Finite Group Databasebeta

← C131×#19423 #45705307

Subgroups — C131×#19423 #45705307

Order 33536.

630 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3209×C131C211yesmaximal, characteristic, complemented
2#3077×C131C211yesmaximal, characteristic
3C2×#474×C131C211yesmaximal, characteristic
4#2975×C131C211yesmaximal, characteristic
5#1703×C131C214yesmaximal, complemented
6#1689×C131C214yesmaximal, complemented
7#1570×C131C211yesmaximal, characteristic, complemented
8#1549×C131C211yesmaximal, characteristic, complemented
9#1542×C131C211yesmaximal, characteristic, complemented
10#533×C131C2211yescharacteristic
11C2×C4⋊Q8×C131C2211yescharacteristic
12C2×C4×D4×C131C2211yescharacteristic
13#494×C131C2212yescomplemented
14#487×C131C2212yescomplemented
15#478×C131—22no—
16#476×C131C2212yes—
17#474×C131—22no—
18#474×C131C2214yes—
19#474×C131C2212yes—
20#462×C131—22no—
21#451×C131—22no—
22#436×C131—22no—
23#436×C131C2214yes—
24#431×C131C2211yescharacteristic
25#431×C131C2211yescharacteristic
26#428×C131—21no—
27C2×#107×C131—21no—
28#423×C131C2211yescharacteristic
29C2×C4⋊C8×C131C2211yescharacteristic
30#418×C131—21no—
31C2×#102×C131—21no—
32#407×C131—22no—
33#334×C131C2214yescomplemented
34#333×C131C2212yescomplemented
35#332×C131C2212yescomplemented
36#332×C131C2214yescomplemented
37C22×Q8×C131—21no—
38C22×D4×C131D411yescharacteristic
39C23×C4×C131—21no—
40C2×Q16×C131—24no—
41C2×M16×C131—21no—
42C2×M16×C131—24no—
43C22×C8×C131—21no—
44C4⋊Q8×C131—21no—
45C4⋊Q8×C131—21no—
46C4⋊Q8×C131—21no—
47C4⋊Q8×C131C2312yes—
48C4⋊Q8×C131C2311yescharacteristic
49C4⋊Q8×C131C2311yescharacteristic
50#125×C131—21no—
51C22⋊Q8×C131—21no—
52C22⋊Q8×C131—21no—
53C4×Q8×C131—21no—
54C4×Q8×C131—21no—
55C4×D4×C131—21no—
56C4×D4×C131—21no—
57C4×D4×C131D412yes—
58C4×D4×C131C2312yes—
59#117×C131—21no—
60C2×C4⋊C4×C131—21no—
61C2×C4⋊C4×C131—21no—
62C2×C4⋊C4×C131D411yescharacteristic
63C2×C22⋊C4×C131—21no—
64C2×C42×C131C2311yescharacteristic
65#107×C131—24no—
66#107×C131—22no—
67#106×C131—22no—
68C4⋊C8×C131—21no—
69C4⋊C8×C131—21no—
70C4⋊C8×C131D412yes—
71C4⋊C8×C131C2312yes—
72C4⋊C8×C131C2312yes—
73C4⋊C8×C131C2312yes—
74#103×C131—24no—
75#102×C131—24no—
76#102×C131—22no—
77#102×C131—22no—
78C22⋊C8×C131—21no—
79C22⋊C8×C131—24no—
80C22⋊C8×C131D412yes—
81C4×C8×C131—21no—
82C4×C8×C131C2312yes—
83C24×C131—21no—
84C2×Q8×C131—22no—
85C2×Q8×C131—21no—
86C2×Q8×C131—21no—
87C2×Q8×C131—41no—
88C2×Q8×C131—82no—
89C2×D4×C131—21no—
90C2×D4×C131—22no—
91C2×D4×C131—22no—
92C2×D4×C131C2×D412yes—
93C22×C4×C131—21no—
94C22×C4×C131—22no—
95C22×C4×C131—22no—
96C22×C4×C131—41no—
97C22×C4×C131—82no—
98C22×C4×C131C2×D411yescharacteristic
99C22×C4×C131C2×D411yescharacteristic
100C22×C4×C131#4111yescharacteristic
101Q16×C131—84no—
102M16×C131—42no—
103M16×C131—84no—
104C2×C8×C131—22no—
105C2×C8×C131—22no—
106C2×C8×C131—22no—
107C2×C8×C131—42no—
108C2×C8×C131C2×D414yes—
109C4⋊C4×C131—21no—
110C4⋊C4×C131—21no—
111C4⋊C4×C131—22no—
112C4⋊C4×C131—21no—
113C4⋊C4×C131—21no—
114C4⋊C4×C131—22no—
115C4⋊C4×C131—21no—
116C4⋊C4×C131—41no—
117C4⋊C4×C131—41no—
118C4⋊C4×C131—41no—
119C4⋊C4×C131—41no—
120C4⋊C4×C131C2×D412yes—
121C22⋊C4×C131—22no—
122C22⋊C4×C131—22no—
123C22⋊C4×C131—41no—
124C42×C131—41no—
125C42×C131C2×D411yescharacteristic
