Finite Group Databasebeta

← C131×#9487 #45695371

Subgroups — C131×#9487 #45695371

Order 33536.

518 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 134 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#2975×C131C211yesmaximal, characteristic
2#2580×C131C211yesmaximal, characteristic
3#1800×C131C211yesmaximal, characteristic
4#1487×C131C212yesmaximal, complemented
5#1286×C131C212yesmaximal, complemented
6C2×C4×Q8×C131C2211yescharacteristic
7C2×C4×D4×C131C2211yescharacteristic
8#436×C131—24no—
9#431×C131C2212yes—
10#423×C131C2212yes—
11C2×#100×C131—21no—
12#407×C131—22no—
13#399×C131C412yes—
14#393×C131C412yes—
15#390×C131—21no—
16#389×C131—21no—
17#385×C131—22no—
18#382×C131C2211yescharacteristic
19#343×C131—21no—
20Q8⋊C8×C131—24no—
21C22×Q8×C131C2×C411yescharacteristic
22C22×D4×C131D411yescharacteristic
23C23×C4×C131D412yes—
24C2×M16×C131—24no—
25C2×M16×C131—22no—
26C4×Q8×C131—22no—
27C4×Q8×C131—22no—
28C4×D4×C131—22no—
29C4×D4×C131—22no—
30C2×C4⋊C4×C131—21no—
31C2×C4⋊C4×C131—21no—
32C2×C4⋊C4×C131—22no—
33C2×C4⋊C4×C131C2×C411yescharacteristic
34C2×C4⋊C4×C131D411yescharacteristic
35C2×C22⋊C4×C131—22no—
36C2×C22⋊C4×C131—22no—
37C2×C22⋊C4×C131C2×C412yes—
38C2×C42×C131—21no—
39C2×C42×C131C2311yescharacteristic
40C4⋊C8×C131—22no—
41C4⋊C8×C131—22no—
42C4⋊C8×C131—22no—
43#100×C131—42no—
44C22⋊C8×C131—24no—
45C22⋊C8×C131—22no—
46C4×C8×C131D414yes—
47#95×C131—22no—
48#95×C131—21no—
49#95×C131C2×C412yes—
50C24×C131C22⋊C412yes—
51C2×Q8×C131—22no—
52C2×Q8×C131—42no—
53C2×D4×C131—22no—
54C2×D4×C131—21no—
55C2×D4×C131—22no—
56C2×D4×C131—21no—
57C22×C4×C131—21no—
58C22×C4×C131—22no—
59C22×C4×C131—22no—
60C22×C4×C131—22no—
61C22×C4×C131—21no—
62C22×C4×C131—82no—
63C22×C4×C131C22⋊C412yes—
64C22×C4×C131C22×C411yescharacteristic
65C22×C4×C131C2×D411yescharacteristic
66C22×C4×C131C2×D411yescharacteristic
67M16×C131—42no—
68M16×C131—42no—
69M16×C131—84no—
70C2×C8×C131—24no—
71C2×C8×C131—42no—
72C4⋊C4×C131—22no—
73C4⋊C4×C131—22no—
74C4⋊C4×C131—41no—
75C4⋊C4×C131—41no—
76C4⋊C4×C131—41no—
77C4⋊C4×C131—41no—
78C4⋊C4×C131—82no—
79C22⋊C4×C131—24no—
80C22⋊C4×C131—44no—
81C22⋊C4×C131—82no—
82C42×C131—42no—
83C42×C131C2×D412yes—
84C42×C131#4112yes—
85C23×C131—22no—
86C23×C131—22no—
87C23×C131—22no—
88C23×C131—42no—
89C23×C131—42no—
90C23×C131C2×C22⋊C411yescharacteristic
91Q8×C131—24no—
92Q8×C131—42no—
93D4×C131—42no—
94D4×C131—42no—
95C2×C4×C131—22no—
96C2×C4×C131—22no—
97C2×C4×C131—41no—
98C2×C4×C131—41no—
99C2×C4×C131—44no—
100C2×C4×C131—41no—
101C2×C4×C131—41no—
102C2×C4×C131—42no—
103C2×C4×C131—42no—
104C2×C4×C131—41no—
105C2×C4×C131—42no—
106C2×C4×C131—41no—
107C2×C4×C131—41no—
108C2×C4×C131—42no—
109C2×C4×C131—82no—
110C2×C4×C131C4×D412yes—
111C2×C4×C131#12011yescharacteristic
112C2×C4×C131#12112yes—
113C2×C4×C131#12311yescharacteristic
114C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C131#13712yes—
116C2×C4×C131#13711yescharacteristic
117C8×C131—44no—
118C8×C131—82no—
119C22×C131—21no—
120C22×C131—21no—
121C22×C131—44no—
122C22×C131—42no—
123C22×C131—42no—
124C22×C131—42no—
125C22×C131—82no—
126C22×C131#38611yescharacteristic
127C22×C131#41711yescharacteristic
128C22×C131#41911yescharacteristic
129C4×C131—22no—
130C4×C131—21no—
131C4×C131—21no—
132C4×C131—42no—
133C4×C131—42no—
134C4×C131—82no—
135C4×C131—81no—
136C4×C131#46812yes—
137C4×C131#47012yes—
