Finite Group Databasebeta

← C131×#7797 #45693681

Subgroups — C131×#7797 #45693681

Order 33536.

478 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 106 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#2683×C131C211yesmaximal, characteristic
2#2093×C131C211yesmaximal, characteristic
3#2083×C131C212yesmaximal, complemented
4#1271×C131C212yesmaximal, complemented
5#1270×C131C211yesmaximal, characteristic
6C2×C22⋊Q8×C131—22no—
7C2×#107×C131—22no—
8C2×#107×C131—21no—
9C2×#102×C131—21no—
10#396×C131—22no—
11#395×C131—21no—
12#390×C131C2211yescharacteristic
13#389×C131C2212yes—
14#386×C131—21no—
15#384×C131C2211yescharacteristic
16#340×C131—22no—
17#336×C131C2212yes—
18#336×C131C2211yescharacteristic
19C22×Q8×C131—21no—
20C22×D4×C131D411yescharacteristic
21C23×C4×C131—21no—
22C22×C8×C131—21no—
23C22×C8×C131—22no—
24C22⋊Q8×C131—44no—
25C22⋊Q8×C131—44no—
26C2×C4⋊C4×C131—22no—
27C2×C4⋊C4×C131—22no—
28C2×C4⋊C4×C131—21no—
29C2×C4⋊C4×C131—22no—
30C2×C4⋊C4×C131D412yes—
31C2×C4⋊C4×C131D412yes—
32C2×C4⋊C4×C131D411yescharacteristic
33C2×C22⋊C4×C131—22no—
34C2×C22⋊C4×C131—22no—
35C2×C22⋊C4×C131—21no—
36C2×C42×C131C2311yescharacteristic
37#107×C131—42no—
38#107×C131—44no—
39#102×C131—42no—
40#95×C131—21no—
41#95×C131—22no—
42C24×C131—21no—
43C2×Q8×C131—44no—
44C2×Q8×C131—81no—
45C2×D4×C131—21no—
46C2×D4×C131—41no—
47C2×D4×C131—41no—
48C2×D4×C131Q1612yes—
49C22×C4×C131—22no—
50C22×C4×C131—22no—
51C22×C4×C131—21no—
52C22×C4×C131—44no—
53C22×C4×C131—41no—
54C22×C4×C131—81no—
55C22×C4×C131C2×D412yes—
56C22×C4×C131C2×D411yescharacteristic
57C2×C8×C131—22no—
58C2×C8×C131—24no—
59C2×C8×C131—42no—
60C2×C8×C131—41no—
61C2×C8×C131—42no—
62C2×C8×C131—41no—
63C4⋊C4×C131—22no—
64C4⋊C4×C131—41no—
65C4⋊C4×C131—42no—
66C4⋊C4×C131—44no—
67C4⋊C4×C131—41no—
68C4⋊C4×C131—41no—
69C4⋊C4×C131—42no—
70C4⋊C4×C131—42no—
71C4⋊C4×C131—42no—
72C4⋊C4×C131—42no—
73C4⋊C4×C131D814yes—
74C22⋊C4×C131—44no—
75C22⋊C4×C131—42no—
76C22⋊C4×C131—42no—
77C22⋊C4×C131—81no—
78C42×C131—41no—
79C23×C131—22no—
80C23×C131—42no—
81C23×C131—41no—
82C23×C131—42no—
83C23×C131—41no—
84C23×C131#12011yescharacteristic
85Q8×C131—84no—
86D4×C131—42no—
87D4×C131—81no—
88C2×C4×C131—21no—
89C2×C4×C131—22no—
90C2×C4×C131—22no—
91C2×C4×C131—21no—
92C2×C4×C131—24no—
93C2×C4×C131—42no—
94C2×C4×C131—42no—
95C2×C4×C131—42no—
96C2×C4×C131—42no—
97C2×C4×C131—41no—
98C2×C4×C131—42no—
99C2×C4×C131—42no—
100C2×C4×C131—84no—
101C2×C4×C131—82no—
102C2×C4×C131—81no—
103C2×C4×C131C2×D812yes—
104C2×C4×C131C2×Q1611yescharacteristic
105C2×C4×C131AGL(1,ℤ/8)12yes—
106C2×C4×C131#13711yescharacteristic
107C8×C131—44no—
108C8×C131—42no—
109C22×C131—42no—
110C22×C131—44no—
111C22×C131—82no—
112C22×C131—81no—
113C22×C131—81no—
114C22×C131#44712yes—
115C22×C131#45111yescharacteristic
116C22×C131#45311yescharacteristic
117C22×C131#45612yes—
118C22×C131#45811yescharacteristic
119C4×C131—22no—
120C4×C131—22no—
121C4×C131—21no—
122C4×C131—21no—
123C4×C131—44no—
124C4×C131—82no—
125C4×C131—81no—
126C4×C131—161no—
127C2×C131—82no—
128C2×C131#161012yes—
129C2×C131#161411yescharacteristic
