Finite Group Databasebeta

← C131×#10352 #45696236

Subgroups — C131×#10352 #45696236

Order 33536.

416 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 138 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#2571×C131C211yesmaximal, characteristic
2#1987×C131C212yesmaximal
3#1956×C131C211yesmaximal, characteristic
4#1296×C131C211yesmaximal, characteristic
5#1279×C131C212yesmaximal
6C2×C4⋊Q8×C131C2211yescharacteristic
7C2×C4⋊C8×C131C2212yes—
8C2×#103×C131—22no—
9C2×C4×C8×C131C2211yescharacteristic
10#400×C131—22no—
11#389×C131—22no—
12#384×C131C2211yescharacteristic
13#382×C131—22no—
14C4×C4⋊C4×C131C2212yes—
15#340×C131—22no—
16#340×C131—22no—
17C22×Q8×C131—21no—
18C22×C8×C131—21no—
19C22×C8×C131—22no—
20C4⋊Q8×C131—22no—
21C4⋊Q8×C131—21no—
22C4⋊Q8×C131Q812yes—
23C2×C4⋊C4×C131—22no—
24C2×C4⋊C4×C131—22no—
25C2×C4⋊C4×C131—22no—
26C2×C4⋊C4×C131D412yes—
27C2×C4⋊C4×C131D412yes—
28C2×C4⋊C4×C131D412yes—
29C2×C42×C131—22no—
30C2×C42×C131C2311yescharacteristic
31C4⋊C8×C131—22no—
32C4⋊C8×C131—22no—
33#103×C131—44no—
34C4×C8×C131—22no—
35#95×C131—24no—
36#95×C131—22no—
37#95×C131—22no—
38C2×Q8×C131—22no—
39C2×Q8×C131—42no—
40C2×Q8×C131—42no—
41C2×Q8×C131—41no—
42C22×C4×C131—22no—
43C22×C4×C131—22no—
44C22×C4×C131—22no—
45C22×C4×C131—41no—
46C22×C4×C131C2×D411yescharacteristic
47C22×C4×C131C2×D412yes—
48C2×C8×C131—22no—
49C2×C8×C131—41no—
50C2×C8×C131—41no—
51C2×C8×C131—42no—
52C2×C8×C131—42no—
53C2×C8×C131—42no—
54C4⋊C4×C131—24no—
55C4⋊C4×C131—22no—
56C4⋊C4×C131—22no—
57C4⋊C4×C131—22no—
58C4⋊C4×C131—22no—
59C4⋊C4×C131—42no—
60C4⋊C4×C131—42no—
61C4⋊C4×C131—42no—
62C4⋊C4×C131—42no—
63C4⋊C4×C131—82no—
64C42×C131—42no—
65C42×C131—42no—
66C42×C131C2×Q811yescharacteristic
67C42×C131#4112yes—
68C42×C131#4111yescharacteristic
69C23×C131#12011yescharacteristic
70Q8×C131—44no—
71Q8×C131—82no—
72C2×C4×C131—21no—
73C2×C4×C131—21no—
74C2×C4×C131—42no—
75C2×C4×C131—42no—
76C2×C4×C131—42no—
77C2×C4×C131—42no—
78C2×C4×C131—42no—
79C2×C4×C131—44no—
80C2×C4×C131—42no—
81C2×C4×C131—42no—
82C2×C4×C131—42no—
83C2×C4×C131—81no—
84C2×C4×C131—81no—
85C2×C4×C131C22⋊Q811yescharacteristic
86C2×C4×C131C22⋊Q812yes—
87C2×C4×C131#12411yescharacteristic
88C2×C4×C131#12412yes—
89C2×C4×C131#13512yes—
90C2×C4×C131#13512yes—
91C2×C4×C131#13712yes—
92C2×C4×C131#13712yes—
93C8×C131—42no—
94C8×C131—82no—
95C22×C131#39311yescharacteristic
96C22×C131#45212yes—
97C22×C131#45212yes—
98C22×C131#45311yescharacteristic
99C22×C131#45411yescharacteristic
100C4×C131—21no—
101C4×C131—21no—
102C4×C131—82no—
103C4×C131—82no—
104C4×C131—82no—
105C4×C131—82no—
106C4×C131#47912yes—
107C4×C131#47912yes—
108C4×C131#48812yes—
109C4×C131#49112yes—
110C2×C131#163011yescharacteristic
111C2×C131#163411yescharacteristic
