Finite Group Databasebeta

← C2×#21445104 #29655798

Subgroups — C2×#21445104 #29655798

Order 15616.

1238 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840415C211yesmaximal, characteristic
2C2×#16840158C211yesmaximal, characteristic, complemented
3C2×#16840043C211yesmaximal, characteristic, complemented
4C2×#16839968C211yesmaximal, characteristic, complemented
5#21445104C218yesmaximal, direct product factor
6C2×#16839489C211yesmaximal, characteristic, complemented
7C2×#16839489C211yesmaximal, characteristic, complemented
8C2×C61×#332C211yesmaximal, characteristic, complemented
9C22×#11758226—21no—
10C22×#11758190—21no—
11#16840415—22no—
12#16840415—22no—
13#16840415—22no—
14#16840415C2214yes—
15C2×#14519777C2211yescharacteristic
16C2×#14519762—22no—
17C2×#14519753—21no—
18C2×#14519752—21no—
19C2×C4×D244C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C4⋊C4×D61—21no—
22#16840158—22no—
23#16840158C2214yescomplemented
24#16840043—22no—
25#16840043C2214yescomplemented
26#16839968—22no—
27#16839968C2214yescomplemented
28C2×#14519711—21no—
29C2×#14519708—22no—
30C2×#14519702—21no—
31C2×#14519699—21no—
32C2×C4×#92418C2211yescharacteristic
33#16839489C2214yescomplemented
34#16839489C2214yescomplemented
35C2×C4⋊Q8×C61C2211yescharacteristic
36C2×C4⋊C8×C61C2211yescharacteristic
37C2×C4⋊C8×C61C2211yescharacteristic
38C61×#332C2214yescomplemented
39C2×#11758226—24no—
40C2×#11758226—24no—
41C2×#11758226—44no—
42C2×#11758226—44no—
43C22×Dic122—21no—
44C22×D244—22no—
45C22×D244D411yescharacteristic
46C22×D244D411yescharacteristic
47C22×C4×D61—22no—
48C22×C4×D61—21no—
49C22×C4×D61—21no—
50C2×#11758190—24no—
51C2×#11758190—44no—
52C22×#92418—21no—
53#14519777—21no—
54#14519777—21no—
55#14519777—21no—
56#14519777C2312yes—
57#14519762—28no—
58#14519762—28no—
59#14519753—24no—
60#14519753—24no—
61#14519752—24no—
62#14519752—24no—
63C4×D244—21no—
64C4×D244—21no—
65C4×D244—21no—
66C4×D244—21no—
67C4×D244D412yes—
68C4×D244D412yes—
69C4×D244C2312yes—
70C4×D244C2312yes—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61D411yescharacteristic
74C2×C4⋊Dic61D411yescharacteristic
75C2×#11758196—22no—
76C4⋊C4×D61—24no—
77C4⋊C4×D61—24no—
78C2×#11758198—22no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81#14519711—24no—
82#14519708—28no—
83#14519702—24no—
84#14519699—24no—
85C4×#92418—21no—
86C4×#92418C2312yes—
87C22×Q8×C61—21no—
88C22×C8×C61—21no—
89C22×C8×C61—21no—
90C4⋊Q8×C61—21no—
91C4⋊Q8×C61—21no—
92C4⋊Q8×C61D412yes—
93C4⋊Q8×C61C2312yes—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61D412yes—
96C2×C42×C61C2311yescharacteristic
97C4⋊C8×C61—21no—
98C4⋊C8×C61—21no—
99C4⋊C8×C61C2312yes—
100C4⋊C8×C61C2312yes—
101C23×D61—21no—
102C23×D61—21no—
103C2×Q8×C61—22no—
104C2×Q8×C61—22no—
105C2×Q8×C61—42no—
106C2×Q8×C61—42no—
107C22×C4×C61—22no—
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×Dic61—21no—
112C22×Dic61—21no—
