Finite Group Databasebeta

← C4×D8×Dic43 #25095062

Subgroups — C4×D8×Dic43 #25095062

Order 11008.

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×Dic43C212yesmaximal
2C4×D4×Dic43C212yesmaximal, complemented
3#107×Dic43C212yesmaximal, complemented
4C4×#13063259C211yesmaximal, characteristic, complemented
5#102×Dic43C214yesmaximal, complemented
6C4×#13063246C212yesmaximal, complemented
7C4×C8×Dic43C211yesmaximal, characteristic, complemented
8C2×C4×D8×C43C211yesmaximal, characteristic
9C2×D4×Dic43C2214yes—
10C22×C4×Dic43—22no—
11D8×Dic43C4116yesdirect product factor
12C2×#13063259C2212yes—
13C2×#13063246C2214yes—
14C2×C4×C43⋊C8C2211yescharacteristic
15C2×C8×Dic43C2212yes—
16C2×C8×Dic43C2212yes—
17C4⋊C4×Dic43C2214yes—
18C4×C4⋊Dic43C2212yes—
19C22⋊C4×Dic43—24no—
20C4×C22⋊Dic43—22no—
21C42×Dic43C2211yescharacteristic
22#14582662C2212yes—
23#14582661C2214yes—
24C22×D8×C43C2211yescharacteristic
25C2×C4×D4×C43C2212yes—
26C4×D8×C43C418yescomplemented
27C2×#107×C43C2211yescharacteristic
28C2×#102×C43C2212yes—
29C2×C4×C8×C43C2211yescharacteristic
30C23×Dic43—24no—
31C22×C43⋊C8C2312yes—
32D4×Dic43—28no—
33D4×Dic43C2×C4116yescomplemented
34C2×C4⋊Dic43C2314yes—
35C2×C22⋊Dic43—24no—
36C2×C4×Dic43—22no—
37C2×C4×Dic43—24no—
38C2×C4×Dic43—48no—
39C2×C4×Dic43D411yescharacteristic
40C2×C4×Dic43D412yes—
41C2×C4×Dic43D411yescharacteristic
42C2×C4×Dic43C2312yes—
43#13063259C2×C418yescomplemented
44#13063246C2×C4116yescomplemented
45C4×C43⋊C8—22no—
46C8×Dic43—24no—
47C8×Dic43C2×C418yescomplemented
48C43⋊#95—22no—
49C43⋊#95—24no—
50C22×D4×C43C2312yes—
51C23×C4×C43—22no—
52C2×D8×C43C2×C418yes—
53C2×D8×C43C2×C414yes—
54C22×C8×C43C2311yescharacteristic
55C22×C8×C43C2311yescharacteristic
56C4×D4×C43—24no—
57C4×D4×C43C2×C418yescomplemented
58C2×C4⋊C4×C43C2312yes—
59C2×C22⋊C4×C43—22no—
60C2×C42×C43C2311yescharacteristic
61#107×C43C2×C414yescomplemented
62#102×C43C2×C418yescomplemented
63C4×C8×C43C2×C414yescomplemented
64C24×C43—22no—
65C2×D4×C43—22no—
66C2×D4×C43—24no—
67C2×D4×C43C22×C418yes—
68C2×D4×C43C22×C414yes—
69C22×C4×C43—28no—
70C22×C4×C43—22no—
71C22×C4×C43—44no—
72C22×C4×C43—44no—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2411yescharacteristic
76C22×Dic43—216no—
77C22×Dic43—24no—
78C22×Dic43—48no—
79C22×Dic43—48no—
80C22×Dic43C2×D412yes—
81C22×Dic43C2×D412yes—
82D8×C43C42116yescomplemented
83C2×C8×C43—22no—
84C2×C8×C43C22×C414yes—
85C2×C8×C43C22×C412yes—
86C2×C8×C43C22×C412yes—
87C4⋊C4×C43—22no—
88C4⋊C4×C43C22×C414yes—
89C22⋊C4×C43—28no—
90C42×C43C22×C412yes—
91C42×C43#4112yes—
92C22⋊Dic43—216no—
93C4⋊Dic43—24no—
94C4⋊Dic43C22×C418yes—
95C4×Dic43—22no—
96C4×Dic43—24no—
97C4×Dic43—44no—
98C4×Dic43—48no—
99C4×Dic43D814yesdirect product factor
100C4×Dic43C22×C414yes—
101C4×Dic43#4114yes—
102C2×C43⋊C8—22no—
103C2×C43⋊C8—22no—
104C2×C43⋊C8C22×C414yes—
105C23×C43—28no—
106C23×C43—24no—
107C23×C43—42no—
108C23×C43—44no—
109C23×C43—42no—
110C23×C43C22×D411yescharacteristic
111D4×C43—28no—
112D4×C43—24no—
113D4×C43C2×C4218yescomplemented
114C2×C4×C43—22no—
