Finite Group Databasebeta

← C131×#11724 #45697608

Subgroups — C131×#11724 #45697608

Order 33536.

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

normal subgroups only

This group has 432 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#2628×C131C211yesmaximal, characteristic
2#1742×C131C211yesmaximal, characteristic
3#1458×C131C211yesmaximal, characteristic
4#1354×C131C214yesmaximal, complemented
5C22×M16×C131—21no—
6C2×C4⋊Q8×C131C411yescharacteristic
7C2×#117×C131C2211yescharacteristic
8#431×C131—21no—
9#400×C131—21no—
10#399×C131—21no—
11#395×C131C2212yes—
12#393×C131C412yes—
13#389×C131—21no—
14#382×C131C411yescharacteristic
15#380×C131—21no—
16#343×C131—21no—
17#343×C131C2212yes—
18#324×C131C2212yes—
19#323×C131—21no—
20C22×Q8×C131C2×C412yes—
21C23×C4×C131D411yescharacteristic
22C2×M16×C131—24no—
23C2×M16×C131—22no—
24C2×M16×C131—41no—
25C2×M16×C131—42no—
26C22×C8×C131—41no—
27C4⋊Q8×C131—41no—
28C4⋊Q8×C131—41no—
29#117×C131—41no—
30#117×C131—41no—
31C2×C4⋊C4×C131—21no—
32C2×C4⋊C4×C131—21no—
33C2×C4⋊C4×C131—21no—
34C2×C4⋊C4×C131—22no—
35C2×C4⋊C4×C131D411yescharacteristic
36C2×C4⋊C4×C131C2311yescharacteristic
37C2×C22⋊C4×C131—22no—
38C2×C22⋊C4×C131C2×C411yescharacteristic
39C2×C22⋊C4×C131D411yescharacteristic
40C2×C42×C131C2×C411yescharacteristic
41C2×C42×C131D411yescharacteristic
42C4⋊C8×C131—41no—
43C22⋊C8×C131—22no—
44C4×C8×C131—41no—
45#95×C131—22no—
46#95×C131—21no—
47#95×C131—22no—
48#95×C131C2×C412yes—
49C24×C131C22⋊C411yescharacteristic
50C2×Q8×C131—42no—
51C2×Q8×C131—82no—
52C22×C4×C131—21no—
53C22×C4×C131—21no—
54C22×C4×C131—22no—
55C22×C4×C131—22no—
56C22×C4×C131—22no—
57C22×C4×C131C22⋊C411yescharacteristic
58C22×C4×C131C22⋊C411yescharacteristic
59C22×C4×C131C22⋊C411yescharacteristic
60C22×C4×C131SD1612yes—
61C22×C4×C131Q1612yes—
62C22×C4×C131C22×C411yescharacteristic
63C22×C4×C131C2×D411yescharacteristic
64C22×C4×C131C2×D411yescharacteristic
65M16×C131—24no—
66M16×C131—44no—
67M16×C131—42no—
68C2×C8×C131—42no—
69C2×C8×C131—44no—
70C2×C8×C131—42no—
71C4⋊C4×C131—41no—
72C4⋊C4×C131—41no—
73C4⋊C4×C131—42no—
74C4⋊C4×C131—41no—
75C4⋊C4×C131—41no—
76C4⋊C4×C131—42no—
77C4⋊C4×C131—82no—
78C22⋊C4×C131—41no—
79C22⋊C4×C131—41no—
80C22⋊C4×C131—82no—
81C42×C131—21no—
82C42×C131—21no—
83C42×C131—21no—
84C42×C131—21no—
85C23×C131—21no—
86C23×C131—21no—
87C23×C131—41no—
88C23×C131—41no—
89C23×C131#10312yes—
90C23×C131C2×C22⋊C411yescharacteristic
91Q8×C131—84no—
92C2×C4×C131—21no—
93C2×C4×C131—21no—
94C2×C4×C131—22no—
95C2×C4×C131—22no—
96C2×C4×C131—22no—
97C2×C4×C131—22no—
98C2×C4×C131—21no—
99C2×C4×C131—21no—
100C2×C4×C131—21no—
101C2×C4×C131—21no—
102C2×C4×C131—41no—
103C2×C4×C131—41no—
104C2×C4×C131—41no—
105C2×C4×C131—41no—
106C2×C4×C131—42no—
107C2×C4×C131—42no—
108C2×C4×C131—42no—
109C2×C4×C131—42no—
110C2×C4×C131—42no—
111C2×C4×C131—42no—
112C2×C4×C131#9911yescharacteristic
113C2×C4×C131#9911yescharacteristic
114C2×C4×C131#10312yes—
115C2×C4×C131#10412yes—
116C2×C4×C131C2×SD1611yescharacteristic
117C2×C4×C131C2×Q1611yescharacteristic
118C8×C131—44no—
119C8×C131—82no—
120C22×C131—21no—
121C22×C131—21no—
122C22×C131—22no—
123C22×C131—42no—
124C22×C131—41no—
125C22×C131—41no—
126C22×C131—81no—
127C22×C131C2×#9911yescharacteristic
128C22×C131C2×#10311yescharacteristic
129C22×C131C2×#10411yescharacteristic
130C4×C131—21no—
131C4×C131—21no—
132C4×C131—41no—
133C4×C131—41no—
134C4×C131—41no—
135C4×C131—41no—
136C4×C131—82no—
137C4×C131—82no—
138C4×C131#32812yes—
