Finite Group Databasebeta

← C131×#9267 #45695151

Subgroups — C131×#9267 #45695151

Order 33536.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3206×C131C211yesmaximal, characteristic
2#2935×C131C211yesmaximal, characteristic
3#1997×C131C211yesmaximal, characteristic, complemented
4#1547×C131C211yesmaximal, characteristic
5C2×#333×C131C211yesmaximal, characteristic, complemented
6#1301×C131C211yesmaximal, characteristic, complemented
7#1283×C131C211yesmaximal, characteristic, complemented
8C2×#131×C131—21no—
9#532×C131C2211yescharacteristic
10C2×C4⋊Q8×C131C2211yescharacteristic
11#492×C131—21no—
12#487×C131—21no—
13#461×C131—22no—
14#448×C131C414yes—
15#436×C131—21no—
16#435×C131—22no—
17C8×D4×C131—21no—
18#431×C131C2211yescharacteristic
19#423×C131C2211yescharacteristic
20C2×C4⋊C8×C131C2211yescharacteristic
21C2×C4⋊C8×C131C2211yescharacteristic
22#408×C131—21no—
23C4×M16×C131C2211yescharacteristic
24#343×C131—21no—
25#343×C131—21no—
26#333×C131—21no—
27#333×C131—21no—
28#332×C131—21no—
29#331×C131—21no—
30C2×#41×C131—21no—
31C22×Q8×C131C2×C412yes—
32C2×SD16×C131—24no—
33#131×C131—42no—
34#131×C131—42no—
35C2×M16×C131—22no—
36C2×M16×C131—21no—
37C2×M16×C131D411yescharacteristic
38C2×M16×C131D411yescharacteristic
39C22×C8×C131—22no—
40C22×C8×C131—21no—
41C22×C8×C131—21no—
42C4⋊Q8×C131—21no—
43C4⋊Q8×C131—21no—
44C4⋊Q8×C131—21no—
45C4⋊Q8×C131—21no—
46C4⋊Q8×C131D411yescharacteristic
47#127×C131D411yescharacteristic
48#124×C131—21no—
49#121×C131—21no—
50#121×C131C2×C412yes—
51C4×D4×C131—21no—
52C4×D4×C131D412yes—
53C2×C4⋊C4×C131—21no—
54C2×C4⋊C4×C131—21no—
55C2×C42×C131C2311yescharacteristic
56C4⋊C8×C131—21no—
57C4⋊C8×C131—21no—
58C4⋊C8×C131—21no—
59C4⋊C8×C131—21no—
60C4⋊C8×C131—21no—
61C4⋊C8×C131—21no—
62C4⋊C8×C131D411yescharacteristic
63C4⋊C8×C131D411yescharacteristic
64#103×C131—24no—
65C22⋊C8×C131—22no—
66C22⋊C8×C131—22no—
67C22⋊C8×C131C2×C412yes—
68#97×C131—21no—
69C4×C8×C131—21no—
70C4×C8×C131—21no—
71#41×C131—41no—
72#41×C131—41no—
73#41×C131—41no—
74#41×C131—41no—
75C2×Q8×C131—21no—
76C2×Q8×C131—22no—
77C2×Q8×C131—22no—
78C2×Q8×C131—82no—
79C2×D4×C131—22no—
80C2×D4×C131—21no—
81C2×D4×C131—21no—
82C2×D4×C131C22⋊C412yes—
83C22×C4×C131—22no—
84C22×C4×C131—22no—
85C22×C4×C131C22×C411yescharacteristic
86C22×C4×C131C2×D411yescharacteristic
87C22×C4×C131#4111yescharacteristic
88SD16×C131—84no—
89M16×C131—21no—
90M16×C131—21no—
91M16×C131—21no—
92M16×C131—44no—
93M16×C131—41no—
94M16×C131—41no—
95M16×C131SD1612yescomplemented
96C2×C8×C131—21no—
97C2×C8×C131—22no—
98C2×C8×C131—21no—
99C2×C8×C131—21no—
100C2×C8×C131—21no—
101C2×C8×C131—44no—
102C2×C8×C131—41no—
103C2×C8×C131—41no—
104C2×C8×C131—41no—
105C2×C8×C131—41no—
106C2×C8×C131—81no—
107C4⋊C4×C131—21no—
108C4⋊C4×C131—41no—
109C4⋊C4×C131—41no—
110C4⋊C4×C131—41no—
111C4⋊C4×C131—41no—
112C4⋊C4×C131C22⋊C412yes—
113C22⋊C4×C131—22no—
114C22⋊C4×C131—22no—
115C42×C131C2×D411yescharacteristic
116C42×C131C2×D411yescharacteristic
117C42×C131C2×D411yescharacteristic
118C42×C131#4111yescharacteristic
119C23×C131—22no—
