Finite Group Databasebeta

← C2×#17989467 #22625633

Subgroups — C2×#17989467 #22625633

Order 9344.

432 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C22×#11924037C212yesmaximal
2#17989467C214yesmaximal, direct product factor
3C22×#11924007C211yesmaximal, characteristic
4C2×#11924037—24no—
5C2×#11924037—22no—
6C2×#11924037C418yescomplemented
7C2×#11924037C2214yes—
8C22×#10596833—22no—
9C23×Dic73C411yescharacteristic
10C23×Dic73C2211yescharacteristic
11C2×#11924007—22no—
12C2×#11924007—22no—
13C2×#11924007C412yes—
14C2×#11924007C2212yes—
15C23×C4×C73C411yescharacteristic
16#11924037—28no—
17#11924037—24no—
18#11924037C2×C418yescomplemented
19C2×#10596833—28no—
20C2×#10596833—24no—
21C22×Dic73—21no—
22C22×Dic73—21no—
23C22×Dic73—42no—
24C22×Dic73C2×C412yes—
25C22×Dic73C2×C411yescharacteristic
26C22×Dic73C2×C414yes—
27C22×Dic73D412yes—
28C22×Dic73D412yes—
29C22×Dic73D412yes—
30C22×Dic73Q812yes—
31C22×Dic73C2311yescharacteristic
32#11924007—24no—
33#11924007—24no—
34C24×C73C2×C411yescharacteristic
35C22×C4×C73—21no—
36C22×C4×C73—21no—
37C22×C4×C73—42no—
38C22×C4×C73C2×C412yes—
39C23×C73—22no—
40C23×C73—22no—
41C23×C73C4212yes—
42C23×C73C22⋊C411yescharacteristic
43C23×C73C22⋊C411yescharacteristic
44C23×C73C4⋊C412yes—
45C23×C73C22×C411yescharacteristic
46C2×C4×C73—22no—
47C2×C4×C73—42no—
48C2×C4×C73—42no—
49C2×C4×C73—42no—
50C2×Dic73—22no—
51C2×Dic73—42no—
52C2×Dic73—42no—
53C2×Dic73—42no—
54C2×Dic73C4212yes—
55C2×Dic73C22⋊C412yes—
56C2×Dic73C22⋊C414yes—
57C2×Dic73C22⋊C414yes—
58C2×Dic73C4⋊C412yes—
59C2×Dic73C4⋊C414yes—
60C2×Dic73C4⋊C414yes—
61C2×Dic73C22×C412yes—
62C2×Dic73C2×D411yescharacteristic
63C2×Dic73C2×D412yes—
64C2×Dic73C2×Q811yescharacteristic
65#10596833—28no—
66C22×C73—24no—
67C22×C73—24no—
68C22×C73—21no—
69C22×C73—21no—
70C22×C73—21no—
71C22×C73—21no—
72C22×C73#9512yes—
73C22×C73#9512yes—
74C22×C73#10012yes—
75C22×C73#10112yes—
76C22×C73C2×C4211yescharacteristic
77C22×C73C2×C22⋊C411yescharacteristic
78C22×C73C2×C4⋊C411yescharacteristic
79C4×C73—42no—
80Dic73—42no—
81Dic73#9514yes—
82Dic73C2×C22⋊C412yes—
83Dic73C2×C4⋊C412yes—
84C2×C73—22no—
85C2×C73—21no—
86C2×C73—21no—
87C2×C73#34314yescomplemented
88C2×C73C2×#9511yescharacteristic
89C2×C73C2×#10011yescharacteristic
90C2×C73C2×#10111yescharacteristic
91C2×#343—731nomaximal, Sylow
92C73C2×#34311yescharacteristic, complemented, Sylow
93C22×M16—732no—
94C22×C4⋊C4—731no—
95#343—734no—
96C23×C4—731no—
97C23×C4—731no—
98C23×C4#6440811yescharacteristic
99C2×M16—738no—
100C2×M16—734no—
101C2×M16—1462no—
102C2×M16—1464no—
103C22×C8—1462no—
104C2×C4⋊C4—732no—
105C2×C4⋊C4—732no—
106C2×C4⋊C4—1462no—
107C2×C4⋊C4—1462no—
108C24C2×#6440811yescharacteristic
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—42no—
112C22×C4—2922no—
113C22×C4—732no—
114C22×C4—734no—
115C22×C4—732no—
116C22×C4—732no—
117C22×C4—732no—
118C22×C4—732no—
119C22×C4—731no—
120C22×C4—731no—
121C22×C4—1461no—
122C22×C4—1461no—
123C22×C4C2×#6440812yes—
124M16—738no—
125M16—1468no—
126M16—1464no—
127C2×C8—1468no—
128C2×C8—1464no—
129C4⋊C4—1464no—
130C4⋊C4—1464no—
131C23—22no—
132C23—22no—
133C23C4×#6440812yes—
134C23C22⋊#6440811yescharacteristic
135C23C22⋊#6440811yescharacteristic
136C23C4⋊#6440812yes—
137C23C22×#6440811yescharacteristic
138C2×C4—22no—
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—2922no—
143C2×C4—2922no—
144C2×C4—2922no—
145C2×C4—734no—
146C2×C4—734no—
147C2×C4—734no—
148C2×C4—734no—
149C2×C4—732no—
150C2×C4—732no—
151C2×C4—732no—
152C2×C4—732no—
153C2×C4—731no—
154C2×C4—732no—
155C2×C4—731no—
156C2×C4—1462no—
157C8—1468no—
158C22—24no—
159C22—24no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—21no—
164C22(C2×#64408)⋊C412yes—
165C22(C2×#64408)⋊C412yes—
166C22#1455665112yes—
167C22#1455665212yes—
168C22C2×C4×#6440811yescharacteristic
169C22C2×C22⋊#6440811yescharacteristic
170C22C2×C4⋊#6440811yescharacteristic
171C4—42no—
172C4—2922no—
173C4—732no—
174C4—734no—
175C4—732no—
176C2—22no—
177C2—21no—
178C2—21no—
179C2#1798946714yesdirect product factor
180C2C2×(C2×#64408)⋊C411yescharacteristic
181C2C2×#1455665111yescharacteristic
182C2C2×#1455665211yescharacteristic
subgroupG/H
centerC23C22⋊#64408
commutatorC22×C73C2×C42
FrattiniC23C22×#64408
FittingC23×C4×C73C4
socleC23×C73C22⋊C4
hypercenterC23×C4#64408
hypocenterC73C2×#343
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #17989467C2direct (N × H)
6. C2×#11924037C4semidirect
18. #11924037C2×C4semidirect
87. C2×C73#343semidirect
92. C73C2×#343semidirect
179. C2#17989467direct (N × H)