Finite Group Databasebeta

← C2×#21445008 #29655696

Subgroups — C2×#21445008 #29655696

Order 15616.

1042 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×#16840497C211yesmaximal, characteristic
2C2×#16840109C211yesmaximal, characteristic
3C2×#16840047C211yesmaximal, characteristic, complemented
4C2×#16839973C211yesmaximal, characteristic, complemented
5#21445008C218yesmaximal, direct product factor
6C2×#16839505C211yesmaximal, characteristic
7C2×#16839494C211yesmaximal, characteristic, complemented
8C2×C61×Q8⋊C8C211yesmaximal, characteristic, complemented
9C22×Dic244—21no—
10#16840497—22no—
11#16840497—22no—
12#16840497—22no—
13#16840497C2214yes—
14C2×#14519777C2211yescharacteristic
15C2×#14519774C2211yescharacteristic
16C2×#14519766—21no—
17C2×#14519765—21no—
18C2×#14519762—22no—
19C2×C4×Dic122C2211yescharacteristic
20C2×C4×D244—21no—
21C2×#14519739—21no—
22#16840109—22no—
23#16840109C2214yes—
24#16840047—22no—
25#16840047C2214yescomplemented
26#16839973—22no—
27#16839973C2214yescomplemented
28C2×#14519708—21no—
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519702—21no—
31C2×#14519701—21no—
32C2×#14519699—22no—
33#16839505C2214yes—
34#16839494C2214yescomplemented
35C2×C4×Q8×C61C2211yescharacteristic
36C2×C4⋊C8×C61C2211yescharacteristic
37C2×C4×C8×C61C2211yescharacteristic
38C61×Q8⋊C8C2214yescomplemented
39C22×Dic122—21no—
40C22×Dic122D411yescharacteristic
41C22×D244—21no—
42C22×D244—21no—
43C22×D244D412yes—
44C22×C4×D61—22no—
45C2×Dic244—24no—
46C2×Dic244—44no—
47C22×#92418—21no—
48#14519777—21no—
49#14519777—21no—
50#14519777—21no—
51#14519777C2312yes—
52#14519774—21no—
53#14519774—21no—
54#14519774D412yes—
55#14519774C2312yes—
56#14519766—24no—
57#14519766—24no—
58#14519765—24no—
59#14519765—24no—
60#14519762—28no—
61#14519762—28no—
62C4×Dic122—21no—
63C4×Dic122—21no—
64C4×Dic122D412yes—
65C4×Dic122C2312yes—
66C4×D244—24no—
67C4×D244—24no—
68#14519739—24no—
69#14519739—24no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61D411yescharacteristic
73C2×#11758196—21no—
74C2×#11758198—22no—
75C2×#11758198—22no—
76C2×#11758198—22no—
77C2×C4×Dic61—21no—
78#14519708—24no—
79C4⋊#92418—21no—
80C4⋊#92418C2312yes—
81#14519702—24no—
82#14519701—24no—
83#14519699—28no—
84C22×Q8×C61D411yescharacteristic
85C22×C8×C61—21no—
86C22×C8×C61—21no—
87C4×Q8×C61—21no—
88C4×Q8×C61—21no—
89C4×Q8×C61D412yes—
90C4×Q8×C61C2312yes—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61D411yescharacteristic
93C2×C42×C61—21no—
94C2×C42×C61C2311yescharacteristic
95C4⋊C8×C61—21no—
96C4⋊C8×C61C2312yes—
97C4×C8×C61—21no—
98C4×C8×C61C2312yes—
99C23×D61—22no—
100C2×Q8×C61—21no—
101C2×Q8×C61—22no—
102C2×Q8×C61—22no—
103C2×Q8×C61C2×D412yes—
104C22×C4×C61—21no—
105C22×C4×C61—21no—
