Finite Group Databasebeta

← C131×#10198 #45696082

Subgroups — C131×#10198 #45696082

Order 33536.

508 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#3246×C131C211yesmaximal, characteristic
2#3209×C131C211yesmaximal, characteristic, complemented
3#3141×C131C211yesmaximal, characteristic
4#1987×C131C211yesmaximal, characteristic, complemented
5#1986×C131C211yesmaximal, characteristic, complemented
6#1502×C131C211yesmaximal, characteristic
7#1283×C131C211yesmaximal, characteristic, complemented
8#533×C131C2211yescharacteristic
9#532×C131C2211yescharacteristic
10C2×C4⋊Q8×C131C2211yescharacteristic
11#494×C131—21no—
12#489×C131—22no—
13#487×C131—21no—
14#487×C131—21no—
15#486×C131—21no—
16#476×C131—21no—
17#475×C131—21no—
18#465×C131—22no—
19#462×C131—22no—
20#461×C131—21no—
21#460×C131—21no—
22#451×C131—22no—
23#431×C131C2211yescharacteristic
24C2×C4⋊C8×C131C2211yescharacteristic
25#417×C131—22no—
26C4×M16×C131C2211yescharacteristic
27C4×C4⋊C4×C131C2211yescharacteristic
28#340×C131—22no—
29#339×C131—22no—
30#327×C131—22no—
31C2×#41×C131—21no—
32C22×Q8×C131—21no—
33C2×Q16×C131—24no—
34C2×SD16×C131—22no—
35C2×M16×C131D412yes—
36C22×C8×C131D412yes—
37C4⋊Q8×C131—21no—
38C4⋊Q8×C131—21no—
39C4⋊Q8×C131—21no—
40C4⋊Q8×C131D411yescharacteristic
41C4⋊Q8×C131D412yes—
42C4⋊Q8×C131D411yescharacteristic
43C4⋊Q8×C131D411yescharacteristic
44#127×C131D411yescharacteristic
45#125×C131—21no—
46#124×C131—21no—
47C22⋊Q8×C131—21no—
48C22⋊Q8×C131—21no—
49#121×C131—21no—
50#121×C131—21no—
51C4×Q8×C131—21no—
52C4×Q8×C131—21no—
53C4×D4×C131—21no—
54C4×D4×C131—21no—
55#117×C131—21no—
56C2×C4⋊C4×C131—21no—
57C2×C4⋊C4×C131—21no—
58C2×C4⋊C4×C131—21no—
59C2×C42×C131—21no—
60C2×C42×C131C2311yescharacteristic
61#106×C131—22no—
62C4⋊C8×C131—21no—
63C4⋊C8×C131—21no—
64C4⋊C8×C131—21no—
65#103×C131—24no—
66#103×C131—24no—
67#103×C131—22no—
68#102×C131—24no—
69#102×C131—22no—
70C22⋊C8×C131D412yes—
71#97×C131—21no—
72C4×C8×C131—21no—
73C4×C8×C131—21no—
74#95×C131—21no—
75#41×C131—42no—
76#41×C131—42no—
77C2×Q8×C131—21no—
78C2×Q8×C131—21no—
79C2×Q8×C131—22no—
80C2×Q8×C131—21no—
81C2×Q8×C131—41no—
82C2×Q8×C131—82no—
83C2×D4×C131—21no—
84C2×D4×C131—21no—
85C2×D4×C131—21no—
86C2×D4×C131—41no—
87C22×C4×C131—41no—
88C22×C4×C131—41no—
89C22×C4×C131—41no—
90C22×C4×C131C2×D411yescharacteristic
91C22×C4×C131C2×D411yescharacteristic
92C22×C4×C131C2×D411yescharacteristic
93Q16×C131—84no—
94SD16×C131—82no—
95M16×C131—22no—
96M16×C131—22no—
97C2×C8×C131—22no—
98C2×C8×C131—22no—
99C2×C8×C131—22no—
100C2×C8×C131—42no—
101C4⋊C4×C131—22no—
102C4⋊C4×C131—22no—
103C4⋊C4×C131—21no—
104C4⋊C4×C131—21no—
105C4⋊C4×C131—21no—
106C4⋊C4×C131—22no—
107C4⋊C4×C131—21no—
108C4⋊C4×C131—21no—
109C4⋊C4×C131—21no—
110C4⋊C4×C131—41no—
111C4⋊C4×C131—41no—
112C4⋊C4×C131—41no—
113C4⋊C4×C131—41no—
114C4⋊C4×C131—41no—
