Finite Group Databasebeta

← #21444355

Subgroups — #21444355

Order 7808.

222 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 69 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
5C61×#382C211yesmaximal, 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×C61C2211yescharacteristic
21#95×C61—21no—
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—42no—
32C42×C61C2×C411yescharacteristic
33C42×C61C2×C411yescharacteristic
34C42×C61D411yescharacteristic
35C42×C61D411yescharacteristic
36C22⋊Dic61—21no—
37#11758198—21no—
38#11758198—21no—
39#11758198—21no—
40#11758198—21no—
41C4⋊Dic61C2×C411yescharacteristic
42C4⋊Dic61C2×C411yescharacteristic
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46#11758196—21no—
47C4×Dic61—21no—
48C2×#92418—22no—
49C23×C61C2×D411yescharacteristic
50C22×D61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61—42no—
56C2×C4×C61—42no—
57C2×C4×C61—42no—
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22⋊C411yescharacteristic
60C2×C4×C61C22⋊C411yescharacteristic
61C2×C4×C61C22⋊C411yescharacteristic
62C2×C4×C61C22×C411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C22⋊D61—41no—
65C22⋊D61—41no—
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—21no—
69D244—41no—
70C4×D61—42no—
71Dic122—41no—
72#92418—42no—
73C22×C61—21no—
74C22×C61—21no—
75C22×C61C2×C22⋊C411yescharacteristic
76C22×C61AGL(1,ℤ/8)11yescharacteristic
77C22×C61#13711yescharacteristic
78C2×D61—41no—
79C2×D61—41no—
80C2×D61—41no—
81C4×C61—21no—
82C4×C61—21no—
83C4×C61—21no—
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—21no—
87C4×C61—82no—
88Dic61—41no—
89Dic61—41no—
90Dic61—41no—
91#1512—611nomaximal, Sylow
92C2×C61—21no—
93C2×C61—21no—
94C2×C61#41011yescharacteristic
95C2×C61#41711yescharacteristic
96C2×C61#42111yescharacteristic
97D61—81no—
98#529—611no—
99#432—611no—
100#382D6111yescharacteristic, complemented
101#328—612no—
102#327—612no—
103C61#151211yescharacteristic, complemented, Sylow
104#126—1221no—
105#125—611no—
106#124—611no—
107#123—1221no—
108C22⋊Q8—611no—
109#121—611no—
110C4×Q8—611no—
111C4×D4—611no—
112C4×D4—1221no—
113#117—1221no—
114C2×C4⋊C4—21no—
115C2×C42C2×D6111yescharacteristic
116C4⋊C8—1221no—
117C22⋊C8—612no—
118#97—1221no—
119#95—21no—
120#95C2×D6112yes—
121C2×Q8—611no—
122C2×D4—611no—
123C2×D4—1221no—
124C22×C4—22no—
125C22×C4—1221no—
126C22×C4C22⋊D6111yescharacteristic
127C22×C4C22⋊D6111yescharacteristic
128C22×C4C22×D6111yescharacteristic
129C2×C8—1222no—
130C4⋊C4—42no—
131C4⋊C4—611no—
132C4⋊C4—611no—
133C4⋊C4—1221no—
134C4⋊C4—1221no—
135C4⋊C4—1221no—
136C4⋊C4—1221no—
137C22⋊C4—1221no—
138C22⋊C4—1221no—
139C22⋊C4—1221no—
140C22⋊C4—1221no—
141C22⋊C4—1221no—
142C42—1221no—
143C42C4×D6111yescharacteristic
144C42C4×D6111yescharacteristic
145C42D24411yescharacteristic
146C42D24411yescharacteristic
147C23—1221no—
148C23C2×C22⋊D6111yescharacteristic
149Q8—2441no—
150D4—2441no—
151D4—2441no—
152D4—2441no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—1221no—
161C2×C4—1221no—
162C2×C4—1221no—
163C2×C4—2442no—
164C2×C4#1175819811yescharacteristic
165C2×C4#1175819811yescharacteristic
166C2×C4#1175819811yescharacteristic
167C2×C4#1175819811yescharacteristic
168C2×C4C2×C4×D6111yescharacteristic
169C2×C4C2×D24411yescharacteristic
170C8—2442no—
171C22—21no—
172C22—21no—
173C22—2441no—
174C22—2441no—
175C22—2441no—
176C22C2×#1175819811yescharacteristic
177C22#1451980311yescharacteristic
178C22#1451980811yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—82no—
186C4—2441no—
187C4—2441no—
188C4—2441no—
189C2—21no—
190C2—21no—
191C2—4881no—
192C2#1683973511yescharacteristic
193C2#1683976111yescharacteristic
194C2#1683978011yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#382C2
socleC22×C61C2×C22⋊C4
hypercenter#382D61
hypocenterC61#1512
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #16839819C2semidirect
3. #16839498C2semidirect
5. C61×#382C2semidirect
7. #14519769C4semidirect
8. #14519765C4semidirect
12. C4×Dic122C4semidirect
13. C4×D244C4semidirect
100. #382D61semidirect
103. C61#1512semidirect