Finite Group Databasebeta

← C131×#13391 #45699275

Subgroups — C131×#13391 #45699275

Order 33536.

390 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3067×C131C211yesmaximal, characteristic
2#2161×C131C211yesmaximal, characteristic, complemented
3#2148×C131C211yesmaximal, characteristic, complemented
4C2×#360×C131C211yesmaximal, characteristic, complemented
5#2115×C131C211yesmaximal, characteristic, complemented
6#1815×C131C211yesmaximal, characteristic, complemented
7#1383×C131C211yesmaximal, characteristic, complemented
8#575×C131—21no—
9C2×#135×C131C2211yescharacteristic
10C2×#131×C131C2211yescharacteristic
11C2×M32×C131C2211yescharacteristic
12C2×M32×C131C2211yescharacteristic
13#473×C131—21no—
14#472×C131—21no—
15#471×C131—22no—
16C2×#108×C131C2211yescharacteristic
17C2×#108×C131C2211yescharacteristic
18C2×#106×C131C2211yescharacteristic
19#417×C131—21no—
20#413×C131—21no—
21#368×C131—22no—
22#362×C131—21no—
23#361×C131—21no—
24#360×C131—22no—
25#349×C131—22no—
26#343×C131—21no—
27C2×#41×C131—21no—
28C2×#41×C131D411yescharacteristic
29#137×C131—22no—
30#137×C131—41no—
31AGL(1,ℤ/8)×C131—22no—
32AGL(1,ℤ/8)×C131—41no—
33#135×C131—21no—
34#135×C131—21no—
35#135×C131—21no—
36#135×C131—21no—
37#135×C131—42no—
38C2×Q16×C131D411yescharacteristic
39C2×SD16×C131—21no—
40C2×D8×C131D411yescharacteristic
41#131×C131—21no—
42#131×C131—21no—
43#131×C131—21no—
44#131×C131—21no—
45C2×M16×C131—21no—
46C2×M16×C131—21no—
47C2×M16×C131—21no—
48C2×M16×C131D411yescharacteristic
49C22×C8×C131—21no—
50C22×C8×C131C2311yescharacteristic
51C2×C4⋊C4×C131—21no—
52M32×C131—21no—
53M32×C131—21no—
54M32×C131—21no—
55M32×C131D412yes—
56C2×C16×C131—21no—
57C2×C16×C131—21no—
58#108×C131—21no—
59#108×C131—21no—
60#108×C131—21no—
61#108×C131D412yes—
62#106×C131—21no—
63#106×C131—21no—
64#103×C131—41no—
65#102×C131—41no—
66#101×C131—22no—
67#100×C131—22no—
68#41×C131—21no—
69#41×C131—21no—
70#41×C131—21no—
71#41×C131—21no—
72#41×C131—41no—
73#41×C131—41no—
74#41×C131—41no—
75#41×C131—41no—
76C2×Q8×C131—21no—
77C2×Q8×C131D811yescharacteristic
78C2×D4×C131—21no—
79C2×D4×C131—21no—
80C2×D4×C131—41no—
81C2×D4×C131D811yescharacteristic
82C22×C4×C131—21no—
83C22×C4×C131—41no—
84C22×C4×C131—41no—
85C22×C4×C131C2×D411yescharacteristic
86Q16×C131—21no—
87Q16×C131—21no—
88Q16×C131—42no—
89SD16×C131—42no—
90SD16×C131—42no—
91SD16×C131—41no—
92SD16×C131—41no—
93D8×C131—21no—
94D8×C131—21no—
95D8×C131—42no—
96M16×C131—21no—
97M16×C131—22no—
98M16×C131—21no—
99M16×C131—41no—
100M16×C131—41no—
101M16×C131—41no—
102M16×C131—41no—
103M16×C131—41no—
104C2×C8×C131—21no—
105C2×C8×C131—41no—
106C2×C8×C131—41no—
107C2×C8×C131—41no—
108C2×C8×C131—41no—
109C2×C8×C131C2×D411yescharacteristic
110C2×C8×C131C2×D411yescharacteristic
111C2×C8×C131C2×D411yescharacteristic
112C2×C8×C131#4111yescharacteristic
113C2×C8×C131#4111yescharacteristic
114C2×C8×C131#4111yescharacteristic
115C4⋊C4×C131—41no—
