×#16839964C211yesmaximal, characteristic, complemented
9C2×#16839916C212yesmaximal, complemented
10C2×#16839902C212yesmaximal
11C2×#16839818C211yesmaximal, characteristic, complemented
12C2×C61×#462C211yesmaximal, characteristic, complemented
13C22×Q8×D61C2212yes—
14C22×#11758202C2212yes—
15C22×#11758190C2212yes—
16C22×#11758201C2212yes—
17C2×#14519777C2211yescharacteristic
18C2×#14519776—21no—
19C2×#14519776—21no—
20C2×#14519775C2212yes—
21C4⋊Q8×D61—24no—
22C4⋊Q8×D61C2218yescomplemented
23#16840299—24no—
24#16840299C2218yes—
25C2×#14519772—21no—
26C2×#14519768C2211yescharacteristic
27C2×#14519766C2211yescharacteristic
28C2×#14519762—21no—
29C2×#14519753C2211yescharacteristic
30C2×#14519752C2211yescharacteristic
31C2×C4×D244—21no—
32C2×C4×D244C2211yescharacteristic
33C2×#14519734—21no—
34C2×C4⋊C4×D61—21no—
35C2×C4⋊C4×D61—21no—
36C2×C42×D61C2211yescharacteristic
37#16840155C22116yescomplemented
38#16840129C22116yescomplemented
39#16839972C2218yescomplemented
40#16839968C2218yescomplemented
41#16839964C2218yescomplemented
42#16839916C22116yescomplemented
43#16839902C22116yes—
44#16839818C2218yescomplemented
45C2×C4⋊#92418C2211yescharacteristic
46C2×#14519702C2212yes—
47C2×#14519701C2212yes—
48C2×#14519700C2212yes—
49C2×#14519689C2212yes—
50C2×#14519687C2212yes—
51C22×Q16×C61C2212yes—
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C61×#462C2218yescomplemented
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#103×C61C2212yes—
57C22×Dic122—22no—
58C22×Dic122C2312yes—
59C2×Q8×D61—24no—
60C2×Q8×D61—44no—
61C2×Q8×D61—44no—
62C2×Q8×D61C2318yes—
63C22×D244—21no—
64C22×D244C2311yescharacteristic
65C22×C4×D61—22no—
66C22×C4×D61—21no—
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61C2311yescharacteristic
70C2×#11758202—44no—
71C2×#11758202C2318yes—
72C2×#11758190—44no—
73C2×#11758190C2318yes—
74C2×#11758201—44no—
75C2×#11758201C2318yes—
76C22×#92418C2312yes—
77#14519777—22no—
78#14519777C2314yes—
79#14519776—28no—
80#14519776—28no—
81#14519775—24no—
82#14519775C2318yes—
83#14519772—28no—
84#14519768—22no—
85#14519768C2314yes—
86#14519766—22no—
87#14519766C2314yes—
88#14519762—28no—
89#14519753—22no—
90#14519753C2314yes—
91#14519752—22no—
92#14519752C2314yes—
93C4×D244—28no—
94C4×D244—22no—
95C4×D244C2314yes—
96#14519734—28no—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61C2311yescharacteristic
101C2×#11758196—22no—
102C2×#11758196—22no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C4⋊C4×D61—28no—
106C4⋊C4×D61—28no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C42×D61D414yes—
116C42×D61C2314yes—
117C4⋊#92418C2314yes—
118#14519702C2318yes—
119#14519701C2318yes—
120#14519700C2318yes—
121#14519689C2318yes—
122#14519687C2318yes—
123C22×Q8×C61C2312yes—
124C22×Q8×C61C2311yescharacteristic
125C2×Q16×C61—44no—
126C2×Q16×C61C2318yes—
127C22×C8×C61C2312yes—
128C4⋊Q8×C61—22no—
129C4⋊Q8×C61C2314yes—
130C4×Q8×C61—22no—
131C4×Q8×C61C2314yes—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C42×C61—21no—
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61C2314yes—
139#103×C61C2318yes—
140C23×D61—21no—
141C23×D61C2×D411yescharacteristic
142C2×Q8×C61—22no—
143C2×Q8×C61—21no—
144C2×Q8×C61—24no—
145C2×Q8×C61—24no—
146C2×Q8×C61—22no—
147C2×Q8×C61—22no—
148C2×Q8×C61C2414yes—
149C2×Q8×C61C2412yes—
