Finite Group Databasebeta

← C2×#21444932 #29655760

Subgroups — C2×#21444932 #29655760

Order 15616.

1062 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×#16840485C211yesmaximal, characteristic, complemented
2C2×#16840109C211yesmaximal, characteristic, complemented
3C2×#16839962C211yesmaximal, characteristic, complemented
4C2×#16839958C211yesmaximal, characteristic
5#21444932C218yesmaximal, direct product factor
6C2×#16839509C211yesmaximal, characteristic, complemented
7C2×#16839491C211yesmaximal, characteristic, complemented
8C2×C61×Q8⋊C8C211yesmaximal, characteristic, complemented
9C22×#11758201—21no—
10C22×D488—21no—
11#16840485—22no—
12#16840485—22no—
13#16840485—22no—
14#16840485C2214yescomplemented
15C2×#14519777C2211yescharacteristic
16C2×#14519774C2211yescharacteristic
17C2×#14519772—22no—
18C2×#14519765—21no—
19C2×#14519753—21no—
20C2×C4×Dic122—21no—
21C2×C4×D244C2211yescharacteristic
22C2×#14519735—21no—
23#16840109—22no—
24#16840109C2214yescomplemented
25#16839962—22no—
26#16839962C2214yescomplemented
27#16839958—22no—
28#16839958C2214yes—
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519699—21no—
31C2×#14519699—22no—
32C2×#14519697—21no—
33#16839509C2214yescomplemented
34#16839491C2214yescomplemented
35C2×C4×Q8×C61C2211yescharacteristic
36C2×C4⋊C8×C61C2211yescharacteristic
37C2×C4×C8×C61C2211yescharacteristic
38C61×Q8⋊C8C2214yescomplemented
39C22×Dic122—21no—
40C22×D244—21no—
41C22×D244—21no—
42C22×D244—21no—
43C22×D244D411yescharacteristic
44C22×C4×D61—21no—
45C2×#11758201—24no—
46C2×#11758201—44no—
47C2×D488—24no—
48C2×D488—44no—
49C22×#92418—21no—
50#14519777—21no—
51#14519777—21no—
52#14519777D412yes—
53#14519777C2312yes—
54#14519774—21no—
55#14519774—21no—
56#14519774—21no—
57#14519774C2312yes—
58#14519772—28no—
59#14519772—28no—
60#14519765—24no—
61#14519765—24no—
62#14519753—24no—
63#14519753—24no—
64C4×Dic122—24no—
65C4×Dic122—24no—
66C4×D244—21no—
67C4×D244—21no—
68C4×D244D412yes—
69C4×D244C2312yes—
70#14519735—24no—
71#14519735—24no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61D411yescharacteristic
74C2×C4⋊Dic61D412yes—
75C2×#11758196—22no—
76C2×#11758198—22no—
77C2×#11758198—22no—
78C2×#11758198—21no—
79C2×C4×Dic61—22no—
80C4⋊#92418—21no—
81C4⋊#92418C2312yes—
82#14519699—24no—
83#14519699—28no—
84#14519697—24no—
85C22×Q8×C61D411yescharacteristic
86C22×C8×C61—21no—
87C22×C8×C61—21no—
88C4×Q8×C61—21no—
89C4×Q8×C61—21no—
90C4×Q8×C61D412yes—
91C4×Q8×C61C2312yes—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61D411yescharacteristic
94C2×C42×C61—21no—
95C2×C42×C61C2311yescharacteristic
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2312yes—
98C4×C8×C61—21no—
99C4×C8×C61C2312yes—
100C23×D61—21no—
101C23×D61—41no—
102C2×Q8×C61—21no—
103C2×Q8×C61—22no—
104C2×Q8×C61—22no—
105C2×Q8×C61C2×D412yes—
