Finite Group Databasebeta

← C131×#19403 #45705287

Subgroups — C131×#19403 #45705287

Order 33536.

644 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3227×C131C211yesmaximal, characteristic
2C2×#477×C131C211yesmaximal, characteristic, complemented
3#3037×C131C211yesmaximal, characteristic
4#2982×C131C211yesmaximal, characteristic, complemented
5#1678×C131C214yesmaximal, complemented
6#1672×C131C214yesmaximal, complemented
7#1570×C131C211yesmaximal, characteristic, complemented
8#1548×C131C211yesmaximal, characteristic, complemented
9#1540×C131C211yesmaximal, characteristic
10C2×#137×C131—21no—
11#532×C131C2211yescharacteristic
12C2×C4⋊Q8×C131C2211yescharacteristic
13C2×C4×Q8×C131C2211yescharacteristic
14#498×C131C2212yes—
15#486×C131C2212yes—
16#481×C131—22no—
17#477×C131—22no—
18#477×C131C2214yes—
19#476×C131—22no—
20#464×C131—22no—
21#462×C131C2212yes—
22#460×C131C2212yes—
23C8×Q8×C131—22no—
24C8×Q8×C131C2214yes—
25#431×C131—22no—
26#431×C131C2211yescharacteristic
27#431×C131C2211yescharacteristic
28C2×#107×C131—21no—
29#423×C131C2211yescharacteristic
30C2×C4⋊C8×C131C2211yescharacteristic
31#417×C131—21no—
32C2×#103×C131—21no—
33#334×C131C2214yes—
34#333×C131C2214yes—
35#332×C131C2212yes—
36#331×C131C2212yes—
37C2×#41×C131—21no—
38C22×Q8×C131—21no—
39C22×Q8×C131D411yescharacteristic
40#137×C131—44no—
41C2×Q16×C131—22no—
42C2×SD16×C131—22no—
43C2×M16×C131—21no—
44C22×C8×C131—21no—
45C4⋊Q8×C131—21no—
46C4⋊Q8×C131—21no—
47C4⋊Q8×C131—21no—
48C4⋊Q8×C131C2311yescharacteristic
49C4⋊Q8×C131C2312yes—
50#127×C131C2311yescharacteristic
51#124×C131—21no—
52#121×C131—21no—
53#121×C131—21no—
54C4×Q8×C131—21no—
55C4×Q8×C131—21no—
56C4×Q8×C131D412yes—
57C4×Q8×C131C2312yes—
58C4×D4×C131—21no—
59C4×D4×C131—21no—
60C2×C4⋊C4×C131—21no—
61C2×C4⋊C4×C131—21no—
62C2×C4⋊C4×C131—21no—
63C2×C4⋊C4×C131D411yescharacteristic
64C2×C42×C131—21no—
65C2×C42×C131C2311yescharacteristic
66#107×C131—24no—
67#106×C131—24no—
68C4⋊C8×C131—24no—
69C4⋊C8×C131—21no—
70C4⋊C8×C131—21no—
71C4⋊C8×C131D412yes—
72C4⋊C8×C131C2312yes—
73C4⋊C8×C131C2312yes—
74C4⋊C8×C131C2312yes—
75#103×C131—24no—
76#103×C131—22no—
77#102×C131—24no—
78#102×C131—22no—
79C22⋊C8×C131—21no—
80C22⋊C8×C131D412yes—
81C4×C8×C131—24no—
82C4×C8×C131—21no—
83C4×C8×C131C2312yes—
84#41×C131—42no—
85#41×C131—42no—
86C2×Q8×C131—21no—
87C2×Q8×C131—22no—
88C2×Q8×C131—21no—
89C2×Q8×C131—22no—
90C2×Q8×C131—41no—
91C2×Q8×C131—82no—
92C2×Q8×C131SD1614yes—
93C2×Q8×C131C2×D412yes—
94C2×D4×C131—21no—
95C2×D4×C131—21no—
96C2×D4×C131—21no—
97C2×D4×C131—41no—
98C22×C4×C131—21no—
99C22×C4×C131—21no—
100C22×C4×C131—41no—
101C22×C4×C131—41no—
102C22×C4×C131C2×D411yescharacteristic
103C22×C4×C131C2×D411yescharacteristic
104C22×C4×C131#4111yescharacteristic
105Q16×C131—44no—
106SD16×C131—44no—
107M16×C131—42no—
108C2×C8×C131—22no—
109C2×C8×C131—22no—
110C2×C8×C131—22no—
111C2×C8×C131—42no—
112C2×C8×C131C2×D414yes—
113C4⋊C4×C131—22no—
114C4⋊C4×C131—21no—
115C4⋊C4×C131—22no—
116C4⋊C4×C131—22no—
117C4⋊C4×C131—22no—
118C4⋊C4×C131—21no—
119C4⋊C4×C131—21no—
120C4⋊C4×C131—41no—
121C4⋊C4×C131—41no—
122C4⋊C4×C131C2×D412yes—
