Finite Group Databasebeta

← #21461090

Subgroups — #21461090

Order 7808.

256 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 62 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
1#16840783C211yesmaximal, characteristic, complemented
2#16840779C211yesmaximal, characteristic, complemented
3#16840606C214yesmaximal, complemented
4C2×#14519766C211yesmaximal, characteristic
5#14519844—21no—
6C4⋊#92420—21no—
7C22⋊#92420C2212yes—
8C22⋊#92420C2212yes—
9#14519832—21no—
10C4×#92420—21no—
11C22×D244C411yescharacteristic
12#14519766—21no—
13#14519766—21no—
14#14519766—21no—
15#14519766—21no—
16C2×#11758198C412yes—
17C2×#11758198C2212yes—
18C2×C4×Dic61C2211yescharacteristic
19C22×Q8×C61C411yescharacteristic
20C23×D61C2×C412yes—
21C2×Q8×C61—21no—
22C2×Q8×C61—21no—
23C2×Q8×C61—42no—
24C22×C4×C61C2×C411yescharacteristic
25C22×C4×C61C2×C412yes—
26C22×Dic61C2×C411yescharacteristic
27C22×Dic61C2311yescharacteristic
28C2×D244—21no—
29C2×D244—21no—
30C2×D244—42no—
31C2×#92420—22no—
32C2×#92420—22no—
33#11758198—22no—
34#11758198—22no—
35#11758198—22no—
36#11758198—22no—
37C4×Dic61D411yescharacteristic
38C4×Dic61D411yescharacteristic
39C4×Dic61D411yescharacteristic
40C4×Dic61D411yescharacteristic
41C23×C61C22×C411yescharacteristic
42C22×D61—22no—
43C22×D61—24no—
44C22×D61—42no—
45C22×D61—42no—
46Q8×C61—42no—
47Q8×C61—42no—
48C2×C4×C61—22no—
49C2×C4×C61—22no—
50C2×C4×C61—42no—
51C2×C4×C61C22⋊C411yescharacteristic
52C2×C4×C61C22⋊C411yescharacteristic
53C2×Dic61—22no—
54C2×Dic61—41no—
55C2×Dic61C22⋊C411yescharacteristic
56C2×Dic61C22⋊C411yescharacteristic
57C2×Dic61C2×D411yescharacteristic
58C2×Dic61C2×D411yescharacteristic
59D244—42no—
60D244—42no—
61#92420—42no—
62#92420—42no—
63C22×C61—21no—
64C22×C61—21no—
65C22×C61C2×C22⋊C411yescharacteristic
66C22×C61#13112yes—
67C2×D61—42no—
68C2×D61—42no—
69C2×D61—42no—
70C2×D61—84no—
71C4×C61—21no—
72C4×C61—42no—
73C4×C61#10012yes—
74Dic61—21no—
75Dic61—21no—
76Dic61—21no—
77Dic61—21no—
78#1469—611nomaximal, Sylow
79C2×C61—22no—
80C2×C61#40811yescharacteristic
81C2×C61#41011yescharacteristic
82C2×C61C2×#10011yescharacteristic
83D61—82no—
84C2×#124—611no—
85#432—611no—
86#431—611no—
87#323—614no—
88C61#146911yescharacteristic, complemented, Sylow
89C22×Q8#692311yescharacteristic
90C22×D4—611no—
91#124—1221no—
92#124—1221no—
93#124—1221no—
94#124—1221no—
95C2×C22⋊C4—612no—
96C2×C22⋊C4—612no—
97C2×C42—611no—
98C4⋊C8—1221no—
99C4⋊C8—1221no—
100C22⋊C8—612no—
101C22⋊C8—612no—
102#97—1221no—
103C4×C8—1221no—
104C24—612no—
105C2×Q8—21no—
106C2×Q8—21no—
107C2×Q8—42no—
108C2×D4—1221no—
109C2×D4—1221no—
110C2×D4—2442no—
111C22×C4—611no—
112C22×C4—611no—
113C22×C4C2×#692312yes—
114C22×C4C2×#692311yescharacteristic
115C2×C8—1222no—
116C2×C8—1222no—
117C22⋊C4—1222no—
118C22⋊C4—1222no—
119C22⋊C4—1222no—
120C22⋊C4—1222no—
121C42—611no—
122C42—611no—
123C42—611no—
124C42—611no—
125C23—1224no—
126C23—1222no—
127C23—2442no—
128C23—2442no—
129C23C22×#692311yescharacteristic
130Q8—42no—
131Q8—42no—
132D4—2442no—
133D4—2442no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—42no—
137C2×C4—611no—
138C2×C4—611no—
139C2×C4—611no—
140C2×C4—611no—
141C2×C4—1222no—
142C2×C4—2441no—
143C2×C4C22⋊#692311yescharacteristic
144C2×C4C22⋊#692311yescharacteristic
145C8—2442no—
146C8—2442no—
147C22—21no—
148C22—21no—
149C22—4884no—
150C22—2442no—
151C22—2442no—
152C22—2442no—
153C22C2×C22⋊#692311yescharacteristic
154C22#1451986512yes—
155C4—21no—
156C4—42no—
157C4—1221no—
158C4—1221no—
159C4—1221no—
160C4—1221no—
161C4#1451983712yes—
162C2—22no—
163C2—4882no—
164C2#1684073711yescharacteristic
165C2#1684074311yescharacteristic
166C2C2×#1451983711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC22×Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22×Q8#6923
hypocenterC61#1469
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. #16840783C2semidirect
2. #16840779C2semidirect
3. #16840606C2semidirect
88. C61#1469semidirect