Finite Group Databasebeta

← C2×#21462139 #30624067

Subgroups — C2×#21462139 #30624067

Order 15616.

1170 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519852C211yesmaximal, characteristic, complemented
2C2×#16840772C211yesmaximal, characteristic, complemented
3#21462139C218yesmaximal, direct product factor
4C2×#16840679C212yesmaximal, complemented
5C2×#16840678C212yesmaximal, complemented
6C2×#135×D61C211yesmaximal, characteristic
7C2×#14519856—21no—
8C2×#14519852—21no—
9C2×#14519852—22no—
10C2×#14519852C2212yescomplemented
11C2×#14519852C2214yescomplemented
12C22×#11758187—21no—
13#16840772—22no—
14#16840772C2214yescomplemented
15C2×#14519846—21no—
16C2×#14519845C2212yescomplemented
17#16840679C2218yescomplemented
18#16840678C2218yescomplemented
19C2×#41×D61—21no—
20C2×#14519800C2211yescharacteristic
21C2×#14519799C411yescharacteristic, complemented
22C2×#14519798—21no—
23C2×#14519797—21no—
24C2×#14519796C2211yescharacteristic
25#135×D61—22no—
26#135×D61—22no—
27#135×D61C414yescomplemented
28#135×D61C2214yes—
29C2×Q16×D61C411yescharacteristic, complemented
30C2×SD16×D61—21no—
31C2×D8×D61C411yescharacteristic, complemented
32C22×C8×D61C2211yescharacteristic
33C2×#135×C61C411yescharacteristic, complemented
34#14519856—24no—
35#14519856—42no—
36C2×C4⋊#6923—22no—
37C2×C22⋊#6923—41no—
38C2×C4×#6923—41no—
39#14519852—24no—
40#14519852—22no—
41#14519852C2314yescomplemented
42C2×#11758187—22no—
43C2×#11758187—24no—
44#14519846—24no—
45#14519845—22no—
46#14519845C2314yescomplemented
47C2×#11758226—21no—
48C2×#11758222—21no—
49C2×#11758222—41no—
50C2×#11758224—21no—
51C2×#11758224—41no—
52#41×D61—24no—
53#41×D61—24no—
54#41×D61—42no—
55#41×D61—42no—
56C2×Q8×D61—21no—
57C2×D4×D61—21no—
58C2×D4×D61—41no—
59C22×C4×D61—41no—
60C22×C4×D61D411yescharacteristic
61#14519800—21no—
62#14519800—21no—
63#14519800C2×C412yes—
64#14519800C2312yes—
65#14519799—22no—
66#14519799C2×C414yescomplemented
67#14519798—24no—
68#14519798—24no—
69#14519797—24no—
70#14519797—24no—
71#14519796—21no—
72#14519796—21no—
73#14519796C2×C412yes—
74#14519796C2312yes—
75C2×Dic244C2×C411yescharacteristic
76C2×#11758202—21no—
77Q16×D61—22no—
78Q16×D61C2×C414yescomplemented
79C2×#11758190—21no—
80C2×#11758200—21no—
81C2×#11758201—21no—
82SD16×D61—24no—
83SD16×D61—24no—
84C2×D488C2×C411yescharacteristic
85C2×#11758199—21no—
86D8×D61—22no—
87D8×D61C2×C414yescomplemented
88C22×#92418D411yescharacteristic
89C2×C8×D61C2×C411yescharacteristic
90C2×C8×D61C2×C412yes—
91C2×C8×D61D411yescharacteristic
92C2×C8×D61D412yes—
93C2×C8×D61D411yescharacteristic
94C2×C8×D61D412yes—
95C2×C8×D61C2311yescharacteristic
96C2×C8×D61C2312yes—
97C2×#41×C61—21no—
