Finite Group Databasebeta

← C4×D8×Dic71 #31995917

Subgroups — C4×D8×Dic71 #31995917

Order 18176.

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×Dic71C212yesmaximal
2C4×D4×Dic71C212yesmaximal, complemented
3#107×Dic71C212yesmaximal, complemented
4C4×#14556062C211yesmaximal, characteristic, complemented
5#102×Dic71C214yesmaximal, complemented
6C4×#14556049C212yesmaximal, complemented
7C4×C8×Dic71C211yesmaximal, characteristic, complemented
8C2×C4×D8×C71C211yesmaximal, characteristic
9C2×D4×Dic71C2214yes—
10C22×C4×Dic71—22no—
11D8×Dic71C4116yesdirect product factor
12C2×#14556062C2212yes—
13C2×#14556049C2214yes—
14C2×C4×C71⋊C8C2211yescharacteristic
15C2×C8×Dic71C2212yes—
16C2×C8×Dic71C2212yes—
17C4⋊C4×Dic71C2214yes—
18C4×C4⋊Dic71C2212yes—
19C22⋊C4×Dic71—24no—
20C4×C22⋊Dic71—22no—
21C42×Dic71C2211yescharacteristic
22#17985762C2212yes—
23#17985761C2214yes—
24C22×D8×C71C2211yescharacteristic
25C2×C4×D4×C71C2212yes—
26C4×D8×C71C418yescomplemented
27C2×#107×C71C2211yescharacteristic
28C2×#102×C71C2212yes—
29C2×C4×C8×C71C2211yescharacteristic
30C23×Dic71—24no—
31C22×C71⋊C8C2312yes—
32D4×Dic71—28no—
33D4×Dic71C2×C4116yescomplemented
34C2×C4⋊Dic71C2314yes—
35C2×C22⋊Dic71—24no—
36C2×C4×Dic71—24no—
37C2×C4×Dic71—22no—
38C2×C4×Dic71—48no—
39C2×C4×Dic71D411yescharacteristic
40C2×C4×Dic71D412yes—
41C2×C4×Dic71D411yescharacteristic
42C2×C4×Dic71C2312yes—
43#14556062C2×C418yescomplemented
44#14556049C2×C4116yescomplemented
45C4×C71⋊C8—22no—
46C8×Dic71—24no—
47C8×Dic71C2×C418yescomplemented
48C71⋊#95—24no—
49C71⋊#95—22no—
50C22×D4×C71C2312yes—
51C23×C4×C71—22no—
52C2×D8×C71C2×C418yes—
53C2×D8×C71C2×C414yes—
54C22×C8×C71C2311yescharacteristic
55C22×C8×C71C2311yescharacteristic
56C4×D4×C71—24no—
57C4×D4×C71C2×C418yescomplemented
58C2×C4⋊C4×C71C2312yes—
59C2×C22⋊C4×C71—22no—
60C2×C42×C71C2311yescharacteristic
61#107×C71C2×C414yescomplemented
62#102×C71C2×C418yescomplemented
63C4×C8×C71C2×C414yescomplemented
64C22×Dic71—24no—
65C22×Dic71—216no—
66C22×Dic71—48no—
67C22×Dic71—48no—
68C22×Dic71C2×D412yes—
69C22×Dic71C2×D412yes—
70C2×C71⋊C8—22no—
71C2×C71⋊C8—22no—
72C2×C71⋊C8C22×C414yes—
73C4⋊Dic71—24no—
74C4⋊Dic71C22×C418yes—
75C22⋊Dic71—216no—
76C4×Dic71—22no—
77C4×Dic71—24no—
78C4×Dic71—44no—
79C4×Dic71—48no—
80C4×Dic71D814yesdirect product factor
81C4×Dic71C22×C414yes—
82C4×Dic71#4114yes—
83C24×C71—22no—
84C2×D4×C71—22no—
85C2×D4×C71—24no—
86C2×D4×C71C22×C418yes—
87C2×D4×C71C22×C414yes—
88C22×C4×C71—22no—
89C22×C4×C71—28no—
90C22×C4×C71—44no—
91C22×C4×C71—44no—
92C22×C4×C71C2×D411yescharacteristic
93C22×C4×C71C2×D411yescharacteristic
94C22×C4×C71C2411yescharacteristic
95D8×C71C42116yescomplemented
96C2×C8×C71—22no—
97C2×C8×C71C22×C414yes—
98C2×C8×C71C22×C412yes—
99C2×C8×C71C22×C412yes—
100C4⋊C4×C71—22no—
101C4⋊C4×C71C22×C414yes—
102C22⋊C4×C71—28no—
103C42×C71C22×C412yes—
104C42×C71#4112yes—
105C23×C71—24no—
106C23×C71—28no—
107C23×C71—42no—
108C23×C71—42no—
109C23×C71—44no—
110C23×C71C22×D411yescharacteristic
111D4×C71—28no—
112D4×C71—24no—
113D4×C71C2×C4218yescomplemented
114C2×C4×C71—22no—
