Finite Group Databasebeta

← C2×#21457184 #30552860

Subgroups — C2×#21457184 #30552860

Order 15616.

2178 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840313C211yesmaximal, characteristic, complemented
2C2×#16840299C211yesmaximal, characteristic, complemented
3#21457184C2116yesmaximal, direct product factor
4C2×#16840061C212yesmaximal, complemented
5C2×#16840039C211yesmaximal, characteristic, complemented
6C2×#16840016C212yesmaximal, complemented
7C2×#16840011C212yesmaximal, complemented
8C2×#16839962C211yesmaximal, characteristic, complemented
9C2×#16839980C212yesmaximal, complemented
10C2×#16839958C211yesmaximal, characteristic, complemented
11C2×#16839784C211yesmaximal, characteristic, complemented
12C2×C61×#475C211yesmaximal, characteristic, complemented
13C22×#11758226—21no—
14C22×#11758201C2212yes—
15C22×D488C2212yes—
16C22×#11758189C2212yes—
17#16840313—24no—
18#16840313C2218yescomplemented
19C2×#14519774C2211yescharacteristic
20#16840299—24no—
21#16840299C2218yescomplemented
22C2×#14519772—21no—
23C2×#14519768C2211yescharacteristic
24C2×#14519766—21no—
25C2×#14519766C2211yescharacteristic
26C2×#14519762—21no—
27C2×#14519753C2211yescharacteristic
28C2×#14519752—21no—
29C2×#14519752C2212yes—
30C2×#14519752C2211yescharacteristic
31C2×C4×D244—21no—
32C2×C4×D244C2211yescharacteristic
33C2×#14519739—21no—
34C2×#14519739C2212yes—
35C2×#14519734—21no—
36C2×C42×D61C2211yescharacteristic
37#16840061C22116yescomplemented
38#16840039C2218yescomplemented
39#16840016C22116yescomplemented
40#16840011C22116yescomplemented
41#16839980C22116yescomplemented
42#16839962C2218yescomplemented
43#16839958C2218yescomplemented
44C2×#14519710C2212yes—
45#16839784C2218yescomplemented
46C2×C4⋊#92418C2211yescharacteristic
47C2×#14519706C2212yes—
48C2×#14519699C2212yes—
49C2×#14519697C2212yes—
50C2×#14519697C2212yes—
51C2×C4⋊Q8×C61C2211yescharacteristic
52C2×C4×Q8×C61C2211yescharacteristic
53C61×#475C2218yescomplemented
54C2×#106×C61C2212yes—
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#103×C61C2212yes—
57C2×#11758226—28no—
58C2×#11758226—48no—
59C22×D244—21no—
60C22×D244—22no—
61C22×D244—21no—
62C22×D244—21no—
63C22×D244C2312yes—
64C22×D244C2311yescharacteristic
65C22×C4×D61—21no—
66C22×C4×D61—22no—
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61C2311yescharacteristic
70C2×#11758201—44no—
71C2×#11758201C2318yes—
72C2×D488—44no—
73C2×D488C2318yes—
74C2×#11758189—44no—
75C2×#11758189C2318yes—
76C22×#92418C2312yes—
77#14519774—22no—
78#14519774C2314yes—
79#14519772—28no—
80#14519768—22no—
81#14519768C2314yes—
82#14519766—28no—
83#14519766—22no—
84#14519766C2314yes—
85#14519762—28no—
86#14519753—22no—
87#14519753C2314yes—
88#14519752—28no—
89#14519752—22no—
90#14519752—24no—
91#14519752C2318yes—
92#14519752C2314yes—
93C4×D244—28no—
94C4×D244—22no—
95C4×D244C2314yes—
96#14519739—28no—
97#14519739—24no—
98#14519739C2318yes—
99#14519734—28no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61C2311yescharacteristic
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—21no—
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114C42×D61D414yes—
115C42×D61C2314yes—
116#14519710C2318yes—
117C4⋊#92418C2314yes—
118#14519706C2318yes—
119#14519699C2318yes—
120#14519697C2318yes—
121#14519697C2318yes—
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×D61—22no—
139C23×D61—21no—
140C23×D61C2×D411yescharacteristic
