Finite Group Databasebeta

← C131×#8217 #45694101

Subgroups — C131×#8217 #45694101

Order 33536.

628 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊Q8×C131C211yesmaximal, characteristic
2#1749×C131C211yesmaximal, characteristic
3C2×#328×C131C212yesmaximal
4#1434×C131C211yesmaximal, characteristic
5#1294×C131C212yesmaximal
6C2×C22⋊Q8×C131C2211yescharacteristic
7C2×C4×Q8×C131C411yescharacteristic, complemented
8C22×C42×C131C2211yescharacteristic
9C2×C22⋊C8×C131C2212yes—
10C2×#97×C131—21no—
11#391×C131C411yescharacteristic, complemented
12#389×C131C411yescharacteristic, complemented
13#387×C131—21no—
14#385×C131—21no—
15#380×C131C2211yescharacteristic
16C4×C4⋊C4×C131—21no—
17C4×C4⋊C4×C131C411yescharacteristic, complemented
18C4×C22⋊C4×C131—21no—
19C2×#95×C131—21no—
20C2×#95×C131—21no—
21C2×#95×C131C2212yes—
22#336×C131—21no—
23#328×C131C418yescomplemented
24C22×Q8×C131C2×C411yescharacteristic
25C23×C4×C131—22no—
26C23×C4×C131D411yescharacteristic
27C23×C4×C131D411yescharacteristic
28C23×C4×C131C2311yescharacteristic
29C22×C8×C131—22no—
30C22⋊Q8×C131—22no—
31C22⋊Q8×C131C2×C414yes—
32C4×Q8×C131—42no—
33C2×C4⋊C4×C131—21no—
34C2×C4⋊C4×C131—21no—
35C2×C4⋊C4×C131—21no—
36C2×C4⋊C4×C131C2×C411yescharacteristic
37C2×C4⋊C4×C131C2×C411yescharacteristic
38C2×C4⋊C4×C131C2×C411yescharacteristic
39C2×C22⋊C4×C131—21no—
40C2×C22⋊C4×C131—21no—
41C2×C42×C131—21no—
42C2×C42×C131—21no—
43C2×C42×C131—42no—
44C2×C42×C131C2×C411yescharacteristic
45C2×C42×C131C2×C411yescharacteristic
46C2×C42×C131D411yescharacteristic
47C2×C42×C131D411yescharacteristic
48C22⋊C8×C131—22no—
49C22⋊C8×C131C2×C414yes—
50#97×C131—42no—
51#95×C131—21no—
52#95×C131—21no—
53#95×C131—21no—
54#95×C131—21no—
55#95×C131—21no—
56#95×C131—22no—
57#95×C131—42no—
58#95×C131—42no—
59#95×C131C2×C414yes—
60C24×C131C2×D411yescharacteristic
61C2×Q8×C131—21no—
62C2×Q8×C131—41no—
63C2×Q8×C131—41no—
64C2×Q8×C131C4212yes—
65C22×C4×C131—21no—
66C22×C4×C131—21no—
67C22×C4×C131—21no—
68C22×C4×C131—22no—
69C22×C4×C131—21no—
70C22×C4×C131—22no—
71C22×C4×C131—21no—
72C22×C4×C131—21no—
73C22×C4×C131—24no—
74C22×C4×C131—41no—
75C22×C4×C131—41no—
76C22×C4×C131—41no—
77C22×C4×C131—41no—
78C22×C4×C131—41no—
79C22×C4×C131—42no—
80C22×C4×C131—42no—
81C22×C4×C131—42no—
82C22×C4×C131—42no—
83C22×C4×C131—42no—
84C22×C4×C131—42no—
85C22×C4×C131C22⋊C411yescharacteristic
86C22×C4×C131C22⋊C411yescharacteristic
87C22×C4×C131C22⋊C411yescharacteristic
88C22×C4×C131C22⋊C411yescharacteristic
89C22×C4×C131C22×C411yescharacteristic
90C22×C4×C131C22×C412yes—
91C22×C4×C131C2×D411yescharacteristic
92C22×C4×C131#4112yes—
93C2×C8×C131—24no—
94C2×C8×C131—42no—
95C2×C8×C131—42no—
96C4⋊C4×C131—21no—
97C4⋊C4×C131—24no—
98C4⋊C4×C131—41no—
99C4⋊C4×C131—41no—
100C4⋊C4×C131—42no—
101C4⋊C4×C131—42no—
102C4⋊C4×C131C4212yes—
103C22⋊C4×C131—24no—
104C22⋊C4×C131—41no—
105C22⋊C4×C131—41no—
106C42×C131—22no—
107C42×C131—22no—
108C42×C131—41no—
109C42×C131—41no—
110C42×C131—42no—
111C42×C131—42no—
112C23×C131—21no—
113C23×C131—21no—
114C23×C131—21no—
115C23×C131—21no—
116C23×C131C2×C22⋊C411yescharacteristic
117C23×C131C4×D412yes—
118C23×C131AGL(1,ℤ/8)11yescharacteristic
