Finite Group Databasebeta

← C4×D8×Dic59 #28587154

Subgroups — C4×D8×Dic59 #28587154

Order 15104.

1350 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic59C212yesmaximal
2C4×D4×Dic59C212yesmaximal, complemented
3#107×Dic59C212yesmaximal, complemented
4C4×#14273661C211yesmaximal, characteristic, complemented
5#102×Dic59C214yesmaximal, complemented
6C4×#14273648C212yesmaximal, complemented
7C4×C8×Dic59C211yesmaximal, characteristic, complemented
8C2×C4×D8×C59C211yesmaximal, characteristic
9C2×D4×Dic59C2214yes—
10C22×C4×Dic59—22no—
11D8×Dic59C4116yesdirect product factor
12C2×#14273661C2212yes—
13C2×#14273648C2214yes—
14C2×C4×C59⋊C8C2211yescharacteristic
15C2×C8×Dic59C2212yes—
16C2×C8×Dic59C2212yes—
17C4⋊C4×Dic59C2214yes—
18C4×C4⋊Dic59C2212yes—
19C22⋊C4×Dic59—24no—
20C4×C22⋊Dic59—22no—
21C42×Dic59C2211yescharacteristic
22#16837165C2212yes—
23#16837164C2214yes—
24C22×D8×C59C2211yescharacteristic
25C2×C4×D4×C59C2212yes—
26C4×D8×C59C418yescomplemented
27C2×#107×C59C2211yescharacteristic
28C2×#102×C59C2212yes—
29C2×C4×C8×C59C2211yescharacteristic
30C23×Dic59—24no—
31C22×C59⋊C8C2312yes—
32D4×Dic59—28no—
33D4×Dic59C2×C4116yescomplemented
34C2×C4⋊Dic59C2314yes—
35C2×C22⋊Dic59—24no—
36C2×C4×Dic59—22no—
37C2×C4×Dic59—24no—
38C2×C4×Dic59—48no—
39C2×C4×Dic59D411yescharacteristic
40C2×C4×Dic59D412yes—
41C2×C4×Dic59D411yescharacteristic
42C2×C4×Dic59C2312yes—
43#14273661C2×C418yescomplemented
44#14273648C2×C4116yescomplemented
45C4×C59⋊C8—22no—
46C8×Dic59—24no—
47C8×Dic59C2×C418yescomplemented
48C59⋊#95—22no—
49C59⋊#95—24no—
50C22×D4×C59C2312yes—
51C23×C4×C59—22no—
52C2×D8×C59C2×C418yes—
53C2×D8×C59C2×C414yes—
54C22×C8×C59C2311yescharacteristic
55C22×C8×C59C2311yescharacteristic
56C4×D4×C59—24no—
57C4×D4×C59C2×C418yescomplemented
58C2×C4⋊C4×C59C2312yes—
59C2×C22⋊C4×C59—22no—
60C2×C42×C59C2311yescharacteristic
61#107×C59C2×C414yescomplemented
62#102×C59C2×C418yescomplemented
63C4×C8×C59C2×C414yescomplemented
64C24×C59—22no—
65C2×D4×C59—22no—
66C2×D4×C59—24no—
67C2×D4×C59C22×C418yes—
68C2×D4×C59C22×C414yes—
69C22×C4×C59—22no—
70C22×C4×C59—28no—
71C22×C4×C59—44no—
72C22×C4×C59—44no—
73C22×C4×C59C2×D411yescharacteristic
74C22×C4×C59C2×D411yescharacteristic
75C22×C4×C59C2411yescharacteristic
76C22×Dic59—24no—
77C22×Dic59—216no—
78C22×Dic59—48no—
79C22×Dic59—48no—
80C22×Dic59C2×D412yes—
81C22×Dic59C2×D412yes—
82D8×C59C42116yescomplemented
83C2×C8×C59—22no—
84C2×C8×C59C22×C412yes—
85C2×C8×C59C22×C414yes—
86C2×C8×C59C22×C412yes—
87C4⋊C4×C59—22no—
88C4⋊C4×C59C22×C414yes—
89C22⋊C4×C59—28no—
90C42×C59C22×C412yes—
91C42×C59#4112yes—
92C22⋊Dic59—216no—
93C4⋊Dic59—24no—
94C4⋊Dic59C22×C418yes—
95C4×Dic59—22no—
96C4×Dic59—24no—
97C4×Dic59—44no—
98C4×Dic59—48no—
99C4×Dic59D814yesdirect product factor
100C4×Dic59C22×C414yes—
101C4×Dic59#4114yes—
102C2×C59⋊C8—22no—
103C2×C59⋊C8—22no—
104C2×C59⋊C8C22×C414yes—
105C23×C59—28no—
106C23×C59—24no—
107C23×C59—42no—
108C23×C59—44no—
109C23×C59—42no—
110C23×C59C22×D411yescharacteristic
111D4×C59—28no—
112D4×C59—24no—
113D4×C59C2×C4218yescomplemented
