Finite Group Databasebeta

← #21446656

Subgroups — #21446656

Order 7808.

408 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14519692C214yesmaximal, complemented
2#16839622C211yesmaximal, characteristic, complemented
3C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
4C2×#121×C61C211yesmaximal, characteristic
5C2×C4⋊Dic61—21no—
6C2×C22⋊Dic61C2212yes—
7C2×C22⋊Dic61C2212yes—
8C2×C4×Dic61—21no—
9#14519692—28no—
10#14519684—21no—
11#14519684—21no—
12C22×D4×C61C411yescharacteristic, complemented
13C22×D4×C61C2212yes—
14C23×C4×C61C2211yescharacteristic
15#121×C61—21no—
16#121×C61—21no—
17#121×C61—21no—
18#121×C61—21no—
19C2×C4⋊C4×C61C411yescharacteristic, complemented
20C2×C22⋊C4×C61C412yescomplemented
21C24×C61C2×C412yes—
22C24×C61C2311yescharacteristic
23C2×D4×C61—22no—
24C2×D4×C61—22no—
25C2×D4×C61—24no—
26C2×D4×C61—24no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61—42no—
30C22×C4×C61—42no—
31C22×C4×C61C2×C412yes—
32C22×C4×C61C2×C411yescharacteristic
33C22×C4×C61C2×C411yescharacteristic
34C22×C4×C61D411yescharacteristic
35C22×C4×C61D411yescharacteristic
36C22×C4×C61D411yescharacteristic
37C22×C4×C61D411yescharacteristic
38C22×Dic61—22no—
39C22×Dic61—22no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—21no—
42C22⋊C4×C61—22no—
43C22⋊C4×C61—22no—
44C22⋊Dic61—22no—
45C22⋊Dic61—24no—
46C22⋊Dic61D414yescomplemented
47C4⋊Dic61—42no—
48C4×Dic61—42no—
49C23×C61—22no—
50C23×C61—24no—
51C23×C61—41no—
52C23×C61—41no—
53C23×C61—42no—
54C23×C61—42no—
55C23×C61C22×C411yescharacteristic
56C23×C61C2×D411yescharacteristic
57C23×C61C2×D411yescharacteristic
58C23×C61C2×D412yes—
59C23×C61#4112yes—
60D4×C61—42no—
61D4×C61—44no—
62D4×C61—42no—
63D4×C61—42no—
64D4×C61—42no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—24no—
70C2×C4×C61—41no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61C22⋊C411yescharacteristic
74C2×C4×C61C22⋊C411yescharacteristic
75C2×C4×C61C22⋊C411yescharacteristic
76C2×C4×C61C22⋊C411yescharacteristic
77C2×Dic61—24no—
78C2×Dic61—42no—
79C2×Dic61—42no—
80C2×Dic61—42no—
81C2×Dic61—42no—
82C2×Dic61—42no—
83C22×C61—21no—
84C22×C61—21no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61—21no—
88C22×C61—21no—
89C22×C61—42no—
90C22×C61—42no—
91C22×C61—42no—
92C22×C61—42no—
93C22×C61—42no—
94C22×C61—84no—
95C22×C61C2×C22⋊C411yescharacteristic
96C22×C61C4×D412yes—
97C22×C61#12112yes—
98C22×C61#12411yescharacteristic
99C22×C61#12711yescharacteristic
100C4×C61—21no—
101C4×C61—21no—
102C4×C61—21no—
103C4×C61—42no—
104C4×C61#9912yescomplemented
105Dic61—44no—
106Dic61—82no—
107#1964—611nomaximal, Sylow
108C2×C61—22no—
109C2×C61—21no—
110C2×C61—22no—
111C2×C61—21no—
112C2×C61—82no—
113C2×C61#39011yescharacteristic
114C2×C61C2×#9911yescharacteristic
115C2×C61#41011yescharacteristic
116C2×#121D6111yescharacteristic
117C2×#99—614no—
118#380—611no—
119C4×C22⋊C4—611no—
120C61#196411yescharacteristic, complemented, Sylow
121C22×D4Dic6111yescharacteristic, complemented
122C22×D4C2×D6112yes—
123C23×C4C2×D6111yescharacteristic
124#121—21no—
125#121—21no—
126#121—21no—
127#121—21no—
128C2×C4⋊C4—1221no—
129C2×C4⋊C4Dic6111yescharacteristic, complemented
130C2×C22⋊C4—612no—
131C2×C22⋊C4—612no—
132C2×C22⋊C4Dic6112yescomplemented
133C2×C42—1221no—
134#99—1228no—
135#95—1221no—
136#95—1221no—
137C24C2×Dic6112yes—
138C24C22×D6111yescharacteristic
139C2×D4—24no—
140C2×D4—24no—
141C2×D4—22no—
142C2×D4—22no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—42no—
146C22×C4—42no—
147C22×C4—1222no—
148C22×C4—1222no—
149C22×C4C2×Dic6112yes—
150C22×C4C2×Dic6111yescharacteristic
151C22×C4C2×Dic6111yescharacteristic
152C22×C4C22⋊D6111yescharacteristic
153C22×C4C22⋊D6111yescharacteristic
154C22×C4C22⋊D6111yescharacteristic
155C22×C4C22⋊D6111yescharacteristic
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—2442no—
159C22⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—614no—
162C22⋊C4—1222no—
163C22⋊C4—1224no—
164C42—2442no—
165C23—22no—
166C23—24no—
167C23—41no—
168C23—41no—
169C23—42no—
170C23—42no—
171C23D4×D6112yes—
172C23#1175822412yes—
173C23C22×Dic6111yescharacteristic
174C23C2×C22⋊D6111yescharacteristic
175C23C2×C22⋊D6111yescharacteristic
176D4—42no—
177D4—44no—
178D4—42no—
179D4—42no—
180D4—42no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—24no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—1224no—
190C2×C4—2442no—
191C2×C4—2442no—
192C2×C4—2442no—
193C2×C4—2442no—
194C2×C4—2442no—
195C2×C4C22⋊Dic6111yescharacteristic
196C2×C4C22⋊Dic6111yescharacteristic
197C2×C4C22⋊Dic6111yescharacteristic
198C2×C4C22⋊Dic6111yescharacteristic
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—42no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—84no—
211C22C2×C22⋊Dic6111yescharacteristic
212C22D4×Dic6112yes—
213C22#1451974812yes—
214C22#1451976411yescharacteristic
215C22#1451977311yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—42no—
220C4—4882no—
221C4—2444no—
222C4#1451969212yescomplemented
223C2—21no—
224C2—22no—
225C2—22no—
226C2—21no—
227C2—82no—
228C2#1683966511yescharacteristic
229C2C2×#1451969211yescharacteristic
230C2#1683973611yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic61
commutatorC23×C61C22×C4
FrattiniC24C22×D61
FittingC2×#121×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×#121D61
hypocenterC61#1964
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14519692C2semidirect
2. #16839622C2semidirect
3. C4×C22⋊Dic61C2semidirect
12. C22×D4×C61C4semidirect
19. C2×C4⋊C4×C61C4semidirect
20. C2×C22⋊C4×C61C4semidirect
46. C22⋊Dic61D4semidirect
104. C4×C61#99semidirect
120. C61#1964semidirect
121. C22×D4Dic61semidirect
129. C2×C4⋊C4Dic61semidirect
132. C2×C22⋊C4Dic61semidirect
222. C4#14519692semidirect