Finite Group Databasebeta

← C2×#21462081 #30623916

Subgroups — C2×#21462081 #30623916

Order 15616.

1214 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840748C211yesmaximal, characteristic
2C2×#16840741C211yesmaximal, characteristic
3#21462081C218yesmaximal, direct product factor
4C2×#16840664C214yesmaximal, complemented
5C2×#16840336C211yesmaximal, characteristic
6C2×D61⋊M16—21no—
7C2×#14519856—21no—
8#16840748—22no—
9#16840748C2214yes—
10C2×#14519838—21no—
11C2×#14519837C2212yes—
12#16840741—22no—
13#16840741C2214yes—
14C2×#14519836—21no—
15C2×#14519835C2212yes—
16#16840664C22116yescomplemented
17C22×#11758222C2211yescharacteristic
18#16840336—22no—
19#16840336—22no—
20#16840336C414yescomplemented
21#16840336C2214yes—
22C2×#14519775—21no—
23C2×#14519766—21no—
24C2×#14519760C412yescomplemented
25C2×#14519760C2212yes—
26C2×#14519753—21no—
27C2×#14519753—21no—
28C2×#14519736C411yescharacteristic, complemented
29C23×Q8×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⋊D61C2×C411yescharacteristic
56C22×C22⋊D61C2311yescharacteristic
57C22×C4×D61D411yescharacteristic
58C22×C4×D61D411yescharacteristic
59#14519775—24no—
60#14519775—24no—
61#14519766—24no—
62#14519766—24no—
63#14519760—24no—
64#14519760—22no—
65#14519760—22no—
66#14519760C2×C414yes—
67#14519760C2×C418yescomplemented
68#14519760C2314yes—
69#14519753—24no—
70#14519753—24no—
71#14519753—24no—
72#14519753—24no—
73#14519736—22no—
74#14519736C2×C414yescomplemented
75C2×C4⋊Dic61—21no—
76C2×#11758196—22no—
77C2×#11758196—22no—
78C2×C22⋊Dic61C2×C412yes—
79C2×#11758198—22no—
80C2×#11758198—22no—
81C2×C4×Dic61—21no—
82C22×Q8×C61—21no—
83C22×Q8×C61—21no—
84C22×Q8×C61—22no—
85C22×Q8×C61—42no—
86C22×Q8×C61—41no—
87C22×Q8×C61—41no—
88C22×Q8×C61C2×C414yescomplemented
89C23×C4×C61C2×C412yes—
90C23×C4×C61C2×C411yescharacteristic
91C24×C61C22×C411yescharacteristic
92C23×D61C22⋊C411yescharacteristic
93C23×D61C2×D411yescharacteristic
94C22×#6923—42no—
95C2×Q8×C61—24no—
96C2×Q8×C61—24no—
97C2×Q8×C61—42no—
98C2×Q8×C61—42no—
99C2×Q8×C61—44no—
100C2×Q8×C61—44no—
101C2×Q8×C61—44no—
102C2×Q8×C61—44no—
103C2×Q8×C61—42no—
104C2×Q8×C61—41no—
105C2×Q8×C61—41no—
106C22×C4×C61—22no—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—42no—
112C22×C4×C61—42no—
113C22×C4×C61C22⋊C411yescharacteristic
114C22×C4×C61C22⋊C412yes—
115C22×C4×C61C22⋊C411yescharacteristic
116C22×C4×C61C22×C412yes—
117C22×C4×C61C22×C414yes—
118C2×C22⋊D61—41no—
119C2×C22⋊D61—41no—
120C2×C22⋊D61—41no—
121C2×C22⋊D61—41no—
122C2×C22⋊D61C22⋊C412yes—
123C2×C22⋊D61C22×C412yes—
124C2×C22⋊D61C22×C411yescharacteristic
125C2×C22⋊D61C2×D411yescharacteristic
126C2×C22⋊D61C2×D411yescharacteristic
127C2×C22⋊D61C2411yescharacteristic
128C22×Dic61—22no—
129C22×Dic61C22⋊C411yescharacteristic
130C22×Dic61C2×D411yescharacteristic
131#11758222—42no—
132#11758222—42no—
