Finite Group Databasebeta

← C2×#16840621 #21461314

Subgroups — C2×#16840621 #21461314

Order 7808.

256 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 90 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×#14519844C211yesmaximal, characteristic
2C2×#14519844C211yesmaximal, characteristic
3#16840621C214yesmaximal, direct product factor
4C2×#14519776C211yesmaximal, characteristic
5C22×#92420—21no—
6C22×#92420—21no—
7#14519844—21no—
8#14519844—21no—
9#14519844C2212yes—
10#14519844C2212yes—
11C22×Dic122—21no—
12#14519776—21no—
13#14519776—21no—
14#14519776C412yes—
15#14519776C2212yes—
16C2×C4⋊Dic61C411yescharacteristic
17C2×#11758196—21no—
18C2×C4×Dic61C2211yescharacteristic
19C2×C4⋊C4×C61C411yescharacteristic
20C22×C4×C61—21no—
21C22×C4×C61C2×C411yescharacteristic
22C22×Dic61—21no—
23C22×Dic61D411yescharacteristic
24C22×Dic61D411yescharacteristic
25C2×Dic122—22no—
26C2×Dic122—22no—
27C2×Dic122—42no—
28C2×Dic122—42no—
29C2×#92420—22no—
30C2×#92420—22no—
31C2×#92420—42no—
32C2×#92420—42no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61C2×C412yes—
35C4⋊Dic61—21no—
36C4⋊Dic61C2×C412yes—
37#11758196—22no—
38#11758196—22no—
39C4×Dic61C2×C411yescharacteristic
40C4×Dic61D411yescharacteristic
41C4×Dic61D411yescharacteristic
42C4×Dic61C2311yescharacteristic
43C23×C61C22⋊C411yescharacteristic
44C2×C4×C61—22no—
45C2×C4×C61—22no—
46C2×C4×C61—42no—
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22×C411yescharacteristic
49C2×Dic61—22no—
50C2×Dic61—42no—
51C2×Dic61C22⋊C411yescharacteristic
52C2×Dic61C22⋊C411yescharacteristic
53C2×Dic61D812yes—
54C2×Dic61SD1612yes—
55C2×Dic61SD1612yes—
56C2×Dic61Q1612yes—
57C2×Dic61C2×D411yescharacteristic
58C2×Dic61C2×D411yescharacteristic
59Dic122—44no—
60Dic122—42no—
61Dic122—42no—
62#92420—42no—
63#92420—42no—
64C22×C61#10112yes—
65C22×C61#10212yes—
66C22×C61#10312yes—
67C22×C61C2×C22⋊C411yescharacteristic
68C4×C61—21no—
69C4×C61—21no—
70C4×C61—42no—
71Dic61—42no—
72Dic61#10212yes—
73Dic61#10312yes—
74Dic61C2×D811yescharacteristic
75Dic61C2×SD1611yescharacteristic
76Dic61C2×SD1611yescharacteristic
77Dic61C2×Q1611yescharacteristic
78C2×#332—611nomaximal, Sylow
79C2×C61#33214yescomplemented
80C2×C61C2×#10111yescharacteristic
81C2×C61C2×#10211yescharacteristic
82C2×C61C2×#10311yescharacteristic
83C2×C4⋊Q8—611no—
84C2×C4⋊C8—611no—
85C2×C4⋊C8—611no—
86#332—614no—
87C61C2×#33211yescharacteristic, complemented, Sylow
88C22×Q8—1221no—
89C22×C8—1221no—
90C22×C8—1221no—
91C4⋊Q8—612no—
92C4⋊Q8—612no—
93C4⋊Q8—1221no—
94C4⋊Q8—1221no—
95C2×C4⋊C4—611no—
96C2×C4⋊C4—1221no—
97C2×C4⋊C4#692311yescharacteristic
98C2×C42—611no—
99C4⋊C8—612no—
100C4⋊C8—612no—
101C4⋊C8—1221no—
102C4⋊C8—1221no—
103C2×Q8—1222no—
104C2×Q8—1222no—
105C2×Q8—2442no—
106C2×Q8—2442no—
107C22×C4—21no—
108C22×C4—611no—
109C22×C4—611no—
110C22×C4—1221no—
111C22×C4C2×#692311yescharacteristic
112C2×C8—1222no—
113C2×C8—1222no—
114C2×C8—2442no—
115C2×C8—2442no—
116C4⋊C4—21no—
117C4⋊C4—612no—
118C4⋊C4—1222no—
119C4⋊C4—1222no—
120C4⋊C4—1221no—
121C4⋊C4C2×#692312yes—
122C42—611no—
123C42—611no—
124C42—611no—
125C42—611no—
126C23C22⋊#692311yescharacteristic
127Q8—2444no—
128Q8—2442no—
129Q8—2442no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—42no—
133C2×C4—612no—
134C2×C4—612no—
135C2×C4—612no—
136C2×C4—612no—
137C2×C4—611no—
138C2×C4—611no—
139C2×C4—611no—
140C2×C4—611no—
141C2×C4—1222no—
142C2×C4—2442no—
143C2×C4C22⋊#692311yescharacteristic
144C2×C4C22×#692311yescharacteristic
145C8—2442no—
146C8—2442no—
147C22#1451983812yes—
148C22#1451983912yes—
149C22#1451984012yes—
150C22C2×C22⋊#692311yescharacteristic
151C4—21no—
152C4—21no—
153C4—42no—
154C4—612no—
155C4—611no—
156C4—611no—
157C4—612no—
158C4—611no—
159C4—611no—
160C4—2442no—
161C2#1684062114yesdirect product factor
162C2C2×#1451983811yescharacteristic
163C2C2×#1451983911yescharacteristic
164C2C2×#1451984011yescharacteristic
subgroupG/H
centerC23C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×C4⋊C4×C61C4
socleC23×C61C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61C2×#332
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #16840621C2direct (N × H)
79. C2×C61#332semidirect
87. C61C2×#332semidirect
161. C2#16840621direct (N × H)