120C23×C131C4×D411yescharacteristic
121Q8×C131—44no—
122Q8×C131—41no—
123Q8×C131—41no—
124Q8×C131—82no—
125D4×C131—42no—
126D4×C131—42no—
127D4×C131—42no—
128D4×C131—41no—
129D4×C131—41no—
130D4×C131—41no—
131D4×C131—41no—
132C2×C4×C131—21no—
133C2×C4×C131—21no—
134C2×C4×C131—22no—
135C2×C4×C131—41no—
136C2×C4×C131—42no—
137C2×C4×C131—42no—
138C2×C4×C131—42no—
139C2×C4×C131—82no—
140C2×C4×C131C2×C22⋊C411yescharacteristic
141C2×C4×C131C4×D411yescharacteristic
142C2×C4×C131#12011yescharacteristic
143C2×C4×C131#12111yescharacteristic
144C2×C4×C131#12111yescharacteristic
145C2×C4×C131#12311yescharacteristic
146C2×C4×C131C2×SD1611yescharacteristic
147C2×C4×C131#13511yescharacteristic
148C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C131#13711yescharacteristic
150C8×C131—22no—
151C8×C131—42no—
152C8×C131—41no—
153C8×C131—41no—
154C8×C131—41no—
155C8×C131—81no—
156C8×C131—81no—
157C22×C131—21no—
158C22×C131—21no—
159C22×C131—42no—
160C22×C131—42no—
161C22×C131—42no—
162C22×C131#38611yescharacteristic
163C22×C131C4×SD1611yescharacteristic
164C22×C131#44011yescharacteristic
165C4×C131—21no—
166C4×C131—21no—
167C4×C131—21no—
168C4×C131—42no—
169C4×C131—82no—
170C4×C131#45011yescharacteristic
171C4×C131#45211yescharacteristic
172C4×C131#46111yescharacteristic
173C4×C131#46311yescharacteristic
174C4×C131#47111yescharacteristic
175C4×C131#47311yescharacteristic
176C2×C131—21no—
177C2×C131—21no—
178C2×C131—82no—
179C2×C131#187711yescharacteristic
180C2×C131#190811yescharacteristic
181C2×C131#191411yescharacteristic
182#9267C13111yesmaximal, characteristic, direct product factor, Sylow
183C131#926711yescharacteristic, direct product factor, Sylow
184#3206C2×C13111yescharacteristic
185#2935C2×C13111yescharacteristic
186#1997C2×C13111yescharacteristic, complemented
187#1547C2×C13111yescharacteristic
188C2×#333C2×C13111yescharacteristic, complemented
189#1301C2×C13111yescharacteristic, complemented
190#1283C2×C13111yescharacteristic, complemented
191C2×#131—21no—
192#532C22×C13111yescharacteristic
193C2×C4⋊Q8C22×C13111yescharacteristic
194#492—21no—
195#487—21no—
196#461—22no—
197#448C4×C13114yes—
198#436—21no—
199#435—22no—
200C8×D4—21no—
201#431C22×C13111yescharacteristic
202#423C22×C13111yescharacteristic
203C2×C4⋊C8C22×C13111yescharacteristic
204C2×C4⋊C8C22×C13111yescharacteristic
205#408—21no—
206C4×M16C22×C13111yescharacteristic
207#343—21no—
208#343—21no—
209#333—21no—
210#333—21no—
211#332—21no—
212#331—21no—
213C2×#41—21no—
214C22×Q8C2×C4×C13112yes—
215C2×SD16—24no—
216#131—42no—
217#131—42no—
218C2×M16—22no—
219C2×M16—21no—
220C2×M16D4×C13111yescharacteristic
221C2×M16D4×C13111yescharacteristic
222C22×C8—22no—
223C22×C8—21no—
224C22×C8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8D4×C13111yescharacteristic
230#127D4×C13111yescharacteristic
231#124—21no—
232#121—21no—
233#121C2×C4×C13112yes—
234C4×D4—21no—
235C4×D4D4×C13112yes—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C42C23×C13111yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8D4×C13111yescharacteristic
