Finite Group Databasebeta

← #22625826

Subgroups — #22625826

Order 9344.

504 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 74 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
1#17989528C212yesmaximal
2#17989465C214yesmaximal, complemented
3C22×#11924005C211yesmaximal, characteristic
4C2×C22⋊#64408—22no—
5C2×C22⋊#64408—22no—
6C2×C22⋊#64408C2214yes—
7C24×D73C2211yescharacteristic
8C23×Dic73C411yescharacteristic, complemented
9C2×#11924005—22no—
10C2×#11924005—22no—
11C2×#11924005C412yescomplemented
12C2×#11924005C2212yes—
13C23×C4×C73C411yescharacteristic, complemented
14C22×#64408—24no—
15C22⋊#64408—28no—
16C22⋊#64408—44no—
17C22⋊#64408—44no—
18C23×D73—24no—
19C23×D73—42no—
20C23×D73—42no—
21C23×D73C2×C411yescharacteristic
22C23×D73D412yes—
23C23×D73D412yes—
24C23×D73C2311yescharacteristic
25C22×Dic73—21no—
26C22×Dic73—21no—
27C22×Dic73—42no—
28C22×Dic73C2×C412yes—
29#11924005—24no—
30#11924005—24no—
31C24×C73C2×C411yescharacteristic
32C22×C4×C73—21no—
33C22×C4×C73—21no—
34C22×C4×C73—42no—
35C22×C4×C73C2×C412yes—
36C23×C73—22no—
37C23×C73—22no—
38C23×C73—22no—
39C23×C73C22⋊C411yescharacteristic
40C23×C73C22⋊C411yescharacteristic
41C23×C73C22×C411yescharacteristic
42C22×D73—24no—
43C22×D73—24no—
44C22×D73—22no—
45C22×D73—24no—
46C22×D73—24no—
47C22×D73—41no—
48C22×D73—41no—
49C22×D73—42no—
50C22×D73—42no—
51C22×D73—41no—
52C22×D73—41no—
53C22×D73—416no—
54C22×D73C22⋊C412yes—
55C22×D73C2×D412yes—
56C22×D73#4114yes—
57C2×#64408—44no—
58C2×#64408—44no—
59C2×#64408—44no—
60C2×C4×C73—22no—
61C2×C4×C73—42no—
62C2×C4×C73—42no—
63C2×C4×C73—42no—
64C2×Dic73—22no—
65C2×Dic73—42no—
66C2×Dic73—42no—
67C2×Dic73—42no—
68C22×C73—28no—
69C22×C73—21no—
70C22×C73—21no—
71C22×C73—21no—
72C22×C73—21no—
73C22×C73—21no—
74C22×C73—21no—
75C22×C73#9912yes—
76C22×C73#9912yes—
77C22×C73C2×C22⋊C411yescharacteristic
78C22×C73#11712yes—
79C2×D73—22no—
80C2×D73—22no—
81C2×D73—22no—
82C2×D73—22no—
83C2×D73—22no—
84C2×D73—44no—
85C2×D73—48no—
86C2×D73—48no—
87C2×D73—44no—
88C2×D73#12314yes—
89#64408—84no—
90C4×C73—42no—
91Dic73—42no—
92C2×C73—22no—
93C2×C73—22no—
94C2×C73—22no—
95C2×C73#38111yescharacteristic
96C2×C73C2×#9911yescharacteristic
97C2×C73C2×#9911yescharacteristic
98D73—24no—
99D73—42no—
100#1819—731nomaximal, Sylow
101C73#181911yescharacteristic, complemented, Sylow
102C22×C22⋊C4—731no—
103#379—732no—
104#342—734no—
105C25—731no—
106C23×C4—731no—
107C23×C4#6440811yescharacteristic, complemented
108C2×C22⋊C4—732no—
109C2×C22⋊C4—732no—
110C2×C22⋊C4—734no—
111C2×C22⋊C4—1462no—
112C2×C22⋊C4—1462no—
113C2×C22⋊C4—1462no—
114C2×C22⋊C4—1462no—
115C24—2922no—
116C24—2922no—
117C24—731no—
118C24—731no—
119C24—732no—
120C24—732no—
121C24—1464no—
122C24C2×#6440811yescharacteristic
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—42no—
126C22×C4—2922no—
127C22×C4—732no—
128C22×C4—1464no—
129C22×C4—1461no—
130C22×C4—1461no—
131C22×C4C2×#6440812yes—
132C22⋊C4—2924no—
133C22⋊C4—2924no—
134C22⋊C4—1464no—
135C22⋊C4—1464no—
136C22⋊C4—1468no—
137C23—22no—
138C23—22no—
139C23—22no—
140C23—29216no—
141C23—2922no—
142C23—2921no—
143C23—2921no—
144C23—2922no—
145C23—2921no—
146C23—2921no—
147C23—734no—
148C23—732no—
149C23—732no—
150C23—1464no—
151C23—1464no—
152C23—1464no—
153C23—1464no—
154C23—1462no—
155C23C22⋊#6440811yescharacteristic
156C23C22⋊#6440811yescharacteristic
157C23C22×#6440811yescharacteristic
158C2×C4—22no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—2922no—
163C2×C4—2922no—
164C2×C4—2922no—
165C2×C4—2924no—
166C2×C4—2924no—
167C2×C4—2924no—
168C2×C4—1462no—
169C22—28no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—2924no—
177C22—2928no—
178C22—2928no—
179C22—2924no—
180C22—734no—
181C22—1462no—
182C22—1462no—
183C22—1462no—
184C22—1462no—
185C22—1462no—
186C22#1455664912yes—
187C22#1455665012yes—
188C22C2×C22⋊#6440811yescharacteristic
189C22#1455667012yes—
190C4—42no—
191C4—2922no—
192C4—5844no—
193C2—22no—
194C2—22no—
195C2—22no—
196C2—2922no—
197C2—1464no—
198C2#1798953011yescharacteristic
199C2C2×#1455664911yescharacteristic
200C2C2×#1455665011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC23×C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC23×C4#64408
hypocenterC73#1819
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #17989465C2semidirect
8. C23×Dic73C4semidirect
11. C2×#11924005C4semidirect
13. C23×C4×C73C4semidirect
101. C73#1819semidirect
107. C23×C4#64408semidirect