Finite Group Databasebeta

← C131×#19161 #45705045

Subgroups — C131×#19161 #45705045

Order 33536.

598 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3170×C131C211yesmaximal, characteristic, complemented
2#3107×C131C212yesmaximal
3#2965×C131C211yesmaximal, characteristic
4#1700×C131C212yesmaximal, complemented
5#1699×C131C212yesmaximal, complemented
6#1694×C131C211yesmaximal, characteristic, complemented
7#1693×C131C211yesmaximal, characteristic, complemented
8#1690×C131C211yesmaximal, characteristic, complemented
9#1689×C131C211yesmaximal, characteristic, complemented
10#1564×C131C211yesmaximal, characteristic, complemented
11#1544×C131C212yesmaximal, complemented
12#533×C131C2212yes—
13C4×#41×C131C2211yescharacteristic
14#500×C131C2211yescharacteristic
15#494×C131C2211yescharacteristic
16#487×C131C2212yes—
17#485×C131—22no—
18#475×C131C2212yes—
19#474×C131C2212yes—
20#467×C131—21no—
21#467×C131—21no—
22#462×C131C2212yes—
23#461×C131C2212yes—
24#452×C131—22no—
25#446×C131C2211yescharacteristic
26#446×C131C2211yescharacteristic
27C4×Q16×C131—22no—
28C4×Q16×C131—21no—
29C4×Q16×C131—21no—
30C4×SD16×C131—22no—
31#436×C131C2211yescharacteristic
32#436×C131C2211yescharacteristic
33#435×C131—21no—
34#435×C131—21no—
35#431×C131—21no—
36#431×C131C2211yescharacteristic
37#431×C131C2212yes—
38C4×M16×C131—21no—
39C2×C4×C8×C131C2211yescharacteristic
40#335×C131C2212yes—
41#334×C131C2211yescharacteristic
42#334×C131C2211yescharacteristic
43#332×C131C2212yes—
44#332×C131C2212yes—
45#332×C131C2212yes—
46#332×C131C2212yes—
47C2×#41×C131D411yescharacteristic
48C2×Q16×C131—22no—
49C2×Q16×C131—21no—
50C2×Q16×C131—21no—
51C2×SD16×C131—22no—
52C2×M16×C131—21no—
53C2×M16×C131—21no—
54C22×C8×C131D411yescharacteristic
55C22×C8×C131D411yescharacteristic
56C4⋊Q8×C131C2312yes—
57C4⋊Q8×C131C2312yes—
58#125×C131—22no—
59C22⋊Q8×C131—22no—
60C22⋊Q8×C131—22no—
61C4×Q8×C131—22no—
62C4×Q8×C131—22no—
63C4×Q8×C131D411yescharacteristic
64C4×Q8×C131C2311yescharacteristic
65C4×D4×C131—21no—
66C4×D4×C131—21no—
67C4×D4×C131D411yescharacteristic
68C4×D4×C131C2311yescharacteristic
69#117×C131—21no—
70#117×C131—22no—
71#117×C131D411yescharacteristic
72C2×C42×C131—21no—
73C2×C42×C131C2311yescharacteristic
74#107×C131—21no—
75#107×C131—21no—
76#107×C131—22no—
77#106×C131—22no—
78C4⋊C8×C131—21no—
79C4⋊C8×C131—21no—
80C4⋊C8×C131C2311yescharacteristic
81C4⋊C8×C131C2311yescharacteristic
82C4⋊C8×C131C2312yes—
83C4⋊C8×C131C2312yes—
84#103×C131—22no—
85#103×C131—22no—
86#103×C131—22no—
87#103×C131—22no—
88#103×C131—22no—
89#102×C131—22no—
90C22⋊C8×C131—21no—
91C22⋊C8×C131—22no—
92C22⋊C8×C131—21no—
93C22⋊C8×C131—21no—
94#97×C131—21no—
95#97×C131—21no—
96C4×C8×C131—21no—
97C4×C8×C131—22no—
98C4×C8×C131D411yescharacteristic
99C4×C8×C131D411yescharacteristic
100C4×C8×C131C2311yescharacteristic
101C4×C8×C131C2311yescharacteristic
102#41×C131—42no—
103C2×Q8×C131—22no—
104C2×Q8×C131—22no—
105C2×Q8×C131C2×D411yescharacteristic
106C2×D4×C131—21no—
107C2×D4×C131C2×D411yescharacteristic
108C22×C4×C131—21no—
109C22×C4×C131—21no—
110C22×C4×C131—21no—
111C22×C4×C131C2×D411yescharacteristic
112C22×C4×C131C2×D411yescharacteristic
113C22×C4×C131#4111yescharacteristic
114Q16×C131—42no—
115Q16×C131—44no—
116Q16×C131—42no—
117SD16×C131—44no—
118M16×C131—42no—
119M16×C131—42no—
120C2×C8×C131—22no—
121C2×C8×C131—21no—
122C2×C8×C131—21no—
123C2×C8×C131—22no—
124C2×C8×C131—22no—
125C2×C8×C131—41no—
126C2×C8×C131C2×D411yescharacteristic
127C2×C8×C131C2×D411yescharacteristic
128C2×C8×C131C2×D411yescharacteristic
129C2×C8×C131C2×D411yescharacteristic
130C4⋊C4×C131—21no—
131C4⋊C4×C131—21no—
132C4⋊C4×C131—22no—
