Finite Group Databasebeta

← C131×#34943 #45720827

Subgroups — C131×#34943 #45720827

Order 33536.

2036 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2572×C131C214yesmaximal, complemented
2#2571×C131C211yesmaximal, characteristic, complemented
3#2563×C131C212yesmaximal, complemented
4#2537×C131C211yesmaximal, characteristic
5#2495×C131C214yesmaximal, complemented
6#2420×C131C214yesmaximal, complemented
7#2398×C131C214yesmaximal, complemented
8C4×C4⋊Q8×C131C211yesmaximal, characteristic, complemented
9C4×#121×C131C214yesmaximal, complemented
10#2283×C131C214yesmaximal, complemented
11C42×D4×C131C212yesmaximal, complemented
12C2×C4⋊Q8×C131C2211yescharacteristic
13C2×#121×C131C2214yes—
14C2×C4×Q8×C131C2212yes—
15C2×C4×D4×C131C2212yes—
16C2×C4×D4×C131C2212yes—
17C2×C4×D4×C131C2212yes—
18C2×C4×D4×C131C2214yes—
19C22×C42×C131C2214yes—
20#400×C131C2214yes—
21#400×C131C2214yes—
22#397×C131C2218yes—
23#394×C131C2214yes—
24#394×C131C2214yes—
25#393×C131C2218yes—
26#391×C131C2212yes—
27#390×C131C2214yes—
28#389×C131C2214yes—
29#389×C131C2214yes—
30#388×C131C2218yes—
31#386×C131C2218yes—
32#384×C131C2211yescharacteristic
33#383×C131C2218yes—
34#382×C131C2214yes—
35#382×C131C2214yes—
36#381×C131C2218yes—
37#380×C131C2214yes—
38#380×C131C2214yes—
39#380×C131C2214yes—
40C4×C4⋊C4×C131C2212yes—
41C4×C4⋊C4×C131C2212yes—
42C4×C4⋊C4×C131C2212yes—
43C4×C4⋊C4×C131C2214yes—
44C4×C22⋊C4×C131C2214yes—
45C4×C22⋊C4×C131C2214yes—
46C4×C22⋊C4×C131C2214yes—
47C4×C22⋊C4×C131C2218yes—
48#376×C131C2214yes—
49C43×C131C2211yescharacteristic
50C22×Q8×C131C2312yes—
51C22×D4×C131C2314yes—
52C22×D4×C131C2312yes—
53C23×C4×C131C2314yes—
54C23×C4×C131C2314yes—
55C23×C4×C131C2314yes—
56C4⋊Q8×C131—24no—
57#121×C131—216no—
58C4×Q8×C131—44no—
59C4×D4×C131—28no—
60C4×D4×C131—28no—
61C4×D4×C131—28no—
62C4×D4×C131—48no—
63C2×C4⋊C4×C131C2312yes—
64C2×C4⋊C4×C131C2314yes—
65C2×C4⋊C4×C131C2314yes—
66C2×C4⋊C4×C131C2312yes—
67C2×C4⋊C4×C131C2312yes—
68C2×C4⋊C4×C131C2314yes—
69C2×C4⋊C4×C131C2314yes—
70C2×C4⋊C4×C131C2312yes—
71C2×C22⋊C4×C131C2314yes—
72C2×C22⋊C4×C131C2318yes—
73C2×C22⋊C4×C131C2314yes—
74C2×C22⋊C4×C131C2314yes—
75C2×C22⋊C4×C131C2318yes—
76C2×C22⋊C4×C131C2318yes—
77C2×C42×C131—216no—
78C2×C42×C131C2314yes—
79C2×C42×C131C2312yes—
80C2×C42×C131C2314yes—
81C2×C42×C131C2314yes—
82C2×C42×C131C2314yes—
83C2×C42×C131C2311yescharacteristic
84C2×C42×C131C2311yescharacteristic
85C2×C42×C131C2311yescharacteristic
86C2×C42×C131C2312yes—
87#95×C131C2318yes—
88#95×C131C2318yes—
89#95×C131C2318yes—
90#95×C131C2314yes—
91#95×C131C2318yes—
92#95×C131C2314yes—
93#95×C131C2314yes—
94#95×C131C2314yes—
95#95×C131C2314yes—
96C24×C131C2414yes—
97C2×Q8×C131—24no—
98C2×Q8×C131—42no—
99C2×Q8×C131—42no—
100C2×D4×C131—216no—
101C2×D4×C131—24no—
