Finite Group Databasebeta

← #32983519

Subgroups — #32983519

Order 18688.

534 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 95 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#22620305C211yesmaximal, characteristic
2#22613108C211yesmaximal, characteristic
3#22608483C212yesmaximal, complemented
4#22607797C212yesmaximal, complemented
5C73×#1555C211yesmaximal, characteristic
6#17989144C2211yescharacteristic
7#17988951—22no—
8#17988933C414yescomplemented
9#17988592—22no—
10C4×#11924012C2211yescharacteristic
11#17988467—24no—
12#17988467—22no—
13#17988455C2212yes—
14#17988325—24no—
15C2×#127×C73C2211yescharacteristic
16#432×C73C2212yes—
17#331×C73—22no—
18C23×Dic73—22no—
19C2×#11924012—21no—
20#14556591C2×C412yescomplemented
21#14556583—21no—
22#14556570—22no—
23C4×Dic146—22no—
24#14556550—21no—
25C2×C22⋊Dic73—24no—
26C2×C22⋊Dic73—22no—
27#14556512—28no—
28#14556502—21no—
29C4×#10596831C2×C412yescomplemented
30#14556498—22no—
31#14556498—22no—
32#14556498D414yes—
33C22×D4×C73—22no—
34C22×D4×C73D412yes—
35#127×C73—22no—
36#127×C73C2×C412yes—
37#127×C73D412yes—
38C2×C42×C73C2311yescharacteristic
39C4⋊C8×C73—22no—
40C22⋊C8×C73—22no—
41#97×C73—22no—
42C2×Dic146—22no—
43C22×Dic73—24no—
44C22×Dic73—84no—
45C22×Dic73—82no—
46#11924012—42no—
47C2×#10596831—22no—
48C4⋊Dic73—22no—
49C4⋊Dic73—22no—
50#11924007—42no—
51C22⋊Dic73—41no—
52C22⋊Dic73—84no—
53C22⋊Dic73—82no—
54C4×Dic73—41no—
55C24×C73—22no—
56C2×D4×C73—24no—
57C2×D4×C73—24no—
58C2×D4×C73—22no—
59C2×D4×C73—42no—
60C2×D4×C73—42no—
61C2×D4×C73—82no—
62C2×D4×C73—82no—
63C2×D4×C73C22⋊C414yes—
64C22×C4×C73C2×D412yes—
65C22×C4×C73C2×D411yescharacteristic
66C2×C8×C73—42no—
67C42×C73C22×C411yescharacteristic
68C42×C73C2×D411yescharacteristic
69C42×C73#4112yes—
70C23×C73—24no—
71C23×C73—44no—
72C23×C73—44no—
73C23×C73—42no—
74C23×C73—42no—
75C23×C73#12011yescharacteristic
76D4×C73—44no—
77D4×C73—82no—
78D4×C73—84no—
79D4×C73—84no—
80C2×C4×C73—22no—
81C2×C4×C73—42no—
82C2×C4×C73C2×C22⋊C411yescharacteristic
83C2×C4×C73C4×D412yes—
84C2×C4×C73#12112yes—
85C2×C4×C73#12311yescharacteristic
86C2×Dic73—48no—
87C2×Dic73—42no—
88C2×Dic73—44no—
89C2×Dic73—88no—
90Dic146—82no—
91C8×C73—82no—
92#10596831—42no—
93C22×C73—22no—
94C22×C73—44no—
95C22×C73—48no—
96C22×C73—82no—
97C22×C73—82no—
98C22×C73—84no—
99C22×C73#38611yescharacteristic
100C22×C73#45512yes—
101C4×C73—21no—
102C4×C73—21no—
103C4×C73—22no—
104C4×C73—22no—
105Dic73—84no—
106Dic73—82no—
107#9425—731nomaximal, Sylow
108C2×C73—22no—
109C2×C73—84no—
110C2×C73#188511yescharacteristic
111C2×C73#190412yes—
112#3138—731no—
113#2380—731no—
114#1555D7311yescharacteristic
115#1515—732no—
116#1288—732no—
117C73#942511yescharacteristic, complemented, Sylow
118#533—731no—
119C2×#127C2×D7311yescharacteristic
120#490—1462no—
121#486—734no—
122#432C2×D7312yes—
123#418—1462no—
124C4×M16—731no—
125#386—1464no—
126#386—1462no—
127#383—732no—
128#331—22no—
129#328—1464no—
130C22×D4—22no—
131C22×D4D29212yes—
132C23×C4—1462no—
133C2×M16—1461no—
134C4⋊Q8—732no—
135#127—22no—
136#127C4×D7312yes—
137#127C22⋊D7312yes—
138#125—1461no—
139C22⋊Q8—1462no—
140C4×Q8—1462no—
141#117—1461no—
142C2×C22⋊C4—1464no—
143C2×C22⋊C4—1462no—
144C2×C42C22×D7311yescharacteristic
145C4⋊C8—22no—
146#102—1468no—
147C22⋊C8—22no—
148#97—22no—
149#97—1461no—
150C4×C8—732no—
151#95—734no—
152#95—1462no—
153#95—1462no—
154C24—22no—
155C2×Q8—1462no—
156C2×D4—24no—
157C2×D4—24no—
158C2×D4—22no—
159C2×D4—42no—
160C2×D4—42no—
161C2×D4—82no—
162C2×D4—82no—
163C2×D4#1192400514yes—
164C22×C4—5844no—
165C22×C4—5842no—
166C22×C4—1464no—
167C22×C4D4×D7312yes—
168C22×C4C2×D29211yescharacteristic
169M16—2922no—
170C2×C8—42no—
171C2×C8—1462no—
172C4⋊C4—2922no—
173C4⋊C4—1462no—
174C4⋊C4—1462no—
175C22⋊C4—2921no—
176C22⋊C4—5844no—
177C22⋊C4—5842no—
178C42—2921no—
179C42C2×C4×D7311yescharacteristic
180C42C2×C22⋊D7311yescharacteristic
181C42#1192402712yes—
182C23—24no—
183C23—44no—
184C23—44no—
185C23—42no—
186C23—42no—
187C23#1455656111yescharacteristic
188Q8—5842no—
189D4—44no—
190D4—82no—
191D4—84no—
192D4—84no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—2928no—
196C2×C4—2922no—
197C2×C4—2924no—
198C2×C4—5848no—
199C2×C4C2×#1192400511yescharacteristic
200C2×C4#1455655112yes—
201C2×C4#1455656312yes—
202C2×C4#1455657511yescharacteristic
203C8—82no—
204C8—2922no—
205C22—22no—
206C22—44no—
207C22—48no—
208C22—82no—
209C22—82no—
210C22—84no—
211C22#1798846411yescharacteristic
212C22#1798876712yes—
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—5844no—
218C4—5842no—
219C2—22no—
220C2—84no—
221C2#2261031711yescharacteristic
222C2#2261041612yes—
subgroupG/H
centerC22#17988464
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1555C2
socleC22×C73#386
prime radicalC2×#127×C73C22
cosocleC2×C42×C73C23
hypercenter#1555D73
hypocenterC73#9425
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1555

Complements

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

NH ≅ G/Ntype
3. #22608483C2semidirect
4. #22607797C2semidirect
8. #17988933C4semidirect
20. #14556591C2×C4semidirect
29. C4×#10596831C2×C4semidirect
117. C73#9425semidirect

Maximal subgroups

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

subgroupindex
#226203052
#226131082
#226084832
#226077972
C73×#15552
#942573