Finite Group Databasebeta

← C2×#1324×C131 #45697329

Subgroups — C2×#1324×C131 #45697329

Order 33536.

510 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 158 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×#382×C131C211yesmaximal, characteristic
2C2×#324×C131C212yesmaximal
3#1324×C131C214yesmaximal, direct product factor
4C22×C4⋊C4×C131C411yescharacteristic
5C22×C4⋊C4×C131C2211yescharacteristic
6C22×C42×C131C411yescharacteristic
7C2×C22⋊C8×C131—22no—
8#382×C131—22no—
9#382×C131C412yes—
10#382×C131C2212yes—
11C2×#95×C131—22no—
12#324×C131—22no—
13#324×C131C2214yes—
14C23×C4×C131—21no—
15C23×C4×C131—21no—
16C23×C4×C131C2×C411yescharacteristic
17C23×C4×C131D412yes—
18C22×C8×C131—42no—
19C2×C4⋊C4×C131—21no—
20C2×C4⋊C4×C131—41no—
21C2×C4⋊C4×C131—41no—
22C2×C4⋊C4×C131—41no—
23C2×C4⋊C4×C131—41no—
24C2×C4⋊C4×C131C2×C412yes—
25C2×C4⋊C4×C131C2×C411yescharacteristic
26C2×C4⋊C4×C131D412yes—
27C2×C4⋊C4×C131C2311yescharacteristic
28C2×C42×C131—21no—
29C2×C42×C131—22no—
30C2×C42×C131C814yescomplemented
31C2×C42×C131C2×C412yes—
32C22⋊C8×C131—24no—
33C22⋊C8×C131—42no—
34#95×C131—24no—
35#95×C131—24no—
36C24×C131C22⋊C411yescharacteristic
37C22×C4×C131—21no—
38C22×C4×C131—21no—
39C22×C4×C131—22no—
40C22×C4×C131—24no—
41C22×C4×C131—22no—
42C22×C4×C131—22no—
43C22×C4×C131—22no—
44C22×C4×C131—22no—
45C22×C4×C131—42no—
46C22×C4×C131—42no—
47C22×C4×C131—44no—
48C22×C4×C131—44no—
49C22×C4×C131—41no—
50C22×C4×C131—41no—
51C22×C4×C131C22⋊C411yescharacteristic
52C22×C4×C131C22⋊C412yes—
53C22×C4×C131C2×C812yes—
54C22×C4×C131M1612yes—
55C22×C4×C131C22×C411yescharacteristic
56C22×C4×C131C2×D412yes—
57C2×C8×C131—44no—
58C2×C8×C131—84no—
59C4⋊C4×C131—41no—
60C4⋊C4×C131—42no—
61C4⋊C4×C131—41no—
62C4⋊C4×C131—42no—
63C4⋊C4×C131—42no—
64C42×C131—24no—
65C42×C131—22no—
66C42×C131C2×C814yescomplemented
67C23×C131—22no—
68C23×C131—22no—
69C23×C131C22⋊C812yes—
70C23×C131#9911yescharacteristic
71C23×C131#9911yescharacteristic
72C23×C131#10112yes—
73C23×C131C2×C22⋊C411yescharacteristic
74C2×C4×C131—22no—
75C2×C4×C131—22no—
76C2×C4×C131—22no—
77C2×C4×C131—22no—
78C2×C4×C131—21no—
79C2×C4×C131—21no—
80C2×C4×C131—21no—
81C2×C4×C131—21no—
82C2×C4×C131—24no—
83C2×C4×C131—22no—
84C2×C4×C131—22no—
85C2×C4×C131—48no—
86C2×C4×C131—42no—
87C2×C4×C131—42no—
88C2×C4×C131—44no—
89C2×C4×C131—42no—
90C2×C4×C131—42no—
91C2×C4×C131—44no—
92C2×C4×C131—42no—
93C2×C4×C131—82no—
94C2×C4×C131—82no—
95C2×C4×C131—82no—
96C2×C4×C131C22⋊C812yes—
97C2×C4×C131C22×C811yescharacteristic
98C2×C4×C131C2×M1611yescharacteristic
99C8×C131—84no—
100C22×C131—24no—
101C22×C131—24no—
102C22×C131—21no—
103C22×C131—21no—
104C22×C131—21no—
105C22×C131—21no—
106C22×C131#32412yes—
107C22×C131#32412yes—
108C22×C131#35412yes—
109C22×C131#35512yes—
110C22×C131C2×C22⋊C811yescharacteristic
111C22×C131C2×#9911yescharacteristic
112C22×C131C2×#10111yescharacteristic
113C4×C131—22no—
114C4×C131—21no—
115C4×C131—21no—
116C4×C131—44no—
117C4×C131—42no—
118C4×C131—42no—
119C4×C131—82no—
120C2×C131—21no—
121C2×C131—22no—
122C2×C131—21no—
123C2×C131#132414yesdirect product factor
124C2×C131C2×#32411yescharacteristic
125C2×C131C2×#35411yescharacteristic
126C2×C131C2×#35511yescharacteristic
127C2×#1324C13111yesmaximal, characteristic, direct product factor, Sylow
