Finite Group Databasebeta

← C131×#9359 #45695243

Subgroups — C131×#9359 #45695243

Order 33536.

540 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3038×C131C211yesmaximal, characteristic
2#2990×C131C211yesmaximal, characteristic, complemented
3#1965×C131C211yesmaximal, characteristic, complemented
4#1545×C131C211yesmaximal, characteristic, complemented
5#1489×C131C211yesmaximal, characteristic, complemented
6#1309×C131C211yesmaximal, characteristic, complemented
7#1299×C131C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C131C412yes—
9C2×#127×C131C2211yescharacteristic
10C4×#41×C131C2211yescharacteristic
11#460×C131—21no—
12#460×C131—21no—
13#459×C131—21no—
14#459×C131—21no—
15#446×C131—21no—
16#435×C131—22no—
17C8×D4×C131—21no—
18#432×C131—21no—
19#431×C131C2211yescharacteristic
20#423×C131C2211yescharacteristic
21#423×C131C2211yescharacteristic
22#423×C131C2211yescharacteristic
23C2×C4⋊C8×C131—21no—
24#418×C131C412yes—
25C2×#100×C131—22no—
26C4×M16×C131C2211yescharacteristic
27#331×C131—21no—
28#331×C131—21no—
29Q8⋊C8×C131—21no—
30D4⋊C8×C131—21no—
31C2×#41×C131C2×C411yescharacteristic
32C22×D4×C131—21no—
33C22×D4×C131—21no—
34C22×D4×C131C2×C412yes—
35AGL(1,ℤ/8)×C131—44no—
36C2×SD16×C131—22no—
37C2×D8×C131—22no—
38C2×M16×C131—21no—
39C2×M16×C131—21no—
40C2×M16×C131C2×C412yes—
41C2×M16×C131D412yes—
42C22×C8×C131—22no—
43#127×C131—21no—
44#127×C131—21no—
45#127×C131—21no—
46#127×C131—21no—
47C4×Q8×C131D411yescharacteristic
48C4×Q8×C131D411yescharacteristic
49C4×D4×C131—21no—
50C4×D4×C131—21no—
51C4×D4×C131D411yescharacteristic
52C4×D4×C131D411yescharacteristic
53#117×C131—21no—
54#117×C131C2×C411yescharacteristic
55C2×C42×C131—21no—
56C2×C42×C131C2311yescharacteristic
57C4⋊C8×C131—22no—
58C4⋊C8×C131—21no—
59C4⋊C8×C131—21no—
60C4⋊C8×C131—21no—
61C4⋊C8×C131—21no—
62C4⋊C8×C131—21no—
63C4⋊C8×C131—21no—
64C4⋊C8×C131D411yescharacteristic
65C4⋊C8×C131D411yescharacteristic
66#102×C131—22no—
67#102×C131—22no—
68#100×C131—44no—
69C22⋊C8×C131—22no—
70C22⋊C8×C131—21no—
71#97×C131—22no—
72#97×C131—21no—
73C4×C8×C131—21no—
74C4×C8×C131—21no—
75C24×C131—22no—
76#41×C131—22no—
77#41×C131—41no—
78C2×Q8×C131C22⋊C411yescharacteristic
79C2×D4×C131—21no—
80C2×D4×C131—22no—
81C2×D4×C131—22no—
82C2×D4×C131—42no—
83C2×D4×C131—42no—
84C2×D4×C131—42no—
85C2×D4×C131—42no—
86C2×D4×C131—41no—
87C2×D4×C131—41no—
88C2×D4×C131—41no—
89C2×D4×C131—41no—
90C2×D4×C131—81no—
91C2×D4×C131—81no—
92C2×D4×C131C22⋊C411yescharacteristic
93C22×C4×C131—21no—
94C22×C4×C131—21no—
95C22×C4×C131—21no—
96C22×C4×C131C22×C411yescharacteristic
97C22×C4×C131C2×D411yescharacteristic
98C22×C4×C131#4111yescharacteristic
99SD16×C131—44no—
100D8×C131—44no—
101M16×C131—22no—
102M16×C131—41no—
103M16×C131—42no—
104M16×C131—42no—
105M16×C131—81no—
106C2×C8×C131—22no—
107C2×C8×C131—21no—
108C2×C8×C131—21no—
109C2×C8×C131—22no—
110C2×C8×C131—41no—
111C2×C8×C131—41no—
112C2×C8×C131—82no—
113C4⋊C4×C131—21no—
114C4⋊C4×C131—21no—
115C4⋊C4×C131C22⋊C411yescharacteristic
116C4⋊C4×C131C22⋊C411yescharacteristic
117C22⋊C4×C131—21no—
118C22⋊C4×C131—21no—
119C22⋊C4×C131—21no—
120C42×C131—21no—
121C42×C131—21no—
122C42×C131—21no—
123C42×C131C2×D411yescharacteristic
124C42×C131C2×D411yescharacteristic