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×Dic61—21no—
110C22×Dic61—21no—
111C22×Dic61—41no—
112C2×D244—22no—
113C2×D244—22no—
114C2×D244—22no—
115C2×D244—22no—
116C2×D244—22no—
117C2×D244—42no—
118C2×D244—42no—
119C2×D244—42no—
120C2×D244—42no—
121C2×D244—44no—
122C2×D244C2×D414yes—
123C2×C4×D61—28no—
124C2×C4×D61—84no—
125C2×Dic122—22no—
126C2×Dic122—22no—
127C2×Dic122—21no—
128C2×Dic122—22no—
129C2×Dic122—42no—
130C2×Dic122—42no—
131C2×Dic122—41no—
132C2×Dic122C2×D412yes—
133C2×C8×C61—22no—
134C2×C8×C61—22no—
135C2×C8×C61—42no—
136C2×C8×C61—42no—
137C4⋊C4×C61—22no—
138C4⋊C4×C61—21no—
139C4⋊C4×C61—22no—
140C4⋊C4×C61C2×D412yes—
141C42×C61—22no—
142C42×C61—22no—
143C42×C61C2×D411yescharacteristic
144C42×C61C2×D411yescharacteristic
145C42×C61C2×D411yescharacteristic
146C42×C61C2411yescharacteristic
147#11758198—28no—
148#11758198—28no—
149#11758198—28no—
150C4⋊Dic61—21no—
151C4⋊Dic61—22no—
152C4⋊Dic61—22no—
153C4⋊Dic61—41no—
154C4⋊Dic61—41no—
155C4⋊Dic61C2×D412yes—
156#11758196—22no—
157#11758196—22no—
158C4×Dic61—22no—
159C4×Dic61—22no—
160C2×#92418—22no—
161C2×#92418—42no—
162Dic244—48no—
163C23×C61#12011yescharacteristic
164C22×D61—24no—
165C22×D61—44no—
166C22×D61—44no—
167C22×D61—44no—
168Q8×C61—22no—
169Q8×C61—22no—
170Q8×C61—42no—
171C2×C4×C61—22no—
172C2×C4×C61—22no—
173C2×C4×C61—22no—
174C2×C4×C61—42no—
175C2×C4×C61—42no—
176C2×C4×C61#12011yescharacteristic
177C2×C4×C61#12011yescharacteristic
178C2×C4×C61#12011yescharacteristic
179C2×C4×C61#13512yes—
180C2×C4×C61#13512yes—
181C2×C4×C61AGL(1,ℤ/8)12yes—
182C2×C4×C61#13712yes—
183C2×C4×C61C22×D411yescharacteristic
184C2×C4×C61C22×D411yescharacteristic
185C2×C4×C61C22×D411yescharacteristic
186C2×Dic61—22no—
187C2×Dic61—22no—
188C2×Dic61—42no—
189C2×Dic61—42no—
190C2×Dic61—42no—
191C2×Dic61—82no—
192D244—44no—
193D244—42no—
194D244—42no—
195D244—42no—
196D244—42no—
197D244—44no—
198D244—44no—
199D244—82no—
200C4×D61—88no—
201Dic122—22no—
202Dic122—22no—
203Dic122—42no—
204Dic122—42no—
205Dic122—42no—
206Dic122—82no—
207C8×C61—42no—
208C8×C61—42no—
209#92418—42no—
210C2×#1640—611nomaximal, Sylow
211C22×C61#44912yes—
212C22×C61#45212yes—
213C22×C61#45512yes—
214C22×C61C2×#12011yescharacteristic
215C2×D61—44no—
216C2×D61—44no—
217C2×D61—44no—
218C2×D61—88no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—42no—
222C4×C61—42no—
223C4×C61#44912yes—
224C4×C61#45212yes—
225C4×C61C2×#13511yescharacteristic
226C4×C61C2×#13511yescharacteristic
227C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
228C4×C61C2×#13711yescharacteristic
229Dic61—42no—
230Dic61—42no—
231Dic61—82no—
232C2×#559—611no—
233C2×#486—611no—
234C2×#475—611no—
235C2×#462—611no—
236#1640—618no—
237C2×#331—611no—