115C2×C4×C71—24no—
116C2×C4×C71—42no—
117C2×C4×C71—42no—
118C2×C4×C71—416no—
119C2×C4×C71C4×D412yes—
120C2×C4×C71C4×D412yes—
121C2×C4×C71C2×D812yes—
122C2×C4×C71#13512yes—
123C2×C4×C71C23×C412yes—
124C2×C4×C71C23×C411yescharacteristic
125C2×C4×C71C2×#4112yes—
126C2×C4×C71C2×#4111yescharacteristic
127C2×Dic71—22no—
128C2×Dic71—22no—
129C2×Dic71—28no—
130C2×Dic71—44no—
131C2×Dic71—44no—
132C2×Dic71—432no—
133C2×Dic71C4×D414yes—
134C2×Dic71C4×D414yes—
135C2×Dic71C2×D814yes—
136C2×Dic71#13514yes—
137C8×C71—22no—
138C8×C71C2×C4214yescomplemented
139C71⋊C8—24no—
140C22×C71—28no—
141C22×C71—48no—
142C22×C71—44no—
143C22×C71—48no—
144C22×C71—44no—
145C22×C71C2×C4×D412yes—
146C22×C71C2×C4×D411yescharacteristic
147C22×C71C22×D811yescharacteristic
148C22×C71C2×#13512yes—
149C22×C71C2×#13511yescharacteristic
150C4×C71—22no—
151C4×C71—44no—
152C4×C71C4×D814yescomplemented
153C4×C71C22×C4211yescharacteristic
154C4×C71C4×#4112yes—
155C4×C71C4×#4111yescharacteristic
156Dic71—24no—
157Dic71—48no—
158Dic71C4×D818yesdirect product factor
159C42×D8—711nomaximal, Sylow
160C2×C71—48no—
161C2×C71C42×D411yescharacteristic
162C2×C71C2×C4×D812yes—
163C2×C71C2×C4×D811yescharacteristic
164C2×C71C4×#13512yes—
165C2×C71C4×#13511yescharacteristic
166C2×C4×D8—712no—
167C2×C4×D8D7111yescharacteristic
168C42×D4—712no—
169C4×#107—712no—
170C4×#107—711no—
171C4×#102—714no—
172C4×#102—712no—
173C42×C8—711no—
174C71C42×D811yescharacteristic, complemented, Sylow
175C22×D8C2×D7111yescharacteristic
176C2×C4×D4—714no—
177C2×C4×D4C2×D7112yes—
178C22×C42—1422no—
179C4×D8—7116no—
180C4×D8Dic7118yesdirect product factor
181C2×#107—712no—
182C2×#107C2×D7111yescharacteristic
183C2×#102—714no—
184C2×#102C2×D7112yes—
185C2×C4×C8—712no—
186C2×C4×C8—712no—
187C2×C4×C8—711no—
188C2×C4×C8C2×D7111yescharacteristic
189C4×C4⋊C4—714no—
190C4×C4⋊C4—712no—
191C4×C22⋊C4—1424no—
192C4×C22⋊C4—1422no—
193C43—711no—
194#340—712no—
195#340—714no—
196C22×D4C22×D7112yes—
197C23×C4—22no—
198C23×C4—1424no—
199C2×D8C4×D7118yes—
200C2×D8C2×Dic7114yes—
201C22×C8—712no—
202C22×C8C22×D7111yescharacteristic
203C22×C8C22×D7111yescharacteristic
204C4×D4—24no—
205C4×D4—7116no—
206C4×D4—1428no—
207C4×D4C2×Dic7118yescomplemented
208C2×C4⋊C4—714no—
209C2×C4⋊C4C22×D7112yes—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—1424no—
212C2×C42—2848no—
213C2×C42—711no—
214C2×C42—712no—
215C2×C42—712no—
216C2×C42—711no—
217C2×C42—1424no—
218C2×C42—1422no—
219C2×C42C22×D7111yescharacteristic
220#107—718no—
221#107C2×Dic7114yescomplemented
222#102—7116no—
223#102C2×Dic7118yescomplemented
224C4×C8—718no—
225C4×C8—1424no—
226C4×C8—1422no—
227C4×C8C2×Dic7114yescomplemented
228#95—1424no—
229#95—1422no—
230C24—22no—
231C2×D4—24no—
232C2×D4—22no—
233C2×D4C2×C4×D7118yes—
234C2×D4C22×Dic7114yes—
235C22×C4—22no—
236C22×C4—28no—
237C22×C4—44no—
238C22×C4—44no—
239C22×C4—2848no—
240C22×C4—2848no—
241C22×C4—712no—
242C22×C4—712no—
243C22×C4—14216no—
244C22×C4—1424no—
245C22×C4D4×D7111yescharacteristic
246C22×C4D4×D7111yescharacteristic
247C22×C4C23×D7111yescharacteristic