116C4⋊C4×C131—41no—
117C16×C131—22no—
118C16×C131—41no—
119C23×C131—21no—
120C23×C131—41no—
121C23×C131#13511yescharacteristic
122Q8×C131—21no—
123Q8×C131—21no—
124Q8×C131—41no—
125Q8×C131—41no—
126D4×C131—21no—
127D4×C131—21no—
128D4×C131—41no—
129D4×C131—41no—
130D4×C131—41no—
131D4×C131—41no—
132D4×C131—81no—
133D4×C131—81no—
134C2×C4×C131—21no—
135C2×C4×C131—41no—
136C2×C4×C131—41no—
137C2×C4×C131—41no—
138C2×C4×C131—81no—
139C2×C4×C131—81no—
140C2×C4×C131—81no—
141C2×C4×C131—161no—
142C2×C4×C131#12011yescharacteristic
143C2×C4×C131#12111yescharacteristic
144C2×C4×C131#12311yescharacteristic
145C2×C4×C131C2×D811yescharacteristic
146C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C131#13711yescharacteristic
148C8×C131—41no—
149C8×C131—42no—
150C8×C131—81no—
151C8×C131#12111yescharacteristic
152C8×C131#12111yescharacteristic
153C8×C131#12311yescharacteristic
154C8×C131#12411yescharacteristic
155C22×C131—41no—
156C22×C131—41no—
157C22×C131—81no—
158C22×C131—81no—
159C22×C131—161no—
160C22×C131#45211yescharacteristic
161C22×C131#46611yescharacteristic
162C22×C131#48211yescharacteristic
163C4×C131—41no—
164C4×C131—81no—
165C4×C131—161no—
166C4×C131#39411yescharacteristic
167C4×C131#44711yescharacteristic
168C4×C131#46811yescharacteristic
169C4×C131#48011yescharacteristic
170C2×C131—21no—
171C2×C131—21no—
172C2×C131—21no—
173C2×C131—81no—
174C2×C131—161no—
175C2×C131#203311yescharacteristic
176#13391C13111yesmaximal, characteristic, direct product factor, Sylow
177C131#1339111yescharacteristic, direct product factor, Sylow
178#3067C2×C13111yescharacteristic
179#2161C2×C13111yescharacteristic, complemented
180#2148C2×C13111yescharacteristic, complemented
181C2×#360C2×C13111yescharacteristic, complemented
182#2115C2×C13111yescharacteristic, complemented
183#1815C2×C13111yescharacteristic, complemented
184#1383C2×C13111yescharacteristic, complemented
185#575—21no—
186C2×#135C22×C13111yescharacteristic
187C2×#131C22×C13111yescharacteristic
188C2×M32C22×C13111yescharacteristic
189C2×M32C22×C13111yescharacteristic
190#473—21no—
191#472—21no—
192#471—22no—
193C2×#108C22×C13111yescharacteristic
194C2×#108C22×C13111yescharacteristic
195C2×#106C22×C13111yescharacteristic
196#417—21no—
197#413—21no—
198#368—22no—
199#362—21no—
200#361—21no—
201#360—22no—
202#349—22no—
203#343—21no—
204C2×#41—21no—
205C2×#41D4×C13111yescharacteristic
206#137—22no—
207#137—41no—
208AGL(1,ℤ/8)—22no—
209AGL(1,ℤ/8)—41no—
210#135—21no—
211#135—21no—
212#135—21no—
213#135—21no—
214#135—42no—
215C2×Q16D4×C13111yescharacteristic
216C2×SD16—21no—
217C2×D8D4×C13111yescharacteristic
218#131—21no—
219#131—21no—
220#131—21no—
221#131—21no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16—21no—
225C2×M16D4×C13111yescharacteristic
226C22×C8—21no—
227C22×C8C23×C13111yescharacteristic
228C2×C4⋊C4—21no—
229M32—21no—
230M32—21no—
231M32—21no—
232M32D4×C13112yes—
233C2×C16—21no—
