Finite Group Databasebeta

← C2×#21444987 #29655736

Subgroups — C2×#21444987 #29655736

Order 15616.

1174 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic122C211yesmaximal, characteristic
2C2×#16840113C211yesmaximal, characteristic, complemented
3C2×#16840058C211yesmaximal, characteristic, complemented
4C2×#16840052C211yesmaximal, characteristic
5#21444987C218yesmaximal, direct product factor
6C2×#16839509C211yesmaximal, characteristic, complemented
7C2×#16839494C211yesmaximal, characteristic, complemented
8C2×C61×D4⋊C8C211yesmaximal, characteristic
9C23×Dic122—21no—
10D4×Dic122—22no—
11D4×Dic122—22no—
12D4×Dic122—22no—
13D4×Dic122C2214yes—
14C2×#14519777C2211yescharacteristic
15C2×#14519777C2211yescharacteristic
16C2×#14519776—21no—
17C2×#14519756—21no—
18C2×#14519754—22no—
19C2×C4×Dic122C2211yescharacteristic
20C2×D4×Dic61—21no—
21#16840113—22no—
22#16840113C2214yescomplemented
23#16840058—22no—
24#16840058C2214yescomplemented
25#16840052—22no—
26#16840052C2214yes—
27C2×#14519711—21no—
28C2×#14519708—21no—
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519702—22no—
31C2×#14519702—21no—
32C2×#14519698—21no—
33#16839509C2214yescomplemented
34#16839494C2214yescomplemented
35C2×C4×D4×C61C2211yescharacteristic
36C2×C4⋊C8×C61C2211yescharacteristic
37C2×C4×C8×C61C2211yescharacteristic
38C61×D4⋊C8C2214yes—
39C22×Dic122—22no—
40C22×Dic122—24no—
41C22×Dic122—21no—
42C22×Dic122—24no—
43C22×Dic122—21no—
44C22×Dic122—44no—
45C22×Dic122—44no—
46C22×Dic122D411yescharacteristic
47C23×Dic61—22no—
48C22×#92418—21no—
49#14519777—21no—
50#14519777—21no—
51#14519777—21no—
52#14519777—21no—
53#14519777—21no—
54#14519777D412yes—
55#14519777C2312yes—
56#14519777C2312yes—
57#14519776—24no—
58#14519776—24no—
59#14519756—24no—
60#14519756—24no—
61#14519754—28no—
62#14519754—28no—
63C4×Dic122—21no—
64C4×Dic122—21no—
65C4×Dic122D412yes—
66C4×Dic122C2312yes—
67D4×Dic61—24no—
68D4×Dic61—24no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61D411yescharacteristic
73C2×C4⋊Dic61D412yes—
74C2×#11758196—22no—
75C2×#11758196—21no—
76C2×C22⋊Dic61—22no—
77C2×C4×Dic61—21no—
78#14519711—24no—
79#14519708—24no—
80C4⋊#92418—21no—
81C4⋊#92418C2312yes—
82#14519702—24no—
83#14519702—28no—
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—
101C2×D4×C61—21no—
102C2×D4×C61—22no—
103C2×D4×C61Q1614yes—
104C2×D4×C61C2×D412yes—
105C22×C4×C61—21no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—42no—
109C22×C4×C61—42no—
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×Dic61—21no—
114C22×Dic61—28no—
115C22×Dic61—22no—
116C22×Dic61—21no—
117C22×Dic61—48no—
118C22×Dic61—41no—
119C2×Dic122—21no—
120C2×Dic122—22no—
121C2×Dic122—28no—
122C2×Dic122—22no—
123C2×Dic122—22no—
124C2×Dic122—22no—
125C2×Dic122—48no—
126C2×Dic122—416no—
127C2×Dic122—48no—
128C2×Dic122—42no—
129C2×Dic122—42no—
130C2×Dic122—48no—
131C2×Dic122—44no—
132C2×Dic122—41no—
133C2×Dic122SD1614yes—
134C2×Dic122C2×D412yes—
135C2×C8×C61—22no—
136C2×C8×C61—22no—
137C2×C8×C61—42no—
138C2×C8×C61—42no—
139C4⋊C4×C61—21no—
140C4⋊C4×C61C2×D412yes—
141C22⋊C4×C61—22no—
142C22⋊C4×C61—22no—
143C42×C61C2×D411yescharacteristic
144C42×C61C2×D411yescharacteristic
145C42×C61C2×D411yescharacteristic
146C42×C61C2411yescharacteristic
147C22⋊Dic61—28no—
148C4⋊Dic61—22no—
149C4⋊Dic61—21no—
150C4⋊Dic61—22no—
151C4⋊Dic61—22no—
152C4⋊Dic61—22no—
153C4⋊Dic61—22no—
154C4⋊Dic61—41no—
155C4⋊Dic61—41no—
156C4⋊Dic61C2×D414yes—
157C4⋊Dic61C2×D412yes—
158#11758196—28no—
159#11758196—22no—
