Finite Group Databasebeta

← C2×#21444911 #29655713

Subgroups — C2×#21444911 #29655713

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×#16840417C211yesmaximal, characteristic, complemented
2C2×#16840109C211yesmaximal, characteristic, complemented
3C2×#16839958C211yesmaximal, characteristic, complemented
4C2×#16839957C211yesmaximal, characteristic, complemented
5#21444911C218yesmaximal, direct product factor
6C2×#16839509C211yesmaximal, characteristic, complemented
7C2×#16839491C211yesmaximal, characteristic, complemented
8C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
9C22×#11758222—21no—
10C22×D488—21no—
11C22×#11758199—21no—
12#16840417—22no—
13#16840417—22no—
14#16840417—22no—
15#16840417C2214yescomplemented
16C2×#14519777C2211yescharacteristic
17C2×#14519774C2211yescharacteristic
18C2×#14519759—22no—
19C2×#14519756—21no—
20C2×#14519748—21no—
21C2×C4×D244C2211yescharacteristic
22C2×C4⋊C4×D61—21no—
23#16840109—22no—
24#16840109C2214yescomplemented
25#16839958—22no—
26#16839958C2214yescomplemented
27#16839957—22no—
28#16839957C2214yescomplemented
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519699—21no—
31C2×#14519699—22no—
32C2×#14519697—21no—
33#16839509C2214yescomplemented
34#16839491C2214yescomplemented
35C2×C4×D4×C61C2211yescharacteristic
36C2×C4⋊C8×C61C2211yescharacteristic
37C2×C4×C8×C61C2211yescharacteristic
38C61×D4⋊C8C2214yescomplemented
39C2×#11758222—24no—
40C2×#11758222—24no—
41C2×#11758222—44no—
42C2×#11758222—44no—
43C22×Dic122—21no—
44C22×D244—21no—
45C22×D244—21no—
46C22×D244—21no—
47C22×D244D411yescharacteristic
48C22×C22⋊D61—22no—
49C22×C4×D61—22no—
50C22×C4×D61—21no—
51C2×D488—24no—
52C2×D488—44no—
53C2×#11758199—24no—
54C2×#11758199—44no—
55C22×#92418—21no—
56#14519777—21no—
57#14519777—21no—
58#14519777D412yes—
59#14519777C2312yes—
60#14519774—21no—
61#14519774—21no—
62#14519774—21no—
63#14519774C2312yes—
64#14519759—28no—
65#14519759—28no—
66#14519756—24no—
67#14519756—24no—
68#14519748—24no—
69#14519748—24no—
70C4×D244—21no—
71C4×D244—21no—
72C4×D244D412yes—
73C4×D244C2312yes—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61D411yescharacteristic
76C2×C4⋊Dic61D412yes—
77C2×#11758196—22no—
78C4⋊C4×D61—24no—
79C4⋊C4×D61—24no—
80C2×C22⋊Dic61—22no—
81C2×#11758198—21no—
82C4⋊#92418—21no—
83C4⋊#92418C2312yes—
84#14519699—24no—
85#14519699—28no—
86#14519697—24no—
87C22×D4×C61D411yescharacteristic
88C23×C4×C61—21no—
89C22×C8×C61—21no—
90C22×C8×C61—21no—
91C4×D4×C61—21no—
92C4×D4×C61—21no—
93C4×D4×C61D412yes—
94C4×D4×C61C2312yes—
95C2×C4⋊C4×C61D411yescharacteristic
96C2×C22⋊C4×C61—21no—
97C2×C42×C61C2311yescharacteristic
98C4⋊C8×C61—21no—
99C4⋊C8×C61C2312yes—
100C4×C8×C61—21no—
101C4×C8×C61C2312yes—
102C24×C61—21no—
103C23×D61—21no—
104C23×D61—41no—
105C2×D4×C61—21no—
106C2×D4×C61—22no—
107C2×D4×C61—22no—
108C2×D4×C61C2×D412yes—
109C22×C4×C61—21no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—42no—
113C22×C4×C61—42no—
