Finite Group Databasebeta

← C2×#21462078 #30623912

Subgroups — C2×#21462078 #30623912

Order 15616.

1406 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840748C211yesmaximal, characteristic, complemented
2C2×#16840741C211yesmaximal, characteristic, complemented
3#21462078C218yesmaximal, direct product factor
4C2×#16840662C214yesmaximal, complemented
5C2×#16840329C211yesmaximal, characteristic
6C2×D61⋊M16—21no—
7C2×#14519856—21no—
8#16840748—22no—
9#16840748C2214yescomplemented
10C2×#14519838—21no—
11C2×#14519837C2212yes—
12#16840741—22no—
13#16840741C2214yescomplemented
14C2×#14519836—21no—
15C2×#14519835C2212yes—
16#16840662C22116yescomplemented
17C22×#11758222C2211yescharacteristic
18#16840329—22no—
19#16840329—22no—
20#16840329C414yescomplemented
21#16840329C2214yes—
22C2×#14519773—21no—
23C2×#14519764—21no—
24C2×#14519748—21no—
25C2×#14519748—21no—
26C2×#14519746C412yescomplemented
27C2×#14519746C2212yes—
28C2×#14519736C411yescharacteristic, complemented
29C23×D4×C61C411yescharacteristic, complemented
30C2×#11758213—41no—
31D61⋊M16—24no—
32D61⋊M16—42no—
33C2×#11758217—22no—
34C2×D61⋊C8—41no—
35#14519856—24no—
36#14519856—42no—
37C2×C4⋊#6923—41no—
38C2×C22⋊#6923—22no—
39C2×C4×#6923—41no—
40#14519838—24no—
41#14519837—22no—
42#14519837C2314yes—
43#14519836—24no—
44#14519835—22no—
45#14519835C2314yes—
46C2×#11758222—41no—
47C2×#11758222—41no—
48C2×#11758222—42no—
49C2×#11758222C2×C412yes—
50C2×#11758222D412yes—
51C2×#11758222D412yes—
52C2×#11758222C2312yes—
53C22×Dic122D411yescharacteristic
54C22×D244D411yescharacteristic
55C22×C22⋊D61—22no—
56C22×C22⋊D61—22no—
57C22×C22⋊D61C2×C411yescharacteristic
58C22×C22⋊D61C2311yescharacteristic
59C22×C4×D61D411yescharacteristic
60C22×C4×D61D411yescharacteristic
61#14519773—24no—
62#14519773—24no—
63#14519764—24no—
64#14519764—24no—
65#14519748—24no—
66#14519748—24no—
67#14519748—24no—
68#14519748—24no—
69#14519746—24no—
70#14519746—22no—
71#14519746—22no—
72#14519746C2×C414yes—
73#14519746C2×C418yescomplemented
74#14519746C2314yes—
75#14519736—22no—
76#14519736C2×C414yescomplemented
77C2×C4⋊Dic61—21no—
78C2×C22⋊Dic61—22no—
79C2×C22⋊Dic61—22no—
80C2×C22⋊Dic61C2×C412yes—
81C2×C4×Dic61—21no—
82C25×C61C2×C412yes—
83C22×D4×C61—21no—
84C22×D4×C61—21no—
85C22×D4×C61—22no—
86C22×D4×C61—42no—
87C22×D4×C61—41no—
88C22×D4×C61—41no—
89C22×D4×C61C2×C414yescomplemented
90C23×C4×C61C2×C411yescharacteristic
91C24×C61—22no—
92C24×C61—22no—
93C24×C61—42no—
94C24×C61—42no—
95C24×C61—84no—
96C24×C61C22×C411yescharacteristic
97C24×C61C22×C414yes—
98C23×D61C22⋊C411yescharacteristic
99C23×D61C2×D411yescharacteristic
100C22×#6923—42no—
101C2×D4×C61—24no—
102C2×D4×C61—24no—
103C2×D4×C61—42no—
104C2×D4×C61—42no—
105C2×D4×C61—44no—
106C2×D4×C61—44no—
107C2×D4×C61—44no—
108C2×D4×C61—44no—
109C2×D4×C61—42no—
110C2×D4×C61—41no—
111C2×D4×C61—41no—
112C22×C4×C61—22no—
113C22×C4×C61—21no—
114C22×C4×C61—21no—
115C22×C4×C61C22⋊C411yescharacteristic
116C22×C4×C61C22⋊C412yes—
117C22×C4×C61C22⋊C411yescharacteristic
118C22×C4×C61C22×C412yes—
119C2×C22⋊D61—24no—
120C2×C22⋊D61—28no—
121C2×C22⋊D61—24no—
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124C2×C22⋊D61—41no—
