Finite Group Databasebeta

← C131×#10037 #45695921

Subgroups — C131×#10037 #45695921

Order 33536.

476 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 122 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#3162×C131C211yesmaximal, characteristic
2#3104×C131C212yesmaximal
3#1985×C131C211yesmaximal, characteristic
4#1481×C131C212yesmaximal
5#1275×C131C211yesmaximal, characteristic
6#533×C131C2212yes—
7C2×C4×Q8×C131C2211yescharacteristic
8#501×C131—22no—
9#501×C131—22no—
10#484×C131—22no—
11#477×C131—22no—
12#462×C131—22no—
13#451×C131—22no—
14C4×Q16×C131—24no—
15#431×C131C2212yes—
16#427×C131—22no—
17C2×C4⋊C8×C131C2211yescharacteristic
18C2×#97×C131C2211yescharacteristic
19#336×C131—22no—
20Q8⋊C8×C131—24no—
21C22×Q8×C131D411yescharacteristic
22C2×Q16×C131—24no—
23C22×C8×C131—21no—
24C22×C8×C131D412yes—
25C4⋊Q8×C131D412yes—
26C4⋊Q8×C131D412yes—
27#125×C131—22no—
28C22⋊Q8×C131—22no—
29C22⋊Q8×C131—22no—
30C4×Q8×C131—22no—
31C4×Q8×C131—22no—
32C4×Q8×C131—22no—
33C4×Q8×C131—22no—
34#117×C131—22no—
35C2×C4⋊C4×C131—21no—
36C2×C4⋊C4×C131D411yescharacteristic
37C2×C42×C131—21no—
38C2×C42×C131C2311yescharacteristic
39#107×C131—22no—
40#107×C131—22no—
41#107×C131—24no—
42#106×C131—24no—
43C4⋊C8×C131—22no—
44C4⋊C8×C131—22no—
45#103×C131—24no—
46#103×C131—24no—
47C22⋊C8×C131—22no—
48#97×C131—22no—
49C4×C8×C131D414yes—
50C2×Q8×C131—22no—
51C2×Q8×C131—22no—
52C2×Q8×C131—22no—
53C2×Q8×C131—42no—
54C22×C4×C131—21no—
55C22×C4×C131—21no—
56C22×C4×C131C2×D411yescharacteristic
57C22×C4×C131C2×D411yescharacteristic
58C22×C4×C131#4111yescharacteristic
59Q16×C131—48no—
60C2×C8×C131—22no—
61C2×C8×C131—22no—
62C2×C8×C131—24no—
63C2×C8×C131—41no—
64C2×C8×C131—42no—
65C2×C8×C131Q1614yescomplemented
66C4⋊C4×C131—22no—
67C4⋊C4×C131—22no—
68C4⋊C4×C131—22no—
69C4⋊C4×C131—22no—
70C4⋊C4×C131—22no—
71C4⋊C4×C131—42no—
72C4⋊C4×C131—42no—
73C4⋊C4×C131—42no—
74C22⋊C4×C131—42no—
75C42×C131—41no—
76C42×C131—41no—
77C42×C131—42no—
78C42×C131C2×D412yes—
79C42×C131C2×D412yes—
80C23×C131#12111yescharacteristic
81Q8×C131—24no—
82Q8×C131—42no—
83Q8×C131—44no—
84Q8×C131—44no—
85C2×C4×C131—22no—
86C2×C4×C131—41no—
87C2×C4×C131—41no—
88C2×C4×C131—41no—
89C2×C4×C131—41no—
90C2×C4×C131—42no—
91C2×C4×C131—41no—
92C2×C4×C131—42no—
93C2×C4×C131—42no—
94C2×C4×C131#12012yes—
95C2×C4×C131#12011yescharacteristic
96C2×C4×C131#12112yes—
97C2×C4×C131#12711yescharacteristic
98C2×C4×C131C2×Q1612yes—
99C2×C4×C131#13712yes—
100C8×C131—24no—
101C8×C131—44no—
102C8×C131—81no—
103C22×C131—21no—
104C22×C131—21no—
105C22×C131#39211yescharacteristic
106C22×C131#46212yes—
107C4×C131—22no—
108C4×C131—22no—
109C4×C131—42no—
110C4×C131—82no—
111C4×C131—81no—
112C4×C131—82no—
113C4×C131#45112yes—
114C4×C131#49411yescharacteristic
115C4×C131#49711yescharacteristic
116C2×C131—22no—
117C2×C131#201011yescharacteristic
118C2×C131#201611yescharacteristic