102C2×D4×C131—24no—
103C2×D4×C131—44no—
104C2×D4×C131#4118yes—
105C22×C4×C131—28no—
106C22×C4×C131—28no—
107C22×C4×C131—28no—
108C22×C4×C131—28no—
109C22×C4×C131—28no—
110C22×C4×C131—28no—
111C22×C4×C131—28no—
112C22×C4×C131—28no—
113C22×C4×C131—44no—
114C22×C4×C131C2414yes—
115C22×C4×C131C2414yes—
116C22×C4×C131C2414yes—
117C22×C4×C131C2414yes—
118C22×C4×C131C2414yes—
119C22×C4×C131C2411yescharacteristic
120C22×C4×C131C2412yes—
121C22×C4×C131C2411yescharacteristic
122C22×C4×C131C2412yes—
123C22×C4×C131C2411yescharacteristic
124C4⋊C4×C131—24no—
125C4⋊C4×C131—24no—
126C4⋊C4×C131—24no—
127C4⋊C4×C131—28no—
128C4⋊C4×C131—28no—
129C4⋊C4×C131—44no—
130C4⋊C4×C131—42no—
131C4⋊C4×C131—44no—
132C22⋊C4×C131—28no—
133C22⋊C4×C131—216no—
134C22⋊C4×C131—28no—
135C22⋊C4×C131—28no—
136C22⋊C4×C131—48no—
137C22⋊C4×C131—48no—
138C42×C131—28no—
139C42×C131—28no—
140C42×C131—28no—
141C42×C131—24no—
142C42×C131—28no—
143C42×C131—22no—
144C42×C131—41no—
145C42×C131#4118yes—
146C42×C131#4114yes—
147C23×C131—24no—
148C23×C131—24no—
149C23×C131—24no—
150C23×C131—24no—
151C23×C131—24no—
152C23×C131—24no—
153C23×C131C2×#4118yes—
154C23×C131C2511yescharacteristic
155Q8×C131—48no—
156D4×C131—216no—
157D4×C131—416no—
158C2×C4×C131—22no—
159C2×C4×C131—21no—
160C2×C4×C131—22no—
161C2×C4×C131—21no—
162C2×C4×C131—24no—
163C2×C4×C131—24no—
164C2×C4×C131—24no—
165C2×C4×C131—22no—
166C2×C4×C131—24no—
167C2×C4×C131—24no—
168C2×C4×C131—24no—
169C2×C4×C131—24no—
170C2×C4×C131—28no—
171C2×C4×C131—24no—
172C2×C4×C131—24no—
173C2×C4×C131—21no—
174C2×C4×C131—24no—
175C2×C4×C131—24no—
176C2×C4×C131—24no—
177C2×C4×C131—24no—
178C2×C4×C131—416no—
179C2×C4×C131—416no—
180C2×C4×C131—416no—
181C2×C4×C131C2×#4114yes—
182C2×C4×C131C2×#4112yes—
183C2×C4×C131C2×#4114yes—
184C2×C4×C131C2×#4114yes—
185C2×C4×C131C2×#4114yes—
186C2×C4×C131C2×#4114yes—
187C2×C4×C131H(5,𝔽2)12yes—
188C22×C131—28no—
189C22×C131—28no—
190C22×C131—28no—
191C22×C131—44no—
192C22×C131—44no—
193C22×C131—44no—
194C22×C131—44no—
195C22×C131C22×#4111yescharacteristic
196C22×C131C22×#4112yes—
197C22×C131C22×#4112yes—
198C22×C131C2×H(5,𝔽2)11yescharacteristic
199C22×C131#58511yescharacteristic
200C4×C131—22no—
201C4×C131—24no—
202C4×C131—44no—
203C4×C131—44no—
204C4×C131—44no—
205C4×C131—44no—
206C4×C131—41no—
207C4×C131—44no—
208C4×C131#52918yes—
209C4×C131#55514yes—
210C2×C131—48no—
211C2×C131C2×#52912yes—
212C2×C131#346011yescharacteristic
213C2×C131C2×#55511yescharacteristic
214C2×C131#347512yes—
215C2×C131#348111yescharacteristic
216#34943C13111yesmaximal, characteristic, direct product factor, Sylow
217C131#3494311yescharacteristic, direct product factor, Sylow
218#2572C2×C13114yescomplemented
219#2571C2×C13111yescharacteristic, complemented
220#2563C2×C13112yescomplemented