98#135×C61—22no—
99#135×C61C2×C414yescomplemented
100C2×Q16×C61C2×C411yescharacteristic
101C2×SD16×C61—21no—
102C2×D8×C61C2×C411yescharacteristic
103C22×C8×C61C2×C411yescharacteristic
104C23×D61—41no—
105C23×D61D811yescharacteristic
106C22×#6923—42no—
107#41×C61—24no—
108#41×C61—42no—
109C2×Q8×C61—21no—
110C2×D4×C61—21no—
111C2×D4×C61—41no—
112C22×C4×C61—41no—
113C22×C4×C61C22⋊C411yescharacteristic
114C2×C22⋊D61—41no—
115C2×C22⋊D61—41no—
116C2×C22⋊D61—41no—
117C22×Dic61—41no—
118C22×Dic61SD1611yescharacteristic
119#11758226—22no—
120#11758226—22no—
121#11758226—41no—
122#11758226—41no—
123Q8×D61—24no—
124Q8×D61—42no—
125#11758224—22no—
126#11758224—22no—
127#11758224—44no—
128#11758224—44no—
129#11758224—41no—
130#11758224—41no—
131D4×D61—24no—
132D4×D61—44no—
133D4×D61—44no—
134D4×D61—42no—
135#11758222—24no—
136#11758222—42no—
137#11758222—44no—
138#11758222—44no—
139C2×D244—21no—
140C2×D244—41no—
141C2×C4×D61—41no—
142C2×C4×D61—41no—
143C2×C4×D61—41no—
144C2×C4×D61—44no—
145C2×C4×D61—44no—
146C2×C4×D61C22⋊C411yescharacteristic
147C2×C4×D61C22⋊C412yes—
148C2×C4×D61D812yes—
149C2×C4×D61D811yescharacteristic
150C2×C4×D61SD1611yescharacteristic
151C2×C4×D61SD1612yes—
152C2×C4×D61C2×D412yes—
153C2×C4×D61C2×D411yescharacteristic
154C2×Dic122—21no—
155C2×Dic122—41no—
156C22⋊#6923—44no—
157C4⋊#6923—24no—
158C4⋊#6923—42no—
159C4×#6923—44no—
160Q16×C61—21no—
161Q16×C61C22×C412yes—
162SD16×C61—24no—
163D8×C61—21no—
164D8×C61C22×C412yes—
165C2×C8×C61C22⋊C411yescharacteristic
166C2×C8×C61C22⋊C412yes—
167C2×C8×C61C22×C411yescharacteristic
168C2×C8×C61C22×C412yes—
169#11758202—24no—
170#11758201—22no—
171#11758201—22no—
172#11758200—22no—
173#11758200—22no—
174#11758199—24no—
175C2×#92418C22⋊C411yescharacteristic
176C2×#92418C22⋊C412yes—
177C2×#92418C2×D411yescharacteristic
178C2×#92418C2×D412yes—
179Dic244—21no—
180Dic244C22×C412yes—
181D488—21no—
182D488C22×C412yes—
183#11758190—24no—
184C8×D61C22⋊C412yes—
185C8×D61C22⋊C412yes—
186C8×D61C22⋊C412yes—
187C8×D61C22×C412yes—
188C8×D61C22×C411yescharacteristic
189C8×D61C2×D411yescharacteristic
190C8×D61C2×D412yes—
191C8×D61C2×D412yes—
192C8×D61C2×D411yescharacteristic
193C8×D61C2411yescharacteristic
194#11758187—24no—
195C23×C61—41no—
196C23×C61#10211yescharacteristic
197C22×D61—42no—
198C22×D61—41no—
199C22×D61—44no—
200C22×D61—84no—
201C22×D61#10211yescharacteristic
202C22×D61#10212yes—
203C22×D61C2×D811yescharacteristic
204C22×D61C2×D812yes—
205C2×#6923—44no—
206C2×#6923—84no—
207Q8×C61—22no—
208Q8×C61—41no—
209D4×C61—22no—
210D4×C61—44no—
211D4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—44no—
214C2×C4×C61#10212yes—
215C2×C4×C61#10211yescharacteristic
