Finite Group Databasebeta

← #21447508

Subgroups — #21447508

Order 7808.

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

normal subgroups only

This group has 230 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×#14519696C212yesmaximal, complemented
2#16839561C212yesmaximal, complemented
3#16839559C212yesmaximal, complemented
4C61×#536C211yesmaximal, characteristic
5C2×#11758194—22no—
6#14519696—22no—
7#14519696C2214yes—
8C2×#41×C61C411yescharacteristic
9C22×Q8×C61C2211yescharacteristic
10C4⋊Q8×C61C411yescharacteristic
11C4⋊Q8×C61C2211yescharacteristic
12#124×C61C411yescharacteristic
13#124×C61C2211yescharacteristic
14#123×C61—22no—
15C22⋊Q8×C61—22no—
16#117×C61C411yescharacteristic
17#41×C61—42no—
18C2×Q8×C61—42no—
19C2×Q8×C61C2×C411yescharacteristic
20C2×Q8×C61C2×C411yescharacteristic
21C2×Q8×C61D412yes—
22C2×Q8×C61C2311yescharacteristic
23C2×D4×C61—21no—
24C2×D4×C61C2×C411yescharacteristic
25C22×C4×C61—21no—
26C22×C4×C61C2×C411yescharacteristic
27C22×C4×C61D412yes—
28C4⋊C4×C61—21no—
29C4⋊C4×C61—22no—
30C4⋊C4×C61—22no—
31C22⋊C4×C61—21no—
32C22⋊C4×C61—22no—
33C22⋊C4×C61—22no—
34C42×C61C2×C411yescharacteristic
35C42×C61C2×C411yescharacteristic
36#11758194—24no—
37#11758194—42no—
38C2×#92418—42no—
39C23×C61—21no—
40C23×C61C22⋊C411yescharacteristic
41Q8×C61—41no—
42Q8×C61—42no—
43Q8×C61—41no—
44Q8×C61—41no—
45D4×C61—41no—
46D4×C61—42no—
47C2×C4×C61—22no—
48C2×C4×C61—22no—
49C2×C4×C61—22no—
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—42no—
54C2×C4×C61C22⋊C412yes—
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22×C411yescharacteristic
57C2×C4×C61C2×D412yes—
58#92418—44no—
59C22×C61—41no—
60C22×C61—42no—
61C22×C61—41no—
62C22×C61#9912yes—
63C22×C61C2×C22⋊C411yescharacteristic
64C4×C61—22no—
65C4×C61—21no—
66C4×C61—22no—
67C4×C61—21no—
68C4×C61—41no—
69C4×C61—41no—
70C4×C61—41no—
71#2133—611nomaximal, Sylow
72C2×C61—21no—
73C2×C61—22no—
74C2×C61—81no—
75C2×C61C2×#9911yescharacteristic
76#536D6111yescharacteristic
77C2×#101—612no—
78#356—612no—
79#355—612no—
80C61#213311yescharacteristic, complemented, Sylow
81C2×#41Dic6111yescharacteristic
82C22×Q8C2×D6111yescharacteristic
83C2×M16—1222no—
84C4⋊Q8Dic6111yescharacteristic
85C4⋊Q8C2×D6111yescharacteristic
86#124Dic6111yescharacteristic
87#124C2×D6111yescharacteristic
88#123—22no—
89C22⋊Q8—22no—
90#117Dic6111yescharacteristic
91#101—614no—
92#101—1222no—
93#41—42no—
94C2×Q8—42no—
95C2×Q8C2×Dic6111yescharacteristic
96C2×Q8C2×Dic6111yescharacteristic
97C2×Q8C22⋊D6112yes—
98C2×Q8C22×D6111yescharacteristic
99C2×D4—21no—
100C2×D4C2×Dic6111yescharacteristic
101C22×C4—21no—
102C22×C4C2×Dic6111yescharacteristic
103C22×C4C22⋊D6112yes—
104M16—1224no—
105M16—2442no—
106C2×C8—2442no—
107C4⋊C4—21no—
108C4⋊C4—22no—
109C4⋊C4—22no—
110C22⋊C4—21no—
111C22⋊C4—22no—
112C22⋊C4—22no—
113C42C2×Dic6111yescharacteristic
114C42C2×Dic6111yescharacteristic
115C23—21no—
116C23C22⋊Dic6111yescharacteristic
117Q8—41no—
118Q8—42no—
119Q8—41no—
120Q8—41no—
121D4—41no—
122D4—42no—
123C2×C4—22no—
124C2×C4—22no—
125C2×C4—22no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—42no—
130C2×C4C22⋊Dic6112yes—
131C2×C4C22⋊Dic6111yescharacteristic
132C2×C4C22×Dic6111yescharacteristic
133C2×C4C2×C22⋊D6112yes—
134C8—2444no—
135C22—41no—
136C22—42no—
137C22—41no—
138C22#1451969212yes—
139C22C2×C22⋊Dic6111yescharacteristic
140C4—22no—
141C4—21no—
142C4—22no—
143C4—21no—
144C4—41no—
145C4—41no—
146C4—41no—
147C2—21no—
148C2—22no—
149C2—81no—
150C2C2×#1451969211yescharacteristic
subgroupG/H
centerC2C2×#14519692
commutatorC2×C4×C61C22×C4
FrattiniC2×Q8C22×D61
FittingC61×#536C2
socleC2×C61C2×#99
hypercenter#536D61
hypocenterC61#2133
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×Q8 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#14519696C2semidirect
2. #16839561C2semidirect
3. #16839559C2semidirect
80. C61#2133semidirect