Finite Group Databasebeta

← C2×#2351×C131 #45719997

Subgroups — C2×#2351×C131 #45719997

Order 33536.

3158 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C131C212yesmaximal
2C22×C4×Q8×C131C211yesmaximal, characteristic
3#2351×C131C2116yesmaximal, direct product factor
4C2×#389×C131C216yesmaximal
5C2×#382×C131C213yesmaximal
6C2×C4×C4⋊C4×C131C213yesmaximal
7C23×Q8×C131C2211yescharacteristic
8C2×C4×Q8×C131—216no—
9C2×C4×Q8×C131C4116yescomplemented
10C2×C4×Q8×C131C22116yes—
11C2×C4×Q8×C131C2218yes—
12C22×C4⋊C4×C131C2216yes—
13C22×C4⋊C4×C131C2216yes—
14C22×C4⋊C4×C131C2213yes—
15C22×C42×C131C2216yes—
16C22×C42×C131C2213yes—
17#389×C131C22148yes—
18#382×C131C22124yes—
19C4×C4⋊C4×C131C22124yes—
20C2×#95×C131C2211yescharacteristic
21C2×#95×C131C2213yes—
22C2×#95×C131C2216yes—
23C22×Q8×C131C2×C418yes—
24C22×Q8×C131D418yes—
25C22×Q8×C131Q818yes—
26C22×Q8×C131C2314yes—
27C23×C4×C131C2316yes—
28C23×C4×C131C2311yescharacteristic
29C23×C4×C131C2313yes—
30C23×C4×C131C2312yes—
31C23×C4×C131C2313yes—
32C4×Q8×C131—264no—
33C4×Q8×C131C2×C4164yescomplemented
34C2×C4⋊C4×C131—224no—
35C2×C4⋊C4×C131—224no—
36C2×C4⋊C4×C131C2×C4124yes—
37C2×C4⋊C4×C131C23124yes—
38C2×C4⋊C4×C131C23124yes—
39C2×C4⋊C4×C131C23112yes—
40C2×C42×C131—224no—
41C2×C42×C131C2×C4124yes—
42C2×C42×C131C23124yes—
43C2×C42×C131C23112yes—
44#95×C131C23124yes—
45#95×C131C2314yes—
46#95×C131C23112yes—
47C24×C131C2411yescharacteristic
48C2×Q8×C131C4⋊C4164yescomplemented
49C2×Q8×C131C22×C4116yes—
50C2×Q8×C131C2×D4116yes—
51C2×Q8×C131C2×Q8116yes—
52C22×C4×C131—24no—
53C22×C4×C131—212no—
54C22×C4×C131—24no—
55C22×C4×C131—24no—
56C22×C4×C131—212no—
57C22×C4×C131—212no—
58C22×C4×C131—212no—
59C22×C4×C131C22×C414yes—
60C22×C4×C131C22×C4112yes—
61C22×C4×C131C22×C4112yes—
62C22×C4×C131C2×D4112yes—
63C22×C4×C131C2×Q8112yes—
64C22×C4×C131#4118yes—
65C22×C4×C131C24112yes—
66C22×C4×C131C2412yes—
67C22×C4×C131C2416yes—
68C22×C4×C131C2414yes—
69C22×C4×C131C2416yes—
70C4⋊C4×C131—248no—
71C4⋊C4×C131—248no—
72C4⋊C4×C131C22×C4148yes—
73C42×C131—248no—
74C42×C131C22×C4148yes—
75C23×C131C23×C412yes—
76C23×C131C22×D412yes—
77C23×C131C22×Q812yes—
78C23×C131C2×#4114yes—
79C23×C1312−1+414yes—
80C23×C131C2511yescharacteristic
81Q8×C131C2×C4⋊C4164yescomplemented
82C2×C4×C131—224no—
83C2×C4×C131—28no—
84C2×C4×C131—216no—
85C2×C4×C131—24no—
86C2×C4×C131—212no—
87C2×C4×C131—24no—
88C2×C4×C131—24no—
89C2×C4×C131—212no—
90C2×C4×C131—212no—
91C2×C4×C131—212no—
92C2×C4×C131—424no—
93C2×C4×C131C2×C4⋊C4148yes—
94C2×C4×C131C23×C414yes—
95C2×C4×C131C23×C4112yes—
96C2×C4×C131C23×C4112yes—
97C2×C4×C131C22×D4112yes—
98C2×C4×C131C22×Q8112yes—
99C2×C4×C131C2×#4118yes—
100C22×C131C22×C4⋊C414yes—
101C22×C131C4×#4114yes—
102C22×C131#51914yes—
103C22×C131#54818yes—
104C22×C131#55718yes—
105C22×C131C24×C411yescharacteristic
106C22×C131C23×D411yescharacteristic
107C22×C131C23×Q811yescharacteristic
108C22×C131C22×#4112yes—
109C22×C131C2×2−1+412yes—
110C4×C131—212no—
111C4×C131—24no—
112C4×C131—28no—
113C4×C131—412no—
114C4×C131C22×C4⋊C4124yes—
115C2×C131#235118yesdirect product factor
116C2×C131C23×C4⋊C411yescharacteristic
117C2×C131C2×C4×#4111yescharacteristic
118C2×C131C2×#51911yescharacteristic
119C2×C131C2×#54812yes—
120C2×C131C2×#55712yes—
121C2×#2351C13111yesmaximal, characteristic, direct product factor, Sylow
122C131C2×#235111yescharacteristic, direct product factor, Sylow
123C22×C4×Q8C2×C13112yes—
124C22×C4×Q8C2×C13111yescharacteristic
125#2351C2×C131116yesdirect product factor
126C2×#389C2×C13116yes—
127C2×#382C2×C13113yes—
