Finite Group Databasebeta

← #21444259

Subgroups — #21444259

Order 7808.

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

normal subgroups only

This group has 266 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
1C4×#11758222C211yesmaximal, characteristic
2#16839786C211yesmaximal, characteristic, complemented
3#16839494C212yesmaximal, complemented
4#16839491C212yesmaximal, complemented
5C4×M16×C61C211yesmaximal, characteristic, complemented
6C2×#11758222C411yescharacteristic
7C2×#11758194—21no—
8C4×Dic122C411yescharacteristic
9C4×Dic122C2211yescharacteristic
10C4×D244C411yescharacteristic
11C4×D244C2211yescharacteristic
12C4×C22⋊D61—21no—
13C4×C22⋊D61—21no—
14#14519736C411yescharacteristic
15#14519734—21no—
16C42×D61—21no—
17C4⋊#92418—21no—
18C4⋊#92418C2212yes—
19C2×M16×C61—21no—
20C2×C42×C61C2211yescharacteristic
21#97×C61—21no—
22C4×C8×C61C2212yes—
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61D411yescharacteristic
25C22×C4×C61D411yescharacteristic
26C2×C22⋊D61—21no—
27#11758222—22no—
28#11758222—22no—
29C2×D244C2×C411yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61—21no—
32C2×C4×D61—21no—
33C2×Dic122C2×C411yescharacteristic
34M16×C61—24no—
35C2×C8×C61—22no—
36C42×C61C2×C411yescharacteristic
37C42×C61D411yescharacteristic
38C42×C61D411yescharacteristic
39C42×C61C2311yescharacteristic
40C22⋊Dic61—21no—
41#11758198—21no—
42#11758198—21no—
43C4⋊Dic61C2×C411yescharacteristic
44C4⋊Dic61C2×C411yescharacteristic
45#11758196—21no—
46#11758196—21no—
47C4×Dic61—21no—
48C4×Dic61—21no—
49C4×Dic61—21no—
50#11758194—42no—
51C2×#92418—22no—
52C23×C61C22⋊C411yescharacteristic
53C22×D61—21no—
54C2×C4×C61—22no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61C22⋊C411yescharacteristic
60C2×C4×C61C22⋊C411yescharacteristic
61C2×C4×C61C22⋊C411yescharacteristic
62C2×C4×C61C22×C411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C22⋊D61—24no—
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—21no—
69D244—21no—
70D244M1612yescomplemented
71C4×D61—24no—
72C4×D61—42no—
73C4×D61—41no—
74C4×D61—41no—
75Dic122—21no—
76Dic122M1612yescomplemented
77C8×C61—24no—
78#92418—42no—
79C22×C61—21no—
80C22×C61—21no—
81C22×C61—21no—
82C22×C61C2×C22⋊C411yescharacteristic
83C2×D61—22no—
84C2×D61—41no—
85C2×D61—41no—
86C4×C61—21no—
87C4×C61—21no—
88C4×C61—21no—
89C4×C61#10412yes—
90C4×C61C2×M1611yescharacteristic
91C4×C61C2×M1611yescharacteristic
92C4×C61AGL(1,ℤ/8)11yescharacteristic
93C4×C61#13711yescharacteristic
94Dic61—22no—
95Dic61—41no—
96Dic61—41no—
97#1489—611nomaximal, Sylow
98C2×C61—41no—
99C2×C61#40711yescharacteristic
100C2×C61#41711yescharacteristic
101C2×C61C2×#10411yescharacteristic
102D61—42no—
103C4×#41—611no—
104#423—611no—
105C4×M16D6111yescharacteristic, complemented
106Q8⋊C8—612no—
107D4⋊C8—612no—
108C61#148911yescharacteristic, complemented, Sylow
109C2×#41—611no—
110C2×M16—21no—
111C2×M16—1221no—
112C4×Q8—611no—
113C4×Q8—611no—
114C4×D4—611no—
115C4×D4—611no—
116C4×D4—1221no—
117C4×D4—1221no—
118#117—611no—
119#117—1221no—
120C2×C42—1221no—
121C2×C42C2×D6111yescharacteristic
122C4⋊C8—612no—
123C4⋊C8—1221no—
124#97—21no—
125C4×C8C2×D6112yes—
126#41—1222no—
127#41—1222no—
128C2×Q8—611no—
129C2×D4—611no—
130C2×D4—1221no—
131C22×C4—1221no—
132C22×C4—1221no—
133C22×C4—1221no—
134C22×C4C4×D6111yescharacteristic
135C22×C4D24411yescharacteristic
136C22×C4C22⋊D6111yescharacteristic
137M16—24no—
138M16—2442no—
139C2×C8—22no—
140C2×C8—1222no—
141C4⋊C4—611no—
142C4⋊C4—611no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C22⋊C4—1221no—
146C22⋊C4—1221no—
147C22⋊C4—1221no—
148C42—1221no—
149C42—1221no—
150C42—1221no—
151C42C4×D6111yescharacteristic
152C42D24411yescharacteristic
153C42C22⋊D6111yescharacteristic
154C42C22×D6111yescharacteristic
155C23—1221no—
156C23#1175819811yescharacteristic
157Q8—612no—
158Q8—1221no—
159D4—612no—
160D4—1224no—
161D4—1221no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—1224no—
168C2×C4—1221no—
169C2×C4—1221no—
170C2×C4—1221no—
171C2×C4—2441no—
172C2×C4—2442no—
173C2×C4—2441no—
174C2×C4#1175819811yescharacteristic
175C2×C4#1175819811yescharacteristic
176C2×C4#1175819811yescharacteristic
177C2×C4C2×C4×D6111yescharacteristic
178C2×C4C2×D24411yescharacteristic
179C2×C4C2×C22⋊D6111yescharacteristic
180C8—24no—
181C8—2442no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—1222no—
186C22—2441no—
187C22—2441no—
188C22C2×#1175819811yescharacteristic
189C4—21no—
190C4—21no—
191C4—21no—
192C4—1222no—
193C4—2441no—
194C4—2441no—
195C4#1451970512yes—
196C4M16×D6111yescharacteristic
197C4M16×D6111yescharacteristic
198C4#1451980511yescharacteristic
199C4#1451981011yescharacteristic
200C2—41no—
201C2—2442no—
202C2#1683972511yescharacteristic
203C2#1683976411yescharacteristic
204C2C2×#1451970511yescharacteristic
subgroupG/H
centerC2×C4C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC4×M16×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC4×M16D61
hypocenterC61#1489
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #16839786C2semidirect
3. #16839494C2semidirect
4. #16839491C2semidirect
5. C4×M16×C61C2semidirect
70. D244M16semidirect
76. Dic122M16semidirect
105. C4×M16D61semidirect
108. C61#1489semidirect