Finite Group Databasebeta

← C131×#29659 #45715543

Subgroups — C131×#29659 #45715543

Order 33536.

974 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 974 conjugacy classes of subgroups — too many to draw. Only its 238 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#3458×C131C211yesmaximal, characteristic
2#2484×C131C213yesmaximal
3#2062×C131C214yesmaximal
4#2030×C131C214yesmaximal
5#1820×C131C213yesmaximal
6#544×C131—23no—
7#544×C131—23no—
8#543×C131C2214yes—
9#533×C131—26no—
10C2×#117×C131C2213yes—
11C22×C4⋊C4×C131C2211yescharacteristic
12#400×C131—23no—
13#398×C131—23no—
14#387×C131—26no—
15#385×C131C2216yes—
16#381×C131C2216yes—
17#381×C131C2213yes—
18#342×C131C22112yes—
19C23×C4×C131C2311yescharacteristic
20C23×C4×C131C2311yescharacteristic
21C23×C4×C131C2311yescharacteristic
22C4⋊Q8×C131—26no—
23C4⋊Q8×C131—26no—
24#125×C131—212no—
25C22⋊Q8×C131—212no—
26C22⋊Q8×C131—212no—
27C4×Q8×C131—24no—
28C4×Q8×C131—24no—
29#117×C131—26no—
30#117×C131—26no—
31C2×C4⋊C4×C131—23no—
32C2×C4⋊C4×C131—26no—
33C2×C4⋊C4×C131—23no—
34C2×C4⋊C4×C131D413yes—
35C2×C4⋊C4×C131D413yes—
36C2×C22⋊C4×C131C2316yes—
37C2×C22⋊C4×C131C2316yes—
38C2×C42×C131D416yes—
39#95×C131—23no—
40#95×C131—26no—
41#95×C131—26no—
42#95×C131—26no—
43#95×C131—23no—
44C24×C131C2411yescharacteristic
45C2×Q8×C131—24no—
46C2×Q8×C131—24no—
47C22×C4×C131—24no—
48C22×C4×C131—23no—
49C22×C4×C131—26no—
50C22×C4×C131—23no—
51C22×C4×C131—24no—
52C22×C4×C131—42no—
53C22×C4×C131C2×D413yes—
54C22×C4×C131C2×D413yes—
55C22×C4×C131C2×D416yes—
56C22×C4×C131C2×D416yes—
57C4⋊C4×C131—212no—
58C4⋊C4×C131—212no—
59C4⋊C4×C131—26no—
60C4⋊C4×C131—26no—
61C4⋊C4×C131—412no—
62C4⋊C4×C131—41no—
63C4⋊C4×C131—43no—
64C22⋊C4×C131—212no—
65C22⋊C4×C131—212no—
66C42×C131—26no—
67C42×C131—26no—
68C23×C131—41no—
69C23×C131—41no—
70C23×C131C22×D413yes—
71C23×C1312−1+414yes—
72Q8×C131—84no—
73Q8×C131—84no—
74C2×C4×C131—26no—
75C2×C4×C131—26no—
76C2×C4×C131—26no—
77C2×C4×C131—26no—
78C2×C4×C131—26no—
79C2×C4×C131—43no—
80C2×C4×C131—41no—
81C2×C4×C131—46no—
82C2×C4×C131—46no—
83C2×C4×C131—46no—
84C2×C4×C131—46no—
85C2×C4×C131—41no—
86C2×C4×C131—46no—
87C2×C4×C131—46no—
88C2×C4×C131#12011yescharacteristic
89C2×C4×C131#12013yes—
90C22×C131—23no—
91C22×C131—23no—
92C22×C131—44no—
93C22×C131C2×#12011yescharacteristic
94C22×C131#53616yes—
95C4×C131—21no—
96C4×C131—23no—
97C4×C131—42no—
98C4×C131—46no—
99C4×C131—46no—
100C4×C131—86no—
101C4×C131—81no—
102C2×C131—26no—
103C2×C131#261411yescharacteristic
104C2×C131#302511yescharacteristic