119C2×C131#201711yescharacteristic
120#10037C13111yesmaximal, characteristic, direct product factor, Sylow
121C131#1003711yescharacteristic, direct product factor, Sylow
122#3162C2×C13111yescharacteristic
123#3104C2×C13112yes—
124#1985C2×C13111yescharacteristic
125#1481C2×C13112yes—
126#1275C2×C13111yescharacteristic
127#533C22×C13112yes—
128C2×C4×Q8C22×C13111yescharacteristic
129#501—22no—
130#501—22no—
131#484—22no—
132#477—22no—
133#462—22no—
134#451—22no—
135C4×Q16—24no—
136#431C22×C13112yes—
137#427—22no—
138C2×C4⋊C8C22×C13111yescharacteristic
139C2×#97C22×C13111yescharacteristic
140#336—22no—
141Q8⋊C8—24no—
142C22×Q8D4×C13111yescharacteristic
143C2×Q16—24no—
144C22×C8—21no—
145C22×C8D4×C13112yes—
146C4⋊Q8D4×C13112yes—
147C4⋊Q8D4×C13112yes—
148#125—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C4×Q8—22no—
152C4×Q8—22no—
153C4×Q8—22no—
154C4×Q8—22no—
155#117—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4D4×C13111yescharacteristic
158C2×C42—21no—
159C2×C42C23×C13111yescharacteristic
160#107—22no—
161#107—22no—
162#107—24no—
163#106—24no—
164C4⋊C8—22no—
165C4⋊C8—22no—
166#103—24no—
167#103—24no—
168C22⋊C8—22no—
169#97—22no—
170C4×C8D4×C13114yes—
171C2×Q8—22no—
172C2×Q8—22no—
173C2×Q8—22no—
174C2×Q8—42no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4C2×D4×C13111yescharacteristic
178C22×C4C2×D4×C13111yescharacteristic
179C22×C4#41×C13111yescharacteristic
180Q16—48no—
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—24no—
184C2×C8—41no—
185C2×C8—42no—
186C2×C8Q16×C13114yescomplemented
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C22⋊C4—42no—
196C42—41no—
197C42—41no—
198C42—42no—
199C42C2×D4×C13112yes—
200C42C2×D4×C13112yes—
201C23#121×C13111yescharacteristic
202Q8—24no—
203Q8—42no—
204Q8—44no—
205Q8—44no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4#120×C13112yes—
216C2×C4#120×C13111yescharacteristic
217C2×C4#121×C13112yes—
218C2×C4#127×C13111yescharacteristic
219C2×C4C2×Q16×C13112yes—
220C2×C4#137×C13112yes—
221C8—24no—
222C8—44no—
223C8—81no—
224C22—21no—
225C22—21no—
226C22#392×C13111yescharacteristic
227C22#462×C13112yes—
228C4—22no—
229C4—22no—
230C4—42no—
231C4—82no—
232C4—81no—
233C4—82no—
234C4#451×C13112yes—
235C4#494×C13111yescharacteristic
236C4#497×C13111yescharacteristic
237C2—22no—
238C2#2010×C13111yescharacteristic
239C2#2016×C13111yescharacteristic
240C2#2017×C13111yescharacteristic
subgroupG/H
centerC2×C4×C131#127
commutator, Frattini, cosocleC2×C42C23×C131
socleC22×C131#392
prime radicalC23×C131#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
65. C2×C8×C131Q16semidirect
120. #10037C131direct (N × H)
121. C131#10037direct (N × H)
186. C2×C8Q16×C131semidirect

Maximal subgroups

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

subgroupindex
#3162×C1312
#3104×C1312
#1985×C1312
#1481×C1312
#1275×C1312
#10037131