Finite Group Databasebeta

← C2×#21457053 #30552149

Subgroups — C2×#21457053 #30552149

Order 15616.

2018 conjugacy classes of subgroups.

The subgroup lattice has 586 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#21457053C2116yesmaximal, direct product factor
4C2×#16840169C212yesmaximal, complemented
5C2×#16840123C212yesmaximal, complemented
6C2×#16840096C212yesmaximal, complemented
7C2×#16840082C212yesmaximal
8C2×#16840047C211yesmaximal, characteristic, complemented
9C2×#16840043C211yesmaximal, characteristic, complemented
10C2×#16840039C211yesmaximal, characteristic, complemented
11C2×#16839818C211yesmaximal, characteristic, complemented
12C2×C61×#475C211yesmaximal, characteristic, complemented
13C22×Q8×D61—21no—
14C2×#14519777C2211yescharacteristic
15C2×#14519776—21no—
16C2×#14519776C2212yes—
17C2×#14519775—21no—
18C4⋊Q8×D61—24no—
19C4⋊Q8×D61C2218yescomplemented
20#16840299—24no—
21#16840299C2218yes—
22C2×#14519772—21no—
23C2×#14519768C2211yescharacteristic
24C2×#14519766C2211yescharacteristic
25C2×#14519762—21no—
26C2×#14519753C2211yescharacteristic
27C2×#14519752C2211yescharacteristic
28C2×C4×D244—21no—
29C2×C4×D244C2211yescharacteristic
30C2×#14519734—21no—
31C2×C4⋊C4×D61—21no—
32C2×C4⋊C4×D61C2212yes—
33C2×C42×D61C2211yescharacteristic
34#16840169C22116yescomplemented
35#16840123C22116yescomplemented
36#16840096C22116yescomplemented
37#16840082C22116yes—
38#16840047C2218yescomplemented
39#16840043C2218yescomplemented
40#16840039C2218yescomplemented
41#16839818C2218yescomplemented
42C2×#14519711C2212yes—
43C2×#14519710C2212yes—
44C2×#14519708C2212yes—
45C2×C4⋊#92418C2211yescharacteristic
46C2×#14519701C2212yes—
47C2×#14519699C2212yes—
48C2×#14519697C2212yes—
49C2×#14519689C2212yes—
50C2×#14519687C2212yes—
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—22no—
59C2×Q8×D61—28no—
60C2×Q8×D61—48no—
61C22×D244—21no—
62C22×D244C2311yescharacteristic
63C22×C4×D61—22no—
64C22×C4×D61—21no—
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61C2311yescharacteristic
68C22×#92418C2312yes—
69#14519777—22no—
70#14519777C2314yes—
71#14519776—24no—
72#14519776—28no—
73#14519776C2318yes—
74#14519775—28no—
75#14519772—28no—
76#14519768—22no—
77#14519768C2314yes—
78#14519766—22no—
79#14519766C2314yes—
80#14519762—28no—
81#14519753—22no—
82#14519753C2314yes—
83#14519752—22no—
84#14519752C2314yes—
85C4×D244—28no—
86C4×D244—22no—
87C4×D244C2314yes—
88#14519734—28no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61C2312yes—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—22no—
94C2×#11758196—22no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C4⋊C4×D61—28no—
98C4⋊C4×D61—24no—
99C4⋊C4×D61C2318yes—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×C4×Dic61D411yescharacteristic
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61C2311yescharacteristic
108C42×D61D414yes—
109C42×D61C2314yes—
110#14519711C2318yes—
111#14519710C2318yes—
112#14519708C2318yes—
113C4⋊#92418C2314yes—
114#14519701C2318yes—
115#14519699C2318yes—
116#14519697C2318yes—
117#14519689C2318yes—
118#14519687C2318yes—
119C22×Q8×C61—21no—
120C22×Q8×C61C2311yescharacteristic
121C22×C8×C61C2312yes—
122C4⋊Q8×C61—22no—
123C4⋊Q8×C61C2314yes—
124C4×Q8×C61—22no—
125C4×Q8×C61C2314yes—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61C2312yes—
