Finite Group Databasebeta

← C131×#7595 #45693479

Subgroups — C131×#7595 #45693479

Order 33536.

630 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 166 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×#391×C131C211yesmaximal, characteristic
2#1817×C131C212yesmaximal
3#1272×C131C214yesmaximal, complemented
4C23×Q8×C131C411yescharacteristic
5C22×C4⋊C4×C131C411yescharacteristic
6C22×C42×C131C2211yescharacteristic
7C2×C22⋊C8×C131—22no—
8#391×C131—22no—
9#391×C131C412yes—
10#391×C131C2212yes—
11C2×#95×C131—22no—
12#336×C131—22no—
13#336×C131C2214yes—
14C22×Q8×C131—21no—
15C22×Q8×C131—22no—
16C22×Q8×C131—42no—
17C22×Q8×C131—42no—
18C22×Q8×C131C814yescomplemented
19C22×Q8×C131C2×C412yes—
20C23×C4×C131—21no—
21C23×C4×C131—21no—
22C23×C4×C131C2×C411yescharacteristic
23C23×C4×C131D412yes—
24C22×C8×C131—24no—
25C2×C4⋊C4×C131—21no—
26C2×C4⋊C4×C131—42no—
27C2×C4⋊C4×C131C2×C412yes—
28C2×C42×C131—42no—
29C2×C42×C131C2×C411yescharacteristic
30C2×C42×C131D412yes—
31C2×C42×C131C2311yescharacteristic
32C22⋊C8×C131—44no—
33#95×C131—24no—
34#95×C131—24no—
35C24×C131C22⋊C411yescharacteristic
36C2×Q8×C131—24no—
37C2×Q8×C131—22no—
38C2×Q8×C131—48no—
39C2×Q8×C131—42no—
40C2×Q8×C131—42no—
41C2×Q8×C131—48no—
42C2×Q8×C131—42no—
43C2×Q8×C131—42no—
44C2×Q8×C131C2×C814yes—
45C22×C4×C131—22no—
46C22×C4×C131—22no—
47C22×C4×C131—24no—
48C22×C4×C131—24no—
49C22×C4×C131—22no—
50C22×C4×C131—24no—
51C22×C4×C131—22no—
52C22×C4×C131—42no—
53C22×C4×C131—42no—
54C22×C4×C131—42no—
55C22×C4×C131—44no—
56C22×C4×C131—42no—
57C22×C4×C131C22⋊C412yes—
58C22×C4×C131C22⋊C411yescharacteristic
59C22×C4×C131C2×C812yes—
60C22×C4×C131M1612yes—
61C22×C4×C131C22×C411yescharacteristic
62C22×C4×C131C2×D412yes—
63C2×C8×C131—44no—
64C2×C8×C131—44no—
65C2×C8×C131—44no—
66C4⋊C4×C131—42no—
67C4⋊C4×C131—42no—
68C42×C131—41no—
69C42×C131—42no—
70C42×C131—41no—
71C23×C131—22no—
72C23×C131—22no—
73C23×C131C22⋊C812yes—
74C23×C131#9912yes—
75C23×C131#10012yes—
76C23×C131C2×C22⋊C411yescharacteristic
77Q8×C131—44no—
78Q8×C131—48no—
79Q8×C131—44no—
80C2×C4×C131—24no—
81C2×C4×C131—24no—
82C2×C4×C131—22no—
83C2×C4×C131—21no—
84C2×C4×C131—21no—
85C2×C4×C131—21no—
86C2×C4×C131—21no—
87C2×C4×C131—22no—
88C2×C4×C131—24no—
89C2×C4×C131—22no—
90C2×C4×C131—22no—
91C2×C4×C131—22no—
92C2×C4×C131—48no—
93C2×C4×C131—48no—
94C2×C4×C131—42no—
95C2×C4×C131—42no—
96C2×C4×C131—42no—
97C2×C4×C131—44no—
98C2×C4×C131—84no—
99C2×C4×C131C22⋊C812yes—
100C2×C4×C131C22×C811yescharacteristic
101C2×C4×C131C2×M1611yescharacteristic
102C2×C4×C131#13714yes—
103C8×C131—84no—
104C22×C131—22no—
105C22×C131—24no—
106C22×C131—24no—
107C22×C131—22no—
108C22×C131#32314yes—
109C22×C131C2×C22⋊C811yescharacteristic
110C22×C131C2×#9911yescharacteristic
111C22×C131C2×#10011yescharacteristic
112C22×C131#41912yes—
113C22×C131#42112yes—
114C4×C131—22no—
115C4×C131—21no—
116C4×C131—21no—
117C4×C131—24no—
118C4×C131—44no—
119C4×C131—42no—
120C4×C131—82no—
121C2×C131—24no—
122C2×C131C2×#32311yescharacteristic
123C2×C131#147912yes—
124C2×C131#151112yes—
125C2×C131#153311yescharacteristic
126C2×C131#155811yescharacteristic
