Finite Group Databasebeta

← C2×#15688862 #20241968

Subgroups — C2×#15688862 #20241968

Order 6016.

284 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 85 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×#13094012C211yesmaximal, characteristic
2C2×#13093935C211yesmaximal, characteristic, complemented
3#15688862C214yesmaximal, direct product factor
4C2×#97×C47C211yesmaximal, characteristic, complemented
5C22×Dic94C411yescharacteristic
6C22×D188C411yescharacteristic
7C22×C47⋊C8—21no—
8#13094012—21no—
9#13094012—21no—
10#13094012C412yes—
11#13094012C2212yes—
12C2×(C2×D47)⋊C4—21no—
13C2×(C2×D47)⋊C4—21no—
14#13093935—21no—
15#13093935C2212yescomplemented
16C22×C8×C47—21no—
17C2×C42×C47C2211yescharacteristic
18#97×C47—21no—
19#97×C47C2212yescomplemented
20C23×D47—21no—
21C22×C4×C47C2×C411yescharacteristic
22C22×C4×C47D411yescharacteristic
23C22×C4×C47D411yescharacteristic
24C22×Dic47—21no—
25C2×D188—21no—
26C2×D188—42no—
27C2×D188C2×C412yes—
28C2×Dic94—21no—
29C2×Dic94—42no—
30C2×Dic94C2×C412yes—
31C2×C8×C47—24no—
32C2×C8×C47—22no—
33C42×C47C2×C411yescharacteristic
34C42×C47D411yescharacteristic
35C42×C47D411yescharacteristic
36C42×C47C2311yescharacteristic
37(C2×D47)⋊C4—22no—
38(C2×D47)⋊C4—22no—
39(C2×D47)⋊C4—22no—
40(C2×D47)⋊C4—22no—
41C2×C47⋊C8—24no—
42C2×C47⋊C8—22no—
43C23×C47C22⋊C411yescharacteristic
44C22×D47—22no—
45C22×D47—42no—
46C22×D47—42no—
47C22×D47—42no—
48C2×C4×C47—22no—
49C2×C4×C47—22no—
50C2×C4×C47—22no—
51C2×C4×C47C22⋊C411yescharacteristic
52C2×C4×C47C22⋊C411yescharacteristic
53C2×C4×C47C22⋊C411yescharacteristic
54C2×C4×C47C22×C411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×Dic47—22no—
58C2×Dic47—42no—
59D188—42no—
60D188—42no—
61Dic94—42no—
62Dic94—42no—
63C8×C47—24no—
64C47⋊C8—24no—
65C22×C47#10012yes—
66C22×C47#10412yes—
67C22×C47#10412yes—
68C22×C47C2×C22⋊C411yescharacteristic
69C2×D47—42no—
70C2×D47—42no—
71C2×D47—42no—
72C2×D47—84no—
73C4×C47—21no—
74C4×C47—21no—
75C4×C47—21no—
76C4×C47—21no—
77C4×C47—21no—
78C4×C47—21no—
79Dic47—42no—
80C2×#329—471nomaximal, Sylow
81C2×C47#32914yescomplemented
82C2×C47C2×#10011yescharacteristic
83C2×C47C2×#10411yescharacteristic
84C2×C47C2×#10411yescharacteristic
85D47—82no—
86C2×#124—471no—
87C2×#97—471no—
88C2×#97D4711yescharacteristic, complemented
89#329—474no—
90C47C2×#32911yescharacteristic, complemented, Sylow
91C22×Q8—471no—
92C22×D4—471no—
93C22×C8—21no—
94C22×C8—941no—
95#124—472no—
96#124—472no—
97#124—941no—
98#124—941no—
99C2×C22⋊C4—941no—
100C2×C22⋊C4—941no—
101C2×C42C2×D4711yescharacteristic
102#97—21no—
103#97—472no—
104#97—941no—
105#97C2×D4712yescomplemented
106C24—941no—
107C2×Q8—472no—
108C2×Q8—941no—
109C2×Q8—1882no—
110C2×D4—472no—
111C2×D4—941no—
112C2×D4—1882no—
113C22×C4—941no—
114C22×C4C4×D4711yescharacteristic
115C22×C4D18811yescharacteristic
116C22×C4C22⋊D4711yescharacteristic
117C2×C8—24no—
118C2×C8—22no—
119C2×C8—944no—
120C2×C8—942no—
121C22⋊C4—942no—
122C22⋊C4—942no—
123C22⋊C4—942no—
124C22⋊C4—942no—
125C42C4×D4711yescharacteristic
126C42D18811yescharacteristic
127C42C22⋊D4711yescharacteristic
128C42C22×D4711yescharacteristic
129C23—942no—
130C23—1882no—
131C23—1882no—
132C23—1882no—
133C23(C2×D47)⋊C411yescharacteristic
134Q8—1882no—
135Q8—1882no—
136D4—1882no—
137D4—1882no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—22no—
141C2×C4—942no—
142C2×C4—1882no—
143C2×C4(C2×D47)⋊C411yescharacteristic
144C2×C4(C2×D47)⋊C411yescharacteristic
145C2×C4(C2×D47)⋊C411yescharacteristic
146C2×C4C2×C4×D4711yescharacteristic
147C2×C4C2×D18811yescharacteristic
148C2×C4C2×C22⋊D4711yescharacteristic
149C8—24no—
150C8—944no—
151C22—3764no—
152C22—1882no—
153C22—1882no—
154C22—1882no—
155C22#1309394012yes—
156C22#1309395012yes—
157C22#1309395212yes—
158C22C2×(C2×D47)⋊C411yescharacteristic
159C4—21no—
160C4—21no—
161C4—21no—
162C4—21no—
163C4—21no—
164C4—21no—
165C4—1882no—
166C2—3762no—
167C2#1568886214yesdirect product factor
168C2C2×#1309394011yescharacteristic
169C2C2×#1309395011yescharacteristic
170C2C2×#1309395211yescharacteristic
subgroupG/H
centerC23(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC2×#97×C47C2
socleC23×C47C22⋊C4
hypercenterC2×#97D47
hypocenterC47C2×#329
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. C2×#13093935C2semidirect
3. #15688862C2direct (N × H)
4. C2×#97×C47C2semidirect
15. #13093935C22semidirect
19. #97×C47C22semidirect
81. C2×C47#329semidirect
88. C2×#97D47semidirect
90. C47C2×#329semidirect
105. #97C2×D47semidirect
167. C2#15688862direct (N × H)