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C42×C61—21no—
131C2×C42×C61C2311yescharacteristic
132#106×C61C2318yes—
133C4⋊C8×C61C2314yes—
134#103×C61C2318yes—
135C23×D61—21no—
136C23×D61C2×D411yescharacteristic
137C2×Q8×C61—24no—
138C2×Q8×C61—21no—
139C2×Q8×C61—22no—
140C2×Q8×C61—22no—
141C2×Q8×C61—44no—
142C2×Q8×C61C2412yes—
143C22×C4×C61—22no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2411yescharacteristic
149C22×Dic61—22no—
150C22×Dic61—21no—
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154Q8×D61—432no—
155C2×D244—22no—
156C2×D244—22no—
157C2×D244—24no—
158C2×D244—21no—
159C2×D244—44no—
160C2×D244C2412yes—
161C2×C4×D61—24no—
162C2×C4×D61—24no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—28no—
166C2×C4×D61—24no—
167C2×C4×D61—48no—
168C2×C4×D61—44no—
169C2×C4×D61C2×D414yes—
170C2×C4×D61C2×D414yes—
171C2×C4×D61C2×D412yes—
172C2×C4×D61C2412yes—
173C2×Dic122—24no—
174C2×Dic122—28no—
175C2×Dic122—48no—
176C2×Dic122—44no—
177C2×C8×C61—24no—
178C2×C8×C61C2414yes—
179C4⋊C4×C61—24no—
180C4⋊C4×C61—24no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61C2414yes—
184C4⋊C4×C61C2412yes—
185C42×C61—24no—
186C42×C61C2×D412yes—
187C42×C61C2412yes—
188#11758198—24no—
189#11758198—24no—
190#11758198—24no—
191#11758198—24no—
192#11758198—24no—
193C4⋊Dic61—24no—
194C4⋊Dic61—22no—
195C4⋊Dic61—21no—
196C4⋊Dic61—24no—
197C4⋊Dic61C2414yes—
198C4⋊Dic61C2412yes—
199#11758196—28no—
200#11758196—28no—
201#11758196—24no—
202#11758196—24no—
203C4×Dic61C2×D412yes—
204C4×Dic61C2×D414yes—
205C4×Dic61C2×D414yes—
206C4×Dic61C2412yes—
207C2×#92418—24no—
208C2×#92418C2414yes—
209C23×C61C22×D411yescharacteristic
210C22×D61—22no—
211C22×D61—22no—
212C22×D61—22no—
213C22×D61—42no—
214C22×D61—42no—
215C22×D61—42no—
216C22×D61#13714yes—
217C22×D61C22×D412yes—
218Q8×C61—22no—
219Q8×C61—22no—
220Q8×C61—42no—
221Q8×C61—48no—
222C2×C4×C61—22no—
223C2×C4×C61—24no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—42no—
227C2×C4×C61—44no—
228C2×C4×C61—42no—
229C2×C4×C61AGL(1,ℤ/8)14yes—
230C2×C4×C61C22×D412yes—
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61C22×D412yes—
233C2×C4×C612−1+412yes—
234C2×C4×C612−1+412yes—
235C2×C4×C61C2511yescharacteristic
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—24no—
241C2×Dic61—44no—
242C2×Dic61—42no—
243C2×Dic61C22×D412yes—
244C2×Dic61C22×D412yes—
245C2×Dic61C22×D412yes—
246D244—22no—
247D244—22no—
248D244—48no—
249D244—42no—
250C4×D61—28no—
251C4×D61—24no—
252C4×D61—28no—
253C4×D61—22no—
254C4×D61—22no—
255C4×D61—416no—
256C4×D61—48no—
257Dic122—416no—
258Dic122—48no—
259C8×C61—24no—
260#92418—24no—
261C2×#3239—611nomaximal, Sylow
262C22×C61#53612yes—
263C22×C61C2×AGL(1,ℤ/8)12yes—
264C22×C61C2×#13712yes—
265C22×C61C23×D411yescharacteristic
266C2×D61—22no—
267C2×D61—28no—
268C2×D61—22no—
269C2×D61—42no—
270C2×D61—42no—
271C2×D61—42no—
272C2×D61—84no—
273C2×D61C2×#13714yes—
274C4×C61—22no—
275C4×C61—42no—
276C4×C61—44no—
277C4×C61—42no—
278C4×C61#53612yes—
279C4×C61C2×AGL(1,ℤ/8)14yes—
280C4×C61C2×2−1+411yescharacteristic
281C4×C61C2×2−1+411yescharacteristic
282Dic61—22no—
283Dic61—22no—
284Dic61—22no—
285Dic61—44no—
286Dic61—42no—
287C22×C4⋊Q8—611no—
288C2×#529—611no—
289#3239—6116no—
290C2×#501—612no—
291C2×#489—612no—
292C2×#484—612no—
293C2×#481—612no—
