Finite Group Databasebeta

← C131×#34643 #45720527

Subgroups — C131×#34643 #45720527

Order 33536.

2234 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
1C2×#529×C131C212yesmaximal, complemented
2#2664×C131C214yesmaximal, complemented
3#2663×C131C214yesmaximal, complemented
4#2662×C131C214yesmaximal, complemented
5#2661×C131C214yesmaximal, complemented
6#2399×C131C211yesmaximal, characteristic, complemented
7#2398×C131C212yesmaximal, complemented
8#2397×C131C211yesmaximal, characteristic, complemented
9#2392×C131C214yesmaximal, complemented
10#2293×C131C214yesmaximal, complemented
11C4×#117×C131C211yesmaximal, characteristic, complemented
12#529×C131—216no—
13C2×#126×C131C2214yes—
14C2×#125×C131C2212yes—
15C2×#124×C131C2212yes—
16C2×#123×C131C2214yes—
17C2×C22⋊Q8×C131C2212yes—
18C2×#121×C131C2212yes—
19C2×C4×Q8×C131C2212yes—
20C2×C4×D4×C131C2214yes—
21C2×C4×D4×C131C2214yes—
22C2×C4×D4×C131C2212yes—
23C2×#117×C131C2212yes—
24C2×#117×C131C2214yes—
25C22×C42×C131C2211yescharacteristic
26#400×C131C2214yes—
27#399×C131C2214yes—
28#398×C131C2214yes—
29#398×C131C2214yes—
30#397×C131C2214yes—
31#397×C131C2214yes—
32#396×C131C2218yes—
33#395×C131C2214yes—
34#394×C131C2218yes—
35#394×C131C2214yes—
36#394×C131C2214yes—
37#393×C131C2214yes—
38#392×C131C2214yes—
39#392×C131C2214yes—
40#390×C131C2218yes—
41#389×C131C2218yes—
42#388×C131C2218yes—
43#388×C131C2218yes—
44C4×C4⋊C4×C131C2214yes—
45C4×C4⋊C4×C131C2214yes—
46C4×C22⋊C4×C131C2214yes—
47C4×C22⋊C4×C131C2218yes—
48#376×C131C2211yescharacteristic
49#376×C131C2211yescharacteristic
50C43×C131C2212yes—
51C22×Q8×C131C2312yes—
52C22×D4×C131C2314yes—
53C22×D4×C131C2314yes—
54C22×D4×C131C2312yes—
55C23×C4×C131C2314yes—
56C23×C4×C131C2311yescharacteristic
57C23×C4×C131C2312yes—
58#126×C131—216no—
59#125×C131—28no—
60#124×C131—28no—
61#123×C131—216no—
62C22⋊Q8×C131—28no—
63#121×C131—28no—
64C4×Q8×C131—28no—
65C4×D4×C131—216no—
66C4×D4×C131—28no—
67C4×D4×C131—216no—
68#117×C131—216no—
69#117×C131—28no—
70C2×C4⋊C4×C131C2314yes—
71C2×C4⋊C4×C131C2314yes—
72C2×C4⋊C4×C131C2314yes—
73C2×C4⋊C4×C131C2314yes—
74C2×C4⋊C4×C131C2314yes—
75C2×C4⋊C4×C131C2314yes—
76C2×C4⋊C4×C131C2312yes—
77C2×C4⋊C4×C131C2312yes—
78C2×C4⋊C4×C131C2318yes—
79C2×C22⋊C4×C131C2314yes—
80C2×C22⋊C4×C131C2314yes—
81C2×C22⋊C4×C131C2318yes—
82C2×C22⋊C4×C131C2314yes—
83C2×C22⋊C4×C131C2314yes—
84C2×C22⋊C4×C131C2314yes—
85C2×C22⋊C4×C131C2314yes—
86C2×C22⋊C4×C131C2318yes—
87C2×C22⋊C4×C131C2318yes—
88C2×C42×C131D418yescomplemented
89C2×C42×C131C2314yes—
90C2×C42×C131C2312yes—
91C2×C42×C131C2318yes—
92C2×C42×C131C2312yes—
93C2×C42×C131C2311yescharacteristic
94C2×C42×C131C2311yescharacteristic
95C2×C42×C131C2312yes—
96#95×C131C2314yes—
97#95×C131C2314yes—