115C22⋊C4×C131—41no—
116C22⋊C4×C131—41no—
117C22⋊C4×C131—41no—
118C42×C131—41no—
119C42×C131—42no—
120C42×C131C2×D411yescharacteristic
121C42×C131C2×D411yescharacteristic
122C42×C131C2×D411yescharacteristic
123C42×C131#4111yescharacteristic
124C23×C131—41no—
125C23×C131#12711yescharacteristic
126Q8×C131—42no—
127Q8×C131—44no—
128Q8×C131—42no—
129Q8×C131—41no—
130Q8×C131—41no—
131Q8×C131—82no—
132D4×C131—42no—
133D4×C131—41no—
134D4×C131—41no—
135D4×C131—81no—
136D4×C131—81no—
137D4×C131—81no—
138C2×C4×C131—21no—
139C2×C4×C131—21no—
140C2×C4×C131—41no—
141C2×C4×C131—42no—
142C2×C4×C131—41no—
143C2×C4×C131—41no—
144C2×C4×C131—41no—
145C2×C4×C131—42no—
146C2×C4×C131—81no—
147C2×C4×C131—82no—
148C2×C4×C131—81no—
149C2×C4×C131—82no—
150C2×C4×C131#12011yescharacteristic
151C2×C4×C131#12011yescharacteristic
152C2×C4×C131#12011yescharacteristic
153C2×C4×C131#12111yescharacteristic
154C2×C4×C131#12111yescharacteristic
155C2×C4×C131#12111yescharacteristic
156C2×C4×C131#13512yes—
157C2×C4×C131#13712yes—
158C8×C131—42no—
159C8×C131—42no—
160C8×C131—42no—
161C22×C131—21no—
162C22×C131—21no—
163C22×C131—81no—
164C22×C131—81no—
165C22×C131—81no—
166C22×C131#39211yescharacteristic
167C22×C131#49511yescharacteristic
168C22×C131#49711yescharacteristic
169C4×C131—21no—
170C4×C131—21no—
171C4×C131—21no—
172C4×C131—82no—
173C4×C131—81no—
174C4×C131—82no—
175C4×C131—81no—
176C4×C131—81no—
177C4×C131#45212yes—
178C4×C131#45511yescharacteristic
179C4×C131#45611yescharacteristic
180C4×C131#46412yes—
181C2×C131—21no—
182C2×C131—21no—
183C2×C131—161no—
184C2×C131#200711yescharacteristic
185C2×C131#200811yescharacteristic
186C2×C131#201511yescharacteristic
187#10198C13111yesmaximal, characteristic, direct product factor, Sylow
188C131#1019811yescharacteristic, direct product factor, Sylow
189#3246C2×C13111yescharacteristic
190#3209C2×C13111yescharacteristic, complemented
191#3141C2×C13111yescharacteristic
192#1987C2×C13111yescharacteristic, complemented
193#1986C2×C13111yescharacteristic, complemented
194#1502C2×C13111yescharacteristic
195#1283C2×C13111yescharacteristic, complemented
196#533C22×C13111yescharacteristic
197#532C22×C13111yescharacteristic
198C2×C4⋊Q8C22×C13111yescharacteristic
199#494—21no—
200#489—22no—
201#487—21no—
202#487—21no—
203#486—21no—
204#476—21no—
205#475—21no—
206#465—22no—
207#462—22no—
208#461—21no—
209#460—21no—
210#451—22no—
211#431C22×C13111yescharacteristic
212C2×C4⋊C8C22×C13111yescharacteristic
213#417—22no—
214C4×M16C22×C13111yescharacteristic
215C4×C4⋊C4C22×C13111yescharacteristic
216#340—22no—
217#339—22no—
218#327—22no—
219C2×#41—21no—
220C22×Q8—21no—
221C2×Q16—24no—
222C2×SD16—22no—
223C2×M16D4×C13112yes—
224C22×C8D4×C13112yes—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8D4×C13112yes—
229C4⋊Q8D4×C13111yescharacteristic
230C4⋊Q8D4×C13111yescharacteristic