105C2×C131#302811yescharacteristic
106#29659C13111yesmaximal, characteristic, direct product factor, Sylow
107C131#2965911yescharacteristic, direct product factor, Sylow
108#3458C2×C13111yescharacteristic
109#2484C2×C13113yes—
110#2062C2×C13114yes—
111#2030C2×C13114yes—
112#1820C2×C13113yes—
113#544—23no—
114#544—23no—
115#543C22×C13114yes—
116#533—26no—
117C2×#117C22×C13113yes—
118C22×C4⋊C4C22×C13111yescharacteristic
119#400—23no—
120#398—23no—
121#387—26no—
122#385C22×C13116yes—
123#381C22×C13113yes—
124#381C22×C13116yes—
125#342C22×C131112yes—
126C23×C4C23×C13111yescharacteristic
127C23×C4C23×C13111yescharacteristic
128C23×C4C23×C13111yescharacteristic
129C4⋊Q8—26no—
130C4⋊Q8—26no—
131#125—212no—
132C22⋊Q8—212no—
133C22⋊Q8—212no—
134C4×Q8—24no—
135C4×Q8—24no—
136#117—26no—
137#117—26no—
138C2×C4⋊C4—23no—
139C2×C4⋊C4—23no—
140C2×C4⋊C4—26no—
141C2×C4⋊C4D4×C13113yes—
142C2×C4⋊C4D4×C13113yes—
143C2×C22⋊C4C23×C13116yes—
144C2×C22⋊C4C23×C13116yes—
145C2×C42D4×C13116yes—
146#95—23no—
147#95—26no—
148#95—26no—
149#95—23no—
150#95—26no—
151C24C24×C13111yescharacteristic
152C2×Q8—24no—
153C2×Q8—24no—
154C22×C4—24no—
155C22×C4—23no—
156C22×C4—26no—
157C22×C4—23no—
158C22×C4—24no—
159C22×C4—42no—
160C22×C4C2×D4×C13113yes—
161C22×C4C2×D4×C13113yes—
162C22×C4C2×D4×C13116yes—
163C22×C4C2×D4×C13116yes—
164C4⋊C4—212no—
165C4⋊C4—212no—
166C4⋊C4—26no—
167C4⋊C4—26no—
168C4⋊C4—412no—
169C4⋊C4—41no—
170C4⋊C4—43no—
171C22⋊C4—212no—
172C22⋊C4—212no—
173C42—26no—
174C42—26no—
175C23—41no—
176C23—41no—
177C23C22×D4×C13113yes—
178C232−1+4×C13114yes—
179Q8—84no—
180Q8—84no—
181C2×C4—26no—
182C2×C4—26no—
183C2×C4—26no—
184C2×C4—26no—
185C2×C4—26no—
186C2×C4—43no—
187C2×C4—41no—
188C2×C4—46no—
189C2×C4—46no—
190C2×C4—46no—
191C2×C4—46no—
192C2×C4—41no—
193C2×C4—46no—
194C2×C4—46no—
195C2×C4#120×C13111yescharacteristic
196C2×C4#120×C13113yes—
197C22—23no—
198C22—23no—
199C22—44no—
200C22C2×#120×C13111yescharacteristic
201C22#536×C13116yes—
202C4—21no—
203C4—23no—
204C4—42no—
205C4—46no—
206C4—46no—
207C4—86no—
208C4—81no—
209C2—26no—
210C2#2614×C13111yescharacteristic
211C2#3025×C13111yescharacteristic
212C2#3028×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC24C24×C131
prime radicalC24×C131C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
106. #29659C131direct (N × H)
107. C131#29659direct (N × H)

Maximal subgroups

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

subgroupindex
#3458×C1312
#2484×C1312
#2062×C1312
#2030×C1312
#1820×C1312
#29659131