Finite Group Databasebeta

← C2×#21444905 #29655707

Subgroups — C2×#21444905 #29655707

Order 15616.

1322 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840415C211yesmaximal, characteristic, complemented
2C2×#16839954C211yesmaximal, characteristic, complemented
3C2×#16839954C211yesmaximal, characteristic, complemented
4#21444905C218yesmaximal, direct product factor
5C2×#16839508C211yesmaximal, characteristic, complemented
6C2×#16839491C211yesmaximal, characteristic, complemented
7C2×#16839491C211yesmaximal, characteristic, complemented
8C2×C61×#486C211yesmaximal, characteristic, complemented
9C22×#11758226—21no—
10C22×#11758199—21no—
11C22×#11758199—21no—
12#16840415—22no—
13#16840415—22no—
14#16840415—22no—
15#16840415C2214yescomplemented
16C2×#14519762—22no—
17C2×#14519753—21no—
18C2×#14519752—21no—
19C2×C4×D244C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C4⋊C4×D61—21no—
22#16839954—22no—
23#16839954—22no—
24#16839954C2214yescomplemented
25#16839954C2214yescomplemented
26C2×C4⋊#92418C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519698—21no—
29C2×#14519698—21no—
30#16839508C2214yescomplemented
31#16839491C2214yescomplemented
32#16839491C2214yescomplemented
33C2×C4⋊Q8×C61C2211yescharacteristic
34C2×#127×C61C2211yescharacteristic
35C61×#486—22no—
36C61×#486C2214yescomplemented
37C2×#102×C61—22no—
38C2×C4×C8×C61C2211yescharacteristic
39C2×#11758226—24no—
40C2×#11758226—24no—
41C2×#11758226—44no—
42C2×#11758226—44no—
43C22×D244—22no—
44C22×D244D411yescharacteristic
45C22×D244D411yescharacteristic
46C22×C4×D61—22no—
47C22×C4×D61—21no—
48C22×C4×D61—21no—
49C2×#11758199—24no—
50C2×#11758199—24no—
51C2×#11758199—44no—
52C2×#11758199—44no—
53C22×#92418—21no—
54C22×#92418—21no—
55#14519762—28no—
56#14519762—28no—
57#14519753—24no—
58#14519753—24no—
59#14519752—24no—
60#14519752—24no—
61C4×D244—21no—
62C4×D244—21no—
63C4×D244—21no—
64C4×D244—21no—
65C4×D244D412yes—
66C4×D244D412yes—
67C4×D244C2312yes—
68C4×D244C2312yes—
69C2×C4⋊Dic61D411yescharacteristic
70C2×C4⋊Dic61D411yescharacteristic
71C2×#11758196—22no—
72C4⋊C4×D61—24no—
73C4⋊C4×D61—24no—
74C2×#11758198—22no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C4⋊#92418—21no—
78C4⋊#92418—21no—
79C4⋊#92418C2312yes—
80C4⋊#92418C2312yes—
81#14519698—24no—
82#14519698—24no—
83C22×Q8×C61—21no—
84C22×D4×C61—21no—
85C22×D4×C61—21no—
86C22×D4×C61—21no—
87C22×C8×C61—21no—
88C4⋊Q8×C61—21no—
89C4⋊Q8×C61—21no—
90C4⋊Q8×C61D412yes—
91C4⋊Q8×C61C2312yes—
92#127×C61—21no—
93#127×C61—21no—
94#127×C61—21no—
95#127×C61C2312yes—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61D412yes—
98C2×C42×C61C2311yescharacteristic
99#102×C61—28no—
100C4×C8×C61—21no—
101C4×C8×C61C2312yes—
102C24×C61—41no—
103C23×D61—21no—
104C23×D61—21no—
105C2×Q8×C61—22no—
106C2×Q8×C61—22no—
107C2×Q8×C61—42no—
108C2×Q8×C61—42no—
109C2×D4×C61—22no—
110C2×D4×C61—22no—
111C2×D4×C61—22no—
112C2×D4×C61—44no—
113C2×D4×C61—41no—
114C2×D4×C61—41no—
115C2×D4×C61—41no—
116C2×D4×C61—42no—
117C2×D4×C61—42no—
118C2×D4×C61—42no—
