Finite Group Databasebeta

← #21444170

Subgroups — #21444170

Order 7808.

256 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 73 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×#14519765C211yesmaximal, characteristic
2#16839819C211yesmaximal, characteristic, complemented
3#16839485C214yesmaximal, complemented
4C61×#431C211yesmaximal, characteristic, complemented
5C22×Dic122C411yescharacteristic
6C22×D244C411yescharacteristic
7#14519765—21no—
8#14519765—21no—
9#14519765—21no—
10#14519765—21no—
11C2×#11758198C412yes—
12C2×#11758198C2212yes—
13C4⋊#92418—21no—
14C22⋊#92418C2212yes—
15#14519688—21no—
16C2×C42×C61C2211yescharacteristic
17C4⋊C8×C61—21no—
18C22⋊C8×C61C2212yes—
19C4×C8×C61—21no—
20C23×D61C2×C412yes—
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61C2×C411yescharacteristic
23C22×C4×C61C2311yescharacteristic
24C22×Dic61C2×C412yes—
25C2×D244—21no—
26C2×D244—21no—
27C2×D244—42no—
28C2×Dic122—21no—
29C2×Dic122—21no—
30C2×Dic122—42no—
31C2×C8×C61—22no—
32C42×C61D411yescharacteristic
33C42×C61D411yescharacteristic
34C42×C61D411yescharacteristic
35C42×C61D411yescharacteristic
36#11758198—22no—
37#11758198—22no—
38#11758198—22no—
39#11758198—22no—
40C2×#92418—22no—
41C23×C61C22×C411yescharacteristic
42C22×D61—22no—
43C22×D61—24no—
44C22×D61—42no—
45C22×D61—42no—
46C2×C4×C61—22no—
47C2×C4×C61—22no—
48C2×C4×C61—41no—
49C2×C4×C61C22⋊C411yescharacteristic
50C2×C4×C61C22⋊C411yescharacteristic
51C2×C4×C61C22⋊C411yescharacteristic
52C2×C4×C61C22⋊C411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C2×Dic61—22no—
56C2×Dic61—42no—
57D244—42no—
58D244—42no—
59Dic122—42no—
60Dic122—42no—
61C8×C61—42no—
62#92418—42no—
63C22×C61—21no—
64C22×C61—21no—
65C22×C61C2×C22⋊C411yescharacteristic
66C22×C61#13112yes—
67C2×D61—42no—
68C2×D61—42no—
69C2×D61—42no—
70C2×D61—84no—
71C4×C61—21no—
72C4×C61—21no—
73C4×C61—21no—
74C4×C61—21no—
75C4×C61—21no—
76C4×C61#10012yes—
77Dic61—42no—
78#1469—611nomaximal, Sylow
79C2×C61—22no—
80C2×C61#40811yescharacteristic
81C2×C61#41011yescharacteristic
82C2×C61C2×#10011yescharacteristic
83D61—82no—
84C2×#124—611no—
85#432—611no—
86#431D6111yescharacteristic, complemented
87#323—614no—
88C61#146911yescharacteristic, complemented, Sylow
89C22×Q8—611no—
90C22×D4—611no—
91#124—1221no—
92#124—1221no—
93#124—1221no—
94#124—1221no—
95C2×C22⋊C4—612no—
96C2×C22⋊C4—612no—
97C2×C42C2×D6111yescharacteristic
98C4⋊C8—21no—
99C4⋊C8—1221no—
100C22⋊C8—612no—
101C22⋊C8C2×D6112yes—
102#97—1221no—
103C4×C8—21no—
104C24—612no—
105C2×Q8—1221no—
106C2×Q8—1221no—
107C2×Q8—2442no—
108C2×D4—1221no—
109C2×D4—1221no—
110C2×D4—2442no—
111C22×C4—612no—
112C22×C4C4×D6111yescharacteristic
113C22×C4C4×D6111yescharacteristic
114C22×C4C22×D6111yescharacteristic
115C2×C8—22no—
116C2×C8—1222no—
117C22⋊C4—1222no—
118C22⋊C4—1222no—
119C22⋊C4—1222no—
120C22⋊C4—1222no—
121C42D24411yescharacteristic
122C42D24411yescharacteristic
123C42C22⋊D6111yescharacteristic
124C42C22⋊D6111yescharacteristic
125C23—1224no—
126C23—1222no—
127C23—2442no—
128C23—2442no—
129C23C2×C4×D6111yescharacteristic
130Q8—2442no—
131Q8—2442no—
132D4—2442no—
133D4—2442no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—41no—
137C2×C4—1222no—
138C2×C4—2442no—
139C2×C4#1175819811yescharacteristic
140C2×C4#1175819811yescharacteristic
141C2×C4#1175819811yescharacteristic
142C2×C4#1175819811yescharacteristic
143C2×C4C2×D24411yescharacteristic
144C2×C4C2×C22⋊D6111yescharacteristic
145C8—42no—
146C8—2442no—
147C22—21no—
148C22—21no—
149C22—4884no—
150C22—2442no—
151C22—2442no—
152C22—2442no—
153C22C2×#1175819811yescharacteristic
154C22#1451978312yes—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—21no—
160C4—2442no—
161C4#1451969312yes—
162C2—22no—
163C2—4882no—
164C2#1683972811yescharacteristic
165C2#1683973511yescharacteristic
166C2C2×#1451969311yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#431C2
socleC22×C61C2×C22⋊C4
hypercenter#431D61
hypocenterC61#1469
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #16839819C2semidirect
3. #16839485C2semidirect
4. C61×#431C2semidirect
86. #431D61semidirect
88. C61#1469semidirect