Finite Group Databasebeta

← #32995146

Subgroups — #32995146

Order 18688.

454 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#17988313C212yesmaximal
2#22607877C212yesmaximal, complemented
3#22607875C212yesmaximal, complemented
4C73×#2317C211yesmaximal, characteristic
5C2×C22⋊#10596831—22no—
6#17988313—22no—
7#17988313C2214yes—
8C2×#117×C73C411yescharacteristic
9C2×#117×C73C411yescharacteristic
10C22×C4⋊C4×C73C2211yescharacteristic
11#389×C73—22no—
12#385×C73—22no—
13#384×C73C411yescharacteristic
14#384×C73C2211yescharacteristic
15#382×C73C411yescharacteristic
16#382×C73C2211yescharacteristic
17C22×#10596831—42no—
18C22⋊#10596831—24no—
19C22⋊#10596831—42no—
20C23×C4×C73C2×C411yescharacteristic
21C23×C4×C73D412yes—
22#117×C73—22no—
23#117×C73—42no—
24#117×C73C814yescomplemented
25C2×C4⋊C4×C73—21no—
26C2×C4⋊C4×C73—22no—
27C2×C4⋊C4×C73—22no—
28C2×C4⋊C4×C73—42no—
29C2×C4⋊C4×C73C2×C411yescharacteristic
30C2×C4⋊C4×C73C2×C411yescharacteristic
31C2×C4⋊C4×C73C2×C411yescharacteristic
32C2×C4⋊C4×C73D412yes—
33C2×C4⋊C4×C73C2311yescharacteristic
34C2×C22⋊C4×C73—21no—
35C2×C22⋊C4×C73—21no—
36C2×C42×C73—21no—
37C2×C42×C73C2×C411yescharacteristic
38C2×C42×C73C2×C411yescharacteristic
39#95×C73—22no—
40#95×C73—22no—
41C2×#10596831—44no—
42C2×#10596831—84no—
43C24×C73C22⋊C411yescharacteristic
44C22×C4×C73—22no—
45C22×C4×C73—22no—
46C22×C4×C73—22no—
47C22×C4×C73—21no—
48C22×C4×C73—21no—
49C22×C4×C73—22no—
50C22×C4×C73—21no—
51C22×C4×C73—21no—
52C22×C4×C73—82no—
53C22×C4×C73C22⋊C411yescharacteristic
54C22×C4×C73C22⋊C412yes—
55C22×C4×C73C2×C812yes—
56C22×C4×C73M1612yes—
57C22×C4×C73C22×C411yescharacteristic
58C22×C4×C73C2×D412yes—
59C4⋊C4×C73—24no—
60C4⋊C4×C73—41no—
61C4⋊C4×C73—42no—
62C4⋊C4×C73—41no—
63C4⋊C4×C73—41no—
64C4⋊C4×C73—41no—
65C4⋊C4×C73—82no—
66C4⋊C4×C73—82no—
67C22⋊C4×C73—24no—
68C22⋊C4×C73—42no—
69C42×C73—21no—
70C42×C73—21no—
71C42×C73—42no—
72C42×C73C2×C812yescomplemented
73C42×C73C2×C812yescomplemented
74C23×C73—41no—
75C23×C73—41no—
76C23×C73C22⋊C812yes—
77C23×C73#9912yes—
78C23×C73#10112yes—
79C23×C73C2×C22⋊C411yescharacteristic
80C2×C4×C73—24no—
81C2×C4×C73—24no—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—41no—
91C2×C4×C73—41no—
92C2×C4×C73—41no—
93C2×C4×C73—41no—
94C2×C4×C73—44no—
95C2×C4×C73—42no—
96C2×C4×C73—42no—
97C2×C4×C73—42no—
98C2×C4×C73—42no—
99C2×C4×C73—41no—
100C2×C4×C73—41no—
101C2×C4×C73—82no—
102C2×C4×C73C22⋊C812yes—
103C2×C4×C73C22×C811yescharacteristic
104C2×C4×C73C2×M1611yescharacteristic
105#10596831—84no—
106C22×C73—21no—
107C22×C73—22no—
108C22×C73—21no—
109C22×C73—22no—
110C22×C73—42no—
111C22×C73—42no—
112C22×C73#32414yes—
113C22×C73C2×C22⋊C811yescharacteristic
114C22×C73C2×#9911yescharacteristic
115C22×C73C2×#10111yescharacteristic
116C4×C73—22no—
117C4×C73—21no—
118C4×C73—21no—
119C4×C73—42no—
120C4×C73—42no—
121C4×C73—42no—
122C4×C73—42no—
123C4×C73—81no—
124C4×C73—81no—
125#11448—731nomaximal, Sylow
126C2×C73—21no—
127C2×C73—24no—
128C2×C73—21no—
129C2×C73C2×#32411yescharacteristic
130C2×C73#212711yescharacteristic
131C2×C73#213311yescharacteristic
132#2317D7311yescharacteristic
133C2×#324—732no—
134#1325—732no—
135#1324—732no—