114C2×C4×C59—22no—
115C2×C4×C59—24no—
116C2×C4×C59—42no—
117C2×C4×C59—42no—
118C2×C4×C59—416no—
119C2×C4×C59C4×D412yes—
120C2×C4×C59C4×D412yes—
121C2×C4×C59C2×D812yes—
122C2×C4×C59#13512yes—
123C2×C4×C59C23×C412yes—
124C2×C4×C59C23×C411yescharacteristic
125C2×C4×C59C2×#4112yes—
126C2×C4×C59C2×#4111yescharacteristic
127C2×Dic59—22no—
128C2×Dic59—22no—
129C2×Dic59—28no—
130C2×Dic59—44no—
131C2×Dic59—44no—
132C2×Dic59—432no—
133C2×Dic59C4×D414yes—
134C2×Dic59C4×D414yes—
135C2×Dic59C2×D814yes—
136C2×Dic59#13514yes—
137C8×C59—22no—
138C8×C59C2×C4214yescomplemented
139C59⋊C8—24no—
140C42×D8—591nomaximal, Sylow
141C22×C59—28no—
142C22×C59—48no—
143C22×C59—44no—
144C22×C59—48no—
145C22×C59—44no—
146C22×C59C2×C4×D412yes—
147C22×C59C2×C4×D411yescharacteristic
148C22×C59C22×D811yescharacteristic
149C22×C59C2×#13512yes—
150C22×C59C2×#13511yescharacteristic
151C4×C59—22no—
152C4×C59—44no—
153C4×C59C4×D814yescomplemented
154C4×C59C22×C4211yescharacteristic
155C4×C59C4×#4112yes—
156C4×C59C4×#4111yescharacteristic
157Dic59—24no—
158Dic59—48no—
159Dic59C4×D818yesdirect product factor
160C2×C4×D8—592no—
161C2×C4×D8D5911yescharacteristic
162C42×D4—592no—
163C4×#107—592no—
164C4×#107—591no—
165C4×#102—594no—
166C4×#102—592no—
167C42×C8—591no—
168C2×C59—48no—
169C2×C59C42×D411yescharacteristic
170C2×C59C2×C4×D812yes—
171C2×C59C2×C4×D811yescharacteristic
172C2×C59C4×#13512yes—
173C2×C59C4×#13511yescharacteristic
174C22×D8C2×D5911yescharacteristic
175C2×C4×D4—594no—
176C2×C4×D4C2×D5912yes—
177C22×C42—1182no—
178C4×D8—5916no—
179C4×D8Dic5918yesdirect product factor
180C2×#107—592no—
181C2×#107C2×D5911yescharacteristic
182C2×#102—594no—
183C2×#102C2×D5912yes—
184C2×C4×C8—592no—
185C2×C4×C8—592no—
186C2×C4×C8—591no—
187C2×C4×C8C2×D5911yescharacteristic
188C4×C4⋊C4—594no—
189C4×C4⋊C4—592no—
190C4×C22⋊C4—1184no—
191C4×C22⋊C4—1182no—
192C43—591no—
193#340—592no—
194#340—594no—
195C59C42×D811yescharacteristic, complemented, Sylow
196C22×D4C22×D5912yes—
197C23×C4—22no—
198C23×C4—1184no—
199C2×D8C4×D5918yes—
200C2×D8C2×Dic5914yes—
201C22×C8—592no—
202C22×C8C22×D5911yescharacteristic
203C22×C8C22×D5911yescharacteristic
204C4×D4—24no—
205C4×D4—5916no—
206C4×D4—1188no—
207C4×D4C2×Dic5918yescomplemented
208C2×C4⋊C4—594no—
209C2×C4⋊C4C22×D5912yes—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—1184no—
212C2×C42—591no—
213C2×C42—592no—
214C2×C42—592no—
215C2×C42—591no—
216C2×C42—1184no—
217C2×C42—1182no—
218C2×C42—2368no—
219C2×C42C22×D5911yescharacteristic
220#107—598no—
221#107C2×Dic5914yescomplemented
222#102—5916no—
223#102C2×Dic5918yescomplemented
224C4×C8—598no—
225C4×C8—1184no—
226C4×C8—1182no—
227C4×C8C2×Dic5914yescomplemented
228#95—1184no—
229#95—1182no—
230C24—22no—
231C2×D4—24no—
232C2×D4—22no—
233C2×D4C2×C4×D5918yes—
234C2×D4C22×Dic5914yes—
235C22×C4—22no—
236C22×C4—28no—
237C22×C4—44no—
238C22×C4—44no—
239C22×C4—592no—
240C22×C4—592no—
241C22×C4—11816no—
242C22×C4—1184no—
243C22×C4—2368no—
244C22×C4—2368no—
245C22×C4D4×D5911yescharacteristic
246C22×C4D4×D5911yescharacteristic
247C22×C4C23×D5911yescharacteristic
