Finite Group Databasebeta

← C4×#14519839 #21461585

Subgroups — C4×#14519839 #21461585

Order 7808.

396 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 110 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×#14519839C212yesmaximal
2C4×D61⋊C8C211yesmaximal, characteristic, complemented
3C4×C4⋊#6923C211yesmaximal, characteristic, complemented
4#16840635C212yesmaximal, complemented
5C4×D4×D61C211yesmaximal, characteristic
6C2×D61⋊C8C2212yes—
7C2×C4⋊#6923C2212yes—
8C2×C4×#6923—21no—
9#14519839C418yesdirect product factor
10C4×#92420—21no—
11C4×#92420—21no—
12(C2×#6923)⋊C4—21no—
13C2×D4×D61C2211yescharacteristic
14C22×C4×D61—21no—
15C4×D244C411yescharacteristic, complemented
16D4×Dic61C411yescharacteristic, complemented
17#14519739C411yescharacteristic, complemented
18C4×C22⋊D61—21no—
19#14519737—21no—
20C4⋊C4×D61C2211yescharacteristic
21C22⋊C4×D61—21no—
22C42×D61C2211yescharacteristic
23C4×D4×C61C411yescharacteristic, complemented
24C23×D61—21no—
25C22×#6923—22no—
26C2×D4×C61C2×C411yescharacteristic
27C22×C4×C61—21no—
28C2×C22⋊D61—21no—
29C22×Dic61—21no—
30D4×D61—22no—
31D4×D61C2×C414yes—
32C2×D244C2×C411yescharacteristic
33C2×C4×D61—21no—
34C2×C4×D61—21no—
35C2×C4×D61—21no—
36C2×C4×D61—42no—
37C2×C4×D61—42no—
38C2×C4×D61D411yescharacteristic
39C2×C4×D61D411yescharacteristic
40C2×C4×D61C2311yescharacteristic
41C2×#92420—22no—
42C4⋊#6923—22no—
43C4⋊#6923C2×C414yescomplemented
44C4×#6923—42no—
45D61⋊C8—22no—
46D61⋊C8C2×C414yescomplemented
47C4⋊C4×C61C2×C411yescharacteristic
48C22⋊C4×C61—21no—
49C42×C61C2×C411yescharacteristic
50C22⋊Dic61—21no—
51#11758198—21no—
52#11758198—21no—
53C4⋊Dic61C2×C411yescharacteristic
54#11758196—21no—
55C4×Dic61C2×C411yescharacteristic
56C4×Dic61D411yescharacteristic
57C4×Dic61D411yescharacteristic
58C23×C61—21no—
59C22×D61—21no—
60C22×D61—24no—
61C22×D61—41no—
62C22×D61—41no—
63C22×D61—42no—
64C22×D61C2×D411yescharacteristic
65C2×#6923—24no—
66C2×#6923—42no—
67C2×#6923—42no—
68D4×C61—21no—
69D4×C61C4212yescomplemented
70C2×C4×C61—21no—
71C2×C4×C61—42no—
72C2×C4×C61C22⋊C411yescharacteristic
73C2×C4×C61C22⋊C411yescharacteristic
74C2×C4×C61C22×C411yescharacteristic
75C22⋊D61—24no—
76C2×Dic61—21no—
77C2×Dic61—42no—
78C2×Dic61C22⋊C411yescharacteristic
79C2×Dic61C22⋊C411yescharacteristic
80C2×Dic61C2×D411yescharacteristic
81D244—21no—
82D244C4212yescomplemented
83C4×D61—22no—
84C4×D61—41no—
85C4×D61—41no—
86C4×D61—42no—
87C4×D61—42no—
88C4×D61D812yes—
89C4×D61SD1612yes—
90C4×D61C22×C412yes—
91C4×D61#4112yes—
92#92420—24no—
93C22×C61—22no—
94C22×C61—41no—
95C22×C61—41no—
96C22×C61C2×C22⋊C411yescharacteristic
97C2×D61—22no—
98C2×D61—41no—
99C2×D61—41no—
100C2×D61—44no—
101C2×D61—44no—
102C2×D61C4×D412yes—
103C2×D61C2×D811yescharacteristic
104C2×D61C2×SD1611yescharacteristic
105C2×D61#13512yes—
106#6923—44no—
107C4×C61—21no—
108C4×C61—41no—
109C4×C61#10212yescomplemented
110C4×C61C2×C4211yescharacteristic
111C4×C61#11711yescharacteristic
112Dic61—21no—
113Dic61—41no—
114Dic61#10212yescomplemented
115Dic61C4×D412yes—
116C4×#102—611nomaximal, Sylow
117C2×C61—42no—
118C2×C61C4×C22⋊C411yescharacteristic