98#95×C131C2318yes—
99#95×C131C2318yes—
100#95×C131C2314yes—
101#95×C131C2314yes—
102C24×C131C2414yes—
103C24×C131C2411yescharacteristic
104C2×Q8×C131—24no—
105C2×Q8×C131—44no—
106C2×D4×C131—28no—
107C2×D4×C131—24no—
108C2×D4×C131—28no—
109C2×D4×C131—48no—
110C2×D4×C131—44no—
111C2×D4×C131—48no—
112C22×C4×C131—24no—
113C22×C4×C131—28no—
114C22×C4×C131—216no—
115C22×C4×C131—44no—
116C22×C4×C131C2×D414yes—
117C22×C4×C131C2×D418yes—
118C22×C4×C131C2414yes—
119C22×C4×C131C2414yes—
120C22×C4×C131C2414yes—
121C22×C4×C131C2414yes—
122C22×C4×C131C2412yes—
123C22×C4×C131C2412yes—
124C22×C4×C131C2411yescharacteristic
125C22×C4×C131C2414yes—
126C22×C4×C131C2411yescharacteristic
127C4⋊C4×C131—28no—
128C4⋊C4×C131—28no—
129C4⋊C4×C131—24no—
130C4⋊C4×C131—28no—
131C4⋊C4×C131—24no—
132C4⋊C4×C131—28no—
133C4⋊C4×C131—28no—
134C4⋊C4×C131—28no—
135C4⋊C4×C131—48no—
136C22⋊C4×C131—28no—
137C22⋊C4×C131—28no—
138C22⋊C4×C131—28no—
139C22⋊C4×C131—28no—
140C22⋊C4×C131—28no—
141C22⋊C4×C131—28no—
142C22⋊C4×C131—216no—
143C22⋊C4×C131—48no—
144C22⋊C4×C131—48no—
145C42×C131—28no—
146C42×C131—24no—
147C42×C131—48no—
148C42×C131C2×D414yes—
149C42×C131C2×D414yes—
150C42×C131C2×D418yes—
151C42×C131#4118yes—
152C23×C131—22no—
153C23×C131—24no—
154C23×C131—24no—
155C23×C131—28no—
156C23×C131—24no—
157C23×C131—28no—
158C23×C131—24no—
159C23×C131C22×D412yes—
160C23×C131C2511yescharacteristic
161Q8×C131—48no—
162D4×C131—48no—
163D4×C131—416no—
164D4×C131—416no—
165C2×C4×C131—22no—
166C2×C4×C131—24no—
167C2×C4×C131—28no—
168C2×C4×C131—24no—
169C2×C4×C131—28no—
170C2×C4×C131—24no—
171C2×C4×C131—24no—
172C2×C4×C131—24no—
173C2×C4×C131—24no—
174C2×C4×C131—28no—
175C2×C4×C131—28no—
176C2×C4×C131—24no—
177C2×C4×C131—28no—
178C2×C4×C131—24no—
179C2×C4×C131—48no—
180C2×C4×C131—416no—
181C2×C4×C131C22×D412yes—
182C2×C4×C131C22×D414yes—
183C2×C4×C131C22×D414yes—
184C2×C4×C131C22×D412yes—
185C2×C4×C131C2×#4118yes—
186C2×C4×C131C2×#4114yes—
187C22×C131—22no—
188C22×C131—24no—
189C22×C131—44no—
190C22×C131—44no—
191C22×C131—44no—
192C22×C131—44no—
193C22×C131—48no—
194C22×C131—48no—
195C22×C131C23×D411yescharacteristic
196C22×C131C22×#4112yes—
197C22×C131#58514yes—
198C4×C131—22no—
199C4×C131—24no—
200C4×C131—24no—
201C4×C131—28no—
202C4×C131—44no—
203C4×C131—44no—
204C4×C131—44no—
205C4×C131—44no—
206C4×C131#53214yes—
207C2×C131—42no—
208C2×C131—84no—
209C2×C131C2×#53211yescharacteristic
210C2×C131#344912yes—
211C2×C131#345514yes—
212#34643C13111yesmaximal, characteristic, direct product factor, Sylow
213C131#3464311yescharacteristic, direct product factor, Sylow
214C2×#529C2×C13112yescomplemented
215#2664C2×C13114yescomplemented
216#2663C2×C13114yescomplemented
217#2662C2×C13114yescomplemented
