Finite Group Databasebeta

← C131×#7616 #45693500

Subgroups — C131×#7616 #45693500

Order 33536.

634 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#121×C131C211yesmaximal, characteristic
2#1797×C131C211yesmaximal, characteristic, complemented
3#1728×C131C211yesmaximal, characteristic, complemented
4#1271×C131C212yesmaximal, complemented
5#1270×C131C212yesmaximal, complemented
6C22×M16×C131—21no—
7C2×#121×C131C411yescharacteristic
8C2×C4×D4×C131—21no—
9C2×C4×D4×C131C411yescharacteristic
10C22×C42×C131C2211yescharacteristic
11C2×C4⋊C8×C131—21no—
12C2×C22⋊C8×C131—21no—
13#390×C131C2211yescharacteristic
14#389×C131C2211yescharacteristic
15#388×C131—21no—
16#386×C131—21no—
17#380×C131C411yescharacteristic
18C4×C4⋊C4×C131C411yescharacteristic
19C4×C22⋊C4×C131—21no—
20#336×C131—21no—
21#336×C131C2212yes—
22#336×C131C2212yes—
23C22×D4×C131—21no—
24C22×D4×C131C2×C411yescharacteristic
25C23×C4×C131—21no—
26C23×C4×C131C2×C411yescharacteristic
27C23×C4×C131D411yescharacteristic
28C23×C4×C131D411yescharacteristic
29C2×M16×C131—24no—
30C2×M16×C131—42no—
31C2×M16×C131—42no—
32C22×C8×C131—22no—
33C22×C8×C131—22no—
34#121×C131—22no—
35#121×C131—22no—
36C4×D4×C131—42no—
37C4×D4×C131—42no—
38C4×D4×C131—42no—
39C2×C4⋊C4×C131—21no—
40C2×C4⋊C4×C131C2×C411yescharacteristic
41C2×C4⋊C4×C131C2×C411yescharacteristic
42C2×C4⋊C4×C131C2×C411yescharacteristic
43C2×C22⋊C4×C131—21no—
44C2×C22⋊C4×C131—21no—
45C2×C22⋊C4×C131—21no—
46C2×C22⋊C4×C131—21no—
47C2×C22⋊C4×C131—21no—
48C2×C42×C131—21no—
49C2×C42×C131—42no—
50C2×C42×C131C2×C411yescharacteristic
51C2×C42×C131D411yescharacteristic
52C2×C42×C131D411yescharacteristic
53C2×C42×C131C2311yescharacteristic
54C4⋊C8×C131—42no—
55C22⋊C8×C131—42no—
56#95×C131—21no—
57#95×C131—21no—
58#95×C131—21no—
59C24×C131—21no—
60C24×C131C22⋊C411yescharacteristic
61C2×D4×C131—24no—
62C2×D4×C131—21no—
63C2×D4×C131—41no—
64C2×D4×C131—41no—
65C2×D4×C131—42no—
66C2×D4×C131—42no—
67C2×D4×C131M1612yescomplemented
68C22×C4×C131—22no—
69C22×C4×C131—22no—
70C22×C4×C131—21no—
71C22×C4×C131—21no—
72C22×C4×C131—21no—
73C22×C4×C131—21no—
74C22×C4×C131—21no—
75C22×C4×C131—21no—
76C22×C4×C131—21no—
77C22×C4×C131—41no—
78C22×C4×C131—41no—
79C22×C4×C131—41no—
80C22×C4×C131—41no—
81C22×C4×C131—42no—
82C22×C4×C131—42no—
83C22×C4×C131—42no—
84C22×C4×C131C22⋊C411yescharacteristic
85C22×C4×C131C22⋊C411yescharacteristic
86C22×C4×C131C22⋊C411yescharacteristic
87C22×C4×C131D812yes—
88C22×C4×C131SD1612yes—
89C22×C4×C131C22×C411yescharacteristic
90C22×C4×C131C2×D411yescharacteristic
91C22×C4×C131C2×D411yescharacteristic
92M16×C131—48no—
93C2×C8×C131—24no—
94C2×C8×C131—42no—
95C2×C8×C131—42no—
96C2×C8×C131—42no—
97C2×C8×C131—42no—
98C2×C8×C131—42no—
99C4⋊C4×C131—21no—
100C4⋊C4×C131—41no—
101C4⋊C4×C131—41no—
102C4⋊C4×C131—41no—
103C4⋊C4×C131—41no—
104C4⋊C4×C131M1612yescomplemented
105C22⋊C4×C131—24no—
106C22⋊C4×C131—42no—
107C22⋊C4×C131—42no—
108C22⋊C4×C131—41no—
109C22⋊C4×C131—41no—
110C22⋊C4×C131—41no—
111C22⋊C4×C131—41no—
112C42×C131—22no—
113C42×C131—22no—
114C42×C131—41no—
115C42×C131—41no—
116C42×C131—42no—
117C23×C131—21no—
118C23×C131—21no—
119C23×C131—21no—
120C23×C131—21no—
121C23×C131—21no—
122C23×C131—21no—
123C23×C131—22no—
124C23×C131—41no—
125C23×C131—41no—
126C23×C131—41no—
127C23×C131—41no—
128C23×C131—41no—
129C23×C131—41no—
