Finite Group Databasebeta

← #21447878

Subgroups — #21447878

Order 7808.

158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 51 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×#14519723C211yesmaximal, characteristic, complemented
2C2×#14519721C211yesmaximal, characteristic
3C4×Dic244C211yesmaximal, characteristic, complemented
4C4⋊#11758185C211yesmaximal, characteristic, complemented
5#16839566C211yesmaximal, characteristic, complemented
6#16839563C211yesmaximal, characteristic
7C61×#495C211yesmaximal, characteristic
8C2×Dic244C2211yescharacteristic
9C4×Dic122—21no—
10#14519723—22no—
11#14519721—22no—
12C2×#11758185C2211yescharacteristic
13C2×#11758185C2211yescharacteristic
14#14519711C2211yescharacteristic
15#14519702—21no—
16C2×Q16×C61C2211yescharacteristic
17C2×SD16×C61—21no—
18C2×D8×C61C2211yescharacteristic
19#124×C61—21no—
20C4×C8×C61C2211yescharacteristic
21C2×Q8×C61—21no—
22C2×D4×C61—21no—
23C2×Dic122—21no—
24Q16×C61—21no—
25Q16×C61—21no—
26SD16×C61—42no—
27D8×C61—21no—
28D8×C61—21no—
29C2×C8×C61D411yescharacteristic
30C2×C8×C61C2311yescharacteristic
31C22⋊C4×C61—41no—
32C22⋊C4×C61—41no—
33C42×C61D411yescharacteristic
34C4⋊Dic61—21no—
35#11758196—41no—
36C4×Dic61—41no—
37Dic244—21no—
38Dic244D412yes—
39#11758185—21no—
40#11758185—21no—
41C23×C61—41no—
42Q8×C61—41no—
43Q8×C61—41no—
44D4×C61—41no—
45D4×C61—41no—
46C2×C4×C61—41no—
47C2×C4×C61D811yescharacteristic
48C2×C4×C61D811yescharacteristic
49C2×C4×C61C2×D411yescharacteristic
50C2×Dic61—41no—
51C2×Dic61—41no—
52Dic122—22no—
53Dic122—41no—
54C8×C61—21no—
55C8×C61C2×D411yescharacteristic
56C8×C61#4111yescharacteristic
57C22×C61—81no—
58C22×C61—81no—
59C22×C61—81no—
60C22×C61C2×D811yescharacteristic
61C4×C61—21no—
62C4×C61—21no—
63C4×C61—81no—
64C4×C61#12111yescharacteristic
65C4×C61AGL(1,ℤ/8)11yescharacteristic
66Dic61—42no—
67Dic61—81no—
68#2211—611nomaximal, Sylow
69C2×C61—161no—
70C2×C61#45911yescharacteristic
71C2×C61#50811yescharacteristic
72C2×C61#51011yescharacteristic
73C2×Q32—611no—
74C2×SD32—611no—
75#495D6111yescharacteristic
76C4×Q16—611no—
77C4⋊C16—611no—
78#358—611no—
79#357—611no—
80C61#221111yescharacteristic, complemented, Sylow
81C2×Q16—611no—
82C2×Q16C2×D6111yescharacteristic
83C2×SD16—21no—
84C2×D8C2×D6111yescharacteristic
85#124—21no—
86C4×Q8—1221no—
87Q32—1222no—
88SD32—1222no—
89C2×C16—611no—
90C2×C16—611no—
91#107—611no—
92#103—1221no—
93C4×C8C2×D6111yescharacteristic
94C2×Q8—21no—
95C2×Q8—1221no—
96C2×D4—21no—
97Q16—21no—
98Q16—21no—
99Q16—612no—
100Q16—1221no—
101SD16—42no—
102D8—21no—
103D8—21no—
104C2×C8C22⋊D6111yescharacteristic
105C2×C8C22×D6111yescharacteristic
106C4⋊C4—1221no—
107C4⋊C4—2441no—
108C22⋊C4—41no—
109C22⋊C4—41no—
110C42—2441no—
111C42C22⋊D6111yescharacteristic
112C16—1221no—
113C16—1221no—
114C23—41no—
115Q8—41no—
116Q8—41no—
117Q8—1222no—
118Q8—2441no—
119D4—41no—
120D4—41no—
121C2×C4—41no—
122C2×C4—2441no—
123C2×C4—2441no—
124C2×C4#1175819911yescharacteristic
125C2×C4#1175819911yescharacteristic
126C2×C4C2×C22⋊D6111yescharacteristic
127C8—21no—
128C8D4×D6111yescharacteristic
129C8#1175822411yescharacteristic
130C22—81no—
131C22—81no—
132C22—81no—
133C22C2×#1175819911yescharacteristic
134C4—21no—
135C4—21no—
136C4—81no—
137C4—4881no—
138C4—2442no—
139C4#1451974811yescharacteristic
140C4#1451980311yescharacteristic
141C2—161no—
142C2#1683995411yescharacteristic
143C2#1684019211yescharacteristic
144C2#1684020211yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#495C2
socleC22×C61C2×D8
hypercenter#495D61
hypocenterC61#2211
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#14519723C2semidirect
3. C4×Dic244C2semidirect
4. C4⋊#11758185C2semidirect
5. #16839566C2semidirect
80. C61#2211semidirect