Finite Group Databasebeta

← C2×#21444973 #29655721

Subgroups — C2×#21444973 #29655721

Order 15616.

1206 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840417C211yesmaximal, characteristic
2C2×#16840113C211yesmaximal, characteristic, complemented
3C2×#16840053C211yesmaximal, characteristic, complemented
4C2×#16840052C211yesmaximal, characteristic, complemented
5#21444973C218yesmaximal, direct product factor
6C2×#16839509C211yesmaximal, characteristic, complemented
7C2×#16839491C211yesmaximal, characteristic, complemented
8C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
9C22×#11758222—21no—
10#16840417—22no—
11#16840417—22no—
12#16840417—22no—
13#16840417C2214yes—
14C2×#14519777C2211yescharacteristic
15C2×#14519777C2211yescharacteristic
16C2×#14519759—22no—
17C2×#14519756—21no—
18C2×#14519748—21no—
19C2×C4×D244C2211yescharacteristic
20C2×C4⋊C4×D61—21no—
21#16840113—22no—
22#16840113C2214yescomplemented
23#16840053—22no—
24#16840053C2214yescomplemented
25#16840052—22no—
26#16840052C2214yescomplemented
27C2×#14519709—21no—
28C2×#14519708—21no—
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519702—22no—
31C2×#14519699—21no—
32C2×#14519698—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×Dic122—21no—
45C22×D244D411yescharacteristic
46C22×C22⋊D61—22no—
47C22×C4×D61—22no—
48C22×C4×D61—21no—
49C22×#92418—21no—
50#14519777—21no—
51#14519777—21no—
52#14519777—21no—
53#14519777—21no—
54#14519777—21no—
55#14519777D412yes—
56#14519777C2312yes—
57#14519777C2312yes—
58#14519759—28no—
59#14519759—28no—
60#14519756—24no—
61#14519756—24no—
62#14519748—24no—
63#14519748—24no—
64C4×D244—21no—
65C4×D244—21no—
66C4×D244D412yes—
67C4×D244C2312yes—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61D411yescharacteristic
72C2×C4⋊Dic61D412yes—
73C2×#11758196—22no—
74C4⋊C4×D61—24no—
75C4⋊C4×D61—24no—
76C2×C22⋊Dic61—22no—
77C2×#11758198—21no—
78#14519709—24no—
79#14519708—24no—
80C4⋊#92418—21no—
81C4⋊#92418C2312yes—
82#14519702—28no—
83#14519699—24no—
84#14519698—24no—
85C22×D4×C61D411yescharacteristic
86C23×C4×C61—21no—
87C22×C8×C61—21no—
88C22×C8×C61—21no—
89C4×D4×C61—21no—
90C4×D4×C61—21no—
91C4×D4×C61D412yes—
92C4×D4×C61C2312yes—
93C2×C4⋊C4×C61D411yescharacteristic
94C2×C22⋊C4×C61—21no—
95C2×C42×C61C2311yescharacteristic
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2312yes—
98C4×C8×C61—21no—
99C4×C8×C61C2312yes—
100C24×C61—21no—
101C23×D61—21no—
102C2×D4×C61—21no—
103C2×D4×C61—22no—
104C2×D4×C61—22no—
105C2×D4×C61C2×D412yes—
106C22×C4×C61—21no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—42no—
110C22×C4×C61—42no—
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C2×C22⋊D61—28no—
115C2×C22⋊D61—48no—
116C22×Dic61—22no—
117C22×Dic61—21no—
118C22×Dic61—41no—
119#11758222—48no—
120#11758222—416no—
