Finite Group Databasebeta

← C131×#36600 #45722484

Subgroups — C131×#36600 #45722484

Order 33536.

1574 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2859×C131C211yesmaximal, characteristic
2#2859×C131C212yesmaximal
3#2585×C131C218yesmaximal
4#2570×C131C214yesmaximal
5#2552×C131C212yesmaximal
6#2453×C131C214yesmaximal
7#2370×C131C214yesmaximal
8#2355×C131C212yesmaximal
9C4×#125×C131C212yesmaximal
10C4×#125×C131C211yesmaximal, characteristic
11C42×Q8×C131C211yesmaximal, characteristic
12C2×#125×C131C2214yes—
13C2×#125×C131C2212yes—
14C2×#125×C131C2211yescharacteristic
15C2×C4×Q8×C131C2212yes—
16C2×C4×Q8×C131C2211yescharacteristic
17#400×C131C2218yes—
18#398×C131C2218yes—
19#398×C131C2218yes—
20#391×C131C2214yes—
21#389×C131C2214yes—
22#389×C131C2214yes—
23#389×C131C2212yes—
24#389×C131C2214yes—
25#389×C131C2218yes—
26#389×C131C2218yes—
27#389×C131C2214yes—
28#387×C131C2214yes—
29#387×C131C2218yes—
30#387×C131C2218yes—
31#387×C131C2218yes—
32#387×C131C2218yes—
33#384×C131C2214yes—
34#384×C131C2212yes—
35#382×C131C2211yescharacteristic
36#382×C131C2212yes—
37#382×C131C2214yes—
38C4×C4⋊C4×C131C2211yescharacteristic
39C4×C4⋊C4×C131C2212yes—
40C4×C4⋊C4×C131C2214yes—
41C4×C4⋊C4×C131C2212yes—
42C4×C4⋊C4×C131C2212yes—
43C4×C4⋊C4×C131C2214yes—
44C4×C4⋊C4×C131C2218yes—
45C4×C4⋊C4×C131C2214yes—
46C4×C4⋊C4×C131C2214yes—
47C43×C131C2211yescharacteristic
48C43×C131C2212yes—
49C22×Q8×C131C2311yescharacteristic
50#125×C131—216no—
51#125×C131—28no—
52#125×C131—24no—
53C4×Q8×C131—28no—
54C4×Q8×C131Q818yes—
55C2×C4⋊C4×C131C2318yes—
56C2×C4⋊C4×C131C2314yes—
57C2×C4⋊C4×C131C2314yes—
58C2×C4⋊C4×C131C2312yes—
59C2×C4⋊C4×C131C2318yes—
60C2×C4⋊C4×C131C2318yes—
61C2×C4⋊C4×C131C2314yes—
62C2×C4⋊C4×C131C2312yes—
63C2×C4⋊C4×C131C2314yes—
64C2×C4⋊C4×C131C2318yes—
65C2×C4⋊C4×C131C2314yes—
66C2×C4⋊C4×C131C2314yes—
67C2×C4⋊C4×C131C2311yescharacteristic
68C2×C4⋊C4×C131C2312yes—
69C2×C4⋊C4×C131C2312yes—
70C2×C42×C131C2312yes—
71C2×C42×C131C2314yes—
72C2×C42×C131C2311yescharacteristic
73C2×C42×C131C2312yes—
74C2×C42×C131C2314yes—
75C2×C42×C131C2314yes—
76C2×C42×C131C2312yes—
77C2×C42×C131C2318yes—
78C2×C42×C131C2312yes—
79C2×C42×C131C2311yescharacteristic
80C2×C42×C131C2311yescharacteristic
81#95×C131C2318yes—
82#95×C131C2318yes—
83#95×C131C2318yes—
84#95×C131C2318yes—
85#95×C131C2314yes—
86#95×C131C2318yes—
87#95×C131C2312yes—
88#95×C131C2314yes—
89#95×C131C2314yes—
90#95×C131C2314yes—
91C2×Q8×C131—24no—
92C2×Q8×C131C2×Q814yes—
93C22×C4×C131C2412yes—
94C22×C4×C131C2414yes—
95C22×C4×C131C2414yes—
96C22×C4×C131C2418yes—
97C22×C4×C131C2412yes—
98C22×C4×C131C2412yes—
99C22×C4×C131C2411yescharacteristic
100C22×C4×C131C2414yes—
101C22×C4×C131C2412yes—
102C22×C4×C131C2411yescharacteristic
103C22×C4×C131C2411yescharacteristic
104C4⋊C4×C131—28no—
105C4⋊C4×C131—216no—
106C4⋊C4×C131—216no—
107C4⋊C4×C131—216no—
108C4⋊C4×C131—28no—
109C4⋊C4×C131—28no—
110C4⋊C4×C131—28no—
111C4⋊C4×C131—24no—
112C4⋊C4×C131—24no—
113C4⋊C4×C131—44no—
114C4⋊C4×C131—48no—
115C4⋊C4×C131—44no—
116C4⋊C4×C131C2×Q818yes—
117C4⋊C4×C131C2×Q814yes—
118C4⋊C4×C131#4118yes—