150C22×C4×C61—22no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2411yescharacteristic
156C22×Dic61—22no—
157C22×Dic61—21no—
158C22×Dic61C2×D411yescharacteristic
159C22×Dic61C2×D411yescharacteristic
160C22×Dic61C2×D411yescharacteristic
161Q8×D61—48no—
162Q8×D61—48no—
163Q8×D61—416no—
164C2×D244—22no—
165C2×D244—22no—
166C2×D244—24no—
167C2×D244—21no—
168C2×D244—44no—
169C2×D244C2412yes—
170C2×C4×D61—24no—
171C2×C4×D61—24no—
172C2×C4×D61—22no—
173C2×C4×D61—22no—
174C2×C4×D61—28no—
175C2×C4×D61—24no—
176C2×C4×D61—48no—
177C2×C4×D61—44no—
178C2×C4×D61C2×D414yes—
179C2×C4×D61C2×D414yes—
180C2×C4×D61C2×D412yes—
181C2×C4×D61C2412yes—
182C2×Dic122—24no—
183C2×Dic122—24no—
184C2×Dic122—22no—
185C2×Dic122—28no—
186C2×Dic122—48no—
187C2×Dic122C2414yes—
188Q16×C61—48no—
189C2×C8×C61—24no—
190C2×C8×C61C2414yes—
191C4⋊C4×C61—24no—
192C4⋊C4×C61—24no—
193C4⋊C4×C61—24no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61C2412yes—
196C42×C61—24no—
197C42×C61C2×D412yes—
198C42×C61C2412yes—
199#11758202—48no—
200#11758201—48no—
201#11758198—24no—
202#11758198—24no—
203#11758198—24no—
204#11758198—24no—
205#11758198—24no—
206C4⋊Dic61—24no—
207C4⋊Dic61—24no—
208C4⋊Dic61—21no—
209C4⋊Dic61—24no—
210C4⋊Dic61C2412yes—
211#11758196—28no—
212#11758196—28no—
213#11758196—24no—
214#11758196—24no—
215C4×Dic61C2×D412yes—
216C4×Dic61C2×D414yes—
217C4×Dic61C2×D414yes—
218C4×Dic61C2412yes—
219C2×#92418—24no—
220C2×#92418C2414yes—
221#11758190—48no—
222C23×C61C22×D411yescharacteristic
223C22×D61—22no—
224C22×D61—22no—
225C22×D61—22no—
226C22×D61—42no—
227C22×D61—42no—
228C22×D61—42no—
229C22×D61#13714yes—
230C22×D61C22×D412yes—
231Q8×C61—24no—
232Q8×C61—22no—
233Q8×C61—22no—
234Q8×C61—24no—
235Q8×C61—44no—
236Q8×C61—42no—
237C2×C4×C61—22no—
238C2×C4×C61—24no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—44no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61#13714yes—
245C2×C4×C61C22×D412yes—
246C2×C4×C61C22×D411yescharacteristic
247C2×C4×C61C22×D412yes—
248C2×C4×C61H(5,𝔽2)12yes—
249C2×C4×C61H(5,𝔽2)12yes—
250C2×C4×C61C2511yescharacteristic
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—24no—
255C2×Dic61—22no—
256C2×Dic61—44no—
257C2×Dic61—42no—
258C2×Dic61C22×D412yes—
259C2×Dic61C22×D412yes—
260C2×Dic61C22×D412yes—
261D244—22no—
262D244—22no—
263D244—48no—
264D244—42no—
265C4×D61—28no—
266C4×D61—24no—
267C4×D61—28no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—416no—
271C4×D61—48no—
272Dic122—24no—
273Dic122—24no—
274Dic122—416no—
275Dic122—44no—
276C8×C61—24no—
277#92418—24no—
278C2×#3218—611nomaximal, Sylow
279C22×C61#53512yes—
280C22×C61C2×#13712yes—
281C22×C61C2×#13712yes—
282C22×C61C23×D411yescharacteristic
283C2×D61—22no—
284C2×D61—28no—
285C2×D61—22no—
286C2×D61—42no—
287C2×D61—42no—
288C2×D61—42no—
289C2×D61—84no—
290C2×D61C2×#13714yes—
291C4×C61—22no—
292C4×C61—44no—
293C4×C61—42no—
294C4×C61—42no—
295C4×C61#53512yes—
296C4×C61C2×#13714yes—
297C4×C61C2×H(5,𝔽2)11yescharacteristic
298C4×C61C2×H(5,𝔽2)11yescharacteristic
299Dic61—22no—
300Dic61—22no—
301Dic61—22no—
302Dic61—44no—
303Dic61—42no—
304C22×C4⋊Q8—611no—
305C2×#529—611no—
306#3218—6116no—
307C2×#497—612no—
308C2×#491—612no—
309C2×#462—611no—
310C2×#462D6111yescharacteristic, complemented
311C2×#461—611no—
312C2×#461—611no—
313C2×#451—612no—
314C2×#448—612no—
315C2×#432—611no—