234C2×C16—21no—
235#108—21no—
236#108—21no—
237#108—21no—
238#108D4×C13112yes—
239#106—21no—
240#106—21no—
241#103—41no—
242#102—41no—
243#101—22no—
244#100—22no—
245#41—21no—
246#41—21no—
247#41—21no—
248#41—21no—
249#41—41no—
250#41—41no—
251#41—41no—
252#41—41no—
253C2×Q8—21no—
254C2×Q8D8×C13111yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4D8×C13111yescharacteristic
259C22×C4—21no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4C2×D4×C13111yescharacteristic
263Q16—21no—
264Q16—21no—
265Q16—42no—
266SD16—42no—
267SD16—42no—
268SD16—41no—
269SD16—41no—
270D8—21no—
271D8—21no—
272D8—42no—
273M16—21no—
274M16—22no—
275M16—21no—
276M16—41no—
277M16—41no—
278M16—41no—
279M16—41no—
280M16—41no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8C2×D4×C13111yescharacteristic
287C2×C8C2×D4×C13111yescharacteristic
288C2×C8C2×D4×C13111yescharacteristic
289C2×C8#41×C13111yescharacteristic
290C2×C8#41×C13111yescharacteristic
291C2×C8#41×C13111yescharacteristic
292C4⋊C4—41no—
293C4⋊C4—41no—
294C16—22no—
295C16—41no—
296C23—21no—
297C23—41no—
298C23#135×C13111yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—41no—
303D4—21no—
304D4—21no—
305D4—41no—
306D4—41no—
307D4—41no—
308D4—41no—
309D4—81no—
310D4—81no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—161no—
319C2×C4#120×C13111yescharacteristic
320C2×C4#121×C13111yescharacteristic
321C2×C4#123×C13111yescharacteristic
322C2×C4C2×D8×C13111yescharacteristic
323C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
324C2×C4#137×C13111yescharacteristic
325C8—41no—
326C8—42no—
327C8—81no—
328C8#121×C13111yescharacteristic
329C8#121×C13111yescharacteristic
330C8#123×C13111yescharacteristic
331C8#124×C13111yescharacteristic
332C22—41no—
333C22—41no—
334C22—81no—
335C22—81no—
336C22—161no—
337C22#452×C13111yescharacteristic
338C22#466×C13111yescharacteristic
339C22#482×C13111yescharacteristic
340C4—41no—
341C4—81no—
342C4—161no—
343C4#394×C13111yescharacteristic
344C4#447×C13111yescharacteristic
345C4#468×C13111yescharacteristic
346C4#480×C13111yescharacteristic
347C2—21no—
348C2—21no—
349C2—21no—
350C2—81no—
351C2—161no—
352C2#2033×C13111yescharacteristic
subgroupG/H
center, socleC2×C131#2033
commutator, Frattini, cosocleC22×C8C23×C131
prime radical#3067×C131C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C22×C4×C131 ◁ C2×#131×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2161×C131C2semidirect
3. #2148×C131C2semidirect
4. C2×#360×C131C2semidirect
5. #2115×C131C2semidirect
6. #1815×C131C2semidirect
7. #1383×C131C2semidirect
176. #13391C131direct (N × H)
177. C131#13391direct (N × H)
179. #2161C2×C131semidirect
180. #2148C2×C131semidirect
181. C2×#360C2×C131semidirect
182. #2115C2×C131semidirect
183. #1815C2×C131semidirect
184. #1383C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3067×C1312
#2161×C1312
#2148×C1312
C2×#360×C1312
#2115×C1312
#1815×C1312
#1383×C1312
#13391131