Finite Group Databasebeta

← C131×#10517 #45696401

Subgroups — C131×#10517 #45696401

Order 33536.

344 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 94 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#3249×C131C211yesmaximal, characteristic
2#1832×C131C211yesmaximal, characteristic
3#1552×C131C212yesmaximal
4#1506×C131C212yesmaximal
5#1290×C131C211yesmaximal, characteristic
6#533×C131C2212yes—
7#477×C131—22no—
8#467×C131—22no—
9#462×C131—22no—
10#432×C131C2212yes—
11C2×C4⋊C8×C131C2211yescharacteristic
12C2×C4⋊C8×C131C2211yescharacteristic
13#376×C131C2211yescharacteristic
14#336×C131—22no—
15#332×C131—22no—
16#332×C131—22no—
17#328×C131—24no—
18C2×Q16×C131—22no—
19C22×C8×C131—21no—
20C22×C8×C131D412yes—
21C4⋊Q8×C131D412yes—
22C4⋊Q8×C131D412yes—
23#125×C131—22no—
24C22⋊Q8×C131—22no—
25C22⋊Q8×C131—22no—
26C4×Q8×C131—22no—
27C4×Q8×C131—22no—
28#117×C131—22no—
29C2×C42×C131—21no—
30C2×C42×C131C2311yescharacteristic
31#107×C131—22no—
32C4⋊C8×C131—22no—
33C4⋊C8×C131—22no—
34C4⋊C8×C131—22no—
35#103×C131—24no—
36C22⋊C8×C131—22no—
37#97×C131—22no—
38#95×C131—21no—
39#95×C131D412yes—
40C2×Q8×C131—22no—
41C2×Q8×C131—22no—
42C22×C4×C131—22no—
43C22×C4×C131C2×D411yescharacteristic
44C22×C4×C131C2×D411yescharacteristic
45C22×C4×C131#4111yescharacteristic
46Q16×C131—82no—
47C2×C8×C131—22no—
48C2×C8×C131—42no—
49C2×C8×C131—42no—
50C2×C8×C131—41no—
51C2×C8×C131—42no—
52C4⋊C4×C131—22no—
53C4⋊C4×C131—22no—
54C4⋊C4×C131—22no—
55C4⋊C4×C131—22no—
56C4⋊C4×C131—42no—
57C4⋊C4×C131—42no—
58C22⋊C4×C131—42no—
59C42×C131—41no—
60C42×C131—41no—
61C42×C131—42no—
62C42×C131C2×D412yes—
63C42×C131#4112yes—
64C23×C131#12111yescharacteristic
65Q8×C131—42no—
66Q8×C131—42no—
67Q8×C131—82no—
68C2×C4×C131—22no—
69C2×C4×C131—21no—
70C2×C4×C131—21no—
71C2×C4×C131—41no—
72C2×C4×C131—42no—
73C2×C4×C131—42no—
74C2×C4×C131—42no—
75C2×C4×C131—42no—
76C2×C4×C131—42no—
77C2×C4×C131#12011yescharacteristic
78C2×C4×C131#12112yes—
79C2×C4×C131#12312yes—
80C2×C4×C131#12411yescharacteristic
81C8×C131—42no—
82C8×C131—82no—
83C8×C131—81no—
84C22×C131—21no—
85C22×C131—21no—
86C22×C131#39411yescharacteristic
87C22×C131#47312yes—
88C4×C131—22no—
89C4×C131—21no—
90C4×C131—22no—
91C4×C131—82no—
92C4×C131—82no—
93C4×C131—82no—
94C4×C131#45411yescharacteristic
95C4×C131#45511yescharacteristic
96C2×C131—22no—
97C2×C131#204011yescharacteristic
98C2×C131#204711yescharacteristic
99C2×C131#205311yescharacteristic
100#10517C13111yesmaximal, characteristic, direct product factor, Sylow
101C131#1051711yescharacteristic, direct product factor, Sylow
102#3249C2×C13111yescharacteristic
103#1832C2×C13111yescharacteristic
104#1552C2×C13112yes—
105#1506C2×C13112yes—
106#1290C2×C13111yescharacteristic
107#533C22×C13112yes—
108#477—22no—
109#467—22no—
110#462—22no—
111#432C22×C13112yes—
112C2×C4⋊C8C22×C13111yescharacteristic
113C2×C4⋊C8C22×C13111yescharacteristic
114#376C22×C13111yescharacteristic
115#336—22no—
116#332—22no—
117#332—22no—
118#328—24no—
119C2×Q16—22no—
120C22×C8—21no—
121C22×C8D4×C13112yes—
122C4⋊Q8D4×C13112yes—
123C4⋊Q8D4×C13112yes—
124#125—22no—
125C22⋊Q8—22no—
126C22⋊Q8—22no—
127C4×Q8—22no—
128C4×Q8—22no—
129#117—22no—
130C2×C42—21no—
131C2×C42C23×C13111yescharacteristic
132#107—22no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136#103—24no—
137C22⋊C8—22no—
138#97—22no—
139#95—21no—
140#95D4×C13112yes—
141C2×Q8—22no—
142C2×Q8—22no—
143C22×C4—22no—
144C22×C4C2×D4×C13111yescharacteristic
145C22×C4C2×D4×C13111yescharacteristic
146C22×C4#41×C13111yescharacteristic
147Q16—82no—
148C2×C8—22no—
149C2×C8—42no—
150C2×C8—42no—
151C2×C8—41no—
152C2×C8—42no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C22⋊C4—42no—
160C42—41no—
161C42—41no—
162C42—42no—
163C42C2×D4×C13112yes—
164C42#41×C13112yes—
165C23#121×C13111yescharacteristic
166Q8—42no—
167Q8—42no—
168Q8—82no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4#120×C13111yescharacteristic
179C2×C4#121×C13112yes—
180C2×C4#123×C13112yes—
181C2×C4#124×C13111yescharacteristic
182C8—42no—
183C8—82no—
184C8—81no—
185C22—21no—
186C22—21no—
187C22#394×C13111yescharacteristic
188C22#473×C13112yes—
189C4—21no—
190C4—22no—
191C4—22no—
192C4—82no—
193C4—82no—
194C4—82no—
195C4#454×C13111yescharacteristic
196C4#455×C13111yescharacteristic
197C2—22no—
198C2#2040×C13111yescharacteristic
199C2#2047×C13111yescharacteristic
200C2#2053×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#394
commutator, Frattini, cosocleC2×C42C23×C131
prime radicalC23×C131#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
100. #10517C131direct (N × H)
101. C131#10517direct (N × H)

Maximal subgroups

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

subgroupindex
#3249×C1312
#1832×C1312
#1552×C1312
#1506×C1312
#1290×C1312
#10517131