Finite Group Databasebeta

← #21444167

Subgroups — #21444167

Order 7808.

280 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 81 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#16839488C212yesmaximal, complemented
4#16839486C212yesmaximal, complemented
5C2×#123×C61C211yesmaximal, characteristic
6C2×#11758194—21no—
7C22×#92418—21no—
8C22⋊#92418—21no—
9C22⋊#92418—21no—
10C22⋊#92418C2212yes—
11C22⋊#92418C2212yes—
12C22×D4×C61C411yescharacteristic
13C23×C4×C61C2211yescharacteristic
14#123×C61—21no—
15#123×C61—21no—
16#123×C61—21no—
17#123×C61—21no—
18C2×C4⋊C4×C61C411yescharacteristic
19C2×C4⋊C4×C61C2211yescharacteristic
20C2×C22⋊C4×C61C411yescharacteristic
21C2×C22⋊C4×C61C411yescharacteristic
22C2×C22⋊C4×C61C2211yescharacteristic
23C24×C61C2×C411yescharacteristic
24C24×C61C2×C411yescharacteristic
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—42no—
28C22×C4×C61—42no—
29C22×C4×C61C2×C411yescharacteristic
30C22×C4×C61C2×C411yescharacteristic
31C22×C4×C61C2×C411yescharacteristic
32C22×C4×C61C2×C411yescharacteristic
33C22×C4×C61D411yescharacteristic
34C22×C4×C61D411yescharacteristic
35C22×C4×C61D411yescharacteristic
36C22×C4×C61D411yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C4⋊C4×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—21no—
42C22⋊C4×C61—21no—
43C22⋊C4×C61—21no—
44C22⋊C4×C61—21no—
45C22⋊C4×C61—21no—
46C22⋊C4×C61—21no—
47C22⋊C4×C61—21no—
48#11758194—42no—
49C2×#92418—22no—
50C2×#92418—22no—
51C2×#92418—42no—
52C23×C61—22no—
53C23×C61—22no—
54C23×C61—21no—
55C23×C61—22no—
56C23×C61—41no—
57C23×C61—41no—
58C23×C61—41no—
59C23×C61C22⋊C411yescharacteristic
60C23×C61C22⋊C411yescharacteristic
61C23×C61C22×C411yescharacteristic
62D4×C61—42no—
63D4×C61—42no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—22no—
70C2×C4×C61—41no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61C22⋊C411yescharacteristic
77C2×C4×C61C22⋊C411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80#92418—42no—
81#92418—42no—
82C22×C61—21no—
83C22×C61—21no—
84C22×C61—21no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61—21no—
88C22×C61—21no—
89C22×C61—44no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61—82no—
94C22×C61#9912yes—
95C22×C61C2×C22⋊C411yescharacteristic
96C22×C61#13112yes—
97C4×C61—21no—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—21no—
101C4×C61—41no—
102C4×C61—41no—
103C4×C61—41no—
104#1468—611nomaximal, Sylow
105C2×C61—22no—
106C2×C61—22no—
107C2×C61—41no—
108C2×C61—81no—
109C2×C61#40811yescharacteristic
110C2×C61C2×#9911yescharacteristic
111C2×C61#41311yescharacteristic
112C2×#123D6111yescharacteristic
113#407—611no—
114C2×C22⋊C8—611no—
115#324—612no—
116#323—612no—
117C61#146811yescharacteristic, complemented, Sylow
118C22×D4Dic6111yescharacteristic
119C23×C4C2×D6111yescharacteristic
120C2×M16—1221no—
121C22×C8—1221no—
122#123—21no—
123#123—21no—
124#123—21no—
125#123—21no—
126C2×C4⋊C4Dic6111yescharacteristic
127C2×C4⋊C4C2×D6111yescharacteristic
128C2×C22⋊C4Dic6111yescharacteristic
129C2×C22⋊C4Dic6111yescharacteristic
130C2×C22⋊C4C2×D6111yescharacteristic
131C22⋊C8—612no—
132C22⋊C8—612no—
133C22⋊C8—1221no—
134C22⋊C8—1221no—
135C24C2×Dic6111yescharacteristic
136C24C2×Dic6111yescharacteristic
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—42no—
140C22×C4—42no—
141C22×C4C2×Dic6111yescharacteristic
142C22×C4C2×Dic6111yescharacteristic
143C22×C4C2×Dic6111yescharacteristic
144C22×C4C2×Dic6111yescharacteristic
145C22×C4C22⋊D6111yescharacteristic
146C22×C4C22⋊D6111yescharacteristic
147C22×C4C22⋊D6111yescharacteristic
148C22×C4C22⋊D6111yescharacteristic
149C22×C4C22×D6111yescharacteristic
150M16—2442no—
151C2×C8—1222no—
152C2×C8—1222no—
153C2×C8—2442no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C23—22no—
165C23—22no—
166C23—21no—
167C23—22no—
168C23—41no—
169C23—41no—
170C23—41no—
171C23C22⋊Dic6111yescharacteristic
172C23C22⋊Dic6111yescharacteristic
173C23C22×Dic6111yescharacteristic
174D4—42no—
175D4—42no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4C22⋊Dic6111yescharacteristic
189C2×C4C22⋊Dic6111yescharacteristic
190C2×C4C2×C22⋊D6111yescharacteristic
191C2×C4C2×C22⋊D6111yescharacteristic
192C8—2442no—
193C8—2442no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—82no—
206C22#1451969212yes—
207C22C2×C22⋊Dic6111yescharacteristic
208C22#1451978412yes—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—41no—
214C4—41no—
215C4—41no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—81no—
220C2#1683972911yescharacteristic
221C2C2×#1451969211yescharacteristic
222C2#1683974611yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic61
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#123×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×#123D61
hypocenterC61#1468
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #16839726C2semidirect
2. C2×C22⋊#92418C2semidirect
3. #16839488C2semidirect
4. #16839486C2semidirect
117. C61#1468semidirect