Finite Group Databasebeta

← #21444179

Subgroups — #21444179

Order 7808.

322 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 85 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#16839726C211yesmaximal, characteristic, complemented
2C2×C22⋊#92418C211yesmaximal, characteristic, complemented
3#16839486C214yesmaximal, complemented
4C2×#121×C61C211yesmaximal, characteristic
5C2×#11758194—21no—
6C22×#92418—21no—
7C22⋊#92418—21no—
8C22⋊#92418—21no—
9C22⋊#92418C2212yes—
10C22⋊#92418C2212yes—
11C22×D4×C61C411yescharacteristic
12C22×D4×C61C412yes—
13C23×C4×C61C2211yescharacteristic
14#121×C61—21no—
15#121×C61—21no—
16#121×C61—21no—
17#121×C61—21no—
18C2×C4⋊C4×C61C411yescharacteristic
19C2×C22⋊C4×C61C2212yes—
20C24×C61C2×C411yescharacteristic
21C24×C61C2×C412yes—
22C2×D4×C61—22no—
23C2×D4×C61—22no—
24C2×D4×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—42no—
27C2×D4×C61—44no—
28C22×C4×C61—42no—
29C22×C4×C61C2×C411yescharacteristic
30C22×C4×C61C2×C412yes—
31C22×C4×C61D411yescharacteristic
32C22×C4×C61D411yescharacteristic
33C22×C4×C61D411yescharacteristic
34C22×C4×C61D411yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C22⋊C4×C61—22no—
39C22⋊C4×C61—22no—
40#11758194—42no—
41C2×#92418—22no—
42C2×#92418—22no—
43C2×#92418—42no—
44C23×C61—22no—
45C23×C61—22no—
46C23×C61—22no—
47C23×C61—24no—
48C23×C61—41no—
49C23×C61—42no—
50C23×C61—42no—
51C23×C61C22⋊C411yescharacteristic
52C23×C61C22⋊C411yescharacteristic
53C23×C61C22×C411yescharacteristic
54D4×C61—42no—
55D4×C61—44no—
56D4×C61—44no—
57D4×C61—42no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—42no—
66C2×C4×C61C22⋊C411yescharacteristic
67C2×C4×C61C22⋊C411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70#92418—42no—
71#92418—42no—
72C22×C61—21no—
73C22×C61—21no—
74C22×C61—21no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61—21no—
78C22×C61—21no—
79C22×C61—44no—
80C22×C61—42no—
81C22×C61—42no—
82C22×C61—42no—
83C22×C61—84no—
84C22×C61#10012yes—
85C22×C61C2×C22⋊C411yescharacteristic
86C22×C61#13112yes—
87C4×C61—21no—
88C4×C61—21no—
89C4×C61—21no—
90C4×C61—42no—
91C4×C61#9912yes—
92#1471—611nomaximal, Sylow
93C2×C61—22no—
94C2×C61—22no—
95C2×C61—41no—
96C2×C61—82no—
97C2×C61#40811yescharacteristic
98C2×C61C2×#9911yescharacteristic
99C2×C61C2×#10011yescharacteristic
100C2×#121D6111yescharacteristic
101#407—611no—
102C2×C22⋊C8—611no—
103#323—614no—
104C61#147111yescharacteristic, complemented, Sylow
105C22×D4Dic6111yescharacteristic
106C22×D4Dic6112yes—
107C23×C4C2×D6111yescharacteristic
108C2×M16—1221no—
109C22×C8—1221no—
110#121—21no—
111#121—21no—
112#121—21no—
113#121—21no—
114C2×C4⋊C4Dic6111yescharacteristic
115C2×C22⋊C4C2×D6112yes—
116C22⋊C8—612no—
117C22⋊C8—612no—
118C22⋊C8—1221no—
119C22⋊C8—1221no—
120C24C2×Dic6111yescharacteristic
121C24C2×Dic6112yes—
122C2×D4—22no—
123C2×D4—22no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—42no—
127C2×D4—44no—
128C22×C4—42no—
129C22×C4C2×Dic6111yescharacteristic
130C22×C4C2×Dic6112yes—
131C22×C4C22⋊D6111yescharacteristic
132C22×C4C22⋊D6111yescharacteristic
133C22×C4C22⋊D6111yescharacteristic
134C22×C4C22⋊D6111yescharacteristic
135C22×C4C22×D6111yescharacteristic
136M16—2442no—
137C2×C8—1222no—
138C2×C8—1222no—
139C2×C8—2442no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C23—22no—
145C23—22no—
146C23—22no—
147C23—24no—
148C23—41no—
149C23—42no—
150C23—42no—
151C23C22⋊Dic6111yescharacteristic
152C23C22⋊Dic6111yescharacteristic
153C23C22×Dic6111yescharacteristic
154D4—42no—
155D4—44no—
156D4—44no—
157D4—42no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4C22⋊Dic6111yescharacteristic
167C2×C4C22⋊Dic6111yescharacteristic
168C2×C4C2×C22⋊D6111yescharacteristic
169C2×C4C2×C22⋊D6111yescharacteristic
170C8—2442no—
171C8—2442no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—21no—
179C22—44no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—84no—
184C22#1451969412yes—
185C22C2×C22⋊Dic6111yescharacteristic
186C22#1451978412yes—
187C4—21no—
188C4—21no—
189C4—21no—
190C4—42no—
191C4#1451969212yes—
192C2—22no—
193C2—22no—
194C2—41no—
195C2—82no—
196C2#1683972911yescharacteristic
197C2C2×#1451969211yescharacteristic
198C2C2×#1451969411yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic61
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#121×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×#121D61
hypocenterC61#1471
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #16839726C2semidirect
2. C2×C22⋊#92418C2semidirect
3. #16839486C2semidirect
104. C61#1471semidirect