113C22×Dic61—41no—
114#11758226—48no—
115#11758226—416no—
116#11758226—48no—
117C2×D244—21no—
118C2×D244—22no—
119C2×D244—22no—
120C2×D244—22no—
121C2×D244—28no—
122C2×D244—21no—
123C2×D244—48no—
124C2×D244SD1614yescomplemented
125C2×D244C2×D412yes—
126C2×D244C2×D412yes—
127C2×C4×D61—28no—
128C2×C4×D61—22no—
129C2×C4×D61—22no—
130C2×C4×D61—22no—
131C2×C4×D61—22no—
132C2×C4×D61—48no—
133C2×C4×D61—42no—
134C2×C4×D61—42no—
135C2×C4×D61—42no—
136C2×C4×D61—42no—
137C2×Dic122—22no—
138C2×Dic122—42no—
139C2×Dic122—42no—
140C2×Dic122—41no—
141C2×C8×C61—22no—
142C2×C8×C61—22no—
143C2×C8×C61—42no—
144C2×C8×C61—42no—
145C4⋊C4×C61—22no—
146C4⋊C4×C61—22no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61C2×D414yes—
149C42×C61C2×D411yescharacteristic
150C42×C61C2×D411yescharacteristic
151C42×C61C2×D411yescharacteristic
152C42×C61C2411yescharacteristic
153#11758198—28no—
154#11758198—22no—
155#11758198—22no—
156#11758198—22no—
157#11758198—22no—
158C4⋊Dic61—21no—
159C4⋊Dic61—21no—
160C4⋊Dic61—22no—
161C4⋊Dic61—22no—
162C4⋊Dic61—41no—
163C4⋊Dic61—41no—
164C4⋊Dic61C2×D412yes—
165C4⋊Dic61C2×D412yes—
166#11758196—28no—
167C2×#92418—24no—
168C2×#92418—22no—
169#11758190—48no—
170C23×C61#12011yescharacteristic
171C22×D61—22no—
172C22×D61—24no—
173C22×D61—22no—
174C22×D61—42no—
175C22×D61—42no—
176C22×D61—42no—
177C22×D61—42no—
178C22×D61—42no—
179Q8×C61—42no—
180Q8×C61—42no—
181Q8×C61—44no—
182C2×C4×C61—22no—
183C2×C4×C61—24no—
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×C61AGL(1,ℤ/8)12yes—
192C2×C4×C61C22×D411yescharacteristic
193C2×C4×C61C22×D411yescharacteristic
194C2×C4×C61C22×D411yescharacteristic
195C2×Dic61—22no—
196C2×Dic61—22no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199C2×Dic61—42no—
200C2×Dic61—82no—
201D244—22no—
202D244—22no—
203D244—22no—
204D244—24no—
205D244—416no—
206D244—42no—
207D244C2×SD1614yescomplemented
208C4×D61—416no—
209C4×D61—42no—
210C4×D61—42no—
211C4×D61—42no—
212C4×D61—42no—
213C4×D61—44no—
214C4×D61—44no—
215Dic122—42no—
216Dic122—42no—
217Dic122—82no—
218C8×C61—42no—
219C8×C61—42no—
220#92418—24no—
221C2×#1654—611nomaximal, Sylow
222C22×C61#44912yes—
223C22×C61#45012yes—
224C22×C61#45612yes—
225C22×C61C2×#12011yescharacteristic
226C2×D61—24no—
227C2×D61—48no—
228C2×D61—42no—
229C2×D61—42no—
230C2×D61—42no—
231C2×D61—42no—
232C2×D61—42no—
233C2×D61—84no—
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—44no—
237C4×C61#44912yes—
238C4×C61#45012yes—
239C4×C61C22×SD1611yescharacteristic
240C4×C61C2×#13511yescharacteristic
241C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
242C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
243Dic61—42no—
244Dic61—42no—
245Dic61—82no—
246C2×#547—611no—
247C2×#498—611no—
248C2×#474—611no—
249C2×#461—611no—
250#1654—618no—
251C2×#332D6111yescharacteristic, complemented
252C2×D4⋊C8—611no—
253C2×D4⋊C8—611no—
254C2×C61#165414yescomplemented