128C131C2×#132411yescharacteristic, direct product factor, Sylow
129C2×#382C2×C13111yescharacteristic
130C2×#324C2×C13112yes—
131#1324C2×C13114yesdirect product factor
132C22×C4⋊C4C4×C13111yescharacteristic
133C22×C4⋊C4C22×C13111yescharacteristic
134C22×C42C4×C13111yescharacteristic
135C2×C22⋊C8—22no—
136#382—22no—
137#382C4×C13112yes—
138#382C22×C13112yes—
139C2×#95—22no—
140#324—22no—
141#324C22×C13114yes—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4C2×C4×C13111yescharacteristic
145C23×C4D4×C13112yes—
146C22×C8—42no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4C2×C4×C13112yes—
153C2×C4⋊C4C2×C4×C13111yescharacteristic
154C2×C4⋊C4D4×C13112yes—
155C2×C4⋊C4C23×C13111yescharacteristic
156C2×C42—21no—
157C2×C42—22no—
158C2×C42C8×C13114yescomplemented
159C2×C42C2×C4×C13112yes—
160C22⋊C8—24no—
161C22⋊C8—42no—
162#95—24no—
163#95—24no—
164C24C22⋊C4×C13111yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—22no—
168C22×C4—24no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4—44no—
176C22×C4—44no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4C22⋊C4×C13111yescharacteristic
180C22×C4C22⋊C4×C13112yes—
181C22×C4C2×C8×C13112yes—
182C22×C4M16×C13112yes—
183C22×C4C22×C4×C13111yescharacteristic
184C22×C4C2×D4×C13112yes—
185C2×C8—44no—
186C2×C8—84no—
187C4⋊C4—41no—
188C4⋊C4—42no—
189C4⋊C4—41no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C42—24no—
193C42—22no—
194C42C2×C8×C13114yescomplemented
195C23—22no—
196C23—22no—
197C23C22⋊C8×C13112yes—
198C23#99×C13111yescharacteristic
199C23#99×C13111yescharacteristic
200C23#101×C13112yes—
201C23C2×C22⋊C4×C13111yescharacteristic
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—24no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—48no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—44no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—44no—
220C2×C4—42no—
221C2×C4—82no—
222C2×C4—82no—
223C2×C4—82no—
224C2×C4C22⋊C8×C13112yes—
225C2×C4C22×C8×C13111yescharacteristic
226C2×C4C2×M16×C13111yescharacteristic
227C8—84no—
228C22—24no—
229C22—24no—
230C22—21no—
231C22—21no—
232C22—21no—
233C22—21no—
234C22#324×C13112yes—
235C22#324×C13112yes—
236C22#354×C13112yes—
237C22#355×C13112yes—
238C22C2×C22⋊C8×C13111yescharacteristic
239C22C2×#99×C13111yescharacteristic
240C22C2×#101×C13111yescharacteristic
241C4—22no—
242C4—21no—
243C4—21no—
244C4—44no—
245C4—42no—
246C4—42no—
247C4—82no—
248C2—21no—
249C2—21no—
250C2—22no—
251C2#1324×C13114yesdirect product factor
252C2C2×#324×C13111yescharacteristic
253C2C2×#354×C13111yescharacteristic
254C2C2×#355×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#99
commutatorC2×C4C22×C8×C131
Frattini, cosocleC2×C4⋊C4C23×C131
prime radicalC24×C131C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C24×C131 ◁ C22×C4⋊C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1324×C131C2direct (N × H)
30. C2×C42×C131C8semidirect
66. C42×C131C2×C8semidirect
123. C2×C131#1324direct (N × H)
127. C2×#1324C131direct (N × H)
128. C131C2×#1324direct (N × H)
131. #1324C2×C131direct (N × H)
158. C2×C42C8×C131semidirect
194. C42C2×C8×C131semidirect
251. C2#1324×C131direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#382×C1312
C2×#324×C1312
#1324×C1312
C2×#1324131