130C2×C131#161911yescharacteristic
131C2×C131#164912yes—
132C2×C131#166011yescharacteristic
133#7797C13111yesmaximal, characteristic, direct product factor, Sylow
134C131#779711yescharacteristic, direct product factor, Sylow
135#2683C2×C13111yescharacteristic
136#2093C2×C13111yescharacteristic
137#2083C2×C13112yescomplemented
138#1271C2×C13112yescomplemented
139#1270C2×C13111yescharacteristic
140C2×C22⋊Q8—22no—
141C2×#107—22no—
142C2×#107—21no—
143C2×#102—21no—
144#396—22no—
145#395—21no—
146#390C22×C13111yescharacteristic
147#389C22×C13112yes—
148#386—21no—
149#384C22×C13111yescharacteristic
150#340—22no—
151#336C22×C13112yes—
152#336C22×C13111yescharacteristic
153C22×Q8—21no—
154C22×D4D4×C13111yescharacteristic
155C23×C4—21no—
156C22×C8—22no—
157C22×C8—21no—
158C22⋊Q8—44no—
159C22⋊Q8—44no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4D4×C13112yes—
165C2×C4⋊C4D4×C13112yes—
166C2×C4⋊C4D4×C13111yescharacteristic
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C22⋊C4—21no—
170C2×C42C23×C13111yescharacteristic
171#107—42no—
172#107—44no—
173#102—42no—
174#95—21no—
175#95—22no—
176C24—21no—
177C2×Q8—44no—
178C2×Q8—81no—
179C2×D4—21no—
180C2×D4—41no—
181C2×D4—41no—
182C2×D4Q16×C13112yes—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—21no—
186C22×C4—44no—
187C22×C4—41no—
188C22×C4—81no—
189C22×C4C2×D4×C13112yes—
190C22×C4C2×D4×C13111yescharacteristic
191C2×C8—22no—
192C2×C8—24no—
193C2×C8—42no—
194C2×C8—41no—
195C2×C8—42no—
196C2×C8—41no—
197C4⋊C4—22no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—44no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4D8×C13114yes—
208C22⋊C4—44no—
209C22⋊C4—42no—
210C22⋊C4—42no—
211C22⋊C4—81no—
212C42—41no—
213C23—22no—
214C23—42no—
215C23—41no—
216C23—42no—
217C23—41no—
218C23#120×C13111yescharacteristic
219Q8—84no—
220D4—42no—
221D4—81no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—24no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—84no—
235C2×C4—82no—
236C2×C4—81no—
237C2×C4C2×D8×C13112yes—
238C2×C4C2×Q16×C13111yescharacteristic
239C2×C4AGL(1,ℤ/8)×C13112yes—
240C2×C4#137×C13111yescharacteristic
241C8—44no—
242C8—42no—
243C22—42no—
244C22—44no—
245C22—82no—
246C22—81no—
247C22—81no—
248C22#447×C13112yes—
249C22#451×C13111yescharacteristic
250C22#453×C13111yescharacteristic
251C22#456×C13112yes—
252C22#458×C13111yescharacteristic
253C4—22no—
254C4—22no—
255C4—21no—
256C4—21no—
257C4—44no—
258C4—82no—
259C4—81no—
260C4—161no—
261C2—82no—
262C2#1610×C13112yes—
263C2#1614×C13111yescharacteristic
264C2#1619×C13111yescharacteristic
265C2#1649×C13112yes—
266C2#1660×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#120
commutator, Frattini, cosocleC2×C42C23×C131
prime radicalC22×D4×C131D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2083×C131C2semidirect
4. #1271×C131C2semidirect
133. #7797C131direct (N × H)
134. C131#7797direct (N × H)
137. #2083C2×C131semidirect
138. #1271C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2683×C1312
#2093×C1312
#2083×C1312
#1271×C1312
#1270×C1312
#7797131