133C4⋊C4×C131—22no—
134C4⋊C4×C131—22no—
135C4⋊C4×C131—22no—
136C4⋊C4×C131—42no—
137C4⋊C4×C131—42no—
138C4⋊C4×C131C2×D411yescharacteristic
139C4⋊C4×C131C2×D411yescharacteristic
140C22⋊C4×C131—21no—
141C22⋊C4×C131—21no—
142C22⋊C4×C131—21no—
143C22⋊C4×C131—42no—
144C42×C131—21no—
145C42×C131—21no—
146C42×C131—21no—
147C42×C131—42no—
148C42×C131C2×D411yescharacteristic
149C42×C131C2×D411yescharacteristic
150C42×C131#4111yescharacteristic
151C42×C131C2411yescharacteristic
152C23×C131—21no—
153C23×C131#12111yescharacteristic
154Q8×C131—22no—
155Q8×C131—42no—
156Q8×C131—42no—
157Q8×C131—42no—
158Q8×C131—42no—
159D4×C131—22no—
160D4×C131—42no—
161C2×C4×C131—21no—
162C2×C4×C131—21no—
163C2×C4×C131—22no—
164C2×C4×C131—22no—
165C2×C4×C131—21no—
166C2×C4×C131—21no—
167C2×C4×C131—21no—
168C2×C4×C131—42no—
169C2×C4×C131—41no—
170C2×C4×C131—41no—
171C2×C4×C131—42no—
172C2×C4×C131—42no—
173C2×C4×C131—42no—
174C2×C4×C131#12111yescharacteristic
175C2×C4×C131#12111yescharacteristic
176C2×C4×C131#12111yescharacteristic
177C2×C4×C131C22×D411yescharacteristic
178C2×C4×C131C22×D411yescharacteristic
179C2×C4×C131C2×#4111yescharacteristic
180C8×C131—21no—
181C8×C131—21no—
182C8×C131—21no—
183C8×C131—41no—
184C8×C131—41no—
185C8×C131—42no—
186C8×C131—42no—
187C8×C131#13512yes—
188C22×C131—21no—
189C22×C131—21no—
190C22×C131—21no—
191C22×C131—41no—
192C22×C131—41no—
193C22×C131—41no—
194C22×C131C2×#12111yescharacteristic
195C4×C131—21no—
196C4×C131—21no—
197C4×C131—21no—
198C4×C131—41no—
199C4×C131—41no—
200C4×C131—41no—
201C4×C131—82no—
202C4×C131—82no—
203C4×C131#47312yes—
204C4×C131C2×#13511yescharacteristic
205C4×C131#57511yescharacteristic
206C4×C131#57512yes—
207C2×C131—41no—
208C2×C131—81no—
209C2×C131#303511yescharacteristic
210C2×C131#305411yescharacteristic
211C2×C131C2×#47311yescharacteristic
212#19161C13111yesmaximal, characteristic, direct product factor, Sylow
213C131#1916111yescharacteristic, direct product factor, Sylow
214#3170C2×C13111yescharacteristic, complemented
215#3107C2×C13112yes—
216#2965C2×C13111yescharacteristic
217#1700C2×C13112yescomplemented
218#1699C2×C13112yescomplemented
219#1694C2×C13111yescharacteristic, complemented
220#1693C2×C13111yescharacteristic, complemented
221#1690C2×C13111yescharacteristic, complemented
222#1689C2×C13111yescharacteristic, complemented
223#1564C2×C13111yescharacteristic, complemented
224#1544C2×C13112yescomplemented
225#533C22×C13112yes—
226C4×#41C22×C13111yescharacteristic
227#500C22×C13111yescharacteristic
228#494C22×C13111yescharacteristic
229#487C22×C13112yes—
230#485—22no—
231#475C22×C13112yes—
232#474C22×C13112yes—
233#467—21no—
234#467—21no—
235#462C22×C13112yes—
236#461C22×C13112yes—
237#452—22no—
238#446C22×C13111yescharacteristic
239#446C22×C13111yescharacteristic
240C4×Q16—22no—
241C4×Q16—21no—
242C4×Q16—21no—
243C4×SD16—22no—
244#436C22×C13111yescharacteristic
245#436C22×C13111yescharacteristic
246#435—21no—
247#435—21no—
248#431—21no—
249#431C22×C13111yescharacteristic
250#431C22×C13112yes—
251C4×M16—21no—
252C2×C4×C8C22×C13111yescharacteristic
253#335C22×C13112yes—
254#334C22×C13111yescharacteristic
255#334C22×C13111yescharacteristic
256#332C22×C13112yes—
257#332C22×C13112yes—
258#332C22×C13112yes—
259#332C22×C13112yes—
260C2×#41D4×C13111yescharacteristic
261C2×Q16—22no—
262C2×Q16—21no—
263C2×Q16—21no—
264C2×SD16—22no—
265C2×M16—21no—
266C2×M16—21no—
267C22×C8D4×C13111yescharacteristic
268C22×C8D4×C13111yescharacteristic
269C4⋊Q8C23×C13112yes—
270C4⋊Q8C23×C13112yes—
271#125—22no—
272C22⋊Q8—22no—
273C22⋊Q8—22no—
274C4×Q8—22no—
275C4×Q8—22no—
276C4×Q8D4×C13111yescharacteristic