216C2×C4×C61C2×C22⋊C411yescharacteristic
217C2×C4×C61C2×C22⋊C412yes—
218C22⋊D61—44no—
219C22⋊D61—42no—
220C22⋊D61—42no—
221C22⋊D61—44no—
222C2×Dic61—41no—
223C2×Dic61—42no—
224C2×Dic61—42no—
225C2×Dic61#10211yescharacteristic
226C2×Dic61#10212yes—
227C2×Dic61C2×SD1611yescharacteristic
228C2×Dic61C2×SD1612yes—
229D244—22no—
230D244—42no—
231D244—42no—
232D244—41no—
233C4×D61—44no—
234C4×D61—44no—
235C4×D61—42no—
236C4×D61—42no—
237C4×D61#10212yes—
238C4×D61#10212yes—
239C4×D61#10212yes—
240C4×D61C2×C22⋊C412yes—
241C4×D61C2×C22⋊C411yescharacteristic
242C4×D61C2×D812yes—
243C4×D61C2×D811yescharacteristic
244C4×D61C2×SD1612yes—
245C4×D61C2×SD1611yescharacteristic
246C4×D61C22×D411yescharacteristic
247Dic122—22no—
248Dic122—41no—
249Dic122—44no—
250C8×C61C2×C22⋊C412yes—
251C8×C61C2×C22⋊C411yescharacteristic
252C8×C61C23×C411yescharacteristic
253#92418C2×C22⋊C412yes—
254#92418C2×C22⋊C411yescharacteristic
255#92418C22×D411yescharacteristic
256C2×#2145—611nomaximal, Sylow
257C22×C61—22no—
258C22×C61—42no—
259C22×C61—82no—
260C22×C61C2×#10212yes—
261C22×C61C2×#10211yescharacteristic
262C2×D61—22no—
263C2×D61—22no—
264C2×D61—42no—
265C2×D61—42no—
266C2×D61—42no—
267C2×D61—88no—
268C2×D61—82no—
269C2×D61C2×#10212yes—
270C2×D61C2×#10211yescharacteristic
271C2×D61C22×D811yescharacteristic
272#6923—84no—
273C4×C61—42no—
274C4×C61C2×#10211yescharacteristic
275C4×C61C2×#10212yes—
276C4×C61C22×C22⋊C411yescharacteristic
277Dic61—42no—
278Dic61C2×#10212yes—
279Dic61C2×#10211yescharacteristic
280Dic61C22×SD1611yescharacteristic
281C22×#135—611no—
282C22×M32—611no—
283C2×#427—611no—
284#2145—618no—
285C2×#360—612no—
286C2×#360—612no—
287C2×C61—22no—
288C2×C61—82no—
289C2×C61#214512yescomplemented
290C2×C61C22×#10211yescharacteristic
291D61—21no—
292D61—22no—
293D61—21no—
294D61—82no—
295C22×#41—1221no—
296C2×#135—614no—
297C2×#135—614no—
298C2×#135—611no—
299C2×#135—611no—
300C2×#135—611no—
301C2×#135—1221no—
302C2×#135—1222no—
303C2×#135—1222no—
304C2×#135—1221no—
305C2×#135#692311yescharacteristic, complemented
306C22×Q16—611no—
307C22×SD16—1221no—
308C22×D8—611no—
309C23×C8—611no—
310C2×#117—1221no—
311C2×M32—612no—
312C2×M32—614no—
313C2×M32—1221no—
314C2×M32—1222no—
315C22×C16—1221no—
316#427—614no—
317#427—1222no—
318C2×#107—1221no—
319C2×#106—612no—
320#360—618no—
321#360—618no—
322C61C2×#214511yescharacteristic, complemented, Sylow
323C2×#41—21no—
324C2×#41—1221no—
325C2×#41—1221no—
326C2×#41—1224no—
327C2×#41—1224no—
328C2×#41—1221no—
329C2×#41—2441no—
330C2×#41—2441no—
331C2×#41—2442no—
332C2×#41—2442no—
333C22×Q8—1221no—
334C22×D4—1221no—
335C22×D4—2441no—
336C23×C4—611no—
337C23×C4—2441no—
338#135—22no—