123C22⋊C4×C131—41no—
124C22⋊C4×C131—41no—
125C42×C131—22no—
126C42×C131—22no—
127C42×C131C2×D411yescharacteristic
128C42×C131C2×D411yescharacteristic
129C42×C131#4111yescharacteristic
130C42×C131C2411yescharacteristic
131C23×C131—41no—
132C23×C131#12111yescharacteristic
133Q8×C131—22no—
134Q8×C131—24no—
135Q8×C131—41no—
136Q8×C131—41no—
137Q8×C131—82no—
138Q8×C131—82no—
139Q8×C131C2×SD1614yes—
140D4×C131—41no—
141D4×C131—41no—
142D4×C131—42no—
143D4×C131—81no—
144D4×C131—82no—
145C2×C4×C131—22no—
146C2×C4×C131—24no—
147C2×C4×C131—22no—
148C2×C4×C131—22no—
149C2×C4×C131—41no—
150C2×C4×C131—41no—
151C2×C4×C131—42no—
152C2×C4×C131—81no—
153C2×C4×C131—82no—
154C2×C4×C131—82no—
155C2×C4×C131#12111yescharacteristic
156C2×C4×C131#12111yescharacteristic
157C2×C4×C131#12111yescharacteristic
158C2×C4×C131C2×SD1612yes—
159C2×C4×C131#13512yes—
160C2×C4×C131C22×D411yescharacteristic
161C2×C4×C131C22×D411yescharacteristic
162C2×C4×C131C2×#4111yescharacteristic
163C8×C131—24no—
164C8×C131—42no—
165C8×C131—42no—
166C8×C131—42no—
167C22×C131—21no—
168C22×C131—21no—
169C22×C131—81no—
170C22×C131—81no—
171C22×C131—81no—
172C22×C131#46512yes—
173C22×C131C2×#12111yescharacteristic
174C4×C131—21no—
175C4×C131—24no—
176C4×C131—21no—
177C4×C131—21no—
178C4×C131—42no—
179C4×C131—81no—
180C4×C131—82no—
181C4×C131#46512yes—
182C4×C131C22×SD1611yescharacteristic
183C4×C131C2×#13511yescharacteristic
184C4×C131#57812yes—
185C2×C131—22no—
186C2×C131—161no—
187C2×C131#304411yescharacteristic
188C2×C131C2×#46511yescharacteristic
189C2×C131#306811yescharacteristic
190#19403C13111yesmaximal, characteristic, direct product factor, Sylow
191C131#1940311yescharacteristic, direct product factor, Sylow
192#3227C2×C13111yescharacteristic
193C2×#477C2×C13111yescharacteristic, complemented
194#3037C2×C13111yescharacteristic
195#2982C2×C13111yescharacteristic, complemented
196#1678C2×C13114yescomplemented
197#1672C2×C13114yescomplemented
198#1570C2×C13111yescharacteristic, complemented
199#1548C2×C13111yescharacteristic, complemented
200#1540C2×C13111yescharacteristic
201C2×#137—21no—
202#532C22×C13111yescharacteristic
203C2×C4⋊Q8C22×C13111yescharacteristic
204C2×C4×Q8C22×C13111yescharacteristic
205#498C22×C13112yes—
206#486C22×C13112yes—
207#481—22no—
208#477—22no—
209#477C22×C13114yes—
210#476—22no—
211#464—22no—
212#462C22×C13112yes—
213#460C22×C13112yes—
214C8×Q8—22no—
215C8×Q8C22×C13114yes—
216#431—22no—
217#431C22×C13111yescharacteristic
218#431C22×C13111yescharacteristic
219C2×#107—21no—
220#423C22×C13111yescharacteristic
221C2×C4⋊C8C22×C13111yescharacteristic
222#417—21no—
223C2×#103—21no—
224#334C22×C13114yes—
225#333C22×C13114yes—
226#332C22×C13112yes—
227#331C22×C13112yes—
228C2×#41—21no—
229C22×Q8—21no—
230C22×Q8D4×C13111yescharacteristic
231#137—44no—
232C2×Q16—22no—
233C2×SD16—22no—
234C2×M16—21no—
235C22×C8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8C23×C13112yes—
240C4⋊Q8C23×C13111yescharacteristic
241#127C23×C13111yescharacteristic
242#124—21no—
243#121—21no—
244#121—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8D4×C13112yes—
