Finite Group Databasebeta

← C131×#11434 #45697318

Subgroups — C131×#11434 #45697318

Order 33536.

526 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 142 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
1#2310×C131C211yesmaximal, characteristic
2#1458×C131C212yesmaximal
3#1319×C131C214yesmaximal, complemented
4C23×Q8×C131C411yescharacteristic
5C2×#117×C131C411yescharacteristic
6C2×#117×C131C2211yescharacteristic
7#431×C131—22no—
8#391×C131—22no—
9#391×C131C412yes—
10#391×C131C2212yes—
11#381×C131—22no—
12#324×C131C2214yes—
13#323×C131—22no—
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×C131C2×C411yescharacteristic
22#117×C131—42no—
23#117×C131—42no—
24C2×C4⋊C4×C131—21no—
25C2×C4⋊C4×C131C2×C411yescharacteristic
26C2×C4⋊C4×C131C2311yescharacteristic
27C2×C22⋊C4×C131—21no—
28C2×C22⋊C4×C131D412yes—
29C2×C42×C131C2×C412yes—
30C2×C42×C131D412yes—
31C4⋊C8×C131—42no—
32C22⋊C8×C131—24no—
33C4×C8×C131—42no—
34#95×C131—24no—
35#95×C131—24no—
36C24×C131C22⋊C411yescharacteristic
37C2×Q8×C131—24no—
38C2×Q8×C131—22no—
39C2×Q8×C131—48no—
40C2×Q8×C131—48no—
41C2×Q8×C131—42no—
42C2×Q8×C131—42no—
43C2×Q8×C131—42no—
44C2×Q8×C131—42no—
45C2×Q8×C131C2×C814yes—
46C22×C4×C131—22no—
47C22×C4×C131—22no—
48C22×C4×C131—24no—
49C22×C4×C131—22no—
50C22×C4×C131—22no—
51C22×C4×C131—42no—
52C22×C4×C131—42no—
53C22×C4×C131C22⋊C412yes—
54C22×C4×C131C22⋊C411yescharacteristic
55C22×C4×C131C2×C812yes—
56C22×C4×C131M1612yes—
57C22×C4×C131C22×C411yescharacteristic
58C22×C4×C131C2×D412yes—
59C2×C8×C131—44no—
60C4⋊C4×C131—41no—
61C4⋊C4×C131—41no—
62C4⋊C4×C131—42no—
63C22⋊C4×C131—42no—
64C22⋊C4×C131—42no—
65C42×C131—22no—
66C42×C131—22no—
67C42×C131—42no—
68C23×C131—21no—
69C23×C131—21no—
70C23×C131—41no—
71C23×C131—41no—
72C23×C131C22⋊C812yes—
73C23×C131C2×C22⋊C411yescharacteristic
74Q8×C131—44no—
75Q8×C131—44no—
76Q8×C131—48no—
77C2×C4×C131—21no—
78C2×C4×C131—21no—
79C2×C4×C131—24no—
80C2×C4×C131—24no—
81C2×C4×C131—24no—
82C2×C4×C131—22no—
83C2×C4×C131—22no—
84C2×C4×C131—48no—
85C2×C4×C131—42no—
86C2×C4×C131—42no—
87C2×C4×C131—42no—
88C2×C4×C131—42no—
89C2×C4×C131—42no—
90C2×C4×C131—42no—
91C2×C4×C131—42no—
92C2×C4×C131C22⋊C812yes—
93C2×C4×C131#9912yes—
94C2×C4×C131#10012yes—
95C2×C4×C131C22×C811yescharacteristic
96C2×C4×C131C2×M1611yescharacteristic
97C8×C131—84no—
98C22×C131—21no—
99C22×C131—21no—
100C22×C131—22no—
101C22×C131—42no—
102C22×C131—42no—
103C22×C131—41no—
104C22×C131—41no—
105C22×C131C2×C22⋊C811yescharacteristic
106C22×C131C2×#9911yescharacteristic
107C22×C131C2×#10011yescharacteristic
108C4×C131—21no—
109C4×C131—21no—
110C4×C131—42no—
111C4×C131—42no—
112C4×C131—44no—
113C4×C131—82no—
114C4×C131#32314yes—
115C2×C131—21no—
116C2×C131—21no—
117C2×C131—42no—
118C2×C131C2×#32311yescharacteristic
119C2×C131#212911yescharacteristic
120C2×C131#213511yescharacteristic
121#11434C13111yesmaximal, characteristic, direct product factor, Sylow
122C131#1143411yescharacteristic, direct product factor, Sylow