248D8C4×Dic59116yesdirect product factor
249C2×C8—22no—
250C2×C8—594no—
251C2×C8—1182no—
252C2×C8—1182no—
253C2×C8C2×C4×D5914yes—
254C2×C8C22×Dic5912yes—
255C2×C8C22×Dic5912yes—
256C4⋊C4—22no—
257C4⋊C4—598no—
258C4⋊C4—1184no—
259C4⋊C4C22×Dic5914yes—
260C22⋊C4—28no—
261C22⋊C4—11816no—
262C42—594no—
263C42—594no—
264C42—594no—
265C42—1184no—
266C42—1182no—
267C42—2368no—
268C42—2364no—
269C42#1174568712yes—
270C42C22×Dic5912yes—
271C23—28no—
272C23—24no—
273C23—42no—
274C23—44no—
275C23—42no—
276C23C2×D4×D5911yescharacteristic
277D4—28no—
278D4—24no—
279D4C2×C4×Dic5918yescomplemented
280C2×C4—22no—
281C2×C4—24no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—416no—
285C2×C4—594no—
286C2×C4—594no—
287C2×C4—594no—
288C2×C4—594no—
289C2×C4—1182no—
290C2×C4—1182no—
291C2×C4—1188no—
292C2×C4—23632no—
293C2×C4—2364no—
294C2×C4—2364no—
295C2×C4D4×Dic5912yes—
296C2×C4D4×Dic5912yes—
297C2×C4D8×D5912yes—
298C2×C4#1427374612yes—
299C2×C4C22×C4×D5912yes—
300C2×C4C23×Dic5911yescharacteristic
301C2×C4#41×D5912yes—
302C2×C4C2×#1174568711yescharacteristic
303C8—22no—
304C8—1184no—
305C8C2×C4×Dic5914yescomplemented
306C22—28no—
307C22—48no—
308C22—44no—
309C22—48no—
310C22—44no—
311C22C4×D4×D5912yes—
312C22C2×D4×Dic5911yescharacteristic
313C22C2×D8×D5911yescharacteristic
314C22#135×D5912yes—
315C22C2×#1427374611yescharacteristic
316C4—22no—
317C4—44no—
318C4—598no—
319C4—1184no—
320C4—2368no—
321C4D8×Dic5914yesdirect product factor
322C4C22×C4×Dic5911yescharacteristic
323C4C4×#1174568712yes—
324C4#41×Dic5911yescharacteristic
325C2—48no—
326C2C4×D4×Dic5911yescharacteristic
327C2C4×D8×D5912yes—
328C2C2×D8×Dic5911yescharacteristic
329C2C4×#1427374612yes—
330C2#135×Dic5911yescharacteristic
subgroupG/H
centerC22×C4D4×D59
commutatorC4×C59C22×C42
FrattiniC22×C4C23×D59
FittingC2×C4×D8×C59C2
socleC23×C59C22×D4
prime radicalC22×D8×C59C22
cosocleC22×C4×C59C24
hypercenterC2×C4×D8D59
hypocenterC59C42×D8
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
2. C4×D4×Dic59C2semidirect
3. #107×Dic59C2semidirect
4. C4×#14273661C2semidirect
5. #102×Dic59C2semidirect
6. C4×#14273648C2semidirect
7. C4×C8×Dic59C2semidirect
11. D8×Dic59C4direct (N × H)
26. C4×D8×C59C4semidirect
33. D4×Dic59C2×C4semidirect
43. #14273661C2×C4semidirect
44. #14273648C2×C4semidirect
47. C8×Dic59C2×C4semidirect
57. C4×D4×C59C2×C4semidirect
61. #107×C59C2×C4semidirect
62. #102×C59C2×C4semidirect
63. C4×C8×C59C2×C4semidirect
82. D8×C59C42semidirect
99. C4×Dic59D8direct (N × H)
113. D4×C59C2×C42semidirect
138. C8×C59C2×C42semidirect
153. C4×C59C4×D8semidirect
159. Dic59C4×D8direct (N × H)
179. C4×D8Dic59direct (N × H)
195. C59C42×D8semidirect
207. C4×D4C2×Dic59semidirect
221. #107C2×Dic59semidirect
223. #102C2×Dic59semidirect
227. C4×C8C2×Dic59semidirect
248. D8C4×Dic59direct (N × H)
279. D4C2×C4×Dic59semidirect
305. C8C2×C4×Dic59semidirect
321. C4D8×Dic59direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D8×Dic592
C4×D4×Dic592
#107×Dic592
C4×#142736612
#102×Dic592
C4×#142736482
C4×C8×Dic592
C2×C4×D8×C592
C42×D859