218#2661C2×C13114yescomplemented
219#2399C2×C13111yescharacteristic, complemented
220#2398C2×C13112yescomplemented
221#2397C2×C13111yescharacteristic, complemented
222#2392C2×C13114yescomplemented
223#2293C2×C13114yescomplemented
224C4×#117C2×C13111yescharacteristic, complemented
225#529—216no—
226C2×#126C22×C13114yes—
227C2×#125C22×C13112yes—
228C2×#124C22×C13112yes—
229C2×#123C22×C13114yes—
230C2×C22⋊Q8C22×C13112yes—
231C2×#121C22×C13112yes—
232C2×C4×Q8C22×C13112yes—
233C2×C4×D4C22×C13114yes—
234C2×C4×D4C22×C13114yes—
235C2×C4×D4C22×C13112yes—
236C2×#117C22×C13112yes—
237C2×#117C22×C13114yes—
238C22×C42C22×C13111yescharacteristic
239#400C22×C13114yes—
240#399C22×C13114yes—
241#398C22×C13114yes—
242#398C22×C13114yes—
243#397C22×C13114yes—
244#397C22×C13114yes—
245#396C22×C13118yes—
246#395C22×C13114yes—
247#394C22×C13118yes—
248#394C22×C13114yes—
249#394C22×C13114yes—
250#393C22×C13114yes—
251#392C22×C13114yes—
252#392C22×C13114yes—
253#390C22×C13118yes—
254#389C22×C13118yes—
255#388C22×C13118yes—
256#388C22×C13118yes—
257C4×C4⋊C4C22×C13114yes—
258C4×C4⋊C4C22×C13114yes—
259C4×C22⋊C4C22×C13118yes—
260C4×C22⋊C4C22×C13114yes—
261#376C22×C13111yescharacteristic
262#376C22×C13111yescharacteristic
263C43C22×C13112yes—
264C22×Q8C23×C13112yes—
265C22×D4C23×C13114yes—
266C22×D4C23×C13112yes—
267C22×D4C23×C13114yes—
268C23×C4C23×C13114yes—
269C23×C4C23×C13111yescharacteristic
270C23×C4C23×C13112yes—
271#126—216no—
272#125—28no—
273#124—28no—
274#123—216no—
275C22⋊Q8—28no—
276#121—28no—
277C4×Q8—28no—
278C4×D4—216no—
279C4×D4—28no—
280C4×D4—216no—
281#117—216no—
282#117—28no—
283C2×C4⋊C4C23×C13114yes—
284C2×C4⋊C4C23×C13114yes—
285C2×C4⋊C4C23×C13114yes—
286C2×C4⋊C4C23×C13112yes—
287C2×C4⋊C4C23×C13114yes—
288C2×C4⋊C4C23×C13114yes—
289C2×C4⋊C4C23×C13112yes—
290C2×C4⋊C4C23×C13114yes—
291C2×C4⋊C4C23×C13118yes—
292C2×C22⋊C4C23×C13114yes—
293C2×C22⋊C4C23×C13114yes—
294C2×C22⋊C4C23×C13114yes—
295C2×C22⋊C4C23×C13114yes—
296C2×C22⋊C4C23×C13114yes—
297C2×C22⋊C4C23×C13114yes—
298C2×C22⋊C4C23×C13118yes—
299C2×C22⋊C4C23×C13118yes—
300C2×C22⋊C4C23×C13118yes—
301C2×C42D4×C13118yescomplemented
302C2×C42C23×C13114yes—
303C2×C42C23×C13112yes—
304C2×C42C23×C13118yes—
305C2×C42C23×C13111yescharacteristic
306C2×C42C23×C13111yescharacteristic
307C2×C42C23×C13112yes—
308C2×C42C23×C13112yes—
309#95C23×C13114yes—
310#95C23×C13114yes—
311#95C23×C13118yes—
312#95C23×C13118yes—
313#95C23×C13114yes—
314#95C23×C13114yes—
315C24C24×C13114yes—
316C24C24×C13111yescharacteristic
317C2×Q8—24no—
318C2×Q8—44no—
319C2×D4—28no—
320C2×D4—24no—
321C2×D4—28no—
322C2×D4—48no—
323C2×D4—44no—
324C2×D4—48no—
325C22×C4—24no—
326C22×C4—28no—
327C22×C4—216no—
328C22×C4—44no—
329C22×C4C2×D4×C13114yes—