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C2×C22⋊D61—28no—
118C2×C22⋊D61—48no—
119C22×Dic61—22no—
120C22×Dic61—21no—
121#11758222—48no—
122#11758222—416no—
123#11758222—48no—
124C2×D244—21no—
125C2×D244—22no—
126C2×D244—22no—
127C2×D244—22no—
128C2×D244—22no—
129C2×D244—44no—
130C2×D244—42no—
131C2×D244—42no—
132C2×D244—42no—
133C2×D244—42no—
134C2×D244—41no—
135C2×D244—41no—
136C2×D244—41no—
137C2×D244D814yescomplemented
138C2×D244C2×D412yes—
139C2×C4×D61—28no—
140C2×C4×D61—22no—
141C2×C4×D61—22no—
142C2×C4×D61—48no—
143C2×C4×D61—42no—
144C2×C4×D61—42no—
145C2×Dic122—22no—
146C2×Dic122—22no—
147C2×Dic122—42no—
148C2×Dic122—42no—
149C2×C8×C61—22no—
150C2×C8×C61—22no—
151C2×C8×C61—42no—
152C2×C8×C61—42no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61C2×D412yes—
155C22⋊C4×C61—22no—
156C22⋊C4×C61—22no—
157C42×C61C2×D411yescharacteristic
158C42×C61C2×D411yescharacteristic
159C42×C61C2×D411yescharacteristic
160C42×C61C2411yescharacteristic
161C22⋊Dic61—28no—
162#11758199—48no—
163#11758198—22no—
164#11758198—22no—
165C4⋊Dic61—22no—
166C4⋊Dic61—21no—
167C4⋊Dic61—22no—
168C4⋊Dic61—22no—
169C4⋊Dic61C2×D412yes—
170C4⋊Dic61C2×D414yes—
171#11758196—28no—
172C2×#92418—22no—
173C2×#92418—42no—
174D488—48no—
175C23×C61—22no—
176C23×C61—42no—
177C23×C61—42no—
178C23×C61—42no—
179C23×C61#12011yescharacteristic
180C22×D61—22no—
181C22×D61—24no—
182C22×D61—42no—
183C22×D61—42no—
184C22×D61—42no—
185C22×D61—82no—
186C22×D61—82no—
187C22×D61—82no—
188D4×C61—22no—
189D4×C61—22no—
190D4×C61—42no—
191C2×C4×C61—22no—
192C2×C4×C61—22no—
193C2×C4×C61—42no—
194C2×C4×C61—42no—
195C2×C4×C61—42no—
196C2×C4×C61—44no—
197C2×C4×C61#12011yescharacteristic
198C2×C4×C61#12011yescharacteristic
199C2×C4×C61#12011yescharacteristic
200C2×C4×C61C2×D812yes—
201C2×C4×C61#13512yes—
202C2×C4×C61AGL(1,ℤ/8)12yes—
203C2×C4×C61AGL(1,ℤ/8)12yes—
204C2×C4×C61C22×D411yescharacteristic
205C2×C4×C61C22×D411yescharacteristic
206C2×C4×C61C22×D411yescharacteristic
207C22⋊D61—416no—
208C2×Dic61—22no—
209C2×Dic61—24no—
210C2×Dic61—44no—
211C2×Dic61—42no—
212D244—22no—
213D244—24no—
214D244—44no—
215D244—42no—
216D244—42no—
217D244—42no—
218D244—42no—
219D244—82no—
220D244—82no—
221D244—82no—
222D244C2×D814yescomplemented
223C4×D61—416no—
224C4×D61—42no—
225C4×D61—42no—
226C4×D61—44no—
227Dic122—42no—
228Dic122—42no—
229Dic122—44no—
230C8×C61—42no—
231C8×C61—42no—
232#92418—42no—
233C2×#1625—611nomaximal, Sylow
234C22×C61—42no—
235C22×C61—42no—
236C22×C61—42no—
237C22×C61—84no—
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—82no—
247C2×D61—82no—
248C2×D61—82no—
249C2×D61—164no—
250C4×C61—21no—
251C4×C61—21no—
252C4×C61—42no—
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—44no—
260Dic61—42no—
261C2×#547—611no—
262C2×#486—611no—
263C2×#459—611no—
264C2×#459—611no—
265#1625—618no—
266C2×#332—611no—
267C2×D4⋊C8—611no—
268C2×D4⋊C8D6111yescharacteristic, complemented
269C2×C61—82no—
270C2×C61#162514yescomplemented
271C2×C61C2×#44711yescharacteristic
