Finite Group Databasebeta

← C131×#10551 #45696435

Subgroups — C131×#10551 #45696435

Order 33536.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3141×C131C211yesmaximal, characteristic
2#1950×C131C211yesmaximal, characteristic, complemented
3#1549×C131C211yesmaximal, characteristic, complemented
4#1547×C131C211yesmaximal, characteristic
5C2×#333×C131C211yesmaximal, characteristic, complemented
6#1480×C131C211yesmaximal, characteristic
7#1283×C131C211yesmaximal, characteristic, complemented
8#532×C131C2211yescharacteristic
9C2×C4⋊Q8×C131C2211yescharacteristic
10#489×C131—22no—
11#487×C131—21no—
12#486×C131—21no—
13#431×C131C2211yescharacteristic
14C2×#108×C131—21no—
15#423×C131C2211yescharacteristic
16C2×C4⋊C8×C131C2211yescharacteristic
17C2×C4⋊C8×C131C2211yescharacteristic
18#417×C131—21no—
19#417×C131—21no—
20C4×M16×C131C2211yescharacteristic
21#341×C131—21no—
22#333×C131—22no—
23#332×C131—21no—
24#332×C131—22no—
25#331×C131—21no—
26D4⋊C8×C131—22no—
27C2×#41×C131—21no—
28C22×Q8×C131—21no—
29C2×M16×C131—21no—
30C2×M16×C131D411yescharacteristic
31C2×M16×C131D411yescharacteristic
32C22×C8×C131—21no—
33C22×C8×C131—21no—
34C4⋊Q8×C131—21no—
35C4⋊Q8×C131—21no—
36C4⋊Q8×C131—21no—
37C4⋊Q8×C131D411yescharacteristic
38C4⋊Q8×C131D412yes—
39#127×C131D411yescharacteristic
40#124×C131—21no—
41#121×C131—21no—
42#121×C131—21no—
43C4×D4×C131—21no—
44C4×D4×C131—21no—
45C2×C4⋊C4×C131—21no—
46C2×C4⋊C4×C131—21no—
47C2×C42×C131C2311yescharacteristic
48#108×C131—42no—
49C4⋊C8×C131—21no—
50C4⋊C8×C131—21no—
51C4⋊C8×C131—21no—
52C4⋊C8×C131—21no—
53C4⋊C8×C131—21no—
54C4⋊C8×C131—21no—
55C4⋊C8×C131D412yes—
56#103×C131—22no—
57#103×C131—22no—
58#102×C131—22no—
59#102×C131—22no—
60C22⋊C8×C131—21no—
61#97×C131—21no—
62C4×C8×C131—21no—
63C4×C8×C131—21no—
64#41×C131—41no—
65#41×C131—41no—
66#41×C131—41no—
67#41×C131—41no—
68C2×Q8×C131—21no—
69C2×Q8×C131—22no—
70C2×Q8×C131—41no—
71C2×Q8×C131—82no—
72C2×D4×C131—21no—
73C2×D4×C131—21no—
74C2×D4×C131—21no—
75C2×D4×C131—41no—
76C22×C4×C131—41no—
77C22×C4×C131—41no—
78C22×C4×C131C2×D411yescharacteristic
79C22×C4×C131#4111yescharacteristic
80C22×C4×C131#4111yescharacteristic
81M16×C131—21no—
82M16×C131—21no—
83M16×C131—21no—
84M16×C131—21no—
85M16×C131—41no—
86M16×C131—41no—
87C2×C8×C131—21no—
88C2×C8×C131—21no—
89C2×C8×C131—22no—
90C2×C8×C131—41no—
91C2×C8×C131—41no—
92C2×C8×C131—41no—
93C2×C8×C131—41no—
94C2×C8×C131—41no—
95C2×C8×C131—81no—
96C4⋊C4×C131—22no—
97C4⋊C4×C131—21no—
98C4⋊C4×C131—22no—
99C4⋊C4×C131—21no—
100C4⋊C4×C131—41no—
101C4⋊C4×C131—41no—
102C22⋊C4×C131—41no—
103C22⋊C4×C131—41no—
104C42×C131C2×D411yescharacteristic
105C42×C131C2×D411yescharacteristic
106C42×C131C2×D411yescharacteristic
107C42×C131#4111yescharacteristic
108C23×C131—41no—
109C23×C131#12411yescharacteristic
110Q8×C131—41no—
111Q8×C131—41no—
112Q8×C131—82no—
113Q8×C131—82no—
114D4×C131—41no—
115D4×C131—41no—
116D4×C131—41no—
117D4×C131—41no—
118D4×C131—81no—
119D4×C131—81no—
120D4×C131—81no—
121C2×C4×C131—21no—
122C2×C4×C131—21no—
123C2×C4×C131—41no—
124C2×C4×C131—41no—
125C2×C4×C131—42no—
126C2×C4×C131—82no—
127C2×C4×C131—81no—
128C2×C4×C131—81no—
129C2×C4×C131#12011yescharacteristic
130C2×C4×C131#12111yescharacteristic
131C2×C4×C131#12111yescharacteristic
132C2×C4×C131#12111yescharacteristic
133C2×C4×C131#12311yescharacteristic
134C2×C4×C131#12311yescharacteristic
135C2×C4×C131#13511yescharacteristic
136C2×C4×C131#13511yescharacteristic
137C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C131#13711yescharacteristic
139C8×C131—41no—
140C8×C131—41no—
141C8×C131—42no—
142C8×C131—81no—
143C8×C131—81no—
144C8×C131—81no—
145C22×C131—21no—
146C22×C131—21no—
147C22×C131—81no—
148C22×C131—81no—
149C22×C131—81no—
150C22×C131#39411yescharacteristic
151C22×C131#48811yescharacteristic
152C22×C131#48911yescharacteristic
153C4×C131—21no—
154C4×C131—21no—
155C4×C131—21no—
156C4×C131—82no—
157C4×C131—81no—
158C4×C131#44911yescharacteristic
159C4×C131#45211yescharacteristic
160C4×C131#46311yescharacteristic
161C4×C131#46411yescharacteristic
162C4×C131#47111yescharacteristic
163C4×C131#47311yescharacteristic
164C2×C131—21no—
165C2×C131—21no—
166C2×C131—161no—
