Finite Group Databasebeta

← C2×#16840681 #21462144

Subgroups — C2×#16840681 #21462144

Order 7808.

216 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 66 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×#14519852C211yesmaximal, characteristic
2C2×#14519847C211yesmaximal, characteristic
3#16840681C214yesmaximal, direct product factor
4C2×Q16×D61C211yesmaximal, characteristic
5C2×#11758213—21no—
6#14519852—21no—
7#14519852C2212yes—
8C2×#11758187—21no—
9#14519847—21no—
10#14519847C2212yes—
11C2×Q8×D61—21no—
12C2×Dic244C411yescharacteristic
13C2×#11758202—21no—
14Q16×D61—21no—
15Q16×D61—21no—
16Q16×D61C412yes—
17Q16×D61C2212yes—
18C2×C8×D61C2211yescharacteristic
19C2×Q16×C61C411yescharacteristic
20C2×Q8×C61—21no—
21Q8×D61—22no—
22Q8×D61—22no—
23Q8×D61—41no—
24Q8×D61—41no—
25C2×C4×D61—41no—
26C2×C4×D61D411yescharacteristic
27C2×Dic122—21no—
28C2×Dic122—41no—
29C2×#92420—41no—
30#11758213—22no—
31#11758213—41no—
32Q16×C61—21no—
33Q16×C61C2×C412yes—
34C2×C8×C61C2×C411yescharacteristic
35#11758202—22no—
36#11758202—22no—
37C2×#92418D411yescharacteristic
38Dic244—21no—
39Dic244C2×C412yes—
40C8×D61C2×C411yescharacteristic
41C8×D61D411yescharacteristic
42C8×D61D411yescharacteristic
43C8×D61C2311yescharacteristic
44#11758187—22no—
45C22×D61SD1611yescharacteristic
46Q8×C61—22no—
47Q8×C61—41no—
48C2×C4×C61—41no—
49C2×C4×C61C22⋊C411yescharacteristic
50C2×Dic61—41no—
51C2×Dic61D811yescharacteristic
52C4×D61—42no—
53C4×D61—42no—
54C4×D61C22⋊C411yescharacteristic
55C4×D61D811yescharacteristic
56C4×D61SD1611yescharacteristic
57C4×D61C2×D411yescharacteristic
58Dic122—22no—
59Dic122—41no—
60Dic122—42no—
61Dic122—42no—
62#92420—42no—
63C8×C61C22⋊C411yescharacteristic
64C8×C61C22×C411yescharacteristic
65#92418C22⋊C411yescharacteristic
66#92418C2×D411yescharacteristic
67C22×C61#10211yescharacteristic
68C2×D61—22no—
69C2×D61#10211yescharacteristic
70C2×D61C2×SD1611yescharacteristic
71C4×C61—42no—
72C4×C61#10211yescharacteristic
73C4×C61C2×C22⋊C411yescharacteristic
74Dic61—42no—
75Dic61#10211yescharacteristic
76Dic61C2×D811yescharacteristic
77C2×#362—611nomaximal, Sylow
78C2×C61#36212yescomplemented
79C2×C61C2×#10211yescharacteristic
80D61—21no—
81D61—21no—
82C22×Q16—611no—
83C2×M32—611no—
84C2×#108—611no—
85#362—614no—
86C61C2×#36211yescharacteristic, complemented, Sylow
87C22×Q8—1221no—
88C2×Q16—612no—
89C2×Q16—612no—
90C2×Q16—611no—
91C2×Q16—1221no—
92C2×Q16—1221no—
93C2×Q16—1221no—
94C2×Q16#692311yescharacteristic
95C2×M16—1221no—
96C22×C8—611no—
97M32—612no—
98M32—1221no—
99C2×C16—1221no—
100#108—612no—
101#108—1221no—
102C2×Q8—21no—
103C2×Q8—1222no—
104C2×Q8—1222no—
105C2×Q8—1221no—
106C2×Q8—2441no—
107C2×Q8—2441no—
108C2×Q8—2441no—
109C22×C4—611no—
110C22×C4—2441no—
111Q16—21no—
112Q16—612no—
113Q16—1222no—
114Q16—1222no—
115Q16—1221no—
116Q16C2×#692312yes—
117M16—1222no—
118M16—2441no—
119C2×C8—611no—
120C2×C8—611no—
121C2×C8—611no—
122C2×C8—611no—
123C2×C8—611no—
124C2×C8—2441no—
125C2×C8C2×#692311yescharacteristic
126C16—1222no—
127C23—611no—
128Q8—22no—
129Q8—41no—
130Q8—1222no—
131Q8—2442no—
132Q8—2442no—
133Q8—2441no—
134C2×C4—41no—
135C2×C4—611no—
136C2×C4—611no—
137C2×C4—611no—
138C2×C4—611no—
139C2×C4—611no—
140C2×C4—2442no—
141C2×C4—2442no—
142C2×C4—2441no—
143C2×C4C22⋊#692311yescharacteristic
144C8—611no—
145C8—611no—
146C8—2442no—
147C8C22⋊#692311yescharacteristic
148C8C22×#692311yescharacteristic
149C22—611no—
150C22—611no—
151C22—1222no—
152C22#1451983911yescharacteristic
153C4—42no—
154C4—611no—
155C4—611no—
156C4—2442no—
157C4#1451983911yescharacteristic
158C4C2×C22⋊#692311yescharacteristic
159C2—1221no—
160C2—1221no—
161C2#1684068112yesdirect product factor
162C2C2×#1451983911yescharacteristic
subgroupG/H
centerC22#14519839
commutatorC8×C61C22×C4
FrattiniC8C22×#6923
FittingC2×Q16×C61C4
socleC22×C61#102
hypercenterC2×Q16#6923
hypocenterC61C2×#362
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. #16840681C2direct (N × H)
78. C2×C61#362semidirect
86. C61C2×#362semidirect
161. C2#16840681direct (N × H)