238C2×Q8⋊C8—611no—
239C2×Q8⋊C8D6111yescharacteristic, complemented
240C2×C61#164014yescomplemented
241C2×C61C2×#44911yescharacteristic
242C2×C61C2×#45211yescharacteristic
243C2×C61C2×#45511yescharacteristic
244D61—84no—
245C22×Q16—1221no—
246#559—614no—
247#559—1222no—
248#559—1222no—
249#559—1222no—
250C2×C4⋊Q8—611no—
251C2×#127—611no—
252C2×#124—1221no—
253C2×#124—1221no—
254C2×#123—1222no—
255C2×C4×Q8—611no—
256C2×C4×Q8C2×D6111yescharacteristic
257C2×C4×D4—1221no—
258C2×C4×D4—1221no—
259#486—614no—
260#486—1222no—
261#475—614no—
262#475—1222no—
263#462—614no—
264#462—1222no—
265C2×#106—1221no—
266C2×C4⋊C8—611no—
267C2×C4⋊C8C2×D6111yescharacteristic
268C2×#103—1221no—
269C2×#103—1221no—
270C2×#102—1222no—
271C2×C4×C8C2×D6111yescharacteristic
272#331—614no—
273Q8⋊C8—614no—
274Q8⋊C8C2×D6114yescomplemented
275C61C2×#164011yescharacteristic, complemented, Sylow
276C22×Q8—611no—
277C22×Q8—1221no—
278C22×Q8D24411yescharacteristic
279C22×D4—612no—
280C22×D4—1221no—
281C22×D4—1221no—
282C23×C4—1222no—
283C2×Q16—1224no—
284C2×Q16—2444no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—1221no—
288C4⋊Q8—612no—
289C4⋊Q8—1221no—
290C4⋊Q8—1221no—
291C4⋊Q8—1221no—
292#127—612no—
293#127—612no—
294#127—1221no—
295#127—1221no—
296#124—1224no—
297#124—1224no—
298#124—1224no—
299#124—1224no—
300#123—1228no—
301#123—1228no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—612no—
305C4×Q8—612no—
306C4×Q8—1221no—
307C4×Q8—1221no—
308C4×Q8D24412yes—
309C4×Q8C22×D6112yes—
310C4×D4—1224no—
311C4×D4—1224no—
312C4×D4—1224no—
313C4×D4—1224no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—611no—
316C2×C4⋊C4—1221no—
317C2×C4⋊C4—1221no—
318C2×C4⋊C4—1221no—
319C2×C4⋊C4D24411yescharacteristic
320C2×C22⋊C4—1222no—
321C2×C22⋊C4—1222no—
322C2×C22⋊C4—1222no—
323C2×C42—21no—
324C2×C42—1221no—
325C2×C42C22×D6111yescharacteristic
326#106—1224no—
327C4⋊C8—21no—
328C4⋊C8—612no—
329C4⋊C8—1221no—
330C4⋊C8C22×D6112yes—
331#103—1224no—
332#103—1224no—
333#102—1228no—
334C4×C8—21no—
335C4×C8C22×D6112yes—
336C24—1222no—
337C2×Q8—21no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—612no—
341C2×Q8—1221no—
342C2×Q8—1222no—
343C2×Q8—1222no—
344C2×Q8—1222no—
345C2×Q8—2442no—
346C2×Q8—2442no—
347C2×Q8—2441no—
348C2×Q8C2×D24412yes—
349C2×D4—614no—
350C2×D4—1222no—
351C2×D4—1222no—
352C2×D4—1222no—
353C2×D4—1222no—
354C2×D4—1222no—
355C2×D4—2444no—
356C2×D4—2442no—
357C2×D4—2442no—
358C2×D4—2442no—
359C2×D4—2442no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—1228no—
363C22×C4—1221no—
364C22×C4—1221no—
365C22×C4—4884no—
366C22×C4—2441no—
367C22×C4C2×D24411yescharacteristic
368C22×C4D4×D6111yescharacteristic
369C22×C4D4×D6111yescharacteristic
370Q16—2448no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—42no—