133#11758222—42no—
134#11758222—42no—
135#11758222—42no—
136#11758222—42no—
137#11758222—42no—
138#11758222—42no—
139C2×D244—41no—
140C2×D244—41no—
141C2×D244C22⋊C412yes—
142C2×D244C2×D412yes—
143C2×C4×D61—21no—
144C2×C4×D61—21no—
145C2×C4×D61—22no—
146C2×C4×D61—21no—
147C2×C4×D61—22no—
148C2×C4×D61—21no—
149C2×C4×D61C22⋊C412yes—
150C2×C4×D61C22⋊C412yes—
151C2×C4×D61C2×D412yes—
152C2×C4×D61C2×D412yes—
153C2×Dic122—41no—
154C2×Dic122—41no—
155C2×Dic122C22⋊C412yes—
156C2×Dic122C2×D412yes—
157C22⋊#6923—24no—
158C22⋊#6923—42no—
159#11758217—24no—
160#11758217—42no—
161C2×#92420—42no—
162C4⋊#6923—44no—
163C4×#6923—44no—
164#11758213—44no—
165D61⋊C8—44no—
166C22⋊Dic61—22no—
167C22⋊Dic61C22×C414yes—
168#11758198—24no—
169#11758198—28no—
170#11758198—24no—
171C4⋊Dic61—24no—
172#11758196—24no—
173#11758196—28no—
174#11758196—24no—
175C4×Dic61—24no—
176C23×C61—21no—
177C23×C61—21no—
178C23×C61—42no—
179C23×C61C2×C22⋊C411yescharacteristic
180C23×C61C2×C22⋊C411yescharacteristic
181C23×C61C23×C411yescharacteristic
182C22×D61—21no—
183C22×D61—21no—
184C22×D61—21no—
185C22×D61—21no—
186C22×D61—42no—
187C22×D61—42no—
188C22×D61C2×C22⋊C411yescharacteristic
189C22×D61C2×C22⋊C412yes—
190C22×D61C22×D411yescharacteristic
191C2×#6923—44no—
192C2×#6923—84no—
193Q8×C61—48no—
194Q8×C61—44no—
195Q8×C61—44no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—22no—
201C2×C4×C61—22no—
202C2×C4×C61—24no—
203C2×C4×C61—44no—
204C2×C4×C61—42no—
205C2×C4×C61—42no—
206C2×C4×C61—44no—
207C2×C4×C61#9912yes—
208C2×C4×C61#9911yescharacteristic
209C2×C4×C61#9911yescharacteristic
210C2×C4×C61C2×C22⋊C412yes—
211C2×C4×C61C2×C22⋊C412yes—
212C22⋊D61—42no—
213C22⋊D61—41no—
214C22⋊D61—42no—
215C22⋊D61—41no—
216C22⋊D61—41no—
217C22⋊D61—41no—
218C2×Dic61—21no—
219C2×Dic61—21no—
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—24no—
223C2×Dic61—44no—
224C2×Dic61C2×C22⋊C411yescharacteristic
225C2×Dic61C2×C22⋊C412yes—
226C2×Dic61C22×D411yescharacteristic
227D244—42no—
228D244—42no—
229C4×D61—22no—
230C4×D61—22no—
231C4×D61—22no—
232C4×D61—22no—
233C4×D61—22no—
234C4×D61—22no—
235C4×D61—22no—
236C4×D61—22no—
237Dic122—42no—
238Dic122—42no—
239#92420—44no—
240C2×#2123—611nomaximal, Sylow
241C22×C61—22no—
242C22×C61—21no—
243C22×C61—21no—
244C22×C61—41no—
245C22×C61—41no—
246C22×C61—42no—
247C22×C61—42no—
248C22×C61C2×#9911yescharacteristic
249C22×C61C2×#9911yescharacteristic
250C22×C61C22×C22⋊C411yescharacteristic
251C2×D61—21no—
252C2×D61—22no—
253C2×D61—21no—
254C2×D61—42no—
255C2×D61—42no—
256C2×D61—42no—
257C2×D61—41no—
258C2×D61—41no—
259C2×D61—81no—
260C2×D61—81no—
261#6923—84no—
262C4×C61—22no—
263C4×C61—44no—
264C4×C61C2×#9912yes—
265C4×C61C2×#9912yes—
266Dic61—21no—
267Dic61—21no—
268Dic61—22no—
269Dic61—44no—
270C2×#536—611no—
271C2×#413—611no—
272C2×#410—611no—
273#2123—618no—
274C2×#352—614no—
