Finite Group Databasebeta

← #21461947

Subgroups — #21461947

Order 7808.

436 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 98 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×#14519839C214yesmaximal, complemented
2C4×D61⋊C8C211yesmaximal, characteristic, complemented
3#16840708C211yesmaximal, characteristic, complemented
4#127×D61C211yesmaximal, characteristic
5C2×D61⋊C8C2212yes—
6C2×C4⋊#6923—22no—
7C2×C4⋊#6923C2212yes—
8#14519839—28no—
9C4×#92420—22no—
10C2×D4×D61—22no—
11C2×D4×D61C2212yes—
12#14519774C411yescharacteristic, complemented
13#14519773—22no—
14#14519773C412yescomplemented
15C42×D61C2211yescharacteristic
16#127×C61C411yescharacteristic, complemented
17C23×D61—22no—
18C22×#6923—22no—
19C2×D4×C61—22no—
20C2×D4×C61C2×C412yes—
21C2×C22⋊D61—24no—
22C2×C22⋊D61—22no—
23D4×D61—24no—
24D4×D61—24no—
25D4×D61—44no—
26D4×D61—44no—
27C2×D244—22no—
28C2×D244C2×C412yes—
29C2×C4×D61D412yes—
30C2×C4×D61C2311yescharacteristic
31C2×#92420—22no—
32C4⋊#6923—24no—
33C4⋊#6923—44no—
34D61⋊C8—22no—
35D61⋊C8D414yescomplemented
36C42×C61C2×C411yescharacteristic
37C4×Dic61C2×C411yescharacteristic
38C4×Dic61D412yes—
39C23×C61—22no—
40C22×D61—22no—
41C22×D61—42no—
42C22×D61—42no—
43C22×D61—44no—
44C22×D61—44no—
45C22×D61C2×D411yescharacteristic
46C2×#6923—42no—
47C2×#6923—44no—
48D4×C61—24no—
49D4×C61—44no—
50C2×C4×C61C22⋊C412yes—
51C2×C4×C61C22×C411yescharacteristic
52C22⋊D61—48no—
53C22⋊D61—44no—
54C2×Dic61C22⋊C412yes—
55C2×Dic61C2×D411yescharacteristic
56D244—24no—
57D244—44no—
58C4×D61D814yes—
59C4×D61SD1614yes—
60C4×D61C2×D412yes—
61C4×D61#4112yes—
62#92420—24no—
63C22×C61—42no—
64C22×C61—44no—
65C22×C61C2×C22⋊C411yescharacteristic
66C2×D61—42no—
67C2×D61—44no—
68C2×D61—84no—
69C2×D61—82no—
70C2×D61—82no—
71C2×D61#12411yescharacteristic
72C2×D61#12711yescharacteristic
73C2×D61C2×D812yes—
74C2×D61C2×SD1612yes—
75#6923—82no—
76C4×C61#10214yescomplemented
77C4×C61C4×D412yes—
78Dic61#10214yescomplemented
79Dic61#12112yes—
80#1957—611nomaximal, Sylow
81C2×C61—82no—
82C2×C61#39011yescharacteristic
83C2×C61C2×#10212yes—
84D61—82no—
85D61#48612yes—
86D61#49211yescharacteristic
87D61#49311yescharacteristic
88C2×#127—611no—
89C2×#102—614no—
90C2×C4×C8—611no—
91#384—611no—
92C61#195711yescharacteristic, complemented, Sylow
93C22×D4—612no—
94C22×D4—1222no—
95C22×C8—612no—
96#127—612no—
97#127—611no—
98#127—1222no—
99#127#692311yescharacteristic, complemented
100C2×C4⋊C4—612no—
101C2×C4⋊C4—1222no—
102C2×C42—611no—
103#102—1228no—
104C4×C8—1222no—
105C24—1222no—
106C2×D4—22no—
107C2×D4—612no—
108C2×D4—1224no—
109C2×D4—1224no—
110C2×D4—1224no—
111C2×D4—1222no—
112C2×D4—1222no—
113C2×D4—2444no—
114C2×D4—2444no—
115C2×D4C2×#692312yes—
116C22×C4—612no—
117C22×C4—611no—
118C22×C4—1222no—
119C2×C8—614no—
120C2×C8—1222no—
121C2×C8—1222no—
122C4⋊C4—1224no—
123C4⋊C4—2444no—
124C42—612no—
125C42—611no—
126C42C2×#692311yescharacteristic
127C23—22no—
128C23—611no—
129C23—1222no—
130C23—2442no—
131C23—2442no—
132C23—2444no—
133C23—2444no—
134D4—24no—
135D4—44no—
136D4—1224no—
137D4—2444no—
138D4—2448no—
139D4—2444no—
140C2×C4—612no—
141C2×C4—611no—
142C2×C4—614no—
143C2×C4—614no—
144C2×C4—612no—
145C2×C4—612no—
146C2×C4—2442no—
147C2×C4—2444no—
148C2×C4C22⋊#692312yes—
149C2×C4C22×#692311yescharacteristic
150C8—1224no—
151C22—42no—
152C22—44no—
153C22—611no—
154C22—611no—
155C22—612no—
156C22—612no—
157C22—4882no—
158C22—4884no—
159C22—4882no—
160C22—2442no—
161C22—2444no—
162C22C2×C22⋊#692311yescharacteristic
163C4—612no—
164C4—614no—
165C4—4882no—
166C4#1451983914yescomplemented
167C4D4×#692312yes—
168C2—82no—
169C2—611no—
170C2—612no—
171C2—611no—
172C2—4882no—
173C2#1684071411yescharacteristic
174C2C2×#1451983912yes—
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#127×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#127#6923
hypocenterC61#1957
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C2×#14519839C2semidirect
2. C4×D61⋊C8C2semidirect
3. #16840708C2semidirect
12. #14519774C4semidirect
14. #14519773C4semidirect
16. #127×C61C4semidirect
35. D61⋊C8D4semidirect
76. C4×C61#102semidirect
78. Dic61#102semidirect
92. C61#1957semidirect
99. #127#6923semidirect
166. C4#14519839semidirect