Finite Group Databasebeta

← C131×#34594 #45720478

Subgroups — C131×#34594 #45720478

Order 33536.

2362 conjugacy classes of subgroups.

The subgroup lattice has 478 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#2662×C131C214yesmaximal, complemented
4#2659×C131C211yesmaximal, characteristic, complemented
5#2656×C131C211yesmaximal, characteristic
6#2639×C131C212yesmaximal, complemented
7#2618×C131C214yesmaximal, complemented
8#2396×C131C214yesmaximal, complemented
9#2392×C131C214yesmaximal, complemented
10C4×#121×C131C214yesmaximal, complemented
11C2×C4×C4⋊C4×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×C131C2214yes—
19C2×#121×C131C2212yes—
20C2×C4×Q8×C131C2212yes—
21C2×C4×D4×C131C2214yes—
22C2×C4×D4×C131C2212yes—
23C2×C4×D4×C131C2214yes—
24C2×#117×C131C2214yes—
25C22×C4⋊C4×C131C2212yes—
26C22×C42×C131C2212yes—
27C22×C42×C131C2211yescharacteristic
28#400×C131C2214yes—
29#399×C131C2214yes—
30#398×C131C2218yes—
31#398×C131C2214yes—
32#397×C131C2214yes—
33#396×C131C2218yes—
34#396×C131C2218yes—
35#395×C131C2214yes—
36#394×C131C2218yes—
37#394×C131C2214yes—
38#393×C131C2214yes—
39#392×C131C2214yes—
40#390×C131C2214yes—
41#389×C131C2214yes—
42#388×C131C2218yes—
43#386×C131C2218yes—
44#380×C131C2214yes—
45C4×C4⋊C4×C131C2214yes—
46C4×C4⋊C4×C131C2214yes—
47C4×C4⋊C4×C131C2214yes—
48C4×C22⋊C4×C131C2218yes—
49C2×#95×C131C2211yescharacteristic
50C2×#95×C131C2211yescharacteristic
51C22×Q8×C131C2312yes—
52C22×D4×C131C2314yes—
53C22×D4×C131C2314yes—
54C22×D4×C131C2312yes—
55C23×C4×C131C2314yes—
56C23×C4×C131C2311yescharacteristic
57C23×C4×C131C2311yescharacteristic
58C23×C4×C131C2312yes—
59C23×C4×C131C2311yescharacteristic
60C23×C4×C131C2312yes—
61#126×C131—216no—
62#125×C131—28no—
63#124×C131—28no—
64#123×C131—216no—
65C22⋊Q8×C131—28no—
66#121×C131—28no—
67#121×C131—216no—
68C4×Q8×C131—28no—
69C4×D4×C131—216no—
70C4×D4×C131—28no—
71C4×D4×C131—48no—
72#117×C131—216no—
73C2×C4⋊C4×C131—28no—
74C2×C4⋊C4×C131C2314yes—
75C2×C4⋊C4×C131C2314yes—
76C2×C4⋊C4×C131C2314yes—
77C2×C4⋊C4×C131C2318yes—
78C2×C4⋊C4×C131C2314yes—
79C2×C4⋊C4×C131C2314yes—
80C2×C4⋊C4×C131C2312yes—
81C2×C4⋊C4×C131C2312yes—
82C2×C4⋊C4×C131C2314yes—
83C2×C4⋊C4×C131C2314yes—
84C2×C22⋊C4×C131C2314yes—
85C2×C22⋊C4×C131C2318yes—
86C2×C22⋊C4×C131C2314yes—
87C2×C22⋊C4×C131C2314yes—
88C2×C22⋊C4×C131C2314yes—
89C2×C22⋊C4×C131C2314yes—
90C2×C22⋊C4×C131C2318yes—
91C2×C22⋊C4×C131C2318yes—
92C2×C42×C131—44no—
93C2×C42×C131D418yescomplemented
94C2×C42×C131C2314yes—
95C2×C42×C131C2314yes—
96C2×C42×C131C2314yes—
97C2×C42×C131C2312yes—
98C2×C42×C131C2312yes—
99#95×C131C2318yes—
100#95×C131C2318yes—
101#95×C131C2318yes—
102#95×C131C2314yes—
103#95×C131C2314yes—
104C24×C131C2414yes—
105C24×C131C2411yescharacteristic
106C2×Q8×C131—24no—
107C2×Q8×C131—44no—
108C2×D4×C131—28no—
109C2×D4×C131—216no—
110C2×D4×C131—24no—
111C2×D4×C131—28no—
112C2×D4×C131—44no—
113C2×D4×C131—44no—
114C2×D4×C131—44no—