272C2×C61C2×#44911yescharacteristic
273C2×C61C2×#45411yescharacteristic
274D61—44no—
275D61—162no—
276C22×#41—1221no—
277C22×D8—1221no—
278C22×D8—1221no—
279#547—614no—
280#547—1222no—
281#547—1222no—
282#547—1222no—
283C2×C4⋊Q8—611no—
284C2×#127—611no—
285C2×#123—1222no—
286C2×C22⋊Q8—1221no—
287C2×#121—1221no—
288C2×C4×D4—611no—
289C2×C4×D4C2×D6111yescharacteristic
290C22×C4⋊C4—1221no—
291#486—614no—
292#486—1222no—
293#459—614no—
294#459—614no—
295#459—1222no—
296#459—1222no—
297C2×C4⋊C8—611no—
298C2×C4⋊C8C2×D6111yescharacteristic
299C2×#102—1222no—
300C2×#102—1221no—
301C2×#102—1221no—
302C2×C4×C8C2×D6111yescharacteristic
303#332—614no—
304D4⋊C8—614no—
305D4⋊C8C2×D6114yescomplemented
306C61C2×#162511yescharacteristic, complemented, Sylow
307C2×#41—1224no—
308C2×#41—1224no—
309C2×#41—2444no—
310C2×#41—2444no—
311C22×Q8—1221no—
312C22×D4—611no—
313C22×D4—1222no—
314C22×D4—1221no—
315C22×D4—1221no—
316C22×D4—1221no—
317C22×D4D24411yescharacteristic
318C23×C4—21no—
319C23×C4—1222no—
320C23×C4—1221no—
321C2×D8—1224no—
322C2×D8—1224no—
323C2×D8—2444no—
324C2×D8—2444no—
325C22×C8—21no—
326C22×C8—21no—
327C22×C8—1221no—
328C4⋊Q8—612no—
329C4⋊Q8—612no—
330C4⋊Q8—1221no—
331C4⋊Q8—1221no—
332#127—612no—
333#127—1221no—
334#127—1221no—
335#127—1221no—
336#123—1228no—
337#123—1228no—
338C22⋊Q8—1224no—
339C22⋊Q8—1224no—
340#121—1224no—
341#121—1224no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4—612no—
345C4×D4—612no—
346C4×D4—1221no—
347C4×D4—1221no—
348C4×D4D24412yes—
349C4×D4C22×D6112yes—
350C2×C4⋊C4—611no—
351C2×C4⋊C4—612no—
352C2×C4⋊C4—1224no—
353C2×C4⋊C4—1222no—
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1224no—
356C2×C4⋊C4D24411yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—1222no—
359C2×C22⋊C4—1221no—
360C2×C42C22×D6111yescharacteristic
361C4⋊C8—21no—
362C4⋊C8—612no—
363C4⋊C8—1221no—
364C4⋊C8C22×D6112yes—
365#102—1224no—
366#102—1228no—
367#102—1224no—
368C4×C8—21no—
369C4×C8C22×D6112yes—
370C24—21no—
371C24—1221no—
372C24—2441no—
373#41—2448no—
374#41—2448no—
375#41—24416no—
376C2×Q8—1222no—
377C2×Q8—1222no—
378C2×Q8—2442no—
379C2×Q8—2442no—
380C2×D4—21no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—612no—
384C2×D4—614no—
385C2×D4—1228no—
386C2×D4—1222no—
387C2×D4—1222no—
388C2×D4—1222no—
389C2×D4—1221no—
390C2×D4—1222no—
391C2×D4—2444no—
392C2×D4—2448no—
393C2×D4—2441no—
394C2×D4—2441no—
395C2×D4—2441no—
396C2×D4—2442no—
397C2×D4—2442no—
398C2×D4—2442no—
399C2×D4—2442no—
400C2×D4C2×D24412yes—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—1228no—
407C22×C4—1221no—
408C22×C4—1222no—
409C22×C4—1222no—
410C22×C4—1222no—
411C22×C4—2448no—
412C22×C4—2442no—
413C22×C4—2442no—
414C22×C4C2×D24411yescharacteristic
415C22×C4D4×D6111yescharacteristic
416C22×C4D4×D6111yescharacteristic
417D8—2448no—
418D8—2448no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—42no—
422C2×C8—42no—
423C2×C8—1222no—
424C2×C8—2442no—
425C4⋊C4—21no—
426C4⋊C4—612no—
427C4⋊C4—614no—
428C4⋊C4—1228no—
