Finite Group Databasebeta

← #3480×C283 #49118963

Subgroups — #3480×C283 #49118963

Order 36224.

1112 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#559×C283C213yesmaximal, complemented
2#557×C283C211yesmaximal, characteristic, complemented
3#556×C283C213yesmaximal, complemented
4#553×C283C216yesmaximal, complemented
5#550×C283C211yesmaximal, characteristic, complemented
6#548×C283C212yesmaximal, complemented
7#532×C283C213yesmaximal, complemented
8#529×C283C216yesmaximal, complemented
9C4×#41×C283C213yesmaximal, complemented
10C4×#41×C283C212yesmaximal, complemented
11C2×C4×Q8×C283C211yesmaximal, characteristic, complemented
12C2×#41×C283C2213yes—
13C2×#41×C283C2212yes—
14C22×Q8×C283C2211yescharacteristic
15C4⋊Q8×C283C2213yes—
16#127×C283C2213yes—
17#126×C283C22112yes—
18#125×C283C2216yes—
19#124×C283C2216yes—
20#124×C283C2216yes—
21#123×C283C22112yes—
22C22⋊Q8×C283C2216yes—
23#121×C283C2216yes—
24#121×C283C2216yes—
25#121×C283C2216yes—
26C4×Q8×C283C2211yescharacteristic
27C4×Q8×C283C2213yes—
28C4×Q8×C283C2211yescharacteristic
29C4×Q8×C283C2213yes—
30C4×Q8×C283C2212yes—
31C4×Q8×C283C2213yes—
32C4×Q8×C283C2213yes—
33C4×D4×C283C2216yes—
34C4×D4×C283C2216yes—
35C4×D4×C283C2213yes—
36C4×D4×C283C2216yes—
37C4×D4×C283C2216yes—
38C4×D4×C283C2213yes—
39C4×D4×C283C2216yes—
40#117×C283C2211yescharacteristic
41#117×C283C2216yes—
42#117×C283C2216yes—
43C2×C4⋊C4×C283C2213yes—
44C2×C42×C283C2213yes—
45C2×C42×C283C2216yes—
46#41×C283—28no—
47#41×C283—212no—
48C2×Q8×C283—24no—
49C2×Q8×C283C2313yes—
50C2×Q8×C283C2313yes—
51C2×Q8×C283C2311yescharacteristic
52C2×D4×C283C2316yes—
53C2×D4×C283C2316yes—
54C2×D4×C283C2313yes—
55C2×D4×C283C2316yes—
56C22×C4×C283C2313yes—
57C22×C4×C283C2316yes—
58C22×C4×C283C2316yes—
59C22×C4×C283C2313yes—
60C22×C4×C283C2316yes—
61C22×C4×C283C2311yescharacteristic
62C4⋊C4×C283C2313yes—
63C4⋊C4×C283C2313yes—
64C4⋊C4×C283C2316yes—
65C4⋊C4×C283C2311yescharacteristic
66C4⋊C4×C283C2311yescharacteristic
67C4⋊C4×C283C2316yes—
68C4⋊C4×C283C2316yes—
69C4⋊C4×C283C2316yes—
70C4⋊C4×C283C2316yes—
71C22⋊C4×C283C2312yes—
72C22⋊C4×C283C2316yes—
73C22⋊C4×C283C23112yes—
74C22⋊C4×C283C2316yes—
75C22⋊C4×C283C23112yes—
76C42×C283C2316yes—
77C42×C283C2316yes—
78C42×C283C2313yes—
79C42×C283C2313yes—
80C42×C283C2312yes—
81C42×C283C2313yes—
82C42×C283C2313yes—
83C23×C283C2416yes—
84C23×C283C2411yescharacteristic
85Q8×C283—26no—
86Q8×C283—26no—
87Q8×C283#4114yescomplemented
88D4×C283—212no—
89D4×C283—212no—
90D4×C283—26no—
91D4×C283—46no—
92C2×C4×C283—26no—
93C2×C4×C283—212no—
94C2×C4×C283—212no—
95C2×C4×C283—46no—
96C2×C4×C283—43no—
97C2×C4×C283#4114yescomplemented
98C2×C4×C283C2412yes—
99C2×C4×C283C2413yes—
100C2×C4×C283C2412yes—
101C2×C4×C283C2413yes—
102C2×C4×C283C2416yes—
103C2×C4×C283C2413yes—
104C2×C4×C283C2411yescharacteristic
105C2×C4×C283C2413yes—
106C2×C4×C283C2411yescharacteristic
107C22×C283—21no—
108C22×C283—21no—
109C22×C283—26no—
110C22×C283—26no—
111C22×C283—26no—
112C22×C283C2×#4112yes—
113C22×C283C2511yescharacteristic
114C4×C283—22no—
115C4×C283—26no—
116C4×C283—23no—
117C4×C283—22no—
118C4×C283—23no—
119C4×C283—23no—
120C4×C283C2×#4112yes—
121C4×C283C2×#4116yes—
122C4×C283C2×#4112yes—
123C2×C283—22no—
124C2×C283—46no—
125C2×C283C22×#4111yescharacteristic
126C2×C283C22×#4111yescharacteristic
127C2×C283#58511yescharacteristic
