Finite Group Databasebeta

← C2×#21446748 #29684068

Subgroups — C2×#21446748 #29684068

Order 15616.

1814 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519766C211yesmaximal, characteristic
2C22×#14519706C211yesmaximal, characteristic, complemented
3C22×#14519701C211yesmaximal, characteristic, complemented
4C22×#14519699C211yesmaximal, characteristic
5C22×#14519697C211yesmaximal, characteristic
6C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
7#21446748C218yesmaximal, direct product factor
8C22×#103×C61C211yesmaximal, characteristic, complemented
9C23×D244C2211yescharacteristic
10C23×#92418C2211yescharacteristic
11C2×#14519766—22no—
12C2×#14519766—24no—
13C2×#14519766C418yescomplemented
14C2×#14519766C2214yes—
15C22×C4⋊Dic61C2211yescharacteristic
16C22×#11758198—21no—
17C22×#11758198—21no—
18C22×C4×Dic61—21no—
19C22×C4×Dic61C2211yescharacteristic
20C2×#14519706—24no—
21C2×#14519706C2214yescomplemented
22C2×#14519701—24no—
23C2×#14519701C2214yescomplemented
24C2×#14519699—24no—
25C2×#14519699C2214yes—
26C2×#14519697—24no—
27C2×#14519697C2214yes—
28C4⋊C4×Dic61—22no—
29C4⋊C4×Dic61C2214yescomplemented
30C2×#14519684—21no—
31C23×Q8×C61C2211yescharacteristic
32C23×C8×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C2×#103×C61—24no—
35C2×#103×C61C2214yescomplemented
36C24×D61—21no—
37C22×D244—22no—
38C22×D244—22no—
39C22×D244—22no—
40C22×D244—22no—
41C22×D244—21no—
42C22×D244—22no—
43C22×D244C2×C414yes—
44C22×D244C2312yes—
45C23×Dic61—21no—
46C23×Dic61D411yescharacteristic
47C23×Dic61D411yescharacteristic
48C22×#92418—22no—
49C22×#92418—22no—
50C22×#92418—22no—
51C22×#92418C2312yes—
52#14519766—216no—
53#14519766—28no—
54#14519766C2×C4116yescomplemented
55C2×C4⋊Dic61—21no—
56C2×C4⋊Dic61—22no—
57C2×C4⋊Dic61D414yes—
58C2×C4⋊Dic61C2312yes—
59C2×#11758198—28no—
60C2×#11758198—28no—
61C2×#11758198—24no—
62C2×#11758198—24no—
63C2×C4×Dic61—24no—
64C2×C4×Dic61—44no—
65C2×C4×Dic61C2×C414yes—
66C2×C4×Dic61D412yes—
67C2×C4×Dic61D414yes—
68C2×C4×Dic61C2312yes—
69#14519706—28no—
70#14519701—28no—
71#14519699—28no—
72#14519697—28no—
73#14519684—24no—
74C22×Q8×C61—22no—
75C22×Q8×C61—21no—
76C22×Q8×C61—22no—
77C22×Q8×C61—22no—
78C22×Q8×C61—22no—
79C22×Q8×C61—22no—
80C22×Q8×C61C2×C414yes—
81C22×Q8×C61C2312yes—
82C23×C4×C61—21no—
83C23×C4×C61—21no—
84C23×C4×C61C2311yescharacteristic
85C22×C8×C61—22no—
86C22×C8×C61—22no—
87C22×C8×C61—22no—
88C22×C8×C61C2312yes—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—22no—
91C2×C4⋊C4×C61D414yes—
92C2×C4⋊C4×C61C2312yes—
93#103×C61—28no—
94C24×C61C2×D411yescharacteristic
95C23×D61—24no—
96C23×D61—22no—
97C23×D61—42no—
98C23×D61—42no—
99C23×D61—42no—