374C2×C8—42no—
375C2×C8—1222no—
376C2×C8—2442no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—612no—
381C4⋊C4—1222no—
382C4⋊C4—1221no—
383C4⋊C4—1222no—
384C4⋊C4—1222no—
385C4⋊C4—1222no—
386C4⋊C4—2441no—
387C4⋊C4—2441no—
388C4⋊C4C2×D24412yes—
389C22⋊C4—1228no—
390C22⋊C4—1228no—
391C22⋊C4—1228no—
392C42—22no—
393C42—22no—
394C42—1222no—
395C42—1222no—
396C42C2×D24411yescharacteristic
397C42D4×D6111yescharacteristic
398C42D4×D6111yescharacteristic
399C42C23×D6111yescharacteristic
400C23—1224no—
401C23—2444no—
402C23—2444no—
403C23—2444no—
404C23#1451974711yescharacteristic
405Q8—22no—
406Q8—22no—
407Q8—42no—
408Q8—1222no—
409Q8—1222no—
410Q8—4882no—
411Q8—2442no—
412Q8—2442no—
413Q8—2442no—
414D4—4882no—
415D4—2444no—
416D4—2442no—
417D4—2442no—
418D4—2442no—
419D4—2442no—
420D4—2444no—
421D4—2444no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—1222no—
428C2×C4—1222no—
429C2×C4—4888no—
430C2×C4—4882no—
431C2×C4—2442no—
432C2×C4—2442no—
433C2×C4—2442no—
434C2×C4#1451974711yescharacteristic
435C2×C4#1451974711yescharacteristic
436C2×C4#1451974711yescharacteristic
437C2×C4#1451979912yes—
438C2×C4#1451980012yes—
439C2×C4#1451980412yes—
440C2×C4#1451981012yes—
441C2×C4C2×D4×D6111yescharacteristic
442C2×C4C2×D4×D6111yescharacteristic
443C2×C4C22×D24411yescharacteristic
444C8—42no—
445C8—42no—
446C8—2442no—
447C22—4888no—
448C22—2444no—
449C22—2444no—
450C22—2444no—
451C22#1683991012yes—
452C22#1683992612yes—
453C22#1683994112yes—
454C22C2×#1451974711yescharacteristic
455C4—21no—
456C4—21no—
457C4—42no—
458C4—42no—
459C4—4882no—
460C4—2442no—
461C4—2442no—
462C4#1683991012yes—
463C4#1683992612yes—
464C4C2×#1451979911yescharacteristic
465C4C2×#1451980011yescharacteristic
466C4C2×#1451980411yescharacteristic
467C4C2×#1451981011yescharacteristic
468C2—4884no—
469C2#2144500814yesdirect product factor
470C2C2×#1683991011yescharacteristic
471C2C2×#1683992611yescharacteristic
472C2C2×#1683994111yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×Q8⋊C8C2
socleC23×C61#120
prime radicalC2×#14519774C22
hypercenterC2×Q8⋊C8D61
hypocenterC61C2×#1640
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
3. C2×#16840047C2semidirect
4. C2×#16839973C2semidirect
5. #21445008C2direct (N × H)
7. C2×#16839494C2semidirect
8. C2×C61×Q8⋊C8C2semidirect
25. #16840047C22semidirect
27. #16839973C22semidirect
34. #16839494C22semidirect
38. C61×Q8⋊C8C22semidirect
239. C2×Q8⋊C8D61semidirect
240. C2×C61#1640semidirect
274. Q8⋊C8C2×D61semidirect
275. C61C2×#1640semidirect
469. C2#21445008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404972
C2×#168401092
C2×#168400472
C2×#168399732
#214450082
C2×#168395052
C2×#168394942
C2×C61×Q8⋊C82
C2×#164061