160#11758196—22no—
161C4×Dic61—22no—
162C4×Dic61—22no—
163C2×#92418—22no—
164C2×#92418—42no—
165C23×C61—22no—
166C23×C61—24no—
167C23×C61—42no—
168C23×C61—42no—
169C23×C61#12011yescharacteristic
170D4×C61—22no—
171D4×C61—24no—
172D4×C61C2×Q1614yes—
173C2×C4×C61—22no—
174C2×C4×C61—22no—
175C2×C4×C61—42no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61—44no—
179C2×C4×C61#12011yescharacteristic
180C2×C4×C61#12011yescharacteristic
181C2×C4×C61#12011yescharacteristic
182C2×C4×C61C2×SD1612yes—
183C2×C4×C61C2×Q1612yes—
184C2×C4×C61AGL(1,ℤ/8)12yes—
185C2×C4×C61#13712yes—
186C2×C4×C61C22×D411yescharacteristic
187C2×C4×C61C22×D411yescharacteristic
188C2×C4×C61C22×D411yescharacteristic
189C2×Dic61—22no—
190C2×Dic61—24no—
191C2×Dic61—22no—
192C2×Dic61—24no—
193C2×Dic61—416no—
194C2×Dic61—44no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61—82no—
198Dic122—22no—
199Dic122—24no—
200Dic122—416no—
201Dic122—42no—
202Dic122—42no—
203Dic122—44no—
204Dic122—44no—
205Dic122—82no—
206Dic122C2×SD1614yes—
207C8×C61—42no—
208C8×C61—42no—
209#92418—42no—
210C2×#1637—611nomaximal, Sylow
211C22×C61—24no—
212C22×C61—48no—
213C22×C61—42no—
214C22×C61—42no—
215C22×C61#45012yes—
216C22×C61#45112yes—
217C22×C61#45412yes—
218C22×C61C2×#12011yescharacteristic
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—42no—
222C4×C61#45012yes—
223C4×C61#45112yes—
224C4×C61C22×SD1611yescharacteristic
225C4×C61C22×Q1611yescharacteristic
226C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
227C4×C61C2×#13711yescharacteristic
228Dic61—24no—
229Dic61—44no—
230Dic61—42no—
231Dic61—82no—
232C2×D4×Q8—611no—
233C2×#487—611no—
234C2×#477—611no—
235C2×#476—611no—
236#1637—618no—
237C2×#332—611no—
238C2×Q8⋊C8—611no—
239C2×D4⋊C8D6111yescharacteristic
240C2×C61—44no—
241C2×C61#163714yescomplemented
242C2×C61C2×#45011yescharacteristic
243C2×C61C2×#45111yescharacteristic
244C2×C61C2×#45411yescharacteristic
245C23×Q8—1221no—
246D4×Q8—614no—
247D4×Q8—1222no—
248D4×Q8—1222no—
249D4×Q8—1222no—
250C2×C4⋊Q8—611no—
251C2×C4⋊Q8—611no—
252C2×C4⋊Q8—1221no—
253C2×C22⋊Q8—1222no—
254C2×C22⋊Q8—1221no—
255C2×C4×Q8—611no—
256C2×C4×D4—1221no—
257C2×C4×D4C2×D6111yescharacteristic
258#487—614no—
259#487—1222no—
260#477—614no—
261#477—1222no—
262#476—614no—
263#476—1222no—
264C2×#107—1221no—
265C2×#106—1221no—
266C2×C4⋊C8—611no—
267C2×C4⋊C8C2×D6111yescharacteristic
268C2×#103—1222no—
269C2×#103—1221no—
270C2×#102—1221no—
271C2×C4×C8C2×D6111yescharacteristic
272#332—614no—
273Q8⋊C8—614no—
274D4⋊C8C2×D6114yes—
275C61C2×#163711yescharacteristic, complemented, Sylow
276C22×Q8—611no—
277C22×Q8—1224no—
278C22×Q8—1222no—
279C22×Q8—1224no—
280C22×Q8—1221no—
281C22×Q8—1221no—
282C22×Q8—2444no—
283C22×Q8—2444no—
284C22×D4D24411yescharacteristic
285C23×C4—21no—
286C23×C4—1222no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—1221no—
290C4⋊Q8—612no—
291C4⋊Q8—612no—
292C4⋊Q8—612no—
293C4⋊Q8—1224no—
294C4⋊Q8—1224no—
295C4⋊Q8—1221no—
296C4⋊Q8—1221no—
297C4⋊Q8—1221no—
298C4⋊Q8—1221no—
299C4⋊Q8—1221no—
300C22⋊Q8—1228no—
301C22⋊Q8—1228no—
302C22⋊Q8—1224no—
303C22⋊Q8—1224no—
304C4×Q8—612no—
305C4×Q8—612no—
306C4×Q8—1221no—
307C4×Q8—1221no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4—1224no—
311C4×D4—1224no—
312C4×D4D24412yes—
313C4×D4C22×D6112yes—
314C2×C4⋊C4—611no—
315C2×C4⋊C4—612no—
316C2×C4⋊C4—1222no—
317C2×C4⋊C4—1221no—
318C2×C4⋊C4—1221no—
319C2×C4⋊C4—1221no—
320C2×C4⋊C4—1221no—
321C2×C4⋊C4D24411yescharacteristic
322C2×C22⋊C4—21no—
