Finite Group Databasebeta

← #32974285

Subgroups — #32974285

Order 18688.

490 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 123 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#22609999C212yesmaximal
2#22607754C214yesmaximal, complemented
3C73×#2296C211yesmaximal, characteristic
4C2×C22⋊#10596831—22no—
5#17988342—22no—
6#17988342C2214yes—
7C2×#117×C73C411yescharacteristic
8C2×#117×C73C411yescharacteristic
9C22×C42×C73C2211yescharacteristic
10#389×C73C412yes—
11#389×C73C2212yes—
12#385×C73—22no—
13C4×C4⋊C4×C73—22no—
14C22×#10596831—24no—
15C22⋊#10596831—44no—
16C23×C4×C73C2×C411yescharacteristic
17C23×C4×C73D412yes—
18#117×C73—24no—
19#117×C73—42no—
20C2×C4⋊C4×C73—22no—
21C2×C4⋊C4×C73—22no—
22C2×C4⋊C4×C73C2×C412yes—
23C2×C4⋊C4×C73C2×C412yes—
24C2×C22⋊C4×C73—21no—
25C2×C22⋊C4×C73—21no—
26C2×C42×C73—21no—
27C2×C42×C73—21no—
28C2×C42×C73—42no—
29C2×C42×C73C2×C411yescharacteristic
30C2×C42×C73D412yes—
31C2×C42×C73C2311yescharacteristic
32#95×C73—22no—
33#95×C73—22no—
34C2×#10596831—44no—
35C2×#10596831—44no—
36C2×#10596831—44no—
37C24×C73C22⋊C411yescharacteristic
38C22×C4×C73—22no—
39C22×C4×C73—22no—
40C22×C4×C73—22no—
41C22×C4×C73—24no—
42C22×C4×C73—22no—
43C22×C4×C73—24no—
44C22×C4×C73—22no—
45C22×C4×C73—42no—
46C22×C4×C73C22⋊C412yes—
47C22×C4×C73C22⋊C411yescharacteristic
48C22×C4×C73C22×C411yescharacteristic
49C22×C4×C73C2×D412yes—
50C4⋊C4×C73—22no—
51C4⋊C4×C73—42no—
52C4⋊C4×C73—44no—
53C4⋊C4×C73—44no—
54C4⋊C4×C73M1614yes—
55C22⋊C4×C73—24no—
56C22⋊C4×C73—42no—
57C42×C73—24no—
58C42×C73—41no—
59C42×C73—42no—
60C42×C73—41no—
61C42×C73—42no—
62C23×C73—21no—
63C23×C73—21no—
64C23×C73—22no—
65C23×C73—22no—
66C23×C73#9912yes—
67C23×C73C2×C22⋊C411yescharacteristic
68C2×C4×C73—28no—
69C2×C4×C73—21no—
70C2×C4×C73—21no—
71C2×C4×C73—21no—
72C2×C4×C73—22no—
73C2×C4×C73—21no—
74C2×C4×C73—22no—
75C2×C4×C73—24no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—48no—
80C2×C4×C73—42no—
81C2×C4×C73—42no—
82C2×C4×C73—42no—
83C2×C4×C73—42no—
84C2×C4×C73—42no—
85C2×C4×C73#10112yes—
86C2×C4×C73C2×M1612yes—
87C2×C4×C73#13514yes—
88#10596831—84no—
89C22×C73—22no—
90C22×C73—24no—
91C22×C73—41no—
92C22×C73—41no—
93C22×C73—42no—
94C22×C73#40711yescharacteristic
95C22×C73C2×#9911yescharacteristic
96C22×C73C2×#10111yescharacteristic
97C22×C73#41612yes—
98C22×C73#42112yes—
99C4×C73—22no—
100C4×C73—22no—
101C4×C73—24no—
102C4×C73—44no—
103C4×C73—42no—
104C4×C73—82no—
105#7646—731nomaximal, Sylow
106C2×C73—42no—
107C2×C73#146311yescharacteristic
108C2×C73#148812yes—
109C2×C73#151612yes—
110C2×C73#153711yescharacteristic
111C2×C73#154411yescharacteristic
112#2296D7311yescharacteristic
113#1817—732no—
114#1271—734no—
115C73#764611yescharacteristic, complemented, Sylow
116C2×#117Dic7311yescharacteristic
117C2×#117Dic7311yescharacteristic
118C22×C42C2×D7311yescharacteristic
119C2×C22⋊C8—1462no—
120#389Dic7312yes—
121#389C2×D7312yes—
122#385—22no—
123C4×C4⋊C4—22no—
124#336—734no—
125#336—1462no—
126C23×C4C2×Dic7311yescharacteristic
127C23×C4C22⋊D7312yes—
128C22×C8—1464no—
129#117—24no—
130#117—42no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4C2×Dic7312yes—
134C2×C4⋊C4C2×Dic7312yes—
135C2×C22⋊C4—21no—
136C2×C22⋊C4—21no—
137C2×C42—21no—
138C2×C42—21no—
139C2×C42—42no—
140C2×C42C2×Dic7311yescharacteristic
141C2×C42C22⋊D7312yes—
142C2×C42C22×D7311yescharacteristic
143C22⋊C8—2924no—
144#95—22no—
145#95—22no—
146C24C22⋊Dic7311yescharacteristic
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—24no—
151C22×C4—22no—
152C22×C4—24no—
153C22×C4—22no—
154C22×C4—42no—
155C22×C4C22⋊Dic7312yes—
156C22×C4C22⋊Dic7311yescharacteristic
157C22×C4C22×Dic7311yescharacteristic
158C22×C4C2×C22⋊D7312yes—
159C2×C8—2924no—
160C2×C8—2924no—
161C2×C8—2924no—
162C4⋊C4—22no—
163C4⋊C4—42no—
164C4⋊C4—44no—
165C4⋊C4—44no—
166C4⋊C4#1192401214yes—
167C22⋊C4—24no—
168C22⋊C4—42no—
169C42—24no—
170C42—41no—
171C42—42no—
172C42—41no—
173C42—42no—
174C23—21no—
175C23—21no—
176C23—22no—
177C23—22no—
178C23#1455650612yes—
179C23C2×C22⋊Dic7311yescharacteristic
180C2×C4—28no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—48no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4#1455651012yes—
198C2×C4C2×#1192401212yes—
199C2×C4#1455661114yes—
200C8—5844no—
201C22—24no—
202C22—22no—
203C22—41no—
204C22—41no—
205C22—42no—
206C22#1798855111yescharacteristic
207C22C2×#1455650611yescharacteristic
208C22C2×#1455651011yescharacteristic
209C22#1798858312yes—
210C22#1798860412yes—
211C4—24no—
212C4—22no—
213C4—22no—
214C4—42no—
215C4—44no—
216C4—82no—
217C2—42no—
218C2#2260826111yescharacteristic
219C2#2260836512yes—
220C2#2260848712yes—
221C2#2260856911yescharacteristic
222C2#2260859611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic73
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#2296C2
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC2×C42×C73C23
hypercenter#2296D73
hypocenterC73#7646
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2296

Complements

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

NH ≅ G/Ntype
2. #22607754C2semidirect
115. C73#7646semidirect

Maximal subgroups

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

subgroupindex
#226099992
#226077542
C73×#22962
#764673