277C4×Q8C23×C13111yescharacteristic
278C4×D4—21no—
279C4×D4—21no—
280C4×D4D4×C13111yescharacteristic
281C4×D4C23×C13111yescharacteristic
282#117—21no—
283#117—22no—
284#117D4×C13111yescharacteristic
285C2×C42—21no—
286C2×C42C23×C13111yescharacteristic
287#107—21no—
288#107—21no—
289#107—22no—
290#106—22no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293C4⋊C8C23×C13111yescharacteristic
294C4⋊C8C23×C13111yescharacteristic
295C4⋊C8C23×C13112yes—
296C4⋊C8C23×C13112yes—
297#103—22no—
298#103—22no—
299#103—22no—
300#103—22no—
301#103—22no—
302#102—22no—
303C22⋊C8—21no—
304C22⋊C8—22no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307#97—21no—
308#97—21no—
309C4×C8—21no—
310C4×C8—22no—
311C4×C8D4×C13111yescharacteristic
312C4×C8D4×C13111yescharacteristic
313C4×C8C23×C13111yescharacteristic
314C4×C8C23×C13111yescharacteristic
315#41—42no—
316C2×Q8—22no—
317C2×Q8—22no—
318C2×Q8C2×D4×C13111yescharacteristic
319C2×D4—21no—
320C2×D4C2×D4×C13111yescharacteristic
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4C2×D4×C13111yescharacteristic
325C22×C4C2×D4×C13111yescharacteristic
326C22×C4#41×C13111yescharacteristic
327Q16—42no—
328Q16—44no—
329Q16—42no—
330SD16—44no—
331M16—42no—
332M16—42no—
333C2×C8—22no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—41no—
339C2×C8C2×D4×C13111yescharacteristic
340C2×C8C2×D4×C13111yescharacteristic
341C2×C8C2×D4×C13111yescharacteristic
342C2×C8C2×D4×C13111yescharacteristic
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4C2×D4×C13111yescharacteristic
352C4⋊C4C2×D4×C13111yescharacteristic
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—42no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—42no—
361C42C2×D4×C13111yescharacteristic
362C42C2×D4×C13111yescharacteristic
363C42#41×C13111yescharacteristic
364C42C24×C13111yescharacteristic
365C23—21no—
366C23#121×C13111yescharacteristic
367Q8—22no—
368Q8—42no—
369Q8—42no—
370Q8—42no—
371Q8—42no—
372D4—22no—
373D4—42no—
374C2×C4—22no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4#121×C13111yescharacteristic
388C2×C4#121×C13111yescharacteristic
389C2×C4#121×C13111yescharacteristic
390C2×C4C22×D4×C13111yescharacteristic
391C2×C4C22×D4×C13111yescharacteristic
392C2×C4C2×#41×C13111yescharacteristic
393C8—21no—
394C8—21no—
395C8—21no—
396C8—41no—
397C8—41no—
398C8—42no—
399C8—42no—
400C8#135×C13112yes—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22C2×#121×C13111yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—82no—
415C4—82no—
416C4#473×C13112yes—
417C4C2×#135×C13111yescharacteristic
418C4#575×C13111yescharacteristic
419C4#575×C13112yes—
420C2—41no—
421C2—81no—
422C2#3035×C13111yescharacteristic
423C2#3054×C13111yescharacteristic
424C2C2×#473×C13111yescharacteristic
subgroupG/H
centerC2×C4×C131#121
commutator, Frattini, cosocleC42C24×C131
socleC22×C131C2×#121
prime radicalC2×#41×C131D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3170×C131C2semidirect
4. #1700×C131C2semidirect
5. #1699×C131C2semidirect
6. #1694×C131C2semidirect
7. #1693×C131C2semidirect
8. #1690×C131C2semidirect
9. #1689×C131C2semidirect
10. #1564×C131C2semidirect
11. #1544×C131C2semidirect
212. #19161C131direct (N × H)
213. C131#19161direct (N × H)
214. #3170C2×C131semidirect
217. #1700C2×C131semidirect
218. #1699C2×C131semidirect
219. #1694C2×C131semidirect
220. #1693C2×C131semidirect
221. #1690C2×C131semidirect
222. #1689C2×C131semidirect
223. #1564C2×C131semidirect
224. #1544C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3170×C1312
#3107×C1312
#2965×C1312
#1700×C1312
#1699×C1312
#1694×C1312
#1693×C1312
#1690×C1312
#1689×C1312
#1564×C1312
#1544×C1312
#19161131