128C283#348011yescharacteristic, direct product factor, Sylow
129#3480C28311yesmaximal, characteristic, direct product factor, Sylow
130#559C2×C28313yescomplemented
131#557C2×C28311yescharacteristic, complemented
132#556C2×C28313yescomplemented
133#553C2×C28316yescomplemented
134#550C2×C28311yescharacteristic, complemented
135#548C2×C28312yescomplemented
136#532C2×C28313yescomplemented
137#529C2×C28316yescomplemented
138C4×#41C2×C28313yescomplemented
139C4×#41C2×C28312yescomplemented
140C2×C4×Q8C2×C28311yescharacteristic, complemented
141C2×#41C22×C28313yes—
142C2×#41C22×C28312yes—
143C22×Q8C22×C28311yescharacteristic
144C4⋊Q8C22×C28313yes—
145#127C22×C28313yes—
146#126C22×C283112yes—
147#125C22×C28316yes—
148#124C22×C28316yes—
149#124C22×C28316yes—
150#123C22×C283112yes—
151C22⋊Q8C22×C28316yes—
152#121C22×C28316yes—
153#121C22×C28316yes—
154#121C22×C28316yes—
155C4×Q8C22×C28311yescharacteristic
156C4×Q8C22×C28313yes—
157C4×Q8C22×C28311yescharacteristic
158C4×Q8C22×C28313yes—
159C4×Q8C22×C28312yes—
160C4×Q8C22×C28313yes—
161C4×Q8C22×C28313yes—
162C4×D4C22×C28316yes—
163C4×D4C22×C28316yes—
164C4×D4C22×C28313yes—
165C4×D4C22×C28316yes—
166C4×D4C22×C28316yes—
167C4×D4C22×C28313yes—
168C4×D4C22×C28316yes—
169#117C22×C28311yescharacteristic
170#117C22×C28316yes—
171#117C22×C28316yes—
172C2×C4⋊C4C22×C28313yes—
173C2×C42C22×C28313yes—
174C2×C42C22×C28316yes—
175#41—28no—
176#41—212no—
177C2×Q8—24no—
178C2×Q8C23×C28313yes—
179C2×Q8C23×C28313yes—
180C2×Q8C23×C28311yescharacteristic
181C2×D4C23×C28316yes—
182C2×D4C23×C28316yes—
183C2×D4C23×C28313yes—
184C2×D4C23×C28316yes—
185C22×C4C23×C28313yes—
186C22×C4C23×C28316yes—
187C22×C4C23×C28316yes—
188C22×C4C23×C28313yes—
189C22×C4C23×C28316yes—
190C22×C4C23×C28311yescharacteristic
191C4⋊C4C23×C28313yes—
192C4⋊C4C23×C28313yes—
193C4⋊C4C23×C28316yes—
194C4⋊C4C23×C28311yescharacteristic
195C4⋊C4C23×C28311yescharacteristic
196C4⋊C4C23×C28316yes—
197C4⋊C4C23×C28316yes—
198C4⋊C4C23×C28316yes—
199C4⋊C4C23×C28316yes—
200C22⋊C4C23×C28312yes—
201C22⋊C4C23×C28316yes—
202C22⋊C4C23×C283112yes—
203C22⋊C4C23×C28316yes—
204C22⋊C4C23×C283112yes—
205C42C23×C28312yes—
206C42C23×C28313yes—
207C42C23×C28313yes—
208C42C23×C28316yes—
209C42C23×C28316yes—
210C42C23×C28313yes—
211C42C23×C28313yes—
212C23C24×C28316yes—
213C23C24×C28311yescharacteristic
214Q8—26no—
215Q8—26no—
216Q8#41×C28314yescomplemented
217D4—212no—
218D4—212no—
219D4—26no—
220D4—46no—
221C2×C4—26no—
222C2×C4—212no—
223C2×C4—212no—
224C2×C4—46no—
225C2×C4—43no—
226C2×C4#41×C28314yescomplemented
227C2×C4C24×C28312yes—
228C2×C4C24×C28312yes—
229C2×C4C24×C28313yes—
230C2×C4C24×C28313yes—
231C2×C4C24×C28316yes—
232C2×C4C24×C28313yes—
233C2×C4C24×C28311yescharacteristic
234C2×C4C24×C28311yescharacteristic
235C2×C4C24×C28313yes—
236C22—21no—
237C22—21no—
238C22—26no—
239C22—26no—
240C22—26no—
241C22C2×#41×C28312yes—
242C22C25×C28311yescharacteristic
243C4—22no—
244C4—26no—
245C4—23no—
246C4—22no—
247C4—23no—
248C4—23no—
249C4C2×#41×C28312yes—
250C4C2×#41×C28316yes—
251C4C2×#41×C28312yes—
252C2—22no—
253C2—46no—
254C2C22×#41×C28311yescharacteristic
255C2C22×#41×C28311yescharacteristic
256C2#585×C28311yescharacteristic
subgroupG/H
centerC2×C4×C283C24
commutator, Frattini, cosocleC22C25×C283
socleC22×C283C25
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C283 ◁ G