123#2310C2×C13111yescharacteristic
124#1458C2×C13112yes—
125#1319C2×C13114yescomplemented
126C23×Q8C4×C13111yescharacteristic
127C2×#117C4×C13111yescharacteristic
128C2×#117C22×C13111yescharacteristic
129#431—22no—
130#391—22no—
131#391C4×C13112yes—
132#391C22×C13112yes—
133#381—22no—
134#324C22×C13114yes—
135#323—22no—
136C22×Q8—21no—
137C22×Q8—22no—
138C22×Q8—42no—
139C22×Q8—42no—
140C22×Q8C8×C13114yescomplemented
141C22×Q8C2×C4×C13112yes—
142C23×C4—21no—
143C23×C4C2×C4×C13111yescharacteristic
144#117—42no—
145#117—42no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4C2×C4×C13111yescharacteristic
148C2×C4⋊C4C23×C13111yescharacteristic
149C2×C22⋊C4—21no—
150C2×C22⋊C4D4×C13112yes—
151C2×C42C2×C4×C13112yes—
152C2×C42D4×C13112yes—
153C4⋊C8—42no—
154C22⋊C8—24no—
155C4×C8—42no—
156#95—24no—
157#95—24no—
158C24C22⋊C4×C13111yescharacteristic
159C2×Q8—24no—
160C2×Q8—22no—
161C2×Q8—48no—
162C2×Q8—48no—
163C2×Q8—42no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8—42no—
167C2×Q8C2×C8×C13114yes—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—24no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4C22⋊C4×C13112yes—
176C22×C4C22⋊C4×C13111yescharacteristic
177C22×C4C2×C8×C13112yes—
178C22×C4M16×C13112yes—
179C22×C4C22×C4×C13111yescharacteristic
180C22×C4C2×D4×C13112yes—
181C2×C8—44no—
182C4⋊C4—41no—
183C4⋊C4—41no—
184C4⋊C4—42no—
185C22⋊C4—42no—
186C22⋊C4—42no—
187C42—22no—
188C42—22no—
189C42—42no—
190C23—21no—
191C23—21no—
192C23—41no—
193C23—41no—
194C23C22⋊C8×C13112yes—
195C23C2×C22⋊C4×C13111yescharacteristic
196Q8—44no—
197Q8—44no—
198Q8—48no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—24no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—48no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4C22⋊C8×C13112yes—
215C2×C4#99×C13112yes—
216C2×C4#100×C13112yes—
217C2×C4C22×C8×C13111yescharacteristic
218C2×C4C2×M16×C13111yescharacteristic
219C8—84no—
220C22—21no—
221C22—21no—
222C22—22no—
223C22—42no—
224C22—42no—
225C22—41no—
226C22—41no—
227C22C2×C22⋊C8×C13111yescharacteristic
228C22C2×#99×C13111yescharacteristic
229C22C2×#100×C13111yescharacteristic
230C4—21no—
231C4—21no—
232C4—44no—
233C4—42no—
234C4—42no—
235C4—82no—
236C4#323×C13114yes—
237C2—21no—
238C2—21no—
239C2—42no—
240C2C2×#323×C13111yescharacteristic
241C2#2129×C13111yescharacteristic
242C2#2135×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#99
commutatorC2×C4C22×C8×C131
Frattini, cosocleC2×C4⋊C4C23×C131
prime radicalC24×C131C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C22×C4×C131 ◁ C2×#117×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1319×C131C2semidirect
18. C22×Q8×C131C8semidirect
121. #11434C131direct (N × H)
122. C131#11434direct (N × H)
125. #1319C2×C131semidirect
140. C22×Q8C8×C131semidirect

Maximal subgroups

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

subgroupindex
#2310×C1312
#1458×C1312
#1319×C1312
#11434131