255C2×C61C2×#45011yescharacteristic
256C2×C61C2×#44911yescharacteristic
257C2×C61C2×#45611yescharacteristic
258D61—44no—
259D61—82no—
260C22×#41—1221no—
261C22×SD16—1221no—
262#547—614no—
263#547—1222no—
264#547—1222no—
265#547—1222no—
266C2×C4⋊Q8—611no—
267C2×C4⋊Q8C2×D6111yescharacteristic
268C2×#123—1222no—
269C2×C22⋊Q8—1221no—
270C2×#121—1221no—
271C2×C4×D4—611no—
272C2×C4×D4—611no—
273C22×C4⋊C4—1221no—
274#498—614no—
275#498—1222no—
276#474—614no—
277#474—1222no—
278#461—614no—
279#461—1222no—
280C2×#107—1221no—
281C2×#106—1222no—
282C2×C4⋊C8C2×D6111yescharacteristic
283C2×C4⋊C8C2×D6111yescharacteristic
284C2×#103—1221no—
285C2×#102—1221no—
286C2×C4×C8—611no—
287#332C2×D6114yescomplemented
288D4⋊C8—614no—
289D4⋊C8—614no—
290C61C2×#165411yescharacteristic, complemented, Sylow
291C2×#41—1224no—
292C2×#41—1224no—
293C2×#41—2444no—
294C2×#41—2444no—
295C22×Q8—21no—
296C22×Q8—1221no—
297C22×D4—611no—
298C22×D4—611no—
299C22×D4—1222no—
300C23×C4—1222no—
301C23×C4—1221no—
302C23×C4—1221no—
303C2×SD16—1224no—
304C2×SD16—2444no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—1221no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—612no—
311C4⋊Q8—1221no—
312C4⋊Q8—1221no—
313C4⋊Q8—1221no—
314C4⋊Q8D24412yes—
315C4⋊Q8C22×D6112yes—
316#123—1228no—
317#123—1228no—
318C22⋊Q8—1224no—
319C22⋊Q8—1224no—
320#121—1224no—
321#121—1224no—
322C4×D4—612no—
323C4×D4—612no—
324C4×D4—612no—
325C4×D4—612no—
326C4×D4—1221no—
327C4×D4—1221no—
328C4×D4—1221no—
329C4×D4—1221no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—611no—
332C2×C4⋊C4—611no—
333C2×C4⋊C4—1224no—
334C2×C4⋊C4—1224no—
335C2×C4⋊C4—1222no—
336C2×C4⋊C4—1221no—
337C2×C4⋊C4—1221no—
338C2×C4⋊C4D24412yes—
339C2×C22⋊C4—1222no—
340C2×C22⋊C4—1221no—
341C2×C22⋊C4—1221no—
342C2×C42C22×D6111yescharacteristic
343#107—1224no—
344#106—1228no—
345C4⋊C8—21no—
346C4⋊C8—21no—
347C4⋊C8C22×D6112yes—
348C4⋊C8C22×D6112yes—
349#103—1224no—
350#102—1224no—
351C4×C8—612no—
352C4×C8—1221no—
353C24—1221no—
354C24—1221no—
355#41—2448no—
356#41—2448no—
357#41—24416no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—42no—
361C2×Q8—42no—
362C2×Q8—1222no—
363C2×Q8—2442no—
364C2×Q8—2442no—
365C2×Q8—2441no—
366C2×D4—612no—
367C2×D4—612no—
368C2×D4—614no—
369C2×D4—1228no—
370C2×D4—1221no—
371C2×D4—1221no—
372C2×D4—1222no—
373C2×D4—1222no—
374C2×D4—1222no—
375C2×D4—2448no—
376C22×C4—22no—
377C22×C4—1228no—
378C22×C4—1221no—
379C22×C4—1221no—
380C22×C4—1222no—
381C22×C4—1222no—
382C22×C4—1222no—
383C22×C4—1222no—
384C22×C4—2448no—
385C22×C4—2441no—
386C22×C4—2442no—
387C22×C4—2442no—
388C22×C4—2442no—
389C22×C4—2442no—
390C22×C4C2×D24411yescharacteristic
391C22×C4D4×D6111yescharacteristic
392C22×C4D4×D6111yescharacteristic
393SD16—2448no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—42no—
397C2×C8—42no—
398C2×C8—1224no—
399C2×C8—1222no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—612no—