Complements

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

NH ≅ G/Ntype
1. #559×C283C2semidirect
2. #557×C283C2semidirect
3. #556×C283C2semidirect
4. #553×C283C2semidirect
5. #550×C283C2semidirect
6. #548×C283C2semidirect
7. #532×C283C2semidirect
8. #529×C283C2semidirect
9. C4×#41×C283C2semidirect
10. C4×#41×C283C2semidirect
11. C2×C4×Q8×C283C2semidirect
87. Q8×C283#41semidirect
97. C2×C4×C283#41semidirect
128. C283#3480direct (N × H)
129. #3480C283direct (N × H)
130. #559C2×C283semidirect
131. #557C2×C283semidirect
132. #556C2×C283semidirect
133. #553C2×C283semidirect
134. #550C2×C283semidirect
135. #548C2×C283semidirect
136. #532C2×C283semidirect
137. #529C2×C283semidirect
138. C4×#41C2×C283semidirect
139. C4×#41C2×C283semidirect
140. C2×C4×Q8C2×C283semidirect
216. Q8#41×C283semidirect
226. C2×C4#41×C283semidirect

Maximal subgroups

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

subgroupindex
#559×C2832
#557×C2832
#556×C2832
#553×C2832
#550×C2832
#548×C2832
#532×C2832
#529×C2832
C4×#41×C2832
C2×C4×Q8×C2832
#3480283