125C42×C131C2×D411yescharacteristic
126C42×C131#4111yescharacteristic
127C23×C131—21no—
128C23×C131—44no—
129C23×C131—42no—
130C23×C131—82no—
131C23×C131—82no—
132C23×C131C4×D411yescharacteristic
133Q8×C131—21no—
134Q8×C131—21no—
135D4×C131—21no—
136D4×C131—42no—
137D4×C131—42no—
138D4×C131—42no—
139D4×C131—82no—
140D4×C131—82no—
141D4×C131—82no—
142D4×C131—81no—
143D4×C131—81no—
144D4×C131—81no—
145D4×C131—81no—
146D4×C131#10012yescomplemented
147C2×C4×C131—21no—
148C2×C4×C131—21no—
149C2×C4×C131—21no—
150C2×C4×C131—21no—
151C2×C4×C131—21no—
152C2×C4×C131—21no—
153C2×C4×C131—21no—
154C2×C4×C131—21no—
155C2×C4×C131—21no—
156C2×C4×C131—42no—
157C2×C4×C131—41no—
158C2×C4×C131—41no—
159C2×C4×C131—41no—
160C2×C4×C131—41no—
161C2×C4×C131C2×C22⋊C411yescharacteristic
162C2×C4×C131C4×D411yescharacteristic
163C2×C4×C131#12011yescharacteristic
164C2×C4×C131#12111yescharacteristic
165C2×C4×C131#12111yescharacteristic
166C2×C4×C131#12311yescharacteristic
167C8×C131—42no—
168C8×C131—42no—
169C8×C131—41no—
170C8×C131—42no—
171C8×C131—41no—
172C8×C131—81no—
173C22×C131—21no—
174C22×C131—21no—
175C22×C131—22no—
176C22×C131—21no—
177C22×C131—41no—
178C22×C131—41no—
179C22×C131—82no—
180C22×C131—82no—
181C22×C131—82no—
182C22×C131—164no—
183C22×C131#38611yescharacteristic
184C4×C131—21no—
185C4×C131—21no—
186C4×C131—21no—
187C4×C131—41no—
188C4×C131—41no—
189C4×C131—41no—
190C4×C131C2×#10011yescharacteristic
191C4×C131#41311yescharacteristic
192C4×C131#45311yescharacteristic
193C4×C131#45411yescharacteristic
194C4×C131#47111yescharacteristic
195C4×C131#47211yescharacteristic
196C2×C131—41no—
197C2×C131—42no—
198C2×C131—162no—
199C2×C131#188311yescharacteristic
200C2×C131#190011yescharacteristic
201C2×C131#190711yescharacteristic
202#9359C13111yesmaximal, characteristic, direct product factor, Sylow
203C131#935911yescharacteristic, direct product factor, Sylow
204#3038C2×C13111yescharacteristic
205#2990C2×C13111yescharacteristic, complemented
206#1965C2×C13111yescharacteristic, complemented
207#1545C2×C13111yescharacteristic, complemented
208#1489C2×C13111yescharacteristic, complemented
209#1309C2×C13111yescharacteristic, complemented
210#1299C2×C13111yescharacteristic, complemented
211C2×AGL(1,ℤ/8)C4×C13112yes—
212C2×#127C22×C13111yescharacteristic
213C4×#41C22×C13111yescharacteristic
214#460—21no—
215#460—21no—
216#459—21no—
217#459—21no—
218#446—21no—
219#435—22no—
220C8×D4—21no—
221#432—21no—
222#431C22×C13111yescharacteristic
223#423C22×C13111yescharacteristic
224#423C22×C13111yescharacteristic
225#423C22×C13111yescharacteristic
226C2×C4⋊C8—21no—
227#418C4×C13112yes—
228C2×#100—22no—
229C4×M16C22×C13111yescharacteristic
230#331—21no—
231#331—21no—
232Q8⋊C8—21no—
233D4⋊C8—21no—
234C2×#41C2×C4×C13111yescharacteristic
235C22×D4—21no—
236C22×D4—21no—
237C22×D4C2×C4×C13112yes—
238AGL(1,ℤ/8)—44no—
239C2×SD16—22no—
240C2×D8—22no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16C2×C4×C13112yes—
244C2×M16D4×C13112yes—
245C22×C8—22no—
246#127—21no—
247#127—21no—
248#127—21no—
249#127—21no—
250C4×Q8D4×C13111yescharacteristic
251C4×Q8D4×C13111yescharacteristic
252C4×D4—21no—
253C4×D4—21no—
254C4×D4D4×C13111yescharacteristic
255C4×D4D4×C13111yescharacteristic
