Finite Group Databasebeta

← C131×#8457 #45694341

Subgroups — C131×#8457 #45694341

Order 33536.

746 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 746 conjugacy classes of subgroups — too many to draw. Only its 154 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#3501×C131C211yesmaximal, characteristic
2#1955×C131C211yesmaximal, characteristic
3#1552×C131C212yesmaximal, complemented
4#1531×C131C212yesmaximal, complemented
5#1466×C131C211yesmaximal, characteristic
6#554×C131—22no—
7#554×C131—24no—
8D4×Q8×C131—22no—
9#544×C131C412yes—
10#543×C131—22no—
11#533×C131C2212yes—
12C2×C22⋊Q8×C131—22no—
13#518×C131C412yes—
14C2×C4×D4×C131C2211yescharacteristic
15#432×C131C2212yes—
16C2×C4⋊C8×C131C2211yescharacteristic
17C2×C22⋊C8×C131—22no—
18C2×#97×C131C2211yescharacteristic
19#332×C131—22no—
20#332×C131—22no—
21#330×C131—24no—
22#323×C131—22no—
23C22×Q8×C131—22no—
24C22×D4×C131C2×C411yescharacteristic
25C23×C4×C131D412yes—
26C22×C8×C131—21no—
27C22×C8×C131—21no—
28C4⋊Q8×C131—24no—
29C4⋊Q8×C131D412yes—
30C4⋊Q8×C131D412yes—
31#125×C131—24no—
32#125×C131D414yes—
33C22⋊Q8×C131—24no—
34C22⋊Q8×C131—24no—
35C22⋊Q8×C131—28no—
36C22⋊Q8×C131—28no—
37C22⋊Q8×C131—24no—
38C22⋊Q8×C131—22no—
39C22⋊Q8×C131—22no—
40C4×Q8×C131—22no—
41C4×Q8×C131—22no—
42C4×D4×C131—24no—
43C4×D4×C131—24no—
44C4×D4×C131—22no—
45C4×D4×C131—22no—
46#117×C131C2×C414yes—
47C2×C4⋊C4×C131—22no—
48C2×C4⋊C4×C131—24no—
49C2×C4⋊C4×C131C2×C411yescharacteristic
50C2×C22⋊C4×C131—24no—
51C2×C22⋊C4×C131D412yes—
52C2×C42×C131C2311yescharacteristic
53C4⋊C8×C131—22no—
54C4⋊C8×C131—22no—
55C22⋊C8×C131—22no—
56C22⋊C8×C131—44no—
57#97×C131—22no—
58#97×C131—22no—
59C24×C131C22⋊C412yes—
60C2×Q8×C131—24no—
61C2×Q8×C131—22no—
62C2×Q8×C131—22no—
63C2×Q8×C131—82no—
64C2×Q8×C131—82no—
65C2×D4×C131—24no—
66C2×D4×C131—22no—
67C22×C4×C131—24no—
68C22×C4×C131—24no—
69C22×C4×C131—22no—
70C22×C4×C131—22no—
71C22×C4×C131—42no—
72C22×C4×C131—42no—
73C22×C4×C131C22⋊C412yes—
74C22×C4×C131C22×C411yescharacteristic
75C22×C4×C131C2×D411yescharacteristic
76C22×C4×C131C2×D411yescharacteristic
77C2×C8×C131—22no—
78C2×C8×C131—41no—
79C2×C8×C131—41no—
80C2×C8×C131—42no—
81C2×C8×C131—42no—
82C2×C8×C131—41no—
83C4⋊C4×C131—24no—
84C4⋊C4×C131—28no—
85C4⋊C4×C131—22no—
86C4⋊C4×C131—24no—
87C4⋊C4×C131—22no—
88C4⋊C4×C131—24no—
89C4⋊C4×C131—22no—
90C4⋊C4×C131C22⋊C414yes—
91C4⋊C4×C131C22⋊C414yes—
92C22⋊C4×C131—28no—
93C22⋊C4×C131—24no—
94C22⋊C4×C131—24no—
95C42×C131—24no—
96C42×C131C2×D412yes—
97C42×C131C2×D412yes—
98C23×C131—22no—
99C23×C131—22no—
100C23×C131—42no—
101C23×C131—42no—
102C23×C131#10114yes—
103C23×C131C2×C22⋊C411yescharacteristic
104Q8×C131—42no—
105Q8×C131—42no—
106Q8×C131—82no—
107Q8×C131—84no—
108D4×C131—28no—
109C2×C4×C131—22no—
110C2×C4×C131—21no—
111C2×C4×C131—21no—
112C2×C4×C131—24no—
113C2×C4×C131—24no—
114C2×C4×C131—22no—
115C2×C4×C131—41no—
116C2×C4×C131—42no—
117C2×C4×C131—42no—
118C2×C4×C131—42no—
119C2×C4×C131—82no—
120C2×C4×C131—84no—
121C2×C4×C131—84no—
122C2×C4×C131C2×C22⋊C412yes—
123C2×C4×C131#12012yes—
124C2×C4×C131#12011yescharacteristic
125C2×C4×C131#12011yescharacteristic
126C8×C131—42no—
127C8×C131—82no—
128C8×C131—81no—
129C22×C131—21no—
130C22×C131—21no—
131C22×C131—24no—
132C22×C131—44no—
133C22×C131—42no—
134C22×C131—42no—
135C22×C131—82no—
136C22×C131#37911yescharacteristic
137C22×C131C2×#10112yes—
138C4×C131—21no—
139C4×C131—22no—
140C4×C131—22no—
141C4×C131—42no—
142C4×C131—44no—
143C4×C131—44no—
144C4×C131#45311yescharacteristic
145C4×C131#45511yescharacteristic
146C2×C131—22no—
