Finite Group Databasebeta

← C131×#7312 #45693196

Subgroups — C131×#7312 #45693196

Order 33536.

456 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 74 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#1785×C131C211yesmaximal, characteristic
2#1785×C131C211yesmaximal, characteristic
3#1782×C131C211yesmaximal, characteristic
4C22×#41×C131C2211yescharacteristic
5C2×#101×C131—21no—
6C2×#101×C131—21no—
7C2×#100×C131—21no—
8C2×#100×C131C412yescomplemented
9C2×#99×C131—21no—
10C2×#99×C131C412yes—
11#407×C131—21no—
12#407×C131C412yescomplemented
13#381×C131—21no—
14C2×#41×C131—42no—
15C2×#41×C131—42no—
16C2×#41×C131—42no—
17C22×Q8×C131D411yescharacteristic
18C22×D4×C131C2×C411yescharacteristic
19C22×D4×C131C2×C411yescharacteristic
20C22×D4×C131D411yescharacteristic
21C23×C4×C131C2×C411yescharacteristic
22C23×C4×C131D411yescharacteristic
23C23×C4×C131Q811yescharacteristic
24C2×M16×C131—22no—
25C2×M16×C131—22no—
26C2×C22⋊C4×C131—22no—
27#101×C131—42no—
28#101×C131—42no—
29#100×C131—42no—
30#100×C131—42no—
31#99×C131—42no—
32#99×C131—42no—
33C22⋊C8×C131—42no—
34C22⋊C8×C131—42no—
35#95×C131—42no—
36C24×C131C4211yescharacteristic
37C24×C131C22⋊C411yescharacteristic
38C24×C131C4⋊C411yescharacteristic
39#41×C131—416no—
40C2×Q8×C131—22no—
41C2×Q8×C131—22no—
42C2×Q8×C131—41no—
43C2×D4×C131—22no—
44C2×D4×C131—22no—
45C2×D4×C131—22no—
46C2×D4×C131—22no—
47C2×D4×C131—41no—
48C2×D4×C131—41no—
49C2×D4×C131—41no—
50C2×D4×C131—41no—
51C2×D4×C131—41no—
52C22×C4×C131—22no—
53C22×C4×C131—22no—
54C22×C4×C131—22no—
55C22×C4×C131—41no—
56C22×C4×C131—41no—
57C22×C4×C131—41no—
58C22×C4×C131—41no—
59C22×C4×C131—41no—
60C22×C4×C131—41no—
61C22×C4×C131—42no—
62C22×C4×C131C22⋊C411yescharacteristic
63C22×C4×C131C22⋊C411yescharacteristic
64C22×C4×C131C4⋊C411yescharacteristic
65C22×C4×C131C4⋊C411yescharacteristic
66M16×C131—42no—
67M16×C131—42no—
68M16×C131—42no—
69M16×C131—42no—
70C2×C8×C131—42no—
71C2×C8×C131—42no—
72C22⋊C4×C131—42no—
73C22⋊C4×C131—42no—
74C23×C131—21no—
75C23×C131—21no—
76C23×C131—21no—
77C23×C131—21no—
78C23×C131—21no—
79C23×C131—21no—
80C23×C131—21no—
81C23×C131—21no—
82C23×C131—81no—
83C23×C131—81no—
84C23×C131—81no—
85C23×C131#9511yescharacteristic
86C23×C131#9912yes—
87Q8×C131—44no—
88D4×C131—44no—
89D4×C131—44no—
90D4×C131—44no—
91C2×C4×C131—21no—
92C2×C4×C131—21no—
93C2×C4×C131—21no—
94C2×C4×C131—21no—
95C2×C4×C131—21no—
96C2×C4×C131—21no—
97C2×C4×C131—21no—
98C2×C4×C131—21no—
99C2×C4×C131—21no—
100C2×C4×C131—21no—
101C2×C4×C131—44no—
102C2×C4×C131—44no—
103C2×C4×C131—44no—
104C2×C4×C131—82no—
105C2×C4×C131—84no—
106C2×C4×C131#9912yes—
107C2×C4×C131#9912yes—
108C8×C131—82no—
109C8×C131—82no—
110C22×C131—22no—
111C22×C131—41no—
112C22×C131—42no—
113C22×C131—42no—
114C22×C131—42no—
115C22×C131—41no—
116C22×C131—41no—
117C22×C131—81no—
118C22×C131—81no—
119C22×C131—81no—
120C22×C131—81no—
121C22×C131—81no—
122C22×C131—81no—
123C22×C131#34211yescharacteristic
124C22×C131#34211yescharacteristic
125C22×C131#34211yescharacteristic
126C4×C131—22no—
127C4×C131—22no—
128C4×C131—41no—
129C4×C131—41no—
130C4×C131—162no—
131C2×C131—21no—
132C2×C131—21no—
133C2×C131—21no—