323C2×C22⋊C4—1222no—
324C2×C42—1221no—
325C2×C42C22×D6111yescharacteristic
326#107—1224no—
327#106—1224no—
328C4⋊C8—21no—
329C4⋊C8—612no—
330C4⋊C8—1221no—
331C4⋊C8C22×D6112yes—
332#103—1228no—
333#103—1224no—
334#102—1224no—
335C4×C8—21no—
336C4×C8C22×D6112yes—
337C24—21no—
338C2×Q8—612no—
339C2×Q8—614no—
340C2×Q8—1228no—
341C2×Q8—1222no—
342C2×Q8—1221no—
343C2×Q8—1222no—
344C2×Q8—1222no—
345C2×Q8—1222no—
346C2×Q8—2444no—
347C2×Q8—2448no—
348C2×Q8—2448no—
349C2×Q8—2448no—
350C2×Q8—24416no—
351C2×Q8—2441no—
352C2×Q8—2442no—
353C2×Q8—2442no—
354C2×D4—22no—
355C2×D4—21no—
356C2×D4Dic24414yes—
357C2×D4C2×D24412yes—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—1221no—
364C22×C4—1228no—
365C22×C4—1221no—
366C22×C4—1222no—
367C22×C4—2448no—
368C22×C4—2441no—
369C22×C4C2×D24411yescharacteristic
370C22×C4D4×D6111yescharacteristic
371C22×C4D4×D6111yescharacteristic
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—42no—
375C2×C8—42no—
376C2×C8—1222no—
377C2×C8—2442no—
378C4⋊C4—21no—
379C4⋊C4—614no—
380C4⋊C4—612no—
381C4⋊C4—1228no—
382C4⋊C4—1222no—
383C4⋊C4—1222no—
384C4⋊C4—1221no—
385C4⋊C4—1222no—
386C4⋊C4—1222no—
387C4⋊C4—1222no—
388C4⋊C4—1222no—
389C4⋊C4—1222no—
390C4⋊C4—2441no—
391C4⋊C4—2441no—
392C4⋊C4C2×D24412yes—
393C22⋊C4—22no—
394C22⋊C4—22no—
395C22⋊C4—1228no—
396C42—1222no—
397C42—1222no—
398C42C2×D24411yescharacteristic
399C42D4×D6111yescharacteristic
400C42D4×D6111yescharacteristic
401C42C23×D6111yescharacteristic
402C23—22no—
403C23—24no—
404C23—42no—
405C23—42no—
406C23#1451974711yescharacteristic
407Q8—614no—
408Q8—1222no—
409Q8—1224no—
410Q8—4882no—
411Q8—2444no—
412Q8—24416no—
413Q8—2442no—
414Q8—2442no—
415Q8—2444no—
416D4—22no—
417D4—24no—
418D4C2×Dic24414yes—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—44no—
425C2×C4—1222no—
426C2×C4—1224no—
427C2×C4—1222no—
428C2×C4—1224no—
429C2×C4—4882no—
430C2×C4—24416no—
431C2×C4—2442no—
432C2×C4—2442no—
433C2×C4—2444no—
434C2×C4#1451974711yescharacteristic
435C2×C4#1451974711yescharacteristic
436C2×C4#1451974711yescharacteristic
437C2×C4SD16×D6112yes—
438C2×C4C2×Dic24412yes—
439C2×C4#1451980112yes—
440C2×C4#1451981012yes—
441C2×C4C2×D4×D6111yescharacteristic
442C2×C4C2×D4×D6111yescharacteristic
443C2×C4C22×D24411yescharacteristic
444C8—42no—
445C8—42no—
446C8—2442no—
447C22—24no—
448C22—42no—
449C22—48no—
450C22—42no—
451C22#1683991412yes—
452C22#1683992012yes—
453C22#1683993612yes—
454C22C2×#1451974711yescharacteristic
455C4—21no—
456C4—21no—
457C4—42no—
458C4—1224no—
459C4—4882no—
460C4—2442no—
461C4—2444no—
462C4#1683991412yes—
463C4#1683992012yes—
464C4C2×SD16×D6111yescharacteristic
465C4C22×Dic24411yescharacteristic
466C4C2×#1451980111yescharacteristic
467C4C2×#1451981011yescharacteristic
468C2—44no—
469C2#2144498714yesdirect product factor
470C2C2×#1683991411yescharacteristic
471C2C2×#1683992011yescharacteristic
472C2C2×#1683993611yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenterC2×D4⋊C8D61
hypocenterC61C2×#1637
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×#16840058C2semidirect
5. #21444987C2direct (N × H)
6. C2×#16839509C2semidirect
7. C2×#16839494C2semidirect
22. #16840113C22semidirect
24. #16840058C22semidirect
33. #16839509C22semidirect
34. #16839494C22semidirect
241. C2×C61#1637semidirect
275. C61C2×#1637semidirect
469. C2#21444987direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Dic1222
C2×#168401132
C2×#168400582
C2×#168400522
#214449872
C2×#168395092
C2×#168394942
C2×C61×D4⋊C82
C2×#163761