125C2×C22⋊D61—41no—
126C2×C22⋊D61—84no—
127C2×C22⋊D61—84no—
128C2×C22⋊D61C22⋊C412yes—
129C2×C22⋊D61C22×C412yes—
130C2×C22⋊D61C22×C411yescharacteristic
131C2×C22⋊D61C2×D411yescharacteristic
132C2×C22⋊D61C2×D411yescharacteristic
133C2×C22⋊D61C2411yescharacteristic
134C22×Dic61—22no—
135C22×Dic61C22⋊C411yescharacteristic
136C22×Dic61C2×D411yescharacteristic
137#11758222—42no—
138#11758222—42no—
139#11758222—42no—
140#11758222—42no—
141#11758222—42no—
142#11758222—42no—
143#11758222—42no—
144#11758222—42no—
145C2×D244—41no—
146C2×D244—41no—
147C2×D244C22⋊C412yes—
148C2×D244C2×D412yes—
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61—22no—
152C2×C4×D61—21no—
153C2×C4×D61—22no—
154C2×C4×D61—21no—
155C2×C4×D61C22⋊C412yes—
156C2×C4×D61C22⋊C412yes—
157C2×C4×D61C2×D412yes—
158C2×C4×D61C2×D412yes—
159C2×Dic122—41no—
160C2×Dic122—41no—
161C2×Dic122C22⋊C412yes—
162C2×Dic122C2×D412yes—
163C22⋊#6923—24no—
164C22⋊#6923—42no—
165#11758217—24no—
166#11758217—42no—
167C2×#92420—42no—
168C4⋊#6923—44no—
169C4×#6923—44no—
170#11758213—44no—
171D61⋊C8—44no—
172C22⋊Dic61—22no—
173C22⋊Dic61—24no—
174C22⋊Dic61—28no—
175C22⋊Dic61—24no—
176C22⋊Dic61C22×C414yes—
177C4⋊Dic61—24no—
178C4×Dic61—24no—
179C23×C61—21no—
180C23×C61—21no—
181C23×C61—24no—
182C23×C61—42no—
183C23×C61—44no—
184C23×C61—44no—
185C23×C61—44no—
186C23×C61—44no—
187C23×C61—42no—
188C23×C61—42no—
189C23×C61—84no—
190C23×C61—84no—
191C23×C61—88no—
192C23×C61—88no—
193C23×C61C2×C22⋊C411yescharacteristic
194C23×C61C2×C22⋊C411yescharacteristic
195C23×C61C23×C411yescharacteristic
196C22×D61—21no—
197C22×D61—21no—
198C22×D61—21no—
199C22×D61—21no—
200C22×D61—42no—
201C22×D61—42no—
202C22×D61C2×C22⋊C411yescharacteristic
203C22×D61C2×C22⋊C412yes—
204C22×D61C22×D411yescharacteristic
205C2×#6923—44no—
206C2×#6923—84no—
207D4×C61—48no—
208D4×C61—44no—
209D4×C61—44no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61#9912yes—
217C2×C4×C61#9911yescharacteristic
218C2×C4×C61#9911yescharacteristic
219C2×C4×C61C2×C22⋊C412yes—
220C2×C4×C61C2×C22⋊C412yes—
221C22⋊D61—42no—
222C22⋊D61—41no—
223C22⋊D61—42no—
224C22⋊D61—41no—
225C22⋊D61—41no—
226C22⋊D61—41no—
227C22⋊D61—84no—
228C22⋊D61—88no—
229C22⋊D61—84no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—24no—
235C2×Dic61—44no—
236C2×Dic61C2×C22⋊C411yescharacteristic
237C2×Dic61C2×C22⋊C412yes—
238C2×Dic61C22×D411yescharacteristic
239D244—42no—
240D244—42no—
241C4×D61—22no—
242C4×D61—22no—
243C4×D61—22no—
244C4×D61—22no—
245C4×D61—22no—
246C4×D61—22no—
247C4×D61—22no—
248C4×D61—22no—
249Dic122—42no—
250Dic122—42no—
251#92420—44no—
252C2×#2122—611nomaximal, Sylow
253C22×C61—22no—
254C22×C61—21no—
255C22×C61—21no—
256C22×C61—41no—
257C22×C61—41no—
258C22×C61—42no—
259C22×C61—44no—
260C22×C61—44no—
261C22×C61—42no—
262C22×C61—44no—
263C22×C61—84no—
264C22×C61—88no—
265C22×C61—88no—
266C22×C61—84no—
267C22×C61C2×#9911yescharacteristic
268C22×C61C2×#9911yescharacteristic
269C22×C61C22×C22⋊C411yescharacteristic
270C2×D61—21no—
271C2×D61—22no—
272C2×D61—21no—
273C2×D61—42no—
274C2×D61—42no—
275C2×D61—42no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—81no—
279C2×D61—81no—