130C23×C131#10212yes—
131C23×C131C2×C22⋊C411yescharacteristic
132D4×C131—42no—
133D4×C131—42no—
134D4×C131—48no—
135C2×C4×C131—21no—
136C2×C4×C131—21no—
137C2×C4×C131—21no—
138C2×C4×C131—21no—
139C2×C4×C131—21no—
140C2×C4×C131—21no—
141C2×C4×C131—24no—
142C2×C4×C131—24no—
143C2×C4×C131—21no—
144C2×C4×C131—22no—
145C2×C4×C131—21no—
146C2×C4×C131—21no—
147C2×C4×C131—21no—
148C2×C4×C131—21no—
149C2×C4×C131—21no—
150C2×C4×C131—42no—
151C2×C4×C131—42no—
152C2×C4×C131—42no—
153C2×C4×C131—42no—
154C2×C4×C131—41no—
155C2×C4×C131—41no—
156C2×C4×C131—41no—
157C2×C4×C131—41no—
158C2×C4×C131—41no—
159C2×C4×C131—41no—
160C2×C4×C131—41no—
161C2×C4×C131—41no—
162C2×C4×C131—84no—
163C2×C4×C131#9912yes—
164C2×C4×C131#10212yes—
165C2×C4×C131#10412yes—
166C2×C4×C131C2×M1611yescharacteristic
167C2×C4×C131C2×M1611yescharacteristic
168C2×C4×C131C2×D811yescharacteristic
169C2×C4×C131C2×SD1611yescharacteristic
170C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C131#13711yescharacteristic
172C8×C131—44no—
173C8×C131—82no—
174C22×C131—22no—
175C22×C131—22no—
176C22×C131—22no—
177C22×C131—41no—
178C22×C131—41no—
179C22×C131—41no—
180C22×C131—41no—
181C22×C131—42no—
182C22×C131—42no—
183C22×C131—42no—
184C22×C131—81no—
185C22×C131—81no—
186C22×C131—81no—
187C22×C131—81no—
188C22×C131#40711yescharacteristic
189C22×C131C2×#9911yescharacteristic
190C22×C131#41311yescharacteristic
191C22×C131C2×#10211yescharacteristic
192C22×C131#41711yescharacteristic
193C22×C131C2×#10411yescharacteristic
194C22×C131#42111yescharacteristic
195C4×C131—21no—
196C4×C131—21no—
197C4×C131—21no—
198C4×C131—21no—
199C4×C131—21no—
200C4×C131—21no—
201C4×C131—41no—
202C4×C131—42no—
203C4×C131—41no—
204C4×C131—81no—
205C4×C131—81no—
206C4×C131#32714yes—
207C2×C131—42no—
208C2×C131—82no—
209C2×C131#146511yescharacteristic
210C2×C131#148611yescharacteristic
211C2×C131#148911yescharacteristic
212C2×C131C2×#32711yescharacteristic
213C2×C131#151311yescharacteristic
214C2×C131#152911yescharacteristic
215C2×C131#154711yescharacteristic
216#7616C13111yesmaximal, characteristic, direct product factor, Sylow
217C131#761611yescharacteristic, direct product factor, Sylow
218C4×#121C2×C13111yescharacteristic
219#1797C2×C13111yescharacteristic, complemented
220#1728C2×C13111yescharacteristic, complemented
221#1271C2×C13112yescomplemented
222#1270C2×C13112yescomplemented
223C22×M16—21no—
224C2×#121C4×C13111yescharacteristic
225C2×C4×D4—21no—
226C2×C4×D4C4×C13111yescharacteristic
227C22×C42C22×C13111yescharacteristic
228C2×C4⋊C8—21no—
229C2×C22⋊C8—21no—
230#390C22×C13111yescharacteristic
231#389C22×C13111yescharacteristic
232#388—21no—
233#386—21no—
234#380C4×C13111yescharacteristic
235C4×C4⋊C4C4×C13111yescharacteristic
236C4×C22⋊C4—21no—
237#336—21no—
238#336C22×C13112yes—
239#336C22×C13112yes—
240C22×D4—21no—
241C22×D4C2×C4×C13111yescharacteristic
242C23×C4—21no—
243C23×C4C2×C4×C13111yescharacteristic
244C23×C4D4×C13111yescharacteristic
245C23×C4D4×C13111yescharacteristic
246C2×M16—24no—
247C2×M16—42no—
248C2×M16—42no—
249C22×C8—22no—
250C22×C8—22no—
251#121—22no—
252#121—22no—
253C4×D4—42no—
254C4×D4—42no—
255C4×D4—42no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4C2×C4×C13111yescharacteristic
258C2×C4⋊C4C2×C4×C13111yescharacteristic
