Finite Group Databasebeta

← #34005239

Subgroups — #34005239

Order 18688.

554 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 112 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#22625657C212yesmaximal
2#22624807C214yesmaximal, complemented
3C2×#17988452C211yesmaximal, characteristic
4C2×C22⋊#10596833—22no—
5C2×#14556646C2214yes—
6#17989453—22no—
7C22×C4⋊Dic73C411yescharacteristic
8C22×C4×Dic73C2211yescharacteristic
9#17988452—22no—
10#17988452C412yes—
11#17988452C2212yes—
12C2×#14556498—22no—
13C22×C4⋊C4×C73C411yescharacteristic
14C22×#10596833—24no—
15C22⋊#10596833—28no—
16#14556646—28no—
17C23×Dic73—21no—
18C23×Dic73D412yes—
19C2×C4⋊Dic73—21no—
20C2×C4⋊Dic73—42no—
21C2×C4⋊Dic73C2×C412yes—
22C2×C4×Dic73—24no—
23C2×C4×Dic73C2×C411yescharacteristic
24C2×C4×Dic73D412yes—
25C2×C4×Dic73C2311yescharacteristic
26#14556498—24no—
27#14556498—24no—
28C23×C4×C73—21no—
29C23×C4×C73C2×C411yescharacteristic
30C2×C4⋊C4×C73—21no—
31C2×C4⋊C4×C73—42no—
32C2×C4⋊C4×C73C2×C412yes—
33C2×#10596833—28no—
34C2×#10596833—44no—
35C2×#10596833—44no—
36C22×Dic73—24no—
37C22×Dic73—24no—
38C22×Dic73—22no—
39C22×Dic73—42no—
40C22×Dic73—42no—
41C22×Dic73—44no—
42C22×Dic73C22⋊C412yes—
43C22×Dic73C2×D412yes—
44C4⋊Dic73—42no—
45C4⋊Dic73—42no—
46C4×Dic73—22no—
47C4×Dic73—24no—
48C4×Dic73#4114yes—
49C24×C73C22⋊C411yescharacteristic
50C22×C4×C73—22no—
51C22×C4×C73—22no—
52C22×C4×C73—22no—
53C22×C4×C73—22no—
54C22×C4×C73—44no—
55C22×C4×C73—42no—
56C22×C4×C73C22⋊C411yescharacteristic
57C22×C4×C73C22×C411yescharacteristic
58C4⋊C4×C73—42no—
59C4⋊C4×C73—42no—
60C23×C73—21no—
61C23×C73—21no—
62C23×C73—22no—
63C23×C73#10012yes—
64C23×C73#10414yes—
65C23×C73C2×C22⋊C411yescharacteristic
66C2×C4×C73—28no—
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—21no—
70C2×C4×C73—21no—
71C2×C4×C73—42no—
72C2×C4×C73—44no—
73C2×C4×C73—84no—
74C2×C4×C73#10112yes—
75C2×C4×C73#11712yes—
76C2×Dic73—22no—
77C2×Dic73—22no—
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73—48no—
82C2×Dic73—42no—
83C2×Dic73—44no—
84C2×Dic73—84no—
85C2×Dic73#12314yes—
86#10596833—48no—
87C22×C73—22no—
88C22×C73—24no—
89C22×C73—24no—
90C22×C73—22no—
91C22×C73#32914yes—
92C22×C73#38111yescharacteristic
93C22×C73C2×#10011yescharacteristic
94C22×C73C2×#10111yescharacteristic
95C22×C73C2×#10412yes—
96C22×C73#42112yes—
97C4×C73—22no—
98C4×C73—22no—
99C4×C73—82no—
100Dic73—24no—
101Dic73—42no—
102Dic73—82no—
103#8718—731nomaximal, Sylow
104C2×C73—24no—
105C2×C73C2×#32911yescharacteristic
106C2×C73#152812yes—
107C2×C73#153311yescharacteristic
108C2×C73#182111yescharacteristic
109C2×C73#182612yes—
110C2×#382—731no—
111#1749—732no—
112#1295—734no—
113C73#871811yescharacteristic, complemented, Sylow
114C22×C4⋊C4—731no—
115C22×C4⋊C4#6440811yescharacteristic
116C22×C42—731no—
117C2×C22⋊C8—1462no—
118C2×#97—734no—
119#382—732no—
120#382—732no—
121#382—1462no—
122C2×#95—1462no—
123#336—1462no—
124C23×C4—21no—
125C23×C4—732no—
126C23×C4—1461no—
127C23×C4C2×#6440811yescharacteristic
128C22×C8—1464no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—42no—
131C2×C4⋊C4—2922no—
132C2×C4⋊C4—732no—
133C2×C4⋊C4—1461no—
134C2×C4⋊C4C2×#6440812yes—
135C2×C42—731no—
136C2×C42—732no—
137C2×C42—731no—
138C2×C42—1464no—
139C22⋊C8—1468no—
140#97—1468no—
141#95—1464no—
142#95—1464no—
143C24C22⋊#6440811yescharacteristic
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—44no—
149C22×C4—42no—
150C22×C4—2922no—
151C22×C4—2922no—
152C22×C4—2924no—
153C22×C4—732no—
154C22×C4—732no—
155C22×C4—1462no—
156C22×C4—1464no—
157C22×C4—1464no—
158C22×C4C22⋊#6440811yescharacteristic
159C22×C4C22×#6440811yescharacteristic
160C2×C8—2924no—
161C2×C8—2924no—
162C2×C8—1468no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—2922no—
166C4⋊C4—2922no—
167C42—734no—
168C42—1464no—
169C42—1462no—
170C23—21no—
171C23—21no—
172C23—22no—
173C23#1455665112yes—
174C23#1455665614yes—
175C23C2×C22⋊#6440811yescharacteristic
176C2×C4—28no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—42no—
182C2×C4—44no—
183C2×C4—84no—
184C2×C4—2928no—
185C2×C4—2922no—
186C2×C4—2924no—
187C2×C4—5844no—
188C2×C4—734no—
189C2×C4—1462no—
190C2×C4—1462no—
191C2×C4—1462no—
192C2×C4—1462no—
193C2×C4—1462no—
194C2×C4#1455665212yes—
195C2×C4#1455667012yes—
196C8—2928no—
197C22—22no—
198C22—24no—
199C22—24no—
200C22—22no—
201C22#1798944314yes—
202C22#1798953011yescharacteristic
203C22C2×#1455665111yescharacteristic
204C22C2×#1455665211yescharacteristic
205C22C2×#1455665612yes—
206C22#1798958512yes—
207C4—22no—
208C4—22no—
209C4—82no—
210C4—2922no—
211C4—5842no—
212C4—1464no—
213C2—24no—
214C2C2×#1798944311yescharacteristic
215C2#2262539512yes—
216C2#2262541011yescharacteristic
217C2#2262583011yescharacteristic
218C2#2262583812yes—
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC22×C4⋊C4×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC22×C4⋊C4#64408
hypocenterC73#8718
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #22624807C2semidirect
113. C73#8718semidirect

Maximal subgroups

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

subgroupindex
#226256572
#226248072
C2×#179884522
#871873