121#11758222—48no—
122C2×D244—21no—
123C2×D244—22no—
124C2×D244SD1614yes—
125C2×D244C2×D412yes—
126C2×C4×D61—28no—
127C2×C4×D61—22no—
128C2×C4×D61—22no—
129C2×C4×D61—48no—
130C2×C4×D61—42no—
131C2×C4×D61—42no—
132C2×Dic122—22no—
133C2×Dic122—22no—
134C2×Dic122—22no—
135C2×Dic122—42no—
136C2×Dic122—42no—
137C2×Dic122—44no—
138C2×Dic122—41no—
139C2×C8×C61—22no—
140C2×C8×C61—22no—
141C2×C8×C61—42no—
142C2×C8×C61—42no—
143C4⋊C4×C61—21no—
144C4⋊C4×C61C2×D412yes—
145C22⋊C4×C61—22no—
146C22⋊C4×C61—22no—
147C42×C61C2×D411yescharacteristic
148C42×C61C2×D411yescharacteristic
149C42×C61C2×D411yescharacteristic
150C42×C61C2411yescharacteristic
151C22⋊Dic61—28no—
152#11758198—22no—
153#11758198—22no—
154C4⋊Dic61—22no—
155C4⋊Dic61—21no—
156C4⋊Dic61—22no—
157C4⋊Dic61—22no—
158C4⋊Dic61—22no—
159C4⋊Dic61—22no—
160C4⋊Dic61—41no—
161C4⋊Dic61—41no—
162C4⋊Dic61C2×D414yes—
163C4⋊Dic61C2×D412yes—
164#11758196—28no—
165C2×#92418—22no—
166C2×#92418—42no—
167C23×C61—22no—
168C23×C61—42no—
169C23×C61—42no—
170C23×C61—42no—
171C23×C61#12011yescharacteristic
172C22×D61—22no—
173C22×D61—24no—
174C22×D61—42no—
175C22×D61—42no—
176D4×C61—22no—
177D4×C61—22no—
178D4×C61—42no—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61—42no—
184C2×C4×C61—44no—
185C2×C4×C61#12011yescharacteristic
186C2×C4×C61#12011yescharacteristic
187C2×C4×C61#12011yescharacteristic
188C2×C4×C61C2×SD1612yes—
189C2×C4×C61#13512yes—
190C2×C4×C61AGL(1,ℤ/8)12yes—
191C2×C4×C61#13712yes—
192C2×C4×C61C22×D411yescharacteristic
193C2×C4×C61C22×D411yescharacteristic
194C2×C4×C61C22×D411yescharacteristic
195C22⋊D61—416no—
196C2×Dic61—22no—
197C2×Dic61—24no—
198C2×Dic61—44no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201C2×Dic61—82no—
202D244—22no—
203D244—24no—
204D244C2×SD1614yes—
205C4×D61—416no—
206C4×D61—42no—
207C4×D61—42no—
208C4×D61—44no—
209Dic122—42no—
210Dic122—42no—
211Dic122—44no—
212Dic122—44no—
213Dic122—82no—
214C8×C61—42no—
215C8×C61—42no—
216#92418—42no—
217C2×#1635—611nomaximal, Sylow
218C22×C61—42no—
219C22×C61—42no—
220C22×C61—42no—
221C22×C61—84no—
222C22×C61#45012yes—
223C22×C61#45212yes—
224C22×C61#45412yes—
225C22×C61C2×#12011yescharacteristic
226C2×D61—24no—
227C2×D61—48no—
228C2×D61—42no—
229C2×D61—42no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—42no—
233C4×C61#45012yes—
234C4×C61#45212yes—
235C4×C61C22×SD1611yescharacteristic
236C4×C61C2×#13511yescharacteristic
237C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
238C4×C61C2×#13711yescharacteristic
239Dic61—44no—
240Dic61—42no—
241Dic61—82no—
242C2×#547—611no—
243C2×#487—611no—
244C2×#476—611no—
245C2×#476—611no—
246#1635—618no—
247C2×#332—611no—
248C2×D4⋊C8—611no—
249C2×D4⋊C8D6111yescharacteristic, complemented
250C2×C61—82no—
251C2×C61#163514yescomplemented