119C42×C131—28no—
120C42×C131—24no—
121C42×C131—28no—
122C42×C131—24no—
123C42×C131—22no—
124C42×C131—44no—
125C42×C131—42no—
126C42×C131—48no—
127C42×C131C2×Q818yes—
128C42×C131C2×Q814yes—
129C42×C131#4114yes—
130C23×C131C2511yescharacteristic
131Q8×C131—28no—
132C2×C4×C131—22no—
133C2×C4×C131—24no—
134C2×C4×C131—24no—
135C2×C4×C131—22no—
136C2×C4×C131—24no—
137C2×C4×C131—22no—
138C2×C4×C131—24no—
139C2×C4×C131—24no—
140C2×C4×C131—22no—
141C2×C4×C131—24no—
142C2×C4×C131—28no—
143C2×C4×C131—24no—
144C2×C4×C131—28no—
145C2×C4×C131—22no—
146C2×C4×C131—24no—
147C2×C4×C131—24no—
148C2×C4×C131—28no—
149C2×C4×C131—22no—
150C2×C4×C131—24no—
151C2×C4×C131C22×Q814yes—
152C2×C4×C131C22×Q812yes—
153C2×C4×C131C22×Q814yes—
154C2×C4×C131C22×Q812yes—
155C2×C4×C131C22×Q812yes—
156C2×C4×C131C2×#4118yes—
157C2×C4×C131C2×#4114yes—
158C2×C4×C131C2×#4114yes—
159C2×C4×C131C2×#4112yes—
160C2×C4×C1312−1+412yes—
161C22×C131C23×Q811yescharacteristic
162C22×C131C22×#4112yes—
163C22×C131C22×#4111yescharacteristic
164C22×C131C2×2−1+411yescharacteristic
165C22×C131#58512yes—
166C4×C131—24no—
167C4×C131—24no—
168C4×C131—24no—
169C4×C131—22no—
170C4×C131—28no—
171C4×C131—44no—
172C4×C131—48no—
173C4×C131—42no—
174C4×C131—44no—
175C4×C131#53314yes—
176C4×C131#55714yes—
177C2×C131C2×#53311yescharacteristic
178C2×C131C2×#55711yescharacteristic
179C2×C131#348012yes—
180C2×C131#350411yescharacteristic
181C2×C131#351512yes—
182#36600C13111yesmaximal, characteristic, direct product factor, Sylow
183C131#3660011yescharacteristic, direct product factor, Sylow
184#2859C2×C13111yescharacteristic
185#2859C2×C13112yes—
186#2585C2×C13118yes—
187#2570C2×C13114yes—
188#2552C2×C13112yes—
189#2453C2×C13114yes—
190#2370C2×C13114yes—
191#2355C2×C13112yes—
192C4×#125C2×C13112yes—
193C4×#125C2×C13111yescharacteristic
194C42×Q8C2×C13111yescharacteristic
195C2×#125C22×C13112yes—
196C2×#125C22×C13111yescharacteristic
197C2×#125C22×C13114yes—
198C2×C4×Q8C22×C13112yes—
199C2×C4×Q8C22×C13111yescharacteristic
200#400C22×C13118yes—
201#398C22×C13118yes—
202#398C22×C13118yes—
203#391C22×C13114yes—
204#389C22×C13112yes—
205#389C22×C13114yes—
206#389C22×C13114yes—
207#389C22×C13118yes—
208#389C22×C13118yes—
209#389C22×C13114yes—
210#389C22×C13114yes—
211#387C22×C13114yes—
212#387C22×C13118yes—
213#387C22×C13118yes—
214#387C22×C13118yes—
215#387C22×C13118yes—
216#384C22×C13114yes—
217#384C22×C13112yes—
218#382C22×C13111yescharacteristic
219#382C22×C13112yes—
220#382C22×C13114yes—
221C4×C4⋊C4C22×C13114yes—
222C4×C4⋊C4C22×C13118yes—
223C4×C4⋊C4C22×C13112yes—
224C4×C4⋊C4C22×C13114yes—
225C4×C4⋊C4C22×C13112yes—
226C4×C4⋊C4C22×C13114yes—
227C4×C4⋊C4C22×C13114yes—
228C4×C4⋊C4C22×C13112yes—
229C4×C4⋊C4C22×C13111yescharacteristic
230C43C22×C13111yescharacteristic
231C43C22×C13112yes—
232C22×Q8C23×C13111yescharacteristic
233#125—216no—
234#125—28no—
235#125—24no—
236C4×Q8—28no—
237C4×Q8Q8×C13118yes—
238C2×C4⋊C4C23×C13114yes—
239C2×C4⋊C4C23×C13114yes—
240C2×C4⋊C4C23×C13112yes—
241C2×C4⋊C4C23×C13114yes—
242C2×C4⋊C4C23×C13118yes—
243C2×C4⋊C4C23×C13118yes—
244C2×C4⋊C4C23×C13114yes—