141C2×Q8×C61—24no—
142C2×Q8×C61—21no—
143C2×Q8×C61—22no—
144C2×Q8×C61—22no—
145C2×Q8×C61—44no—
146C2×Q8×C61C2412yes—
147C22×C4×C61—22no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2411yescharacteristic
153C22×Dic61—21no—
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157#11758226—432no—
158C2×D244—22no—
159C2×D244—24no—
160C2×D244—24no—
161C2×D244—22no—
162C2×D244—28no—
163C2×D244—24no—
164C2×D244—24no—
165C2×D244—24no—
166C2×D244—22no—
167C2×D244—21no—
168C2×D244—44no—
169C2×D244—44no—
170C2×D244—48no—
171C2×D244—44no—
172C2×D244C2412yes—
173C2×D244C2414yes—
174C2×C4×D61—24no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—24no—
178C2×C4×D61—28no—
179C2×C4×D61—42no—
180C2×C4×D61—48no—
181C2×C4×D61—44no—
182C2×C4×D61C2×D414yes—
183C2×C4×D61C2×D412yes—
184C2×C4×D61C2×D414yes—
185C2×C4×D61C2412yes—
186C2×C8×C61—24no—
187C2×C8×C61C2414yes—
188C4⋊C4×C61—24no—
189C4⋊C4×C61—24no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—22no—
192C4⋊C4×C61C2414yes—
193C4⋊C4×C61C2412yes—
194C42×C61—24no—
195C42×C61C2×D412yes—
196C42×C61C2412yes—
197#11758201—48no—
198#11758198—24no—
199#11758198—24no—
200#11758198—24no—
201#11758198—24no—
202#11758198—28no—
203#11758198—28no—
204#11758198—24no—
205C4⋊Dic61—21no—
206C4⋊Dic61—24no—
207C4⋊Dic61C2412yes—
208#11758196—24no—
209#11758196—24no—
210C4×Dic61C2×D412yes—
211C4×Dic61C2×D414yes—
212C4×Dic61C2×D414yes—
213C4×Dic61C2412yes—
214C2×#92418—24no—
215C2×#92418C2414yes—
216D488—48no—
217#11758189—48no—
218C23×C61C22×D411yescharacteristic
219C22×D61—22no—
220C22×D61—22no—
221C22×D61—22no—
222C22×D61—22no—
223C22×D61—24no—
224C22×D61—42no—
225C22×D61—44no—
226C22×D61—44no—
227C22×D61—42no—
228C22×D61—44no—
229C22×D61—42no—
230C22×D61C22×D412yes—
231Q8×C61—22no—
232Q8×C61—22no—
233Q8×C61—42no—
234Q8×C61—48no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—24no—
239C2×C4×C61—42no—
240C2×C4×C61—44no—
241C2×C4×C61—42no—
242C2×C4×C61AGL(1,ℤ/8)14yes—
243C2×C4×C61C22×D412yes—
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C22×D412yes—
246C2×C4×C61H(5,𝔽2)12yes—
247C2×C4×C612−1+412yes—
248C2×C4×C61C2511yescharacteristic
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—42no—
254C2×Dic61C22×D412yes—
255C2×Dic61C22×D412yes—
256C2×Dic61C22×D412yes—
257D244—22no—
258D244—24no—
259D244—22no—
260D244—24no—
261D244—48no—
262D244—48no—
263D244—416no—
264D244—42no—
265D244—44no—
266D244—48no—
267C4×D61—24no—
268C4×D61—28no—
269C4×D61—22no—
270C4×D61—22no—
271C4×D61—44no—
272C4×D61—416no—
273C4×D61—48no—
274C8×C61—24no—
275#92418—24no—
276C2×#3251—611nomaximal, Sylow
277C22×C61#53712yes—
278C22×C61C2×AGL(1,ℤ/8)12yes—
279C22×C61#57512yes—
280C22×C61C23×D411yescharacteristic
281C2×D61—22no—
282C2×D61—22no—
283C2×D61—22no—
284C2×D61—44no—
285C2×D61—42no—
286C2×D61—44no—
287C2×D61—44no—
288C2×D61—42no—
289C2×D61—44no—
290C2×D61—42no—
291C2×D61—88no—
292C2×D61—84no—
293C4×C61—22no—
294C4×C61—42no—
295C4×C61—44no—
296C4×C61—42no—
297C4×C61#53712yes—
298C4×C61C2×AGL(1,ℤ/8)14yes—
299C4×C61C2×H(5,𝔽2)11yescharacteristic
300C4×C61C2×2−1+411yescharacteristic
301Dic61—22no—
302Dic61—22no—
303Dic61—22no—
304Dic61—42no—
305C2×#532—611no—
306C2×#529—611no—
307#3251—6116no—
308C2×#475D6111yescharacteristic, complemented
309C2×#478—612no—
310C2×#474—611no—
311C2×#469—612no—
312C2×#468—612no—
313C2×#460—611no—
314C2×#463—612no—
315C2×#459—611no—
316C2×#423—611no—
317C2×C61#325114yescomplemented