138C2×C131—21no—
139C2×C131—21no—
140C2×C131—82no—
141C2×C131#189111yescharacteristic
142C2×C131#189411yescharacteristic
143C2×C131#191111yescharacteristic
144#9487C13111yesmaximal, characteristic, direct product factor, Sylow
145C131#948711yescharacteristic, direct product factor, Sylow
146#2975C2×C13111yescharacteristic
147#2580C2×C13111yescharacteristic
148#1800C2×C13111yescharacteristic
149#1487C2×C13112yescomplemented
150#1286C2×C13112yescomplemented
151C2×C4×Q8C22×C13111yescharacteristic
152C2×C4×D4C22×C13111yescharacteristic
153#436—24no—
154#431C22×C13112yes—
155#423C22×C13112yes—
156C2×#100—21no—
157#407—22no—
158#399C4×C13112yes—
159#393C4×C13112yes—
160#390—21no—
161#389—21no—
162#385—22no—
163#382C22×C13111yescharacteristic
164#343—21no—
165Q8⋊C8—24no—
166C22×Q8C2×C4×C13111yescharacteristic
167C22×D4D4×C13111yescharacteristic
168C23×C4D4×C13112yes—
169C2×M16—24no—
170C2×M16—22no—
171C4×Q8—22no—
172C4×Q8—22no—
173C4×D4—22no—
174C4×D4—22no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4C2×C4×C13111yescharacteristic
179C2×C4⋊C4D4×C13111yescharacteristic
180C2×C22⋊C4—22no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4C2×C4×C13112yes—
183C2×C42—21no—
184C2×C42C23×C13111yescharacteristic
185C4⋊C8—22no—
186C4⋊C8—22no—
187C4⋊C8—22no—
188#100—42no—
189C22⋊C8—24no—
190C22⋊C8—22no—
191C4×C8D4×C13114yes—
192#95—22no—
193#95—21no—
194#95C2×C4×C13112yes—
195C24C22⋊C4×C13112yes—
196C2×Q8—22no—
197C2×Q8—42no—
198C2×D4—22no—
199C2×D4—21no—
200C2×D4—22no—
201C2×D4—21no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—21no—
207C22×C4—82no—
208C22×C4C22⋊C4×C13112yes—
209C22×C4C22×C4×C13111yescharacteristic
210C22×C4C2×D4×C13111yescharacteristic
211C22×C4C2×D4×C13111yescharacteristic
212M16—42no—
213M16—42no—
214M16—84no—
215C2×C8—24no—
216C2×C8—42no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—82no—
224C22⋊C4—24no—
225C22⋊C4—44no—
226C22⋊C4—82no—
227C42—42no—
228C42C2×D4×C13112yes—
229C42#41×C13112yes—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—42no—
234C23—42no—
235C23C2×C22⋊C4×C13111yescharacteristic
236Q8—24no—
237Q8—42no—
238D4—42no—
239D4—42no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—44no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—82no—
255C2×C4C4×D4×C13112yes—
256C2×C4#120×C13111yescharacteristic
257C2×C4#121×C13112yes—
258C2×C4#123×C13111yescharacteristic
259C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
260C2×C4#137×C13112yes—
261C2×C4#137×C13111yescharacteristic
262C8—44no—
263C8—82no—
264C22—21no—
265C22—21no—
266C22—44no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—82no—
271C22#386×C13111yescharacteristic
272C22#417×C13111yescharacteristic
273C22#419×C13111yescharacteristic
274C4—22no—
275C4—21no—
276C4—21no—
277C4—42no—
278C4—42no—
279C4—82no—
280C4—81no—
281C4#468×C13112yes—
282C4#470×C13112yes—
283C2—21no—
284C2—21no—
285C2—82no—
286C2#1891×C13111yescharacteristic
287C2#1894×C13111yescharacteristic
288C2#1911×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#386
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. #1487×C131C2semidirect
5. #1286×C131C2semidirect
144. #9487C131direct (N × H)
145. C131#9487direct (N × H)
149. #1487C2×C131semidirect
150. #1286C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2975×C1312
#2580×C1312
#1800×C1312
#1487×C1312
#1286×C1312
#9487131