Finite Group Databasebeta

← #21455295

Subgroups — #21455295

Order 7808.

584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519803C212yesmaximal, complemented
2C4×#11758222C211yesmaximal, characteristic, complemented
3#16839959C214yesmaximal, complemented
4#16839954C214yesmaximal, complemented
5#16839786C211yesmaximal, characteristic, complemented
6#16839767C212yesmaximal, complemented
7C2×#127×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519803—28no—
10C2×#11758200C2214yescomplemented
11C2×#11758199C2214yescomplemented
12C2×#11758194C2212yes—
13C4×Dic122C2212yescomplemented
14C4×D244C2212yescomplemented
15C4×C22⋊D61—22no—
16#14519736C2211yescharacteristic
17#14519734—21no—
18C42×D61—21no—
19C4⋊#92418C2214yescomplemented
20#14519698C2218yescomplemented
21C22×D4×C61—22no—
22C22×D4×C61C2212yes—
23#127×C61—21no—
24#127×C61—21no—
25#127×C61C2214yes—
26C2×C42×C61C2211yescharacteristic
27C24×C61—22no—
28C2×D4×C61—24no—
29C2×D4×C61—22no—
30C2×D4×C61—24no—
31C2×D4×C61—24no—
32C2×D4×C61—24no—
33C2×D4×C61—48no—
34C2×D4×C61C2314yes—
35C22×C4×C61D412yes—
36C22×C4×C61C2311yescharacteristic
37C2×C22⋊D61—21no—
38#11758222—22no—
39#11758222D414yescomplemented
40C2×D244C2311yescharacteristic
41C2×C4×D61—21no—
42C2×C4×D61—22no—
43C2×Dic122C2311yescharacteristic
44C42×C61D411yescharacteristic
45C42×C61D411yescharacteristic
46C42×C61C2312yes—
47C22⋊Dic61—21no—
48#11758200—28no—
49#11758199—28no—
50#11758198—22no—
51C4⋊Dic61C2312yes—
52#11758196—22no—
53C4×Dic61—21no—
54C4×Dic61—22no—
55#11758194—24no—
56C2×#92418C2314yes—
57C23×C61—24no—
58C23×C61—48no—
59C23×C61—44no—
60C23×C61C2×D411yescharacteristic
61C22×D61—21no—
62D4×C61—24no—
63D4×C61—24no—
64D4×C61—48no—
65D4×C61—44no—
66D4×C61—48no—
67C2×C4×C61—24no—
68C2×C4×C61C2×D412yes—
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D412yes—
71C2×C4×C61C2×D412yes—
72C2×C4×C61#4112yes—
73C2×C4×C61C2411yescharacteristic
74C22⋊D61—24no—
75C2×Dic61—21no—
76C2×Dic61—22no—
77D244—21no—
78D244C2×D412yescomplemented
79C4×D61—24no—
80C4×D61—44no—
81Dic122—21no—
82Dic122C2×D412yescomplemented
83#92418—24no—
84C22×C61—22no—
85C22×C61—44no—
86C22×C61—48no—
87C22×C61—88no—
88C22×C61#12112yes—
89C22×C61C22×D411yescharacteristic
90C2×D61—22no—
91C2×D61—42no—
92C4×C61—22no—
93C4×C61#12112yes—
94C4×C61AGL(1,ℤ/8)14yescomplemented
95C4×C61C22×D411yescharacteristic
96C4×C61C2×#4111yescharacteristic
97Dic61—22no—
98Dic61—42no—
99#3038—611nomaximal, Sylow
100C2×C61—22no—
101C2×C61—84no—
102C2×C61C2×#12111yescharacteristic
103C2×C61C2×AGL(1,ℤ/8)12yes—
104D61—42no—
105C2×AGL(1,ℤ/8)—612no—
106C2×#127D6111yescharacteristic, complemented