318C2×C61C2×#53711yescharacteristic
319C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
320C2×C61C2×#57511yescharacteristic
321D61—42no—
322D61—84no—
323D61—82no—
324C22×#41—1221no—
325C22×SD16—612no—
326C22×D8—612no—
327C22×M16—612no—
328#532—618no—
329#532—1224no—
330C2×C4⋊Q8C2×D6111yescharacteristic
331C2×#127—611no—
332#529—618no—
333#529—1224no—
334C2×#126—1221no—
335C2×#125—611no—
336C2×#124—611no—
337C2×#124—1221no—
338C2×#123—1221no—
339C2×C22⋊Q8—611no—
340C2×#121—611no—
341C2×#121—612no—
342C2×#121—1221no—
343C2×C4×Q8C2×D6111yescharacteristic
344C2×C4×D4—612no—
345C2×C4×D4—611no—
346C2×C4×D4—1221no—
347C2×C4×D4—1221no—
348C2×#117—1221no—
349C22×C42—611no—
350#478—6116no—
351#475C2×D6118yescomplemented
352#474—618no—
353#469—6116no—
354#468—6116no—
355#463—6116no—
356#460—618no—
357#459—618no—
358C2×#107—612no—
359C2×#106C2×D6112yes—
360#423—618no—
361C2×C4⋊C8—612no—
362C2×C4⋊C8—611no—
363C2×C4⋊C8C2×D6111yescharacteristic
364C2×#103C2×D6112yes—
365C2×#102—612no—
366C2×#102—612no—
367C2×#102—612no—
368C61C2×#325111yescharacteristic, complemented, Sylow
369C2×#41—1228no—
370C2×#41—2448no—
371C22×Q8—21no—
372C22×Q8C22×D6111yescharacteristic
373C22×D4—611no—
374C22×D4—612no—
375C22×D4—1221no—
376C22×D4—1222no—
377C22×D4—1221no—
378C22×D4—1221no—
379C23×C4—611no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—1222no—
383C23×C4—1221no—
384C2×SD16—618no—
385C2×SD16—2444no—
386C2×D8—618no—
387C2×D8—2444no—
388C2×M16—618no—
389C2×M16—2444no—
390C22×C8—612no—
391C22×C8C22×D6112yes—
392C4⋊Q8—22no—
393C4⋊Q8C22×D6114yes—
394#127—614no—
395#127—1222no—
396#126—1228no—
397#125—614no—
398#125—1222no—
399#124—614no—
400#124—1222no—
401#124—1228no—
402#123—1228no—
403C22⋊Q8—614no—
404C22⋊Q8—1222no—
405#121—614no—
406#121—618no—
407#121—1222no—
408#121—1224no—
409#121—1228no—
410C4×Q8—22no—
411C4×Q8C22×D6114yes—
412C4×D4—618no—
413C4×D4—614no—
414C4×D4—1228no—
415C4×D4—1224no—
416C4×D4—1228no—
417C4×D4—1222no—
418#117—1228no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4—1221no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4C22×D6112yes—
426C2×C4⋊C4C22×D6111yescharacteristic
427C2×C22⋊C4—1221no—
428C2×C22⋊C4—1221no—
429C2×C22⋊C4—1222no—
430C2×C22⋊C4—1222no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—1221no—
433C2×C22⋊C4—1221no—
434C2×C42—21no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—614no—
439C2×C42—614no—
440C2×C42C22×D6111yescharacteristic
441#107—618no—
442#106C22×D6118yes—
443C4⋊C8—618no—
444C4⋊C8—614no—
445C4⋊C8C22×D6114yes—
446#103C22×D6118yes—
447#102—618no—
448#102—618no—
449#102—618no—
450C24—611no—
451C24—1221no—
452C24—1222no—
453#41—24432no—
454C2×Q8—21no—
455C2×Q8—24no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—44no—
459C2×Q8C23×D6112yes—
460C2×D4—612no—
461C2×D4—614no—
462C2×D4—1224no—
463C2×D4—1228no—
464C2×D4—1221no—
465C2×D4—1224no—
466C2×D4—1222no—
467C2×D4—1224no—
468C2×D4—1222no—
469C2×D4—1224no—
470C2×D4—1222no—
471C2×D4—1224no—
472C2×D4—2444no—
473C2×D4—2448no—
474C2×D4—2444no—
475C2×D4—2444no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—614no—
483C22×C4—612no—
484C22×C4—612no—
485C22×C4—614no—
486C22×C4—1228no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1224no—
490C22×C4—1221no—
491C22×C4—1224no—
492C22×C4—2442no—
493C22×C4—2448no—
494C22×C4—2444no—
495C22×C4D4×D6111yescharacteristic
496C22×C4D4×D6111yescharacteristic
