Finite Group Databasebeta

← C131×#11484 #45697368

Subgroups — C131×#11484 #45697368

Order 33536.

368 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 126 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#2930×C131C211yesmaximal, characteristic
2#2115×C131C212yesmaximal, complemented
3#1328×C131C212yesmaximal, complemented
4#1320×C131C212yesmaximal, complemented
5C2×#131×C131C2211yescharacteristic
6C22×M16×C131C411yescharacteristic
7#525×C131C411yescharacteristic
8C2×M32×C131—22no—
9#436×C131—22no—
10#435×C131—22no—
11#424×C131C2211yescharacteristic
12#408×C131C411yescharacteristic
13#407×C131C2211yescharacteristic
14#405×C131C411yescharacteristic
15#349×C131—22no—
16#349×C131C2214yes—
17C2×#41×C131C2×C411yescharacteristic
18C23×C4×C131C2×C411yescharacteristic
19#131×C131—42no—
20C2×M16×C131—21no—
21C2×M16×C131—21no—
22C2×M16×C131—42no—
23C2×M16×C131C2×C411yescharacteristic
24C2×M16×C131D412yes—
25C2×M16×C131C2311yescharacteristic
26C22×C8×C131C2×C411yescharacteristic
27C22×C8×C131C2×C411yescharacteristic
28C22×C8×C131D412yes—
29#123×C131C812yes—
30C22⋊Q8×C131—21no—
31#121×C131—21no—
32#120×C131C812yes—
33C4×D4×C131—22no—
34#117×C131C2×C411yescharacteristic
35M32×C131—24no—
36M32×C131—42no—
37C2×C16×C131—42no—
38C4⋊C8×C131—22no—
39C22⋊C8×C131—22no—
40C22⋊C8×C131—22no—
41#97×C131—21no—
42C4×C8×C131—21no—
43C24×C131C2×C811yescharacteristic
44#41×C131—41no—
45#41×C131—41no—
46C2×Q8×C131M1611yescharacteristic
47C2×D4×C131—22no—
48C2×D4×C131C2×C812yes—
49C2×D4×C131M1611yescharacteristic
50C22×C4×C131—21no—
51C22×C4×C131—21no—
52C22×C4×C131—41no—
53C22×C4×C131—41no—
54C22×C4×C131C22⋊C412yes—
55C22×C4×C131C2×C811yescharacteristic
56C22×C4×C131C22×C411yescharacteristic
57M16×C131—42no—
58M16×C131—41no—
59M16×C131—42no—
60M16×C131—42no—
61M16×C131—41no—
62C2×C8×C131—22no—
63C2×C8×C131—22no—
64C2×C8×C131—22no—
65C2×C8×C131—21no—
66C2×C8×C131—21no—
67C2×C8×C131—41no—
68C2×C8×C131C22⋊C411yescharacteristic
69C2×C8×C131C22⋊C411yescharacteristic
70C2×C8×C131C2×D412yes—
71C4⋊C4×C131—22no—
72C4⋊C4×C131—21no—
73C22⋊C4×C131—22no—
74C22⋊C4×C131—22no—
75C22⋊C4×C131C2×C812yes—
76C42×C131—21no—
77C16×C131—44no—
78C23×C131—21no—
79C23×C131—41no—
80C23×C131—81no—
81C23×C131C22⋊C812yes—
82C23×C131C22×C811yescharacteristic
83Q8×C131—41no—
84D4×C131—42no—
85D4×C131—41no—
86D4×C131—82no—
87C2×C4×C131—21no—
88C2×C4×C131—22no—
89C2×C4×C131—21no—
90C2×C4×C131—22no—
91C2×C4×C131—22no—
92C2×C4×C131—21no—
93C2×C4×C131—42no—
94C2×C4×C131—41no—
95C2×C4×C131—41no—
96C2×C4×C131—41no—
97C2×C4×C131C22⋊C812yes—
98C2×C4×C131C2×C22⋊C411yescharacteristic
99C2×C4×C131C2×M1611yescharacteristic
100C8×C131—22no—
101C8×C131—21no—
102C8×C131—41no—
103C8×C131—41no—
104C8×C131#9912yes—
105C22×C131—21no—
106C22×C131—22no—
107C22×C131—42no—
108C22×C131—41no—
109C22×C131—41no—
110C22×C131—41no—
111C22×C131—41no—
112C22×C131—82no—
113C22×C131C2×C22⋊C811yescharacteristic
114C4×C131—21no—
115C4×C131—22no—
116C4×C131—42no—
117C4×C131—41no—
118C4×C131C2×#9911yescharacteristic
119C4×C131#41311yescharacteristic
120C2×C131—21no—
121C2×C131—42no—
122C2×C131—41no—
123C2×C131—81no—
124C2×C131#145911yescharacteristic