119C2×C61C2×#10211yescharacteristic
120C2×C61#41611yescharacteristic
121D61—42no—
122D61C4×D812yes—
123D61C4×SD1612yes—
124C2×C4×D4—611no—
125C2×#102—612no—
126C2×C4×C8—611no—
127C4×C4⋊C4—611no—
128#340—612no—
129C61C4×#10211yescharacteristic, complemented, Sylow
130C22×D4—611no—
131C23×C4—1221no—
132C22×C8—612no—
133C4×D4—611no—
134C4×D4—611no—
135C4×D4—611no—
136C4×D4—1221no—
137C4×D4—1221no—
138C4×D4#692311yescharacteristic, complemented
139C2×C4⋊C4—612no—
140C2×C4⋊C4—611no—
141C2×C22⋊C4—1221no—
142C2×C42—611no—
143C2×C42—1221no—
144#102—618no—
145C4×C8—1221no—
146C4×C8—1221no—
147#95—1221no—
148C24—1221no—
149C2×D4—614no—
150C2×D4—611no—
151C2×D4—1222no—
152C2×D4—1221no—
153C2×D4C2×#692311yescharacteristic
154C22×C4—21no—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4—611no—
158C22×C4—1221no—
159C22×C4—1221no—
160C22×C4—1221no—
161C22×C4—1222no—
162C22×C4—1221no—
163C22×C4—2442no—
164C22×C4—2442no—
165C2×C8—614no—
166C2×C8—1222no—
167C2×C8—1222no—
168C4⋊C4—614no—
169C4⋊C4—611no—
170C4⋊C4—1221no—
171C4⋊C4—1222no—
172C4⋊C4C2×#692311yescharacteristic
173C22⋊C4—21no—
174C22⋊C4—1221no—
175C22⋊C4—1221no—
176C22⋊C4—1221no—
177C42—611no—
178C42—611no—
179C42—611no—
180C42—2442no—
181C42C2×#692311yescharacteristic
182C23—21no—
183C23—611no—
184C23—1224no—
185C23—1221no—
186C23—2441no—
187C23—2441no—
188C23—2442no—
189D4—21no—
190D4—612no—
191D4—1224no—
192D4—1221no—
193D4C4×#692312yescomplemented
194C2×C4—21no—
195C2×C4—42no—
196C2×C4—611no—
197C2×C4—611no—
198C2×C4—612no—
199C2×C4—612no—
200C2×C4—612no—
201C2×C4—612no—
202C2×C4—611no—
203C2×C4—1222no—
204C2×C4—1224no—
205C2×C4—1221no—
206C2×C4—2442no—
207C2×C4—2441no—
208C2×C4—2441no—
209C2×C4—2442no—
210C2×C4—2442no—
211C2×C4—2442no—
212C2×C4—2442no—
213C2×C4C22⋊#692311yescharacteristic
214C2×C4C22⋊#692311yescharacteristic
215C2×C4C22×#692311yescharacteristic
216C8—1224no—
217C22—22no—
218C22—41no—
219C22—41no—
220C22—611no—
221C22—611no—
222C22—612no—
223C22—612no—
224C22—1222no—
225C22—2444no—
226C22—2444no—
227C22—2441no—
228C22—2441no—
229C22C2×C22⋊#692311yescharacteristic
230C4—21no—
231C4—41no—
232C4—612no—
233C4—612no—
234C4—1221no—
235C4—2444no—
236C4—2441no—
237C4#1451983912yesdirect product factor
238C4C2×C4×#692311yescharacteristic
239C4#1451985611yescharacteristic
240C2—42no—
241C2—612no—
242C2—612no—
243C2—2442no—
244C2C4×C22⋊#692311yescharacteristic
245C2C2×#1451983911yescharacteristic
246C2#1684075211yescharacteristic
subgroupG/H
centerC2×C4C22⋊#6923
commutatorC4×C61C2×C42
FrattiniC2×C4C22×#6923
FittingC4×D4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×D4#6923
hypocenterC61C4×#102
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×D61⋊C8C2semidirect
3. C4×C4⋊#6923C2semidirect
4. #16840635C2semidirect
9. #14519839C4direct (N × H)
15. C4×D244C4semidirect
16. D4×Dic61C4semidirect
17. #14519739C4semidirect
23. C4×D4×C61C4semidirect
43. C4⋊#6923C2×C4semidirect
46. D61⋊C8C2×C4semidirect
69. D4×C61C42semidirect
82. D244C42semidirect
109. C4×C61#102semidirect
114. Dic61#102semidirect
129. C61C4×#102semidirect
138. C4×D4#6923semidirect
193. D4C4×#6923semidirect
237. C4#14519839direct (N × H)