Finite Group Databasebeta

← C4×#14581706 #24907252

Subgroups — C4×#14581706 #24907252

Order 10624.

412 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D83C211yesmaximal, characteristic
2C2×#14581706C212yesmaximal
3C4×C22⋊Dic83C211yesmaximal, characteristic, complemented
4#19127467C212yesmaximal, complemented
5C4×C22⋊C4×C83C211yesmaximal, characteristic, complemented
6C22×C22⋊D83C2211yescharacteristic
7C22×C4×D83C411yescharacteristic, complemented
8C4×C22⋊D83—21no—
9C4×C22⋊D83—21no—
10C4×C22⋊D83—21no—
11C4×C22⋊D83—21no—
12C2×Dic83⋊C4C411yescharacteristic, complemented
13C2×C22⋊Dic83C2211yescharacteristic
14C2×C22⋊Dic83C2212yes—
15C2×(C2×D83)⋊C4C411yescharacteristic, complemented
16C2×C4×Dic83—21no—
17C2×C4×Dic83C411yescharacteristic, complemented
18#14581706C418yesdirect product factor
19C83⋊#95—21no—
20C23×C4×C83C2211yescharacteristic
21C2×C22⋊C4×C83C2212yes—
22C2×C42×C83—21no—
23#95×C83—21no—
24C23×D83C2×C411yescharacteristic
25C2×C22⋊D83—21no—
26C2×C22⋊D83—21no—
27C2×C22⋊D83—22no—
28C2×C22⋊D83C2×C414yes—
29C22×Dic83—22no—
30C22×Dic83C2×C411yescharacteristic
31C22×Dic83C2×C411yescharacteristic
32C22×Dic83C2×C411yescharacteristic
33C2×C4×D83—21no—
34C2×C4×D83—21no—
35C2×C4×D83—42no—
36Dic83⋊C4—21no—
37Dic83⋊C4—21no—
38C22⋊Dic83—21no—
39C22⋊Dic83—21no—
40C22⋊Dic83—22no—
41C22⋊Dic83C2×C414yescomplemented
42(C2×D83)⋊C4—21no—
43(C2×D83)⋊C4—21no—
44C4×Dic83—21no—
45C4×Dic83—21no—
46C4×Dic83—42no—
47C24×C83C2311yescharacteristic
48C22×C4×C83—22no—
49C22×C4×C83—42no—
50C22×C4×C83C2×C411yescharacteristic
51C22×C4×C83C2×C411yescharacteristic
52C22×C4×C83D411yescharacteristic
53C22×C4×C83D411yescharacteristic
54C22×C4×C83D411yescharacteristic
55C22×C4×C83D411yescharacteristic
56C22⋊C4×C83—22no—
57C22⋊C4×C83C2×C414yescomplemented
58C42×C83—42no—
59C23×C83—41no—
60C23×C83—41no—
61C23×C83C22×C411yescharacteristic
62C23×C83C22×C412yes—
63C23×C83C2×D411yescharacteristic
64C23×C83C2×D411yescharacteristic
65C23×C83#4112yes—
66C22×D83—21no—
67C22×D83—21no—
68C22×D83—41no—
69C22×D83—41no—
70C22×D83C4212yescomplemented
71C2×C4×C83—22no—
72C2×C4×C83—22no—
73C2×C4×C83—22no—
74C2×C4×C83—24no—
75C2×C4×C83—41no—
76C2×C4×C83—41no—
77C2×C4×C83—41no—
78C2×C4×C83—42no—
79C2×C4×C83—42no—
80C2×C4×C83C22⋊C411yescharacteristic
81C2×C4×C83C22⋊C411yescharacteristic
82C2×C4×C83C22⋊C411yescharacteristic
83C2×C4×C83C22⋊C411yescharacteristic
84C22⋊D83—24no—
85C22⋊D83—24no—
86C2×Dic83—21no—
87C2×Dic83—21no—
88C2×Dic83—21no—
89C2×Dic83—21no—
90C2×Dic83—24no—
91C2×Dic83—42no—
92C2×Dic83—42no—
93C2×Dic83—41no—
94C2×Dic83—41no—
95C2×Dic83C4212yescomplemented
96C4×D83—42no—
97C4×D83—42no—
98C22×C83—21no—
99C22×C83—21no—
100C22×C83—21no—
101C22×C83—21no—
102C22×C83—21no—
103C22×C83—21no—
104C22×C83—42no—
105C22×C83—42no—
106C22×C83C2×C4211yescharacteristic
107C22×C83C2×C22⋊C411yescharacteristic
108C22×C83#11711yescharacteristic
109C22×C83C4×D412yes—
110C22×C83C4×D412yes—
111C2×D83—22no—
112C2×D83—42no—
113C2×D83—41no—
114C2×D83—41no—
115C2×D83—42no—
116C4×C83—21no—
117C4×C83—21no—
118C4×C83—21no—
119C4×C83—44no—
120C4×C83#9912yescomplemented
121Dic83—22no—
122Dic83—44no—
123Dic83—41no—
124Dic83—41no—
125C2×C83—22no—
126C2×C83—22no—
127C2×C83—21no—
128C2×C83—21no—
129C2×C83C4×C22⋊C411yescharacteristic
130C2×C83C2×#9911yescharacteristic
131C2×C83#41011yescharacteristic
132D83—42no—
133C4×#99—831nomaximal, Sylow
134C83C4×#9911yescharacteristic, complemented, Sylow
