Finite Group Databasebeta

← C131×#7821 #45693705

Subgroups — C131×#7821 #45693705

Order 33536.

422 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 98 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#2804×C131C211yesmaximal, characteristic
2#2093×C131C211yesmaximal, characteristic
3#2072×C131C212yesmaximal, complemented
4#1272×C131C212yesmaximal, complemented
5#1270×C131C211yesmaximal, characteristic
6C2×#107×C131—21no—
7C2×#103×C131—22no—
8C2×#102×C131—21no—
9#400×C131—21no—
10#393×C131—22no—
11#391×C131C2212yes—
12#390×C131C2211yescharacteristic
13#386×C131—21no—
14#385×C131—22no—
15#384×C131C2211yescharacteristic
16#340×C131—22no—
17#336×C131C2212yes—
18#336×C131C2211yescharacteristic
19C22×Q8×C131D412yes—
20C22×D4×C131D411yescharacteristic
21C23×C4×C131—21no—
22C22×C8×C131—21no—
23C22×C8×C131—22no—
24C2×C4⋊C4×C131—21no—
25C2×C4⋊C4×C131—22no—
26C2×C4⋊C4×C131—21no—
27C2×C4⋊C4×C131D411yescharacteristic
28C2×C4⋊C4×C131D412yes—
29C2×C22⋊C4×C131—22no—
30C2×C22⋊C4×C131—21no—
31C2×C22⋊C4×C131—22no—
32C2×C42×C131C2311yescharacteristic
33#107×C131—42no—
34#103×C131—44no—
35#102×C131—42no—
36#95×C131—21no—
37#95×C131—22no—
38#95×C131—22no—
39#95×C131—22no—
40C24×C131—21no—
41C2×Q8×C131—22no—
42C2×Q8×C131—22no—
43C2×Q8×C131—42no—
44C2×Q8×C131—42no—
45C2×D4×C131—21no—
46C2×D4×C131—41no—
47C2×D4×C131—41no—
48C2×D4×C131Q1612yes—
49C22×C4×C131—22no—
50C22×C4×C131—21no—
51C22×C4×C131—22no—
52C22×C4×C131—41no—
53C22×C4×C131—81no—
54C22×C4×C131—82no—
55C22×C4×C131C2×D411yescharacteristic
56C22×C4×C131C2×D412yes—
57C2×C8×C131—22no—
58C2×C8×C131—41no—
59C2×C8×C131—41no—
60C2×C8×C131—42no—
61C2×C8×C131—42no—
62C2×C8×C131—42no—
63C4⋊C4×C131—41no—
64C4⋊C4×C131—42no—
65C4⋊C4×C131—41no—
66C4⋊C4×C131—41no—
67C4⋊C4×C131—42no—
68C4⋊C4×C131—42no—
69C4⋊C4×C131—81no—
70C22⋊C4×C131—42no—
71C22⋊C4×C131—42no—
72C22⋊C4×C131—82no—
73C22⋊C4×C131—81no—
74C42×C131—41no—
75C23×C131—22no—
76C23×C131—42no—
77C23×C131—41no—
78C23×C131—42no—
79C23×C131—41no—
80C23×C131#12011yescharacteristic
81Q8×C131—44no—
82Q8×C131—82no—
83D4×C131—42no—
84D4×C131—81no—
85C2×C4×C131—21no—
86C2×C4×C131—22no—
87C2×C4×C131—21no—
88C2×C4×C131—22no—
89C2×C4×C131—42no—
90C2×C4×C131—42no—
91C2×C4×C131—41no—
92C2×C4×C131—42no—
93C2×C4×C131—42no—
94C2×C4×C131—42no—
95C2×C4×C131—42no—
96C2×C4×C131—42no—
97C2×C4×C131—84no—
98C2×C4×C131—82no—
99C2×C4×C131—81no—
100C2×C4×C131C2×Q1611yescharacteristic
101C2×C4×C131#13512yes—
102C2×C4×C131AGL(1,ℤ/8)12yes—
103C2×C4×C131#13711yescharacteristic
104C8×C131—42no—
105C8×C131—82no—
106C22×C131—42no—
107C22×C131—44no—
108C22×C131—82no—
109C22×C131—81no—
110C22×C131—81no—
111C22×C131#44912yes—
112C22×C131#45111yescharacteristic
113C22×C131#45311yescharacteristic
114C22×C131#45512yes—
115C22×C131#45811yescharacteristic
116C4×C131—22no—
117C4×C131—22no—
118C4×C131—21no—
119C4×C131—21no—
120C4×C131—82no—
121C4×C131—81no—
122C4×C131—82no—
