Finite Group Databasebeta

← #21446764

Subgroups — #21446764

Order 7808.

260 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C4×#11758194C211yesmaximal, characteristic
2C4×C4⋊Dic61C211yesmaximal, characteristic
3#16839521C214yesmaximal
4C61×#533C211yesmaximal, characteristic
5C2×#11758194C2212yes—
6C2×C4⋊Dic61—21no—
7C2×C4×Dic61C2212yes—
8#14519688—21no—
9C4×#92418—21no—
10#14519684—21no—
11C4⋊Q8×C61C411yescharacteristic, complemented
12C4⋊Q8×C61C411yescharacteristic, complemented
13#125×C61C412yescomplemented
14C22⋊Q8×C61—21no—
15C22⋊Q8×C61—21no—
16C4×Q8×C61—21no—
17C4×Q8×C61—21no—
18#117×C61C2212yes—
19C2×C42×C61C2211yescharacteristic
20C2×Q8×C61—21no—
21C2×Q8×C61—21no—
22C22×C4×C61D411yescharacteristic
23C22×C4×C61D411yescharacteristic
24C22×C4×C61C2311yescharacteristic
25C22×Dic61—22no—
26C4⋊C4×C61—22no—
27C4⋊C4×C61—22no—
28C4⋊C4×C61—21no—
29C4⋊C4×C61—21no—
30C4⋊C4×C61C2×C412yes—
31C4⋊C4×C61C2×C412yes—
32C22⋊C4×C61—22no—
33C42×C61—22no—
34C42×C61C2×C411yescharacteristic
35C42×C61C2×C411yescharacteristic
36C42×C61D411yescharacteristic
37C42×C61D411yescharacteristic
38C4⋊Dic61—24no—
39C4×Dic61—24no—
40#11758194—22no—
41#11758194Q814yescomplemented
42C2×#92418—22no—
43C23×C61C2×D411yescharacteristic
44Q8×C61—42no—
45Q8×C61—42no—
46C2×C4×C61—22no—
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×C61C22×C411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×Q812yes—
57C2×C4×C61#4112yes—
58C2×Dic61—24no—
59C2×Dic61—42no—
60C2×Dic61—42no—
61#92418—24no—
62C22×C61—21no—
63C22×C61—21no—
64C22×C61C2×C22⋊C411yescharacteristic
65C22×C61#12411yescharacteristic
66C22×C61C4⋊Q811yescharacteristic
67C4×C61—21no—
68C4×C61—21no—
69C4×C61—21no—
70C4×C61—42no—
71C4×C61—42no—
72C4×C61#10412yes—
73C4×C61C4×Q812yes—
74C4×C61C22⋊Q812yes—
75Dic61—44no—
76#1986—611nomaximal, Sylow
77C2×C61—21no—
78C2×C61—21no—
79C2×C61#39111yescharacteristic
80C2×C61C2×#10411yescharacteristic
81C2×C61#42111yescharacteristic
82#533D6111yescharacteristic
83C4×M16—611no—
84C4×C4⋊C4—611no—
85#339—614no—
86C61#198611yescharacteristic, complemented, Sylow
87C2×M16—612no—
88C4⋊Q8Dic6111yescharacteristic, complemented
89C4⋊Q8Dic6111yescharacteristic, complemented
90#125Dic6112yescomplemented
91C22⋊Q8—21no—
92C22⋊Q8—21no—
93C4×Q8—21no—
94C4×Q8—21no—
95#117C2×D6112yes—
96C2×C4⋊C4—1221no—
97C2×C42—612no—
98C2×C42C2×D6111yescharacteristic
99#97—1221no—
100C4×C8—1221no—
101#95—1221no—
102C2×Q8—21no—
103C2×Q8—21no—
104C22×C4—1222no—
105C22×C4C22⋊D6111yescharacteristic
106C22×C4C22⋊D6111yescharacteristic
107C22×C4C22×D6111yescharacteristic
108M16—614no—
109M16—1222no—
110C2×C8—1222no—
111C4⋊C4—22no—
112C4⋊C4—22no—
113C4⋊C4—21no—
114C4⋊C4—21no—
115C4⋊C4—1224no—
116C4⋊C4C2×Dic6112yes—
117C4⋊C4C2×Dic6112yes—
118C22⋊C4—22no—
119C42—22no—
120C42—1224no—
121C42C2×Dic6111yescharacteristic
122C42C2×Dic6111yescharacteristic
123C42C22⋊D6111yescharacteristic
124C42C22⋊D6111yescharacteristic
125C23C2×C22⋊D6111yescharacteristic
126Q8—42no—
127Q8—42no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—1224no—
133C2×C4—2442no—
134C2×C4—2442no—
135C2×C4C22⋊Dic6111yescharacteristic
136C2×C4C22⋊Dic6111yescharacteristic
137C2×C4C22⋊Dic6111yescharacteristic
138C2×C4C22⋊Dic6111yescharacteristic
139C2×C4Q8×D6112yes—
140C2×C4#1175822612yes—
141C2×C4C22×Dic6111yescharacteristic
142C2×C4C2×C22⋊D6111yescharacteristic
143C8—1224no—
144C22—21no—
145C22—21no—
146C22C2×C22⋊Dic6111yescharacteristic
147C22#1451976611yescharacteristic
148C22#1451977511yescharacteristic
149C4—21no—
150C4—21no—
151C4—21no—
152C4—42no—
153C4—42no—
154C4—2444no—
155C4#1451970412yes—
156C4Q8×Dic6112yes—
157C4#1451975312yes—
158C2—21no—
159C2—21no—
160C2#1683966911yescharacteristic
161C2C2×#1451970411yescharacteristic
162C2#1683977911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#533C2
socleC22×C61C2×C22⋊C4
hypercenter#533D61
hypocenterC61#1986
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
11. C4⋊Q8×C61C4semidirect
12. C4⋊Q8×C61C4semidirect
13. #125×C61C4semidirect
41. #11758194Q8semidirect
86. C61#1986semidirect
88. C4⋊Q8Dic61semidirect
89. C4⋊Q8Dic61semidirect
90. #125Dic61semidirect