429C4⋊C4—1222no—
430C4⋊C4—1221no—
431C4⋊C4—1222no—
432C4⋊C4—1222no—
433C4⋊C4C2×D24412yes—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—1228no—
437C22⋊C4—1222no—
438C22⋊C4—1222no—
439C42C2×D24411yescharacteristic
440C42D4×D6111yescharacteristic
441C42D4×D6111yescharacteristic
442C42C23×D6111yescharacteristic
443C23—22no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—1222no—
448C23—1224no—
449C23—4882no—
450C23—4882no—
451C23—4882no—
452C23—2442no—
453C23—2442no—
454C23—2442no—
455C23#1451974711yescharacteristic
456Q8—2442no—
457Q8—2442no—
458Q8—2444no—
459D4—22no—
460D4—22no—
461D4—42no—
462D4—614no—
463D4—1222no—
464D4—1224no—
465D4—4882no—
466D4—4882no—
467D4—4882no—
468D4—2444no—
469D4—24416no—
470D4—2442no—
471D4—2442no—
472D4—2442no—
473D4—2442no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—44no—
480C2×C4—1222no—
481C2×C4—1224no—
482C2×C4—24416no—
483C2×C4—2444no—
484C2×C4—2442no—
485C2×C4—2442no—
486C2×C4—2442no—
487C2×C4—2444no—
488C2×C4#1451974711yescharacteristic
489C2×C4#1451974711yescharacteristic
490C2×C4#1451974711yescharacteristic
491C2×C4D8×D6112yes—
492C2×C4#1451979912yes—
493C2×C4#1451980412yes—
494C2×C4#1451980512yes—
495C2×C4C2×D4×D6111yescharacteristic
496C2×C4C2×D4×D6111yescharacteristic
497C2×C4C22×D24411yescharacteristic
498C8—42no—
499C8—42no—
500C8—2442no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—84no—
505C22—1224no—
506C22—9764no—
507C22—4882no—
508C22—4882no—
509C22—4882no—
510C22—2448no—
511C22—2442no—
512C22—2442no—
513C22#1683989712yes—
514C22#1683990912yes—
515C22#1683993612yes—
516C22C2×#1451974711yescharacteristic
517C4—21no—
518C4—21no—
519C4—42no—
520C4—2444no—
521C4—2442no—
522C4#1683989712yes—
523C4#1683990912yes—
524C4C2×D8×D6111yescharacteristic
525C4C2×#1451979911yescharacteristic
526C4C2×#1451980411yescharacteristic
527C4C2×#1451980511yescharacteristic
528C2—82no—
529C2—9762no—
530C2—2444no—
531C2#2144491114yesdirect product factor
532C2C2×#1683989711yescharacteristic
533C2C2×#1683990911yescharacteristic
534C2C2×#1683993611yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61#120
hypercenterC2×D4⋊C8D61
hypocenterC61C2×#1625
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#16840417C2semidirect
2. C2×#16840109C2semidirect
3. C2×#16839958C2semidirect
4. C2×#16839957C2semidirect
5. #21444911C2direct (N × H)
6. C2×#16839509C2semidirect
7. C2×#16839491C2semidirect
8. C2×C61×D4⋊C8C2semidirect
15. #16840417C22semidirect
24. #16840109C22semidirect
26. #16839958C22semidirect
28. #16839957C22semidirect
33. #16839509C22semidirect
34. #16839491C22semidirect
38. C61×D4⋊C8C22semidirect
137. C2×D244D8semidirect
222. D244C2×D8semidirect
268. C2×D4⋊C8D61semidirect
270. C2×C61#1625semidirect
305. D4⋊C8C2×D61semidirect
306. C61C2×#1625semidirect
531. C2#21444911direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404172
C2×#168401092
C2×#168399582
C2×#168399572
#214449112
C2×#168395092
C2×#168394912
C2×C61×D4⋊C82
C2×#162561