107C4×#41—611no—
108#460—614no—
109#459—614no—
110#423—611no—
111#418—612no—
112C61#303811yescharacteristic, complemented, Sylow
113C2×#41—611no—
114C22×D4—22no—
115C22×D4C2×D6112yes—
116AGL(1,ℤ/8)—1228no—
117C2×SD16—614no—
118C2×D8—614no—
119C2×M16—612no—
120#127—21no—
121#127—21no—
122#127C2×D6114yes—
123C4×Q8—612no—
124C4×D4—612no—
125C4×D4—1222no—
126#117—611no—
127#117—1221no—
128C2×C42—1221no—
129C2×C42C2×D6111yescharacteristic
130C4⋊C8—614no—
131#102—618no—
132C24—22no—
133#41—614no—
134#41—1222no—
135C2×Q8—611no—
136C2×D4—24no—
137C2×D4—24no—
138C2×D4—22no—
139C2×D4—24no—
140C2×D4—24no—
141C2×D4—48no—
142C2×D4—611no—
143C2×D4—1221no—
144C2×D4C22×D6114yes—
145C22×C4—1221no—
146C22×C4—1222no—
147C22×C4C22⋊D6112yes—
148C22×C4C22×D6111yescharacteristic
149SD16—1228no—
150D8—1228no—
151M16—1224no—
152C2×C8—614no—
153C4⋊C4—612no—
154C4⋊C4—1222no—
155C22⋊C4—1221no—
156C22⋊C4—1222no—
157C42—1221no—
158C42—1222no—
159C42C22⋊D6111yescharacteristic
160C42C22⋊D6111yescharacteristic
161C42C22×D6112yes—
162C23—24no—
163C23—48no—
164C23—44no—
165C23—1221no—
166C23C2×C22⋊D6111yescharacteristic
167Q8—612no—
168Q8—1221no—
169D4—24no—
170D4—24no—
171D4—48no—
172D4—44no—
173D4—48no—
174D4—612no—
175D4—1224no—
176D4—1221no—
177C2×C4—24no—
178C2×C4—1221no—
179C2×C4—1224no—
180C2×C4—1222no—
181C2×C4—2444no—
182C2×C4D4×D6112yes—
183C2×C4#1175822412yes—
184C2×C4C2×C22⋊D6112yes—
185C2×C4C2×C22⋊D6111yescharacteristic
186C2×C4C2×C22⋊D6112yes—
187C2×C4C23×D6111yescharacteristic
188C8—1224no—
189C22—22no—
190C22—44no—
191C22—48no—
192C22—88no—
193C22—1222no—
194C22—2442no—
195C22#1451974812yes—
196C22C22×C22⋊D6111yescharacteristic
197C4—22no—
198C4—1222no—
199C4—2442no—
200C4#1451974812yes—
201C4#1451980314yescomplemented
202C4C2×D4×D6111yescharacteristic
203C4C2×#1175822411yescharacteristic
204C2—22no—
205C2—84no—
206C2—2442no—
207C2C2×#1451974811yescharacteristic
208C2C2×#1451980312yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#127×C61C2
socleC22×C61C22×D4
hypercenterC2×#127D61
hypocenterC61#3038
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#14519803C2semidirect
2. C4×#11758222C2semidirect
3. #16839959C2semidirect
4. #16839954C2semidirect
5. #16839786C2semidirect
6. #16839767C2semidirect
7. C2×#127×C61C2semidirect
10. C2×#11758200C22semidirect
11. C2×#11758199C22semidirect
13. C4×Dic122C22semidirect
14. C4×D244C22semidirect
19. C4⋊#92418C22semidirect
20. #14519698C22semidirect
39. #11758222D4semidirect
78. D244C2×D4semidirect
82. Dic122C2×D4semidirect
94. C4×C61AGL(1,ℤ/8)semidirect
106. C2×#127D61semidirect
112. C61#3038semidirect
201. C4#14519803semidirect