Finite Group Databasebeta

← C131×#8764 #45694648

Subgroups — C131×#8764 #45694648

Order 33536.

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

normal subgroups only

This group has 498 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#2349×C131C211yesmaximal, characteristic
2#1800×C131C211yesmaximal, characteristic
3#1460×C131C211yesmaximal, characteristic
4#1303×C131C212yesmaximal, complemented
5#1286×C131C212yesmaximal, complemented
6C2×C4×D4×C131—21no—
7C2×C4×D4×C131C2211yescharacteristic
8#431×C131C2212yes—
9#423×C131C2212yes—
10C2×#100×C131—21no—
11#389×C131—21no—
12#385×C131—22no—
13#382×C131C2211yescharacteristic
14#380×C131C412yes—
15C4×C4⋊C4×C131C2211yescharacteristic
16C2×#95×C131C412yes—
17#343×C131—21no—
18#323×C131—22no—
19C22×D4×C131D411yescharacteristic
20C23×C4×C131—22no—
21C23×C4×C131C2×C412yes—
22C2×M16×C131—22no—
23C4×D4×C131—22no—
24C4×D4×C131—22no—
25C4×D4×C131—42no—
26C4×D4×C131—42no—
27C2×C4⋊C4×C131—21no—
28C2×C4⋊C4×C131—21no—
29C2×C4⋊C4×C131—22no—
30C2×C4⋊C4×C131D411yescharacteristic
31C2×C22⋊C4×C131—22no—
32C2×C22⋊C4×C131D412yes—
33C2×C42×C131—21no—
34C2×C42×C131C2311yescharacteristic
35C4⋊C8×C131—22no—
36C4⋊C8×C131—22no—
37C4⋊C8×C131—22no—
38#100×C131—42no—
39C22⋊C8×C131—22no—
40C4×C8×C131—22no—
41#95×C131—22no—
42#95×C131—21no—
43#95×C131C2×C411yescharacteristic
44#95×C131C2×C412yes—
45#95×C131C2×C411yescharacteristic
46C24×C131C22⋊C412yes—
47C2×D4×C131—22no—
48C2×D4×C131—22no—
49C2×D4×C131D812yes—
50C2×D4×C131SD1612yes—
51C22×C4×C131—21no—
52C22×C4×C131—22no—
53C22×C4×C131—22no—
54C22×C4×C131—22no—
55C22×C4×C131—21no—
56C22×C4×C131—44no—
57C22×C4×C131—44no—
58C22×C4×C131—82no—
59C22×C4×C131—82no—
60C22×C4×C131C22⋊C412yes—
61C22×C4×C131C22×C411yescharacteristic
62C22×C4×C131C2×D411yescharacteristic
63C22×C4×C131C2×D411yescharacteristic
64M16×C131—42no—
65M16×C131—42no—
66C2×C8×C131—42no—
67C2×C8×C131—42no—
68C4⋊C4×C131—22no—
69C4⋊C4×C131—42no—
70C4⋊C4×C131—41no—
71C4⋊C4×C131—41no—
72C4⋊C4×C131—82no—
73C22⋊C4×C131—24no—
74C22⋊C4×C131—44no—
75C42×C131—41no—
76C42×C131—41no—
77C42×C131#4112yes—
78C42×C131#4112yes—
79C23×C131—22no—
80C23×C131—22no—
81C23×C131—42no—
82C23×C131—42no—
83C23×C131#10214yes—
84C23×C131C2×C22⋊C411yescharacteristic
85D4×C131—24no—
86D4×C131—24no—
87C2×C4×C131—22no—
88C2×C4×C131—22no—
89C2×C4×C131—41no—
90C2×C4×C131—41no—
91C2×C4×C131—41no—
92C2×C4×C131—41no—
93C2×C4×C131—42no—
94C2×C4×C131—41no—
95C2×C4×C131—41no—
96C2×C4×C131—42no—
97C2×C4×C131—42no—
98C2×C4×C131—41no—
99C2×C4×C131—42no—
100C2×C4×C131—82no—
101C2×C4×C131—82no—
102C2×C4×C131—88no—
103C2×C4×C131#11711yescharacteristic
104C2×C4×C131#11711yescharacteristic
105C2×C4×C131#12312yes—
106C2×C4×C131#12312yes—
107C2×C4×C131C2×D811yescharacteristic
108C2×C4×C131C2×SD1611yescharacteristic
109C2×C4×C131#13712yes—
110C8×C131—82no—
111C8×C131—82no—
112C22×C131—21no—
113C22×C131—21no—
114C22×C131—24no—
115C22×C131—44no—
116C22×C131—44no—
117C22×C131—42no—
118C22×C131—42no—
119C22×C131#38111yescharacteristic
120C22×C131C2×#10211yescharacteristic
121C22×C131#41911yescharacteristic
122C4×C131—22no—
123C4×C131—21no—
124C4×C131—21no—
125C4×C131—42no—
126C4×C131—42no—
127C4×C131—81no—
128C4×C131—82no—
129C4×C131#48012yes—
130C4×C131#48312yes—
131C2×C131—21no—
132C2×C131—21no—