127#7595C13111yesmaximal, characteristic, direct product factor, Sylow
128C131#759511yescharacteristic, direct product factor, Sylow
129C2×#391C2×C13111yescharacteristic
130#1817C2×C13112yes—
131#1272C2×C13114yescomplemented
132C23×Q8C4×C13111yescharacteristic
133C22×C4⋊C4C4×C13111yescharacteristic
134C22×C42C22×C13111yescharacteristic
135C2×C22⋊C8—22no—
136#391—22no—
137#391C4×C13112yes—
138#391C22×C13112yes—
139C2×#95—22no—
140#336—22no—
141#336C22×C13114yes—
142C22×Q8—21no—
143C22×Q8—22no—
144C22×Q8—42no—
145C22×Q8—42no—
146C22×Q8C8×C13114yescomplemented
147C22×Q8C2×C4×C13112yes—
148C23×C4—21no—
149C23×C4—21no—
150C23×C4C2×C4×C13111yescharacteristic
151C23×C4D4×C13112yes—
152C22×C8—24no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—42no—
155C2×C4⋊C4C2×C4×C13112yes—
156C2×C42—42no—
157C2×C42C2×C4×C13111yescharacteristic
158C2×C42D4×C13112yes—
159C2×C42C23×C13111yescharacteristic
160C22⋊C8—44no—
161#95—24no—
162#95—24no—
163C24C22⋊C4×C13111yescharacteristic
164C2×Q8—24no—
165C2×Q8—22no—
166C2×Q8—42no—
167C2×Q8—42no—
168C2×Q8—48no—
169C2×Q8—48no—
170C2×Q8—42no—
171C2×Q8—42no—
172C2×Q8C2×C8×C13114yes—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—24no—
176C22×C4—24no—
177C22×C4—22no—
178C22×C4—24no—
179C22×C4—22no—
180C22×C4—42no—
181C22×C4—42no—
182C22×C4—42no—
183C22×C4—44no—
184C22×C4—42no—
185C22×C4C22⋊C4×C13112yes—
186C22×C4C22⋊C4×C13111yescharacteristic
187C22×C4C2×C8×C13112yes—
188C22×C4M16×C13112yes—
189C22×C4C22×C4×C13111yescharacteristic
190C22×C4C2×D4×C13112yes—
191C2×C8—44no—
192C2×C8—44no—
193C2×C8—44no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C42—41no—
197C42—42no—
198C42—41no—
199C23—22no—
200C23—22no—
201C23C22⋊C8×C13112yes—
202C23#99×C13112yes—
203C23#100×C13112yes—
204C23C2×C22⋊C4×C13111yescharacteristic
205Q8—44no—
206Q8—48no—
207Q8—44no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—24no—
215C2×C4—24no—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—48no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—48no—
224C2×C4—42no—
225C2×C4—44no—
226C2×C4—84no—
227C2×C4C22⋊C8×C13112yes—
228C2×C4C22×C8×C13111yescharacteristic
229C2×C4C2×M16×C13111yescharacteristic
230C2×C4#137×C13114yes—
231C8—84no—
232C22—24no—
233C22—24no—
234C22—22no—
235C22—22no—
236C22#323×C13114yes—
237C22C2×C22⋊C8×C13111yescharacteristic
238C22C2×#99×C13111yescharacteristic
239C22C2×#100×C13111yescharacteristic
240C22#419×C13112yes—
241C22#421×C13112yes—
242C4—22no—
243C4—21no—
244C4—21no—
245C4—24no—
246C4—44no—
247C4—42no—
248C4—82no—
249C2—24no—
250C2C2×#323×C13111yescharacteristic
251C2#1479×C13112yes—
252C2#1511×C13112yes—
253C2#1533×C13111yescharacteristic
254C2#1558×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C2×C22⋊C4
commutatorC2×C4C22×C8×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC24×C131C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1272×C131C2semidirect
18. C22×Q8×C131C8semidirect
127. #7595C131direct (N × H)
128. C131#7595direct (N × H)
131. #1272C2×C131semidirect
146. C22×Q8C8×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#391×C1312
#1817×C1312
#1272×C1312
#7595131