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×Dic61—21no—
112C22×Dic61—22no—
113C2×D244—22no—
114C2×D244—22no—
115C2×D244—21no—
116C2×D244—22no—
117C2×D244—22no—
118C2×D244—22no—
119C2×D244—44no—
120C2×D244—42no—
121C2×D244—42no—
122C2×D244—42no—
123C2×D244—42no—
124C2×D244—41no—
125C2×D244—41no—
126C2×D244—41no—
127C2×D244C2×D412yes—
128C2×C4×D61—22no—
129C2×C4×D61—22no—
130C2×C4×D61—42no—
131C2×C4×D61—42no—
132C2×Dic122—22no—
133C2×Dic122—22no—
134C2×Dic122—42no—
135C2×Dic122—42no—
136C2×C8×C61—22no—
137C2×C8×C61—22no—
138C2×C8×C61—42no—
139C2×C8×C61—42no—
140C4⋊C4×C61—22no—
141C4⋊C4×C61—21no—
142C4⋊C4×C61—22no—
143C4⋊C4×C61C2×D412yes—
144C42×C61—22no—
145C42×C61—22no—
146C42×C61C2×D411yescharacteristic
147C42×C61C2×D411yescharacteristic
148C42×C61C2×D411yescharacteristic
149C42×C61C2411yescharacteristic
150#11758201—48no—
151#11758198—28no—
152#11758198—28no—
153#11758198—22no—
154#11758198—22no—
155C4⋊Dic61—22no—
156C4⋊Dic61—21no—
157C4⋊Dic61—22no—
158C4⋊Dic61—22no—
159C4⋊Dic61C2×D412yes—
160C4⋊Dic61C2×D414yes—
161#11758196—28no—
162C4×Dic61—28no—
163C2×#92418—22no—
164C2×#92418—42no—
165D488—48no—
166C23×C61#12011yescharacteristic
167C22×D61—22no—
168C22×D61—42no—
169C22×D61—42no—
170C22×D61—42no—
171C22×D61—42no—
172C22×D61—82no—
173C22×D61—82no—
174C22×D61—82no—
175Q8×C61—22no—
176Q8×C61—22no—
177Q8×C61—42no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61#12011yescharacteristic
184C2×C4×C61#12011yescharacteristic
185C2×C4×C61#12011yescharacteristic
186C2×C4×C61#13512yes—
187C2×C4×C61#13512yes—
188C2×C4×C61AGL(1,ℤ/8)12yes—
189C2×C4×C61AGL(1,ℤ/8)12yes—
190C2×C4×C61C22×D411yescharacteristic
191C2×C4×C61C22×D411yescharacteristic
192C2×C4×C61C22×D411yescharacteristic
193C2×Dic61—22no—
194C2×Dic61—24no—
195C2×Dic61—44no—
196C2×Dic61—42no—
197D244—22no—
198D244—22no—
199D244—44no—
200D244—42no—
201D244—42no—
202D244—42no—
203D244—42no—
204D244—42no—
205D244—82no—
206D244—82no—
207D244—82no—
208C4×D61—42no—
209C4×D61—42no—
210C4×D61—44no—
211Dic122—42no—
212Dic122—42no—
213Dic122—44no—
214C8×C61—42no—
215C8×C61—42no—
216#92418—42no—
217C2×#1628—611nomaximal, Sylow
218C22×C61#44912yes—
219C22×C61#44912yes—
220C22×C61#45412yes—
221C22×C61C2×#12011yescharacteristic
222C2×D61—42no—
223C2×D61—42no—
224C2×D61—42no—
225C2×D61—84no—
226C2×D61—82no—
227C2×D61—82no—
228C2×D61—82no—
229C2×D61—164no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—42no—
233C4×C61—42no—
234C4×C61#44912yes—
235C4×C61#44912yes—
236C4×C61C2×#13511yescharacteristic
237C4×C61C2×#13511yescharacteristic
238C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
239C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
240Dic61—44no—
241Dic61—42no—
242C2×#556—611no—
243C2×#486—611no—
244C2×#460—611no—
245C2×#459—611no—
246#1628—618no—
247C2×#332—611no—
248C2×Q8⋊C8D6111yescharacteristic, complemented
249C2×D4⋊C8—611no—