316C2×C61#321814yescomplemented
317C2×C61C2×#53511yescharacteristic
318C2×C61C22×#13711yescharacteristic
319C2×C61C22×#13711yescharacteristic
320D61—24no—
321D61—82no—
322C23×Q8—612no—
323C22×Q16—612no—
324C22×Q16C2×D6112yes—
325C22×SD16—612no—
326C22×SD16—612no—
327C2×C4⋊Q8—612no—
328C2×C4⋊Q8—618no—
329C2×C4⋊Q8—611no—
330C2×C4⋊Q8—1221no—
331C2×C4⋊Q8—1221no—
332C2×C4⋊Q8—1224no—
333C2×C4⋊Q8C2×D6111yescharacteristic
334#529—618no—
335#529—1224no—
336C2×#126—1221no—
337C2×#125—611no—
338C2×#124—611no—
339C2×#123—1221no—
340C2×C22⋊Q8—611no—
341C2×#121—611no—
342C2×C4×Q8C2×D6111yescharacteristic
343C2×C4×D4—611no—
344C2×C4×D4—1221no—
345C2×#117—1221no—
346C22×C4⋊C4—1221no—
347C22×C4⋊C4—1221no—
348C22×C42—611no—
349#497—6116no—
350#491—6116no—
351#462—618no—
352#462C2×D6118yescomplemented
353#461—618no—
354#461—618no—
355#451—6116no—
356#448—6116no—
357#432—618no—
358C2×C4⋊C8—611no—
359C2×C4⋊C8C2×D6111yescharacteristic
360C2×#103—612no—
361C2×#103—612no—
362C2×#103—612no—
363C2×#103C2×D6112yes—
364C2×C22⋊C8—612no—
365C2×#97—612no—
366C61C2×#321811yescharacteristic, complemented, Sylow
367C22×Q8—618no—
368C22×Q8—612no—
369C22×Q8—1222no—
370C22×Q8—1224no—
371C22×Q8—2444no—
372C22×Q8—2444no—
373C22×Q8C22×D6111yescharacteristic
374C22×Q8C22×D6112yes—
375C22×D4—611no—
376C22×D4—1221no—
377C23×C4—611no—
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—1222no—
381C23×C4—1221no—
382C2×Q16—44no—
383C2×Q16—618no—
384C2×Q16—2444no—
385C2×Q16C22×D6118yes—
386C2×SD16—618no—
387C2×SD16—618no—
388C2×SD16—2444no—
389C2×SD16—2444no—
390C22×C8—612no—
391C22×C8C22×D6112yes—
392C4⋊Q8—22no—
393C4⋊Q8—618no—
394C4⋊Q8—614no—
395C4⋊Q8—1228no—
396C4⋊Q8—1228no—
397C4⋊Q8—1224no—
398C4⋊Q8—1222no—
399C4⋊Q8C22×D6114yes—
400#126—1228no—
401#125—614no—
402#125—1222no—
403#124—614no—
404#124—1222no—
405#123—1228no—
406C22⋊Q8—614no—
407C22⋊Q8—1222no—
408#121—614no—
409#121—1222no—
410C4×Q8—22no—
411C4×Q8C22×D6114yes—
412C4×D4—614no—
413C4×D4—1228no—
414C4×D4—1222no—
415#117—1228no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—1228no—
421C2×C4⋊C4—1228no—
422C2×C4⋊C4—1222no—
423C2×C4⋊C4—1222no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4C22×D6111yescharacteristic
430C2×C22⋊C4—1221no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—1221no—
433C2×C22⋊C4—1221no—
434C2×C22⋊C4—1221no—
435C2×C42—21no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—614no—
440C2×C42—614no—
441C2×C42C22×D6111yescharacteristic
442C4⋊C8—614no—
443C4⋊C8C22×D6114yes—
444#103—618no—
445#103—618no—
446#103—618no—
447#103C22×D6118yes—
448C22⋊C8—618no—
449#97—618no—
450C24—611no—
451C24—1221no—
452C2×Q8—21no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—24no—
456C2×Q8—24no—
457C2×Q8—22no—
458C2×Q8—614no—
459C2×Q8—1228no—
460C2×Q8—1222no—
461C2×Q8—1224no—
462C2×Q8—1224no—
463C2×Q8—2448no—
464C2×Q8—2448no—
465C2×Q8—2448no—
466C2×Q8—24416no—
467C2×Q8C23×D6114yes—
468C2×Q8C23×D6112yes—
469C2×D4—612no—
470C2×D4—1224no—
471C2×D4—1221no—
472C2×D4—1222no—
473C2×D4—1222no—
474C2×D4—2444no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—614no—
482C22×C4—614no—
483C22×C4—612no—
484C22×C4—612no—
485C22×C4—1224no—
486C22×C4—1228no—
487C22×C4—1224no—
488C22×C4—1222no—
489C22×C4—1222no—
490C22×C4—1221no—
491C22×C4—1222no—
492C22×C4—1224no—
493C22×C4—2448no—
