Finite Group Databasebeta

← C131×#10271 #45696155

Subgroups — C131×#10271 #45696155

Order 33536.

594 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#498×C131C211yesmaximal, characteristic, complemented
2C2×#476×C131C211yesmaximal, characteristic
3C2×#461×C131C211yesmaximal, characteristic
4#1954×C131C211yesmaximal, characteristic
5C2×#333×C131C211yesmaximal, characteristic, complemented
6C2×#332×C131C211yesmaximal, characteristic, complemented
7#1277×C131C211yesmaximal, characteristic, complemented
8C22×SD16×C131—21no—
9C2×C4⋊Q8×C131C2211yescharacteristic
10C2×C4⋊Q8×C131C2211yescharacteristic
11C2×C4×D4×C131C2211yescharacteristic
12#498×C131—22no—
13#498×C131—22no—
14#476×C131—22no—
15#476×C131—22no—
16#461×C131—22no—
17#461×C131—22no—
18C2×#106×C131—22no—
19C2×#106×C131—21no—
20C2×C4⋊C8×C131C2211yescharacteristic
21C2×C4⋊C8×C131C2211yescharacteristic
22C2×C4⋊C8×C131C2211yescharacteristic
23C2×#103×C131—21no—
24C2×#102×C131—21no—
25C2×C22⋊C8×C131—22no—
26C2×C4×C8×C131C2211yescharacteristic
27#333×C131—22no—
28#332×C131—22no—
29C22×Q8×C131—21no—
30C22×Q8×C131—21no—
31C22×D4×C131D411yescharacteristic
32C23×C4×C131—21no—
33C2×SD16×C131—24no—
34C2×SD16×C131—42no—
35C2×SD16×C131—42no—
36C22×C8×C131—21no—
37C22×C8×C131—21no—
38C22×C8×C131—21no—
39C22×C8×C131D412yes—
40C4⋊Q8×C131—21no—
41C4⋊Q8×C131—21no—
42C4⋊Q8×C131—21no—
43C4⋊Q8×C131—21no—
44C4⋊Q8×C131—21no—
45C4⋊Q8×C131—21no—
46C4⋊Q8×C131D412yes—
47C4⋊Q8×C131D412yes—
48C4×D4×C131—21no—
49C4×D4×C131—21no—
50C4×D4×C131—21no—
51C4×D4×C131—21no—
52C2×C4⋊C4×C131—21no—
53C2×C4⋊C4×C131—21no—
54C2×C4⋊C4×C131—21no—
55C2×C4⋊C4×C131—21no—
56C2×C4⋊C4×C131D411yescharacteristic
57C2×C22⋊C4×C131—21no—
58C2×C42×C131C2311yescharacteristic
59#106×C131—24no—
60#106×C131—28no—
61C4⋊C8×C131—21no—
62C4⋊C8×C131—21no—
63C4⋊C8×C131—21no—
64C4⋊C8×C131—21no—
65C4⋊C8×C131D412yes—
66C4⋊C8×C131D412yes—
67#103×C131—24no—
68#102×C131—24no—
69C22⋊C8×C131—44no—
70C4×C8×C131—21no—
71C4×C8×C131—21no—
72C24×C131—21no—
73C2×Q8×C131—22no—
74C2×Q8×C131—22no—
75C2×Q8×C131—41no—
76C2×Q8×C131—41no—
77C2×Q8×C131—41no—
78C2×Q8×C131—41no—
79C2×Q8×C131—41no—
80C2×Q8×C131—41no—
81C2×Q8×C131—82no—
82C2×D4×C131—21no—
83C2×D4×C131—21no—
84C2×D4×C131—21no—
85C2×D4×C131—21no—
86C2×D4×C131—21no—
87C2×D4×C131SD1612yes—
88C22×C4×C131—21no—
89C22×C4×C131—41no—
90C22×C4×C131—41no—
91C22×C4×C131—41no—
92C22×C4×C131—41no—
93C22×C4×C131—42no—
94C22×C4×C131—42no—
95C22×C4×C131C2×D411yescharacteristic
96C22×C4×C131C2×D411yescharacteristic
97C22×C4×C131#4111yescharacteristic
98SD16×C131—48no—
99C2×C8×C131—22no—
100C2×C8×C131—22no—
101C2×C8×C131—22no—
102C2×C8×C131—22no—
103C2×C8×C131—41no—
104C2×C8×C131—41no—
105C2×C8×C131—41no—
106C2×C8×C131—41no—
107C2×C8×C131—41no—
108C2×C8×C131—42no—
109C2×C8×C131SD1614yescomplemented
110C4⋊C4×C131—22no—
111C4⋊C4×C131—21no—
112C4⋊C4×C131—22no—
113C4⋊C4×C131—22no—
114C4⋊C4×C131—21no—
115C4⋊C4×C131—22no—
116C4⋊C4×C131—41no—
117C4⋊C4×C131—41no—
118C4⋊C4×C131—41no—
119C4⋊C4×C131—41no—
120C22⋊C4×C131—41no—
121C22⋊C4×C131—41no—
122C42×C131C2×D411yescharacteristic