294C2×#475—611no—
295C2×#475D6111yescharacteristic, complemented
296C2×#474—611no—
297C2×#474—611no—
298C2×#432—611no—
299C2×C61#323914yescomplemented
300C2×C61C2×#53611yescharacteristic
301C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
302C2×C61C22×#13711yescharacteristic
303D61—24no—
304D61—82no—
305C23×Q8—1221no—
306C2×C4⋊Q8—618no—
307C2×C4⋊Q8—612no—
308C2×C4⋊Q8—611no—
309C2×C4⋊Q8—1221no—
310C2×C4⋊Q8—1224no—
311C2×C4⋊Q8—1221no—
312C2×C4⋊Q8C2×D6111yescharacteristic
313#529—618no—
314#529—1224no—
315C2×#126—1221no—
316C2×#125—611no—
317C2×#124—611no—
318C2×#123—1221no—
319C2×C22⋊Q8—611no—
320C2×#121—611no—
321C2×C4×Q8C2×D6111yescharacteristic
322C2×C4×D4—611no—
323C2×C4×D4—1221no—
324C2×#117—1221no—
325C22×C4⋊C4—612no—
326C22×C4⋊C4—1221no—
327C22×C42—611no—
328#501—6116no—
329#489—6116no—
330#484—6116no—
331#481—6116no—
332#475—618no—
333#475C2×D6118yescomplemented
334#474—618no—
335#474—618no—
336#432—618no—
337C2×#107—612no—
338C2×#107—612no—
339C2×#106—612no—
340C2×#106C2×D6112yes—
341C2×C4⋊C8—611no—
342C2×C4⋊C8C2×D6111yescharacteristic
343C2×#103—612no—
344C2×#103C2×D6112yes—
345C2×#102—612no—
346C2×#102—612no—
347C2×C22⋊C8—612no—
348C2×#97—612no—
349C61C2×#323911yescharacteristic, complemented, Sylow
350C22×Q8—21no—
351C22×Q8—1222no—
352C22×Q8—1228no—
353C22×Q8—1221no—
354C22×Q8—2448no—
355C22×Q8C22×D6111yescharacteristic
356C22×D4—611no—
357C22×D4—1221no—
358C23×C4—611no—
359C23×C4—611no—
360C23×C4—611no—
361C23×C4—1222no—
362C23×C4—1221no—
363C22×C8—612no—
364C22×C8C22×D6112yes—
365C4⋊Q8—22no—
366C4⋊Q8—618no—
367C4⋊Q8—614no—
368C4⋊Q8—1224no—
369C4⋊Q8—1228no—
370C4⋊Q8—1228no—
371C4⋊Q8—1222no—
372C4⋊Q8C22×D6114yes—
373#126—1228no—
374#125—614no—
375#125—1222no—
376#124—614no—
377#124—1222no—
378#123—1228no—
379C22⋊Q8—614no—
380C22⋊Q8—1222no—
381#121—614no—
382#121—1222no—
383C4×Q8—22no—
384C4×Q8C22×D6114yes—
385C4×D4—614no—
386C4×D4—1228no—
387C4×D4—1222no—
388#117—1228no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—612no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—618no—
394C2×C4⋊C4—1224no—
395C2×C4⋊C4—1228no—
396C2×C4⋊C4—1222no—
397C2×C4⋊C4—1222no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4C22×D6112yes—
403C2×C4⋊C4C22×D6111yescharacteristic
404C2×C22⋊C4—1221no—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4—1221no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4—1221no—
409C2×C42—21no—
410C2×C42—611no—
411C2×C42—611no—
412C2×C42—611no—
413C2×C42—614no—
414C2×C42—614no—
415C2×C42C22×D6111yescharacteristic
416#107—618no—
417#107—618no—
418#106—618no—
419#106C22×D6118yes—
420C4⋊C8—614no—
421C4⋊C8C22×D6114yes—
422#103—618no—
423#103C22×D6118yes—
424#102—618no—
425#102—618no—
426C22⋊C8—618no—
427#97—618no—
428C24—611no—
429C24—1221no—
430C2×Q8—21no—
431C2×Q8—24no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—44no—
435C2×Q8—1228no—
436C2×Q8—1224no—
437C2×Q8—2448no—
438C2×Q8—24432no—
439C2×Q8—2444no—
440C2×Q8C23×D6112yes—
441C2×D4—612no—
442C2×D4—1224no—
443C2×D4—1221no—
444C2×D4—1222no—
445C2×D4—1222no—
446C2×D4—2444no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—612no—
454C22×C4—614no—
455C22×C4—614no—
456C22×C4—612no—
457C22×C4—1224no—
458C22×C4—1228no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—1224no—
462C22×C4—1221no—
463C22×C4—1222no—
