Finite Group Databasebeta

← C2×#16840638 #21461510

Subgroups — C2×#16840638 #21461510

Order 7808.

392 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C22×#11758213C212yesmaximal
2#16840638C214yesmaximal, direct product factor
3C22×C8×D61C211yesmaximal, characteristic
4C2×#11758213—22no—
5C2×#11758213—24no—
6C2×#11758213C418yes—
7C2×#11758213C2214yes—
8C22×#92420—22no—
9C22×C4×D61C2211yescharacteristic
10C22×#92418C411yescharacteristic
11C2×C8×D61—24no—
12C2×C8×D61C412yes—
13C2×C8×D61C2212yes—
14C22×C8×C61C411yescharacteristic
15C23×D61Q811yescharacteristic
16C22×C4×C61C2×C411yescharacteristic
17C22×Dic61D411yescharacteristic
18C2×C4×D61C2×C411yescharacteristic
19C2×C4×D61C2×C414yes—
20C2×C4×D61D411yescharacteristic
21C2×C4×D61D414yes—
22C2×C4×D61Q811yescharacteristic
23C2×C4×D61C2311yescharacteristic
24C2×#92420—28no—
25C2×#92420—24no—
26#11758213—28no—
27#11758213—24no—
28#11758213C2×C418yes—
29C2×C8×C61—22no—
30C2×C8×C61C2×C412yes—
31C2×#92418—22no—
32C2×#92418C2×C412yes—
33C8×D61—24no—
34C8×D61—24no—
35C23×C61C4⋊C411yescharacteristic
36C22×D61—22no—
37C22×D61—22no—
38C22×D61C4⋊C411yescharacteristic
39C22×D61C4⋊C414yes—
40C22×D61C2×Q811yescharacteristic
41C2×C4×C61C4212yes—
42C2×C4×C61C22⋊C412yes—
43C2×C4×C61C4⋊C411yescharacteristic
44C2×C4×C61C22×C411yescharacteristic
45C2×Dic61C22⋊C414yes—
46C2×Dic61C4⋊C411yescharacteristic
47C2×Dic61C2×D411yescharacteristic
48C4×D61C4212yes—
49C4×D61C22⋊C412yes—
50C4×D61C22⋊C414yes—
51C4×D61C4⋊C414yes—
52C4×D61C22×C412yes—
53C4×D61C2×D412yes—
54#92420—28no—
55C8×C61—22no—
56#92418—22no—
57C22×C61#9512yes—
58C22×C61#10812yes—
59C22×C61#10812yes—
60C22×C61C2×C4⋊C411yescharacteristic
61C2×D61—28no—
62C2×D61—21no—
63C2×D61—21no—
64C2×D61—21no—
65C2×D61—21no—
66C2×D61#9512yes—
67C2×D61C2×C4⋊C412yes—
68C4×C61#9512yes—
69C4×C61C2×C4211yescharacteristic
70C4×C61C2×C22⋊C411yescharacteristic
71Dic61#9512yes—
72Dic61C2×C22⋊C412yes—
73C2×#341—611nomaximal, Sylow
74C2×C61#34114yescomplemented
75C2×C61C2×#9511yescharacteristic
76C2×C61C2×#10811yescharacteristic
77C2×C61C2×#10811yescharacteristic
78D61—22no—
79D61—22no—
80C22×M16—612no—
81C23×C8—611no—
82#341—614no—
83C61C2×#34111yescharacteristic, complemented, Sylow
84C23×C4—611no—
85C2×M16—618no—
86C2×M16—614no—
87C2×M16—1222no—
88C2×M16—1224no—
89C22×C8—611no—
90C22×C8—612no—
91C22×C8—612no—
92C22×C8—1224no—
93C22×C8—1222no—
94C22×C8#692311yescharacteristic
95C24—611no—
96C22×C4—611no—
97C22×C4—614no—
98C22×C4—611no—
99C22×C4—611no—
100C22×C4—614no—
101C22×C4—611no—
102C22×C4—611no—
103C22×C4C2×#692311yescharacteristic
104M16—618no—
105M16—1228no—
106M16—1224no—
107C2×C8—22no—
108C2×C8—612no—
109C2×C8—1224no—
110C2×C8—1224no—
111C2×C8—1228no—
112C2×C8—1224no—
113C2×C8—1222no—
114C2×C8C2×#692312yes—
115C23—614no—
116C23—611no—
117C23—611no—
118C23—1222no—
119C23—1222no—
120C23C4⋊#692311yescharacteristic
121C2×C4—614no—
122C2×C4—611no—
123C2×C4—611no—
124C2×C4—614no—
125C2×C4—614no—
126C2×C4—612no—
127C2×C4—612no—
128C2×C4—612no—
129C2×C4—612no—
130C2×C4C4×#692312yes—
131C2×C4C4⋊#692311yescharacteristic
132C2×C4C22⋊#692312yes—
133C2×C4C22×#692311yescharacteristic
134C8—22no—
135C8—1228no—
136C8—1222no—
137C22—612no—
138C22—612no—
139C22—1221no—
140C22—1221no—
141C22—1221no—
142C22—1221no—
143C22—1228no—
144C22(C2×#6923)⋊C412yes—
145C22#1451984712yes—
146C22#1451984812yes—
147C22C2×C4⋊#692311yescharacteristic
148C4—612no—
149C4—612no—
150C4(C2×#6923)⋊C412yes—
151C4C2×C4×#692311yescharacteristic
152C4C2×C22⋊#692311yescharacteristic
153C2—1222no—
154C2—1222no—
155C2#1684063814yesdirect product factor
156C2C2×(C2×#6923)⋊C411yescharacteristic
157C2C2×#1451984711yescharacteristic
158C2C2×#1451984811yescharacteristic
subgroupG/H
centerC23C4⋊#6923
commutatorC4×C61C2×C42
FrattiniC2×C4C22×#6923
FittingC22×C8×C61C4
socleC23×C61C4⋊C4
hypercenterC22×C8#6923
hypocenterC61C2×#341
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #16840638C2direct (N × H)
74. C2×C61#341semidirect
83. C61C2×#341semidirect
155. C2#16840638direct (N × H)