280#6923—84no—
281C4×C61—22no—
282C4×C61C2×#9912yes—
283C4×C61C2×#9912yes—
284Dic61—21no—
285Dic61—21no—
286Dic61—22no—
287Dic61—44no—
288C2×#535—611no—
289C2×#413—611no—
290C2×#410—611no—
291#2122—618no—
292C2×AΣL(1,𝔽16)—614no—
293C2×C61—21no—
294C2×C61—21no—
295C2×C61—41no—
296C2×C61—41no—
297C2×C61—84no—
298C2×C61#212212yescomplemented
299C2×C61C22×#9911yescharacteristic
300D61—41no—
301D61—41no—
302D61—42no—
303C22×#41—611no—
304C23×D4#692311yescharacteristic, complemented
305C22×M16—1221no—
306#535—614no—
307#535—614no—
308#535—1222no—
309#535—1222no—
310C2×#127—1221no—
311C2×#124—1221no—
312C2×#121—1221no—
313C2×#121—1221no—
314C2×#120—612no—
315C2×#120—612no—
316C2×#117—611no—
317C2×#117—1221no—
318#413—614no—
319#413—1222no—
320C2×#101—1221no—
321C2×#100—612no—
322#410—614no—
323#410—1222no—
324C2×#99—612no—
325C2×#99—1221no—
326AΣL(1,𝔽16)—6116no—
327C61C2×#212211yescharacteristic, complemented, Sylow
328C25C2×#692312yes—
329C2×#41—612no—
330C2×#41—612no—
331C2×#41—612no—
332C2×#41—612no—
333C2×#41—2441no—
334C2×#41—2441no—
335C2×#41—2442no—
336C22×Q8—611no—
337C22×D4—21no—
338C22×D4—22no—
339C22×D4—21no—
340C22×D4—42no—
341C22×D4—41no—
342C22×D4—41no—
343C22×D4—611no—
344C22×D4—611no—
345C22×D4—611no—
346C22×D4—1222no—
347C22×D4—1222no—
348C22×D4C2×#692314yescomplemented
349C23×C4—611no—
350C23×C4—611no—
351C23×C4C2×#692311yescharacteristic
352C2×M16—1222no—
353C2×M16—1224no—
354C2×M16—2442no—
355C2×M16—2441no—
356C22×C8—2441no—
357#127—1224no—
358#127—1224no—
359#124—1224no—
360#124—1224no—
361#121—1224no—
362#121—1224no—
363#121—1224no—
364#121—1224no—
365#120—614no—
366#120—614no—
367#120—618no—
368#120—1222no—
369#120—1222no—
370#120—1224no—
371#117—614no—
372#117—1222no—
373#117—1224no—
374#117—2442no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—2441no—
377C2×C22⋊C4—612no—
378C2×C22⋊C4—1222no—
379C2×C22⋊C4—1222no—
380C2×C22⋊C4—1222no—
381C2×C42—1221no—
382C2×C42—2441no—
383#101—1224no—
384#100—614no—
385#100—1222no—
386#99—614no—
387#99—1222no—
388#99—1224no—
389C24—22no—
390C24—22no—
391C24—42no—
392C24—42no—
393C24—84no—
394C24—611no—
395C24—611no—
396C24C22×#692311yescharacteristic
397C24C22×#692314yes—
398#41—2442no—
399#41—2442no—
400#41—2442no—
401#41—2442no—
402#41—2442no—
403#41—2442no—
404#41—2442no—
405#41—2442no—
406C2×Q8—612no—
407C2×Q8—612no—
408C2×Q8—2441no—
409C2×Q8—2441no—
410C2×D4—24no—
411C2×D4—24no—
412C2×D4—42no—
413C2×D4—42no—
414C2×D4—44no—
415C2×D4—44no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—42no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—611no—
422C2×D4—611no—
423C2×D4—612no—
424C2×D4—611no—
425C2×D4—611no—
426C2×D4—612no—
427C2×D4—612no—
428C2×D4—612no—
429C2×D4—1224no—
430C2×D4—1228no—
431C2×D4—1224no—
432C2×D4—4884no—
433C2×D4—4884no—
434C2×D4—2441no—
435C2×D4—2441no—
436C2×D4—2441no—
437C2×D4—2441no—
438C2×D4—2441no—
439C2×D4—2441no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—612no—
446C22×C4—612no—
447C22×C4—612no—
448C22×C4—612no—
449C22×C4—1221no—
450C22×C4—1221no—
451C22×C4—1222no—
452C22×C4—1221no—
453C22×C4—1222no—
454C22×C4—1221no—
455C22×C4—1222no—
456C22×C4—2442no—
457C22×C4C22⋊#692311yescharacteristic