221#2537C2×C13111yescharacteristic
222#2495C2×C13114yescomplemented
223#2420C2×C13114yescomplemented
224#2398C2×C13114yescomplemented
225C4×C4⋊Q8C2×C13111yescharacteristic, complemented
226C4×#121C2×C13114yescomplemented
227#2283C2×C13114yescomplemented
228C42×D4C2×C13112yescomplemented
229C2×C4⋊Q8C22×C13111yescharacteristic
230C2×#121C22×C13114yes—
231C2×C4×Q8C22×C13112yes—
232C2×C4×D4C22×C13112yes—
233C2×C4×D4C22×C13112yes—
234C2×C4×D4C22×C13112yes—
235C2×C4×D4C22×C13114yes—
236C22×C42C22×C13114yes—
237#400C22×C13114yes—
238#400C22×C13114yes—
239#397C22×C13118yes—
240#394C22×C13114yes—
241#394C22×C13114yes—
242#393C22×C13118yes—
243#391C22×C13112yes—
244#390C22×C13114yes—
245#389C22×C13114yes—
246#389C22×C13114yes—
247#388C22×C13118yes—
248#386C22×C13118yes—
249#384C22×C13111yescharacteristic
250#383C22×C13118yes—
251#382C22×C13114yes—
252#382C22×C13114yes—
253#381C22×C13118yes—
254#380C22×C13114yes—
255#380C22×C13114yes—
256#380C22×C13114yes—
257C4×C4⋊C4C22×C13114yes—
258C4×C4⋊C4C22×C13112yes—
259C4×C4⋊C4C22×C13112yes—
260C4×C4⋊C4C22×C13112yes—
261C4×C22⋊C4C22×C13114yes—
262C4×C22⋊C4C22×C13114yes—
263C4×C22⋊C4C22×C13118yes—
264C4×C22⋊C4C22×C13114yes—
265#376C22×C13114yes—
266C43C22×C13111yescharacteristic
267C22×Q8C23×C13112yes—
268C22×D4C23×C13114yes—
269C22×D4C23×C13112yes—
270C23×C4C23×C13114yes—
271C23×C4C23×C13114yes—
272C23×C4C23×C13114yes—
273C4⋊Q8—24no—
274#121—216no—
275C4×Q8—44no—
276C4×D4—28no—
277C4×D4—28no—
278C4×D4—28no—
279C4×D4—48no—
280C2×C4⋊C4C23×C13112yes—
281C2×C4⋊C4C23×C13112yes—
282C2×C4⋊C4C23×C13112yes—
283C2×C4⋊C4C23×C13114yes—
284C2×C4⋊C4C23×C13114yes—
285C2×C4⋊C4C23×C13114yes—
286C2×C4⋊C4C23×C13112yes—
287C2×C4⋊C4C23×C13114yes—
288C2×C22⋊C4C23×C13114yes—
289C2×C22⋊C4C23×C13114yes—
290C2×C22⋊C4C23×C13114yes—
291C2×C22⋊C4C23×C13118yes—
292C2×C22⋊C4C23×C13118yes—
293C2×C22⋊C4C23×C13118yes—
294C2×C42—216no—
295C2×C42C23×C13114yes—
296C2×C42C23×C13112yes—
297C2×C42C23×C13111yescharacteristic
298C2×C42C23×C13114yes—
299C2×C42C23×C13114yes—
300C2×C42C23×C13114yes—
301C2×C42C23×C13111yescharacteristic
302C2×C42C23×C13111yescharacteristic
303C2×C42C23×C13112yes—
304#95C23×C13114yes—
305#95C23×C13118yes—
306#95C23×C13114yes—
307#95C23×C13114yes—
308#95C23×C13114yes—
309#95C23×C13114yes—
310#95C23×C13118yes—
311#95C23×C13118yes—
312#95C23×C13118yes—
313C24C24×C13114yes—
314C2×Q8—24no—
315C2×Q8—42no—
316C2×Q8—42no—
317C2×D4—216no—
318C2×D4—24no—
319C2×D4—24no—
320C2×D4—44no—
321C2×D4#41×C13118yes—
322C22×C4—28no—
323C22×C4—28no—
324C22×C4—28no—
325C22×C4—28no—
326C22×C4—28no—
327C22×C4—28no—
328C22×C4—28no—
329C22×C4—28no—
330C22×C4—44no—
331C22×C4C24×C13114yes—
332C22×C4C24×C13114yes—
333C22×C4C24×C13114yes—
334C22×C4C24×C13114yes—
335C22×C4C24×C13114yes—