112C2×C131#163812yes—
113C2×C131#202612yes—
114C2×C131#202711yescharacteristic
115#10352C13111yesmaximal, characteristic, direct product factor, Sylow
116C131#1035211yescharacteristic, direct product factor, Sylow
117#2571C2×C13111yescharacteristic
118#1987C2×C13112yes—
119#1956C2×C13111yescharacteristic
120#1296C2×C13111yescharacteristic
121#1279C2×C13112yes—
122C2×C4⋊Q8C22×C13111yescharacteristic
123C2×C4⋊C8C22×C13112yes—
124C2×#103—22no—
125C2×C4×C8C22×C13111yescharacteristic
126#400—22no—
127#389—22no—
128#384C22×C13111yescharacteristic
129#382—22no—
130C4×C4⋊C4C22×C13112yes—
131#340—22no—
132#340—22no—
133C22×Q8—21no—
134C22×C8—21no—
135C22×C8—22no—
136C4⋊Q8—22no—
137C4⋊Q8—21no—
138C4⋊Q8Q8×C13112yes—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4D4×C13112yes—
143C2×C4⋊C4D4×C13112yes—
144C2×C4⋊C4D4×C13112yes—
145C2×C42—22no—
146C2×C42C23×C13111yescharacteristic
147C4⋊C8—22no—
148C4⋊C8—22no—
149#103—44no—
150C4×C8—22no—
151#95—22no—
152#95—24no—
153#95—22no—
154C2×Q8—22no—
155C2×Q8—42no—
156C2×Q8—42no—
157C2×Q8—41no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—41no—
162C22×C4C2×D4×C13111yescharacteristic
163C22×C4C2×D4×C13112yes—
164C2×C8—22no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—42no—
168C2×C8—42no—
169C2×C8—42no—
170C4⋊C4—24no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C4⋊C4—82no—
180C42—42no—
181C42—42no—
182C42C2×Q8×C13111yescharacteristic
183C42#41×C13112yes—
184C42#41×C13111yescharacteristic
185C23#120×C13111yescharacteristic
186Q8—44no—
187Q8—82no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—44no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—81no—
200C2×C4—81no—
201C2×C4C22⋊Q8×C13111yescharacteristic
202C2×C4C22⋊Q8×C13112yes—
203C2×C4#124×C13111yescharacteristic
204C2×C4#124×C13112yes—
205C2×C4#135×C13112yes—
206C2×C4#135×C13112yes—
207C2×C4#137×C13112yes—
208C2×C4#137×C13112yes—
209C8—42no—
210C8—82no—
211C22#393×C13111yescharacteristic
212C22#452×C13112yes—
213C22#452×C13112yes—
214C22#453×C13111yescharacteristic
215C22#454×C13111yescharacteristic
216C4—21no—
217C4—21no—
218C4—82no—
219C4—82no—
220C4—82no—
221C4—82no—
222C4#479×C13112yes—
223C4#479×C13112yes—
224C4#488×C13112yes—
225C4#491×C13112yes—
226C2#1630×C13111yescharacteristic
227C2#1634×C13111yescharacteristic
228C2#1638×C13112yes—
229C2#2026×C13112yes—
230C2#2027×C13111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C131#120
commutator, Frattini, cosocleC2×C42C23×C131
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
115. #10352C131direct (N × H)
116. C131#10352direct (N × H)

Maximal subgroups

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

subgroupindex
#2571×C1312
#1987×C1312
#1956×C1312
#1296×C1312
#1279×C1312
#10352131