128C2×C4×C4⋊C4C2×C13113yes—
129C23×Q8C22×C13111yescharacteristic
130C2×C4×Q8—216no—
131C2×C4×Q8C4×C131116yescomplemented
132C2×C4×Q8C22×C131116yes—
133C2×C4×Q8C22×C13118yes—
134C22×C4⋊C4C22×C13116yes—
135C22×C4⋊C4C22×C13116yes—
136C22×C4⋊C4C22×C13113yes—
137C22×C42C22×C13116yes—
138C22×C42C22×C13113yes—
139#389C22×C131148yes—
140#382C22×C131124yes—
141C4×C4⋊C4C22×C131124yes—
142C2×#95C22×C13111yescharacteristic
143C2×#95C22×C13113yes—
144C2×#95C22×C13116yes—
145C22×Q8C2×C4×C13118yes—
146C22×Q8D4×C13118yes—
147C22×Q8Q8×C13118yes—
148C22×Q8C23×C13114yes—
149C23×C4C23×C13116yes—
150C23×C4C23×C13113yes—
151C23×C4C23×C13111yescharacteristic
152C23×C4C23×C13112yes—
153C23×C4C23×C13113yes—
154C4×Q8—264no—
155C4×Q8C2×C4×C131164yescomplemented
156C2×C4⋊C4—224no—
157C2×C4⋊C4—224no—
158C2×C4⋊C4C2×C4×C131124yes—
159C2×C4⋊C4C23×C131124yes—
160C2×C4⋊C4C23×C131124yes—
161C2×C4⋊C4C23×C131112yes—
162C2×C42—224no—
163C2×C42C2×C4×C131124yes—
164C2×C42C23×C131124yes—
165C2×C42C23×C131112yes—
166#95C23×C13114yes—
167#95C23×C131112yes—
168#95C23×C131124yes—
169C24C24×C13111yescharacteristic
170C2×Q8C4⋊C4×C131164yescomplemented
171C2×Q8C22×C4×C131116yes—
172C2×Q8C2×D4×C131116yes—
173C2×Q8C2×Q8×C131116yes—
174C22×C4—24no—
175C22×C4—212no—
176C22×C4—24no—
177C22×C4—24no—
178C22×C4—212no—
179C22×C4—212no—
180C22×C4—212no—
181C22×C4C22×C4×C13114yes—
182C22×C4C22×C4×C131112yes—
183C22×C4C22×C4×C131112yes—
184C22×C4C2×D4×C131112yes—
185C22×C4C2×Q8×C131112yes—
186C22×C4#41×C13118yes—
187C22×C4C24×C131112yes—
188C22×C4C24×C13112yes—
189C22×C4C24×C13116yes—
190C22×C4C24×C13114yes—
191C22×C4C24×C13116yes—
192C4⋊C4—248no—
193C4⋊C4—248no—
194C4⋊C4C22×C4×C131148yes—
195C42—248no—
196C42C22×C4×C131148yes—
197C23C23×C4×C13112yes—
198C23C22×D4×C13112yes—
199C23C22×Q8×C13112yes—
200C23C2×#41×C13114yes—
201C232−1+4×C13114yes—
202C23C25×C13111yescharacteristic
203Q8C2×C4⋊C4×C131164yescomplemented
204C2×C4—224no—
205C2×C4—28no—
206C2×C4—216no—
207C2×C4—24no—
208C2×C4—212no—
209C2×C4—24no—
210C2×C4—24no—
211C2×C4—212no—
212C2×C4—212no—
213C2×C4—212no—
214C2×C4—424no—
215C2×C4C2×C4⋊C4×C131148yes—
216C2×C4C23×C4×C13114yes—
217C2×C4C23×C4×C131112yes—
218C2×C4C23×C4×C131112yes—
219C2×C4C22×D4×C131112yes—
220C2×C4C22×Q8×C131112yes—
221C2×C4C2×#41×C13118yes—
222C22C22×C4⋊C4×C13114yes—
223C22C4×#41×C13114yes—
224C22#519×C13114yes—
225C22#548×C13118yes—
226C22#557×C13118yes—
227C22C24×C4×C13111yescharacteristic
228C22C23×D4×C13111yescharacteristic
229C22C23×Q8×C13111yescharacteristic
230C22C22×#41×C13112yes—
231C22C2×2−1+4×C13112yes—
232C4—212no—
233C4—24no—
234C4—28no—
235C4—412no—
236C4C22×C4⋊C4×C131124yes—
237C2#2351×C13118yesdirect product factor
238C2C23×C4⋊C4×C13111yescharacteristic
239C2C2×C4×#41×C13111yescharacteristic
240C2C2×#519×C13111yescharacteristic
241C2C2×#548×C13112yes—
242C2C2×#557×C13112yes—
subgroupG/H
center, socle, prime radicalC24×C131C24
commutatorC22C24×C4×C131
Frattini, cosocleC23C25×C131
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2351×C131C2direct (N × H)
9. C2×C4×Q8×C131C4semidirect
33. C4×Q8×C131C2×C4semidirect
48. C2×Q8×C131C4⋊C4semidirect
81. Q8×C131C2×C4⋊C4semidirect
115. C2×C131#2351direct (N × H)
121. C2×#2351C131direct (N × H)
122. C131C2×#2351direct (N × H)
125. #2351C2×C131direct (N × H)
131. C2×C4×Q8C4×C131semidirect
155. C4×Q8C2×C4×C131semidirect
170. C2×Q8C4⋊C4×C131semidirect
203. Q8C2×C4⋊C4×C131semidirect
237. C2#2351×C131direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C1312
#2351×C1312
C2×#389×C1312
C2×#382×C1312
C2×C4×C4⋊C4×C1312
C2×#2351131