Finite Group Databasebeta

← #21447166

Subgroups — #21447166

Order 7808.

230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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#16839805C212yesmaximal
2#16839627C211yesmaximal, characteristic
3#16839531C211yesmaximal, characteristic
4#16839521C212yesmaximal
5C61×#544C211yesmaximal, characteristic
6C2×#11758194C2212yes—
7C2×C4⋊Dic61C2211yescharacteristic
8C2×C4×Dic61C2211yescharacteristic
9#14519710—22no—
10#14519708—22no—
11#14519684—22no—
12C4⋊Q8×C61—22no—
13#125×C61—22no—
14C22⋊Q8×C61—22no—
15#117×C61C2212yes—
16C2×C4⋊C4×C61C2211yescharacteristic
17C2×Q8×C61—22no—
18C22×C4×C61D412yes—
19C22×C4×C61C2311yescharacteristic
20C22×Dic61—21no—
21C22×Dic61—21no—
22C4⋊C4×C61—22no—
23C4⋊C4×C61—24no—
24C4⋊C4×C61—22no—
25C4⋊C4×C61D412yes—
26C4⋊C4×C61D412yes—
27C22⋊C4×C61—22no—
28C42×C61—22no—
29C4⋊Dic61—22no—
30C4×Dic61—21no—
31C4×Dic61Q812yescomplemented
32#11758194—22no—
33#11758194Q814yescomplemented
34C2×#92418—22no—
35C23×C61C2×D411yescharacteristic
36Q8×C61—82no—
37C2×C4×C61—22no—
38C2×C4×C61—22no—
39C2×C4×C61—22no—
40C2×C4×C61—42no—
41C2×C4×C61C2×D412yes—
42C2×C4×C61C2×Q812yes—
43C2×C4×C61C2×Q811yescharacteristic
44C2×C4×C61#4111yescharacteristic
45C2×Dic61—22no—
46C2×Dic61—41no—
47C2×Dic61—41no—
48C2×Dic61—42no—
49C2×Dic61—41no—
50#92418—24no—
51C22×C61—21no—
52C22×C61—21no—
53C22×C61#12011yescharacteristic
54C22×C61C22⋊Q811yescharacteristic
55C22×C61C4⋊Q811yescharacteristic
56C4×C61—42no—
57C4×C61—42no—
58C4×C61—42no—
59C4×C61C22⋊Q812yes—
60C4×C61C4⋊Q812yes—
61Dic61—42no—
62Dic61—81no—
63#2061—611nomaximal, Sylow
64C2×C61—21no—
65C2×C61—21no—
66C2×C61#39511yescharacteristic
67C2×C61#45411yescharacteristic
68C2×C61#45511yescharacteristic
69#544D6111yescharacteristic
70#428—612no—
71#382—611no—
72#343—611no—
73#339—612no—
74C61#206111yescharacteristic, complemented, Sylow
75C2×M16—612no—
76C4⋊Q8—22no—
77#125—22no—
78C22⋊Q8—22no—
79#117C2×D6112yes—
80C2×C4⋊C4—611no—
81C2×C4⋊C4C2×D6111yescharacteristic
82C2×C42—611no—
83#107—1222no—
84#106—1222no—
85#95—1222no—
86C2×Q8—22no—
87C22×C4—1221no—
88C22×C4—1221no—
89C22×C4C22⋊D6112yes—
90C22×C4C22×D6111yescharacteristic
91M16—614no—
92M16—1222no—
93C2×C8—1222no—
94C4⋊C4—22no—
95C4⋊C4—24no—
96C4⋊C4—22no—
97C4⋊C4—1222no—
98C4⋊C4C22⋊D6112yes—
99C4⋊C4C22⋊D6112yes—
100C22⋊C4—22no—
101C42—22no—
102C42—612no—
103C42—1221no—
104C23C2×C22⋊D6111yescharacteristic
105Q8—82no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—1222no—
111C2×C4—2442no—
112C2×C4—2441no—
113C2×C4—2441no—
114C2×C4—2441no—
115C2×C4Q8×D6112yes—
116C2×C4Q8×D6111yescharacteristic
117C2×C4#1175822611yescharacteristic
118C2×C4C2×C22⋊D6112yes—
119C8—1224no—
120C22—21no—
121C22—21no—
122C22#1451974611yescharacteristic
123C22#1451975311yescharacteristic
124C22#1451977511yescharacteristic
125C4—42no—
126C4—42no—
127C4—42no—
128C4—4881no—
129C4—2442no—
130C4#1451975312yes—
131C4#1451977512yes—
132C2—21no—
133C2—21no—
134C2#1683968111yescharacteristic
135C2#1683993511yescharacteristic
136C2#1683994011yescharacteristic
subgroupG/H
centerC22#14519746
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#544C2
socleC22×C61#120
hypercenter#544D61
hypocenterC61#2061
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
31. C4×Dic61Q8semidirect
33. #11758194Q8semidirect
74. C61#2061semidirect