250C2×C61#162814yescomplemented
251C2×C61C2×#44911yescharacteristic
252C2×C61C2×#44911yescharacteristic
253C2×C61C2×#45411yescharacteristic
254D61—82no—
255D61—162no—
256C22×SD16—1221no—
257C22×D8—1221no—
258#556—614no—
259#556—1222no—
260#556—1222no—
261#556—1222no—
262C2×C4⋊Q8—611no—
263C2×#127—611no—
264C2×#126—1222no—
265C2×#124—1221no—
266C2×C22⋊Q8—1221no—
267C2×C4×Q8—1221no—
268C2×C4×Q8C2×D6111yescharacteristic
269C2×C4×D4—611no—
270C2×#117—1221no—
271#486—614no—
272#486—1222no—
273#460—614no—
274#460—1222no—
275#459—614no—
276#459—1222no—
277C2×C4⋊C8—611no—
278C2×C4⋊C8C2×D6111yescharacteristic
279C2×#102—1222no—
280C2×#102—1221no—
281C2×#102—1221no—
282C2×C4×C8C2×D6111yescharacteristic
283#332—614no—
284Q8⋊C8C2×D6114yescomplemented
285D4⋊C8—614no—
286C61C2×#162811yescharacteristic, complemented, Sylow
287C22×Q8—1221no—
288C22×Q8D24411yescharacteristic
289C22×D4—611no—
290C22×D4—1221no—
291C22×D4—1221no—
292C22×D4—1221no—
293C23×C4—1221no—
294C2×SD16—1224no—
295C2×SD16—2444no—
296C2×D8—1224no—
297C2×D8—2444no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—1221no—
301C4⋊Q8—612no—
302C4⋊Q8—612no—
303C4⋊Q8—1221no—
304C4⋊Q8—1221no—
305#127—612no—
306#127—1221no—
307#127—1221no—
308#127—1221no—
309#126—1228no—
310#126—1228no—
311#124—1224no—
312#124—1224no—
313C22⋊Q8—1224no—
314C22⋊Q8—1224no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×Q8—1224no—
318C4×Q8—1224no—
319C4×Q8D24412yes—
320C4×Q8C22×D6112yes—
321C4×D4—612no—
322C4×D4—612no—
323C4×D4—1221no—
324C4×D4—1221no—
325#117—1224no—
326#117—1224no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—611no—
329C2×C4⋊C4—612no—
330C2×C4⋊C4—1222no—
331C2×C4⋊C4—1221no—
332C2×C4⋊C4D24411yescharacteristic
333C2×C22⋊C4—1222no—
334C2×C22⋊C4—1222no—
335C2×C22⋊C4—1221no—
336C2×C42—21no—
337C2×C42—1222no—
338C2×C42C22×D6111yescharacteristic
339C4⋊C8—21no—
340C4⋊C8—612no—
341C4⋊C8—1221no—
342C4⋊C8C22×D6112yes—
343#102—1224no—
344#102—1228no—
345#102—1224no—
346C4×C8—21no—
347C4×C8C22×D6112yes—
348C24—1221no—
349C24—2441no—
350C2×Q8—21no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—1222no—
354C2×Q8—1222no—
355C2×Q8—2442no—
356C2×Q8—2442no—
357C2×Q8C2×D24412yes—
358C2×D4—612no—
359C2×D4—1222no—
360C2×D4—1222no—
361C2×D4—1222no—
362C2×D4—1221no—
363C2×D4—1222no—
364C2×D4—1222no—
365C2×D4—2444no—
366C2×D4—2441no—
367C2×D4—2441no—
368C2×D4—2441no—
369C2×D4—2442no—
370C2×D4—2442no—
371C2×D4—2442no—
372C2×D4—2442no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—1221no—
376C22×C4—1222no—
377C22×C4—1222no—
378C22×C4—1222no—
379C22×C4—2442no—
380C22×C4—2442no—
381C22×C4C2×D24411yescharacteristic
382C22×C4D4×D6111yescharacteristic
383C22×C4D4×D6111yescharacteristic
384SD16—2448no—
385D8—2448no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—42no—
389C2×C8—42no—
390C2×C8—1222no—
391C2×C8—2442no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—21no—