119C2×D4×C61—42no—
120C22×C4×C61—22no—
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×Dic61—21no—
125C22×Dic61—21no—
126#11758226—48no—
127#11758226—416no—
128#11758226—48no—
129C2×D244—21no—
130C2×D244—22no—
131C2×D244—22no—
132C2×D244—22no—
133C2×D244—28no—
134C2×D244—21no—
135C2×D244—48no—
136C2×D244D814yescomplemented
137C2×D244C2×D412yes—
138C2×D244C2×D412yes—
139C2×C4×D61—28no—
140C2×C4×D61—22no—
141C2×C4×D61—22no—
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—48no—
145C2×C4×D61—42no—
146C2×C4×D61—42no—
147C2×C4×D61—42no—
148C2×C4×D61—42no—
149C2×C8×C61—22no—
150C2×C8×C61—42no—
151C4⋊C4×C61—22no—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61C2×D414yes—
155C42×C61C2×D411yescharacteristic
156C42×C61C2×D411yescharacteristic
157C42×C61C2×D411yescharacteristic
158C42×C61C2411yescharacteristic
159#11758199—48no—
160#11758199—48no—
161#11758198—28no—
162#11758198—22no—
163#11758198—22no—
164#11758198—22no—
165#11758198—22no—
166C4⋊Dic61—21no—
167C4⋊Dic61—21no—
168C4⋊Dic61C2×D412yes—
169C4⋊Dic61C2×D412yes—
170#11758196—28no—
171C2×#92418—22no—
172C2×#92418—22no—
173C2×#92418—42no—
174C2×#92418—42no—
175C23×C61—42no—
176C23×C61—82no—
177C23×C61—82no—
178C23×C61—82no—
179C23×C61#12011yescharacteristic
180C22×D61—22no—
181C22×D61—24no—
182C22×D61—22no—
183C22×D61—42no—
184C22×D61—42no—
185C22×D61—42no—
186C22×D61—42no—
187C22×D61—42no—
188Q8×C61—42no—
189Q8×C61—42no—
190Q8×C61—44no—
191D4×C61—44no—
192D4×C61—42no—
193D4×C61—42no—
194D4×C61—42no—
195D4×C61—42no—
196D4×C61—82no—
197D4×C61—82no—
198D4×C61—82no—
199C2×C4×C61—22no—
200C2×C4×C61—24no—
201C2×C4×C61—44no—
202C2×C4×C61#12011yescharacteristic
203C2×C4×C61#12011yescharacteristic
204C2×C4×C61#12011yescharacteristic
205C2×C4×C61C2×D812yes—
206C2×C4×C61#13512yes—
207C2×C4×C61AGL(1,ℤ/8)12yes—
208C2×C4×C61AGL(1,ℤ/8)12yes—
209C2×C4×C61C22×D411yescharacteristic
210C2×C4×C61C22×D411yescharacteristic
211C2×C4×C61C22×D411yescharacteristic
212C2×Dic61—22no—
213C2×Dic61—22no—
214C2×Dic61—42no—
215C2×Dic61—42no—
216D244—22no—
217D244—22no—
218D244—22no—
219D244—24no—
220D244—416no—
221D244—42no—
222D244C2×D814yescomplemented
223C4×D61—416no—
224C4×D61—42no—
225C4×D61—42no—
226C4×D61—42no—
227C4×D61—42no—
228C4×D61—44no—
229C4×D61—44no—
230C8×C61—42no—
231#92418—42no—
232#92418—42no—
233C2×#1625—611nomaximal, Sylow
234C22×C61—82no—
235C22×C61—82no—
236C22×C61—82no—
237C22×C61—164no—
238C22×C61#44712yes—
239C22×C61#44912yes—
240C22×C61#45412yes—
241C22×C61C2×#12011yescharacteristic
242C2×D61—24no—
243C2×D61—48no—
244C2×D61—42no—
245C2×D61—42no—
246C2×D61—42no—
247C2×D61—42no—
248C2×D61—42no—
249C2×D61—84no—
250C4×C61—21no—
251C4×C61—21no—
252C4×C61—44no—
253C4×C61#44712yes—
254C4×C61#44912yes—
255C4×C61C22×D811yescharacteristic
256C4×C61C2×#13511yescharacteristic
257C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
258C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
259Dic61—42no—
260Dic61—42no—
261C2×#547—611no—
262C2×#486D6111yescharacteristic, complemented
263C2×#459—611no—