115C2×C4×C43—24no—
116C2×C4×C43—42no—
117C2×C4×C43—42no—
118C2×C4×C43—416no—
119C2×C4×C43C4×D412yes—
120C2×C4×C43C4×D412yes—
121C2×C4×C43C2×D812yes—
122C2×C4×C43#13512yes—
123C2×C4×C43C23×C412yes—
124C2×C4×C43C23×C411yescharacteristic
125C2×C4×C43C2×#4112yes—
126C2×C4×C43C2×#4111yescharacteristic
127C2×Dic43—22no—
128C2×Dic43—22no—
129C2×Dic43—28no—
130C2×Dic43—44no—
131C2×Dic43—44no—
132C2×Dic43—432no—
133C2×Dic43C4×D414yes—
134C2×Dic43C4×D414yes—
135C2×Dic43C2×D814yes—
136C2×Dic43#13514yes—
137C8×C43—22no—
138C8×C43C2×C4214yescomplemented
139C43⋊C8—24no—
140C42×D8—431nomaximal, Sylow
141C22×C43—28no—
142C22×C43—48no—
143C22×C43—44no—
144C22×C43—48no—
145C22×C43—44no—
146C22×C43C2×C4×D412yes—
147C22×C43C2×C4×D411yescharacteristic
148C22×C43C22×D811yescharacteristic
149C22×C43C2×#13512yes—
150C22×C43C2×#13511yescharacteristic
151C4×C43—22no—
152C4×C43—44no—
153C4×C43C4×D814yescomplemented
154C4×C43C22×C4211yescharacteristic
155C4×C43C4×#4112yes—
156C4×C43C4×#4111yescharacteristic
157Dic43—24no—
158Dic43—48no—
159Dic43C4×D818yesdirect product factor
160C2×C4×D8—432no—
161C2×C4×D8D4311yescharacteristic
162C42×D4—432no—
163C4×#107—432no—
164C4×#107—431no—
165C4×#102—434no—
166C4×#102—432no—
167C42×C8—431no—
168C2×C43—48no—
169C2×C43C42×D411yescharacteristic
170C2×C43C2×C4×D812yes—
171C2×C43C2×C4×D811yescharacteristic
172C2×C43C4×#13512yes—
173C2×C43C4×#13511yescharacteristic
174C22×D8C2×D4311yescharacteristic
175C2×C4×D4—434no—
176C2×C4×D4C2×D4312yes—
177C22×C42—862no—
178C4×D8—4316no—
179C4×D8Dic4318yesdirect product factor
180C2×#107—432no—
181C2×#107C2×D4311yescharacteristic
182C2×#102—434no—
183C2×#102C2×D4312yes—
184C2×C4×C8—432no—
185C2×C4×C8—432no—
186C2×C4×C8—431no—
187C2×C4×C8C2×D4311yescharacteristic
188C4×C4⋊C4—434no—
189C4×C4⋊C4—432no—
190C4×C22⋊C4—864no—
191C4×C22⋊C4—862no—
192C43—431no—
193#340—432no—
194#340—434no—
195C43C42×D811yescharacteristic, complemented, Sylow
196C22×D4C22×D4312yes—
197C23×C4—22no—
198C23×C4—864no—
199C2×D8C4×D4318yes—
200C2×D8C2×Dic4314yes—
201C22×C8—432no—
202C22×C8C22×D4311yescharacteristic
203C22×C8C22×D4311yescharacteristic
204C4×D4—24no—
205C4×D4—4316no—
206C4×D4—868no—
207C4×D4C2×Dic4318yescomplemented
208C2×C4⋊C4—434no—
209C2×C4⋊C4C22×D4312yes—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—864no—
212C2×C42—431no—
213C2×C42—432no—
214C2×C42—432no—
215C2×C42—431no—
216C2×C42—864no—
217C2×C42—862no—
218C2×C42—1728no—
219C2×C42C22×D4311yescharacteristic
220#107—438no—
221#107C2×Dic4314yescomplemented
222#102—4316no—
223#102C2×Dic4318yescomplemented
224C4×C8—438no—
225C4×C8—864no—
226C4×C8—862no—
227C4×C8C2×Dic4314yescomplemented
228#95—864no—
229#95—862no—
230C24—22no—
231C2×D4—24no—
232C2×D4—22no—
233C2×D4C2×C4×D4318yes—
234C2×D4C22×Dic4314yes—
235C22×C4—22no—
236C22×C4—28no—
237C22×C4—44no—
238C22×C4—44no—
239C22×C4—432no—
240C22×C4—432no—
241C22×C4—8616no—
242C22×C4—864no—
243C22×C4—1728no—
244C22×C4—1728no—
245C22×C4D4×D4311yescharacteristic
246C22×C4D4×D4311yescharacteristic
247C22×C4C23×D4311yescharacteristic
