Finite Group Databasebeta

← C2×#21445048 #29655944

Subgroups — C2×#21445048 #29655944

Order 15616.

1042 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840478C211yesmaximal, characteristic
2C2×#16840112C211yesmaximal, characteristic, complemented
3C2×#16840043C211yesmaximal, characteristic, complemented
4C2×#16839968C211yesmaximal, characteristic, complemented
5#21445048C218yesmaximal, direct product factor
6C2×#16839489C211yesmaximal, characteristic, complemented
7C2×#16839489C211yesmaximal, characteristic, complemented
8C2×C61×#333C211yesmaximal, characteristic, complemented
9C22×#11758190—21no—
10#16840478—22no—
11#16840478—22no—
12#16840478—22no—
13#16840478C2214yes—
14C2×#14519777C2211yescharacteristic
15C2×#14519766—22no—
16C2×#14519752—21no—
17C2×#14519752—21no—
18C2×C4×D244C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×#14519735—21no—
21C2×#14519735—21no—
22#16840112—22no—
23#16840112C2214yescomplemented
24#16840043—22no—
25#16840043C2214yescomplemented
26#16839968—22no—
27#16839968C2214yescomplemented
28C2×#14519711—21no—
29C2×#14519702—21no—
30C2×#14519701—22no—
31C2×#14519699—21no—
32C2×C4×#92418C2211yescharacteristic
33#16839489C2214yescomplemented
34#16839489C2214yescomplemented
35C2×C4⋊Q8×C61C2211yescharacteristic
36C2×C4⋊C8×C61C2211yescharacteristic
37C2×C4⋊C8×C61C2211yescharacteristic
38C61×#333C2214yescomplemented
39C22×Dic122—21no—
40C22×D244—22no—
41C22×D244D411yescharacteristic
42C22×D244D411yescharacteristic
43C22×C4×D61—21no—
44C22×C4×D61—21no—
45C2×#11758190—24no—
46C2×#11758190—44no—
47C22×#92418—21no—
48#14519777—21no—
49#14519777—21no—
50#14519777—21no—
51#14519777C2312yes—
52#14519766—28no—
53#14519766—28no—
54#14519752—24no—
55#14519752—24no—
56#14519752—24no—
57#14519752—24no—
58C4×D244—21no—
59C4×D244—21no—
60C4×D244—21no—
61C4×D244—21no—
62C4×D244D412yes—
63C4×D244D412yes—
64C4×D244C2312yes—
65C4×D244C2312yes—
66#14519735—24no—
67#14519735—24no—
68#14519735—24no—
69#14519735—24no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61D411yescharacteristic
73C2×C4⋊Dic61D411yescharacteristic
74C2×#11758198—22no—
75C2×#11758198—22no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×C4×Dic61—22no—
79#14519711—24no—
80#14519702—24no—
81#14519701—28no—
82#14519699—24no—
83C4×#92418—21no—
84C4×#92418C2312yes—
85C22×Q8×C61D412yes—
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×C61—21no—
94C2×C42×C61C2311yescharacteristic
95C4⋊C8×C61—21no—
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2312yes—
98C4⋊C8×C61C2312yes—
99C23×D61—21no—
100C23×D61—21no—
101C2×Q8×C61—22no—
102C2×Q8×C61—44no—
103C2×Q8×C61C2×D414yes—
104C22×C4×C61—22no—
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×Dic61—21no—
109C22×Dic61—21no—
110C22×Dic61—41no—
111C2×D244—22no—
112C2×D244—22no—