139C4×C131#32812yes—
140C2×C131—21no—
141C2×C131—21no—
142C2×C131—42no—
143C2×C131C2×#32811yescharacteristic
144C2×C131#212211yescharacteristic
145C2×C131#213511yescharacteristic
146#11724C13111yesmaximal, characteristic, direct product factor, Sylow
147C131#1172411yescharacteristic, direct product factor, Sylow
148#2628C2×C13111yescharacteristic
149#1742C2×C13111yescharacteristic
150#1458C2×C13111yescharacteristic
151#1354C2×C13114yescomplemented
152C22×M16—21no—
153C2×C4⋊Q8C4×C13111yescharacteristic
154C2×#117C22×C13111yescharacteristic
155#431—21no—
156#400—21no—
157#399—21no—
158#395C22×C13112yes—
159#393C4×C13112yes—
160#389—21no—
161#382C4×C13111yescharacteristic
162#380—21no—
163#343—21no—
164#343C22×C13112yes—
165#324C22×C13112yes—
166#323—21no—
167C22×Q8C2×C4×C13112yes—
168C23×C4D4×C13111yescharacteristic
169C2×M16—24no—
170C2×M16—22no—
171C2×M16—41no—
172C2×M16—42no—
173C22×C8—41no—
174C4⋊Q8—41no—
175C4⋊Q8—41no—
176#117—41no—
177#117—41no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4D4×C13111yescharacteristic
183C2×C4⋊C4C23×C13111yescharacteristic
184C2×C22⋊C4—22no—
185C2×C22⋊C4C2×C4×C13111yescharacteristic
186C2×C22⋊C4D4×C13111yescharacteristic
187C2×C42C2×C4×C13111yescharacteristic
188C2×C42D4×C13111yescharacteristic
189C4⋊C8—41no—
190C22⋊C8—22no—
191C4×C8—41no—
192#95—21no—
193#95—22no—
194#95—22no—
195#95C2×C4×C13112yes—
196C24C22⋊C4×C13111yescharacteristic
197C2×Q8—42no—
198C2×Q8—82no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4C22⋊C4×C13111yescharacteristic
205C22×C4C22⋊C4×C13111yescharacteristic
206C22×C4C22⋊C4×C13111yescharacteristic
207C22×C4SD16×C13112yes—
208C22×C4Q16×C13112yes—
209C22×C4C22×C4×C13111yescharacteristic
210C22×C4C2×D4×C13111yescharacteristic
211C22×C4C2×D4×C13111yescharacteristic
212M16—24no—
213M16—44no—
214M16—42no—
215C2×C8—42no—
216C2×C8—44no—
217C2×C8—42no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—42no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C4⋊C4—82no—
225C22⋊C4—41no—
226C22⋊C4—41no—
227C22⋊C4—82no—
228C42—21no—
229C42—21no—
230C42—21no—
231C42—21no—
232C23—21no—
233C23—21no—
234C23—41no—
235C23—41no—
236C23#103×C13112yes—
237C23C2×C22⋊C4×C13111yescharacteristic
238Q8—84no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4#99×C13111yescharacteristic
260C2×C4#99×C13111yescharacteristic
261C2×C4#103×C13112yes—
262C2×C4#104×C13112yes—
263C2×C4C2×SD16×C13111yescharacteristic
264C2×C4C2×Q16×C13111yescharacteristic
265C8—44no—
266C8—82no—
267C22—21no—
268C22—21no—
269C22—22no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—81no—
274C22C2×#99×C13111yescharacteristic
275C22C2×#103×C13111yescharacteristic
276C22C2×#104×C13111yescharacteristic
277C4—21no—
278C4—21no—
279C4—41no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—82no—
284C4—82no—
285C4#328×C13112yes—
286C4#328×C13112yes—
287C2—21no—
288C2—21no—
289C2—42no—
290C2C2×#328×C13111yescharacteristic
291C2#2122×C13111yescharacteristic
292C2#2135×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#99
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C4⋊C4C23×C131
prime radicalC24×C131C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C22×C4×C131 ◁ C2×#117×C131 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1354×C131C2semidirect
146. #11724C131direct (N × H)
147. C131#11724direct (N × H)
151. #1354C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2628×C1312
#1742×C1312
#1458×C1312
#1354×C1312
#11724131