Finite Group Databasebeta

← #21444151

Subgroups — #21444151

Order 7808.

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

normal subgroups only

This group has 252 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
1C2×#14519734C211yesmaximal, characteristic
2#16839819C211yesmaximal, characteristic, complemented
3#16839487C212yesmaximal, complemented
4#16839485C212yesmaximal
5C61×#432C211yesmaximal, characteristic, complemented
6C22×C4×D61C411yescharacteristic
7#14519734—21no—
8#14519734—21no—
9#14519734—21no—
10#14519734—21no—
11C2×#11758196C411yescharacteristic
12C2×#11758196C2211yescharacteristic
13C2×#11758198C411yescharacteristic
14C2×#11758198C2211yescharacteristic
15C2×C4×Dic61C411yescharacteristic
16C4⋊#92418—21no—
17C22⋊#92418C2212yes—
18#14519688—21no—
19C2×C42×C61C2211yescharacteristic
20C4⋊C8×C61—21no—
21C22⋊C8×C61C2212yes—
22#97×C61—21no—
23C23×D61C2×C411yescharacteristic
24C22×C4×C61C2×C411yescharacteristic
25C22×C4×C61C2×C411yescharacteristic
26C22×C4×C61C2311yescharacteristic
27C22×Dic61C2×C411yescharacteristic
28C22×Dic61C2×C411yescharacteristic
29C22×Dic61C2×C411yescharacteristic
30C2×C4×D61—22no—
31C2×C4×D61—21no—
32C2×C4×D61—21no—
33C2×C4×D61—22no—
34C2×C8×C61—22no—
35C42×C61D411yescharacteristic
36C42×C61D411yescharacteristic
37C42×C61D411yescharacteristic
38C42×C61D411yescharacteristic
39#11758198—21no—
40#11758198—21no—
41#11758198—21no—
42#11758198—21no—
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46#11758196—21no—
47C4×Dic61—21no—
48C4×Dic61—21no—
49C2×#92418—22no—
50C23×C61C22×C411yescharacteristic
51C22×D61—21no—
52C22×D61—21no—
53C22×D61—41no—
54C22×D61—41no—
55C22×D61M1612yes—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—41no—
59C2×C4×C61—41no—
60C2×C4×C61C22⋊C411yescharacteristic
61C2×C4×C61C22⋊C411yescharacteristic
62C2×C4×C61C22⋊C411yescharacteristic
63C2×C4×C61C22⋊C411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—21no—
69C2×Dic61—21no—
70C2×Dic61—41no—
71C2×Dic61—41no—
72C2×Dic61M1612yes—
73C4×D61—24no—
74C4×D61—24no—
75C8×C61—42no—
76#92418—42no—
77C22×C61—21no—
78C22×C61—21no—
79C22×C61C2×C22⋊C411yescharacteristic
80C22×C61C2×M1611yescharacteristic
81C22×C61C2×M1611yescharacteristic
82C2×D61—22no—
83C2×D61—42no—
84C2×D61—41no—
85C2×D61—41no—
86C2×D61—42no—
87C4×C61—21no—
88C4×C61—21no—
89C4×C61—21no—
90C4×C61—21no—
91C4×C61—21no—
92C4×C61—21no—
93Dic61—22no—
94Dic61—41no—
95Dic61—41no—
96#1464—611nomaximal, Sylow
97C2×C61—21no—
98C2×C61—21no—
99C2×C61#40711yescharacteristic
100C2×C61#41011yescharacteristic
101C2×C61#41311yescharacteristic
102D61—42no—
103C2×#117—611no—
104#432—611no—
105#432D6111yescharacteristic, complemented
106#324—612no—
107#323—612no—
108C61#146411yescharacteristic, complemented, Sylow
109C23×C4—611no—
110#117—1221no—
111#117—1221no—
112#117—1221no—
113#117—1221no—
114C2×C4⋊C4—611no—
115C2×C4⋊C4—611no—
116C2×C22⋊C4—611no—
117C2×C22⋊C4—611no—
118C2×C42—611no—
119C2×C42C2×D6111yescharacteristic
120C4⋊C8—21no—
121C4⋊C8—1221no—
122C22⋊C8—612no—
123C22⋊C8C2×D6112yes—
124#97—21no—
125#97—1221no—
126C24—611no—
127C22×C4—611no—
128C22×C4—611no—
129C22×C4—611no—
130C22×C4—1222no—
131C22×C4—1222no—
132C22×C4—1221no—
133C22×C4—1221no—
134C22×C4C4×D6111yescharacteristic
135C22×C4C4×D6111yescharacteristic
136C22×C4C22×D6111yescharacteristic
137C2×C8—22no—
138C2×C8—1222no—
139C4⋊C4—1221no—
140C4⋊C4—1221no—
141C4⋊C4—1221no—
142C4⋊C4—1221no—
143C22⋊C4—1221no—
144C22⋊C4—1221no—
145C22⋊C4—1221no—
146C22⋊C4—1221no—
147C42—1221no—
148C42—1221no—
149C42D24411yescharacteristic
150C42D24411yescharacteristic
151C42C22⋊D6111yescharacteristic
152C42C22⋊D6111yescharacteristic
153C23—612no—
154C23—1221no—
155C23—1221no—
156C23—2441no—
157C23—2441no—
158C23C2×C4×D6111yescharacteristic
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—612no—
164C2×C4—1224no—
165C2×C4—1224no—
166C2×C4—1221no—
167C2×C4—1221no—
168C2×C4—1221no—
169C2×C4—1221no—
170C2×C4—2441no—
171C2×C4—2441no—
172C2×C4#1175819811yescharacteristic
173C2×C4#1175819811yescharacteristic
174C2×C4#1175819811yescharacteristic
175C2×C4#1175819811yescharacteristic
176C2×C4C2×D24411yescharacteristic
177C2×C4C2×C22⋊D6111yescharacteristic
178C8—42no—
179C8—2442no—
180C22—21no—
181C22—21no—
182C22—1222no—
183C22—2442no—
184C22—2442no—
185C22—2441no—
186C22—2441no—
187C22C2×#1175819811yescharacteristic
188C22M16×D6111yescharacteristic
189C22M16×D6111yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—21no—
196C4—1222no—
197C4—2441no—
198C4—2441no—
199C2—21no—
200C2—21no—
201C2—2442no—
202C2#1683972511yescharacteristic
203C2#1683973511yescharacteristic
204C2#1683974411yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#432C2
socleC22×C61C2×C22⋊C4
hypercenter#432D61
hypocenterC61#1464
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #16839819C2semidirect
3. #16839487C2semidirect
5. C61×#432C2semidirect
105. #432D61semidirect
108. C61#1464semidirect