Finite Group Databasebeta

← #21444507

Subgroups — #21444507

Order 7808.

216 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 89 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#16840319C211yesmaximal, characteristic
2#16839786C211yesmaximal, characteristic
3#16839510C212yesmaximal, complemented
4#16839509C212yesmaximal, complemented
5C2×C4⋊C8×C61C211yesmaximal, characteristic
6C2×#11758194—21no—
7#14519777C2211yescharacteristic
8#14519777C2211yescharacteristic
9#14519769—21no—
10#14519756—21no—
11#14519756C412yes—
12C4×Dic122—21no—
13C4×Dic122C412yes—
14#14519736—21no—
15C4⋊#92418—21no—
16C4⋊#92418C2212yes—
17C22×C8×C61—21no—
18C2×C42×C61C2211yescharacteristic
19C4⋊C8×C61—21no—
20C4⋊C8×C61C2212yes—
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61D411yescharacteristic
24C2×Dic122—21no—
25C2×Dic122C2×C412yes—
26C2×C8×C61—22no—
27C2×C8×C61—42no—
28C42×C61C2×C411yescharacteristic
29C42×C61D411yescharacteristic
30C42×C61D411yescharacteristic
31C42×C61C2311yescharacteristic
32C22⋊Dic61—22no—
33C4⋊Dic61—21no—
34C4⋊Dic61—21no—
35C4⋊Dic61—21no—
36C4⋊Dic61C2×C412yes—
37#11758196—22no—
38#11758196—22no—
39C4×Dic61—22no—
40#11758194—42no—
41C2×#92418—22no—
42C23×C61C22⋊C411yescharacteristic
43C2×C4×C61—21no—
44C2×C4×C61—21no—
45C2×C4×C61—41no—
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61SD1612yes—
50C2×C4×C61Q1612yes—
51C2×C4×C61C22×C411yescharacteristic
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C2×Dic61—22no—
55C2×Dic61—22no—
56Dic122—41no—
57Dic122—41no—
58Dic122—42no—
59C8×C61—42no—
60#92418—42no—
61C22×C61—21no—
62C22×C61—21no—
63C22×C61#10312yes—
64C22×C61C2×C22⋊C411yescharacteristic
65C4×C61—21no—
66C4×C61—21no—
67C4×C61—21no—
68C4×C61#10312yes—
69C4×C61C2×SD1611yescharacteristic
70C4×C61C2×Q1611yescharacteristic
71C4×C61AGL(1,ℤ/8)11yescharacteristic
72C4×C61#13711yescharacteristic
73Dic61—42no—
74Dic61—42no—
75#1550—611nomaximal, Sylow
76C2×C61—22no—
77C2×C61#41311yescharacteristic
78C2×C61C2×#10311yescharacteristic
79C2×C61#41711yescharacteristic
80#533—611no—
81#423—611no—
82C2×C4⋊C8D6111yescharacteristic
83#333—612no—
84#332—612no—
85C61#155011yescharacteristic, complemented, Sylow
86C2×M16—1221no—
87C22×C8—21no—
88C4⋊Q8—611no—
89C4⋊Q8—611no—
90#125—1221no—
91C22⋊Q8—612no—
92C22⋊Q8—1221no—
93C4×Q8—612no—
94C4×Q8—1221no—
95#117—1221no—
96C2×C42C2×D6111yescharacteristic
97C4⋊C8—21no—
98C4⋊C8—612no—
99C4⋊C8—1221no—
100C4⋊C8C2×D6112yes—
101C2×Q8—612no—
102C2×Q8—1221no—
103C22×C4C4×D6111yescharacteristic
104C22×C4D24411yescharacteristic
105C22×C4C22⋊D6111yescharacteristic
106M16—2442no—
107C2×C8—22no—
108C2×C8—42no—
109C2×C8—1222no—
110C4⋊C4—612no—
111C4⋊C4—1222no—
112C4⋊C4—1222no—
113C4⋊C4—1221no—
114C4⋊C4—1221no—
115C4⋊C4—1221no—
116C22⋊C4—1222no—
117C42—1222no—
118C42C4×D6111yescharacteristic
119C42D24411yescharacteristic
120C42C22⋊D6111yescharacteristic
121C42C22×D6111yescharacteristic
122C23#1175819811yescharacteristic
123Q8—2442no—
124Q8—2441no—
125Q8—2441no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—41no—
129C2×C4—1222no—
130C2×C4—1222no—
131C2×C4#1175819012yes—
132C2×C4Dic24412yes—
133C2×C4#1175819811yescharacteristic
134C2×C4#1175819811yescharacteristic
135C2×C4#1175819811yescharacteristic
136C2×C4C2×C4×D6111yescharacteristic
137C2×C4C2×D24411yescharacteristic
138C2×C4C2×C22⋊D6111yescharacteristic
139C8—42no—
140C8—2442no—
141C22—21no—
142C22—21no—
143C22#1451970212yes—
144C22C2×#1175819811yescharacteristic
145C4—21no—
146C4—21no—
147C4—21no—
148C4—2442no—
149C4—2442no—
150C4#1451970212yes—
151C4C2×#1175819011yescharacteristic
152C4C2×Dic24411yescharacteristic
153C4#1451980311yescharacteristic
154C4#1451980811yescharacteristic
155C2—22no—
156C2#1683974411yescharacteristic
157C2C2×#1451970211yescharacteristic
158C2#1683976111yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC2×C4⋊C8×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C8D61
hypocenterC61#1550
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #16839510C2semidirect
4. #16839509C2semidirect
85. C61#1550semidirect