Finite Group Databasebeta

← C2×#17989431 #22625158

Subgroups — C2×#17989431 #22625158

Order 9344.

456 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 98 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×C22⋊#10596833C212yesmaximal, complemented
2#17989431C214yesmaximal, direct product factor
3C22×#11924005C211yesmaximal, characteristic
4C22×#10596833—22no—
5C22⋊#10596833—22no—
6C22⋊#10596833C2214yescomplemented
7C24×D73C411yescharacteristic
8C23×Dic73C2211yescharacteristic
9C2×#11924005—22no—
10C2×#11924005—22no—
11C2×#11924005C412yes—
12C2×#11924005C2212yes—
13C23×C4×C73C411yescharacteristic
14C2×#10596833—24no—
15C2×#10596833—44no—
16C23×D73—21no—
17C23×D73—21no—
18C23×D73—22no—
19C23×D73—42no—
20C23×D73—42no—
21C23×D73C814yescomplemented
22C23×D73C2×C412yes—
23C22×Dic73—42no—
24C22×Dic73C2×C411yescharacteristic
25C22×Dic73D412yes—
26C22×Dic73D412yes—
27C22×Dic73C2311yescharacteristic
28#11924005—24no—
29#11924005—24no—
30C24×C73C2×C411yescharacteristic
31C22×C4×C73—21no—
32C22×C4×C73—21no—
33C22×C4×C73—42no—
34C22×C4×C73C2×C412yes—
35C23×C73—22no—
36C23×C73—22no—
37C23×C73C22⋊C411yescharacteristic
38C23×C73C22⋊C411yescharacteristic
39C23×C73C2×C812yes—
40C23×C73M1612yes—
41C23×C73C22×C411yescharacteristic
42C22×D73—24no—
43C22×D73—24no—
44C22×D73—22no—
45C22×D73—22no—
46C22×D73—48no—
47C22×D73—42no—
48C22×D73—42no—
49C22×D73—42no—
50C22×D73—42no—
51C22×D73—48no—
52C22×D73—42no—
53C22×D73—42no—
54C22×D73C2×C814yescomplemented
55C2×C4×C73—22no—
56C2×C4×C73—42no—
57C2×C4×C73—42no—
58C2×C4×C73—42no—
59C2×Dic73—24no—
60C2×Dic73—41no—
61C2×Dic73—42no—
62C2×Dic73—41no—
63C2×Dic73C22⋊C412yes—
64C2×Dic73C2×D412yes—
65#10596833—44no—
66C22×C73—24no—
67C22×C73—24no—
68C22×C73—21no—
69C22×C73—21no—
70C22×C73—21no—
71C22×C73—21no—
72C22×C73C22⋊C812yes—
73C22×C73C22⋊C812yes—
74C22×C73#9912yes—
75C22×C73#10012yes—
76C22×C73C2×C22⋊C411yescharacteristic
77C22×C73C22×C811yescharacteristic
78C22×C73C2×M1611yescharacteristic
79C2×D73—24no—
80C2×D73—48no—
81C2×D73—44no—
82C2×D73—48no—
83C2×D73—42no—
84C2×D73—42no—
85C2×D73—44no—
86C4×C73—42no—
87Dic73—22no—
88Dic73—22no—
89C2×C73—22no—
90C2×C73—21no—
91C2×C73—21no—
92C2×C73#32314yescomplemented
93C2×C73C2×C22⋊C811yescharacteristic
94C2×C73C2×#9911yescharacteristic
95C2×C73C2×#10011yescharacteristic
96D73—44no—
97C2×#323—731nomaximal, Sylow
98C73C2×#32311yescharacteristic, complemented, Sylow
99C22×C22⋊C4—731no—
100C2×C22⋊C8—732no—
101#323—734no—
102C25—731no—
103C23×C4—731no—
104C23×C4#6440811yescharacteristic
105C22×C8—1462no—
106C2×C22⋊C4—732no—
107C2×C22⋊C4—732no—
108C2×C22⋊C4—1462no—
109C2×C22⋊C4—1462no—
110C22⋊C8—734no—
111C22⋊C8—1462no—
112C24—2922no—
113C24—2922no—
114C24—734no—
115C24—732no—
116C24—1461no—
117C24—1461no—
118C24—1462no—
119C24C2×#6440811yescharacteristic
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—42no—
123C22×C4—2922no—
124C22×C4—732no—
125C22×C4—731no—
126C22×C4—731no—
127C22×C4—732no—
128C22×C4C2×#6440812yes—
129C2×C8—2924no—
130C2×C8—1464no—
131C22⋊C4—1464no—
132C22⋊C4—1464no—
133C23—22no—
134C23—22no—
135C23—2928no—
136C23—2922no—
137C23—2922no—
138C23—2928no—
139C23—2922no—
140C23—2922no—
141C23—2922no—
142C23—2922no—
143C23—734no—
144C23—1462no—
145C23—1464no—
146C23—1464no—
147C23—1462no—
148C23C22⋊#6440811yescharacteristic
149C23C22⋊#6440811yescharacteristic
150C23#1192403612yes—
151C23#1192403812yes—
152C23C22×#6440811yescharacteristic
153C2×C4—22no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—2921no—
158C2×C4—2922no—
159C2×C4—2921no—
160C2×C4—732no—
161C2×C4—732no—
162C2×C4—1464no—
163C8—2924no—
164C22—24no—
165C22—24no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—2924no—
171C22—2924no—
172C22—2928no—
173C22—2928no—
174C22—2922no—
175C22—2922no—
176C22—1464no—
177C22#1455664812yes—
178C22#1455664812yes—
179C22#1455665012yes—
180C22#1455665112yes—
181C22C2×C22⋊#6440811yescharacteristic
182C22C2×#1192403611yescharacteristic
183C22C2×#1192403811yescharacteristic
184C4—42no—
185C4—1462no—
186C4—1462no—
187C2—21no—
188C2—21no—
189C2—22no—
190C2—2924no—
191C2#1798943114yesdirect product factor
192C2C2×#1455664811yescharacteristic
193C2C2×#1455665011yescharacteristic
194C2C2×#1455665111yescharacteristic
subgroupG/H
centerC23C22⋊#64408
commutatorC22×C73C22×C8
FrattiniC23C22×#64408
FittingC23×C4×C73C4
socleC23×C73C22⋊C4
hypercenterC23×C4#64408
hypocenterC73C2×#323
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
1. C2×C22⋊#10596833C2semidirect
2. #17989431C2direct (N × H)
6. C22⋊#10596833C22semidirect
21. C23×D73C8semidirect
54. C22×D73C2×C8semidirect
92. C2×C73#323semidirect
98. C73C2×#323semidirect
191. C2#17989431direct (N × H)