Finite Group Databasebeta

← C131×#10224 #45696108

Subgroups — C131×#10224 #45696108

Order 33536.

462 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3230×C131C211yesmaximal, characteristic
2#3209×C131C211yesmaximal, characteristic
3#3162×C131C211yesmaximal, characteristic
4#1993×C131C211yesmaximal, characteristic
5#1518×C131C211yesmaximal, characteristic
6#1518×C131C211yesmaximal, characteristic
7#1281×C131C211yesmaximal, characteristic
8#533×C131C2211yescharacteristic
9#533×C131C2211yescharacteristic
10C2×C4⋊Q8×C131C2211yescharacteristic
11#501×C131—21no—
12#501×C131—21no—
13#501×C131—21no—
14#501×C131—21no—
15#500×C131—21no—
16#494×C131—21no—
17#487×C131—21no—
18#487×C131—21no—
19#484×C131—22no—
20#477×C131—22no—
21#462×C131—22no—
22#451×C131—22no—
23#431×C131C2211yescharacteristic
24#431×C131C2211yescharacteristic
25#427×C131—22no—
26C2×#97×C131C2211yescharacteristic
27#382×C131C2211yescharacteristic
28#340×C131—22no—
29#328×C131—22no—
30#328×C131—22no—
31C22×Q8×C131—21no—
32C2×Q16×C131—24no—
33C22×C8×C131D412yes—
34C4⋊Q8×C131—21no—
35C4⋊Q8×C131—21no—
36C4⋊Q8×C131—21no—
37C4⋊Q8×C131D412yes—
38C4⋊Q8×C131D411yescharacteristic
39C4⋊Q8×C131D411yescharacteristic
40C4⋊Q8×C131D411yescharacteristic
41C4⋊Q8×C131D411yescharacteristic
42#125×C131—21no—
43#125×C131—21no—
44C22⋊Q8×C131—21no—
45C22⋊Q8×C131—21no—
46C22⋊Q8×C131—21no—
47C22⋊Q8×C131—21no—
48C4×Q8×C131—21no—
49C4×Q8×C131—21no—
50C4×Q8×C131—21no—
51C4×Q8×C131—21no—
52#117×C131—21no—
53#117×C131—21no—
54C2×C4⋊C4×C131—21no—
55C2×C4⋊C4×C131—21no—
56C2×C4⋊C4×C131—21no—
57C2×C42×C131C2311yescharacteristic
58#107×C131—22no—
59#107×C131—22no—
60#107×C131—24no—
61#106×C131—22no—
62#106×C131—22no—
63C4⋊C8×C131—21no—
64C4⋊C8×C131—21no—
65#103×C131—24no—
66#103×C131—24no—
67C22⋊C8×C131D412yes—
68C22⋊C8×C131D412yes—
69#97×C131—21no—
70#97×C131—21no—
71C4×C8×C131—21no—
72C4×C8×C131—21no—
73#95×C131—21no—
74#95×C131—21no—
75C2×Q8×C131—21no—
76C2×Q8×C131—22no—
77C2×Q8×C131—21no—
78C2×Q8×C131—21no—
79C2×Q8×C131—21no—
80C2×Q8×C131—41no—
81C2×Q8×C131—82no—
82C22×C4×C131—41no—
83C22×C4×C131—41no—
84C22×C4×C131C2×D411yescharacteristic
85C22×C4×C131C2×D411yescharacteristic
86C22×C4×C131C2×D411yescharacteristic
87Q16×C131—84no—
88C2×C8×C131—22no—
89C2×C8×C131—22no—
90C2×C8×C131—22no—
91C2×C8×C131—22no—
92C2×C8×C131Q1614yescomplemented
93C4⋊C4×C131—21no—
94C4⋊C4×C131—22no—
95C4⋊C4×C131—21no—
96C4⋊C4×C131—21no—
97C4⋊C4×C131—21no—
98C4⋊C4×C131—21no—
99C4⋊C4×C131—21no—
100C4⋊C4×C131—22no—
101C4⋊C4×C131—21no—
102C4⋊C4×C131—21no—
103C4⋊C4×C131—41no—
104C4⋊C4×C131—41no—
105C4⋊C4×C131—41no—
106C4⋊C4×C131—41no—
107C4⋊C4×C131—41no—
108C4⋊C4×C131—41no—
109C4⋊C4×C131—42no—
110C22⋊C4×C131—41no—
111C22⋊C4×C131—41no—
112C42×C131—41no—
113C42×C131—41no—
114C42×C131C2×D411yescharacteristic
115C42×C131C2×D411yescharacteristic
116C42×C131C2×D411yescharacteristic
117C42×C131#4111yescharacteristic
118C23×C131#12711yescharacteristic
119Q8×C131—42no—
120Q8×C131—44no—
121Q8×C131—42no—
122Q8×C131—81no—
123Q8×C131—81no—
124Q8×C131—82no—
125C2×C4×C131—41no—
126C2×C4×C131—41no—
127C2×C4×C131—41no—
128C2×C4×C131—41no—
129C2×C4×C131—41no—
130C2×C4×C131—41no—
131C2×C4×C131—42no—
132C2×C4×C131—82no—
133C2×C4×C131—81no—
134C2×C4×C131—81no—
135C2×C4×C131—81no—
136C2×C4×C131#12011yescharacteristic
137C2×C4×C131#12011yescharacteristic
138C2×C4×C131#12011yescharacteristic
139C2×C4×C131#12111yescharacteristic
140C2×C4×C131#12111yescharacteristic
141C2×C4×C131#12111yescharacteristic
142C2×C4×C131C2×Q1612yes—
143C2×C4×C131#13712yes—
144C8×C131—24no—
145C8×C131—42no—
146C8×C131—42no—
147C22×C131—21no—
148C22×C131—21no—
149C22×C131#39211yescharacteristic
150C22×C131#49411yescharacteristic
151C22×C131#49711yescharacteristic
152C4×C131—21no—
153C4×C131—21no—
154C4×C131—21no—
155C4×C131—21no—
156C4×C131—82no—
157C4×C131—81no—
158C4×C131—81no—