100C23×D61—42no—
101C23×D61—42no—
102C23×D61—42no—
103C2×Q8×C61—24no—
104C2×Q8×C61—22no—
105C2×Q8×C61—28no—
106C2×Q8×C61—28no—
107C2×Q8×C61—22no—
108C2×Q8×C61—22no—
109C2×Q8×C61—22no—
110C2×Q8×C61—22no—
111C2×Q8×C61—42no—
112C2×Q8×C61—42no—
113C2×Q8×C61—44no—
114C2×Q8×C61—44no—
115C2×Q8×C61C22×C414yes—
116C22×C4×C61—24no—
117C22×C4×C61—24no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—42no—
121C22×C4×C61—42no—
122C22×C4×C61—42no—
123C22×C4×C61—42no—
124C22×C4×C61C22×C412yes—
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D412yes—
127C22×C4×C61C2×D412yes—
128C22×C4×C61C2×D412yes—
129C22×C4×C61#4112yes—
130C22×C4×C61#4112yes—
131C22×C4×C61C2411yescharacteristic
132C22×Dic61—22no—
133C22×Dic61—22no—
134C22×Dic61—22no—
135C22×Dic61—22no—
136C22×Dic61—24no—
137C22×Dic61—22no—
138C22×Dic61—42no—
139C22×Dic61—42no—
140C22×Dic61C22⋊C414yes—
141C22×Dic61C22⋊C414yes—
142C22×Dic61C2×D412yes—
143C22×Dic61C2×D412yes—
144C2×D244—28no—
145C2×D244—28no—
146C2×D244—22no—
147C2×D244—22no—
148C2×D244—22no—
149C2×D244—22no—
150C2×D244—24no—
151C2×D244—22no—
152C2×D244—42no—
153C2×D244—42no—
154C2×D244—44no—
155C2×D244—44no—
156C2×D244C22×C414yes—
157C2×C8×C61—22no—
158C2×C8×C61—22no—
159C2×C8×C61—22no—
160C2×C8×C61—44no—
161C4⋊C4×C61—24no—
162C4⋊C4×C61—22no—
163C4⋊C4×C61C2×D414yes—
164#11758198—216no—
165#11758198—216no—
166C4⋊Dic61—24no—
167C4⋊Dic61—22no—
168C4⋊Dic61C2×D414yes—
169C4×Dic61—48no—
170C4×Dic61C22⋊C418yes—
171C4×Dic61C22×C414yes—
172C4×Dic61C2×D414yes—
173C2×#92418—22no—
174C2×#92418—22no—
175C2×#92418—22no—
176C2×#92418—44no—
177C23×C61C2×C22⋊C412yes—
178C23×C61#12112yes—
179C23×C61#12112yes—
180C23×C61#13512yes—
181C23×C61#13512yes—
182C23×C61AGL(1,ℤ/8)12yes—
183C23×C61#13712yes—
184C23×C61C22×D411yescharacteristic
185C22×D61—24no—
186C22×D61—42no—
187C22×D61—42no—
188C22×D61—42no—
189C22×D61—42no—
190C22×D61—42no—
191C22×D61—42no—
192C22×D61—48no—
193C22×D61—48no—
194C22×D61—48no—
195C22×D61—84no—
196C22×D61—84no—
197C22×D61—84no—
198C22×D61—84no—
199Q8×C61—24no—
200Q8×C61—24no—
201Q8×C61—42no—
202Q8×C61—42no—
203Q8×C61—48no—
204C2×C4×C61—24no—
205C2×C4×C61—24no—
206C2×C4×C61—42no—
207C2×C4×C61—42no—
208C2×C4×C61—42no—
209C2×C4×C61—42no—
210C2×C4×C61—48no—
211C2×C4×C61—48no—
212C2×C4×C61C2×C22⋊C412yes—
213C2×C4×C61C4×D414yes—
214C2×C4×C61C4×D414yes—
215C2×C4×C61#12112yes—
216C2×C4×C61#12112yes—
217C2×C4×C61#12414yes—
218C2×C4×C61#12714yes—
219C2×C4×C61C23×C411yescharacteristic
220C2×C4×C61C22×D411yescharacteristic
221C2×C4×C61C22×D411yescharacteristic
222C2×C4×C61C22×D411yescharacteristic
223C2×C4×C61C2×#4111yescharacteristic
224C2×C4×C61C2×#4111yescharacteristic
225C2×Dic61—22no—