497C22×C4C23×D6111yescharacteristic
498SD16—2448no—
499D8—2448no—
500M16—2448no—
501C2×C8—24no—
502C2×C8—614no—
503C2×C8—1224no—
504C2×C8C23×D6114yes—
505C4⋊C4—24no—
506C4⋊C4—24no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—612no—
510C4⋊C4—1224no—
511C4⋊C4—1224no—
512C4⋊C4—1224no—
513C4⋊C4—1221no—
514C4⋊C4C23×D6112yes—
515C4⋊C4C23×D6114yes—
516C22⋊C4—1224no—
517C22⋊C4—1224no—
518C22⋊C4—1228no—
519C22⋊C4—1228no—
520C22⋊C4—1224no—
521C22⋊C4—1224no—
522C22⋊C4—1224no—
523C42—24no—
524C42—614no—
525C42—612no—
526C42—614no—
527C42—612no—
528C42D4×D6112yes—
529C42C23×D6112yes—
530C23—612no—
531C23—1222no—
532C23—1222no—
533C23—1222no—
534C23—1222no—
535C23—1224no—
536C23—2444no—
537C23—2442no—
538C23—2444no—
539C23—2442no—
540C23—2442no—
541C23—2444no—
542C23C2×D4×D6111yescharacteristic
543Q8—22no—
544Q8—22no—
545Q8—48no—
546Q8—42no—
547D4—1222no—
548D4—1224no—
549D4—1222no—
550D4—1224no—
551D4—2448no—
552D4—2448no—
553D4—24416no—
554D4—2448no—
555D4—2442no—
556D4—2444no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—44no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—612no—
565C2×C4—612no—
566C2×C4—612no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1228no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1224no—
574C2×C4—1222no—
575C2×C4—2444no—
576C2×C4—24416no—
577C2×C4—2442no—
578C2×C4—2448no—
579C2×C4#1451980414yes—
580C2×C4C2×D4×D6112yes—
581C2×C4C2×D4×D6112yes—
582C2×C4C2×D4×D6111yescharacteristic
583C2×C4#1451982312yes—
584C2×C4#1451982512yes—
585C2×C4C24×D6111yescharacteristic
586C8—24no—
587C8—1224no—
588C22—1222no—
589C22—1222no—
590C22—1222no—
591C22—4888no—
592C22—4884no—
593C22—2444no—
594C22—2442no—
595C22—2444no—
596C22—2442no—
597C22—2442no—
598C22—2444no—
599C22—2444no—
600C22#1684034212yes—
601C22C2×#1451980412yes—
602C22#1684056112yes—
603C22C22×D4×D6111yescharacteristic
604C4—22no—
605C4—44no—
606C4—42no—
607C4—42no—
608C4—1222no—
609C4—1222no—
610C4—1222no—
611C4—2442no—
612C4#1684034212yes—
613C4C2×#1451980414yes—
614C4C2×#1451982311yescharacteristic
615C4C2×#1451982511yescharacteristic
616C2—4884no—
617C2—4882no—
618C2—2442no—
619C2#2145718414yesdirect product factor
620C2C2×#1684034211yescharacteristic
621C2C22×#1451980411yescharacteristic
622C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#475C2
socleC23×C61C22×D4
hypercenterC2×#475D61
hypocenterC61C2×#3251
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×#16840313C2semidirect
2. C2×#16840299C2semidirect
3. #21457184C2direct (N × H)
4. C2×#16840061C2semidirect
5. C2×#16840039C2semidirect
6. C2×#16840016C2semidirect
7. C2×#16840011C2semidirect
8. C2×#16839962C2semidirect
9. C2×#16839980C2semidirect
10. C2×#16839958C2semidirect
11. C2×#16839784C2semidirect
12. C2×C61×#475C2semidirect
18. #16840313C22semidirect
21. #16840299C22semidirect
37. #16840061C22semidirect
38. #16840039C22semidirect
39. #16840016C22semidirect
40. #16840011C22semidirect
41. #16839980C22semidirect
42. #16839962C22semidirect
43. #16839958C22semidirect
45. #16839784C22semidirect
53. C61×#475C22semidirect
308. C2×#475D61semidirect
317. C2×C61#3251semidirect
351. #475C2×D61semidirect
368. C61C2×#3251semidirect
619. C2#21457184direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403132
C2×#168402992
#214571842
C2×#168400612
C2×#168400392
C2×#168400162
C2×#168400112
C2×#168399622
C2×#168399802
C2×#168399582
C2×#168397842
C2×C61×#4752
C2×#325161