Finite Group Databasebeta

← C131×#8225 #45694109

Subgroups — C131×#8225 #45694109

Order 33536.

444 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 178 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
1C4×#125×C131C211yesmaximal, characteristic
2#1745×C131C212yesmaximal
3C2×#330×C131C212yesmaximal
4#1295×C131C212yesmaximal
5C2×#125×C131C2211yescharacteristic
6C2×#97×C131C2214yes—
7#389×C131C412yes—
8#387×C131—22no—
9#382×C131C2211yescharacteristic
10C4×C4⋊C4×C131—22no—
11C4×C4⋊C4×C131C412yes—
12C43×C131C2211yescharacteristic
13#336×C131—22no—
14#336×C131—22no—
15#330×C131C418yescomplemented
16C22×C8×C131—24no—
17#125×C131—22no—
18#125×C131C2×C414yes—
19C2×C4⋊C4×C131—22no—
20C2×C4⋊C4×C131—22no—
21C2×C4⋊C4×C131C2×C412yes—
22C2×C4⋊C4×C131C2×C412yes—
23C2×C42×C131—22no—
24C2×C42×C131C2×C411yescharacteristic
25C2×C42×C131C2×C411yescharacteristic
26C2×C42×C131D412yes—
27C2×C42×C131D412yes—
28C2×C42×C131C2311yescharacteristic
29#97×C131—24no—
30#97×C131C2×C418yes—
31#95×C131—22no—
32#95×C131—22no—
33#95×C131—22no—
34C22×C4×C131—22no—
35C22×C4×C131—22no—
36C22×C4×C131C22⋊C411yescharacteristic
37C22×C4×C131C22⋊C412yes—
38C22×C4×C131C22⋊C411yescharacteristic
39C22×C4×C131C22×C411yescharacteristic
40C22×C4×C131C2×D412yes—
41C2×C8×C131—28no—
42C2×C8×C131—44no—
43C2×C8×C131—44no—
44C4⋊C4×C131—22no—
45C4⋊C4×C131—28no—
46C4⋊C4×C131—42no—
47C4⋊C4×C131—44no—
48C4⋊C4×C131C4214yes—
49C42×C131—22no—
50C42×C131—41no—
51C42×C131—42no—
52C42×C131—42no—
53C42×C131—44no—
54C42×C131C22×C412yes—
55C42×C131#4112yes—
56C23×C131C2×C22⋊C411yescharacteristic
57C2×C4×C131—21no—
58C2×C4×C131—21no—
59C2×C4×C131—22no—
60C2×C4×C131—22no—
61C2×C4×C131—22no—
62C2×C4×C131—24no—
63C2×C4×C131—21no—
64C2×C4×C131—22no—
65C2×C4×C131—22no—
66C2×C4×C131—22no—
67C2×C4×C131—22no—
68C2×C4×C131—42no—
69C2×C4×C131—42no—
70C2×C4×C131—42no—
71C2×C4×C131—42no—
72C2×C4×C131—42no—
73C2×C4×C131#10112yes—
74C2×C4×C131C2×C4211yescharacteristic
75C2×C4×C131#11711yescharacteristic
76C2×C4×C131C4×D414yes—
77C8×C131—48no—
78C22×C131C4×C22⋊C411yescharacteristic
79C22×C131C2×#10111yescharacteristic
80C22×C131#41311yescharacteristic
81C22×C131#42112yes—
82C22×C131#42112yes—
83C4×C131—21no—
84C4×C131—21no—
85C4×C131—24no—
86C4×C131—22no—
87C4×C131—41no—
88C4×C131—44no—
89C4×C131—42no—
90C4×C131—82no—
91C2×C131#153411yescharacteristic
92C2×C131#153512yes—
93C2×C131#153711yescharacteristic
94C2×C131C4×#10111yescharacteristic
95C2×C131#175912yes—
96#8225C13111yesmaximal, characteristic, direct product factor, Sylow
97C131#822511yescharacteristic, direct product factor, Sylow
98C4×#125C2×C13111yescharacteristic
99#1745C2×C13112yes—
100C2×#330C2×C13112yes—
101#1295C2×C13112yes—
102C2×#125C22×C13111yescharacteristic
103C2×#97C22×C13114yes—
104#389C4×C13112yes—
105#387—22no—
106#382C22×C13111yescharacteristic
107C4×C4⋊C4—22no—
108C4×C4⋊C4C4×C13112yes—
109C43C22×C13111yescharacteristic
110#336—22no—
111#336—22no—
112#330C4×C13118yescomplemented
113C22×C8—24no—
114#125—22no—
115#125C2×C4×C13114yes—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4C2×C4×C13112yes—
119C2×C4⋊C4C2×C4×C13112yes—
120C2×C42—22no—
121C2×C42C2×C4×C13111yescharacteristic
122C2×C42C2×C4×C13111yescharacteristic
123C2×C42D4×C13112yes—
124C2×C42D4×C13112yes—
125C2×C42C23×C13111yescharacteristic
126#97—24no—
127#97C2×C4×C13118yes—
128#95—22no—
129#95—22no—
130#95—22no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4C22⋊C4×C13111yescharacteristic
134C22×C4C22⋊C4×C13112yes—
135C22×C4C22⋊C4×C13111yescharacteristic
136C22×C4C22×C4×C13111yescharacteristic
137C22×C4C2×D4×C13112yes—
138C2×C8—28no—
139C2×C8—44no—
140C2×C8—44no—
141C4⋊C4—22no—
142C4⋊C4—28no—
143C4⋊C4—42no—
144C4⋊C4—44no—
145C4⋊C4C42×C13114yes—
146C42—22no—
147C42—41no—
148C42—42no—
149C42—42no—
150C42—44no—
151C42C22×C4×C13112yes—
152C42#41×C13112yes—
153C23C2×C22⋊C4×C13111yescharacteristic
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—24no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4#101×C13112yes—
171C2×C4C2×C42×C13111yescharacteristic
172C2×C4#117×C13111yescharacteristic
173C2×C4C4×D4×C13114yes—
174C8—48no—
175C22C4×C22⋊C4×C13111yescharacteristic
176C22C2×#101×C13111yescharacteristic
177C22#413×C13111yescharacteristic
178C22#421×C13112yes—
179C22#421×C13112yes—
180C4—21no—
181C4—21no—
182C4—24no—
183C4—22no—
184C4—44no—
185C4—42no—
186C4—41no—
187C4—82no—
188C2#1534×C13111yescharacteristic
189C2#1535×C13112yes—
190C2#1537×C13111yescharacteristic
191C2C4×#101×C13111yescharacteristic
192C2#1759×C13112yes—
subgroupG/H
center, socle, prime radicalC23×C131C2×C22⋊C4
commutatorC2×C4C2×C42×C131
Frattini, cosocleC2×C42C23×C131
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C43×C131 ◁ G

Complements

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

NH ≅ G/Ntype
15. #330×C131C4semidirect
96. #8225C131direct (N × H)
97. C131#8225direct (N × H)
112. #330C4×C131semidirect

Maximal subgroups

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

subgroupindex
C4×#125×C1312
#1745×C1312
C2×#330×C1312
#1295×C1312
#8225131