113C2×D244—22no—
114C2×D244—22no—
115C2×D244—21no—
116C2×D244—21no—
117C2×D244—28no—
118C2×D244—84no—
119C2×D244C2×D412yes—
120C2×D244C2×D412yes—
121C2×C4×D61—22no—
122C2×C4×D61—22no—
123C2×C4×D61—22no—
124C2×C4×D61—22no—
125C2×C4×D61—42no—
126C2×C4×D61—42no—
127C2×C4×D61—42no—
128C2×C4×D61—42no—
129C2×Dic122—22no—
130C2×Dic122—42no—
131C2×Dic122—42no—
132C2×Dic122—41no—
133C2×C8×C61—22no—
134C2×C8×C61—22no—
135C2×C8×C61—42no—
136C2×C8×C61—42no—
137C4⋊C4×C61—22no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61—22no—
140C4⋊C4×C61—22no—
141C42×C61C2×D411yescharacteristic
142C42×C61C2×D411yescharacteristic
143C42×C61C2×D411yescharacteristic
144C42×C61C2411yescharacteristic
145#11758198—28no—
146#11758198—28no—
147#11758198—22no—
148#11758198—22no—
149#11758198—22no—
150#11758198—22no—
151C4⋊Dic61—21no—
152C4⋊Dic61—21no—
153C4⋊Dic61—22no—
154C4⋊Dic61—22no—
155C4⋊Dic61—41no—
156C4⋊Dic61—41no—
157C4⋊Dic61C2×D412yes—
158C4⋊Dic61C2×D412yes—
159C4×Dic61—28no—
160C2×#92418—22no—
161C2×#92418—42no—
162#11758190—48no—
163C23×C61#12011yescharacteristic
164C22×D61—22no—
165C22×D61—22no—
166C22×D61—42no—
167C22×D61—42no—
168C22×D61—42no—
169C22×D61—42no—
170C22×D61—42no—
171C22×D61—42no—
172Q8×C61—44no—
173Q8×C61—82no—
174C2×C4×C61—22no—
175C2×C4×C61—24no—
176C2×C4×C61—44no—
177C2×C4×C61#12011yescharacteristic
178C2×C4×C61#12011yescharacteristic
179C2×C4×C61#12011yescharacteristic
180C2×C4×C61#13512yes—
181C2×C4×C61#13512yes—
182C2×C4×C61AGL(1,ℤ/8)12yes—
183C2×C4×C61#13712yes—
184C2×C4×C61C22×D411yescharacteristic
185C2×C4×C61C22×D411yescharacteristic
186C2×C4×C61C22×D411yescharacteristic
187C2×Dic61—22no—
188C2×Dic61—22no—
189C2×Dic61—42no—
190C2×Dic61—42no—
191C2×Dic61—42no—
192C2×Dic61—82no—
193D244—22no—
194D244—22no—
195D244—22no—
196D244—22no—
197D244—42no—
198D244—42no—
199D244—88no—
200C4×D61—42no—
201C4×D61—42no—
202C4×D61—42no—
203C4×D61—42no—
204C4×D61—44no—
205C4×D61—44no—
206Dic122—42no—
207Dic122—42no—
208Dic122—82no—
209C8×C61—42no—
210C8×C61—42no—
211#92418—42no—
212C2×#1646—611nomaximal, Sylow
213C22×C61#44912yes—
214C22×C61#45212yes—
215C22×C61#45512yes—
216C22×C61C2×#12011yescharacteristic
217C2×D61—42no—
218C2×D61—42no—
219C2×D61—42no—
220C2×D61—42no—
221C2×D61—42no—
222C2×D61—42no—
223C2×D61—84no—
224C2×D61—84no—
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—44no—
228C4×C61#44912yes—
229C4×C61#45212yes—
230C4×C61C2×#13511yescharacteristic
231C4×C61C2×#13511yescharacteristic
232C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
233C4×C61C2×#13711yescharacteristic
234Dic61—42no—
235Dic61—42no—
236Dic61—82no—
237C2×#555—611no—
238C2×#487—611no—
239C2×#474—611no—
240C2×#461—611no—
241#1646—618no—
242C2×#333D6111yescharacteristic, complemented
243C2×D4⋊C8—611no—
244C2×D4⋊C8—611no—
