Finite Group Databasebeta

← #21446763

Subgroups — #21446763

Order 7808.

260 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 97 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
2C4×C4⋊Dic61C211yesmaximal, characteristic
3#16839523C214yesmaximal
4C4×M16×C61C211yesmaximal, characteristic
5#14519777C411yescharacteristic, complemented
6#14519777C411yescharacteristic, complemented
7#14519769C412yescomplemented
8#14519756—21no—
9#14519756—21no—
10C4×Dic122—21no—
11C4×Dic122—21no—
12#14519736C2212yes—
13C2×C4⋊Dic61—21no—
14C2×C4×Dic61C2212yes—
15#14519684—21no—
16C2×M16×C61C2212yes—
17C2×C42×C61C2211yescharacteristic
18#97×C61—21no—
19C4×C8×C61—21no—
20C22×C4×C61D411yescharacteristic
21C22×C4×C61D411yescharacteristic
22C22×C4×C61C2311yescharacteristic
23C22×Dic61—22no—
24C2×Dic122—21no—
25C2×Dic122—21no—
26M16×C61—22no—
27M16×C61Q814yescomplemented
28C2×C8×C61—22no—
29C42×C61C2×C411yescharacteristic
30C42×C61C2×C411yescharacteristic
31C42×C61D411yescharacteristic
32C42×C61D411yescharacteristic
33C22⋊Dic61—22no—
34C4⋊Dic61—24no—
35C4⋊Dic61—21no—
36C4⋊Dic61—21no—
37C4⋊Dic61C2×C412yes—
38C4⋊Dic61C2×C412yes—
39#11758196—22no—
40#11758196—22no—
41C4×Dic61—22no—
42C4×Dic61—24no—
43C23×C61C2×D411yescharacteristic
44C2×C4×C61—22no—
45C2×C4×C61—41no—
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61C22⋊C411yescharacteristic
50C2×C4×C61C22×C411yescharacteristic
51C2×C4×C61C2×D411yescharacteristic
52C2×C4×C61C2×Q812yes—
53C2×C4×C61#4112yes—
54C2×Dic61—24no—
55C2×Dic61—22no—
56C2×Dic61—22no—
57C2×Dic61—42no—
58C2×Dic61—42no—
59Dic122—42no—
60Dic122—42no—
61C8×C61—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#10412yes—
71C4×C61C4×Q812yes—
72C4×C61C22⋊Q812yes—
73Dic61—44no—
74Dic61—42no—
75Dic61—42no—
76#1986—611nomaximal, Sylow
77C2×C61—21no—
78C2×C61—21no—
79C2×C61#39111yescharacteristic
80C2×C61C2×#10411yescharacteristic
81C2×C61#42111yescharacteristic
82#533—611no—
83C4×M16D6111yescharacteristic
84C4×C4⋊C4—611no—
85#339—614no—
86C61#198611yescharacteristic, complemented, Sylow
87C2×M16C2×D6112yes—
88C4⋊Q8—611no—
89C4⋊Q8—611no—
90#125—612no—
91C22⋊Q8—1221no—
92C22⋊Q8—1221no—
93C4×Q8—1221no—
94C4×Q8—1221no—
95#117—612no—
96C2×C4⋊C4—1221no—
97C2×C42—612no—
98C2×C42C2×D6111yescharacteristic
99#97—21no—
100C4×C8—21no—
101#95—1221no—
102C2×Q8—1221no—
103C2×Q8—1221no—
104C22×C4—1222no—
105C22×C4D24411yescharacteristic
106C22×C4D24411yescharacteristic
107C22×C4C22×D6111yescharacteristic
108M16—22no—
109M16Dic12214yescomplemented
110C2×C8—22no—
111C4⋊C4—612no—
112C4⋊C4—612no—
113C4⋊C4—1224no—
114C4⋊C4—1222no—
115C4⋊C4—1222no—
116C4⋊C4—1221no—
117C4⋊C4—1221no—
118C22⋊C4—1222no—
119C42—1222no—
120C42—1224no—
121C42C4×D6111yescharacteristic
122C42C4×D6111yescharacteristic
123C42C22⋊D6111yescharacteristic
124C42C22⋊D6111yescharacteristic
125C23C2×D24411yescharacteristic
126Q8—2442no—
127Q8—2442no—
128C2×C4—22no—
129C2×C4—41no—
130C2×C4—1224no—
131C2×C4—1222no—
132C2×C4—1222no—
133C2×C4—2442no—
134C2×C4—2442no—
135C2×C4#1175819811yescharacteristic
136C2×C4#1175819811yescharacteristic
137C2×C4#1175819811yescharacteristic
138C2×C4#1175819811yescharacteristic
139C2×C4C2×Dic12212yes—
140C2×C4C2×C4×D6111yescharacteristic
141C2×C4#1175822212yes—
142C2×C4C2×C22⋊D6111yescharacteristic
143C8—24no—
144C22—21no—
145C22—21no—
146C22C2×#1175819811yescharacteristic
147C22#1451976511yescharacteristic
148C22#1451977711yescharacteristic
149C4—21no—
150C4—21no—
151C4—21no—
152C4—2444no—
153C4—2442no—
154C4—2442no—
155C4#1451970312yes—
156C4C4×Dic12212yes—
157C4#1451975612yes—
158C2—21no—
159C2—21no—
160C2#1683966811yescharacteristic
161C2C2×#1451970311yescharacteristic
162C2#1683977811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC4×M16×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC4×M16D61
hypocenterC61#1986
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
5. #14519777C4semidirect
6. #14519777C4semidirect
7. #14519769C4semidirect
27. M16×C61Q8semidirect
86. C61#1986semidirect
109. M16Dic122semidirect