246C4⋊C8D4×C13111yescharacteristic
247#103—24no—
248C22⋊C8—22no—
249C22⋊C8—22no—
250C22⋊C8C2×C4×C13112yes—
251#97—21no—
252C4×C8—21no—
253C4×C8—21no—
254#41—41no—
255#41—41no—
256#41—41no—
257#41—41no—
258C2×Q8—21no—
259C2×Q8—22no—
260C2×Q8—22no—
261C2×Q8—82no—
262C2×D4—22no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4C22⋊C4×C13112yes—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4C22×C4×C13111yescharacteristic
269C22×C4C2×D4×C13111yescharacteristic
270C22×C4#41×C13111yescharacteristic
271SD16—84no—
272M16—21no—
273M16—21no—
274M16—21no—
275M16—44no—
276M16—41no—
277M16—41no—
278M16SD16×C13112yescomplemented
279C2×C8—21no—
280C2×C8—22no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—44no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—81no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4C22⋊C4×C13112yes—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C42C2×D4×C13111yescharacteristic
299C42C2×D4×C13111yescharacteristic
300C42C2×D4×C13111yescharacteristic
301C42#41×C13111yescharacteristic
302C23—22no—
303C23C4×D4×C13111yescharacteristic
304Q8—44no—
305Q8—41no—
306Q8—41no—
307Q8—82no—
308D4—42no—
309D4—42no—
310D4—42no—
311D4—41no—
312D4—41no—
313D4—41no—
314D4—41no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—82no—
323C2×C4C2×C22⋊C4×C13111yescharacteristic
324C2×C4C4×D4×C13111yescharacteristic
325C2×C4#120×C13111yescharacteristic
326C2×C4#121×C13111yescharacteristic
327C2×C4#121×C13111yescharacteristic
328C2×C4#123×C13111yescharacteristic
329C2×C4C2×SD16×C13111yescharacteristic
330C2×C4#135×C13111yescharacteristic
331C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
332C2×C4#137×C13111yescharacteristic
333C8—22no—
334C8—42no—
335C8—41no—
336C8—41no—
337C8—41no—
338C8—81no—
339C8—81no—
340C22—21no—
341C22—21no—
342C22—42no—
343C22—42no—
344C22—42no—
345C22#386×C13111yescharacteristic
346C22C4×SD16×C13111yescharacteristic
347C22#440×C13111yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—42no—
352C4—82no—
353C4#450×C13111yescharacteristic
354C4#452×C13111yescharacteristic
355C4#461×C13111yescharacteristic
356C4#463×C13111yescharacteristic
357C4#471×C13111yescharacteristic
358C4#473×C13111yescharacteristic
359C2—21no—
360C2—21no—
361C2—82no—
362C2#1877×C13111yescharacteristic
363C2#1908×C13111yescharacteristic
364C2#1914×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#386
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radical#532×C131C22
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. #1997×C131C2semidirect
5. C2×#333×C131C2semidirect
6. #1301×C131C2semidirect
7. #1283×C131C2semidirect
95. M16×C131SD16semidirect
182. #9267C131direct (N × H)
183. C131#9267direct (N × H)
186. #1997C2×C131semidirect
188. C2×#333C2×C131semidirect
189. #1301C2×C131semidirect
190. #1283C2×C131semidirect
278. M16SD16×C131semidirect

Maximal subgroups

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

subgroupindex
#3206×C1312
#2935×C1312
#1997×C1312
#1547×C1312
C2×#333×C1312
#1301×C1312
#1283×C1312
#9267131