226C2×Dic61—22no—
227C2×Dic61—22no—
228C2×Dic61—22no—
229C2×Dic61—28no—
230C2×Dic61—28no—
231C2×Dic61—24no—
232C2×Dic61—42no—
233C2×Dic61—42no—
234C2×Dic61—48no—
235C2×Dic61C2×C22⋊C414yes—
236C2×Dic61C2×C22⋊C414yes—
237D244—24no—
238D244—24no—
239D244—42no—
240D244—42no—
241D244—48no—
242C8×C61—42no—
243#92418—42no—
244C2×#1983—611nomaximal, Sylow
245C22×C61#39014yes—
246C22×C61#41614yes—
247C22×C61#41714yes—
248C22×C61#46314yes—
249C22×C61#46314yes—
250C22×C61#46414yes—
251C22×C61#46414yes—
252C22×C61C22×C22⋊C411yescharacteristic
253C22×C61C2×#12111yescharacteristic
254C22×C61C2×#12111yescharacteristic
255C22×C61C2×#13511yescharacteristic
256C22×C61C2×#13511yescharacteristic
257C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
258C22×C61C2×#13711yescharacteristic
259C2×D61—44no—
260C2×D61—44no—
261C2×D61—44no—
262C2×D61—816no—
263C2×D61—82no—
264C2×D61—82no—
265C2×D61—82no—
266C2×D61—82no—
267C4×C61—44no—
268C4×C61—44no—
269C4×C61#39014yes—
270C4×C61C2×C4×D411yescharacteristic
271C4×C61C2×C4×D411yescharacteristic
272C4×C61C2×#12411yescharacteristic
273C4×C61C2×#12711yescharacteristic
274Dic61—24no—
275Dic61—24no—
276Dic61—44no—
277C22×#124—611no—
278C22×C4⋊C8—611no—
279C22×#103—611no—
280C22×#103D6111yescharacteristic, complemented
281C22×#102—611no—
282C22×#102—611no—
283C2×C4×C4⋊C4—611no—
284#1983—618no—
285C2×C61#198318yescomplemented
286C2×C61C2×#39011yescharacteristic
287C2×C61C2×#41611yescharacteristic
288C2×C61C2×#41711yescharacteristic
289C2×C61C2×#46311yescharacteristic
290C2×C61C2×#46311yescharacteristic
291C2×C61C2×#46411yescharacteristic
292C2×C61C2×#46411yescharacteristic
293D61—84no—
294C23×Q8C2×D6111yescharacteristic
295C23×D4—611no—
296C23×C8—611no—
297C23×C8C2×D6111yescharacteristic
298C2×#124—618no—
299C2×#124—614no—
300C2×#124—1222no—
301C2×#124—1224no—
302C22×C4⋊C4—611no—
303C22×C4⋊C4C2×D6111yescharacteristic
304C22×C22⋊C4—1221no—
305C22×C22⋊C4—1221no—
306C22×C42—611no—
307C22×C42—1221no—
308C2×C4⋊C8—614no—
309C2×C4⋊C8—1224no—
310C2×#103—24no—
311C2×#103—614no—
312C2×#103—1224no—
313C2×#103C2×D6114yescomplemented
314C2×#102—614no—
315C2×#102—614no—
316C2×#102—1224no—
317C2×#102—1224no—
318C4×C4⋊C4—614no—
319C4×C4⋊C4—1222no—
320C2×#95—1221no—
321C61C2×#198311yescharacteristic, complemented, Sylow
322C25—1221no—
323C22×Q8—21no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—22no—
329C22×Q8C4×D6114yes—
330C22×Q8C22×D6112yes—
331C22×D4—614no—
332C22×D4—612no—
333C22×D4—1222no—
334C22×D4—1222no—
335C22×D4—1222no—
336C22×D4—1221no—
337C22×D4—1222no—
338C22×D4—1222no—
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—611no—
342C23×C4—611no—
343C23×C4—1221no—