252C2×C61C2×#45011yescharacteristic
253C2×C61C2×#45211yescharacteristic
254C2×C61C2×#45411yescharacteristic
255D61—44no—
256C22×#41—1221no—
257#547—614no—
258#547—1222no—
259#547—1222no—
260#547—1222no—
261C2×C4⋊Q8—611no—
262C2×C4⋊Q8—611no—
263C2×#123—1222no—
264C2×C22⋊Q8—1221no—
265C2×#121—1221no—
266C2×C4×D4—611no—
267C2×C4×D4C2×D6111yescharacteristic
268C22×C4⋊C4—1221no—
269#487—614no—
270#487—1222no—
271#476—614no—
272#476—614no—
273#476—1222no—
274#476—1222no—
275C2×#106—1221no—
276C2×#106—1221no—
277C2×C4⋊C8—611no—
278C2×C4⋊C8C2×D6111yescharacteristic
279C2×#103—1222no—
280C2×#102—1221no—
281C2×#102—1221no—
282C2×C4×C8C2×D6111yescharacteristic
283#332—614no—
284D4⋊C8—614no—
285D4⋊C8C2×D6114yescomplemented
286C61C2×#163511yescharacteristic, complemented, Sylow
287C2×#41—1224no—
288C2×#41—1224no—
289C2×#41—2444no—
290C2×#41—2444no—
291C22×Q8—1221no—
292C22×Q8—1221no—
293C22×D4—611no—
294C22×D4—1222no—
295C22×D4D24411yescharacteristic
296C23×C4—21no—
297C23×C4—1222no—
298C23×C4—1221no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—1221no—
302C4⋊Q8—612no—
303C4⋊Q8—612no—
304C4⋊Q8—612no—
305C4⋊Q8—1221no—
306C4⋊Q8—1221no—
307C4⋊Q8—1221no—
308C4⋊Q8—1221no—
309C4⋊Q8—1221no—
310#123—1228no—
311#123—1228no—
312C22⋊Q8—1224no—
313C22⋊Q8—1224no—
314#121—1224no—
315#121—1224no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—612no—
319C4×D4—612no—
320C4×D4—1221no—
321C4×D4—1221no—
322C4×D4D24412yes—
323C4×D4C22×D6112yes—
324C2×C4⋊C4—611no—
325C2×C4⋊C4—612no—
326C2×C4⋊C4—1224no—
327C2×C4⋊C4—1222no—
328C2×C4⋊C4—1221no—
329C2×C4⋊C4—1224no—
330C2×C4⋊C4—1221no—
331C2×C4⋊C4—1221no—
332C2×C4⋊C4D24411yescharacteristic
333C2×C22⋊C4—21no—
334C2×C22⋊C4—1222no—
335C2×C22⋊C4—1221no—
336C2×C42C22×D6111yescharacteristic
337#106—1224no—
338#106—1224no—
339C4⋊C8—21no—
340C4⋊C8—612no—
341C4⋊C8—1221no—
342C4⋊C8C22×D6112yes—
343#103—1228no—
344#102—1224no—
345#102—1224no—
346C4×C8—21no—
347C4×C8C22×D6112yes—
348C24—21no—
349C24—1221no—
350#41—2448no—
351#41—2448no—
352#41—24416no—
353C2×Q8—1222no—
354C2×Q8—1222no—
355C2×Q8—1222no—
356C2×Q8—2444no—
357C2×Q8—2441no—
358C2×Q8—2442no—
359C2×Q8—2442no—
360C2×D4—22no—
361C2×D4—21no—
362C2×D4—22no—
363C2×D4—612no—
364C2×D4—614no—
365C2×D4—1228no—
366C2×D4—1221no—
367C2×D4—1222no—
368C2×D4—2448no—
369C2×D4C2×D24412yes—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—1228no—
376C22×C4—1221no—
377C22×C4—1222no—
378C22×C4—1222no—
379C22×C4—1222no—
380C22×C4—2448no—
381C22×C4—2441no—
382C22×C4—2442no—
383C22×C4—2442no—
384C22×C4C2×D24411yescharacteristic
385C22×C4D4×D6111yescharacteristic
386C22×C4D4×D6111yescharacteristic
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—42no—
390C2×C8—42no—
391C2×C8—1222no—
392C2×C8—2442no—
393C4⋊C4—21no—
394C4⋊C4—614no—
395C4⋊C4—612no—
396C4⋊C4—1228no—