248D8C4×Dic43116yesdirect product factor
249C2×C8—22no—
250C2×C8—434no—
251C2×C8—862no—
252C2×C8—862no—
253C2×C8C2×C4×D4314yes—
254C2×C8C22×Dic4312yes—
255C2×C8C22×Dic4312yes—
256C4⋊C4—22no—
257C4⋊C4—438no—
258C4⋊C4—864no—
259C4⋊C4C22×Dic4314yes—
260C22⋊C4—28no—
261C22⋊C4—8616no—
262C42—434no—
263C42—434no—
264C42—434no—
265C42—864no—
266C42—862no—
267C42—1728no—
268C42—1724no—
269C42#1062190012yes—
270C42C22×Dic4312yes—
271C23—28no—
272C23—24no—
273C23—42no—
274C23—44no—
275C23—42no—
276C23C2×D4×D4311yescharacteristic
277D4—28no—
278D4—24no—
279D4C2×C4×Dic4318yescomplemented
280C2×C4—22no—
281C2×C4—24no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—416no—
285C2×C4—434no—
286C2×C4—434no—
287C2×C4—434no—
288C2×C4—434no—
289C2×C4—862no—
290C2×C4—862no—
291C2×C4—868no—
292C2×C4—17232no—
293C2×C4—1724no—
294C2×C4—1724no—
295C2×C4D4×Dic4312yes—
296C2×C4D4×Dic4312yes—
297C2×C4D8×D4312yes—
298C2×C4#1306334412yes—
299C2×C4C22×C4×D4312yes—
300C2×C4C23×Dic4311yescharacteristic
301C2×C4#41×D4312yes—
302C2×C4C2×#1062190011yescharacteristic
303C8—22no—
304C8—864no—
305C8C2×C4×Dic4314yescomplemented
306C22—28no—
307C22—48no—
308C22—44no—
309C22—48no—
310C22—44no—
311C22C4×D4×D4312yes—
312C22C2×D4×Dic4311yescharacteristic
313C22C2×D8×D4311yescharacteristic
314C22#135×D4312yes—
315C22C2×#1306334411yescharacteristic
316C4—22no—
317C4—44no—
318C4—438no—
319C4—864no—
320C4—1728no—
321C4D8×Dic4314yesdirect product factor
322C4C22×C4×Dic4311yescharacteristic
323C4C4×#1062190012yes—
324C4#41×Dic4311yescharacteristic
325C2—48no—
326C2C4×D4×Dic4311yescharacteristic
327C2C4×D8×D4312yes—
328C2C2×D8×Dic4311yescharacteristic
329C2C4×#1306334412yes—
330C2#135×Dic4311yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC2×C4×D8×C43C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
cosocleC22×C4×C43C24
hypercenterC2×C4×D8D43
hypocenterC43C42×D8
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
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×Dic43C2semidirect
3. #107×Dic43C2semidirect
4. C4×#13063259C2semidirect
5. #102×Dic43C2semidirect
6. C4×#13063246C2semidirect
7. C4×C8×Dic43C2semidirect
11. D8×Dic43C4direct (N × H)
26. C4×D8×C43C4semidirect
33. D4×Dic43C2×C4semidirect
43. #13063259C2×C4semidirect
44. #13063246C2×C4semidirect
47. C8×Dic43C2×C4semidirect
57. C4×D4×C43C2×C4semidirect
61. #107×C43C2×C4semidirect
62. #102×C43C2×C4semidirect
63. C4×C8×C43C2×C4semidirect
82. D8×C43C42semidirect
99. C4×Dic43D8direct (N × H)
113. D4×C43C2×C42semidirect
138. C8×C43C2×C42semidirect
153. C4×C43C4×D8semidirect
159. Dic43C4×D8direct (N × H)
179. C4×D8Dic43direct (N × H)
195. C43C42×D8semidirect
207. C4×D4C2×Dic43semidirect
221. #107C2×Dic43semidirect
223. #102C2×Dic43semidirect
227. C4×C8C2×Dic43semidirect
248. D8C4×Dic43direct (N × H)
279. D4C2×C4×Dic43semidirect
305. C8C2×C4×Dic43semidirect
321. C4D8×Dic43direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D8×Dic432
C4×D4×Dic432
#107×Dic432
C4×#130632592
#102×Dic432
C4×#130632462
C4×C8×Dic432
C2×C4×D8×C432
C42×D843