Finite Group Databasebeta

← C2×#17985740 #22586923

Subgroups — C2×#17985740 #22586923

Order 9088.

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

normal subgroups only

This group has 232 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×#14556120C211yesmaximal, characteristic
2C2×#14556039C211yesmaximal, characteristic
3#17985740C214yesmaximal, direct product factor
4C2×#97×C71C211yesmaximal, characteristic
5C22×C71⋊C8—21no—
6#14556120—21no—
7#14556120—21no—
8#14556120C412yes—
9#14556120C2212yes—
10C2×C4⋊Dic71C411yescharacteristic
11C2×C4⋊Dic71C411yescharacteristic
12C2×Dic71⋊C4—21no—
13C2×Dic71⋊C4—21no—
14#14556039—21no—
15#14556039C2212yes—
16C22×C8×C71—21no—
17C2×C42×C71C2211yescharacteristic
18#97×C71—21no—
19#97×C71C2212yes—
20C22×Dic71—21no—
21C22×Dic71—21no—
22C2×C71⋊C8—24no—
23C2×C71⋊C8—22no—
24C4⋊Dic71—21no—
25C4⋊Dic71—21no—
26C4⋊Dic71C2×C412yes—
27C4⋊Dic71C2×C412yes—
28Dic71⋊C4—22no—
29Dic71⋊C4—22no—
30Dic71⋊C4—22no—
31Dic71⋊C4—22no—
32C22×C4×C71C2×C411yescharacteristic
33C22×C4×C71D411yescharacteristic
34C22×C4×C71D411yescharacteristic
35C2×C8×C71—24no—
36C2×C8×C71—22no—
37C42×C71C2×C411yescharacteristic
38C42×C71D411yescharacteristic
39C42×C71D411yescharacteristic
40C42×C71C2311yescharacteristic
41C23×C71C22⋊C411yescharacteristic
42C2×C4×C71—22no—
43C2×C4×C71—22no—
44C2×C4×C71—22no—
45C2×C4×C71C22⋊C411yescharacteristic
46C2×C4×C71C22⋊C411yescharacteristic
47C2×C4×C71C22⋊C411yescharacteristic
48C2×C4×C71C22×C411yescharacteristic
49C2×C4×C71C2×D411yescharacteristic
50C2×C4×C71C2×D411yescharacteristic
51C2×Dic71—22no—
52C2×Dic71—22no—
53C2×Dic71—42no—
54C2×Dic71—42no—
55C8×C71—24no—
56C71⋊C8—24no—
57C22×C71#10112yes—
58C22×C71#10412yes—
59C22×C71#10412yes—
60C22×C71C2×C22⋊C411yescharacteristic
61C4×C71—21no—
62C4×C71—21no—
63C4×C71—21no—
64C4×C71—21no—
65C4×C71—21no—
66C4×C71—21no—
67Dic71—42no—
68Dic71—42no—
69C2×C71#33014yescomplemented
70C2×C71C2×#10111yescharacteristic
71C2×C71C2×#10411yescharacteristic
72C2×C71C2×#10411yescharacteristic
73C2×#330—711nomaximal, Sylow
74C71C2×#33011yescharacteristic, complemented, Sylow
75C2×#125—711no—
76C2×#97—711no—
77C2×#97D7111yescharacteristic
78#330—714no—
79C22×C8—21no—
80C22×C8—1421no—
81#125—712no—
82#125—712no—
83#125—1421no—
84#125—1421no—
85C2×C4⋊C4—711no—
86C2×C4⋊C4—711no—
87C2×C4⋊C4—1421no—
88C2×C4⋊C4—1421no—
89C2×C42C2×D7111yescharacteristic
90#97—21no—
91#97—712no—
92#97—1421no—
93#97C2×D7112yes—
94C22×C4—1421no—
95C22×C4—1421no—
96C22×C4C4×D7111yescharacteristic
97C22×C4D28411yescharacteristic
98C22×C4C22⋊D7111yescharacteristic
99C2×C8—24no—
100C2×C8—22no—
101C2×C8—1424no—
102C2×C8—1422no—
103C4⋊C4—712no—
104C4⋊C4—712no—
105C4⋊C4—1422no—
106C4⋊C4—1422no—
107C4⋊C4—1421no—
108C4⋊C4—1421no—
109C4⋊C4—1422no—
110C4⋊C4—1422no—
111C42C4×D7111yescharacteristic
112C42D28411yescharacteristic
113C42C22⋊D7111yescharacteristic
114C42C22×D7111yescharacteristic
115C23(C2×D71)⋊C411yescharacteristic
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—22no—
119C2×C4—2842no—
120C2×C4—2842no—
121C2×C4—1422no—
122C2×C4—1422no—
123C2×C4(C2×D71)⋊C411yescharacteristic
124C2×C4(C2×D71)⋊C411yescharacteristic
125C2×C4(C2×D71)⋊C411yescharacteristic
126C2×C4C2×C4×D7111yescharacteristic
127C2×C4C2×C22⋊D7111yescharacteristic
128C2×C4C2×D28411yescharacteristic
129C8—24no—
130C8—1424no—
131C22#1455604612yes—
132C22#1455605412yes—
133C22#1455605612yes—
134C22C2×(C2×D71)⋊C411yescharacteristic
135C4—21no—
136C4—21no—
137C4—21no—
138C4—21no—
139C4—21no—
140C4—21no—
141C4—2842no—
142C4—2842no—
143C2#1798574014yesdirect product factor
144C2C2×#1455604611yescharacteristic
145C2C2×#1455605411yescharacteristic
146C2C2×#1455605611yescharacteristic
subgroupG/H
centerC23(C2×D71)⋊C4
commutatorC2×C4×C71C22×C4
FrattiniC42C22×D71
FittingC2×#97×C71C2
socleC23×C71C22⋊C4
hypercenterC2×#97D71
hypocenterC71C2×#330
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
3. #17985740C2direct (N × H)
69. C2×C71#330semidirect
74. C71C2×#330semidirect
143. C2#17985740direct (N × H)