147C2×C131—44no—
148C2×C131#178411yescharacteristic
149C2×C131#179211yescharacteristic
150C2×C131#179411yescharacteristic
151#8457C13111yesmaximal, characteristic, direct product factor, Sylow
152C131#845711yescharacteristic, direct product factor, Sylow
153#3501C2×C13111yescharacteristic
154#1955C2×C13111yescharacteristic
155#1552C2×C13112yescomplemented
156#1531C2×C13112yescomplemented
157#1466C2×C13111yescharacteristic
158#554—22no—
159#554—24no—
160D4×Q8—22no—
161#544C4×C13112yes—
162#543—22no—
163#533C22×C13112yes—
164C2×C22⋊Q8—22no—
165#518C4×C13112yes—
166C2×C4×D4C22×C13111yescharacteristic
167#432C22×C13112yes—
168C2×C4⋊C8C22×C13111yescharacteristic
169C2×C22⋊C8—22no—
170C2×#97C22×C13111yescharacteristic
171#332—22no—
172#332—22no—
173#330—24no—
174#323—22no—
175C22×Q8—22no—
176C22×D4C2×C4×C13111yescharacteristic
177C23×C4D4×C13112yes—
178C22×C8—21no—
179C22×C8—21no—
180C4⋊Q8—24no—
181C4⋊Q8D4×C13112yes—
182C4⋊Q8D4×C13112yes—
183#125—24no—
184#125D4×C13114yes—
185C22⋊Q8—24no—
186C22⋊Q8—24no—
187C22⋊Q8—28no—
188C22⋊Q8—28no—
189C22⋊Q8—24no—
190C22⋊Q8—22no—
191C22⋊Q8—22no—
192C4×Q8—22no—
193C4×Q8—22no—
194C4×D4—24no—
195C4×D4—24no—
196C4×D4—22no—
197C4×D4—22no—
198#117C2×C4×C13114yes—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4C2×C4×C13111yescharacteristic
202C2×C22⋊C4—24no—
203C2×C22⋊C4D4×C13112yes—
204C2×C42C23×C13111yescharacteristic
205C4⋊C8—22no—
206C4⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—44no—
209#97—22no—
210#97—22no—
211C24C22⋊C4×C13112yes—
212C2×Q8—24no—
213C2×Q8—22no—
214C2×Q8—22no—
215C2×Q8—82no—
216C2×Q8—82no—
217C2×D4—24no—
218C2×D4—22no—
219C22×C4—24no—
220C22×C4—24no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4C22⋊C4×C13112yes—
226C22×C4C22×C4×C13111yescharacteristic
227C22×C4C2×D4×C13111yescharacteristic
228C22×C4C2×D4×C13111yescharacteristic
229C2×C8—22no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—41no—
235C4⋊C4—24no—
236C4⋊C4—28no—
237C4⋊C4—22no—
238C4⋊C4—24no—
239C4⋊C4—22no—
240C4⋊C4—24no—
241C4⋊C4—22no—
242C4⋊C4C22⋊C4×C13114yes—
243C4⋊C4C22⋊C4×C13114yes—
244C22⋊C4—28no—
245C22⋊C4—24no—
246C22⋊C4—24no—
247C42—24no—
248C42C2×D4×C13112yes—
249C42C2×D4×C13112yes—
250C23—22no—
251C23—22no—
252C23—42no—
253C23—42no—
254C23#101×C13114yes—
255C23C2×C22⋊C4×C13111yescharacteristic
256Q8—42no—
257Q8—42no—
258Q8—82no—
259Q8—84no—
260D4—28no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—24no—
265C2×C4—24no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—82no—
272C2×C4—84no—
273C2×C4—84no—
274C2×C4C2×C22⋊C4×C13112yes—
275C2×C4#120×C13112yes—
276C2×C4#120×C13111yescharacteristic
277C2×C4#120×C13111yescharacteristic
278C8—42no—
279C8—82no—
280C8—81no—
281C22—21no—
282C22—21no—
283C22—24no—
284C22—44no—
285C22—42no—
286C22—42no—
287C22—82no—
288C22#379×C13111yescharacteristic
289C22C2×#101×C13112yes—
290C4—22no—
291C4—21no—
292C4—22no—
293C4—42no—
294C4—44no—
295C4—44no—
296C4#453×C13111yescharacteristic
297C4#455×C13111yescharacteristic
298C2—22no—
299C2—44no—
300C2#1784×C13111yescharacteristic
301C2#1792×C13111yescharacteristic
302C2#1794×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#379
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC22×D4×C131C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1552×C131C2semidirect
4. #1531×C131C2semidirect
151. #8457C131direct (N × H)
152. C131#8457direct (N × H)
155. #1552C2×C131semidirect
156. #1531C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3501×C1312
#1955×C1312
#1552×C1312
#1531×C1312
#1466×C1312
#8457131