336C22×C4C24×C13111yescharacteristic
337C22×C4C24×C13112yes—
338C22×C4C24×C13111yescharacteristic
339C22×C4C24×C13112yes—
340C22×C4C24×C13111yescharacteristic
341C4⋊C4—24no—
342C4⋊C4—24no—
343C4⋊C4—24no—
344C4⋊C4—28no—
345C4⋊C4—28no—
346C4⋊C4—44no—
347C4⋊C4—42no—
348C4⋊C4—44no—
349C22⋊C4—28no—
350C22⋊C4—216no—
351C22⋊C4—28no—
352C22⋊C4—28no—
353C22⋊C4—48no—
354C22⋊C4—48no—
355C42—28no—
356C42—28no—
357C42—28no—
358C42—24no—
359C42—28no—
360C42—22no—
361C42—41no—
362C42#41×C13118yes—
363C42#41×C13114yes—
364C23—24no—
365C23—24no—
366C23—24no—
367C23—24no—
368C23—24no—
369C23—24no—
370C23C2×#41×C13118yes—
371C23C25×C13111yescharacteristic
372Q8—48no—
373D4—216no—
374D4—416no—
375C2×C4—22no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—21no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—22no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—28no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—21no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—416no—
396C2×C4—416no—
397C2×C4—416no—
398C2×C4C2×#41×C13114yes—
399C2×C4C2×#41×C13112yes—
400C2×C4C2×#41×C13114yes—
401C2×C4C2×#41×C13114yes—
402C2×C4C2×#41×C13114yes—
403C2×C4C2×#41×C13114yes—
404C2×C4H(5,𝔽2)×C13112yes—
405C22—28no—
406C22—28no—
407C22—28no—
408C22—44no—
409C22—44no—
410C22—44no—
411C22—44no—
412C22C22×#41×C13111yescharacteristic
413C22C22×#41×C13112yes—
414C22C22×#41×C13112yes—
415C22C2×H(5,𝔽2)×C13111yescharacteristic
416C22#585×C13111yescharacteristic
417C4—22no—
418C4—24no—
419C4—44no—
420C4—44no—
421C4—44no—
422C4—44no—
423C4—44no—
424C4—41no—
425C4#529×C13118yes—
426C4#555×C13114yes—
427C2—48no—
428C2C2×#529×C13112yes—
429C2#3460×C13111yescharacteristic
430C2C2×#555×C13111yescharacteristic
431C2#3475×C13112yes—
432C2#3481×C13111yescharacteristic
subgroupG/H
centerC22×C4×C131C24
commutator, Frattini, cosocleC23C25×C131
socleC23×C131C25
prime radical#2537×C131C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2572×C131C2semidirect
2. #2571×C131C2semidirect
3. #2563×C131C2semidirect
5. #2495×C131C2semidirect
6. #2420×C131C2semidirect
7. #2398×C131C2semidirect
8. C4×C4⋊Q8×C131C2semidirect
9. C4×#121×C131C2semidirect
10. #2283×C131C2semidirect
11. C42×D4×C131C2semidirect
216. #34943C131direct (N × H)
217. C131#34943direct (N × H)
218. #2572C2×C131semidirect
219. #2571C2×C131semidirect
220. #2563C2×C131semidirect
222. #2495C2×C131semidirect
223. #2420C2×C131semidirect
224. #2398C2×C131semidirect
225. C4×C4⋊Q8C2×C131semidirect
226. C4×#121C2×C131semidirect
227. #2283C2×C131semidirect
228. C42×D4C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2572×C1312
#2571×C1312
#2563×C1312
#2537×C1312
#2495×C1312
#2420×C1312
#2398×C1312
C4×C4⋊Q8×C1312
C4×#121×C1312
#2283×C1312
C42×D4×C1312
#34943131