344C23×C4C22×D6111yescharacteristic
345C22×C8—22no—
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—612no—
349C22×C8—1222no—
350C22×C8—1222no—
351C22×C8—1222no—
352C22×C8C22×D6112yes—
353#124—6116no—
354#124—1228no—
355#124—12216no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—614no—
359C2×C4⋊C4—612no—
360C2×C4⋊C4—1222no—
361C2×C4⋊C4—1221no—
362C2×C4⋊C4C22⋊D6114yes—
363C2×C4⋊C4C22×D6112yes—
364C2×C22⋊C4—1224no—
365C2×C22⋊C4—1224no—
366C2×C22⋊C4—1228no—
367C2×C22⋊C4—1228no—
368C2×C42—614no—
369C2×C42—612no—
370C2×C42—614no—
371C2×C42—612no—
372C2×C42—1224no—
373C2×C42—2444no—
374C4⋊C8—1228no—
375#103—28no—
376#103—1228no—
377#102—1228no—
378#102—1228no—
379#95—1224no—
380C24—1222no—
381C24—1224no—
382C24—2442no—
383C24—2442no—
384C24—2442no—
385C24—2442no—
386C24—2442no—
387C24—2442no—
388C24D4×D6111yescharacteristic
389C2×Q8—22no—
390C2×Q8—24no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—28no—
396C2×Q8—28no—
397C2×Q8—42no—
398C2×Q8—42no—
399C2×Q8—44no—
400C2×Q8—44no—
401C2×Q8C2×C4×D6114yes—
402C2×D4—614no—
403C2×D4—1222no—
404C2×D4—1222no—
405C2×D4—1222no—
406C2×D4—1222no—
407C2×D4—1222no—
408C2×D4—1224no—
409C2×D4—1228no—
410C2×D4—1228no—
411C2×D4—2442no—
412C2×D4—2442no—
413C2×D4—2444no—
414C2×D4—2444no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—612no—
424C22×C4—612no—
425C22×C4—614no—
426C22×C4—614no—
427C22×C4—1222no—
428C22×C4—1222no—
429C22×C4—1222no—
430C22×C4—1222no—
431C22×C4—1222no—
432C22×C4—1224no—
433C22×C4—2442no—
434C22×C4—2442no—
435C22×C4C2×C4×D6112yes—
436C22×C4#1175822212yes—
437C22×C4D4×D6112yes—
438C22×C4D4×D6112yes—
439C22×C4D4×D6111yescharacteristic
440C22×C4#1175822412yes—
441C22×C4C2×C22⋊D6112yes—
442C22×C4C23×D6111yescharacteristic
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—44no—
447C2×C8—1222no—
448C2×C8—1222no—
449C2×C8—1222no—
450C2×C8—2444no—
451C4⋊C4—22no—
452C4⋊C4—24no—
453C4⋊C4—614no—
454C4⋊C4—1222no—
455C4⋊C4—1224no—
456C4⋊C4C2×C22⋊D6114yes—
457C22⋊C4—12216no—
458C22⋊C4—12216no—
459C42—614no—
460C42—614no—
461C42—618no—
462C42—2448no—
463C23—1224no—
464C23—4884no—
465C23—4884no—
466C23—4884no—
467C23—4884no—
468C23—2442no—
469C23—2442no—
470C23—2448no—
471C23—2448no—
472C23—2442no—
473C23—2442no—
474C23—2442no—
475C23—2442no—
476C23—2448no—
477C23C22⋊C4×D6112yes—
478C23#1451974912yes—
479C23#1451975012yes—
480C23#1451979812yes—
481C23#1451980012yes—
482C23#1451980412yes—
483C23#1451980912yes—
484C23C2×D4×D6111yescharacteristic
485Q8—24no—
486Q8—24no—
487Q8—42no—
488Q8—42no—
489Q8—48no—
490D4—1224no—
491D4—1224no—
492D4—2442no—
493D4—2442no—
494D4—2448no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—48no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—48no—