339#135—612no—
340#135—612no—
341#135—612no—
342#135—612no—
343#135—614no—
344#135—1221no—
345#135—1221no—
346#135—1224no—
347#135—1224no—
348#135—1221no—
349#135—1221no—
350#135—1224no—
351#135—1224no—
352#135—1222no—
353#135C2×#692314yescomplemented
354C2×Q16—614no—
355C2×Q16—611no—
356C2×Q16—1222no—
357C2×Q16—1221no—
358C2×Q16C2×#692311yescharacteristic
359C2×SD16—21no—
360C2×SD16—1224no—
361C2×SD16—1224no—
362C2×SD16—1221no—
363C2×SD16—1221no—
364C2×SD16—1221no—
365C2×D8—614no—
366C2×D8—611no—
367C2×D8—1222no—
368C2×D8—1221no—
369C2×D8C2×#692311yescharacteristic
370C22×C8—611no—
371C22×C8—611no—
372C22×C8—611no—
373C22×C8—612no—
374C22×C8—612no—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8—612no—
378C22×C8—612no—
379C22×C8C2×#692311yescharacteristic
380#117—1224no—
381#117—2442no—
382C2×C4⋊C4—1222no—
383C2×C22⋊C4—2441no—
384C2×C42—2441no—
385M32—614no—
386M32—1224no—
387M32—1222no—
388C2×C16—1222no—
389C2×C16—1224no—
390#107—1224no—
391#106—614no—
392#106—1222no—
393C24—611no—
394C24—2441no—
395#41—24no—
396#41—42no—
397#41—1222no—
398#41—1222no—
399#41—1222no—
400#41—1222no—
401#41—1224no—
402#41—2444no—
403#41—2444no—
404#41—2444no—
405#41—2444no—
406#41—2441no—
407#41—2441no—
408#41—2441no—
409#41—2441no—
410#41—2442no—
411C2×Q8—21no—
412C2×Q8—1224no—
413C2×Q8—1221no—
414C2×Q8—2441no—
415C2×Q8—2442no—
416C2×D4—21no—
417C2×D4—41no—
418C2×D4—1224no—
419C2×D4—1221no—
420C2×D4—2441no—
421C2×D4—2442no—
422C2×D4—2441no—
423C2×D4—2444no—
424C2×D4—2444no—
425C2×D4—2441no—
426C2×D4—2441no—
427C22×C4—41no—
428C22×C4—611no—
429C22×C4—612no—
430C22×C4—612no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—612no—
435C22×C4—611no—
436C22×C4—612no—
437C22×C4—2441no—
438C22×C4—2444no—
439C22×C4—2444no—
440C22×C4—2441no—
441C22×C4—2441no—
442C22×C4—2442no—
443C22×C4—2441no—
444C22×C4C22⋊#692311yescharacteristic
445Q16—21no—
446Q16—612no—
447Q16—1224no—
448Q16—1221no—
449Q16C22×#692312yes—
450SD16—24no—
451SD16—1222no—
452SD16—1222no—
453SD16—1222no—
454SD16—1222no—
455SD16—1224no—
456D8—21no—
457D8—612no—
458D8—1224no—
459D8—1221no—
460D8C22×#692312yes—
461C2×C8—611no—
462C2×C8—612no—
463C2×C8—611no—
464C2×C8—612no—
465C2×C8—611no—
466C2×C8—612no—
467C2×C8—612no—
468C2×C8—612no—
469C2×C8—612no—
470C2×C8—612no—
471C2×C8—611no—
472C2×C8—611no—
473C2×C8—612no—
474C2×C8—611no—
475C2×C8C22⋊#692311yescharacteristic
476C2×C8C22⋊#692312yes—
477C2×C8C22×#692311yescharacteristic
478C2×C8C22×#692312yes—
479C4⋊C4—1224no—
480C4⋊C4—2442no—
481C22⋊C4—2444no—
482C42—2444no—
483C16—1224no—
484C23—41no—
485C23—611no—
486C23—611no—
487C23—612no—
488C23—612no—
489C23—4884no—
490C23—2442no—
491C23—2444no—
492C23—2441no—