167C2×C131#204211yescharacteristic
168C2×C131#204811yescharacteristic
169C2×C131#205211yescharacteristic
170#10551C13111yesmaximal, characteristic, direct product factor, Sylow
171C131#1055111yescharacteristic, direct product factor, Sylow
172#3141C2×C13111yescharacteristic
173#1950C2×C13111yescharacteristic, complemented
174#1549C2×C13111yescharacteristic, complemented
175#1547C2×C13111yescharacteristic
176C2×#333C2×C13111yescharacteristic, complemented
177#1480C2×C13111yescharacteristic
178#1283C2×C13111yescharacteristic, complemented
179#532C22×C13111yescharacteristic
180C2×C4⋊Q8C22×C13111yescharacteristic
181#489—22no—
182#487—21no—
183#486—21no—
184#431C22×C13111yescharacteristic
185C2×#108—21no—
186#423C22×C13111yescharacteristic
187C2×C4⋊C8C22×C13111yescharacteristic
188C2×C4⋊C8C22×C13111yescharacteristic
189#417—21no—
190#417—21no—
191C4×M16C22×C13111yescharacteristic
192#341—21no—
193#333—22no—
194#332—21no—
195#332—22no—
196#331—21no—
197D4⋊C8—22no—
198C2×#41—21no—
199C22×Q8—21no—
200C2×M16—21no—
201C2×M16D4×C13111yescharacteristic
202C2×M16D4×C13111yescharacteristic
203C22×C8—21no—
204C22×C8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8D4×C13112yes—
209C4⋊Q8D4×C13111yescharacteristic
210#127D4×C13111yescharacteristic
211#124—21no—
212#121—21no—
213#121—21no—
214C4×D4—21no—
215C4×D4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C42C23×C13111yescharacteristic
219#108—42no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8D4×C13112yes—
227#103—22no—
228#103—22no—
229#102—22no—
230#102—22no—
231C22⋊C8—21no—
232#97—21no—
233C4×C8—21no—
234C4×C8—21no—
235#41—41no—
236#41—41no—
237#41—41no—
238#41—41no—
239C2×Q8—21no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×Q8—82no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4C2×D4×C13111yescharacteristic
250C22×C4#41×C13111yescharacteristic
251C22×C4#41×C13111yescharacteristic
252M16—21no—
253M16—21no—
254M16—21no—
255M16—21no—
256M16—41no—
257M16—41no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—81no—
267C4⋊C4—22no—
268C4⋊C4—21no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C42C2×D4×C13111yescharacteristic
276C42C2×D4×C13111yescharacteristic
277C42C2×D4×C13111yescharacteristic
278C42#41×C13111yescharacteristic
279C23—41no—
280C23#124×C13111yescharacteristic
281Q8—41no—
282Q8—41no—
283Q8—82no—
284Q8—82no—
285D4—41no—
286D4—41no—
287D4—41no—
288D4—41no—
289D4—81no—
290D4—81no—
291D4—81no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—82no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4#120×C13111yescharacteristic
301C2×C4#121×C13111yescharacteristic
302C2×C4#121×C13111yescharacteristic
303C2×C4#121×C13111yescharacteristic
304C2×C4#123×C13111yescharacteristic
305C2×C4#123×C13111yescharacteristic
306C2×C4#135×C13111yescharacteristic
307C2×C4#135×C13111yescharacteristic
308C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
309C2×C4#137×C13111yescharacteristic
310C8—41no—
311C8—41no—
312C8—42no—
313C8—81no—
314C8—81no—
315C8—81no—
316C22—21no—
317C22—21no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22#394×C13111yescharacteristic
322C22#488×C13111yescharacteristic
323C22#489×C13111yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—81no—
328C4—82no—
329C4#449×C13111yescharacteristic
330C4#452×C13111yescharacteristic
331C4#463×C13111yescharacteristic
332C4#464×C13111yescharacteristic
333C4#471×C13111yescharacteristic
334C4#473×C13111yescharacteristic
335C2—21no—
336C2—21no—
337C2—161no—
338C2#2042×C13111yescharacteristic
339C2#2048×C13111yescharacteristic
340C2#2052×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#394
commutator, Frattini, cosocleC2×C42C23×C131
prime radical#532×C131C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1950×C131C2semidirect
3. #1549×C131C2semidirect
5. C2×#333×C131C2semidirect
7. #1283×C131C2semidirect
170. #10551C131direct (N × H)
171. C131#10551direct (N × H)
173. #1950C2×C131semidirect
174. #1549C2×C131semidirect
176. C2×#333C2×C131semidirect
178. #1283C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3141×C1312
#1950×C1312
#1549×C1312
#1547×C1312
C2×#333×C1312
#1480×C1312
#1283×C1312
#10551131