123C42×C131C2×D411yescharacteristic
124C42×C131C2×D411yescharacteristic
125C42×C131C2×D411yescharacteristic
126C23×C131—22no—
127C23×C131—41no—
128C23×C131—42no—
129C23×C131—41no—
130C23×C131—42no—
131C23×C131#12111yescharacteristic
132Q8×C131—42no—
133Q8×C131—42no—
134Q8×C131—82no—
135Q8×C131—82no—
136Q8×C131—81no—
137Q8×C131—81no—
138D4×C131—22no—
139D4×C131—22no—
140D4×C131—41no—
141D4×C131—41no—
142C2×C4×C131—22no—
143C2×C4×C131—41no—
144C2×C4×C131—42no—
145C2×C4×C131—42no—
146C2×C4×C131—42no—
147C2×C4×C131—81no—
148C2×C4×C131—81no—
149C2×C4×C131—82no—
150C2×C4×C131—82no—
151C2×C4×C131—81no—
152C2×C4×C131—81no—
153C2×C4×C131#12011yescharacteristic
154C2×C4×C131#12011yescharacteristic
155C2×C4×C131#12011yescharacteristic
156C2×C4×C131#12111yescharacteristic
157C2×C4×C131#12111yescharacteristic
158C2×C4×C131#12711yescharacteristic
159C2×C4×C131C2×SD1611yescharacteristic
160C2×C4×C131C2×SD1612yes—
161C2×C4×C131#13511yescharacteristic
162C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C131#13711yescharacteristic
164C2×C4×C131#13712yes—
165C8×C131—24no—
166C8×C131—42no—
167C8×C131—42no—
168C8×C131—81no—
169C22×C131—44no—
170C22×C131—42no—
171C22×C131—82no—
172C22×C131—81no—
173C22×C131—81no—
174C22×C131#39211yescharacteristic
175C22×C131#46112yes—
176C22×C131#46511yescharacteristic
177C22×C131#46811yescharacteristic
178C22×C131#47112yes—
179C4×C131—21no—
180C4×C131—21no—
181C4×C131—82no—
182C4×C131—81no—
183C4×C131—82no—
184C4×C131#44811yescharacteristic
185C4×C131#44812yes—
186C4×C131#44911yescharacteristic
187C4×C131#45011yescharacteristic
188C4×C131#45211yescharacteristic
189C4×C131#49211yescharacteristic
190C4×C131#49711yescharacteristic
191C2×C131—82no—
192C2×C131#167112yes—
193C2×C131#169112yes—
194C2×C131#200011yescharacteristic
195C2×C131#201311yescharacteristic
196C2×C131#201911yescharacteristic
197#10271C13111yesmaximal, characteristic, direct product factor, Sylow
198C131#1027111yescharacteristic, direct product factor, Sylow
199C2×#498C2×C13111yescharacteristic, complemented
200C2×#476C2×C13111yescharacteristic
201C2×#461C2×C13111yescharacteristic
202#1954C2×C13111yescharacteristic
203C2×#333C2×C13111yescharacteristic, complemented
204C2×#332C2×C13111yescharacteristic, complemented
205#1277C2×C13111yescharacteristic, complemented
206C22×SD16—21no—
207C2×C4⋊Q8C22×C13111yescharacteristic
208C2×C4⋊Q8C22×C13111yescharacteristic
209C2×C4×D4C22×C13111yescharacteristic
210#498—22no—
211#498—22no—
212#476—22no—
213#476—22no—
214#461—22no—
215#461—22no—
216C2×#106—22no—
217C2×#106—21no—
218C2×C4⋊C8C22×C13111yescharacteristic
219C2×C4⋊C8C22×C13111yescharacteristic
220C2×C4⋊C8C22×C13111yescharacteristic
221C2×#103—21no—
222C2×#102—21no—
223C2×C22⋊C8—22no—
224C2×C4×C8C22×C13111yescharacteristic
225#333—22no—
226#332—22no—
227C22×Q8—21no—
228C22×Q8—21no—
229C22×D4D4×C13111yescharacteristic
230C23×C4—21no—
231C2×SD16—24no—
232C2×SD16—42no—
233C2×SD16—42no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8D4×C13112yes—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8D4×C13112yes—