248C4×Q8C23×C13112yes—
249C4×D4—21no—
250C4×D4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4D4×C13111yescharacteristic
255C2×C42—21no—
256C2×C42C23×C13111yescharacteristic
257#107—24no—
258#106—24no—
259C4⋊C8—24no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8D4×C13112yes—
263C4⋊C8C23×C13112yes—
264C4⋊C8C23×C13112yes—
265C4⋊C8C23×C13112yes—
266#103—24no—
267#103—22no—
268#102—24no—
269#102—22no—
270C22⋊C8—21no—
271C22⋊C8D4×C13112yes—
272C4×C8—24no—
273C4×C8—21no—
274C4×C8C23×C13112yes—
275#41—42no—
276#41—42no—
277C2×Q8—21no—
278C2×Q8—22no—
279C2×Q8—21no—
280C2×Q8—22no—
281C2×Q8—41no—
282C2×Q8—82no—
283C2×Q8SD16×C13114yes—
284C2×Q8C2×D4×C13112yes—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4C2×D4×C13111yescharacteristic
294C22×C4C2×D4×C13111yescharacteristic
295C22×C4#41×C13111yescharacteristic
296Q16—44no—
297SD16—44no—
298M16—42no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—42no—
303C2×C8C2×D4×C13114yes—
304C4⋊C4—22no—
305C4⋊C4—21no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4C2×D4×C13112yes—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C42—22no—
317C42—22no—
318C42C2×D4×C13111yescharacteristic
319C42C2×D4×C13111yescharacteristic
320C42#41×C13111yescharacteristic
321C42C24×C13111yescharacteristic
322C23—41no—
323C23#121×C13111yescharacteristic
324Q8—24no—
325Q8—22no—
326Q8—41no—
327Q8—41no—
328Q8—82no—
329Q8—82no—
330Q8C2×SD16×C13114yes—
331D4—41no—
332D4—41no—
333D4—42no—
334D4—81no—
335D4—82no—
336C2×C4—24no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—81no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4#121×C13111yescharacteristic
347C2×C4#121×C13111yescharacteristic
348C2×C4#121×C13111yescharacteristic
349C2×C4C2×SD16×C13112yes—
350C2×C4#135×C13112yes—
351C2×C4C22×D4×C13111yescharacteristic
352C2×C4C22×D4×C13111yescharacteristic
353C2×C4C2×#41×C13111yescharacteristic
354C8—24no—
355C8—42no—
356C8—42no—
357C8—42no—
358C22—21no—
359C22—21no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22#465×C13112yes—
364C22C2×#121×C13111yescharacteristic
365C4—21no—
366C4—24no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—81no—
371C4—82no—
372C4#465×C13112yes—
373C4C22×SD16×C13111yescharacteristic
374C4C2×#135×C13111yescharacteristic
375C4#578×C13112yes—
376C2—22no—
377C2—161no—
378C2#3044×C13111yescharacteristic
379C2C2×#465×C13111yescharacteristic
380C2#3068×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#121
commutator, Frattini, cosocleC42C24×C131
prime radical#532×C131C22
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
2. C2×#477×C131C2semidirect
4. #2982×C131C2semidirect
5. #1678×C131C2semidirect
6. #1672×C131C2semidirect
7. #1570×C131C2semidirect
8. #1548×C131C2semidirect
190. #19403C131direct (N × H)
191. C131#19403direct (N × H)
193. C2×#477C2×C131semidirect
195. #2982C2×C131semidirect
196. #1678C2×C131semidirect
197. #1672C2×C131semidirect
198. #1570C2×C131semidirect
199. #1548C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3227×C1312
C2×#477×C1312
#3037×C1312
#2982×C1312
#1678×C1312
#1672×C1312
#1570×C1312
#1548×C1312
#1540×C1312
#19403131