Finite Group Databasebeta

← #33252157

Subgroups — #33252157

Order 18688.

1800 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22613117C213yesmaximal
2#22613037C216yesmaximal
3#22613031C216yesmaximal
4#22612737C216yesmaximal
5#22612673C216yesmaximal
6#125×Dic73C213yesmaximal
7C2×#564×C73C211yesmaximal, characteristic
8#17988486C2213yes—
9#17988486C2216yes—
10#17988486C2213yes—
11#17988486C2216yes—
12#17988486C2216yes—
13#17988486C2216yes—
14#17988473C2216yes—
15#17988473C2216yes—
16#17988473C2216yes—
17#17988473C2216yes—
18#17988473C2216yes—
19#17988473C2216yes—
20#17988473C2216yes—
21#17988473C2216yes—
22#17988473C2216yes—
23#17988473C2216yes—
24#17988457C2212yes—
25#17988455C2212yes—
26#17988453C2213yes—
27C4⋊C4×Dic73C2216yes—
28C4⋊C4×Dic73C2216yes—
29C4⋊C4×Dic73C2213yes—
30C4⋊C4×Dic73C2216yes—
31C4⋊C4×Dic73C2213yes—
32C4⋊C4×Dic73C2216yes—
33C4×C4⋊Dic73C2216yes—
34#17988433C2216yes—
35C42×Dic73C2211yescharacteristic
36#564×C73C4116yescomplemented
37C2×#125×C73C2216yes—
38C2×#125×C73C2213yes—
39C2×#125×C73C2216yes—
40C2×C4⋊Dic73C2316yes—
41C2×C4⋊Dic73C2316yes—
42C2×C4⋊Dic73C2313yes—
43C2×C4⋊Dic73C2313yes—
44C2×C4⋊Dic73C2316yes—
45C2×C4⋊Dic73C2316yes—
46C2×C4×Dic73C2313yes—
47C2×C4×Dic73C2316yes—
48C2×C4×Dic73C2313yes—
49C2×C4×Dic73C2316yes—
50C2×C4×Dic73C2316yes—
51C2×C4×Dic73C2316yes—
52#14556498C2316yes—
53#14556498C2316yes—
54#14556498C2316yes—
55#14556498C2316yes—
56#14556498C2316yes—
57#14556498C2316yes—
58#14556498C2316yes—
59#14556498C2316yes—
60#14556498C2316yes—
61#14556498C2316yes—
62#125×C73C2×C4148yes—
63#125×C73C2×C4124yes—
64#125×C73C2×C4148yes—
65C2×C4⋊C4×C73C2316yes—
66C2×C4⋊C4×C73C2316yes—
67C2×C4⋊C4×C73C2313yes—
68C2×C4⋊C4×C73C2316yes—
69C2×C4⋊C4×C73C2313yes—
70C2×C4⋊C4×C73C2316yes—
71C2×C42×C73C2311yescharacteristic
72C2×C42×C73C2312yes—
73C2×C42×C73C2312yes—
74C22×Dic73C2416yes—
75C22×Dic73C2416yes—
76C22×Dic73C2411yescharacteristic
77C22×Dic73C2413yes—
78C4⋊Dic73—212no—
79C4⋊Dic73—43no—
80C4⋊Dic73—46no—
81C4⋊Dic73—46no—
82C4⋊Dic73—46no—
83C4⋊Dic73—43no—
84C4×Dic73—26no—
85C4×Dic73—212no—
86C4×Dic73—46no—
87C4×Dic73—43no—
88C4×Dic73—46no—
89C4×Dic73—46no—
90C22×C4×C73C2413yes—
91C22×C4×C73C2416yes—
92C22×C4×C73C2416yes—
93C4⋊C4×C73C22×C4124yes—
94C4⋊C4×C73C22×C4124yes—
95C4⋊C4×C73C22×C4112yes—
96C4⋊C4×C73C22×C4124yes—
97C4⋊C4×C73C22×C4112yes—
98C4⋊C4×C73C22×C4124yes—
99C42×C73C22×C414yes—
100C42×C73C22×C418yes—
101C42×C73C22×C418yes—
102C23×C73C2511yescharacteristic
103C2×C4×C73—23no—
104C2×C4×C73—26no—
105C2×C4×C73—26no—
106C2×C4×C73—26no—
107C2×C4×C73—23no—
108C2×C4×C73—26no—
109C2×C4×C73C23×C416yes—
110C2×C4×C73C23×C4112yes—
111C2×C4×C73C23×C4112yes—
112C2×Dic73—23no—
113C2×Dic73—23no—
114C2×Dic73—26no—
115C2×Dic73—26no—
116C2×Dic73—26no—
117C2×Dic73—26no—
118C2×Dic73—26no—
119C2×Dic73—23no—
120C2×Dic73—26no—
121C2×Dic732−1+416yes—
122C22×C73C24×C411yescharacteristic
123C22×C73C2×2−1+413yes—
124C22×C73#58513yes—
125C4×C73—26no—
126C4×C73—212no—
127C4×C73—212no—
128Dic73—26no—
129Dic73—46no—
130Dic73—46no—
131Dic73—41no—
132#34530—731nomaximal, Sylow
133C2×C73C4×2−1+413yes—
134C2×C73#356313yes—