404C4⋊C4—612no—
405C4⋊C4—1228no—
406C4⋊C4—1221no—
407C4⋊C4—1221no—
408C4⋊C4—1222no—
409C4⋊C4—1222no—
410C4⋊C4—2441no—
411C4⋊C4—2441no—
412C4⋊C4C2×D24414yes—
413C22⋊C4—1228no—
414C22⋊C4—1222no—
415C22⋊C4—1222no—
416C22⋊C4—1222no—
417C22⋊C4—1222no—
418C42C2×D24411yescharacteristic
419C42D4×D6111yescharacteristic
420C42D4×D6111yescharacteristic
421C42C23×D6111yescharacteristic
422C23—1222no—
423C23—1224no—
424C23—1222no—
425C23—2442no—
426C23—2442no—
427C23—2442no—
428C23—2442no—
429C23—2442no—
430C23#1451974711yescharacteristic
431Q8—42no—
432Q8—42no—
433Q8—44no—
434Q8—4882no—
435Q8—2442no—
436Q8—2442no—
437D4—614no—
438D4—1222no—
439D4—1222no—
440D4—1222no—
441D4—1224no—
442D4—24416no—
443D4—2442no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—44no—
447C2×C4—1222no—
448C2×C4—1222no—
449C2×C4—4882no—
450C2×C4—24416no—
451C2×C4—2442no—
452C2×C4—2442no—
453C2×C4—2442no—
454C2×C4—2442no—
455C2×C4—2442no—
456C2×C4—2442no—
457C2×C4—2442no—
458C2×C4—2444no—
459C2×C4—2444no—
460C2×C4#1451974711yescharacteristic
461C2×C4#1451974711yescharacteristic
462C2×C4#1451974711yescharacteristic
463C2×C4SD16×D6112yes—
464C2×C4#1451980012yes—
465C2×C4#1451980112yes—
466C2×C4#1451980412yes—
467C2×C4C2×D4×D6111yescharacteristic
468C2×C4C2×D4×D6111yescharacteristic
469C2×C4C22×D24411yescharacteristic
470C8—42no—
471C8—42no—
472C8—1224no—
473C22—1224no—
474C22—4884no—
475C22—2442no—
476C22—2442no—
477C22—2442no—
478C22—2442no—
479C22—2442no—
480C22—2448no—
481C22#1683991012yes—
482C22#1683991412yes—
483C22#1683994712yes—
484C22C2×#1451974711yescharacteristic
485C4—21no—
486C4—21no—
487C4—44no—
488C4—4882no—
489C4—2442no—
490C4—2442no—
491C4#1683991012yes—
492C4#1683991412yes—
493C4C2×SD16×D6111yescharacteristic
494C4C2×#1451980011yescharacteristic
495C4C2×#1451980111yescharacteristic
496C4C2×#1451980411yescharacteristic
497C2—4882no—
498C2—2444no—
499C2#2144510414yesdirect product factor
500C2C2×#1683991411yescharacteristic
501C2C2×#1683991011yescharacteristic
502C2C2×#1683994711yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#332C2
socleC23×C61#120
prime radicalC2×#16840415C2
hypercenterC2×#332D61
hypocenterC61C2×#1654
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. C2×#16840158C2semidirect
3. C2×#16840043C2semidirect
4. C2×#16839968C2semidirect
5. #21445104C2direct (N × H)
6. C2×#16839489C2semidirect
7. C2×#16839489C2semidirect
8. C2×C61×#332C2semidirect
23. #16840158C22semidirect
25. #16840043C22semidirect
27. #16839968C22semidirect
33. #16839489C22semidirect
34. #16839489C22semidirect
38. C61×#332C22semidirect
124. C2×D244SD16semidirect
207. D244C2×SD16semidirect
251. C2×#332D61semidirect
254. C2×C61#1654semidirect
287. #332C2×D61semidirect
290. C61C2×#1654semidirect
499. C2#21445104direct (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×#168401582
C2×#168400432
C2×#168399682
#214451042
C2×#168394892
C2×C61×#3322
C2×#165461