395C4⋊C4—612no—
396C4⋊C4—614no—
397C4⋊C4—1228no—
398C4⋊C4—1222no—
399C4⋊C4—1221no—
400C4⋊C4—1222no—
401C4⋊C4—1222no—
402C4⋊C4C2×D24412yes—
403C22⋊C4—1228no—
404C22⋊C4—1228no—
405C22⋊C4—1222no—
406C22⋊C4—1222no—
407C42—22no—
408C42—22no—
409C42—1228no—
410C42C2×D24411yescharacteristic
411C42D4×D6111yescharacteristic
412C42D4×D6111yescharacteristic
413C42C23×D6111yescharacteristic
414C23—1222no—
415C23—4882no—
416C23—4882no—
417C23—4882no—
418C23—2442no—
419C23—2442no—
420C23—2442no—
421C23—2442no—
422C23#1451974711yescharacteristic
423Q8—22no—
424Q8—22no—
425Q8—42no—
426Q8—2442no—
427Q8—2442no—
428Q8—2444no—
429D4—1222no—
430D4—1222no—
431D4—4882no—
432D4—4882no—
433D4—4882no—
434D4—2444no—
435D4—2442no—
436D4—2442no—
437D4—2442no—
438D4—2442no—
439D4—2442no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—1222no—
446C2×C4—1224no—
447C2×C4—2442no—
448C2×C4—2444no—
449C2×C4—2442no—
450C2×C4—2442no—
451C2×C4—2444no—
452C2×C4#1451974711yescharacteristic
453C2×C4#1451974711yescharacteristic
454C2×C4#1451974711yescharacteristic
455C2×C4#1451979912yes—
456C2×C4#1451980012yes—
457C2×C4#1451980412yes—
458C2×C4#1451980512yes—
459C2×C4C2×D4×D6111yescharacteristic
460C2×C4C2×D4×D6111yescharacteristic
461C2×C4C22×D24411yescharacteristic
462C8—42no—
463C8—42no—
464C8—2442no—
465C22—9764no—
466C22—4882no—
467C22—4882no—
468C22—4882no—
469C22—4884no—
470C22—2442no—
471C22—2442no—
472C22—2442no—
473C22#1683990912yes—
474C22#1683991012yes—
475C22#1683993612yes—
476C22C2×#1451974711yescharacteristic
477C4—21no—
478C4—21no—
479C4—42no—
480C4—42no—
481C4—2442no—
482C4—2444no—
483C4#1683990912yes—
484C4#1683991012yes—
485C4C2×#1451979911yescharacteristic
486C4C2×#1451980011yescharacteristic
487C4C2×#1451980411yescharacteristic
488C4C2×#1451980511yescharacteristic
489C2—9762no—
490C2—4882no—
491C2#2144493214yesdirect product factor
492C2C2×#1683990911yescharacteristic
493C2C2×#1683991011yescharacteristic
494C2C2×#1683993611yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×Q8⋊C8C2
socleC23×C61#120
prime radicalC2×#16839958C2
hypercenterC2×Q8⋊C8D61
hypocenterC61C2×#1628
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#16840485C2semidirect
2. C2×#16840109C2semidirect
3. C2×#16839962C2semidirect
5. #21444932C2direct (N × H)
6. C2×#16839509C2semidirect
7. C2×#16839491C2semidirect
8. C2×C61×Q8⋊C8C2semidirect
14. #16840485C22semidirect
24. #16840109C22semidirect
26. #16839962C22semidirect
33. #16839509C22semidirect
34. #16839491C22semidirect
38. C61×Q8⋊C8C22semidirect
248. C2×Q8⋊C8D61semidirect
250. C2×C61#1628semidirect
284. Q8⋊C8C2×D61semidirect
286. C61C2×#1628semidirect
491. C2#21444932direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404852
C2×#168401092
C2×#168399622
C2×#168399582
#214449322
C2×#168395092
C2×#168394912
C2×C61×Q8⋊C82
C2×#162861