245C4⋊Q8D4×C13112yes—
246C4×D4—21no—
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4D4×C13111yescharacteristic
255C2×C22⋊C4—21no—
256C2×C42C23×C13111yescharacteristic
257#106—24no—
258#106—28no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8D4×C13112yes—
264C4⋊C8D4×C13112yes—
265#103—24no—
266#102—24no—
267C22⋊C8—44no—
268C4×C8—21no—
269C4×C8—21no—
270C24—21no—
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—82no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4SD16×C13112yes—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4C2×D4×C13111yescharacteristic
294C22×C4C2×D4×C13111yescharacteristic
295C22×C4#41×C13111yescharacteristic
296SD16—48no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—42no—
307C2×C8SD16×C13114yescomplemented
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C42C2×D4×C13111yescharacteristic
321C42C2×D4×C13111yescharacteristic
322C42C2×D4×C13111yescharacteristic
323C42C2×D4×C13111yescharacteristic
324C23—22no—
325C23—41no—
326C23—42no—
327C23—41no—
328C23—42no—
329C23#121×C13111yescharacteristic
330Q8—42no—
331Q8—42no—
332Q8—82no—
333Q8—82no—
334Q8—81no—
335Q8—81no—
336D4—22no—
337D4—22no—
338D4—41no—
339D4—41no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4#120×C13111yescharacteristic
352C2×C4#120×C13111yescharacteristic
353C2×C4#120×C13111yescharacteristic
354C2×C4#121×C13111yescharacteristic
355C2×C4#121×C13111yescharacteristic
356C2×C4#127×C13111yescharacteristic
357C2×C4C2×SD16×C13111yescharacteristic
358C2×C4C2×SD16×C13112yes—
359C2×C4#135×C13111yescharacteristic
360C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
361C2×C4#137×C13111yescharacteristic
362C2×C4#137×C13112yes—
363C8—24no—
364C8—42no—
365C8—42no—
366C8—81no—
367C22—42no—
368C22—44no—
369C22—81no—
370C22—81no—
371C22—82no—
372C22#392×C13111yescharacteristic
373C22#461×C13112yes—
374C22#465×C13111yescharacteristic
375C22#468×C13111yescharacteristic
376C22#471×C13112yes—
377C4—21no—
378C4—21no—
379C4—82no—
380C4—81no—
381C4—82no—
382C4#448×C13111yescharacteristic
383C4#448×C13112yes—
384C4#449×C13111yescharacteristic
385C4#450×C13111yescharacteristic
386C4#452×C13111yescharacteristic
387C4#492×C13111yescharacteristic
388C4#497×C13111yescharacteristic
389C2—82no—
390C2#1671×C13112yes—
391C2#1691×C13112yes—
392C2#2000×C13111yescharacteristic
393C2#2013×C13111yescharacteristic
394C2#2019×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#121
commutator, Frattini, cosocleC2×C42C23×C131
prime radicalC22×D4×C131D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#498×C131C2semidirect
5. C2×#333×C131C2semidirect
6. C2×#332×C131C2semidirect
7. #1277×C131C2semidirect
109. C2×C8×C131SD16semidirect
197. #10271C131direct (N × H)
198. C131#10271direct (N × H)
199. C2×#498C2×C131semidirect
203. C2×#333C2×C131semidirect
204. C2×#332C2×C131semidirect
205. #1277C2×C131semidirect
307. C2×C8SD16×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#498×C1312
C2×#476×C1312
C2×#461×C1312
#1954×C1312
C2×#333×C1312
C2×#332×C1312
#1277×C1312
#10271131