464C22×C4—1224no—
465C22×C4—2448no—
466C22×C4—2444no—
467C22×C4D4×D6111yescharacteristic
468C22×C4D4×D6111yescharacteristic
469C22×C4C23×D6111yescharacteristic
470C2×C8—24no—
471C2×C8—614no—
472C2×C8—1224no—
473C2×C8C23×D6114yes—
474C4⋊C4—24no—
475C4⋊C4—24no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—614no—
479C4⋊C4—612no—
480C4⋊C4—1228no—
481C4⋊C4—1228no—
482C4⋊C4—1224no—
483C4⋊C4—1224no—
484C4⋊C4—1224no—
485C4⋊C4—1222no—
486C4⋊C4—1221no—
487C4⋊C4—1224no—
488C4⋊C4C23×D6114yes—
489C4⋊C4C23×D6112yes—
490C22⋊C4—1224no—
491C22⋊C4—1224no—
492C22⋊C4—1224no—
493C22⋊C4—1224no—
494C22⋊C4—1224no—
495C42—24no—
496C42—614no—
497C42—612no—
498C42—614no—
499C42—612no—
500C42D4×D6112yes—
501C42C23×D6112yes—
502C23—614no—
503C23—612no—
504C23—1222no—
505C23—1222no—
506C23—1222no—
507C23—2442no—
508C23—2442no—
509C23—2442no—
510C23C2×D4×D6111yescharacteristic
511Q8—22no—
512Q8—22no—
513Q8—48no—
514Q8—42no—
515Q8—24416no—
516Q8—2448no—
517D4—1222no—
518D4—1222no—
519D4—2448no—
520D4—2442no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—44no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—612no—
529C2×C4—612no—
530C2×C4—612no—
531C2×C4—1228no—
532C2×C4—1222no—
533C2×C4—1222no—
534C2×C4—1222no—
535C2×C4—1228no—
536C2×C4—1224no—
537C2×C4—1222no—
538C2×C4—1222no—
539C2×C4—1222no—
540C2×C4—1224no—
541C2×C4—24416no—
542C2×C4—2442no—
543C2×C4—2444no—
544C2×C4—2448no—
545C2×C4#1451980414yes—
546C2×C4C2×D4×D6112yes—
547C2×C4C2×D4×D6112yes—
548C2×C4C2×D4×D6111yescharacteristic
549C2×C4#1451982412yes—
550C2×C4#1451982512yes—
551C2×C4C24×D6111yescharacteristic
552C8—24no—
553C8—1224no—
554C22—614no—
555C22—1222no—
556C22—1228no—
557C22—1222no—
558C22—4884no—
559C22—2442no—
560C22—2442no—
561C22—2442no—
562C22#1684033512yes—
563C22C2×#1451980412yes—
564C22#137×D6112yes—
565C22C22×D4×D6111yescharacteristic
566C4—22no—
567C4—44no—
568C4—42no—
569C4—42no—
570C4—1222no—
571C4—1222no—
572C4—1222no—
573C4—2442no—
574C4—2444no—
575C4#1684033512yes—
576C4C2×#1451980414yes—
577C4C2×#1451982411yescharacteristic
578C4C2×#1451982511yescharacteristic
579C2—1224no—
580C2—4882no—
581C2#2145705314yesdirect product factor
582C2C2×#1684033511yescharacteristic
583C2C22×#1451980411yescharacteristic
584C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#475C2
socleC23×C61C22×D4
prime radicalC2×#14519752C22
hypercenterC2×#475D61
hypocenterC61C2×#3239
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
1. C2×C4⋊Q8×D61C2semidirect
3. #21457053C2direct (N × H)
4. C2×#16840169C2semidirect
5. C2×#16840123C2semidirect
6. C2×#16840096C2semidirect
8. C2×#16840047C2semidirect
9. C2×#16840043C2semidirect
10. C2×#16840039C2semidirect
11. C2×#16839818C2semidirect
12. C2×C61×#475C2semidirect
19. C4⋊Q8×D61C22semidirect
34. #16840169C22semidirect
35. #16840123C22semidirect
36. #16840096C22semidirect
38. #16840047C22semidirect
39. #16840043C22semidirect
40. #16840039C22semidirect
41. #16839818C22semidirect
53. C61×#475C22semidirect
295. C2×#475D61semidirect
299. C2×C61#3239semidirect
333. #475C2×D61semidirect
349. C61C2×#3239semidirect
581. C2#21457053direct (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
#214570532
C2×#168401692
C2×#168401232
C2×#168400962
C2×#168400822
C2×#168400472
C2×#168400432
C2×#168400392
C2×#168398182
C2×C61×#4752
C2×#323961