119C23×C131#13711yescharacteristic
120C23×C131#13712yes—
121Q8×C131—42no—
122Q8×C131—42no—
123C2×C4×C131—21no—
124C2×C4×C131—21no—
125C2×C4×C131—21no—
126C2×C4×C131—21no—
127C2×C4×C131—21no—
128C2×C4×C131—21no—
129C2×C4×C131—22no—
130C2×C4×C131—22no—
131C2×C4×C131—21no—
132C2×C4×C131—21no—
133C2×C4×C131—21no—
134C2×C4×C131—21no—
135C2×C4×C131—21no—
136C2×C4×C131—21no—
137C2×C4×C131—21no—
138C2×C4×C131—21no—
139C2×C4×C131—21no—
140C2×C4×C131—42no—
141C2×C4×C131—42no—
142C2×C4×C131—44no—
143C2×C4×C131—42no—
144C2×C4×C131—42no—
145C2×C4×C131—41no—
146C2×C4×C131—41no—
147C2×C4×C131—41no—
148C2×C4×C131—41no—
149C2×C4×C131—44no—
150C2×C4×C131—44no—
151C2×C4×C131—41no—
152C2×C4×C131—41no—
153C2×C4×C131—41no—
154C2×C4×C131—41no—
155C2×C4×C131—41no—
156C2×C4×C131—41no—
157C2×C4×C131—44no—
158C2×C4×C131—82no—
159C2×C4×C131—82no—
160C2×C4×C131—82no—
161C2×C4×C131—82no—
162C2×C4×C131#9912yes—
163C2×C4×C131C2×C4211yescharacteristic
164C2×C4×C131#11711yescharacteristic
165C2×C4×C131C4×D412yes—
166C8×C131—44no—
167C22×C131—22no—
168C22×C131—22no—
169C22×C131—22no—
170C22×C131—21no—
171C22×C131—21no—
172C22×C131—21no—
173C22×C131—21no—
174C22×C131—22no—
175C22×C131C4×C22⋊C411yescharacteristic
176C22×C131C2×#9911yescharacteristic
177C22×C131#41011yescharacteristic
178C22×C131#41711yescharacteristic
179C22×C131#41911yescharacteristic
180C22×C131#42111yescharacteristic
181C22×C131#42111yescharacteristic
182C22×C131#44012yes—
183C22×C131#44112yes—
184C4×C131—22no—
185C4×C131—21no—
186C4×C131—21no—
187C4×C131—22no—
188C4×C131—42no—
189C4×C131—42no—
190C4×C131—41no—
191C4×C131—41no—
192C4×C131—41no—
193C4×C131—84no—
194C4×C131—81no—
195C4×C131—81no—
196C2×C131—22no—
197C2×C131—22no—
198C2×C131#151111yescharacteristic
199C2×C131#151211yescharacteristic
200C2×C131#151311yescharacteristic
201C2×C131#151511yescharacteristic
202C2×C131C4×#9911yescharacteristic
203C2×C131#175911yescharacteristic
204C2×C131#176311yescharacteristic
205#8217C13111yesmaximal, characteristic, direct product factor, Sylow
206C131#821711yescharacteristic, direct product factor, Sylow
207C4×C22⋊Q8C2×C13111yescharacteristic
208#1749C2×C13111yescharacteristic
209C2×#328C2×C13112yes—
210#1434C2×C13111yescharacteristic
211#1294C2×C13112yes—
212C2×C22⋊Q8C22×C13111yescharacteristic
213C2×C4×Q8C4×C13111yescharacteristic, complemented
214C22×C42C22×C13111yescharacteristic
215C2×C22⋊C8C22×C13112yes—
216C2×#97—21no—
217#391C4×C13111yescharacteristic, complemented
218#389C4×C13111yescharacteristic, complemented
219#387—21no—
220#385—21no—
221#380C22×C13111yescharacteristic
222C4×C4⋊C4—21no—
223C4×C4⋊C4C4×C13111yescharacteristic, complemented
224C4×C22⋊C4—21no—
225C2×#95—21no—
226C2×#95—21no—
227C2×#95C22×C13112yes—
228#336—21no—
229#328C4×C13118yescomplemented
230C22×Q8C2×C4×C13111yescharacteristic
231C23×C4—22no—
232C23×C4D4×C13111yescharacteristic
233C23×C4D4×C13111yescharacteristic
234C23×C4C23×C13111yescharacteristic
235C22×C8—22no—
236C22⋊Q8—22no—
237C22⋊Q8C2×C4×C13114yes—
238C4×Q8—42no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4C2×C4×C13111yescharacteristic
243C2×C4⋊C4C2×C4×C13111yescharacteristic
