Finite Group Databasebeta

← #21444390

Subgroups — #21444390

Order 7808.

288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#14519756C211yesmaximal, characteristic
2C2×C22⋊#92418C211yesmaximal, characteristic
3#16839498C214yesmaximal, complemented
4C61×#380C211yesmaximal, characteristic
5C22×Dic122C411yescharacteristic, complemented
6C22×#92418—21no—
7#14519756—21no—
8#14519756—21no—
9#14519756C412yescomplemented
10#14519756C2212yes—
11C2×C4⋊Dic61C411yescharacteristic, complemented
12C2×#11758196—21no—
13C2×C22⋊Dic61—21no—
14C22⋊#92418—21no—
15C22⋊#92418C2212yes—
16C23×C4×C61C2211yescharacteristic
17C2×C4⋊C4×C61—21no—
18C2×C22⋊C4×C61—21no—
19#95×C61C2212yes—
20C24×C61D411yescharacteristic
21C22×C4×C61—22no—
22C22×C4×C61—42no—
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61C2×C411yescharacteristic
25C22×C4×C61D411yescharacteristic
26C22×C4×C61D411yescharacteristic
27C22×C4×C61D411yescharacteristic
28C22×C4×C61C2311yescharacteristic
29C22×Dic61—21no—
30C22×Dic61—21no—
31C2×Dic122—21no—
32C2×Dic122—42no—
33C2×Dic122C2×C412yes—
34C4⋊C4×C61—42no—
35C22⋊C4×C61—42no—
36C22⋊Dic61—22no—
37C22⋊Dic61—22no—
38C4⋊Dic61—21no—
39C4⋊Dic61C2×C412yes—
40#11758196—22no—
41#11758196—22no—
42C2×#92418—22no—
43C2×#92418—42no—
44C23×C61—41no—
45C23×C61—41no—
46C23×C61C22⋊C411yescharacteristic
47C23×C61C22⋊C411yescharacteristic
48C23×C61SD1612yes—
49C23×C61Q1612yes—
50C23×C61C2×D411yescharacteristic
51C2×C4×C61—22no—
52C2×C4×C61—22no—
53C2×C4×C61—22no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61—42no—
58C2×C4×C61—42no—
59C2×C4×C61—42no—
60C2×C4×C61C22⋊C411yescharacteristic
61C2×C4×C61C22⋊C411yescharacteristic
62C2×C4×C61C22×C411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×Dic61—22no—
65C2×Dic61—22no—
66C2×Dic61—42no—
67C2×Dic61—42no—
68Dic122—42no—
69Dic122—42no—
70#92418—42no—
71C22×C61—21no—
72C22×C61—21no—
73C22×C61—21no—
74C22×C61—21no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61—42no—
78C22×C61—42no—
79C22×C61#10312yes—
80C22×C61#10312yes—
81C22×C61C2×C22⋊C411yescharacteristic
82C22×C61C2×SD1611yescharacteristic
83C22×C61C2×Q1611yescharacteristic
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—21no—
87C4×C61—82no—
88C4×C61#9912yes—
89Dic61—42no—
90Dic61—42no—
91#1520—611nomaximal, Sylow
92C2×C61—21no—
93C2×C61—22no—
94C2×C61—22no—
95C2×C61—21no—
96C2×C61C2×#9911yescharacteristic
97C2×C61C2×#10311yescharacteristic
98C2×C61#42111yescharacteristic
99C2×C22⋊Q8—611no—
100C2×C22⋊C8—611no—
101#380D6111yescharacteristic
102#328—614no—
103C61#152011yescharacteristic, complemented, Sylow
104C22×Q8—611no—
105C23×C4C2×D6111yescharacteristic
106C22×C8—1221no—
107C22⋊Q8—612no—
108C22⋊Q8—612no—
109C22⋊Q8—1221no—
110C22⋊Q8—1221no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—611no—
113C2×C4⋊C4—1221no—
114C2×C22⋊C4—21no—
115C2×C22⋊C4—1221no—
116C22⋊C8—612no—
117C22⋊C8—1221no—
118#95C2×D6112yes—
119C24C22⋊D6111yescharacteristic
120C2×Q8—612no—
121C2×Q8—1221no—
122C2×Q8—2442no—
123C22×C4—22no—
124C22×C4—42no—
125C22×C4—1221no—
126C22×C4—1221no—
127C22×C4C4×D6111yescharacteristic
128C22×C4C4×D6111yescharacteristic
129C22×C4D24411yescharacteristic
130C22×C4D24411yescharacteristic
131C22×C4C22⋊D6111yescharacteristic
132C22×C4C22×D6111yescharacteristic
133C2×C8—1222no—
134C2×C8—2442no—
135C4⋊C4—42no—
136C4⋊C4—612no—
137C4⋊C4—1221no—
138C4⋊C4—1222no—
139C4⋊C4—1222no—
140C22⋊C4—42no—
141C22⋊C4—1222no—
142C22⋊C4—1222no—
143C23—41no—
144C23—41no—
145C23#1175819811yescharacteristic
146C23#1175819811yescharacteristic
147C23#1175820012yes—
148C23#1175820212yes—
149C23C2×C22⋊D6111yescharacteristic
150Q8—2442no—
151Q8—2442no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—1222no—
162C2×C4—1222no—
163C2×C4—2442no—
164C2×C4—2442no—
165C2×C4#1175819811yescharacteristic
166C2×C4#1175819811yescharacteristic
167C2×C4C2×C4×D6111yescharacteristic
168C2×C4C2×D24411yescharacteristic
169C8—2442no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—42no—
177C22—42no—
178C22#1451970012yes—
179C22#1451970012yes—
180C22C2×#1175819811yescharacteristic
181C22C2×#1175820011yescharacteristic
182C22C2×#1175820211yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—82no—
187C4—2442no—
188C4—2442no—
189C4#1451969112yes—
190C2—21no—
191C2—22no—
192C2—22no—
193C2—21no—
194C2C2×#1451969111yescharacteristic
195C2C2×#1451970011yescharacteristic
196C2#1683978011yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#380C2
socleC22×C61C2×C22⋊C4
hypercenter#380D61
hypocenterC61#1520
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #16839498C2semidirect
5. C22×Dic122C4semidirect
9. #14519756C4semidirect
11. C2×C4⋊Dic61C4semidirect
103. C61#1520semidirect