275C2×C61—21no—
276C2×C61—21no—
277C2×C61—41no—
278C2×C61—41no—
279C2×C61#212312yescomplemented
280C2×C61C22×#9911yescharacteristic
281D61—41no—
282D61—41no—
283D61—42no—
284C22×#41—611no—
285C23×Q8#692311yescharacteristic, complemented
286C22×M16—1221no—
287#536—614no—
288#536—614no—
289#536—1222no—
290#536—1222no—
291C2×C4⋊Q8—1221no—
292C2×#124—1221no—
293C2×#123—612no—
294C2×#123—612no—
295C2×C22⋊Q8—1221no—
296C2×C22⋊Q8—1221no—
297C2×#117—611no—
298C2×#117—1221no—
299#413—614no—
300#413—1222no—
301C2×#101—1221no—
302C2×#100—612no—
303#410—614no—
304#410—1222no—
305C2×#99—612no—
306C2×#99—1221no—
307#352—6116no—
308C61C2×#212311yescharacteristic, complemented, Sylow
309C2×#41—612no—
310C2×#41—612no—
311C2×#41—612no—
312C2×#41—612no—
313C2×#41—2441no—
314C2×#41—2441no—
315C2×#41—2442no—
316C22×Q8—21no—
317C22×Q8—22no—
318C22×Q8—21no—
319C22×Q8—42no—
320C22×Q8—41no—
321C22×Q8—41no—
322C22×Q8—611no—
323C22×Q8C2×#692314yescomplemented
324C22×D4—611no—
325C22×D4—611no—
326C22×D4—611no—
327C23×C4—611no—
328C23×C4—611no—
329C23×C4C2×#692312yes—
330C23×C4C2×#692311yescharacteristic
331C2×M16—1222no—
332C2×M16—1224no—
333C2×M16—2442no—
334C2×M16—2441no—
335C22×C8—2441no—
336C4⋊Q8—1224no—
337C4⋊Q8—1224no—
338#124—1224no—
339#124—1224no—
340#123—614no—
341#123—614no—
342#123—618no—
343#123—1222no—
344#123—1222no—
345#123—1224no—
346C22⋊Q8—1224no—
347C22⋊Q8—1224no—
348C22⋊Q8—1224no—
349C22⋊Q8—1224no—
350#117—614no—
351#117—1222no—
352#117—1224no—
353#117—2442no—
354C2×C4⋊C4—1222no—
355C2×C4⋊C4—1222no—
356C2×C4⋊C4—1221no—
357C2×C4⋊C4—2441no—
358C2×C22⋊C4—612no—
359C2×C22⋊C4—1222no—
360C2×C22⋊C4—1222no—
361C2×C22⋊C4—1222no—
362C2×C42—1221no—
363C2×C42—2441no—
364#101—1224no—
365#100—614no—
366#100—1222no—
367#99—614no—
368#99—1222no—
369#99—1224no—
370C24—611no—
371C24—611no—
372C24C22×#692311yescharacteristic
373#41—2442no—
374#41—2442no—
375#41—2442no—
376#41—2442no—
377#41—2442no—
378#41—2442no—
379#41—2442no—
380#41—2442no—
381C2×Q8—24no—
382C2×Q8—24no—
383C2×Q8—44no—
384C2×Q8—44no—
385C2×Q8—42no—
386C2×Q8—42no—
387C2×Q8—44no—
388C2×Q8—44no—
389C2×Q8—42no—
390C2×Q8—41no—
391C2×Q8—41no—
392C2×Q8—612no—
393C2×Q8—612no—
394C2×Q8—2441no—
395C2×Q8—2441no—
396C2×D4—611no—
397C2×D4—611no—
398C2×D4—612no—
399C2×D4—611no—
400C2×D4—611no—
401C2×D4—612no—
402C2×D4—612no—
403C2×D4—612no—
404C2×D4—2441no—
405C2×D4—2441no—
406C2×D4—2441no—
407C2×D4—2441no—
408C2×D4—2441no—
409C2×D4—2441no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—611no—
418C22×C4—611no—
419C22×C4—612no—
420C22×C4—612no—
421C22×C4—612no—
422C22×C4—612no—
423C22×C4—1221no—
424C22×C4—1221no—
425C22×C4—1222no—
426C22×C4—1221no—
427C22×C4—1222no—
428C22×C4—1221no—
429C22×C4—1222no—
430C22×C4—2442no—
431C22×C4C22⋊#692311yescharacteristic
432C22×C4C22⋊#692312yes—
433C22×C4C22⋊#692311yescharacteristic
434C22×C4C22×#692312yes—