115C22×C4×C131—24no—
116C22×C4×C131—22no—
117C22×C4×C131—22no—
118C22×C4×C131—24no—
119C22×C4×C131—28no—
120C22×C4×C131—28no—
121C22×C4×C131—28no—
122C22×C4×C131—42no—
123C22×C4×C131—42no—
124C22×C4×C131—42no—
125C22×C4×C131—42no—
126C22×C4×C131—42no—
127C22×C4×C131C2×D414yes—
128C22×C4×C131C2×D414yes—
129C22×C4×C131C2×D414yes—
130C22×C4×C131#4118yes—
131C22×C4×C131C2414yes—
132C22×C4×C131C2414yes—
133C22×C4×C131C2414yes—
134C22×C4×C131C2414yes—
135C22×C4×C131C2412yes—
136C22×C4×C131C2411yescharacteristic
137C22×C4×C131C2412yes—
138C22×C4×C131C2414yes—
139C22×C4×C131C2411yescharacteristic
140C4⋊C4×C131—28no—
141C4⋊C4×C131—28no—
142C4⋊C4×C131—24no—
143C4⋊C4×C131—28no—
144C4⋊C4×C131—24no—
145C4⋊C4×C131—28no—
146C4⋊C4×C131—216no—
147C4⋊C4×C131—28no—
148C4⋊C4×C131—44no—
149C4⋊C4×C131—44no—
150C22⋊C4×C131—28no—
151C22⋊C4×C131—28no—
152C22⋊C4×C131—28no—
153C22⋊C4×C131—28no—
154C22⋊C4×C131—28no—
155C22⋊C4×C131—216no—
156C22⋊C4×C131—48no—
157C22⋊C4×C131—48no—
158C42×C131—28no—
159C42×C131—28no—
160C42×C131—44no—
161C42×C131C2×D418yes—
162C42×C131C2×D418yes—
163C23×C131—21no—
164C23×C131—21no—
165C23×C131—22no—
166C23×C131—24no—
167C23×C131—28no—
168C23×C131—24no—
169C23×C131—24no—
170C23×C131—28no—
171C23×C131C22×D412yes—
172C23×C131C2×#4114yes—
173C23×C131C2511yescharacteristic
174Q8×C131—48no—
175D4×C131—48no—
176D4×C131—416no—
177D4×C131—416no—
178C2×C4×C131—28no—
179C2×C4×C131—24no—
180C2×C4×C131—24no—
181C2×C4×C131—21no—
182C2×C4×C131—21no—
183C2×C4×C131—24no—
184C2×C4×C131—24no—
185C2×C4×C131—28no—
186C2×C4×C131—24no—
187C2×C4×C131—24no—
188C2×C4×C131—24no—
189C2×C4×C131—28no—
190C2×C4×C131—24no—
191C2×C4×C131—24no—
192C2×C4×C131—24no—
193C2×C4×C131—24no—
194C2×C4×C131—24no—
195C2×C4×C131—28no—
196C2×C4×C131—44no—
197C2×C4×C131—48no—
198C2×C4×C131—48no—
199C2×C4×C131—416no—
200C2×C4×C131C22×D414yes—
201C2×C4×C131C22×D412yes—
202C2×C4×C131C22×D414yes—
203C2×C4×C131C22×D412yes—
204C2×C4×C131C2×#4118yes—
205C2×C4×C131H(5,𝔽2)12yes—
206C2×C4×C1312−1+412yes—
207C22×C131—22no—
208C22×C131—22no—
209C22×C131—24no—
210C22×C131—24no—
211C22×C131—44no—
212C22×C131—44no—
213C22×C131—44no—
214C22×C131—48no—
215C22×C131—48no—
216C22×C131#53214yes—
217C22×C131C23×D411yescharacteristic
218C22×C131C22×#4112yes—
219C22×C131C2×H(5,𝔽2)11yescharacteristic
220C22×C131C2×2−1+411yescharacteristic
221C22×C131#58512yes—
222C4×C131—24no—
223C4×C131—22no—
224C4×C131—24no—
225C4×C131—28no—
226C4×C131—44no—
227C4×C131—44no—
228C4×C131—44no—
229C4×C131—44no—
230C4×C131#53714yes—
231C2×C131—24no—
232C2×C131—84no—
233C2×C131C2×#53211yescharacteristic
234C2×C131C2×#53711yescharacteristic
235C2×C131#344911yescharacteristic
236C2×C131#345912yes—
237C2×C131#346112yes—
238#34594C13111yesmaximal, characteristic, direct product factor, Sylow
239C131#3459411yescharacteristic, direct product factor, Sylow
240C2×#529C2×C13112yescomplemented
241#2664C2×C13114yescomplemented
242#2662C2×C13114yescomplemented
