Finite Group Databasebeta

← #21461648

Subgroups — #21461648

Order 7808.

612 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 86 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×#14519836C212yesmaximal, complemented
2C2×#14519835C212yesmaximal, complemented
3#16840705C212yesmaximal, complemented
4C22×#11758222C211yesmaximal, characteristic
5C2×C22⋊#6923C2214yes—
6#14519836—24no—
7#14519835—24no—
8(C2×#6923)⋊C4—24no—
9C2×#11758222—24no—
10C2×#11758222—24no—
11C2×#11758222—24no—
12C22×Dic122C411yescharacteristic, complemented
13C22×D244C2211yescharacteristic
14C22×C22⋊D61C411yescharacteristic, complemented
15C22×C22⋊D61C2211yescharacteristic
16C22×C4×D61C411yescharacteristic, complemented
17C22×C4×D61C2211yescharacteristic
18C23×C4×C61C411yescharacteristic, complemented
19C24×C61C2×C411yescharacteristic
20C23×D61C2×C411yescharacteristic
21C23×D61C2311yescharacteristic
22C22×#6923—24no—
23C22×C4×C61—22no—
24C22×C4×C61—22no—
25C22×C4×C61—22no—
26C22×C4×C61C2×C411yescharacteristic
27C22×C4×C61C2×C411yescharacteristic
28C2×C22⋊D61—22no—
29C2×C22⋊D61—22no—
30C2×C22⋊D61—22no—
31C2×C22⋊D61—22no—
32C2×C22⋊D61—22no—
33C2×C22⋊D61D414yes—
34C22×Dic61C2×C411yescharacteristic
35C22×Dic61C2×C411yescharacteristic
36#11758222—232no—
37C2×D244—22no—
38C2×D244—22no—
39C2×D244D414yes—
40C2×C4×D61—22no—
41C2×C4×D61—22no—
42C2×C4×D61—22no—
43C2×C4×D61—22no—
44C2×C4×D61—22no—
45C2×C4×D61D414yes—
46C2×Dic122—22no—
47C2×Dic122—22no—
48C2×Dic122—22no—
49C22⋊#6923—24no—
50C22⋊#6923—24no—
51C23×C61—21no—
52C23×C61—21no—
53C23×C61—42no—
54C23×C61C22⋊C412yes—
55C23×C61C22×C411yescharacteristic
56C22×D61—21no—
57C22×D61—21no—
58C22×D61—42no—
59C22×D61—42no—
60C22×D61C22⋊C412yes—
61C22×D61C2×D412yes—
62C22×D61C2×D412yes—
63C22×D61C2×D412yes—
64C2×#6923—48no—
65C2×#6923—44no—
66C2×C4×C61—28no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61C22⋊C412yes—
72C2×C4×C61C22⋊C412yes—
73C22⋊D61—28no—
74C22⋊D61—28no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61C22⋊C412yes—
80C2×Dic61C22⋊C412yes—
81D244—28no—
82C4×D61—28no—
83C4×D61—28no—
84Dic122—28no—
85C22×C61—22no—
86C22×C61—22no—
87C22×C61—42no—
88C22×C61—42no—
89C22×C61—42no—
90C22×C61C2×C22⋊C411yescharacteristic
91C22×C61C2×C22⋊C411yescharacteristic
92C22×C61C2×C22⋊C411yescharacteristic
93C2×D61—24no—
94C2×D61—22no—
95C2×D61—42no—
96C2×D61—42no—
97C2×D61—42no—
98C2×D61—42no—
99C2×D61—42no—
100C2×D61#12014yes—
101#6923—84no—
102C4×C61—22no—
103C4×C61—22no—
104Dic61—22no—
105Dic61—22no—
106#1782—611nomaximal, Sylow
107C2×C61—21no—
108C2×C61—21no—
109C2×C61—42no—
110C2×C61#37911yescharacteristic
111C2×C61#41012yes—
112D61—24no—
113D61—42no—
114C22×#41—611no—
115C2×#99—612no—
116C2×#99—612no—
117#381—612no—
118C61#178211yescharacteristic, complemented, Sylow
119C2×#41—1224no—
120C2×#41—1224no—
121C2×#41—1224no—
122C22×Q8—611no—
123C22×D4—611no—
124C22×D4—611no—
125C22×D4—611no—
126C23×C4—611no—
127C23×C4—611no—
128C23×C4#692311yescharacteristic, complemented
129C2×C22⋊C4—614no—
130#99—1224no—
131#99—1224no—
132#95—1224no—
133C24—611no—
134C24—611no—
135C24C2×#692311yescharacteristic
136#41—12232no—
137C2×Q8—1222no—
138C2×Q8—1222no—
139C2×Q8—1222no—
140C2×D4—614no—
141C2×D4—614no—
142C2×D4—1222no—
143C2×D4—1222no—
144C2×D4—1222no—
145C2×D4—1222no—
146C2×D4—1222no—
147C2×D4—1222no—
148C2×D4—1222no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—611no—
153C22×C4—611no—
154C22×C4—614no—
155C22×C4—1222no—
156C22×C4—1222no—
157C22×C4—1222no—
158C22×C4—1222no—
159C22×C4—1222no—
160C22×C4—1224no—
161C22×C4C2×#692311yescharacteristic
162C22×C4C2×#692311yescharacteristic
163C22⋊C4—1224no—
164C22⋊C4—1224no—
165C23—21no—
166C23—21no—
167C23—42no—
168C23—612no—
169C23—612no—
170C23—612no—
171C23—612no—
172C23—1221no—
173C23—1221no—
174C23—2442no—
175C23—2442no—
176C23C22⋊#692312yes—
177C23C22×#692311yescharacteristic
178Q8—1228no—
179D4—1228no—
180D4—1228no—
181D4—1228no—
182C2×C4—28no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—612no—
188C2×C4—612no—
189C2×C4—1228no—
190C2×C4—1228no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—2444no—
196C2×C4—2448no—
197C2×C4C22⋊#692312yes—
198C2×C4C22⋊#692312yes—
199C22—22no—
200C22—22no—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—614no—
205C22—1224no—
206C22—1222no—
207C22—2442no—
208C22—2442no—
209C22—2442no—
210C22—2442no—
211C22—2442no—
212C22C2×C22⋊#692311yescharacteristic
213C22C2×C22⋊#692311yescharacteristic
214C22C2×C22⋊#692311yescharacteristic
215C4—22no—
216C4—22no—
217C4—1222no—
218C4—1222no—
219C4—4884no—
220C2—21no—
221C2—21no—
222C2—42no—
223C2—1224no—
224C2—2442no—
225C2#1684070311yescharacteristic
226C2#1684074112yes—
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC23×C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC23×C4#6923
hypocenterC61#1782
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#14519836C2semidirect
2. C2×#14519835C2semidirect
3. #16840705C2semidirect
12. C22×Dic122C4semidirect
14. C22×C22⋊D61C4semidirect
16. C22×C4×D61C4semidirect
18. C23×C4×C61C4semidirect
118. C61#1782semidirect
128. C23×C4#6923semidirect