397C4⋊C4—1222no—
398C4⋊C4—1221no—
399C4⋊C4—1222no—
400C4⋊C4—1222no—
401C4⋊C4—1222no—
402C4⋊C4—1222no—
403C4⋊C4—2441no—
404C4⋊C4—2441no—
405C4⋊C4C2×D24412yes—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C22⋊C4—1228no—
409C22⋊C4—1222no—
410C22⋊C4—1222no—
411C42C2×D24411yescharacteristic
412C42D4×D6111yescharacteristic
413C42D4×D6111yescharacteristic
414C42C23×D6111yescharacteristic
415C23—22no—
416C23—42no—
417C23—42no—
418C23—42no—
419C23—1222no—
420C23—1224no—
421C23—2442no—
422C23—2442no—
423C23#1451974711yescharacteristic
424Q8—4882no—
425Q8—2444no—
426Q8—2442no—
427Q8—2442no—
428Q8—2444no—
429D4—22no—
430D4—22no—
431D4—42no—
432D4—614no—
433D4—1222no—
434D4—1224no—
435D4—24416no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—44no—
442C2×C4—1222no—
443C2×C4—1224no—
444C2×C4—4882no—
445C2×C4—24416no—
446C2×C4—2442no—
447C2×C4—2444no—
448C2×C4—2442no—
449C2×C4—2442no—
450C2×C4—2442no—
451C2×C4—2444no—
452C2×C4#1451974711yescharacteristic
453C2×C4#1451974711yescharacteristic
454C2×C4#1451974711yescharacteristic
455C2×C4SD16×D6112yes—
456C2×C4#1451979912yes—
457C2×C4#1451980112yes—
458C2×C4#1451981012yes—
459C2×C4C2×D4×D6111yescharacteristic
460C2×C4C2×D4×D6111yescharacteristic
461C2×C4C22×D24411yescharacteristic
462C8—42no—
463C8—42no—
464C8—2442no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—84no—
469C22—1224no—
470C22—2442no—
471C22—2448no—
472C22—2442no—
473C22#1683991412yes—
474C22#1683992612yes—
475C22#1683993612yes—
476C22C2×#1451974711yescharacteristic
477C4—21no—
478C4—21no—
479C4—42no—
480C4—4882no—
481C4—2444no—
482C4—2442no—
483C4#1683991412yes—
484C4#1683992612yes—
485C4C2×SD16×D6111yescharacteristic
486C4C2×#1451979911yescharacteristic
487C4C2×#1451980111yescharacteristic
488C4C2×#1451981011yescharacteristic
489C2—82no—
490C2—2444no—
491C2#2144497314yesdirect product factor
492C2C2×#1683991411yescharacteristic
493C2C2×#1683992611yescharacteristic
494C2C2×#1683993611yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61#120
prime radicalC2×#16840417C2
hypercenterC2×D4⋊C8D61
hypocenterC61C2×#1635
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
2. C2×#16840113C2semidirect
3. C2×#16840053C2semidirect
4. C2×#16840052C2semidirect
5. #21444973C2direct (N × H)
6. C2×#16839509C2semidirect
7. C2×#16839491C2semidirect
8. C2×C61×D4⋊C8C2semidirect
22. #16840113C22semidirect
24. #16840053C22semidirect
26. #16840052C22semidirect
33. #16839509C22semidirect
34. #16839491C22semidirect
38. C61×D4⋊C8C22semidirect
249. C2×D4⋊C8D61semidirect
251. C2×C61#1635semidirect
285. D4⋊C8C2×D61semidirect
286. C61C2×#1635semidirect
491. C2#21444973direct (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×#168401132
C2×#168400532
C2×#168400522
#214449732
C2×#168395092
C2×#168394912
C2×C61×D4⋊C82
C2×#163561