243#2659C2×C13111yescharacteristic, complemented
244#2656C2×C13111yescharacteristic
245#2639C2×C13112yescomplemented
246#2618C2×C13114yescomplemented
247#2396C2×C13114yescomplemented
248#2392C2×C13114yescomplemented
249C4×#121C2×C13114yescomplemented
250C2×C4×C4⋊C4C2×C13111yescharacteristic, complemented
251#529—216no—
252C2×#126C22×C13114yes—
253C2×#125C22×C13112yes—
254C2×#124C22×C13112yes—
255C2×#123C22×C13114yes—
256C2×C22⋊Q8C22×C13112yes—
257C2×#121C22×C13114yes—
258C2×#121C22×C13112yes—
259C2×C4×Q8C22×C13112yes—
260C2×C4×D4C22×C13112yes—
261C2×C4×D4C22×C13114yes—
262C2×C4×D4C22×C13114yes—
263C2×#117C22×C13114yes—
264C22×C4⋊C4C22×C13112yes—
265C22×C42C22×C13112yes—
266C22×C42C22×C13111yescharacteristic
267#400C22×C13114yes—
268#399C22×C13114yes—
269#398C22×C13118yes—
270#398C22×C13114yes—
271#397C22×C13114yes—
272#396C22×C13118yes—
273#396C22×C13118yes—
274#395C22×C13114yes—
275#394C22×C13118yes—
276#394C22×C13114yes—
277#393C22×C13114yes—
278#392C22×C13114yes—
279#390C22×C13114yes—
280#389C22×C13114yes—
281#388C22×C13118yes—
282#386C22×C13118yes—
283#380C22×C13114yes—
284C4×C4⋊C4C22×C13114yes—
285C4×C4⋊C4C22×C13114yes—
286C4×C4⋊C4C22×C13114yes—
287C4×C22⋊C4C22×C13118yes—
288C2×#95C22×C13111yescharacteristic
289C2×#95C22×C13111yescharacteristic
290C22×Q8C23×C13112yes—
291C22×D4C23×C13114yes—
292C22×D4C23×C13112yes—
293C22×D4C23×C13114yes—
294C23×C4C23×C13114yes—
295C23×C4C23×C13111yescharacteristic
296C23×C4C23×C13111yescharacteristic
297C23×C4C23×C13112yes—
298C23×C4C23×C13111yescharacteristic
299C23×C4C23×C13112yes—
300#126—216no—
301#125—28no—
302#124—28no—
303#123—216no—
304C22⋊Q8—28no—
305#121—28no—
306#121—216no—
307C4×Q8—28no—
308C4×D4—216no—
309C4×D4—28no—
310C4×D4—48no—
311#117—216no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4C23×C13118yes—
314C2×C4⋊C4C23×C13114yes—
315C2×C4⋊C4C23×C13114yes—
316C2×C4⋊C4C23×C13112yes—
317C2×C4⋊C4C23×C13114yes—
318C2×C4⋊C4C23×C13112yes—
319C2×C4⋊C4C23×C13114yes—
320C2×C4⋊C4C23×C13114yes—
321C2×C4⋊C4C23×C13114yes—
322C2×C4⋊C4C23×C13114yes—
323C2×C22⋊C4C23×C13114yes—
324C2×C22⋊C4C23×C13114yes—
325C2×C22⋊C4C23×C13114yes—
326C2×C22⋊C4C23×C13114yes—
327C2×C22⋊C4C23×C13114yes—
328C2×C22⋊C4C23×C13118yes—
329C2×C22⋊C4C23×C13118yes—
330C2×C22⋊C4C23×C13118yes—
331C2×C42—44no—
332C2×C42D4×C13118yescomplemented
333C2×C42C23×C13114yes—
334C2×C42C23×C13114yes—
335C2×C42C23×C13114yes—
336C2×C42C23×C13112yes—
337C2×C42C23×C13112yes—
338#95C23×C13114yes—
339#95C23×C13114yes—
340#95C23×C13118yes—
341#95C23×C13118yes—
342#95C23×C13118yes—
343C24C24×C13114yes—
344C24C24×C13111yescharacteristic
345C2×Q8—24no—
346C2×Q8—44no—
347C2×D4—28no—
348C2×D4—216no—
349C2×D4—24no—
350C2×D4—28no—
351C2×D4—44no—
352C2×D4—44no—
353C2×D4—44no—
354C22×C4—24no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—24no—
358C22×C4—28no—
359C22×C4—28no—
360C22×C4—28no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4C2×D4×C13114yes—
