Finite Group Databasebeta

← C2×#17989446 #22625426

Subgroups — C2×#17989446 #22625426

Order 9344.

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×#14556658C211yesmaximal, characteristic
2C2×#14556658C211yesmaximal, characteristic
3#17989446C214yesmaximal, direct product factor
4C2×#14556590C211yesmaximal, characteristic
5C22×#10596833—21no—
6C22×#10596833—21no—
7#14556658—21no—
8#14556658—21no—
9#14556658C2212yes—
10#14556658C2212yes—
11C22×Dic146—21no—
12#14556590—21no—
13#14556590—21no—
14#14556590C412yes—
15#14556590C2212yes—
16C2×C4⋊Dic73C411yescharacteristic
17C2×#11924007—21no—
18C2×C4×Dic73C2211yescharacteristic
19C2×C4⋊C4×C73C411yescharacteristic
20C2×#10596833—22no—
21C2×#10596833—22no—
22C2×#10596833—42no—
23C2×#10596833—42no—
24C2×Dic146—22no—
25C2×Dic146—22no—
26C2×Dic146—42no—
27C2×Dic146—42no—
28C22×Dic73—21no—
29C22×Dic73D411yescharacteristic
30C22×Dic73D411yescharacteristic
31C4⋊Dic73—21no—
32C4⋊Dic73C2×C412yes—
33#11924007—22no—
34#11924007—22no—
35C4×Dic73C2×C411yescharacteristic
36C4×Dic73D411yescharacteristic
37C4×Dic73D411yescharacteristic
38C4×Dic73C2311yescharacteristic
39C22×C4×C73—21no—
40C22×C4×C73C2×C411yescharacteristic
41C4⋊C4×C73—21no—
42C4⋊C4×C73C2×C412yes—
43C23×C73C22⋊C411yescharacteristic
44C2×C4×C73—22no—
45C2×C4×C73—22no—
46C2×C4×C73—42no—
47C2×C4×C73C22⋊C411yescharacteristic
48C2×C4×C73C22×C411yescharacteristic
49C2×Dic73—22no—
50C2×Dic73—42no—
51C2×Dic73C22⋊C411yescharacteristic
52C2×Dic73C22⋊C411yescharacteristic
53C2×Dic73D812yes—
54C2×Dic73SD1612yes—
55C2×Dic73SD1612yes—
56C2×Dic73Q1612yes—
57C2×Dic73C2×D411yescharacteristic
58C2×Dic73C2×D411yescharacteristic
59Dic146—44no—
60Dic146—42no—
61Dic146—42no—
62#10596833—42no—
63#10596833—42no—
64C22×C73#10112yes—
65C22×C73#10212yes—
66C22×C73#10312yes—
67C22×C73C2×C22⋊C411yescharacteristic
68C4×C73—21no—
69C4×C73—21no—
70C4×C73—42no—
71Dic73—42no—
72Dic73#10212yes—
73Dic73#10312yes—
74Dic73C2×D811yescharacteristic
75Dic73C2×SD1611yescharacteristic
76Dic73C2×SD1611yescharacteristic
77Dic73C2×Q1611yescharacteristic
78C2×C73#33214yescomplemented
79C2×C73C2×#10111yescharacteristic
80C2×C73C2×#10211yescharacteristic
81C2×C73C2×#10311yescharacteristic
82C2×#332—731nomaximal, Sylow
83C73C2×#33211yescharacteristic, complemented, Sylow
84C2×C4⋊Q8—731no—
85C2×C4⋊C8—731no—
86C2×C4⋊C8—731no—
87#332—734no—
88C22×Q8—1461no—
89C22×C8—1461no—
90C22×C8—1461no—
91C4⋊Q8—732no—
92C4⋊Q8—732no—
93C4⋊Q8—1461no—
94C4⋊Q8—1461no—
95C2×C4⋊C4—731no—
96C2×C4⋊C4—1461no—
97C2×C4⋊C4#6440811yescharacteristic
98C2×C42—731no—
99C4⋊C8—732no—
100C4⋊C8—732no—
101C4⋊C8—1461no—
102C4⋊C8—1461no—
103C2×Q8—2922no—
104C2×Q8—2922no—
105C2×Q8—1462no—
106C2×Q8—1462no—
107C22×C4—21no—
108C22×C4—731no—
109C22×C4—731no—
110C22×C4—1461no—
111C22×C4C2×#6440811yescharacteristic
112C2×C8—2922no—
113C2×C8—2922no—
114C2×C8—1462no—
115C2×C8—1462no—
116C4⋊C4—21no—
117C4⋊C4—732no—
118C4⋊C4—1462no—
119C4⋊C4—1462no—
120C4⋊C4—1461no—
121C4⋊C4C2×#6440812yes—
122C42—731no—
123C42—731no—
124C42—731no—
125C42—731no—
126C23C22⋊#6440811yescharacteristic
127Q8—2922no—
128Q8—2924no—
129Q8—2922no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—42no—
133C2×C4—2922no—
134C2×C4—732no—
135C2×C4—732no—
136C2×C4—732no—
137C2×C4—732no—
138C2×C4—731no—
139C2×C4—731no—
140C2×C4—731no—
141C2×C4—731no—
142C2×C4—1462no—
143C2×C4C22⋊#6440811yescharacteristic
144C2×C4C22×#6440811yescharacteristic
145C8—2922no—
146C8—2922no—
147C22#1455665212yes—
148C22#1455665312yes—
149C22#1455665412yes—
150C22C2×C22⋊#6440811yescharacteristic
151C4—21no—
152C4—21no—
153C4—42no—
154C4—2922no—
155C4—731no—
156C4—732no—
157C4—731no—
158C4—731no—
159C4—732no—
160C4—731no—
161C2#1798944614yesdirect product factor
162C2C2×#1455665211yescharacteristic
163C2C2×#1455665311yescharacteristic
164C2C2×#1455665411yescharacteristic
subgroupG/H
centerC23C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC2×C4⋊C4×C73C4
socleC23×C73C22⋊C4
hypercenterC2×C4⋊C4#64408
hypocenterC73C2×#332
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #17989446C2direct (N × H)
78. C2×C73#332semidirect
83. C73C2×#332semidirect
161. C2#17989446direct (N × H)