135C2×C73#356711yescharacteristic
136C2×#564D7311yescharacteristic
137#2382—733no—
138#2371—736no—
139#2370—736no—
140#2336—736no—
141#2330—736no—
142C4×#125—733no—
143C73#3453011yescharacteristic, complemented, Sylow
144#564Dic73116yescomplemented
145C2×#125C2×D7313yes—
146C2×#125C2×D7316yes—
147C2×#125C2×D7316yes—
148#389—733no—
149#389—733no—
150#389—736no—
151#389—736no—
152#389—736no—
153#389—736no—
154#387—736no—
155#387—736no—
156#387—736no—
157#387—736no—
158#387—736no—
159#387—736no—
160#387—736no—
161#387—736no—
162#387—736no—
163#387—736no—
164#384—732no—
165#383—732no—
166#382—733no—
167C4×C4⋊C4—736no—
168C4×C4⋊C4—733no—
169C4×C4⋊C4—736no—
170C4×C4⋊C4—733no—
171C4×C4⋊C4—736no—
172C4×C4⋊C4—736no—
173C4×C4⋊C4—736no—
174#376—736no—
175C43—731no—
176#125C2×Dic73124yes—
177#125C2×Dic73148yes—
178#125C2×Dic73148yes—
179C2×C4⋊C4—733no—
180C2×C4⋊C4—733no—
181C2×C4⋊C4—736no—
182C2×C4⋊C4—736no—
183C2×C4⋊C4—736no—
184C2×C4⋊C4—736no—
185C2×C4⋊C4C22×D7313yes—
186C2×C4⋊C4C22×D7316yes—
187C2×C4⋊C4C22×D7316yes—
188C2×C4⋊C4C22×D7313yes—
189C2×C4⋊C4C22×D7316yes—
190C2×C4⋊C4C22×D7316yes—
191C2×C42—733no—
192C2×C42—736no—
193C2×C42—736no—
194C2×C42—736no—
195C2×C42—733no—
196C2×C42—736no—
197C2×C42C22×D7311yescharacteristic
198C2×C42C22×D7312yes—
199C2×C42C22×D7312yes—
200#95—736no—
201#95—736no—
202#95—736no—
203#95—736no—
204#95—736no—
205#95—736no—
206#95—736no—
207#95—736no—
208#95—736no—
209#95—736no—
210C22×C4—733no—
211C22×C4—736no—
212C22×C4—736no—
213C22×C4—731no—
214C22×C4C23×D7316yes—
215C22×C4C23×D7313yes—
216C22×C4C23×D7316yes—
217C4⋊C4—2926no—
218C4⋊C4—2923no—
219C4⋊C4—2926no—
220C4⋊C4—2926no—
221C4⋊C4—2923no—
222C4⋊C4—14612no—
223C4⋊C4C22×Dic73112yes—
224C4⋊C4C22×Dic73124yes—
225C4⋊C4C22×Dic73124yes—
226C4⋊C4C22×Dic73112yes—
227C4⋊C4C22×Dic73124yes—
228C4⋊C4C22×Dic73124yes—
229C42—2926no—
230C42—2926no—
231C42—2926no—
232C42—2923no—
233C42—14612no—
234C42—1466no—
235C42C22×Dic7314yes—
236C42C22×Dic7318yes—
237C42C22×Dic7318yes—
238C23C24×D7311yescharacteristic
239C2×C4—26no—
240C2×C4—23no—
241C2×C4—26no—
242C2×C4—26no—
243C2×C4—26no—
244C2×C4—23no—
245C2×C4—736no—
246C2×C4—1466no—
247C2×C4—1466no—
248C2×C4—1466no—
249C2×C4—1466no—
250C2×C4—1466no—
251C2×C4—1463no—
252C2×C4—1466no—
253C2×C4—1463no—
254C2×C4—1463no—
255C2×C4C23×Dic7316yes—
256C2×C4C23×Dic73112yes—
257C2×C4C23×Dic73112yes—
258C22C24×Dic7311yescharacteristic
259C222−1+4×D7313yes—
260C22#1798942413yes—
261C4—212no—
262C4—26no—
263C4—212no—
264C4—2926no—
265C4—2926no—
266C4—2921no—
267C4—1466no—
268C22−1+4×Dic7313yes—
269C2#2262454013yes—
270C2#2262462111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC2×#564×C73C2
socle, prime radical, cosocleC23×C73C25
hypercenterC2×#564D73
hypocenterC73#34530
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#564

Complements

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

NH ≅ G/Ntype
36. #564×C73C4semidirect
143. C73#34530semidirect
144. #564Dic73semidirect

Maximal subgroups

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

subgroupindex
#226131172
#226130372
#226130312
#226127372
#226126732
#125×Dic732
C2×#564×C732
#3453073