Finite Group Databasebeta

← #34004114

Subgroups — #34004114

Order 18688.

810 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 132 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#22625822C212yesmaximal
2C2×#17989432C214yesmaximal
3C22×#14556582C211yesmaximal, characteristic
4C2×C22⋊#10596833C2214yes—
5#17989453—24no—
6#17989432—28no—
7C2×#14556582—28no—
8C2×#14556582—24no—
9C22×C4⋊Dic73C411yescharacteristic
10C22×C4⋊Dic73C2212yes—
11C22×#11924007C412yes—
12C22×C4×Dic73C2211yescharacteristic
13C22×C4⋊C4×C73C411yescharacteristic
14C22×#10596833—24no—
15C22⋊#10596833—28no—
16C23×Dic73C2×C411yescharacteristic
17C23×Dic73C2×C412yes—
18C23×Dic73C2311yescharacteristic
19#14556582—232no—
20C2×C4⋊Dic73—24no—
21C2×C4⋊Dic73—24no—
22C2×C4⋊Dic73—24no—
23C2×C4⋊Dic73—22no—
24C2×C4⋊Dic73D418yes—
25C2×#11924007—24no—
26C2×#11924007—24no—
27C2×#11924007—24no—
28C2×C4×Dic73—24no—
29C2×C4×Dic73D414yes—
30C23×C4×C73C2×C412yes—
31C23×C4×C73C2×C411yescharacteristic
32C2×C4⋊C4×C73—24no—
33C2×C4⋊C4×C73—22no—
34C2×#10596833—48no—
35C2×#10596833—44no—
36C22×Dic73—22no—
37C22×Dic73—22no—
38C22×Dic73—22no—
39C22×Dic73—24no—
40C22×Dic73—42no—
41C22×Dic73—44no—
42C22×Dic73C22⋊C412yes—
43C22×Dic73C22⋊C414yes—
44C22×Dic73C2×D412yes—
45C22×Dic73C2×D414yes—
46C4⋊Dic73—28no—
47C4⋊Dic73—216no—
48#11924007—216no—
49C4×Dic73—28no—
50C24×C73C22×C411yescharacteristic
51C22×C4×C73—22no—
52C22×C4×C73—24no—
53C22×C4×C73—22no—
54C22×C4×C73—22no—
55C22×C4×C73—28no—
56C22×C4×C73C22⋊C414yes—
57C22×C4×C73C22⋊C412yes—
58C4⋊C4×C73—28no—
59C23×C73—22no—
60C23×C73—22no—
61C23×C73C2×C22⋊C412yes—
62C23×C73C2×C22⋊C411yescharacteristic
63C23×C73#13114yes—
64C2×C4×C73—28no—
65C2×C4×C73—22no—
66C2×C4×C73—22no—
67C2×C4×C73—24no—
68C2×C4×C73—28no—
69C2×C4×C73—44no—
70C2×C4×C73—44no—
71C2×C4×C73#10114yes—
72C2×Dic73—24no—
73C2×Dic73—22no—
74C2×Dic73—24no—
75C2×Dic73—24no—
76C2×Dic73—44no—
77C2×Dic73—44no—
78C2×Dic73—44no—
79C2×Dic73—44no—
80C2×Dic73—44no—
81C2×Dic73#12014yes—
82#10596833—84no—
83C22×C73—28no—
84C22×C73—22no—
85C22×C73—22no—
86C22×C73#37911yescharacteristic
87C22×C73#40814yes—
88C22×C73#40812yes—
89C22×C73#41012yes—
90C22×C73C2×#10112yes—
91C4×C73—24no—
92C4×C73—44no—
93Dic73—24no—
94Dic73—42no—
95Dic73—44no—
96#8306—731nomaximal, Sylow
97C2×C73—24no—
98C2×C73#147014yes—
99C2×C73#178011yescharacteristic
100C2×C73#178211yescharacteristic
101C2×C73#178411yescharacteristic
102C22×#125—731no—
103#1817—732no—
104C2×#324—734no—
105C73#830611yescharacteristic, complemented, Sylow
106C2×#125—1464no—
107C2×#125—1468no—
108C22×C4⋊C4—732no—
109C22×C4⋊C4—732no—
110C22×C4⋊C4—731no—
111C22×C4⋊C4#6440811yescharacteristic
112C22×C42—731no—
113C2×C22⋊C8—734no—
114#336—1464no—
115#324—1468no—
116C23×C4—731no—
117C23×C4—732no—
118C23×C4—731no—
119C23×C4C2×#6440812yes—
120C23×C4C2×#6440811yescharacteristic
121C22×C8—1464no—
122#125—14632no—
123C2×C4⋊C4—24no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—738no—
126C2×C4⋊C4—1464no—
127C2×C4⋊C4—1464no—
128C2×C4⋊C4—1464no—
129C2×C4⋊C4—1464no—
130C2×C4⋊C4—1464no—
131C2×C4⋊C4—1464no—
132C2×C4⋊C4—1462no—
133C2×C42—734no—
134C2×C42—1464no—
135C22⋊C8—1468no—
136C24C22×#6440811yescharacteristic
137C22×C4—22no—
138C22×C4—24no—
139C22×C4—28no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—2924no—
143C22×C4—2922no—
144C22×C4—734no—
145C22×C4—734no—
146C22×C4—732no—
147C22×C4—732no—
148C22×C4—1464no—
149C22×C4—1462no—
150C22×C4—1462no—
151C22×C4—1462no—
152C22×C4C22⋊#6440814yes—
153C22×C4C22⋊#6440812yes—
154C2×C8—2924no—
155C2×C8—2928no—
156C4⋊C4—28no—
157C4⋊C4—14616no—
158C4⋊C4—14616no—
159C4⋊C4—1468no—
160C42—1468no—
161C23—22no—
162C23—22no—
163C23C2×C22⋊#6440812yes—
164C23C2×C22⋊#6440811yescharacteristic
165C23#1455667814yes—
166C2×C4—28no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—28no—
171C2×C4—44no—
172C2×C4—44no—
173C2×C4—2924no—
174C2×C4—2924no—
175C2×C4—2924no—
176C2×C4—2924no—
177C2×C4—2924no—
178C2×C4—734no—
179C2×C4—1462no—
180C2×C4—1464no—
181C2×C4—1464no—
182C2×C4—1464no—
183C2×C4#1455665214yes—
184C8—5844no—
185C22—28no—
186C22—22no—
187C22—22no—
188C22#1798952811yescharacteristic
189C22#1798956014yes—
190C22#1798956112yes—
191C22#1798956812yes—
192C22C2×#1455665212yes—
193C4—24no—
194C4—44no—
195C4—2922no—
196C4—2924no—
197C4—1464no—
198C2—24no—
199C2#2262520414yes—
200C2#2262575511yescharacteristic
201C2#2262576211yescharacteristic
202C2#2262576511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutator, prime radicalC24×C73C22×C4
FrattiniC24C22×#64408
FittingC22×C4⋊C4×C73C4
socleC23×C73C2×C22⋊C4
cosocleC23×Dic73C23
hypercenterC22×C4⋊C4#64408
hypocenterC73#8306
LCSG ▷ C24×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
105. C73#8306semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226258222
C2×#179894322
C22×#145565822
#830673