435C22×C4C22×#692314yes—
436M16—1224no—
437M16—2444no—
438M16—2442no—
439C2×C8—2444no—
440C2×C8—2442no—
441C4⋊C4—1224no—
442C4⋊C4—1228no—
443C4⋊C4—1224no—
444C4⋊C4—1224no—
445C4⋊C4—2444no—
446C22⋊C4—614no—
447C22⋊C4—1224no—
448C22⋊C4—1228no—
449C22⋊C4—1224no—
450C22⋊C4—1222no—
451C22⋊C4—1224no—
452C22⋊C4—2442no—
453C42—1224no—
454C42—2444no—
455C23—21no—
456C23—21no—
457C23—42no—
458C23—611no—
459C23—612no—
460C23—611no—
461C23—1221no—
462C23—1221no—
463C23—1221no—
464C23—1221no—
465C23—2442no—
466C23—2442no—
467C23C2×C22⋊#692311yescharacteristic
468C23C2×C22⋊#692311yescharacteristic
469C23C23×#692311yescharacteristic
470Q8—48no—
471Q8—44no—
472Q8—44no—
473Q8—2442no—
474Q8—2442no—
475D4—2442no—
476D4—2442no—
477D4—2441no—
478D4—2441no—
479D4—2441no—
480D4—2442no—
481D4—2441no—
482D4—2442no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—44no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—44no—
494C2×C4—611no—
495C2×C4—612no—
496C2×C4—611no—
497C2×C4—1221no—
498C2×C4—1221no—
499C2×C4—1221no—
500C2×C4—1221no—
501C2×C4—1222no—
502C2×C4—1222no—
503C2×C4—1222no—
504C2×C4—1222no—
505C2×C4—1222no—
506C2×C4—1222no—
507C2×C4—1222no—
508C2×C4—1222no—
509C2×C4—1224no—
510C2×C4—4884no—
511C2×C4—2444no—
512C2×C4—2444no—
513C2×C4#1451983512yes—
514C2×C4#1451983511yescharacteristic
515C2×C4#1451983511yescharacteristic
516C2×C4C2×C22⋊#692312yes—
517C2×C4C2×C22⋊#692312yes—
518C8—2444no—
519C22—22no—
520C22—21no—
521C22—21no—
522C22—41no—
523C22—41no—
524C22—42no—
525C22—42no—
526C22—1221no—
527C22—1222no—
528C22—1221no—
529C22—4881no—
530C22—4881no—
531C22—2441no—
532C22—2441no—
533C22—2442no—
534C22—2442no—
535C22—2442no—
536C22C2×#1451983511yescharacteristic
537C22C2×#1451983511yescharacteristic
538C22C22×C22⋊#692311yescharacteristic
539C4—22no—
540C4—44no—
541C4—1221no—
542C4—1221no—
543C4—1222no—
544C4—4884no—
545C4—2444no—
546C4C2×#1451983512yes—
547C4C2×#1451983512yes—
548C2—21no—
549C2—21no—
550C2—41no—
551C2—41no—
552C2—2441no—
553C2—2441no—
554C2—2442no—
555C2#2146208112yesdirect product factor
556C2C22×#1451983511yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC23×Q8×C61C4
socleC22×C61C2×#99
prime radicalC22×#11758222C22
cosocleC2×C22⋊D61C24
hypercenterC23×Q8#6923
hypocenterC61C2×#2123
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
3. #21462081C2direct (N × H)
4. C2×#16840664C2semidirect
16. #16840664C22semidirect
20. #16840336C4semidirect
24. C2×#14519760C4semidirect
28. C2×#14519736C4semidirect
29. C23×Q8×C61C4semidirect
67. #14519760C2×C4semidirect
74. #14519736C2×C4semidirect
88. C22×Q8×C61C2×C4semidirect
279. C2×C61#2123semidirect
285. C23×Q8#6923semidirect
308. C61C2×#2123semidirect
323. C22×Q8C2×#6923semidirect
555. C2#21462081direct (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
#214620812
C2×#168406642
C2×#168403362
C2×#212361