245C2×C61#164614yescomplemented
246C2×C61C2×#44911yescharacteristic
247C2×C61C2×#45211yescharacteristic
248C2×C61C2×#45511yescharacteristic
249D61—82no—
250D61—82no—
251C22×SD16—1221no—
252#555—614no—
253#555—1222no—
254#555—1222no—
255#555—1222no—
256C2×C4⋊Q8—611no—
257C2×C4⋊Q8C2×D6111yescharacteristic
258C2×#124—1222no—
259C2×#121—1221no—
260C2×#121—1221no—
261C2×C4×D4—611no—
262C2×C4×D4—611no—
263C2×#117—1221no—
264C2×#117—1221no—
265#487—614no—
266#487—1222no—
267#474—614no—
268#474—1222no—
269#461—614no—
270#461—1222no—
271C2×#107—1221no—
272C2×C4⋊C8C2×D6111yescharacteristic
273C2×C4⋊C8C2×D6111yescharacteristic
274C2×#103—1221no—
275C2×#103—1222no—
276C2×#102—1221no—
277C2×C4×C8—611no—
278#333C2×D6114yescomplemented
279D4⋊C8—614no—
280D4⋊C8—614no—
281C61C2×#164611yescharacteristic, complemented, Sylow
282C22×Q8—1221no—
283C22×Q8D24412yes—
284C22×D4—611no—
285C22×D4—611no—
286C22×D4—1222no—
287C23×C4—1221no—
288C23×C4—1221no—
289C2×SD16—1224no—
290C2×SD16—2444no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—1221no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—612no—
297C4⋊Q8—1221no—
298C4⋊Q8—1221no—
299C4⋊Q8—1221no—
300C4⋊Q8D24412yes—
301C4⋊Q8C22×D6112yes—
302#124—1228no—
303#124—1228no—
304#121—1224no—
305#121—1224no—
306#121—1224no—
307#121—1224no—
308C4×D4—612no—
309C4×D4—612no—
310C4×D4—612no—
311C4×D4—612no—
312C4×D4—1221no—
313C4×D4—1221no—
314C4×D4—1221no—
315C4×D4—1221no—
316#117—1224no—
317#117—1224no—
318#117—1224no—
319#117—1224no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—611no—
323C2×C4⋊C4—611no—
324C2×C4⋊C4—1221no—
325C2×C4⋊C4—1221no—
326C2×C22⋊C4—1222no—
327C2×C22⋊C4—1222no—
328C2×C22⋊C4—1221no—
329C2×C22⋊C4—1221no—
330C2×C42—1222no—
331C2×C42C22×D6111yescharacteristic
332#107—1224no—
333C4⋊C8—21no—
334C4⋊C8—21no—
335C4⋊C8C22×D6112yes—
336C4⋊C8C22×D6112yes—
337#103—1224no—
338#103—1228no—
339#102—1224no—
340C4×C8—612no—
341C4×C8—1221no—
342C24—1221no—
343C24—1221no—
344C2×Q8—22no—
345C2×Q8—44no—
346C2×Q8—1222no—
347C2×Q8—2442no—
348C2×Q8—2442no—
349C2×Q8—2441no—
350C2×Q8C2×D24414yes—
351C2×D4—612no—
352C2×D4—612no—
353C2×D4—1228no—
354C2×D4—1222no—
355C2×D4—1221no—
356C2×D4—1221no—
357C2×D4—1222no—
358C2×D4—1222no—
359C2×D4—1222no—
360C2×D4—4884no—
361C22×C4—22no—
362C22×C4—1221no—
363C22×C4—1221no—
364C22×C4—1222no—
365C22×C4—1222no—
366C22×C4—1222no—
367C22×C4—1222no—
368C22×C4—2441no—
369C22×C4—2442no—
370C22×C4—2442no—
371C22×C4—2442no—
372C22×C4—2442no—
373C22×C4C2×D24411yescharacteristic
374C22×C4D4×D6111yescharacteristic
375C22×C4D4×D6111yescharacteristic
376SD16—2448no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—42no—
380C2×C8—42no—
381C2×C8—1222no—
382C2×C8—2442no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—612no—
388C4⋊C4—612no—
389C4⋊C4—1221no—
