Finite Group Databasebeta

← #21444342

Subgroups — #21444342

Order 7808.

242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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#16840296C211yesmaximal, characteristic
2#16839819C211yesmaximal, characteristic, complemented
3#16839498C212yesmaximal, complemented
4#16839495C212yesmaximal
5C4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
6#14519771—21no—
7#14519769C411yescharacteristic, complemented
8#14519765C411yescharacteristic, complemented
9#14519760—21no—
10#14519756C2211yescharacteristic
11#14519751C2211yescharacteristic
12C4×Dic122C411yescharacteristic, complemented
13C4×D244C411yescharacteristic, complemented
14C4×C22⋊D61—21no—
15#14519734—21no—
16C4⋊#92418—21no—
17C22⋊#92418C2212yes—
18#14519688—21no—
19C2×C4⋊C4×C61—21no—
20C2×C42×C61—21no—
21C2×C42×C61C2211yescharacteristic
22#95×C61C2212yes—
23C22×C4×C61—22no—
24C22×C4×C61D411yescharacteristic
25C22×C4×C61D411yescharacteristic
26C22×C4×C61C2311yescharacteristic
27C2×C22⋊D61—21no—
28C2×D244C2×C411yescharacteristic
29C2×C4×D61—21no—
30C2×Dic122C2×C411yescharacteristic
31C4⋊C4×C61—24no—
32C42×C61—42no—
33C42×C61C2×C411yescharacteristic
34C42×C61C2×C411yescharacteristic
35C42×C61D411yescharacteristic
36C42×C61D411yescharacteristic
37C22⋊Dic61—21no—
38#11758198—21no—
39#11758198—21no—
40#11758198—21no—
41#11758198—21no—
42C4⋊Dic61C2×C411yescharacteristic
43C4⋊Dic61C2×C411yescharacteristic
44#11758196—21no—
45#11758196—21no—
46#11758196—21no—
47#11758196—21no—
48C4×Dic61—21no—
49C2×#92418—22no—
50C23×C61C2×D411yescharacteristic
51C22×D61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—22no—
55C2×C4×C61—24no—
56C2×C4×C61—41no—
57C2×C4×C61—42no—
58C2×C4×C61—42no—
59C2×C4×C61C22⋊C411yescharacteristic
60C2×C4×C61C22⋊C411yescharacteristic
61C2×C4×C61C22⋊C411yescharacteristic
62C2×C4×C61C22⋊C411yescharacteristic
63C2×C4×C61C22×C411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C22⋊D61—41no—
66C22⋊D61—41no—
67C2×Dic61—21no—
68C2×Dic61—21no—
69C2×Dic61—21no—
70D244—41no—
71C4×D61—42no—
72Dic122—41no—
73#92418—42no—
74C22×C61—21no—
75C22×C61—21no—
76C22×C61C2×C22⋊C411yescharacteristic
77C22×C61AGL(1,ℤ/8)11yescharacteristic
78C22×C61#13711yescharacteristic
79C2×D61—41no—
80C2×D61—41no—
81C2×D61—41no—
82C4×C61—21no—
83C4×C61—21no—
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—21no—
87C4×C61—44no—
88C4×C61#10412yes—
89Dic61—41no—
90Dic61—41no—
91Dic61—41no—
92#1509—611nomaximal, Sylow
93C2×C61—21no—
94C2×C61—21no—
95C2×C61#41011yescharacteristic
96C2×C61#41711yescharacteristic
97C2×C61C2×#10411yescharacteristic
98D61—81no—
99#529—611no—
100#432—611no—
101C4×C4⋊C4D6111yescharacteristic, complemented
102#328—612no—
103#327—612no—
104C61#150911yescharacteristic, complemented, Sylow
105#126—1221no—
106#125—611no—
107#124—611no—
108#123—1221no—
109C22⋊Q8—611no—
110#121—611no—
111C4×Q8—611no—
112C4×D4—611no—
113C4×D4—1221no—
114#117—1221no—
115C2×C4⋊C4—21no—
116C2×C42—21no—
117C2×C42C2×D6111yescharacteristic
118C4⋊C8—1221no—
119C22⋊C8—612no—
120#97—1221no—
121#95C2×D6112yes—
122C2×Q8—611no—
123C2×D4—611no—
124C2×D4—1221no—
125C22×C4—22no—
126C22×C4—1221no—
127C22×C4C22⋊D6111yescharacteristic
128C22×C4C22⋊D6111yescharacteristic
129C22×C4C22×D6111yescharacteristic
130C2×C8—1222no—
131C4⋊C4—24no—
132C4⋊C4—611no—
133C4⋊C4—611no—
134C4⋊C4—1221no—
135C4⋊C4—1221no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C22⋊C4—1221no—
139C22⋊C4—1221no—
140C22⋊C4—1221no—
141C22⋊C4—1221no—
142C22⋊C4—1221no—
143C42—42no—
144C42—1221no—
145C42C4×D6111yescharacteristic
146C42C4×D6111yescharacteristic
147C42D24411yescharacteristic
148C42D24411yescharacteristic
149C23—1221no—
150C23C2×C22⋊D6111yescharacteristic
151Q8—2441no—
152D4—2441no—
153D4—2441no—
154D4—2441no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—1221no—
163C2×C4—1221no—
164C2×C4—1221no—
165C2×C4—2442no—
166C2×C4#1175819811yescharacteristic
167C2×C4#1175819811yescharacteristic
168C2×C4#1175819811yescharacteristic
169C2×C4#1175819811yescharacteristic
170C2×C4C2×C4×D6111yescharacteristic
171C2×C4C2×D24411yescharacteristic
172C8—2442no—
173C22—21no—
174C22—21no—
175C22—2441no—
176C22—2441no—
177C22—2441no—
178C22C2×#1175819811yescharacteristic
179C22#1451980311yescharacteristic
180C22#1451980811yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—44no—
187C4—2441no—
188C4—2441no—
189C4—2441no—
190C4#1451970512yes—
191C2—21no—
192C2—21no—
193C2—4881no—
194C2#1683973511yescharacteristic
195C2#1683976111yescharacteristic
196C2C2×#1451970511yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC4×C4⋊C4×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC4×C4⋊C4D61
hypocenterC61#1509
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #16839819C2semidirect
3. #16839498C2semidirect
5. C4×C4⋊C4×C61C2semidirect
7. #14519769C4semidirect
8. #14519765C4semidirect
12. C4×Dic122C4semidirect
13. C4×D244C4semidirect
101. C4×C4⋊C4D61semidirect
104. C61#1509semidirect