264C2×#459—611no—
265#1625—618no—
266C2×#332—611no—
267C2×D4⋊C8—611no—
268C2×D4⋊C8—611no—
269C2×C61—162no—
270C2×C61#162514yescomplemented
271C2×C61C2×#44711yescharacteristic
272C2×C61C2×#44911yescharacteristic
273C2×C61C2×#45411yescharacteristic
274D61—44no—
275D61—82no—
276C22×#41—1221no—
277C22×D8—1221no—
278C22×D8—1221no—
279#547—614no—
280#547—1222no—
281#547—1222no—
282#547—1222no—
283C2×C4⋊Q8C2×D6111yescharacteristic
284C2×#127C2×D6111yescharacteristic
285C2×#123—1222no—
286C2×C22⋊Q8—1221no—
287C2×#121—1221no—
288C2×C4×D4—611no—
289C2×C4×D4—611no—
290C22×C4⋊C4—1221no—
291#486—22no—
292#486C2×D6114yescomplemented
293#459—614no—
294#459—614no—
295#459—1222no—
296#459—1222no—
297C2×C4⋊C8—611no—
298C2×C4⋊C8—611no—
299C2×#102—22no—
300C2×#102—1221no—
301C2×#102—1221no—
302C2×C4×C8C2×D6111yescharacteristic
303#332—614no—
304D4⋊C8—614no—
305D4⋊C8—614no—
306C61C2×#162511yescharacteristic, complemented, Sylow
307C2×#41—1224no—
308C2×#41—1224no—
309C2×#41—2444no—
310C2×#41—2444no—
311C22×Q8—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—611no—
316C22×D4—611no—
317C22×D4—1222no—
318C23×C4—1222no—
319C23×C4—1221no—
320C23×C4—1221no—
321C2×D8—1224no—
322C2×D8—1224no—
323C2×D8—2444no—
324C2×D8—2444no—
325C22×C8—21no—
326C22×C8—1221no—
327C22×C8—1221no—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8C22⋊D6112yes—
331C4⋊Q8C22×D6112yes—
332#127—21no—
333#127—21no—
334#127—21no—
335#127C22×D6112yes—
336#123—1228no—
337#123—1228no—
338C22⋊Q8—1224no—
339C22⋊Q8—1224no—
340#121—1224no—
341#121—1224no—
342C4×D4—612no—
343C4×D4—612no—
344C4×D4—612no—
345C4×D4—612no—
346C4×D4—1221no—
347C4×D4—1221no—
348C4×D4—1221no—
349C4×D4—1221no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—611no—
352C2×C4⋊C4—611no—
353C2×C4⋊C4—1224no—
354C2×C4⋊C4—1224no—
355C2×C4⋊C4—1222no—
356C2×C4⋊C4C22⋊D6112yes—
357C2×C22⋊C4—1222no—
358C2×C22⋊C4—1221no—
359C2×C22⋊C4—1221no—
360C2×C42C22×D6111yescharacteristic
361C4⋊C8—612no—
362C4⋊C8—612no—
363C4⋊C8—1221no—
364C4⋊C8—1221no—
365#102—28no—
366#102—1224no—
367#102—1224no—
368C4×C8—21no—
369C4×C8C22×D6112yes—
370C24—41no—
371C24—1221no—
372C24—1221no—
373#41—2448no—
374#41—2448no—
375#41—24416no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—42no—
379C2×Q8—42no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—44no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—42no—
391C2×D4—612no—
392C2×D4—612no—
393C2×D4—614no—
394C2×D4—1228no—
395C2×D4—1221no—
396C2×D4—1221no—
397C2×D4—1222no—
398C2×D4—1222no—
399C2×D4—1222no—
400C2×D4—2448no—
401C22×C4—22no—
402C22×C4—1228no—
403C22×C4—1221no—
404C22×C4—1221no—
405C22×C4—1222no—
406C22×C4—1222no—
407C22×C4—1222no—
408C22×C4—1222no—
409C22×C4—2448no—
410C22×C4—2442no—
411C22×C4—2442no—
412C22×C4—2442no—
413C22×C4—2442no—
414C22×C4D4×D6111yescharacteristic
415C22×C4D4×D6111yescharacteristic
416C22×C4C2×C22⋊D6111yescharacteristic
417D8—2448no—
418D8—2448no—
419C2×C8—22no—
420C2×C8—42no—
421C2×C8—1222no—
422C2×C8—1222no—
423C2×C8—2442no—
424C2×C8—2442no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—612no—
