Finite Group Databasebeta

← #21462096

Subgroups — #21462096

Order 7808.

286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 54 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×#14519836C212yesmaximal, complemented
2#16840669C212yesmaximal, complemented
3#16840667C212yesmaximal, complemented
4#16840331C211yesmaximal, characteristic
5C2×C22⋊#6923—22no—
6#14519836—22no—
7#14519836C2214yes—
8C2×#11758222C411yescharacteristic, complemented
9C22×D244C2211yescharacteristic
10#14519774C411yescharacteristic, complemented
11#14519774C2211yescharacteristic
12#14519765C411yescharacteristic, complemented
13#14519765C2211yescharacteristic
14#14519752—22no—
15#14519747—22no—
16#117×C61C411yescharacteristic, complemented
17C23×D61D412yes—
18C22×#6923—42no—
19C22×C4×C61C2×C411yescharacteristic
20C2×C22⋊D61—21no—
21#11758222—42no—
22C2×D244—22no—
23C2×D244—22no—
24C2×D244—42no—
25C2×D244C2×C411yescharacteristic
26C2×D244C2×C411yescharacteristic, complemented
27C2×D244D412yes—
28C2×D244C2311yescharacteristic
29C2×C4×D61—21no—
30C2×Dic122C2×C411yescharacteristic, complemented
31C22⋊#6923—24no—
32C22⋊#6923—42no—
33C4⋊C4×C61—21no—
34C22⋊C4×C61—21no—
35C42×C61C2×C411yescharacteristic, complemented
36C42×C61C2×C411yescharacteristic, complemented
37#11758198—22no—
38#11758198—22no—
39C23×C61C22⋊C411yescharacteristic
40C22×D61—22no—
41C22×D61—22no—
42C22×D61—21no—
43C22×D61—82no—
44C22×D61C22⋊C412yes—
45C22×D61C2×D412yes—
46C2×#6923—44no—
47C2×#6923—84no—
48C2×C4×C61—22no—
49C2×C4×C61—21no—
50C2×C4×C61—21no—
51C2×C4×C61C22⋊C411yescharacteristic
52C2×C4×C61C22×C411yescharacteristic
53C22⋊D61—42no—
54C2×Dic61—21no—
55D244—41no—
56D244—42no—
57D244—41no—
58D244—41no—
59D244—82no—
60D244—82no—
61C4×D61—42no—
62Dic122—41no—
63C22×C61—41no—
64C22×C61#9912yes—
65C22×C61C2×C22⋊C411yescharacteristic
66C2×D61—22no—
67C2×D61—22no—
68C2×D61—44no—
69C2×D61—42no—
70C2×D61—42no—
71C2×D61—42no—
72C2×D61—41no—
73C2×D61—82no—
74#6923—84no—
75C4×C61—21no—
76C4×C61—21no—
77C4×C61—41no—
78C4×C61—41no—
79Dic61—41no—
80#2127—611nomaximal, Sylow
81C2×C61—21no—
82C2×C61—22no—
83C2×C61C2×#9911yescharacteristic
84D61—42no—
85D61—42no—
86D61—81no—
87#535—611no—
88C2×#99—612no—
89#354—612no—
90#353—612no—
91C61#212711yescharacteristic, complemented, Sylow
92C2×#41—611no—
93C22×D4—611no—
94#127—611no—
95#127—611no—
96#124—611no—
97#124—611no—
98#121—1222no—
99#120—1222no—
100#117#692311yescharacteristic, complemented
101C2×C22⋊C4—1222no—
102#99—614no—
103#99—1222no—
104C24—612no—
105#41—2442no—
106C2×Q8—611no—
107C2×D4—612no—
108C2×D4—611no—
109C2×D4—611no—
110C2×D4—611no—
111C2×D4—1222no—
112C2×D4—1222no—
113C2×D4—1221no—
114C2×D4—2442no—
115C22×C4—1221no—
116C22×C4—2442no—
117C22×C4C2×#692311yescharacteristic
118C4⋊C4—21no—
119C22⋊C4—21no—
120C22⋊C4—1222no—
121C22⋊C4—1222no—
122C22⋊C4—1224no—
123C22⋊C4—2442no—
124C42C2×#692311yescharacteristic, complemented
125C42C2×#692311yescharacteristic, complemented
126C23—612no—
127C23—612no—
128C23—1222no—
129C23—1222no—
130C23—1221no—
131C23—4882no—
132C23C22⋊#692311yescharacteristic
133Q8—2441no—
134D4—4882no—
135D4—4882no—
136D4—2442no—
137D4—2441no—
138D4—2441no—
139D4—2441no—
140D4—2442no—
141C2×C4—22no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—1221no—
145C2×C4—4884no—
146C2×C4—2442no—
147C2×C4—2444no—
148C2×C4C22⋊#692311yescharacteristic
149C2×C4C22×#692311yescharacteristic
150C22—41no—
151C22—1222no—
152C22—1222no—
153C22—4882no—
154C22—2442no—
155C22—2442no—
156C22—2442no—
157C22—2444no—
158C22—2441no—
159C22#1451983612yes—
160C22C2×C22⋊#692311yescharacteristic
161C4—21no—
162C4—21no—
163C4—41no—
164C4—41no—
165C4—4884no—
166C4—2441no—
167C2—21no—
168C2—22no—
169C2—4881no—
170C2—2442no—
171C2—2442no—
172C2C2×#1451983611yescharacteristic
subgroupG/H
centerC2C2×#14519836
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#117×C61C4
socleC2×C61C2×#99
hypercenter#117#6923
hypocenterC61#2127
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#14519836C2semidirect
2. #16840669C2semidirect
3. #16840667C2semidirect
8. C2×#11758222C4semidirect
10. #14519774C4semidirect
12. #14519765C4semidirect
16. #117×C61C4semidirect
26. C2×D244C2×C4semidirect
30. C2×Dic122C2×C4semidirect
35. C42×C61C2×C4semidirect
36. C42×C61C2×C4semidirect
91. C61#2127semidirect
100. #117#6923semidirect
124. C42C2×#6923semidirect
125. C42C2×#6923semidirect