136C73#1144811yescharacteristic, complemented, Sylow
137C2×#117Dic7311yescharacteristic
138C2×#117Dic7311yescharacteristic
139C22×C4⋊C4C2×D7311yescharacteristic
140C2×C22⋊C8—1462no—
141#389—22no—
142#385—22no—
143#384Dic7311yescharacteristic
144#384C2×D7311yescharacteristic
145#382Dic7311yescharacteristic
146#382C2×D7311yescharacteristic
147#324—734no—
148#324—1462no—
149C23×C4C2×Dic7311yescharacteristic
150C23×C4C22⋊D7312yes—
151C22×C8—2922no—
152#117—22no—
153#117—42no—
154#117#1059683114yescomplemented
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—42no—
159C2×C4⋊C4C2×Dic7311yescharacteristic
160C2×C4⋊C4C2×Dic7311yescharacteristic
161C2×C4⋊C4C2×Dic7311yescharacteristic
162C2×C4⋊C4C22⋊D7312yes—
163C2×C4⋊C4C22×D7311yescharacteristic
164C2×C22⋊C4—21no—
165C2×C22⋊C4—21no—
166C2×C42—21no—
167C2×C42C2×Dic7311yescharacteristic
168C2×C42C2×Dic7311yescharacteristic
169C22⋊C8—2922no—
170C22⋊C8—1464no—
171#95—22no—
172#95—22no—
173C24C22⋊Dic7311yescharacteristic
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—22no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—82no—
183C22×C4C22⋊Dic7311yescharacteristic
184C22×C4C22⋊Dic7312yes—
185C22×C4C2×#1059683112yes—
186C22×C4#1192401212yes—
187C22×C4C22×Dic7311yescharacteristic
188C22×C4C2×C22⋊D7312yes—
189C2×C8—2924no—
190C2×C8—5844no—
191C4⋊C4—24no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—82no—
198C4⋊C4—82no—
199C22⋊C4—24no—
200C22⋊C4—42no—
201C42—21no—
202C42—21no—
203C42—42no—
204C42C2×#1059683112yescomplemented
205C42C2×#1059683112yescomplemented
206C23—41no—
207C23—41no—
208C23C22⋊#1059683112yes—
209C23#1455650612yes—
210C23#1455651012yes—
211C23C2×C22⋊Dic7311yescharacteristic
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—44no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—82no—
234C2×C4C22⋊#1059683112yes—
235C2×C4C22×#1059683111yescharacteristic
236C2×C4C2×#1192401211yescharacteristic
237C8—5844no—
238C22—21no—
239C22—22no—
240C22—21no—
241C22—22no—
242C22—42no—
243C22—42no—
244C22#1798831314yes—
245C22C2×C22⋊#1059683111yescharacteristic
246C22C2×#1455650611yescharacteristic
247C22C2×#1455651011yescharacteristic
248C4—22no—
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—42no—
254C4—42no—
255C4—81no—
256C4—81no—
257C2—21no—
258C2—21no—
259C2—24no—
260C2C2×#1798831311yescharacteristic
261C2#2261160011yescharacteristic
262C2#2261162011yescharacteristic
subgroupG/H
centerC22C2×#14556506
commutatorC2×C4×C73C22×C8
FrattiniC2×C4⋊C4C22×D73
FittingC73×#2317C2
socleC22×C73C2×#99
prime radicalC24×C73C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#2317D73
hypocenterC73#11448
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2317

Complements

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

NH ≅ G/Ntype
2. #22607877C2semidirect
3. #22607875C2semidirect
24. #117×C73C8semidirect
72. C42×C73C2×C8semidirect
73. C42×C73C2×C8semidirect
136. C73#11448semidirect
154. #117#10596831semidirect
204. C42C2×#10596831semidirect
205. C42C2×#10596831semidirect

Maximal subgroups

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

subgroupindex
C2×#179883132
#226078772
#226078752
C73×#23172
#1144873