125#11484C13111yesmaximal, characteristic, direct product factor, Sylow
126C131#1148411yescharacteristic, direct product factor, Sylow
127#2930C2×C13111yescharacteristic
128#2115C2×C13112yescomplemented
129#1328C2×C13112yescomplemented
130#1320C2×C13112yescomplemented
131C2×#131C22×C13111yescharacteristic
132C22×M16C4×C13111yescharacteristic
133#525C4×C13111yescharacteristic
134C2×M32—22no—
135#436—22no—
136#435—22no—
137#424C22×C13111yescharacteristic
138#408C4×C13111yescharacteristic
139#407C22×C13111yescharacteristic
140#405C4×C13111yescharacteristic
141#349—22no—
142#349C22×C13114yes—
143C2×#41C2×C4×C13111yescharacteristic
144C23×C4C2×C4×C13111yescharacteristic
145#131—42no—
146C2×M16—21no—
147C2×M16—21no—
148C2×M16—42no—
149C2×M16C2×C4×C13111yescharacteristic
150C2×M16D4×C13112yes—
151C2×M16C23×C13111yescharacteristic
152C22×C8C2×C4×C13111yescharacteristic
153C22×C8C2×C4×C13111yescharacteristic
154C22×C8D4×C13112yes—
155#123C8×C13112yes—
156C22⋊Q8—21no—
157#121—21no—
158#120C8×C13112yes—
159C4×D4—22no—
160#117C2×C4×C13111yescharacteristic
161M32—24no—
162M32—42no—
163C2×C16—42no—
164C4⋊C8—22no—
165C22⋊C8—22no—
166C22⋊C8—22no—
167#97—21no—
168C4×C8—21no—
169C24C2×C8×C13111yescharacteristic
170#41—41no—
171#41—41no—
172C2×Q8M16×C13111yescharacteristic
173C2×D4—22no—
174C2×D4C2×C8×C13112yes—
175C2×D4M16×C13111yescharacteristic
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4C22⋊C4×C13112yes—
181C22×C4C2×C8×C13111yescharacteristic
182C22×C4C22×C4×C13111yescharacteristic
183M16—42no—
184M16—41no—
185M16—42no—
186M16—42no—
187M16—41no—
188C2×C8—22no—
189C2×C8—22no—
190C2×C8—22no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—41no—
194C2×C8C22⋊C4×C13111yescharacteristic
195C2×C8C22⋊C4×C13111yescharacteristic
196C2×C8C2×D4×C13112yes—
197C4⋊C4—22no—
198C4⋊C4—21no—
199C22⋊C4—22no—
200C22⋊C4—22no—
201C22⋊C4C2×C8×C13112yes—
202C42—21no—
203C16—44no—
204C23—21no—
205C23—41no—
206C23—81no—
207C23C22⋊C8×C13112yes—
208C23C22×C8×C13111yescharacteristic
209Q8—41no—
210D4—42no—
211D4—41no—
212D4—82no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4C22⋊C8×C13112yes—
224C2×C4C2×C22⋊C4×C13111yescharacteristic
225C2×C4C2×M16×C13111yescharacteristic
226C8—22no—
227C8—21no—
228C8—41no—
229C8—41no—
230C8#99×C13112yes—
231C22—21no—
232C22—22no—
233C22—42no—
234C22—41no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—82no—
239C22C2×C22⋊C8×C13111yescharacteristic
240C4—21no—
241C4—22no—
242C4—42no—
243C4—41no—
244C4C2×#99×C13111yescharacteristic
245C4#413×C13111yescharacteristic
246C2—21no—
247C2—41no—
248C2—42no—
249C2—81no—
250C2#1459×C13111yescharacteristic
subgroupG/H
centerC4×C131C2×#99
commutatorC23C22×C8×C131
Frattini, cosocleC2×M16C23×C131
socleC2×C131#1459
prime radical#525×C131C4
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C131 ◁ C2×C8×C131 ◁ C2×#131×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2115×C131C2semidirect
3. #1328×C131C2semidirect
4. #1320×C131C2semidirect
125. #11484C131direct (N × H)
126. C131#11484direct (N × H)
128. #2115C2×C131semidirect
129. #1328C2×C131semidirect
130. #1320C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2930×C1312
#2115×C1312
#1328×C1312
#1320×C1312
#11484131