Finite Group Databasebeta

← C131×#7700 #45693584

Subgroups — C131×#7700 #45693584

Order 33536.

394 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 126 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#2859×C131C211yesmaximal, characteristic
2#1839×C131C211yesmaximal, characteristic
3#1745×C131C211yesmaximal, characteristic
4#1271×C131C214yesmaximal
5C2×#125×C131—21no—
6C2×#97×C131—21no—
7#389×C131—21no—
8#389×C131—21no—
9#389×C131C412yes—
10#389×C131C2212yes—
11#384×C131C411yescharacteristic
12#384×C131C411yescharacteristic
13#382×C131—21no—
14C43×C131C2211yescharacteristic
15#336×C131—21no—
16#336×C131—21no—
17#336×C131—21no—
18#336×C131C2212yes—
19#336×C131C2212yes—
20C22×C8×C131—22no—
21C22×C8×C131—22no—
22#125×C131—44no—
23C2×C4⋊C4×C131—21no—
24C2×C4⋊C4×C131—21no—
25C2×C4⋊C4×C131—22no—
26C2×C4⋊C4×C131—21no—
27C2×C4⋊C4×C131—21no—
28C2×C4⋊C4×C131—22no—
29C2×C4⋊C4×C131C2×C412yes—
30C2×C4⋊C4×C131C2×C412yes—
31C2×C42×C131C2×C411yescharacteristic
32C2×C42×C131C2×C411yescharacteristic
33C2×C42×C131D411yescharacteristic
34C2×C42×C131D411yescharacteristic
35C2×C42×C131D411yescharacteristic
36C2×C42×C131D411yescharacteristic
37C2×C42×C131C2311yescharacteristic
38#97×C131—24no—
39#95×C131—22no—
40#95×C131—22no—
41C22×C4×C131—22no—
42C22×C4×C131—22no—
43C22×C4×C131C22⋊C411yescharacteristic
44C22×C4×C131C22⋊C411yescharacteristic
45C22×C4×C131C22⋊C411yescharacteristic
46C22×C4×C131C22⋊C411yescharacteristic
47C22×C4×C131C22×C411yescharacteristic
48C22×C4×C131C2×D411yescharacteristic
49C22×C4×C131C2×D411yescharacteristic
50C2×C8×C131—24no—
51C2×C8×C131—42no—
52C2×C8×C131—42no—
53C2×C8×C131—42no—
54C2×C8×C131—42no—
55C2×C8×C131—42no—
56C4⋊C4×C131—24no—
57C4⋊C4×C131—42no—
58C4⋊C4×C131—42no—
59C4⋊C4×C131—42no—
60C4⋊C4×C131—42no—
61C4⋊C4×C131—44no—
62C4⋊C4×C131—42no—
63C4⋊C4×C131—44no—
64C42×C131—22no—
65C42×C131—22no—
66C42×C131—22no—
67C42×C131—22no—
68C42×C131—22no—
69C42×C131—41no—
70C42×C131—41no—
71C23×C131C2×C22⋊C411yescharacteristic
72C2×C4×C131—21no—
73C2×C4×C131—21no—
74C2×C4×C131—21no—
75C2×C4×C131—21no—
76C2×C4×C131—21no—
77C2×C4×C131—21no—
78C2×C4×C131—21no—
79C2×C4×C131—21no—
80C2×C4×C131—21no—
81C2×C4×C131—21no—
82C2×C4×C131—21no—
83C2×C4×C131—21no—
84C2×C4×C131—21no—
85C2×C4×C131—21no—
86C2×C4×C131—21no—
87C2×C4×C131—21no—
88C2×C4×C131—42no—
89C2×C4×C131—42no—
90C2×C4×C131—42no—
91C2×C4×C131—42no—
92C2×C4×C131—42no—
93C2×C4×C131—42no—
94C2×C4×C131#10112yes—
95C2×C4×C131#10412yes—
96C2×C4×C131#13112yes—
97C2×C4×C131AGL(1,ℤ/8)12yes—
98C2×C4×C131#13712yes—
99C8×C131—44no—
100C8×C131—82no—
101C22×C131#40811yescharacteristic
102C22×C131#41011yescharacteristic
103C22×C131C2×#10111yescharacteristic
104C22×C131#41811yescharacteristic
105C22×C131#41911yescharacteristic
106C22×C131C2×#10411yescharacteristic
107C22×C131#42111yescharacteristic
108C4×C131—22no—
109C4×C131—22no—
110C4×C131—22no—
111C4×C131—22no—
112C4×C131—22no—
113C4×C131—41no—
114C4×C131—41no—
115C4×C131—82no—
116C4×C131—82no—
117C2×C131#147011yescharacteristic
118C2×C131#148511yescharacteristic