390C4⋊C4—1221no—
391C4⋊C4—1222no—
392C4⋊C4—1222no—
393C4⋊C4—2441no—
394C4⋊C4—2441no—
395C22⋊C4—1228no—
396C22⋊C4—1228no—
397C22⋊C4—1222no—
398C22⋊C4—1222no—
399C22⋊C4—1222no—
400C22⋊C4—1222no—
401C42—1228no—
402C42C2×D24411yescharacteristic
403C42D4×D6111yescharacteristic
404C42D4×D6111yescharacteristic
405C42C23×D6111yescharacteristic
406C23—1222no—
407C23—1222no—
408C23—2442no—
409C23—2442no—
410C23—2442no—
411C23—2442no—
412C23—2442no—
413C23—2442no—
414C23#1451974711yescharacteristic
415Q8—44no—
416Q8—82no—
417Q8—4882no—
418Q8—2442no—
419Q8—2442no—
420D4—1222no—
421D4—1222no—
422D4—1222no—
423D4—1222no—
424D4—4888no—
425D4—2442no—
426D4—2442no—
427C2×C4—22no—
428C2×C4—24no—
429C2×C4—44no—
430C2×C4—1222no—
431C2×C4—1222no—
432C2×C4—4882no—
433C2×C4—2442no—
434C2×C4—2442no—
435C2×C4—2442no—
436C2×C4—2442no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4—2442no—
440C2×C4—2444no—
441C2×C4—2444no—
442C2×C4#1451974711yescharacteristic
443C2×C4#1451974711yescharacteristic
444C2×C4#1451974711yescharacteristic
445C2×C4#1451979812yes—
446C2×C4#1451980012yes—
447C2×C4#1451980412yes—
448C2×C4#1451980912yes—
449C2×C4C2×D4×D6111yescharacteristic
450C2×C4C2×D4×D6111yescharacteristic
451C2×C4C22×D24411yescharacteristic
452C8—42no—
453C8—42no—
454C8—2442no—
455C22—4884no—
456C22—4884no—
457C22—2442no—
458C22—2442no—
459C22—2442no—
460C22—2442no—
461C22—2442no—
462C22—2442no—
463C22#1683991012yes—
464C22#1683992712yes—
465C22#1683994212yes—
466C22C2×#1451974711yescharacteristic
467C4—21no—
468C4—21no—
469C4—44no—
470C4—4882no—
471C4—2442no—
472C4—2442no—
473C4#1683991012yes—
474C4#1683992712yes—
475C4C2×#1451979811yescharacteristic
476C4C2×#1451980011yescharacteristic
477C4C2×#1451980411yescharacteristic
478C4C2×#1451980911yescharacteristic
479C2—4882no—
480C2—4882no—
481C2#2144504814yesdirect product factor
482C2C2×#1683991011yescharacteristic
483C2C2×#1683992711yescharacteristic
484C2C2×#1683994211yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#333C2
socleC23×C61#120
prime radicalC2×#16840478C2
hypercenterC2×#333D61
hypocenterC61C2×#1646
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
2. C2×#16840112C2semidirect
3. C2×#16840043C2semidirect
4. C2×#16839968C2semidirect
5. #21445048C2direct (N × H)
6. C2×#16839489C2semidirect
7. C2×#16839489C2semidirect
8. C2×C61×#333C2semidirect
23. #16840112C22semidirect
25. #16840043C22semidirect
27. #16839968C22semidirect
33. #16839489C22semidirect
34. #16839489C22semidirect
38. C61×#333C22semidirect
242. C2×#333D61semidirect
245. C2×C61#1646semidirect
278. #333C2×D61semidirect
281. C61C2×#1646semidirect
481. C2#21445048direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404782
C2×#168401122
C2×#168400432
C2×#168399682
#214450482
C2×#168394892
C2×C61×#3332
C2×#164661