Finite Group Databasebeta

← #21444159

Subgroups — #21444159

Order 7808.

300 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 77 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×D244C211yesmaximal, characteristic
2#16839819C211yesmaximal, characteristic, complemented
3#16839485C214yesmaximal, complemented
4C61×#432C211yesmaximal, characteristic, complemented
5C22×D244C411yescharacteristic
6C22×C4×D61C412yes—
7C4×D244—21no—
8C4×D244—21no—
9C4×D244—21no—
10C4×D244—21no—
11C2×C4⋊Dic61C411yescharacteristic
12C2×#11758198C2212yes—
13C4⋊#92418—21no—
14C22⋊#92418C2212yes—
15#14519688—21no—
16C2×C42×C61C2211yescharacteristic
17C4⋊C8×C61—21no—
18C22⋊C8×C61C2212yes—
19#97×C61—21no—
20C23×D61C2×C412yes—
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61C2×C411yescharacteristic
23C22×C4×C61C2311yescharacteristic
24C22×Dic61C2×C412yes—
25C2×D244—24no—
26C2×D244—21no—
27C2×D244—21no—
28C2×C4×D61—22no—
29C2×C4×D61—22no—
30C2×C4×D61—44no—
31C2×C8×C61—22no—
32C42×C61D411yescharacteristic
33C42×C61D411yescharacteristic
34C42×C61D411yescharacteristic
35C42×C61D411yescharacteristic
36#11758198—22no—
37#11758198—22no—
38C4⋊Dic61—21no—
39C4⋊Dic61—21no—
40C2×#92418—22no—
41C23×C61C22×C411yescharacteristic
42C22×D61—22no—
43C22×D61—22no—
44C22×D61—42no—
45C22×D61—42no—
46C22×D61M1614yes—
47C2×C4×C61—22no—
48C2×C4×C61—22no—
49C2×C4×C61—41no—
50C2×C4×C61C22⋊C411yescharacteristic
51C2×C4×C61C22⋊C411yescharacteristic
52C2×C4×C61C22⋊C411yescharacteristic
53C2×C4×C61C22⋊C411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×Dic61—22no—
57C2×Dic61—42no—
58D244—24no—
59D244—24no—
60C4×D61—44no—
61C4×D61—44no—
62C8×C61—42no—
63#92418—42no—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61C2×C22⋊C411yescharacteristic
67C22×C61C2×M1612yes—
68C2×D61—24no—
69C2×D61—44no—
70C2×D61—42no—
71C2×D61—42no—
72C2×D61—44no—
73C4×C61—21no—
74C4×C61—21no—
75C4×C61—21no—
76C4×C61—21no—
77C4×C61—21no—
78C4×C61#10012yes—
79Dic61—42no—
80#1466—611nomaximal, Sylow
81C2×C61—22no—
82C2×C61#40711yescharacteristic
83C2×C61#41011yescharacteristic
84C2×C61C2×#10011yescharacteristic
85D61—44no—
86C2×C4×D4—611no—
87#432—611no—
88#432D6111yescharacteristic, complemented
89#323—614no—
90C61#146611yescharacteristic, complemented, Sylow
91C22×D4—611no—
92C23×C4—612no—
93C4×D4—1221no—
94C4×D4—1221no—
95C4×D4—1221no—
96C4×D4—1221no—
97C2×C4⋊C4—611no—
98C2×C22⋊C4—612no—
99C2×C42C2×D6111yescharacteristic
100C4⋊C8—21no—
101C4⋊C8—1221no—
102C22⋊C8—612no—
103C22⋊C8C2×D6112yes—
104#97—21no—
105#97—1221no—
106C24—612no—
107C2×D4—1224no—
108C2×D4—1221no—
109C2×D4—1221no—
110C22×C4—612no—
111C22×C4—1222no—
112C22×C4—1222no—
113C22×C4—2444no—
114C22×C4C4×D6111yescharacteristic
115C22×C4C4×D6111yescharacteristic
116C22×C4C22×D6111yescharacteristic
117C2×C8—22no—
118C2×C8—1222no—
119C4⋊C4—1221no—
120C4⋊C4—1221no—
121C22⋊C4—1222no—
122C22⋊C4—1222no—
123C42D24411yescharacteristic
124C42D24411yescharacteristic
125C42C22⋊D6111yescharacteristic
126C42C22⋊D6111yescharacteristic
127C23—614no—
128C23—1222no—
129C23—1222no—
130C23—2442no—
131C23—2442no—
132C23C2×C4×D6111yescharacteristic
133D4—1224no—
134D4—1224no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—41no—
138C2×C4—1222no—
139C2×C4—2444no—
140C2×C4—2444no—
141C2×C4—2442no—
142C2×C4#1175819811yescharacteristic
143C2×C4#1175819811yescharacteristic
144C2×C4#1175819811yescharacteristic
145C2×C4#1175819811yescharacteristic
146C2×C4C2×D24411yescharacteristic
147C2×C4C2×C22⋊D6111yescharacteristic
148C8—42no—
149C8—2442no—
150C22—21no—
151C22—21no—
152C22—1224no—
153C22—2444no—
154C22—2444no—
155C22—2442no—
156C22—2442no—
157C22C2×#1175819811yescharacteristic
158C22M16×D6112yes—
159C4—21no—
160C4—21no—
161C4—21no—
162C4—21no—
163C4—21no—
164C4—2442no—
165C4#1451969312yes—
166C2—22no—
167C2—2444no—
168C2#1683972511yescharacteristic
169C2#1683973511yescharacteristic
170C2C2×#1451969311yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#432C2
socleC22×C61C2×C22⋊C4
hypercenter#432D61
hypocenterC61#1466
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #16839819C2semidirect
3. #16839485C2semidirect
4. C61×#432C2semidirect
88. #432D61semidirect
90. C61#1466semidirect