135C2×C4×D4—831no—
136C2×#99—832no—
137C4×C22⋊C4—831no—
138C4×C22⋊C4D8311yescharacteristic, complemented
139#342—832no—
140C22×D4—831no—
141C23×C4—831no—
142C23×C4C2×D8311yescharacteristic
143C4×D4—1661no—
144C4×D4—1661no—
145C4×D4—1661no—
146C4×D4—1661no—
147C2×C4⋊C4—831no—
148C2×C22⋊C4—832no—
149C2×C22⋊C4—831no—
150C2×C22⋊C4—831no—
151C2×C22⋊C4C2×D8312yes—
152C2×C42—21no—
153C2×C42—831no—
154C2×C42—1661no—
155#99—838no—
156#95—21no—
157#95—1661no—
158C24—831no—
159C24C22×D8311yescharacteristic
160C2×D4—834no—
161C2×D4—1661no—
162C2×D4—1661no—
163C2×D4—1662no—
164C22×C4—22no—
165C22×C4—42no—
166C22×C4—3322no—
167C22×C4—831no—
168C22×C4—831no—
169C22×C4—831no—
170C22×C4—1662no—
171C22×C4—1661no—
172C22×C4—1661no—
173C22×C4C4×D8311yescharacteristic
174C22×C4C4×D8311yescharacteristic
175C22×C4D33211yescharacteristic
176C22×C4D33211yescharacteristic
177C22×C4C22⋊D8311yescharacteristic
178C22×C4C22⋊D8311yescharacteristic
179C4⋊C4—1661no—
180C4⋊C4—1661no—
181C22⋊C4—22no—
182C22⋊C4—834no—
183C22⋊C4—1661no—
184C22⋊C4—1661no—
185C22⋊C4—1662no—
186C22⋊C4—1661no—
187C22⋊C4—1661no—
188C22⋊C4C4×D8314yescomplemented
189C42—42no—
190C42—3322no—
191C42—1661no—
192C42—1661no—
193C23—41no—
194C23—41no—
195C23—3321no—
196C23—3321no—
197C23—832no—
198C23—1661no—
199C23—1661no—
200C23C2×C4×D8311yescharacteristic
201C23C2×C4×D8312yes—
202C23C2×C22⋊D8311yescharacteristic
203C23C2×D33211yescharacteristic
204C23#1305059012yes—
205D4—1664no—
206D4—1664no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—24no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—3322no—
217C2×C4—3322no—
218C2×C4—3322no—
219C2×C4—3322no—
220C2×C4—3321no—
221C2×C4—3321no—
222C2×C4—832no—
223C2×C4—1661no—
224C2×C4—1661no—
225C2×C4—1664no—
226C2×C4—1661no—
227C2×C4—1661no—
228C2×C4(C2×D83)⋊C411yescharacteristic
229C2×C4(C2×D83)⋊C411yescharacteristic
230C2×C4(C2×D83)⋊C411yescharacteristic
231C2×C4(C2×D83)⋊C411yescharacteristic
232C22—21no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—42no—
240C22—3322no—
241C22—3322no—
242C22—3321no—
243C22—3321no—
244C22—1662no—
245C22C42×D8311yescharacteristic
246C22C2×(C2×D83)⋊C411yescharacteristic
247C22#1458174911yescharacteristic
248C22C4×C22⋊D8312yes—
249C22C4×D33212yes—
250C4—21no—
251C4—21no—
252C4—21no—
253C4—44no—
254C4—3324no—
255C4—3321no—
256C4—3321no—
257C4—1662no—
258C4#1458170612yesdirect product factor
259C2—22no—
260C2—22no—
261C2—21no—
262C2—21no—
263C2—3322no—
264C2C4×(C2×D83)⋊C411yescharacteristic
265C2C2×#1458170611yescharacteristic
266C2#1912767411yescharacteristic
subgroupG/H
centerC2×C4(C2×D83)⋊C4
commutatorC22×C83C2×C42
FrattiniC24C22×D83
FittingC4×C22⋊C4×C83C2
socleC22×C83C2×C22⋊C4
prime radicalC22×C22⋊D83C22
cosocleC24×C83C23
hypercenterC4×C22⋊C4D83
hypocenterC83C4×#99
LCSG ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C4×C22⋊Dic83C2semidirect
4. #19127467C2semidirect
5. C4×C22⋊C4×C83C2semidirect
7. C22×C4×D83C4semidirect
12. C2×Dic83⋊C4C4semidirect
15. C2×(C2×D83)⋊C4C4semidirect
17. C2×C4×Dic83C4semidirect
18. #14581706C4direct (N × H)
41. C22⋊Dic83C2×C4semidirect
57. C22⋊C4×C83C2×C4semidirect
70. C22×D83C42semidirect
95. C2×Dic83C42semidirect
120. C4×C83#99semidirect
134. C83C4×#99semidirect
138. C4×C22⋊C4D83semidirect
188. C22⋊C4C4×D83semidirect
258. C4#14581706direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D832
C2×#145817062
C4×C22⋊Dic832
#191274672
C4×C22⋊C4×C832
C4×#9983