Finite Group Databasebeta

← #21462097

Subgroups — #21462097

Order 7808.

286 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 52 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
1D61⋊#99C212yesmaximal, complemented
2#16840668C212yesmaximal, complemented
3#16840667C212yesmaximal, complemented
4#16840330C211yesmaximal, characteristic
5C2×C22⋊#6923—22no—
6#14519836C2214yes—
7#14519835—22no—
8C2×#11758226C411yescharacteristic, complemented
9C2×D4×D61C2211yescharacteristic
10#14519774C2211yescharacteristic
11#14519773C411yescharacteristic, complemented
12#14519766C2211yescharacteristic
13#14519750—22no—
14#14519747—22no—
15#14519734C411yescharacteristic, complemented
16#124×C61C411yescharacteristic, complemented
17C23×D61D412yes—
18C22×#6923—42no—
19C2×Q8×C61C2×C411yescharacteristic, complemented
20C2×D4×C61C2×C411yescharacteristic
21C2×C22⋊D61—22no—
22C2×C22⋊D61D412yes—
23#11758226—42no—
24D4×D61—42no—
25C2×D244—21no—
26C2×D244—22no—
27C2×D244C2×C411yescharacteristic, complemented
28C2×D244C2311yescharacteristic
29C2×C4×D61—21no—
30C2×C4×D61C2×C411yescharacteristic
31C22⋊#6923—24no—
32C22⋊#6923—42no—
33C22⋊C4×C61—22no—
34C42×C61C2×C411yescharacteristic, complemented
35#11758198—21no—
36#11758198—22no—
37#11758196—21no—
38C4×Dic61C2×C411yescharacteristic, complemented
39C23×C61C22⋊C412yes—
40C22×D61—22no—
41C22×D61—22no—
42C22×D61—21no—
43C22×D61—82no—
44C22×D61C22⋊C411yescharacteristic
45C22×D61C2×D412yes—
46C2×#6923—44no—
47C2×#6923—84no—
48Q8×C61—41no—
49D4×C61—41no—
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61C22×C411yescharacteristic
53C22⋊D61—42no—
54C22⋊D61—82no—
55C2×Dic61—21no—
56C2×Dic61C22⋊C411yescharacteristic
57D244—41no—
58D244—41no—
59D244—42no—
60D244—82no—
61C4×D61—22no—
62C4×D61—42no—
63C22×C61—22no—
64C22×C61—42no—
65C22×C61C2×C22⋊C411yescharacteristic
66C2×D61—22no—
67C2×D61—41no—
68C2×D61—44no—
69C2×D61—42no—
70C2×D61—42no—
71C2×D61—41no—
72C2×D61—82no—
73C2×D61#9912yes—
74#6923—84no—
75C4×C61—21no—
76C4×C61—41no—
77C4×C61—41no—
78Dic61—21no—
79Dic61—41no—
80#2127—611nomaximal, Sylow
81C2×C61—21no—
82C2×C61—42no—
83C2×C61C2×#9911yescharacteristic
84D61—22no—
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#692311yescharacteristic, complemented
98#121—1222no—
99#120—1222no—
100#117—611no—
101C2×C22⋊C4—1222no—
102#99—614no—
103#99—1222no—
104C24—612no—
105#41—2442no—
106C2×Q8C2×#692311yescharacteristic, complemented
107C2×D4—612no—
108C2×D4—611no—
109C2×D4—611no—
110C2×D4—1222no—
111C2×D4—1221no—
112C2×D4—1222no—
113C2×D4—2442no—
114C2×D4C2×#692311yescharacteristic
115C22×C4—611no—
116C22×C4—1221no—
117C22×C4—2442no—
118C4⋊C4—1221no—
119C22⋊C4—22no—
120C22⋊C4—1221no—
121C22⋊C4—1222no—
122C22⋊C4—1224no—
123C22⋊C4—2442no—
124C42—611no—
125C42C2×#692311yescharacteristic, complemented
126C23—611no—
127C23—612no—
128C23—1222no—
129C23—1222no—
130C23—1221no—
131C23—4882no—
132C23C22⋊#692312yes—
133Q8—41no—
134D4—41no—
135D4—4882no—
136D4—4882no—
137D4—2441no—
138D4—2441no—
139D4—2442no—
140D4—2442no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—611no—
144C2×C4—1222no—
145C2×C4—1221no—
146C2×C4—4884no—
147C2×C4—2442no—
148C2×C4—2444no—
149C2×C4C22×#692311yescharacteristic
150C22—22no—
151C22—42no—
152C22—612no—
153C22—1222no—
154C22—4882no—
155C22—2441no—
156C22—2442no—
157C22—2442no—
158C22—2444no—
159C22—2441no—
160C22C2×C22⋊#692311yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—1221no—
165C4—4884no—
166C4—2441no—
167C2—21no—
168C2—42no—
169C2—1222no—
170C2—4881no—
171C2—2442no—
172C2D61⋊#9911yescharacteristic
subgroupG/H
centerC2D61⋊#99
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC2×C61C2×#99
hypercenter#124#6923
hypocenterC61#2127
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. D61⋊#99C2semidirect
2. #16840668C2semidirect
3. #16840667C2semidirect
8. C2×#11758226C4semidirect
11. #14519773C4semidirect
15. #14519734C4semidirect
16. #124×C61C4semidirect
19. C2×Q8×C61C2×C4semidirect
27. C2×D244C2×C4semidirect
34. C42×C61C2×C4semidirect
38. C4×Dic61C2×C4semidirect
91. C61#2127semidirect
97. #124#6923semidirect
106. C2×Q8C2×#6923semidirect
125. C42C2×#6923semidirect