330C22×C4C2×D4×C13118yes—
331C22×C4C24×C13114yes—
332C22×C4C24×C13114yes—
333C22×C4C24×C13114yes—
334C22×C4C24×C13114yes—
335C22×C4C24×C13112yes—
336C22×C4C24×C13112yes—
337C22×C4C24×C13111yescharacteristic
338C22×C4C24×C13114yes—
339C22×C4C24×C13111yescharacteristic
340C4⋊C4—28no—
341C4⋊C4—28no—
342C4⋊C4—24no—
343C4⋊C4—28no—
344C4⋊C4—24no—
345C4⋊C4—28no—
346C4⋊C4—28no—
347C4⋊C4—28no—
348C4⋊C4—48no—
349C22⋊C4—28no—
350C22⋊C4—28no—
351C22⋊C4—28no—
352C22⋊C4—28no—
353C22⋊C4—28no—
354C22⋊C4—28no—
355C22⋊C4—216no—
356C22⋊C4—48no—
357C22⋊C4—48no—
358C42—28no—
359C42—24no—
360C42—48no—
361C42C2×D4×C13114yes—
362C42C2×D4×C13114yes—
363C42C2×D4×C13118yes—
364C42#41×C13118yes—
365C23—22no—
366C23—24no—
367C23—24no—
368C23—28no—
369C23—24no—
370C23—28no—
371C23—24no—
372C23C22×D4×C13112yes—
373C23C25×C13111yescharacteristic
374Q8—48no—
375D4—48no—
376D4—416no—
377D4—416no—
378C2×C4—22no—
379C2×C4—24no—
380C2×C4—28no—
381C2×C4—24no—
382C2×C4—28no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—28no—
388C2×C4—28no—
389C2×C4—24no—
390C2×C4—28no—
391C2×C4—24no—
392C2×C4—48no—
393C2×C4—416no—
394C2×C4C22×D4×C13112yes—
395C2×C4C22×D4×C13114yes—
396C2×C4C22×D4×C13114yes—
397C2×C4C22×D4×C13112yes—
398C2×C4C2×#41×C13118yes—
399C2×C4C2×#41×C13114yes—
400C22—22no—
401C22—24no—
402C22—44no—
403C22—44no—
404C22—44no—
405C22—44no—
406C22—48no—
407C22—48no—
408C22C23×D4×C13111yescharacteristic
409C22C22×#41×C13112yes—
410C22#585×C13114yes—
411C4—22no—
412C4—24no—
413C4—24no—
414C4—28no—
415C4—44no—
416C4—44no—
417C4—44no—
418C4—44no—
419C4#532×C13114yes—
420C2—42no—
421C2—84no—
422C2C2×#532×C13111yescharacteristic
423C2#3449×C13112yes—
424C2#3455×C13114yes—
subgroupG/H
centerC22×C4×C131C24
commutator, Frattini, cosocleC23C25×C131
socleC23×C131C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#529×C131C2semidirect
2. #2664×C131C2semidirect
3. #2663×C131C2semidirect
4. #2662×C131C2semidirect
5. #2661×C131C2semidirect
6. #2399×C131C2semidirect
7. #2398×C131C2semidirect
8. #2397×C131C2semidirect
9. #2392×C131C2semidirect
10. #2293×C131C2semidirect
11. C4×#117×C131C2semidirect
88. C2×C42×C131D4semidirect
212. #34643C131direct (N × H)
213. C131#34643direct (N × H)
214. C2×#529C2×C131semidirect
215. #2664C2×C131semidirect
216. #2663C2×C131semidirect
217. #2662C2×C131semidirect
218. #2661C2×C131semidirect
219. #2399C2×C131semidirect
220. #2398C2×C131semidirect
221. #2397C2×C131semidirect
222. #2392C2×C131semidirect
223. #2293C2×C131semidirect
224. C4×#117C2×C131semidirect
301. C2×C42D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#529×C1312
#2664×C1312
#2663×C1312
#2662×C1312
#2661×C1312
#2399×C1312
#2398×C1312
#2397×C1312
#2392×C1312
#2293×C1312
C4×#117×C1312
#34643131