Finite Group Databasebeta

← #21445043

Subgroups — #21445043

Order 7808.

200 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×Dic122C211yesmaximal, characteristic
2#16840113C211yesmaximal, characteristic
3#16840047C211yesmaximal, characteristic
4#16839973C211yesmaximal, characteristic
5#16839510C211yesmaximal, characteristic
6#16839494C211yesmaximal, characteristic
7C61×Q8⋊C8C211yesmaximal, characteristic
8C2×Dic244—21no—
9#14519777—21no—
10#14519777C2211yescharacteristic
11#14519777C2211yescharacteristic
12#14519776—22no—
13#14519776—21no—
14Q8×Dic61—21no—
15C4×Dic122—21no—
16C4×Dic122C2211yescharacteristic
17#14519708—21no—
18C4⋊#92418C2211yescharacteristic
19#14519702—22no—
20#14519702—21no—
21#14519701—21no—
22C4×Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×Q8×C61D411yescharacteristic
26C2×Dic122—21no—
27C2×Dic122—22no—
28C2×Dic122D411yescharacteristic
29C2×Dic122D412yes—
30C2×C8×C61—21no—
31C2×C8×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61D411yescharacteristic
34C42×C61—21no—
35C42×C61C2311yescharacteristic
36C4⋊Dic61—22no—
37C4⋊Dic61—21no—
38C4⋊Dic61—21no—
39C4⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61D411yescharacteristic
42#11758196—22no—
43#11758196—21no—
44C4×Dic61—22no—
45C4×Dic61—21no—
46C2×#92418—21no—
47Dic244—42no—
48Q8×C61—21no—
49Q8×C61Q1612yescomplemented
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C2×Dic61—21no—
56C2×Dic61—22no—
57C2×Dic61—21no—
58C2×Dic61—41no—
59Dic122—21no—
60Dic122—42no—
61Dic122—41no—
62Dic122—41no—
63Dic122—82no—
64Dic122SD1612yes—
65C8×C61—41no—
66C8×C61—41no—
67#92418—41no—
68C22×C61#12011yescharacteristic
69C4×C61—22no—
70C4×C61—21no—
71C4×C61—41no—
72C4×C61C2×SD1611yescharacteristic
73C4×C61C2×Q1611yescharacteristic
74C4×C61#13711yescharacteristic
75C4×C61#13711yescharacteristic
76Dic61—22no—
77Dic61—42no—
78Dic61—41no—
79Dic61—81no—
80#1645—611nomaximal, Sylow
81C2×C61#44811yescharacteristic
82C2×C61#45111yescharacteristic
83C2×C61#45511yescharacteristic
84Q82—611no—
85#487—611no—
86#475—611no—
87#462—611no—
88#333—611no—
89Q8⋊C8—611no—
90Q8⋊C8D6111yescharacteristic
91C61#164511yescharacteristic, complemented, Sylow
92C2×Q16—1221no—
93C4⋊Q8—611no—
94C4⋊Q8—611no—
95C4⋊Q8—1221no—
96C4⋊Q8—1222no—
97C4⋊Q8—1221no—
98C4×Q8—611no—
99C4×Q8—1221no—
100C4×Q8—1221no—
101C4×Q8C2×D6111yescharacteristic
102#106—1221no—
103C4⋊C8—611no—
104C4⋊C8C2×D6111yescharacteristic
105#103—1221no—
106#103—1222no—
107#103—1221no—
108C4×C8C2×D6111yescharacteristic
109C2×Q8—611no—
110C2×Q8—612no—
111C2×Q8—1222no—
112C2×Q8—1221no—
113C2×Q8D24411yescharacteristic
114Q16—2442no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—1221no—
118C4⋊C4—21no—
119C4⋊C4—611no—
120C4⋊C4—1222no—
121C4⋊C4—1222no—
122C4⋊C4—1221no—
123C4⋊C4—1221no—
124C4⋊C4—1221no—
125C4⋊C4—1221no—
126C4⋊C4—1221no—
127C4⋊C4D24411yescharacteristic
128C42—21no—
129C42—1222no—
130C42—1221no—
131C42C22×D6111yescharacteristic
132Q8—21no—
133Q8—612no—
134Q8—1221no—
135Q8—4882no—
136Q8—2442no—
137Q8—2441no—
138Q8—2441no—
139Q8Dic24412yescomplemented
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—1221no—
143C2×C4—1221no—
144C2×C4—1222no—
145C2×C4—2441no—
146C2×C4C2×D24411yescharacteristic
147C2×C4D4×D6111yescharacteristic
148C2×C4D4×D6111yescharacteristic
149C8—41no—
150C8—41no—
151C8—2441no—
152C22#1451974711yescharacteristic
153C4—21no—
154C4—22no—
155C4—41no—
156C4—1222no—
157C4—4881no—
158C4—2441no—
159C4—2442no—
160C4SD16×D6111yescharacteristic
161C4C2×Dic24411yescharacteristic
162C4#1451980911yescharacteristic
163C4#1451981011yescharacteristic
164C2#1683990211yescharacteristic
165C2#1683992011yescharacteristic
166C2#1683994111yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×Q8⋊C8C2
socleC22×C61#120
hypercenterQ8⋊C8D61
hypocenterC61#1645
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
49. Q8×C61Q16semidirect
91. C61#1645semidirect
139. Q8Dic244semidirect