231C4⋊Q8D4×C13111yescharacteristic
232#127D4×C13111yescharacteristic
233#125—21no—
234#124—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237#121—21no—
238#121—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×D4—21no—
242C4×D4—21no—
243#117—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C42—21no—
248C2×C42C23×C13111yescharacteristic
249#106—22no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253#103—24no—
254#103—24no—
255#103—22no—
256#102—24no—
257#102—22no—
258C22⋊C8D4×C13112yes—
259#97—21no—
260C4×C8—21no—
261C4×C8—21no—
262#95—21no—
263#41—42no—
264#41—42no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—22no—
268C2×Q8—21no—
269C2×Q8—41no—
270C2×Q8—82no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4C2×D4×C13111yescharacteristic
279C22×C4C2×D4×C13111yescharacteristic
280C22×C4C2×D4×C13111yescharacteristic
281Q16—84no—
282SD16—82no—
283M16—22no—
284M16—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—42no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C42—41no—
307C42—42no—
308C42C2×D4×C13111yescharacteristic
309C42C2×D4×C13111yescharacteristic
310C42C2×D4×C13111yescharacteristic
311C42#41×C13111yescharacteristic
312C23—41no—
313C23#127×C13111yescharacteristic
314Q8—42no—
315Q8—44no—
316Q8—42no—
317Q8—41no—
318Q8—41no—
319Q8—82no—
320D4—42no—
321D4—41no—
322D4—41no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—82no—
338C2×C4#120×C13111yescharacteristic
339C2×C4#120×C13111yescharacteristic
340C2×C4#120×C13111yescharacteristic
341C2×C4#121×C13111yescharacteristic
342C2×C4#121×C13111yescharacteristic
343C2×C4#121×C13111yescharacteristic
344C2×C4#135×C13112yes—
345C2×C4#137×C13112yes—
346C8—42no—
347C8—42no—
348C8—42no—
349C22—21no—
350C22—21no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22#392×C13111yescharacteristic
355C22#495×C13111yescharacteristic
356C22#497×C13111yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—82no—
361C4—81no—
362C4—82no—
363C4—81no—
364C4—81no—
365C4#452×C13112yes—
366C4#455×C13111yescharacteristic
367C4#456×C13111yescharacteristic
368C4#464×C13112yes—
369C2—21no—
370C2—21no—
371C2—161no—
372C2#2007×C13111yescharacteristic
373C2#2008×C13111yescharacteristic
374C2#2015×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#392
commutator, Frattini, cosocleC2×C42C23×C131
prime radical#532×C131C22
LCSG ▷ C2×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. #3209×C131C2semidirect
4. #1987×C131C2semidirect
5. #1986×C131C2semidirect
7. #1283×C131C2semidirect
187. #10198C131direct (N × H)
188. C131#10198direct (N × H)
190. #3209C2×C131semidirect
192. #1987C2×C131semidirect
193. #1986C2×C131semidirect
195. #1283C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3246×C1312
#3209×C1312
#3141×C1312
#1987×C1312
#1986×C1312
#1502×C1312
#1283×C1312
#10198131