126C42×C131C2×D411yescharacteristic
127C42×C131#4111yescharacteristic
128C42×C131C2411yescharacteristic
129C23×C131—22no—
130C23×C131—42no—
131C23×C131—81no—
132C23×C131—81no—
133C23×C131#12111yescharacteristic
134Q8×C131—42no—
135Q8×C131—44no—
136Q8×C131—81no—
137Q8×C131—82no—
138D4×C131—22no—
139D4×C131—22no—
140D4×C131—42no—
141C2×C4×C131—22no—
142C2×C4×C131—22no—
143C2×C4×C131—41no—
144C2×C4×C131—44no—
145C2×C4×C131—41no—
146C2×C4×C131—41no—
147C2×C4×C131—42no—
148C2×C4×C131—82no—
149C2×C4×C131—81no—
150C2×C4×C131—82no—
151C2×C4×C131#12111yescharacteristic
152C2×C4×C131#12111yescharacteristic
153C2×C4×C131#12111yescharacteristic
154C2×C4×C131#13712yes—
155C2×C4×C131#13712yes—
156C2×C4×C131C22×D411yescharacteristic
157C2×C4×C131C22×D411yescharacteristic
158C2×C4×C131C2×#4111yescharacteristic
159C8×C131—24no—
160C8×C131—42no—
161C8×C131—42no—
162C8×C131—42no—
163C22×C131—21no—
164C22×C131—21no—
165C22×C131—42no—
166C22×C131—42no—
167C22×C131—42no—
168C22×C131—84no—
169C22×C131#47012yes—
170C22×C131C2×#12111yescharacteristic
171C4×C131—21no—
172C4×C131—21no—
173C4×C131—21no—
174C4×C131—42no—
175C4×C131—82no—
176C4×C131—81no—
177C4×C131—81no—
178C4×C131#47012yes—
179C4×C131C2×#13711yescharacteristic
180C4×C131C2×#13711yescharacteristic
181C4×C131#57612yes—
182C2×C131—22no—
183C2×C131—82no—
184C2×C131#304111yescharacteristic
185C2×C131C2×#47011yescharacteristic
186C2×C131#306911yescharacteristic
187#19423C13111yesmaximal, characteristic, direct product factor, Sylow
188C131#1942311yescharacteristic, direct product factor, Sylow
189#3209C2×C13111yescharacteristic, complemented
190#3077C2×C13111yescharacteristic
191C2×#474C2×C13111yescharacteristic
192#2975C2×C13111yescharacteristic
193#1703C2×C13114yescomplemented
194#1689C2×C13114yescomplemented
195#1570C2×C13111yescharacteristic, complemented
196#1549C2×C13111yescharacteristic, complemented
197#1542C2×C13111yescharacteristic, complemented
198#533C22×C13111yescharacteristic
199C2×C4⋊Q8C22×C13111yescharacteristic
200C2×C4×D4C22×C13111yescharacteristic
201#494C22×C13112yescomplemented
202#487C22×C13112yescomplemented
203#478—22no—
204#476C22×C13112yes—
205#474—22no—
206#474C22×C13112yes—
207#474C22×C13114yes—
208#462—22no—
209#451—22no—
210#436—22no—
211#436C22×C13114yes—
212#431C22×C13111yescharacteristic
213#431C22×C13111yescharacteristic
214#428—21no—
215C2×#107—21no—
216#423C22×C13111yescharacteristic
217C2×C4⋊C8C22×C13111yescharacteristic
218#418—21no—
219C2×#102—21no—
220#407—22no—
221#334C22×C13114yescomplemented
222#333C22×C13112yescomplemented
223#332C22×C13112yescomplemented
224#332C22×C13114yescomplemented
225C22×Q8—21no—
226C22×D4D4×C13111yescharacteristic
227C23×C4—21no—
228C2×Q16—24no—
229C2×M16—21no—
230C2×M16—24no—
231C22×C8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8C23×C13112yes—
236C4⋊Q8C23×C13111yescharacteristic
237C4⋊Q8C23×C13111yescharacteristic
238#125—21no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4D4×C13112yes—
246C4×D4C23×C13112yes—
247#117—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4D4×C13111yescharacteristic
251C2×C22⋊C4—21no—
252C2×C42C23×C13111yescharacteristic
253#107—24no—
254#107—22no—
255#106—22no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8D4×C13112yes—