248D8C4×Dic71116yesdirect product factor
249C2×C8—22no—
250C2×C8—714no—
251C2×C8—1422no—
252C2×C8—1422no—
253C2×C8C2×C4×D7114yes—
254C2×C8C22×Dic7112yes—
255C2×C8C22×Dic7112yes—
256C4⋊C4—22no—
257C4⋊C4—718no—
258C4⋊C4—1424no—
259C4⋊C4C22×Dic7114yes—
260C22⋊C4—28no—
261C22⋊C4—14216no—
262C42—2848no—
263C42—2844no—
264C42—714no—
265C42—714no—
266C42—714no—
267C42—1424no—
268C42—1422no—
269C42C22×Dic7112yes—
270C42#1176586412yes—
271C23—28no—
272C23—24no—
273C23—42no—
274C23—44no—
275C23—42no—
276C23C2×D4×D7111yescharacteristic
277D4—28no—
278D4—24no—
279D4C2×C4×Dic7118yescomplemented
280C2×C4—22no—
281C2×C4—24no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—416no—
285C2×C4—2844no—
286C2×C4—2844no—
287C2×C4—28432no—
288C2×C4—714no—
289C2×C4—714no—
290C2×C4—714no—
291C2×C4—714no—
292C2×C4—1428no—
293C2×C4—1422no—
294C2×C4—1422no—
295C2×C4D4×Dic7112yes—
296C2×C4D4×Dic7112yes—
297C2×C4D8×D7112yes—
298C2×C4#1455614712yes—
299C2×C4C22×C4×D7112yes—
300C2×C4C23×Dic7111yescharacteristic
301C2×C4#41×D7112yes—
302C2×C4C2×#1176586411yescharacteristic
303C8—22no—
304C8—1424no—
305C8C2×C4×Dic7114yescomplemented
306C22—28no—
307C22—48no—
308C22—44no—
309C22—48no—
310C22—44no—
311C22C4×D4×D7112yes—
312C22C2×D4×Dic7111yescharacteristic
313C22C2×D8×D7111yescharacteristic
314C22#135×D7112yes—
315C22C2×#1455614711yescharacteristic
316C4—22no—
317C4—44no—
318C4—2848no—
319C4—718no—
320C4—1424no—
321C4D8×Dic7114yesdirect product factor
322C4C22×C4×Dic7111yescharacteristic
323C4C4×#1176586412yes—
324C4#41×Dic7111yescharacteristic
325C2—48no—
326C2C4×D4×Dic7111yescharacteristic
327C2C4×D8×D7112yes—
328C2C2×D8×Dic7111yescharacteristic
329C2C4×#1455614712yes—
330C2#135×Dic7111yescharacteristic
subgroupG/H
centerC22×C4D4×D71
commutatorC4×C71C22×C42
FrattiniC22×C4C23×D71
FittingC2×C4×D8×C71C2
socleC23×C71C22×D4
prime radicalC22×D8×C71C22
cosocleC22×C4×C71C24
hypercenterC2×C4×D8D71
hypocenterC71C42×D8
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
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×Dic71C2semidirect
3. #107×Dic71C2semidirect
4. C4×#14556062C2semidirect
5. #102×Dic71C2semidirect
6. C4×#14556049C2semidirect
7. C4×C8×Dic71C2semidirect
11. D8×Dic71C4direct (N × H)
26. C4×D8×C71C4semidirect
33. D4×Dic71C2×C4semidirect
43. #14556062C2×C4semidirect
44. #14556049C2×C4semidirect
47. C8×Dic71C2×C4semidirect
57. C4×D4×C71C2×C4semidirect
61. #107×C71C2×C4semidirect
62. #102×C71C2×C4semidirect
63. C4×C8×C71C2×C4semidirect
80. C4×Dic71D8direct (N × H)
95. D8×C71C42semidirect
113. D4×C71C2×C42semidirect
138. C8×C71C2×C42semidirect
152. C4×C71C4×D8semidirect
158. Dic71C4×D8direct (N × H)
174. C71C42×D8semidirect
180. C4×D8Dic71direct (N × H)
207. C4×D4C2×Dic71semidirect
221. #107C2×Dic71semidirect
223. #102C2×Dic71semidirect
227. C4×C8C2×Dic71semidirect
248. D8C4×Dic71direct (N × H)
279. D4C2×C4×Dic71semidirect
305. C8C2×C4×Dic71semidirect
321. C4D8×Dic71direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D8×Dic712
C4×D4×Dic712
#107×Dic712
C4×#145560622
#102×Dic712
C4×#145560492
C4×C8×Dic712
C2×C4×D8×C712
C42×D871