Finite Group Databasebeta

← #21444255

Subgroups — #21444255

Order 7808.

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

normal subgroups only

This group has 266 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
1C4×#11758224C211yesmaximal, characteristic
2#16839784C211yesmaximal, characteristic, complemented
3C4×#11758189C211yesmaximal, characteristic, complemented
4#16839494C211yesmaximal, characteristic, complemented
5#16839492C211yesmaximal, characteristic, complemented
6D4⋊#92418C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758224C411yescharacteristic
9C2×#11758189—21no—
10C2×#11758189—21no—
11C4×Dic122C2211yescharacteristic
12#14519742C411yescharacteristic
13D4×Dic61C411yescharacteristic
14C4×C22⋊D61—21no—
15#14519737—21no—
16#14519735C411yescharacteristic
17#14519733—21no—
18C2×C4×Dic61—21no—
19C42×D61C2211yescharacteristic
20C4⋊#92418C2211yescharacteristic
21#14519706—21no—
22#14519687—21no—
23C4×#92418C2211yescharacteristic
24C4×D4×C61C2211yescharacteristic
25C4⋊C8×C61C2211yescharacteristic
26C4×C8×C61C2211yescharacteristic
27C2×D4×C61C2×C411yescharacteristic
28C22×C4×C61—21no—
29C2×C22⋊D61—21no—
30C22×Dic61—21no—
31C22×Dic61—21no—
32#11758224—22no—
33#11758224—22no—
34C2×C4×D61C2×C411yescharacteristic
35C2×C4×D61D411yescharacteristic
36C2×C4×D61D411yescharacteristic
37C2×Dic122C2×C411yescharacteristic
38C2×C8×C61—21no—
39C2×C8×C61—21no—
40C4⋊C4×C61C2×C411yescharacteristic
41C22⋊C4×C61—21no—
42C42×C61C2311yescharacteristic
43C22⋊Dic61—21no—
44#11758198—21no—
45C4⋊Dic61C2×C411yescharacteristic
46#11758196—21no—
47#11758196—21no—
48C4×Dic61—21no—
49C4×Dic61—21no—
50C4×Dic61—21no—
51C4×Dic61C2×C411yescharacteristic
52C4×Dic61D411yescharacteristic
53C4×Dic61D411yescharacteristic
54C2×#92418—21no—
55C2×#92418—21no—
56#11758189—24no—
57#11758189—42no—
58C23×C61—21no—
59C22×D61C22⋊C411yescharacteristic
60D4×C61—21no—
61D4×C61M1612yescomplemented
62C2×C4×C61—21no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61C22×C411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C22⋊D61—24no—
69C2×Dic61—24no—
70C2×Dic61—21no—
71C2×Dic61—21no—
72C2×Dic61—42no—
73C2×Dic61C22⋊C411yescharacteristic
74C2×Dic61C22⋊C411yescharacteristic
75C2×Dic61C22⋊C411yescharacteristic
76C4×D61—21no—
77C4×D61—21no—
78C4×D61—21no—
79C4×D61—21no—
80C4×D61—22no—
81Dic122—21no—
82Dic122M1612yescomplemented
83C8×C61—22no—
84C8×C61—41no—
85#92418—22no—
86#92418—41no—
87C22×C61—22no—
88C22×C61—41no—
89C22×C61—41no—
90C22×C61C2×C22⋊C411yescharacteristic
91C2×D61—21no—
92C2×D61—21no—
93C2×D61—21no—
94C4×C61—21no—
95C4×C61—41no—
96C4×C61C2×M1611yescharacteristic
97C4×C61C2×M1611yescharacteristic
98C4×C61AGL(1,ℤ/8)11yescharacteristic
99C4×C61#13711yescharacteristic
100Dic61—22no—
101Dic61—21no—
102Dic61—21no—
103Dic61—41no—
104Dic61#10412yes—
105#1489—611nomaximal, Sylow
106C2×C61—42no—
107C2×C61#40711yescharacteristic
108C2×C61#41711yescharacteristic
109C2×C61C2×#10411yescharacteristic
110D61—41no—
111C4×#41—611no—
112#423—611no—
113C4×M16—611no—
114Q8⋊C8—611no—
115Q8⋊C8—611no—
116D4⋊C8—611no—
117D4⋊C8D6111yescharacteristic, complemented
118C61#148911yescharacteristic, complemented, Sylow
119C2×#41—611no—
120C2×M16—1221no—
121C2×M16—1221no—
122C4×Q8—611no—
123C4×Q8—611no—
124C4×D4—611no—
125C4×D4—1221no—
126C4×D4—1221no—
127C4×D4C2×D6111yescharacteristic
128#117—611no—
129#117—1221no—
130C2×C42—611no—
131C2×C42—1221no—
132C4⋊C8—611no—
133C4⋊C8—1221no—
134C4⋊C8C2×D6111yescharacteristic
135#97—1221no—
136C4×C8—611no—
137C4×C8C2×D6111yescharacteristic
138#41—1222no—
139#41—1222no—
140C2×Q8—611no—
141C2×D4—1221no—
142C2×D4C4×D6111yescharacteristic
143C22×C4—21no—
144C22×C4—611no—
145C22×C4—611no—
146C22×C4—611no—
147C22×C4—1221no—
148C22×C4—1221no—
149M16—1224no—
150M16—2442no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—1221no—
154C2×C8—1221no—
155C4⋊C4—611no—
156C4⋊C4—1221no—
157C4⋊C4—1221no—
158C4⋊C4C4×D6111yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—1221no—
161C22⋊C4—1221no—
162C42—611no—
163C42—611no—
164C42—611no—
165C42—1221no—
166C42—1221no—
167C42—1221no—
168C42C22×D6111yescharacteristic
169C23—21no—
170C23—611no—
171Q8—612no—
172Q8—1221no—
173D4—21no—
174D4—1224no—
175D4#1175818912yescomplemented
176C2×C4—21no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—611no—
180C2×C4—611no—
181C2×C4—611no—
182C2×C4—1222no—
183C2×C4—1224no—
184C2×C4—1221no—
185C2×C4—1221no—
186C2×C4—1221no—
187C2×C4—1221no—
188C2×C4—1221no—
189C2×C4—1221no—
190C2×C4—2442no—
191C2×C4C2×C4×D6111yescharacteristic
192C2×C4D4×D6111yescharacteristic
193C2×C4D4×D6111yescharacteristic
194C8—22no—
195C8—41no—
196C8—1222no—
197C8—2441no—
198C22—22no—
199C22—41no—
200C22—41no—
201C22—1221no—
202C22—1221no—
203C22—1221no—
204C22C22⋊C4×D6111yescharacteristic
205C4—21no—
206C4—41no—
207C4—612no—
208C4—1221no—
209C4—1222no—
210C4—1221no—
211C4—2441no—
212C4M16×D6111yescharacteristic
213C4C2×#1175818911yescharacteristic
214C4#1451980111yescharacteristic
215C4#1451980611yescharacteristic
216C2—42no—
217C2—2441no—
218C2#1683972411yescharacteristic
219C2#1683976011yescharacteristic
220C2#104×D6111yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61C2×C22⋊C4
hypercenterD4⋊C8D61
hypocenterC61#1489
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #16839784C2semidirect
3. C4×#11758189C2semidirect
4. #16839494C2semidirect
5. #16839492C2semidirect
6. D4⋊#92418C2semidirect
7. C61×D4⋊C8C2semidirect
61. D4×C61M16semidirect
82. Dic122M16semidirect
117. D4⋊C8D61semidirect
118. C61#1489semidirect
175. D4#11758189semidirect