123C4×C131—161no—
124C2×C131—82no—
125C2×C131#161212yes—
126C2×C131#161411yescharacteristic
127C2×C131#162011yescharacteristic
128C2×C131#164412yes—
129C2×C131#165911yescharacteristic
130#7821C13111yesmaximal, characteristic, direct product factor, Sylow
131C131#782111yescharacteristic, direct product factor, Sylow
132#2804C2×C13111yescharacteristic
133#2093C2×C13111yescharacteristic
134#2072C2×C13112yescomplemented
135#1272C2×C13112yescomplemented
136#1270C2×C13111yescharacteristic
137C2×#107—21no—
138C2×#103—22no—
139C2×#102—21no—
140#400—21no—
141#393—22no—
142#391C22×C13112yes—
143#390C22×C13111yescharacteristic
144#386—21no—
145#385—22no—
146#384C22×C13111yescharacteristic
147#340—22no—
148#336C22×C13112yes—
149#336C22×C13111yescharacteristic
150C22×Q8D4×C13112yes—
151C22×D4D4×C13111yescharacteristic
152C23×C4—21no—
153C22×C8—21no—
154C22×C8—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4D4×C13112yes—
159C2×C4⋊C4D4×C13111yescharacteristic
160C2×C22⋊C4—22no—
161C2×C22⋊C4—22no—
162C2×C22⋊C4—21no—
163C2×C42C23×C13111yescharacteristic
164#107—42no—
165#103—44no—
166#102—42no—
167#95—22no—
168#95—21no—
169#95—22no—
170#95—22no—
171C24—21no—
172C2×Q8—22no—
173C2×Q8—22no—
174C2×Q8—42no—
175C2×Q8—42no—
176C2×D4—21no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4Q16×C13112yes—
180C22×C4—22no—
181C22×C4—21no—
182C22×C4—22no—
183C22×C4—41no—
184C22×C4—81no—
185C22×C4—82no—
186C22×C4C2×D4×C13111yescharacteristic
187C22×C4C2×D4×C13112yes—
188C2×C8—22no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—42no—
192C2×C8—42no—
193C2×C8—42no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—81no—
201C22⋊C4—42no—
202C22⋊C4—42no—
203C22⋊C4—82no—
204C22⋊C4—81no—
205C42—41no—
206C23—22no—
207C23—42no—
208C23—41no—
209C23—42no—
210C23—41no—
211C23#120×C13111yescharacteristic
212Q8—44no—
213Q8—82no—
214D4—42no—
215D4—81no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—84no—
229C2×C4—82no—
230C2×C4—81no—
231C2×C4C2×Q16×C13111yescharacteristic
232C2×C4#135×C13112yes—
233C2×C4AGL(1,ℤ/8)×C13112yes—
234C2×C4#137×C13111yescharacteristic
235C8—42no—
236C8—82no—
237C22—42no—
238C22—44no—
239C22—82no—
240C22—81no—
241C22—81no—
242C22#449×C13112yes—
243C22#451×C13111yescharacteristic
244C22#453×C13111yescharacteristic
245C22#455×C13112yes—
246C22#458×C13111yescharacteristic
247C4—22no—
248C4—22no—
249C4—21no—
250C4—21no—
251C4—82no—
252C4—81no—
253C4—82no—
254C4—161no—
255C2—82no—
256C2#1612×C13112yes—
257C2#1614×C13111yescharacteristic
258C2#1620×C13111yescharacteristic
259C2#1644×C13112yes—
260C2#1659×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. #2072×C131C2semidirect
4. #1272×C131C2semidirect
130. #7821C131direct (N × H)
131. C131#7821direct (N × H)
134. #2072C2×C131semidirect
135. #1272C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2804×C1312
#2093×C1312
#2072×C1312
#1272×C1312
#1270×C1312
#7821131