256#117—21no—
257#117C2×C4×C13111yescharacteristic
258C2×C42—21no—
259C2×C42C23×C13111yescharacteristic
260C4⋊C8—22no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8D4×C13111yescharacteristic
268C4⋊C8D4×C13111yescharacteristic
269#102—22no—
270#102—22no—
271#100—44no—
272C22⋊C8—22no—
273C22⋊C8—21no—
274#97—22no—
275#97—21no—
276C4×C8—21no—
277C4×C8—21no—
278C24—22no—
279#41—22no—
280#41—41no—
281C2×Q8C22⋊C4×C13111yescharacteristic
282C2×D4—21no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—81no—
294C2×D4—81no—
295C2×D4C22⋊C4×C13111yescharacteristic
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4C22×C4×C13111yescharacteristic
300C22×C4C2×D4×C13111yescharacteristic
301C22×C4#41×C13111yescharacteristic
302SD16—44no—
303D8—44no—
304M16—22no—
305M16—41no—
306M16—42no—
307M16—42no—
308M16—81no—
309C2×C8—22no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—82no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4C22⋊C4×C13111yescharacteristic
319C4⋊C4C22⋊C4×C13111yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C42—21no—
324C42—21no—
325C42—21no—
326C42C2×D4×C13111yescharacteristic
327C42C2×D4×C13111yescharacteristic
328C42C2×D4×C13111yescharacteristic
329C42#41×C13111yescharacteristic
330C23—21no—
331C23—44no—
332C23—42no—
333C23—82no—
334C23—82no—
335C23C4×D4×C13111yescharacteristic
336Q8—21no—
337Q8—21no—
338D4—21no—
339D4—42no—
340D4—42no—
341D4—42no—
342D4—82no—
343D4—82no—
344D4—82no—
345D4—81no—
346D4—81no—
347D4—81no—
348D4—81no—
349D4#100×C13112yescomplemented
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4C2×C22⋊C4×C13111yescharacteristic
365C2×C4C4×D4×C13111yescharacteristic
366C2×C4#120×C13111yescharacteristic
367C2×C4#121×C13111yescharacteristic
368C2×C4#121×C13111yescharacteristic
369C2×C4#123×C13111yescharacteristic
370C8—42no—
371C8—42no—
372C8—41no—
373C8—42no—
374C8—41no—
375C8—81no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—21no—
380C22—41no—
381C22—41no—
382C22—82no—
383C22—82no—
384C22—82no—
385C22—164no—
386C22#386×C13111yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4C2×#100×C13111yescharacteristic
394C4#413×C13111yescharacteristic
395C4#453×C13111yescharacteristic
396C4#454×C13111yescharacteristic
397C4#471×C13111yescharacteristic
398C4#472×C13111yescharacteristic
399C2—41no—
400C2—42no—
401C2—162no—
402C2#1883×C13111yescharacteristic
403C2#1900×C13111yescharacteristic
404C2#1907×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#386
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radical#3038×C131C2
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
2. #2990×C131C2semidirect
3. #1965×C131C2semidirect
4. #1545×C131C2semidirect
5. #1489×C131C2semidirect
6. #1309×C131C2semidirect
7. #1299×C131C2semidirect
146. D4×C131#100semidirect
202. #9359C131direct (N × H)
203. C131#9359direct (N × H)
205. #2990C2×C131semidirect
206. #1965C2×C131semidirect
207. #1545C2×C131semidirect
208. #1489C2×C131semidirect
209. #1309C2×C131semidirect
210. #1299C2×C131semidirect
349. D4#100×C131semidirect

Maximal subgroups

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

subgroupindex
#3038×C1312
#2990×C1312
#1965×C1312
#1545×C1312
#1489×C1312
#1309×C1312
#1299×C1312
#9359131