259C4⋊C8C23×C13112yes—
260C4⋊C8C23×C13112yes—
261C4⋊C8C23×C13112yes—
262#103—24no—
263#102—24no—
264#102—22no—
265#102—22no—
266C22⋊C8—21no—
267C22⋊C8—24no—
268C22⋊C8D4×C13112yes—
269C4×C8—21no—
270C4×C8C23×C13112yes—
271C24—21no—
272C2×Q8—22no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—41no—
276C2×Q8—82no—
277C2×D4—21no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4C2×D4×C13112yes—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—82no—
286C22×C4C2×D4×C13111yescharacteristic
287C22×C4C2×D4×C13111yescharacteristic
288C22×C4#41×C13111yescharacteristic
289Q16—84no—
290M16—42no—
291M16—84no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—42no—
296C2×C8C2×D4×C13114yes—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—22no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4C2×D4×C13112yes—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C22⋊C4—41no—
312C42—41no—
313C42C2×D4×C13111yescharacteristic
314C42C2×D4×C13111yescharacteristic
315C42#41×C13111yescharacteristic
316C42C24×C13111yescharacteristic
317C23—22no—
318C23—42no—
319C23—81no—
320C23—81no—
321C23#121×C13111yescharacteristic
322Q8—42no—
323Q8—44no—
324Q8—81no—
325Q8—82no—
326D4—22no—
327D4—22no—
328D4—42no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—44no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—82no—
337C2×C4—81no—
338C2×C4—82no—
339C2×C4#121×C13111yescharacteristic
340C2×C4#121×C13111yescharacteristic
341C2×C4#121×C13111yescharacteristic
342C2×C4#137×C13112yes—
343C2×C4#137×C13112yes—
344C2×C4C22×D4×C13111yescharacteristic
345C2×C4C22×D4×C13111yescharacteristic
346C2×C4C2×#41×C13111yescharacteristic
347C8—24no—
348C8—42no—
349C8—42no—
350C8—42no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—42no—
355C22—42no—
356C22—84no—
357C22#470×C13112yes—
358C22C2×#121×C13111yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—42no—
363C4—82no—
364C4—81no—
365C4—81no—
366C4#470×C13112yes—
367C4C2×#137×C13111yescharacteristic
368C4C2×#137×C13111yescharacteristic
369C4#576×C13112yes—
370C2—22no—
371C2—82no—
372C2#3041×C13111yescharacteristic
373C2C2×#470×C13111yescharacteristic
374C2#3069×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#121
commutator, Frattini, cosocleC42C24×C131
prime radicalC22×D4×C131D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3209×C131C2semidirect
5. #1703×C131C2semidirect
6. #1689×C131C2semidirect
7. #1570×C131C2semidirect
8. #1549×C131C2semidirect
9. #1542×C131C2semidirect
13. #494×C131C22semidirect
14. #487×C131C22semidirect
33. #334×C131C22semidirect
34. #333×C131C22semidirect
35. #332×C131C22semidirect
36. #332×C131C22semidirect
187. #19423C131direct (N × H)
188. C131#19423direct (N × H)
189. #3209C2×C131semidirect
193. #1703C2×C131semidirect
194. #1689C2×C131semidirect
195. #1570C2×C131semidirect
196. #1549C2×C131semidirect
197. #1542C2×C131semidirect
201. #494C22×C131semidirect
202. #487C22×C131semidirect
221. #334C22×C131semidirect
222. #333C22×C131semidirect
223. #332C22×C131semidirect
224. #332C22×C131semidirect

Maximal subgroups

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

subgroupindex
#3209×C1312
#3077×C1312
C2×#474×C1312
#2975×C1312
#1703×C1312
#1689×C1312
#1570×C1312
#1549×C1312
#1542×C1312
#19423131