245C2×C4⋊C4C23×C13118yes—
246C2×C4⋊C4C23×C13112yes—
247C2×C4⋊C4C23×C13114yes—
248C2×C4⋊C4C23×C13114yes—
249C2×C4⋊C4C23×C13118yes—
250C2×C4⋊C4C23×C13111yescharacteristic
251C2×C4⋊C4C23×C13112yes—
252C2×C4⋊C4C23×C13112yes—
253C2×C42C23×C13112yes—
254C2×C42C23×C13114yes—
255C2×C42C23×C13114yes—
256C2×C42C23×C13111yescharacteristic
257C2×C42C23×C13112yes—
258C2×C42C23×C13114yes—
259C2×C42C23×C13112yes—
260C2×C42C23×C13118yes—
261C2×C42C23×C13112yes—
262C2×C42C23×C13111yescharacteristic
263C2×C42C23×C13111yescharacteristic
264#95C23×C13114yes—
265#95C23×C13114yes—
266#95C23×C13112yes—
267#95C23×C13118yes—
268#95C23×C13114yes—
269#95C23×C13114yes—
270#95C23×C13118yes—
271#95C23×C13118yes—
272#95C23×C13118yes—
273#95C23×C13118yes—
274C2×Q8—24no—
275C2×Q8C2×Q8×C13114yes—
276C22×C4C24×C13112yes—
277C22×C4C24×C13114yes—
278C22×C4C24×C13114yes—
279C22×C4C24×C13118yes—
280C22×C4C24×C13112yes—
281C22×C4C24×C13112yes—
282C22×C4C24×C13111yescharacteristic
283C22×C4C24×C13114yes—
284C22×C4C24×C13112yes—
285C22×C4C24×C13111yescharacteristic
286C22×C4C24×C13111yescharacteristic
287C4⋊C4—28no—
288C4⋊C4—216no—
289C4⋊C4—216no—
290C4⋊C4—216no—
291C4⋊C4—28no—
292C4⋊C4—28no—
293C4⋊C4—28no—
294C4⋊C4—24no—
295C4⋊C4—24no—
296C4⋊C4—44no—
297C4⋊C4—48no—
298C4⋊C4—44no—
299C4⋊C4C2×Q8×C13118yes—
300C4⋊C4C2×Q8×C13114yes—
301C4⋊C4#41×C13118yes—
302C42—28no—
303C42—24no—
304C42—28no—
305C42—24no—
306C42—22no—
307C42—44no—
308C42—42no—
309C42—48no—
310C42C2×Q8×C13118yes—
311C42C2×Q8×C13114yes—
312C42#41×C13114yes—
313C23C25×C13111yescharacteristic
314Q8—28no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—24no—
322C2×C4—22no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—28no—
326C2×C4—24no—
327C2×C4—28no—
328C2×C4—22no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—22no—
332C2×C4—28no—
333C2×C4—24no—
334C2×C4C22×Q8×C13114yes—
335C2×C4C22×Q8×C13112yes—
336C2×C4C22×Q8×C13114yes—
337C2×C4C22×Q8×C13112yes—
338C2×C4C22×Q8×C13112yes—
339C2×C4C2×#41×C13118yes—
340C2×C4C2×#41×C13114yes—
341C2×C4C2×#41×C13114yes—
342C2×C4C2×#41×C13112yes—
343C2×C42−1+4×C13112yes—
344C22C23×Q8×C13111yescharacteristic
345C22C22×#41×C13112yes—
346C22C22×#41×C13111yescharacteristic
347C22C2×2−1+4×C13111yescharacteristic
348C22#585×C13112yes—
349C4—24no—
350C4—22no—
351C4—28no—
352C4—24no—
353C4—24no—
354C4—42no—
355C4—44no—
356C4—44no—
357C4—48no—
358C4#533×C13114yes—
359C4#557×C13114yes—
360C2C2×#533×C13111yescharacteristic
361C2C2×#557×C13111yescharacteristic
362C2#3480×C13112yes—
363C2#3504×C13111yescharacteristic
364C2#3515×C13112yes—
subgroupG/H
center, socle, prime radicalC23×C131C25
commutator, Frattini, cosocleC23C25×C131
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C131 ◁ G

Complements

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

NH ≅ G/Ntype
182. #36600C131direct (N × H)
183. C131#36600direct (N × H)

Maximal subgroups

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

subgroupindex
#2859×C1312
#2585×C1312
#2570×C1312
#2552×C1312
#2453×C1312
#2370×C1312
#2355×C1312
C4×#125×C1312
C42×Q8×C1312
#36600131