134C2×C131—42no—
135C2×C131—81no—
136C2×C131—81no—
137C2×C131#130411yescharacteristic
138#7312C13111yesmaximal, characteristic, direct product factor, Sylow
139C131#731211yescharacteristic, direct product factor, Sylow
140#1785C2×C13111yescharacteristic
141#1785C2×C13111yescharacteristic
142#1782C2×C13111yescharacteristic
143C22×#41C22×C13111yescharacteristic
144C2×#101—21no—
145C2×#101—21no—
146C2×#100—21no—
147C2×#100C4×C13112yescomplemented
148C2×#99—21no—
149C2×#99C4×C13112yes—
150#407—21no—
151#407C4×C13112yescomplemented
152#381—21no—
153C2×#41—42no—
154C2×#41—42no—
155C2×#41—42no—
156C22×Q8D4×C13111yescharacteristic
157C22×D4C2×C4×C13111yescharacteristic
158C22×D4C2×C4×C13111yescharacteristic
159C22×D4D4×C13111yescharacteristic
160C23×C4C2×C4×C13111yescharacteristic
161C23×C4D4×C13111yescharacteristic
162C23×C4Q8×C13111yescharacteristic
163C2×M16—22no—
164C2×M16—22no—
165C2×C22⋊C4—22no—
166#101—42no—
167#101—42no—
168#100—42no—
169#100—42no—
170#99—42no—
171#99—42no—
172C22⋊C8—42no—
173C22⋊C8—42no—
174#95—42no—
175C24C42×C13111yescharacteristic
176C24C22⋊C4×C13111yescharacteristic
177C24C4⋊C4×C13111yescharacteristic
178#41—416no—
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—41no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—41no—
187C2×D4—41no—
188C2×D4—41no—
189C2×D4—41no—
190C2×D4—41no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—42no—
201C22×C4C22⋊C4×C13111yescharacteristic
202C22×C4C22⋊C4×C13111yescharacteristic
203C22×C4C4⋊C4×C13111yescharacteristic
204C22×C4C4⋊C4×C13111yescharacteristic
205M16—42no—
206M16—42no—
207M16—42no—
208M16—42no—
209C2×C8—42no—
210C2×C8—42no—
211C22⋊C4—42no—
212C22⋊C4—42no—
213C23—21no—
214C23—21no—
215C23—21no—
216C23—21no—
217C23—21no—
218C23—21no—
219C23—21no—
220C23—21no—
221C23—81no—
222C23—81no—
223C23—81no—
224C23#95×C13111yescharacteristic
225C23#99×C13112yes—
226Q8—44no—
227D4—44no—
228D4—44no—
229D4—44no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—44no—
241C2×C4—44no—
242C2×C4—44no—
243C2×C4—82no—
244C2×C4—84no—
245C2×C4#99×C13112yes—
246C2×C4#99×C13112yes—
247C8—82no—
248C8—82no—
249C22—22no—
250C22—41no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—41no—
255C22—41no—
256C22—81no—
257C22—81no—
258C22—81no—
259C22—81no—
260C22—81no—
261C22—81no—
262C22#342×C13111yescharacteristic
263C22#342×C13111yescharacteristic
264C22#342×C13111yescharacteristic
265C4—22no—
266C4—22no—
267C4—41no—
268C4—41no—
269C4—162no—
270C2—21no—
271C2—21no—
272C2—21no—
273C2—42no—
274C2—81no—
275C2—81no—
276C2#1304×C13111yescharacteristic
subgroupG/H
center, socleC2×C131#1304
commutatorC24C42×C131
Frattini, cosocleC22×#41C22×C131
prime radicalC22×#41×C131C22
LCSG ▷ C24 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C23×C131 ◁ C22×#41×C131 ◁ G

Complements

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

NH ≅ G/Ntype
8. C2×#100×C131C4semidirect
12. #407×C131C4semidirect
138. #7312C131direct (N × H)
139. C131#7312direct (N × H)
147. C2×#100C4×C131semidirect
151. #407C4×C131semidirect

Maximal subgroups

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

subgroupindex
#1785×C1312
#1782×C1312
#7312131