494C22×C4—2444no—
495C22×C4D4×D6111yescharacteristic
496C22×C4D4×D6111yescharacteristic
497C22×C4C23×D6111yescharacteristic
498Q16—48no—
499Q16—2448no—
500SD16—2448no—
501SD16—2448no—
502C2×C8—24no—
503C2×C8—614no—
504C2×C8—1224no—
505C2×C8C23×D6114yes—
506C4⋊C4—24no—
507C4⋊C4—24no—
508C4⋊C4—24no—
509C4⋊C4—21no—
510C4⋊C4—612no—
511C4⋊C4—1228no—
512C4⋊C4—1228no—
513C4⋊C4—1224no—
514C4⋊C4—1224no—
515C4⋊C4—1224no—
516C4⋊C4—1221no—
517C4⋊C4—1224no—
518C4⋊C4—1224no—
519C4⋊C4C23×D6112yes—
520C22⋊C4—1224no—
521C22⋊C4—1224no—
522C22⋊C4—1224no—
523C22⋊C4—1224no—
524C22⋊C4—1224no—
525C42—24no—
526C42—614no—
527C42—612no—
528C42—614no—
529C42—612no—
530C42D4×D6112yes—
531C42C23×D6112yes—
532C23—614no—
533C23—612no—
534C23—1222no—
535C23—1222no—
536C23—1222no—
537C23—2442no—
538C23—2442no—
539C23—2442no—
540C23C2×D4×D6111yescharacteristic
541Q8—22no—
542Q8—24no—
543Q8—24no—
544Q8—22no—
545Q8—42no—
546Q8—44no—
547Q8—1224no—
548Q8—1224no—
549Q8—24416no—
550Q8—2444no—
551D4—1222no—
552D4—1222no—
553D4—2448no—
554D4—2442no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—42no—
560C2×C4—44no—
561C2×C4—42no—
562C2×C4—612no—
563C2×C4—612no—
564C2×C4—612no—
565C2×C4—1228no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1228no—
570C2×C4—1224no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1224no—
575C2×C4—24416no—
576C2×C4—2442no—
577C2×C4—2444no—
578C2×C4—2448no—
579C2×C4#1451980914yes—
580C2×C4C2×D4×D6112yes—
581C2×C4C2×D4×D6112yes—
582C2×C4C2×D4×D6111yescharacteristic
583C2×C4#1451982212yes—
584C2×C4#1451982312yes—
585C2×C4C24×D6111yescharacteristic
586C8—24no—
587C8—1224no—
588C22—614no—
589C22—1222no—
590C22—1222no—
591C22—1228no—
592C22—4884no—
593C22—2442no—
594C22—2442no—
595C22—2442no—
596C22#1684032812yes—
597C22#137×D6112yes—
598C22C2×#1451980912yes—
599C22C22×D4×D6111yescharacteristic
600C4—22no—
601C4—42no—
602C4—44no—
603C4—42no—
604C4—1222no—
605C4—1222no—
606C4—1222no—
607C4—2442no—
608C4—2444no—
609C4#1684032812yes—
610C4C2×#1451980914yes—
611C4C2×#1451982211yescharacteristic
612C4C2×#1451982311yescharacteristic
613C2—1224no—
614C2—4882no—
615C2#2145685014yesdirect product factor
616C2C2×#1684032811yescharacteristic
617C2C2×#137×D6111yescharacteristic
618C2C22×#1451980911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#462C2
socleC23×C61C22×D4
prime radicalC2×#14519752C22
hypercenterC2×#462D61
hypocenterC61C2×#3218
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Q8×D61C2semidirect
3. #21456850C2direct (N × H)
4. C2×#16840155C2semidirect
5. C2×#16840129C2semidirect
6. C2×#16839972C2semidirect
7. C2×#16839968C2semidirect
8. C2×#16839964C2semidirect
9. C2×#16839916C2semidirect
11. C2×#16839818C2semidirect
12. C2×C61×#462C2semidirect
22. C4⋊Q8×D61C22semidirect
37. #16840155C22semidirect
38. #16840129C22semidirect
39. #16839972C22semidirect
40. #16839968C22semidirect
41. #16839964C22semidirect
42. #16839916C22semidirect
44. #16839818C22semidirect
54. C61×#462C22semidirect
310. C2×#462D61semidirect
316. C2×C61#3218semidirect
352. #462C2×D61semidirect
366. C61C2×#3218semidirect
615. C2#21456850direct (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×#168402992
#214568502
C2×#168401552
C2×#168401292
C2×#168399722
C2×#168399682
C2×#168399642
C2×#168399162
C2×#168399022
C2×#168398182
C2×C61×#4622
C2×#321861