244C2×C4⋊C4C2×C4×C13111yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C42—21no—
248C2×C42—21no—
249C2×C42—42no—
250C2×C42C2×C4×C13111yescharacteristic
251C2×C42C2×C4×C13111yescharacteristic
252C2×C42D4×C13111yescharacteristic
253C2×C42D4×C13111yescharacteristic
254C22⋊C8—22no—
255C22⋊C8C2×C4×C13114yes—
256#97—42no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—22no—
263#95—42no—
264#95—42no—
265#95C2×C4×C13114yes—
266C24C2×D4×C13111yescharacteristic
267C2×Q8—21no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8C42×C13112yes—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—24no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4C22⋊C4×C13111yescharacteristic
292C22×C4C22⋊C4×C13111yescharacteristic
293C22×C4C22⋊C4×C13111yescharacteristic
294C22×C4C22⋊C4×C13111yescharacteristic
295C22×C4C22×C4×C13111yescharacteristic
296C22×C4C22×C4×C13112yes—
297C22×C4C2×D4×C13111yescharacteristic
298C22×C4#41×C13112yes—
299C2×C8—24no—
300C2×C8—42no—
301C2×C8—42no—
302C4⋊C4—21no—
303C4⋊C4—24no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C4⋊C4C42×C13112yes—
309C22⋊C4—24no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C42—22no—
313C42—22no—
314C42—41no—
315C42—41no—
316C42—42no—
317C42—42no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23C2×C22⋊C4×C13111yescharacteristic
323C23C4×D4×C13112yes—
324C23AGL(1,ℤ/8)×C13111yescharacteristic
325C23#137×C13111yescharacteristic
326C23#137×C13112yes—
327Q8—42no—
328Q8—42no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—44no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—44no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4#99×C13112yes—
369C2×C4C2×C42×C13111yescharacteristic
370C2×C4#117×C13111yescharacteristic
371C2×C4C4×D4×C13112yes—
372C8—44no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22C4×C22⋊C4×C13111yescharacteristic
382C22C2×#99×C13111yescharacteristic
383C22#410×C13111yescharacteristic
384C22#417×C13111yescharacteristic
385C22#419×C13111yescharacteristic
386C22#421×C13111yescharacteristic
387C22#421×C13111yescharacteristic
388C22#440×C13112yes—
389C22#441×C13112yes—
390C4—22no—
391C4—21no—
392C4—21no—
393C4—22no—
394C4—42no—
395C4—42no—
396C4—41no—
397C4—41no—
398C4—41no—
399C4—84no—
400C4—81no—
401C4—81no—
402C2—22no—
403C2—22no—
404C2#1511×C13111yescharacteristic
405C2#1512×C13111yescharacteristic
406C2#1513×C13111yescharacteristic
407C2#1515×C13111yescharacteristic
408C2C4×#99×C13111yescharacteristic
409C2#1759×C13111yescharacteristic
410C2#1763×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C2×C22⋊C4
commutatorC2×C4C2×C42×C131
Frattini, cosocleC23×C4C23×C131
prime radicalC24×C131C2×D4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
7. C2×C4×Q8×C131C4semidirect
11. #391×C131C4semidirect
12. #389×C131C4semidirect
17. C4×C4⋊C4×C131C4semidirect
23. #328×C131C4semidirect
205. #8217C131direct (N × H)
206. C131#8217direct (N × H)
213. C2×C4×Q8C4×C131semidirect
217. #391C4×C131semidirect
218. #389C4×C131semidirect
223. C4×C4⋊C4C4×C131semidirect
229. #328C4×C131semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊Q8×C1312
#1749×C1312
C2×#328×C1312
#1434×C1312
#1294×C1312
#8217131