503C2×C4—614no—
504C2×C4—614no—
505C2×C4—1228no—
506C2×C4—1228no—
507C2×C4—1222no—
508C2×C4—1222no—
509C2×C4—1222no—
510C2×C4—1222no—
511C2×C4—1224no—
512C2×C4—2448no—
513C2×C4—2442no—
514C2×C4—2442no—
515C2×C4C22⋊C4×D6112yes—
516C2×C4#1451973714yes—
517C2×C4C4×C22⋊D6114yes—
518C2×C4#1451974912yes—
519C2×C4#1451975012yes—
520C2×C4#1451976314yes—
521C2×C4#1451977314yes—
522C2×C4C22×C4×D6111yescharacteristic
523C2×C4C2×D4×D6111yescharacteristic
524C2×C4C2×D4×D6111yescharacteristic
525C2×C4C22×C22⋊D6111yescharacteristic
526C2×C4C2×#1175822411yescharacteristic
527C2×C4C2×#1175822211yescharacteristic
528C8—42no—
529C8—2442no—
530C22—48816no—
531C22—4882no—
532C22—4882no—
533C22—4882no—
534C22—4882no—
535C22—2444no—
536C22—2444no—
537C22—2444no—
538C22#1683966214yes—
539C22#1683975714yes—
540C22#1683976214yes—
541C22#1683997914yes—
542C22#1683998014yes—
543C22#1683998614yes—
544C22#1683998714yes—
545C22C2×C22⋊C4×D6111yescharacteristic
546C22C2×#1451974911yescharacteristic
547C22C2×#1451975011yescharacteristic
548C22C2×#1451979811yescharacteristic
549C22C2×#1451980011yescharacteristic
550C22C2×#1451980411yescharacteristic
551C22C2×#1451980911yescharacteristic
552C4—44no—
553C4—44no—
554C4—1224no—
555C4—1224no—
556C4—2444no—
557C4#1683966214yes—
558C4C2×#1451973711yescharacteristic
559C4C2×C4×C22⋊D6111yescharacteristic
560C4C2×#1451976311yescharacteristic
561C4C2×#1451977311yescharacteristic
562C2—4884no—
563C2#2144674818yesdirect product factor
564C2C2×#1683966211yescharacteristic
565C2C2×#1683975711yescharacteristic
566C2C2×#1683976211yescharacteristic
567C2C2×#1683997911yescharacteristic
568C2C2×#1683998011yescharacteristic
569C2C2×#1683998611yescharacteristic
570C2C2×#1683998711yescharacteristic
subgroupG/H
centerC24D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×#103×C61C2
socleC24×C61C2×D4
prime radicalC23×D244C22
cosocleC22×C4×C61C24
hypercenterC22×#103D61
hypocenterC61C2×#1983
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C22×#14519706C2semidirect
3. C22×#14519701C2semidirect
6. C2×C4⋊C4×Dic61C2semidirect
7. #21446748C2direct (N × H)
8. C22×#103×C61C2semidirect
13. C2×#14519766C4semidirect
21. C2×#14519706C22semidirect
23. C2×#14519701C22semidirect
29. C4⋊C4×Dic61C22semidirect
35. C2×#103×C61C22semidirect
54. #14519766C2×C4semidirect
280. C22×#103D61semidirect
285. C2×C61#1983semidirect
313. C2×#103C2×D61semidirect
321. C61C2×#1983semidirect
563. C2#21446748direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197662
C22×#145197062
C22×#145197012
C22×#145196992
C22×#145196972
C2×C4⋊C4×Dic612
#214467482
C22×#103×C612
C2×#198361