Finite Group Databasebeta

← #21444790

Subgroups — #21444790

Order 7808.

282 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 53 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
1#16840343C211yesmaximal, characteristic
2#16839903C212yesmaximal, complemented
3#16839682C211yesmaximal, characteristic, complemented
4#16839497C212yesmaximal, complemented
5C61×#324C211yesmaximal, characteristic, complemented
6C2×#11758222—21no—
7C22×Dic122C2211yescharacteristic
8C2×#11758190—22no—
9#14519757—22no—
10#14519752—22no—
11#14519751—21no—
12#14519751C2212yes—
13C2×#11758196—21no—
14#14519702—22no—
15#14519684—21no—
16#14519684C2211yescharacteristic
17C2×C4⋊C4×C61C2211yescharacteristic
18C22⋊C8×C61C2212yes—
19C22×C4×C61D411yescharacteristic
20C22×C4×C61D411yescharacteristic
21C22×C4×C61C2311yescharacteristic
22C2×C22⋊D61—22no—
23C22×Dic61—21no—
24C22×Dic61—21no—
25#11758222—42no—
26#11758222—42no—
27C2×D244—21no—
28C2×D244—21no—
29C2×D244D412yes—
30C2×C4×D61—22no—
31C2×Dic122—22no—
32C2×Dic122—21no—
33C2×Dic122—42no—
34C2×C8×C61—22no—
35C4⋊C4×C61—22no—
36#11758198—22no—
37#11758198—22no—
38C4⋊Dic61—21no—
39C4⋊Dic61D412yes—
40#11758196—42no—
41#11758190—44no—
42C23×C61C2×D411yescharacteristic
43C22×D61—22no—
44C2×C4×C61—21no—
45C2×C4×C61—21no—
46C2×C4×C61—21no—
47C2×C4×C61—41no—
48C2×C4×C61—41no—
49C2×C4×C61SD1612yescomplemented
50C2×C4×C61C2×D412yes—
51C22⋊D61—42no—
52C22⋊D61—42no—
53C2×Dic61—22no—
54C2×Dic61—22no—
55C2×Dic61—22no—
56C2×Dic61—41no—
57C2×Dic61—41no—
58C2×Dic61—41no—
59C2×Dic61—41no—
60D244—42no—
61D244—42no—
62D244—81no—
63C4×D61—44no—
64Dic122—24no—
65Dic122—42no—
66Dic122—42no—
67C8×C61—42no—
68C22×C61—21no—
69C22×C61—21no—
70C22×C61#12011yescharacteristic
71C22×C61C2×SD1611yescharacteristic
72C22×C61AGL(1,ℤ/8)11yescharacteristic
73C2×D61—42no—
74C2×D61—42no—
75C2×D61—42no—
76C4×C61—22no—
77C4×C61—22no—
78C4×C61—41no—
79Dic61—42no—
80Dic61—42no—
81Dic61—42no—
82#1604—611nomaximal, Sylow
83C2×C61—21no—
84C2×C61—21no—
85C2×C61#45011yescharacteristic
86C2×C61#45611yescharacteristic
87C2×C61B(4,𝔽2)11yescharacteristic
88D61—82no—
89#537—611no—
90#448—612no—
91#395—611no—
92#327—612no—
93#324D6111yescharacteristic, complemented
94C61#160411yescharacteristic, complemented, Sylow
95C2×#41—1221no—
96C22×Q8—611no—
97C2×SD16—1222no—
98C22⋊Q8—1222no—
99#121—612no—
100#121—1222no—
101#121—1221no—
102C2×C4⋊C4—1221no—
103C2×C4⋊C4C2×D6111yescharacteristic
104#103—1222no—
105C22⋊C8C2×D6112yes—
106#95—611no—
107#95—1221no—
108#41—2442no—
109#41—2442no—
110C2×Q8—1221no—
111C2×Q8—1222no—
112C2×Q8—2442no—
113C2×D4—612no—
114C2×D4—1221no—
115C2×D4—1221no—
116C2×D4—1222no—
117C22×C4—1222no—
118C22×C4—1221no—
119C22×C4—1221no—
120C22×C4D24411yescharacteristic
121C22×C4D24411yescharacteristic
122C22×C4C22×D6111yescharacteristic
123SD16—2444no—
124C2×C8—22no—
125C4⋊C4—22no—
126C4⋊C4—612no—
127C4⋊C4—1221no—
128C4⋊C4—2442no—
129C22⋊C4—1222no—
130C22⋊C4—1222no—
131C23—1222no—
132C23C2×D24411yescharacteristic
133Q8—1224no—
134Q8—2442no—
135Q8—2442no—
136D4—4881no—
137D4—2442no—
138D4—2442no—
139D4—2442no—
140D4—2442no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—1222no—
147C2×C4—1222no—
148C2×C4—1222no—
149C2×C4—2444no—
150C2×C4—2441no—
151C2×C4—2441no—
152C2×C4—2441no—
153C2×C4—2441no—
154C2×C4#1175819012yescomplemented
155C2×C4D4×D6112yes—
156C8—42no—
157C22—21no—
158C22—21no—
159C22—2442no—
160C22—2442no—
161C22—2442no—
162C22#1451974711yescharacteristic
163C22C2×#1175819011yescharacteristic
164C22#1451980511yescharacteristic
165C4—22no—
166C4—22no—
167C4—41no—
168C4—2442no—
169C4—2442no—
170C4—2442no—
171C2—21no—
172C2—21no—
173C2—4882no—
174C2#1683991511yescharacteristic
175C2#1683994711yescharacteristic
176C2#1683995011yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#324C2
socleC22×C61#120
hypercenter#324D61
hypocenterC61#1604
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #16839903C2semidirect
3. #16839682C2semidirect
4. #16839497C2semidirect
5. C61×#324C2semidirect
49. C2×C4×C61SD16semidirect
93. #324D61semidirect
94. C61#1604semidirect
154. C2×C4#11758190semidirect