259C2×C4⋊C4C2×C4×C13111yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C42—21no—
266C2×C42—42no—
267C2×C42C2×C4×C13111yescharacteristic
268C2×C42D4×C13111yescharacteristic
269C2×C42D4×C13111yescharacteristic
270C2×C42C23×C13111yescharacteristic
271C4⋊C8—42no—
272C22⋊C8—42no—
273#95—21no—
274#95—21no—
275#95—21no—
276C24—21no—
277C24C22⋊C4×C13111yescharacteristic
278C2×D4—24no—
279C2×D4—21no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4M16×C13112yescomplemented
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4C22⋊C4×C13111yescharacteristic
302C22×C4C22⋊C4×C13111yescharacteristic
303C22×C4C22⋊C4×C13111yescharacteristic
304C22×C4D8×C13112yes—
305C22×C4SD16×C13112yes—
306C22×C4C22×C4×C13111yescharacteristic
307C22×C4C2×D4×C13111yescharacteristic
308C22×C4C2×D4×C13111yescharacteristic
309M16—48no—
310C2×C8—24no—
311C2×C8—42no—
312C2×C8—42no—
313C2×C8—42no—
314C2×C8—42no—
315C2×C8—42no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4M16×C13112yescomplemented
322C22⋊C4—24no—
323C22⋊C4—42no—
324C22⋊C4—42no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C42—22no—
330C42—22no—
331C42—41no—
332C42—41no—
333C42—42no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—22no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23#102×C13112yes—
348C23C2×C22⋊C4×C13111yescharacteristic
349D4—42no—
350D4—42no—
351D4—48no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—21no—
361C2×C4—22no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—84no—
380C2×C4#99×C13112yes—
381C2×C4#102×C13112yes—
382C2×C4#104×C13112yes—
383C2×C4C2×M16×C13111yescharacteristic
384C2×C4C2×M16×C13111yescharacteristic
385C2×C4C2×D8×C13111yescharacteristic
386C2×C4C2×SD16×C13111yescharacteristic
387C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
388C2×C4#137×C13111yescharacteristic
389C8—44no—
390C8—82no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—42no—
399C22—42no—
400C22—42no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22#407×C13111yescharacteristic
406C22C2×#99×C13111yescharacteristic
407C22#413×C13111yescharacteristic
408C22C2×#102×C13111yescharacteristic
409C22#417×C13111yescharacteristic
410C22C2×#104×C13111yescharacteristic
411C22#421×C13111yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—41no—
419C4—42no—
420C4—41no—
421C4—81no—
422C4—81no—
423C4#327×C13114yes—
424C2—42no—
425C2—82no—
426C2#1465×C13111yescharacteristic
427C2#1486×C13111yescharacteristic
428C2#1489×C13111yescharacteristic
429C2C2×#327×C13111yescharacteristic
430C2#1513×C13111yescharacteristic
431C2#1529×C13111yescharacteristic
432C2#1547×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C2×C22⋊C4
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC2×#121×C131C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1797×C131C2semidirect
3. #1728×C131C2semidirect
4. #1271×C131C2semidirect
5. #1270×C131C2semidirect
67. C2×D4×C131M16semidirect
104. C4⋊C4×C131M16semidirect
216. #7616C131direct (N × H)
217. C131#7616direct (N × H)
219. #1797C2×C131semidirect
220. #1728C2×C131semidirect
221. #1271C2×C131semidirect
222. #1270C2×C131semidirect
284. C2×D4M16×C131semidirect
321. C4⋊C4M16×C131semidirect

Maximal subgroups

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

subgroupindex
C4×#121×C1312
#1797×C1312
#1728×C1312
#1271×C1312
#1270×C1312
#7616131