159C4×C131—81no—
160C4×C131—81no—
161C4×C131—161no—
162C4×C131#45112yes—
163C4×C131#46212yes—
164C2×C131—21no—
165C2×C131—21no—
166C2×C131#200811yescharacteristic
167C2×C131#200911yescharacteristic
168C2×C131#201611yescharacteristic
169#10224C13111yesmaximal, characteristic, direct product factor, Sylow
170C131#1022411yescharacteristic, direct product factor, Sylow
171#3230C2×C13111yescharacteristic
172#3209C2×C13111yescharacteristic
173#3162C2×C13111yescharacteristic
174#1993C2×C13111yescharacteristic
175#1518C2×C13111yescharacteristic
176#1518C2×C13111yescharacteristic
177#1281C2×C13111yescharacteristic
178#533C22×C13111yescharacteristic
179#533C22×C13111yescharacteristic
180C2×C4⋊Q8C22×C13111yescharacteristic
181#501—21no—
182#501—21no—
183#501—21no—
184#501—21no—
185#500—21no—
186#494—21no—
187#487—21no—
188#487—21no—
189#484—22no—
190#477—22no—
191#462—22no—
192#451—22no—
193#431C22×C13111yescharacteristic
194#431C22×C13111yescharacteristic
195#427—22no—
196C2×#97C22×C13111yescharacteristic
197#382C22×C13111yescharacteristic
198#340—22no—
199#328—22no—
200#328—22no—
201C22×Q8—21no—
202C2×Q16—24no—
203C22×C8D4×C13112yes—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8D4×C13112yes—
208C4⋊Q8D4×C13111yescharacteristic
209C4⋊Q8D4×C13111yescharacteristic
210C4⋊Q8D4×C13111yescharacteristic
211C4⋊Q8D4×C13111yescharacteristic
212#125—21no—
213#125—21no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218C4×Q8—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222#117—21no—
223#117—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C42C23×C13111yescharacteristic
228#107—22no—
229#107—22no—
230#107—24no—
231#106—22no—
232#106—22no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235#103—24no—
236#103—24no—
237C22⋊C8D4×C13112yes—
238C22⋊C8D4×C13112yes—
239#97—21no—
240#97—21no—
241C4×C8—21no—
242C4×C8—21no—
243#95—21no—
244#95—21no—
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—41no—
251C2×Q8—82no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4C2×D4×C13111yescharacteristic
255C22×C4C2×D4×C13111yescharacteristic
256C22×C4C2×D4×C13111yescharacteristic
257Q16—84no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8Q16×C13114yescomplemented
263C4⋊C4—21no—
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C42—41no—
283C42—41no—
284C42C2×D4×C13111yescharacteristic
285C42C2×D4×C13111yescharacteristic
286C42C2×D4×C13111yescharacteristic
287C42#41×C13111yescharacteristic
288C23#127×C13111yescharacteristic
289Q8—42no—
290Q8—44no—
291Q8—42no—
292Q8—81no—
293Q8—81no—
294Q8—82no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—82no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4#120×C13111yescharacteristic
307C2×C4#120×C13111yescharacteristic
308C2×C4#120×C13111yescharacteristic
309C2×C4#121×C13111yescharacteristic
310C2×C4#121×C13111yescharacteristic
311C2×C4#121×C13111yescharacteristic
312C2×C4C2×Q16×C13112yes—
313C2×C4#137×C13112yes—
314C8—24no—
315C8—42no—
316C8—42no—
317C22—21no—
318C22—21no—
319C22#392×C13111yescharacteristic
320C22#494×C13111yescharacteristic
321C22#497×C13111yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—82no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4—161no—
332C4#451×C13112yes—
333C4#462×C13112yes—
334C2—21no—
335C2—21no—
336C2#2008×C13111yescharacteristic
337C2#2009×C13111yescharacteristic
338C2#2016×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#392
commutator, Frattini, cosocleC2×C42C23×C131
prime radicalC23×C131#127
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
92. C2×C8×C131Q16semidirect
169. #10224C131direct (N × H)
170. C131#10224direct (N × H)
262. C2×C8Q16×C131semidirect

Maximal subgroups

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

subgroupindex
#3230×C1312
#3209×C1312
#3162×C1312
#1993×C1312
#1518×C1312
#1281×C1312
#10224131