Finite Group Databasebeta

← #34000740

Subgroups — #34000740

Order 18688.

374 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 58 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#22625179C212yesmaximal
2#22608198C211yesmaximal, characteristic
3#17989557—22no—
4#17989432—22no—
5#17989432C414yescomplemented
6C22×C4⋊Dic73C2211yescharacteristic
7C2×#14556498—22no—
8C2×#14556498C411yescharacteristic
9C2×#95×C73C411yescharacteristic
10C2×#11924037—42no—
11C22⋊#10596833—24no—
12C22⋊#10596833—42no—
13C23×Dic73—21no—
14C23×Dic73D412yes—
15C2×C4⋊Dic73—41no—
16C2×C4⋊Dic73—41no—
17C2×C4⋊Dic73C2×C412yes—
18C2×C4⋊Dic73D411yescharacteristic
19C2×C4⋊Dic73Q811yescharacteristic
20#14556498—44no—
21#14556498—41no—
22C23×C4×C73—21no—
23C23×C4×C73C2×C411yescharacteristic
24#95×C73—41no—
25#11924037—82no—
26#11924037—82no—
27C2×#10596833—44no—
28C22×Dic73—22no—
29C22×Dic73—22no—
30C22×Dic73—22no—
31C22×Dic73—42no—
32C22×Dic73—42no—
33C22×Dic73—42no—
34C22×Dic73—42no—
35C22×Dic73—41no—
36C22×Dic73—41no—
37C22×Dic73C22⋊C412yes—
38C22×Dic73C4⋊C412yes—
39C4⋊Dic73—42no—
40C4⋊Dic73—41no—
41C4⋊Dic73—41no—
42C24×C73C22⋊C411yescharacteristic
43C22×C4×C73—21no—
44C22×C4×C73—21no—
45C22×C4×C73—22no—
46C22×C4×C73—42no—
47C22×C4×C73—42no—
48C22×C4×C73—41no—
49C22×C4×C73—42no—
50C22×C4×C73—41no—
51C22×C4×C73C4211yescharacteristic
52C22×C4×C73C4⋊C411yescharacteristic
53C23×C73—22no—
54C23×C73—21no—
55C23×C73—21no—
56C23×C73—21no—
57C23×C73—21no—
58C23×C73#9511yescharacteristic
59C23×C73#9911yescharacteristic
60C23×C73#9911yescharacteristic
61C2×C4×C73—21no—
62C2×C4×C73—21no—
63C2×C4×C73—22no—
64C2×C4×C73—22no—
65C2×C4×C73—42no—
66C2×C4×C73—42no—
67C2×C4×C73—44no—
68C2×C4×C73—42no—
69C2×C4×C73—82no—
70C2×C4×C73—81no—
71C2×C4×C73—81no—
72C2×Dic73—22no—
73C2×Dic73—22no—
74C2×Dic73—42no—
75C2×Dic73—42no—
76C2×Dic73—42no—
77C2×Dic73—42no—
78C2×Dic73—44no—
79C2×Dic73—42no—
80C2×Dic73—82no—
81C2×Dic73—82no—
82C2×Dic73—81no—
83C2×Dic73—81no—
84#10596833—84no—
85C22×C73—22no—
86C22×C73—22no—
87C22×C73—22no—
88C22×C73—22no—
89C22×C73—21no—
90C22×C73—21no—
91C22×C73—21no—
92C22×C73—21no—
93C22×C73—21no—
94C22×C73—21no—
95C22×C73#34211yescharacteristic
96C22×C73#34412yes—
97C22×C73#35311yescharacteristic
98C22×C73#35411yescharacteristic
99C22×C73#35511yescharacteristic
100C22×C73#35611yescharacteristic
101C4×C73—41no—
102C4×C73—41no—
103C4×C73—82no—
104Dic73—42no—
105Dic73—42no—
106Dic73—82no—
107#7326—731nomaximal, Sylow
108C2×C73—21no—
109C2×C73—21no—
110C2×C73—22no—
111C2×C73—21no—
112C2×C73—21no—
113C2×C73#130611yescharacteristic
114C2×C73#139311yescharacteristic
115C2×C73#139411yescharacteristic
116#1463—732no—
117#1445—731no—
118C73#732611yescharacteristic, complemented, Sylow
119C22×C4⋊C4—731no—
120#407—1462no—
121C2×#95—731no—
122C2×#95—1462no—
123C2×#95#6440811yescharacteristic
124#324—734no—
125#324—1462no—
126C23×C4—21no—
127C23×C4—732no—
128C23×C4—1461no—
129C23×C4C2×#6440811yescharacteristic
130C2×M16—2922no—
131C2×C4⋊C4—2921no—
132C2×C4⋊C4—2921no—
133C2×C4⋊C4—732no—
134C2×C4⋊C4—731no—
135C2×C4⋊C4—731no—
136C22⋊C8—2922no—
137C22⋊C8—1464no—
138#95—41no—
139#95—2921no—
140#95—2924no—
141C24C22⋊#6440811yescharacteristic
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—22no—
145C22×C4—42no—
146C22×C4—42no—
147C22×C4—41no—
148C22×C4—42no—
149C22×C4—41no—
150C22×C4—2922no—
151C22×C4—2922no—
152C22×C4—2922no—
153C22×C4—2922no—
154C22×C4—2921no—
155C22×C4—2921no—
156C22×C4—732no—
157C22×C4—732no—
158C22×C4—1462no—
159C22×C4—1462no—
160C22×C4—1462no—
161C22×C4C4×#6440811yescharacteristic
162C22×C4C4⋊#6440811yescharacteristic
163M16—5842no—
164M16—5842no—
165C2×C8—2924no—
166C4⋊C4—2922no—
167C4⋊C4—2921no—
168C4⋊C4—2921no—
169C23—22no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23(C2×#64408)⋊C411yescharacteristic
175C23#1455664911yescharacteristic
176C23#1455665011yescharacteristic
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—44no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4—2922no—
189C2×C4—2922no—
190C2×C4—2922no—
191C2×C4—2922no—
192C2×C4—2924no—
193C2×C4—2922no—
194C2×C4—5842no—
195C2×C4—5842no—
196C2×C4—5841no—
197C2×C4—5841no—
198C2×C4—1462no—
199C2×C4—1462no—
200C8—5844no—
201C22—22no—
202C22—22no—
203C22—22no—
204C22—22no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#1798946511yescharacteristic
212C22#1798946812yes—
213C22#1798949211yescharacteristic
214C22#1798949411yescharacteristic
215C22#1798949511yescharacteristic
216C22#1798949711yescharacteristic
217C4—41no—
218C4—41no—
219C4—82no—
220C4—2922no—
221C4—2922no—
222C4—5842no—
223C2—21no—
224C2—21no—
225C2—22no—
226C2—21no—
227C2—21no—
228C2#2262483411yescharacteristic
229C2#2262502511yescharacteristic
230C2#2262502911yescharacteristic
subgroupG/H
centerC22#17989465
commutatorC22×C4×C73C42
FrattiniC23×C4C2×#64408
FittingC2×#95×C73C4
socleC22×C73#342
prime radicalC24×C73C22⋊C4
cosocleC22×C4⋊Dic73C22
hypercenterC2×#95#64408
hypocenterC73#7326
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
5. #17989432C4semidirect
118. C73#7326semidirect

Maximal subgroups

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

subgroupindex
#226251792
#226081982
#732673