119C2×C131#149611yescharacteristic
120C2×C131#150511yescharacteristic
121C2×C131#151511yescharacteristic
122C2×C131#152811yescharacteristic
123C2×C131#155611yescharacteristic
124#7700C13111yesmaximal, characteristic, direct product factor, Sylow
125C131#770011yescharacteristic, direct product factor, Sylow
126#2859C2×C13111yescharacteristic
127#1839C2×C13111yescharacteristic
128#1745C2×C13111yescharacteristic
129#1271C2×C13114yes—
130C2×#125—21no—
131C2×#97—21no—
132#389—21no—
133#389—21no—
134#389C4×C13112yes—
135#389C22×C13112yes—
136#384C4×C13111yescharacteristic
137#384C4×C13111yescharacteristic
138#382—21no—
139C43C22×C13111yescharacteristic
140#336—21no—
141#336—21no—
142#336—21no—
143#336C22×C13112yes—
144#336C22×C13112yes—
145C22×C8—22no—
146C22×C8—22no—
147#125—44no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4C2×C4×C13112yes—
155C2×C4⋊C4C2×C4×C13112yes—
156C2×C42C2×C4×C13111yescharacteristic
157C2×C42C2×C4×C13111yescharacteristic
158C2×C42D4×C13111yescharacteristic
159C2×C42D4×C13111yescharacteristic
160C2×C42D4×C13111yescharacteristic
161C2×C42D4×C13111yescharacteristic
162C2×C42C23×C13111yescharacteristic
163#97—24no—
164#95—22no—
165#95—22no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4C22⋊C4×C13111yescharacteristic
169C22×C4C22⋊C4×C13111yescharacteristic
170C22×C4C22⋊C4×C13111yescharacteristic
171C22×C4C22⋊C4×C13111yescharacteristic
172C22×C4C22×C4×C13111yescharacteristic
173C22×C4C2×D4×C13111yescharacteristic
174C22×C4C2×D4×C13111yescharacteristic
175C2×C8—24no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—42no—
181C4⋊C4—24no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—44no—
187C4⋊C4—42no—
188C4⋊C4—44no—
189C42—22no—
190C42—22no—
191C42—22no—
192C42—22no—
193C42—22no—
194C42—41no—
195C42—41no—
196C23C2×C22⋊C4×C13111yescharacteristic
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4#101×C13112yes—
220C2×C4#104×C13112yes—
221C2×C4#131×C13112yes—
222C2×C4AGL(1,ℤ/8)×C13112yes—
223C2×C4#137×C13112yes—
224C8—44no—
225C8—82no—
226C22#408×C13111yescharacteristic
227C22#410×C13111yescharacteristic
228C22C2×#101×C13111yescharacteristic
229C22#418×C13111yescharacteristic
230C22#419×C13111yescharacteristic
231C22C2×#104×C13111yescharacteristic
232C22#421×C13111yescharacteristic
233C4—22no—
234C4—22no—
235C4—22no—
236C4—22no—
237C4—22no—
238C4—41no—
239C4—41no—
240C4—82no—
241C4—82no—
242C2#1470×C13111yescharacteristic
243C2#1485×C13111yescharacteristic
244C2#1496×C13111yescharacteristic
245C2#1505×C13111yescharacteristic
246C2#1515×C13111yescharacteristic
247C2#1528×C13111yescharacteristic
248C2#1556×C13111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C131C2×C22⋊C4
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C43×C131 ◁ G

Complements

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

NH ≅ G/Ntype
124. #7700C131direct (N × H)
125. C131#7700direct (N × H)

Maximal subgroups

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

subgroupindex
#2859×C1312
#1839×C1312
#1745×C1312
#1271×C1312
#7700131