493C23#1451983911yescharacteristic
494Q8—22no—
495Q8—41no—
496Q8—1222no—
497Q8—2444no—
498Q8—2441no—
499D4—22no—
500D4—44no—
501D4—41no—
502D4—1222no—
503D4—2442no—
504D4—2442no—
505D4—2444no—
506D4—2442no—
507D4—2442no—
508D4—2444no—
509D4—2441no—
510C2×C4—41no—
511C2×C4—44no—
512C2×C4—611no—
513C2×C4—612no—
514C2×C4—611no—
515C2×C4—612no—
516C2×C4—612no—
517C2×C4—612no—
518C2×C4—612no—
519C2×C4—612no—
520C2×C4—611no—
521C2×C4—612no—
522C2×C4—611no—
523C2×C4—612no—
524C2×C4—611no—
525C2×C4—611no—
526C2×C4—4884no—
527C2×C4—2442no—
528C2×C4—2442no—
529C2×C4—2444no—
530C2×C4—2442no—
531C2×C4—2442no—
532C2×C4—2444no—
533C2×C4—2441no—
534C2×C4—2444no—
535C2×C4#1451983912yes—
536C2×C4#1451983911yescharacteristic
537C2×C4C2×C22⋊#692311yescharacteristic
538C2×C4C2×C22⋊#692312yes—
539C8—612no—
540C8—611no—
541C8—611no—
542C8C2×C22⋊#692311yescharacteristic
543C8C2×C22⋊#692312yes—
544C8C23×#692311yescharacteristic
545C22—22no—
546C22—42no—
547C22—82no—
548C22—611no—
549C22—612no—
550C22—611no—
551C22—1222no—
552C22—1222no—
553C22—4888no—
554C22—4882no—
555C22—2442no—
556C22—2442no—
557C22—2442no—
558C22C2×#1451983912yes—
559C22C2×#1451983911yescharacteristic
560C4—42no—
561C4—611no—
562C4—611no—
563C4—612no—
564C4—4884no—
565C4—2442no—
566C4C2×#1451983912yes—
567C4C2×#1451983911yescharacteristic
568C4C22×C22⋊#692311yescharacteristic
569C2—22no—
570C2—82no—
571C2—1221no—
572C2—1222no—
573C2—1221no—
574C2—4882no—
575C2#2146213912yesdirect product factor
576C2C22×#1451983911yescharacteristic
subgroupG/H
centerC2×C4#14519839
commutatorC8×C61C23×C4
FrattiniC8C23×#6923
FittingC2×#135×C61C4
socleC22×C61C2×#102
prime radicalC2×#135×D61C2
cosocleC8×D61C24
hypercenterC2×#135#6923
hypocenterC61C2×#2145
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C22×#14519852C2semidirect
2. C2×#16840772C2semidirect
3. #21462139C2direct (N × H)
4. C2×#16840679C2semidirect
5. C2×#16840678C2semidirect
10. C2×#14519852C22semidirect
11. C2×#14519852C22semidirect
14. #16840772C22semidirect
16. C2×#14519845C22semidirect
17. #16840679C22semidirect
18. #16840678C22semidirect
21. C2×#14519799C4semidirect
27. #135×D61C4semidirect
29. C2×Q16×D61C4semidirect
31. C2×D8×D61C4semidirect
33. C2×#135×C61C4semidirect
41. #14519852C23semidirect
46. #14519845C23semidirect
66. #14519799C2×C4semidirect
78. Q16×D61C2×C4semidirect
87. D8×D61C2×C4semidirect
99. #135×C61C2×C4semidirect
289. C2×C61#2145semidirect
305. C2×#135#6923semidirect
322. C61C2×#2145semidirect
353. #135C2×#6923semidirect
575. C2#21462139direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198522
C2×#168407722
#214621392
C2×#168406792
C2×#168406782
C2×#135×D612
C2×#214561