Finite Group Databasebeta

← C131×#7666 #45693550

Subgroups — C131×#7666 #45693550

Order 33536.

438 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2860×C131C211yesmaximal, characteristic
2#1831×C131C211yesmaximal, characteristic, complemented
3#1744×C131C211yesmaximal, characteristic, complemented
4#1271×C131C212yesmaximal, complemented
5#1270×C131C212yesmaximal
6C2×#126×C131—21no—
7C2×C4⋊C8×C131—21no—
8C2×C4×C8×C131—21no—
9#390×C131C411yescharacteristic
10#390×C131C411yescharacteristic
11#390×C131C2211yescharacteristic
12#389×C131C411yescharacteristic
13#389×C131C411yescharacteristic
14#389×C131C2211yescharacteristic
15#388×C131—21no—
16#388×C131—21no—
17#388×C131—21no—
18C43×C131C2211yescharacteristic
19#336×C131—21no—
20#336×C131—21no—
21#336×C131C2212yes—
22#336×C131C2212yes—
23C22×D4×C131C2×C411yescharacteristic
24C22×C8×C131—22no—
25C22×C8×C131—22no—
26#126×C131—42no—
27#126×C131—42no—
28C2×C4⋊C4×C131—21no—
29C2×C4⋊C4×C131—21no—
30C2×C4⋊C4×C131—21no—
31C2×C4⋊C4×C131C2×C411yescharacteristic
32C2×C4⋊C4×C131C2×C411yescharacteristic
33C2×C4⋊C4×C131C2×C411yescharacteristic
34C2×C22⋊C4×C131—21no—
35C2×C22⋊C4×C131—21no—
36C2×C22⋊C4×C131—21no—
37C2×C22⋊C4×C131—21no—
38C2×C22⋊C4×C131—21no—
39C2×C22⋊C4×C131—21no—
40C2×C42×C131C2×C411yescharacteristic
41C2×C42×C131C2×C411yescharacteristic
42C2×C42×C131D411yescharacteristic
43C2×C42×C131D411yescharacteristic
44C2×C42×C131D411yescharacteristic
45C2×C42×C131D411yescharacteristic
46C2×C42×C131C2311yescharacteristic
47C4⋊C8×C131—42no—
48C4×C8×C131—24no—
49#95×C131—21no—
50#95×C131—21no—
51#95×C131—21no—
52C24×C131—21no—
53C2×D4×C131—22no—
54C2×D4×C131—41no—
55C2×D4×C131—41no—
56C22×C4×C131—21no—
57C22×C4×C131—21no—
58C22×C4×C131—21no—
59C22×C4×C131C22⋊C411yescharacteristic
60C22×C4×C131C22⋊C411yescharacteristic
61C22×C4×C131C22⋊C411yescharacteristic
62C22×C4×C131C22⋊C411yescharacteristic
63C22×C4×C131C22×C411yescharacteristic
64C22×C4×C131C2×D411yescharacteristic
65C22×C4×C131C2×D411yescharacteristic
66C2×C8×C131—24no—
67C2×C8×C131—42no—
68C2×C8×C131—42no—
69C2×C8×C131—42no—
70C2×C8×C131—42no—
71C2×C8×C131—42no—
72C4⋊C4×C131—22no—
73C4⋊C4×C131—41no—
74C4⋊C4×C131—41no—
75C4⋊C4×C131—42no—
76C4⋊C4×C131—42no—
77C4⋊C4×C131—41no—
78C4⋊C4×C131—41no—
79C22⋊C4×C131—42no—
80C22⋊C4×C131—42no—
81C22⋊C4×C131—42no—
82C22⋊C4×C131—42no—
83C22⋊C4×C131—41no—
84C22⋊C4×C131—41no—
85C22⋊C4×C131—42no—
86C42×C131—22no—
87C42×C131—22no—
88C42×C131—22no—
89C42×C131—41no—
90C42×C131—41no—
91C42×C131—41no—
92C42×C131D812yes—
93C42×C131SD1612yes—
94C23×C131—41no—
95C23×C131—41no—
96C23×C131—41no—
97C23×C131—41no—
98C23×C131—41no—
99C23×C131—41no—
100C23×C131—41no—
101C23×C131C2×C22⋊C411yescharacteristic
102D4×C131—82no—
103C2×C4×C131—21no—
104C2×C4×C131—21no—
105C2×C4×C131—21no—
106C2×C4×C131—21no—
107C2×C4×C131—21no—
108C2×C4×C131—21no—
109C2×C4×C131—21no—
110C2×C4×C131—21no—
111C2×C4×C131—21no—
112C2×C4×C131—21no—
113C2×C4×C131—21no—
114C2×C4×C131—21no—
115C2×C4×C131—21no—
116C2×C4×C131—21no—
117C2×C4×C131—21no—
118C2×C4×C131—41no—
119C2×C4×C131—41no—
120C2×C4×C131—41no—
121C2×C4×C131—41no—
122C2×C4×C131—41no—
123C2×C4×C131—41no—
124C2×C4×C131—41no—
125C2×C4×C131—41no—
126C2×C4×C131—41no—
127C2×C4×C131#10212yes—
128C2×C4×C131#10212yes—
129C2×C4×C131#10412yes—
130C2×C4×C131#13112yes—
131C2×C4×C131C2×D811yescharacteristic
132C2×C4×C131C2×SD1611yescharacteristic
133C2×C4×C131#13512yes—
134C8×C131—44no—
135C8×C131—82no—
136C22×C131—81no—
137C22×C131—81no—
138C22×C131—81no—
139C22×C131—81no—
140C22×C131—81no—
141C22×C131—81no—
142C22×C131—81no—
143C22×C131#40811yescharacteristic
144C22×C131#41011yescharacteristic
145C22×C131#41311yescharacteristic
146C22×C131C2×#10211yescharacteristic
147C22×C131#41611yescharacteristic
148C22×C131C2×#10411yescharacteristic
149C22×C131#42111yescharacteristic
150C4×C131—22no—
151C4×C131—22no—
152C4×C131—22no—
153C4×C131—22no—
154C4×C131—21no—
155C4×C131—21no—
156C4×C131—22no—
157C4×C131—41no—