429C4⋊C4—612no—
430C4⋊C4—1228no—
431C4⋊C4—1221no—
432C4⋊C4—1221no—
433C4⋊C4C2×C22⋊D6114yes—
434C22⋊C4—1228no—
435C22⋊C4—1222no—
436C22⋊C4—1222no—
437C22⋊C4—1222no—
438C22⋊C4—1222no—
439C42D4×D6111yescharacteristic
440C42D4×D6111yescharacteristic
441C42C2×C22⋊D6111yescharacteristic
442C42C23×D6111yescharacteristic
443C23—42no—
444C23—82no—
445C23—82no—
446C23—82no—
447C23—1222no—
448C23—1224no—
449C23—1222no—
450C23—2442no—
451C23—2442no—
452C23—2442no—
453C23—2442no—
454C23—2442no—
455C23#1451974511yescharacteristic
456Q8—42no—
457Q8—42no—
458Q8—44no—
459D4—44no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—42no—
464D4—82no—
465D4—82no—
466D4—82no—
467D4—614no—
468D4—1222no—
469D4—1222no—
470D4—1222no—
471D4—1224no—
472D4—24416no—
473D4—2442no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—44no—
477C2×C4—1222no—
478C2×C4—1222no—
479C2×C4—24416no—
480C2×C4—2442no—
481C2×C4—2442no—
482C2×C4—2442no—
483C2×C4—2442no—
484C2×C4—2442no—
485C2×C4—2442no—
486C2×C4—2444no—
487C2×C4—2444no—
488C2×C4#1451974511yescharacteristic
489C2×C4#1451974511yescharacteristic
490C2×C4#1451974511yescharacteristic
491C2×C4D8×D6112yes—
492C2×C4#1451979812yes—
493C2×C4#1451980112yes—
494C2×C4#1451980412yes—
495C2×C4C2×D4×D6111yescharacteristic
496C2×C4C2×D4×D6111yescharacteristic
497C2×C4C22×C22⋊D6111yescharacteristic
498C8—42no—
499C8—2442no—
500C8—2442no—
501C22—82no—
502C22—82no—
503C22—82no—
504C22—164no—
505C22—1224no—
506C22—4884no—
507C22—2442no—
508C22—2442no—
509C22—2442no—
510C22—2448no—
511C22—2442no—
512C22—2442no—
513C22#1683989412yes—
514C22#1683990612yes—
515C22#1683993412yes—
516C22C2×#1451974511yescharacteristic
517C4—21no—
518C4—21no—
519C4—44no—
520C4—2442no—
521C4—2442no—
522C4#1683989412yes—
523C4#1683990612yes—
524C4C2×D8×D6111yescharacteristic
525C4C2×#1451979811yescharacteristic
526C4C2×#1451980111yescharacteristic
527C4C2×#1451980411yescharacteristic
528C2—162no—
529C2—4882no—
530C2—2444no—
531C2#2144490514yesdirect product factor
532C2C2×#1683989411yescharacteristic
533C2C2×#1683990611yescharacteristic
534C2C2×#1683993411yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#486C2
socleC23×C61#120
hypercenterC2×#486D61
hypocenterC61C2×#1625
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×#16840415C2semidirect
2. C2×#16839954C2semidirect
3. C2×#16839954C2semidirect
4. #21444905C2direct (N × H)
5. C2×#16839508C2semidirect
6. C2×#16839491C2semidirect
7. C2×#16839491C2semidirect
8. C2×C61×#486C2semidirect
15. #16840415C22semidirect
24. #16839954C22semidirect
25. #16839954C22semidirect
30. #16839508C22semidirect
31. #16839491C22semidirect
32. #16839491C22semidirect
36. C61×#486C22semidirect
136. C2×D244D8semidirect
222. D244C2×D8semidirect
262. C2×#486D61semidirect
270. C2×C61#1625semidirect
292. #486C2×D61semidirect
306. C61C2×#1625semidirect
531. C2#21444905direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404152
C2×#168399542
#214449052
C2×#168395082
C2×#168394912
C2×C61×#4862
C2×#162561