133C2×C131—44no—
134C2×C131#182311yescharacteristic
135C2×C131#182711yescharacteristic
136C2×C131#182911yescharacteristic
137#8764C13111yesmaximal, characteristic, direct product factor, Sylow
138C131#876411yescharacteristic, direct product factor, Sylow
139#2349C2×C13111yescharacteristic
140#1800C2×C13111yescharacteristic
141#1460C2×C13111yescharacteristic
142#1303C2×C13112yescomplemented
143#1286C2×C13112yescomplemented
144C2×C4×D4—21no—
145C2×C4×D4C22×C13111yescharacteristic
146#431C22×C13112yes—
147#423C22×C13112yes—
148C2×#100—21no—
149#389—21no—
150#385—22no—
151#382C22×C13111yescharacteristic
152#380C4×C13112yes—
153C4×C4⋊C4C22×C13111yescharacteristic
154C2×#95C4×C13112yes—
155#343—21no—
156#323—22no—
157C22×D4D4×C13111yescharacteristic
158C23×C4—22no—
159C23×C4C2×C4×C13112yes—
160C2×M16—22no—
161C4×D4—22no—
162C4×D4—22no—
163C4×D4—42no—
164C4×D4—42no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4D4×C13111yescharacteristic
169C2×C22⋊C4—22no—
170C2×C22⋊C4D4×C13112yes—
171C2×C42—21no—
172C2×C42C23×C13111yescharacteristic
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176#100—42no—
177C22⋊C8—22no—
178C4×C8—22no—
179#95—22no—
180#95—21no—
181#95C2×C4×C13111yescharacteristic
182#95C2×C4×C13112yes—
183#95C2×C4×C13111yescharacteristic
184C24C22⋊C4×C13112yes—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4D8×C13112yes—
188C2×D4SD16×C13112yes—
189C22×C4—21no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—21no—
194C22×C4—44no—
195C22×C4—44no—
196C22×C4—82no—
197C22×C4—82no—
198C22×C4C22⋊C4×C13112yes—
199C22×C4C22×C4×C13111yescharacteristic
200C22×C4C2×D4×C13111yescharacteristic
201C22×C4C2×D4×C13111yescharacteristic
202M16—42no—
203M16—42no—
204C2×C8—42no—
205C2×C8—42no—
206C4⋊C4—22no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—82no—
211C22⋊C4—24no—
212C22⋊C4—44no—
213C42—41no—
214C42—41no—
215C42#41×C13112yes—
216C42#41×C13112yes—
217C23—22no—
218C23—22no—
219C23—42no—
220C23—42no—
221C23#102×C13114yes—
222C23C2×C22⋊C4×C13111yescharacteristic
223D4—24no—
224D4—24no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—82no—
239C2×C4—82no—
240C2×C4—88no—
241C2×C4#117×C13111yescharacteristic
242C2×C4#117×C13111yescharacteristic
243C2×C4#123×C13112yes—
244C2×C4#123×C13112yes—
245C2×C4C2×D8×C13111yescharacteristic
246C2×C4C2×SD16×C13111yescharacteristic
247C2×C4#137×C13112yes—
248C8—82no—
249C8—82no—
250C22—21no—
251C22—21no—
252C22—24no—
253C22—44no—
254C22—44no—
255C22—42no—
256C22—42no—
257C22#381×C13111yescharacteristic
258C22C2×#102×C13111yescharacteristic
259C22#419×C13111yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—42no—
264C4—42no—
265C4—82no—
266C4—81no—
267C4#480×C13112yes—
268C4#483×C13112yes—
269C2—21no—
270C2—21no—
271C2—44no—
272C2#1823×C13111yescharacteristic
273C2#1827×C13111yescharacteristic
274C2#1829×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#381
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC22×D4×C131D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1303×C131C2semidirect
5. #1286×C131C2semidirect
137. #8764C131direct (N × H)
138. C131#8764direct (N × H)
142. #1303C2×C131semidirect
143. #1286C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2349×C1312
#1800×C1312
#1460×C1312
#1303×C1312
#1286×C1312
#8764131