367C22×C4C2×D4×C13114yes—
368C22×C4C2×D4×C13114yes—
369C22×C4#41×C13118yes—
370C22×C4C24×C13114yes—
371C22×C4C24×C13114yes—
372C22×C4C24×C13114yes—
373C22×C4C24×C13114yes—
374C22×C4C24×C13112yes—
375C22×C4C24×C13111yescharacteristic
376C22×C4C24×C13112yes—
377C22×C4C24×C13114yes—
378C22×C4C24×C13111yescharacteristic
379C4⋊C4—28no—
380C4⋊C4—28no—
381C4⋊C4—24no—
382C4⋊C4—28no—
383C4⋊C4—24no—
384C4⋊C4—28no—
385C4⋊C4—216no—
386C4⋊C4—28no—
387C4⋊C4—44no—
388C4⋊C4—44no—
389C22⋊C4—28no—
390C22⋊C4—28no—
391C22⋊C4—28no—
392C22⋊C4—28no—
393C22⋊C4—28no—
394C22⋊C4—216no—
395C22⋊C4—48no—
396C22⋊C4—48no—
397C42—28no—
398C42—28no—
399C42—44no—
400C42C2×D4×C13118yes—
401C42C2×D4×C13118yes—
402C23—21no—
403C23—21no—
404C23—22no—
405C23—24no—
406C23—28no—
407C23—24no—
408C23—24no—
409C23—28no—
410C23C22×D4×C13112yes—
411C23C2×#41×C13114yes—
412C23C25×C13111yescharacteristic
413Q8—48no—
414D4—48no—
415D4—416no—
416D4—416no—
417C2×C4—28no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—28no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—28no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—28no—
435C2×C4—44no—
436C2×C4—48no—
437C2×C4—48no—
438C2×C4—416no—
439C2×C4C22×D4×C13114yes—
440C2×C4C22×D4×C13112yes—
441C2×C4C22×D4×C13114yes—
442C2×C4C22×D4×C13112yes—
443C2×C4C2×#41×C13118yes—
444C2×C4H(5,𝔽2)×C13112yes—
445C2×C42−1+4×C13112yes—
446C22—22no—
447C22—22no—
448C22—24no—
449C22—24no—
450C22—44no—
451C22—44no—
452C22—44no—
453C22—48no—
454C22—48no—
455C22#532×C13114yes—
456C22C23×D4×C13111yescharacteristic
457C22C22×#41×C13112yes—
458C22C2×H(5,𝔽2)×C13111yescharacteristic
459C22C2×2−1+4×C13111yescharacteristic
460C22#585×C13112yes—
461C4—24no—
462C4—22no—
463C4—24no—
464C4—28no—
465C4—44no—
466C4—44no—
467C4—44no—
468C4—44no—
469C4#537×C13114yes—
470C2—24no—
471C2—84no—
472C2C2×#532×C13111yescharacteristic
473C2C2×#537×C13111yescharacteristic
474C2#3449×C13111yescharacteristic
475C2#3459×C13112yes—
476C2#3461×C13112yes—
subgroupG/H
centerC22×C4×C131C24
commutator, Frattini, cosocleC23C25×C131
socleC23×C131C25
prime radical#2656×C131C2
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. #2662×C131C2semidirect
4. #2659×C131C2semidirect
6. #2639×C131C2semidirect
7. #2618×C131C2semidirect
8. #2396×C131C2semidirect
9. #2392×C131C2semidirect
10. C4×#121×C131C2semidirect
11. C2×C4×C4⋊C4×C131C2semidirect
93. C2×C42×C131D4semidirect
238. #34594C131direct (N × H)
239. C131#34594direct (N × H)
240. C2×#529C2×C131semidirect
241. #2664C2×C131semidirect
242. #2662C2×C131semidirect
243. #2659C2×C131semidirect
245. #2639C2×C131semidirect
246. #2618C2×C131semidirect
247. #2396C2×C131semidirect
248. #2392C2×C131semidirect
249. C4×#121C2×C131semidirect
250. C2×C4×C4⋊C4C2×C131semidirect
332. 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
#2662×C1312
#2659×C1312
#2656×C1312
#2639×C1312
#2618×C1312
#2396×C1312
#2392×C1312
C4×#121×C1312
C2×C4×C4⋊C4×C1312
#34594131