158C4×C131—81no—
159C4×C131—81no—
160C4×C131—81no—
161C2×C131—161no—
162C2×C131#147311yescharacteristic
163C2×C131#148211yescharacteristic
164C2×C131#149211yescharacteristic
165C2×C131#150011yescharacteristic
166C2×C131#151711yescharacteristic
167C2×C131#153211yescharacteristic
168C2×C131#154011yescharacteristic
169#7666C13111yesmaximal, characteristic, direct product factor, Sylow
170C131#766611yescharacteristic, direct product factor, Sylow
171#2860C2×C13111yescharacteristic
172#1831C2×C13111yescharacteristic, complemented
173#1744C2×C13111yescharacteristic, complemented
174#1271C2×C13112yescomplemented
175#1270C2×C13112yes—
176C2×#126—21no—
177C2×C4⋊C8—21no—
178C2×C4×C8—21no—
179#390C4×C13111yescharacteristic
180#390C4×C13111yescharacteristic
181#390C22×C13111yescharacteristic
182#389C4×C13111yescharacteristic
183#389C4×C13111yescharacteristic
184#389C22×C13111yescharacteristic
185#388—21no—
186#388—21no—
187#388—21no—
188C43C22×C13111yescharacteristic
189#336—21no—
190#336—21no—
191#336C22×C13112yes—
192#336C22×C13112yes—
193C22×D4C2×C4×C13111yescharacteristic
194C22×C8—22no—
195C22×C8—22no—
196#126—42no—
197#126—42no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C2×C4×C13111yescharacteristic
202C2×C4⋊C4C2×C4×C13111yescharacteristic
203C2×C4⋊C4C2×C4×C13111yescharacteristic
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C42C2×C4×C13111yescharacteristic
211C2×C42C2×C4×C13111yescharacteristic
212C2×C42D4×C13111yescharacteristic
213C2×C42D4×C13111yescharacteristic
214C2×C42D4×C13111yescharacteristic
215C2×C42D4×C13111yescharacteristic
216C2×C42C23×C13111yescharacteristic
217C4⋊C8—42no—
218C4×C8—24no—
219#95—21no—
220#95—21no—
221#95—21no—
222C24—21no—
223C2×D4—22no—
224C2×D4—41no—
225C2×D4—41no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4C22⋊C4×C13111yescharacteristic
230C22×C4C22⋊C4×C13111yescharacteristic
231C22×C4C22⋊C4×C13111yescharacteristic
232C22×C4C22⋊C4×C13111yescharacteristic
233C22×C4C22×C4×C13111yescharacteristic
234C22×C4C2×D4×C13111yescharacteristic
235C22×C4C2×D4×C13111yescharacteristic
236C2×C8—24no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C4⋊C4—22no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—42no—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—41no—
260C42—41no—
261C42—41no—
262C42D8×C13112yes—
263C42SD16×C13112yes—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23C2×C22⋊C4×C13111yescharacteristic
272D4—82no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4#102×C13112yes—
298C2×C4#102×C13112yes—
299C2×C4#104×C13112yes—
300C2×C4#131×C13112yes—
301C2×C4C2×D8×C13111yescharacteristic
302C2×C4C2×SD16×C13111yescharacteristic
303C2×C4#135×C13112yes—
304C8—44no—
305C8—82no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22#408×C13111yescharacteristic
314C22#410×C13111yescharacteristic
315C22#413×C13111yescharacteristic
316C22C2×#102×C13111yescharacteristic
317C22#416×C13111yescharacteristic
318C22C2×#104×C13111yescharacteristic
319C22#421×C13111yescharacteristic
320C4—22no—
321C4—22no—
322C4—22no—
323C4—21no—
324C4—21no—
325C4—22no—
326C4—22no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C2—161no—
332C2#1473×C13111yescharacteristic
333C2#1482×C13111yescharacteristic
334C2#1492×C13111yescharacteristic
335C2#1500×C13111yescharacteristic
336C2#1517×C13111yescharacteristic
337C2#1532×C13111yescharacteristic
338C2#1540×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C2×C22⋊C4
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC22×D4×C131C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C43×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1831×C131C2semidirect
3. #1744×C131C2semidirect
4. #1271×C131C2semidirect
169. #7666C131direct (N × H)
170. C131#7666direct (N × H)
172. #1831C2×C131semidirect
173. #1744C2×C131semidirect
174. #1271C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2860×C1312
#1831×C1312
#1744×C1312
#1271×C1312
#1270×C1312
#7666131