458C22×C4C22⋊#692312yes—
459C22×C4C22⋊#692311yescharacteristic
460C22×C4C22×#692312yes—
461M16—1224no—
462M16—2444no—
463M16—2442no—
464C2×C8—2444no—
465C2×C8—2442no—
466C4⋊C4—1224no—
467C4⋊C4—2444no—
468C22⋊C4—614no—
469C22⋊C4—1224no—
470C22⋊C4—1228no—
471C22⋊C4—1224no—
472C22⋊C4—1222no—
473C22⋊C4—1224no—
474C22⋊C4—2442no—
475C42—1224no—
476C42—2444no—
477C23—21no—
478C23—21no—
479C23—24no—
480C23—42no—
481C23—44no—
482C23—44no—
483C23—44no—
484C23—44no—
485C23—42no—
486C23—42no—
487C23—84no—
488C23—84no—
489C23—88no—
490C23—88no—
491C23—611no—
492C23—612no—
493C23—611no—
494C23—1221no—
495C23—1221no—
496C23—1221no—
497C23—1221no—
498C23—2442no—
499C23—2442no—
500C23C2×C22⋊#692311yescharacteristic
501C23C2×C22⋊#692311yescharacteristic
502C23C23×#692311yescharacteristic
503Q8—2442no—
504Q8—2442no—
505D4—48no—
506D4—44no—
507D4—44no—
508D4—4884no—
509D4—4884no—
510D4—4888no—
511D4—2442no—
512D4—2442no—
513D4—2441no—
514D4—2441no—
515D4—2441no—
516D4—2442no—
517D4—2441no—
518D4—2442no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—611no—
526C2×C4—612no—
527C2×C4—611no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1222no—
533C2×C4—1222no—
534C2×C4—1222no—
535C2×C4—1222no—
536C2×C4—1222no—
537C2×C4—1222no—
538C2×C4—1222no—
539C2×C4—1222no—
540C2×C4—1224no—
541C2×C4—4884no—
542C2×C4—2444no—
543C2×C4—2444no—
544C2×C4#1451983512yes—
545C2×C4#1451983511yescharacteristic
546C2×C4#1451983511yescharacteristic
547C2×C4C2×C22⋊#692312yes—
548C2×C4C2×C22⋊#692312yes—
549C8—2444no—
550C22—22no—
551C22—21no—
552C22—21no—
553C22—41no—
554C22—41no—
555C22—42no—
556C22—44no—
557C22—44no—
558C22—42no—
559C22—44no—
560C22—84no—
561C22—88no—
562C22—88no—
563C22—84no—
564C22—1221no—
565C22—1222no—
566C22—1221no—
567C22—4881no—
568C22—4881no—
569C22—2441no—
570C22—2441no—
571C22—2442no—
572C22—2442no—
573C22—2442no—
574C22C2×#1451983511yescharacteristic
575C22C2×#1451983511yescharacteristic
576C22C22×C22⋊#692311yescharacteristic
577C4—22no—
578C4—1221no—
579C4—1221no—
580C4—1222no—
581C4—4884no—
582C4—2444no—
583C4C2×#1451983512yes—
584C4C2×#1451983512yes—
585C2—21no—
586C2—21no—
587C2—41no—
588C2—41no—
589C2—84no—
590C2—2441no—
591C2—2441no—
592C2—2442no—
593C2#2146207812yesdirect product factor
594C2C22×#1451983511yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC23×D4×C61C4
socleC22×C61C2×#99
prime radicalC2×#16840329C2
cosocleC2×C22⋊D61C24
hypercenterC23×D4#6923
hypocenterC61C2×#2122
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16840748C2semidirect
2. C2×#16840741C2semidirect
3. #21462078C2direct (N × H)
4. C2×#16840662C2semidirect
9. #16840748C22semidirect
13. #16840741C22semidirect
16. #16840662C22semidirect
20. #16840329C4semidirect
26. C2×#14519746C4semidirect
28. C2×#14519736C4semidirect
29. C23×D4×C61C4semidirect
73. #14519746C2×C4semidirect
76. #14519736C2×C4semidirect
89. C22×D4×C61C2×C4semidirect
298. C2×C61#2122semidirect
304. C23×D4#6923semidirect
327. C61C2×#2122semidirect
348. C22×D4C2×#6923semidirect
593. C2#21462078direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407482
C2×#168407412
#214620782
C2×#168406622
C2×#168403292
C2×#212261