Finite Group Databasebeta

← C131×#9214 #45695098

Subgroups — C131×#9214 #45695098

Order 33536.

428 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3107×C131C211yesmaximal, characteristic
2#2922×C131C211yesmaximal, characteristic
3#1526×C131C211yesmaximal, characteristic, complemented
4#1493×C131C211yesmaximal, characteristic, complemented
5#1489×C131C211yesmaximal, characteristic
6#1299×C131C211yesmaximal, characteristic, complemented
7#1278×C131C211yesmaximal, characteristic, complemented
8#533×C131C2211yescharacteristic
9C4×#41×C131C2211yescharacteristic
10#485×C131—21no—
11#475×C131C411yescharacteristic
12#474×C131C411yescharacteristic
13#462×C131C411yescharacteristic
14#461×C131C411yescharacteristic
15#452×C131—21no—
16C4×Q16×C131—21no—
17C4×SD16×C131—21no—
18#433×C131—22no—
19#431×C131—22no—
20#431×C131C2211yescharacteristic
21#424×C131—21no—
22#423×C131C2211yescharacteristic
23#408×C131—21no—
24C4×M16×C131C2211yescharacteristic
25C4×M16×C131C2211yescharacteristic
26C2×C4×C8×C131C2211yescharacteristic
27#330×C131—22no—
28Q8⋊C8×C131—21no—
29Q8⋊C8×C131—22no—
30D4⋊C8×C131—21no—
31C2×#41×C131D411yescharacteristic
32C2×Q16×C131—21no—
33C2×SD16×C131—21no—
34C2×M16×C131—21no—
35C2×M16×C131—21no—
36C2×M16×C131—21no—
37C22×C8×C131—21no—
38C4⋊Q8×C131C2×C411yescharacteristic
39C4⋊Q8×C131C2×C411yescharacteristic
40#125×C131—21no—
41C22⋊Q8×C131—21no—
42C22⋊Q8×C131—21no—
43C4×Q8×C131—21no—
44C4×Q8×C131—21no—
45C4×Q8×C131C2×C411yescharacteristic
46C4×Q8×C131D411yescharacteristic
47C4×D4×C131—21no—
48C4×D4×C131—21no—
49C4×D4×C131C2×C411yescharacteristic
50C4×D4×C131D411yescharacteristic
51#117×C131—21no—
52#117×C131—21no—
53#117×C131D411yescharacteristic
54C2×C42×C131—21no—
55C2×C42×C131C2311yescharacteristic
56#107×C131—21no—
57#106×C131—21no—
58C4⋊C8×C131—24no—
59C4⋊C8×C131—21no—
60C4⋊C8×C131—21no—
61C4⋊C8×C131C2×C411yescharacteristic
62C4⋊C8×C131C2×C411yescharacteristic
63#103×C131—21no—
64#103×C131—21no—
65#103×C131—21no—
66#102×C131—21no—
67C22⋊C8×C131—24no—
68C22⋊C8×C131—21no—
69#97×C131—21no—
70#97×C131D412yes—
71C4×C8×C131—21no—
72C4×C8×C131—21no—
73C4×C8×C131—21no—
74C4×C8×C131—21no—
75C4×C8×C131D412yes—
76#41×C131—41no—
77#41×C131—41no—
78C2×Q8×C131—21no—
79C2×Q8×C131—21no—
80C2×Q8×C131C22⋊C411yescharacteristic
81C2×D4×C131—21no—
82C2×D4×C131C22⋊C411yescharacteristic
83C22×C4×C131—21no—
84C22×C4×C131—21no—
85C22×C4×C131—21no—
86C22×C4×C131C2×D411yescharacteristic
87C22×C4×C131#4111yescharacteristic
88C22×C4×C131#4111yescharacteristic
89Q16×C131—42no—
90SD16×C131—42no—
91M16×C131—22no—
92M16×C131—41no—
93M16×C131—41no—
94M16×C131—41no—
95M16×C131—81no—
96C2×C8×C131—21no—
97C2×C8×C131—21no—
98C2×C8×C131—22no—
99C2×C8×C131—22no—
100C2×C8×C131—41no—
101C2×C8×C131—41no—
102C2×C8×C131—41no—
103C2×C8×C131—41no—
104C4⋊C4×C131—21no—
105C4⋊C4×C131—21no—
106C4⋊C4×C131—21no—
107C4⋊C4×C131—21no—
108C4⋊C4×C131—21no—
109C4⋊C4×C131—21no—
110C4⋊C4×C131—41no—
111C4⋊C4×C131—41no—
112C4⋊C4×C131C22⋊C411yescharacteristic
113C4⋊C4×C131C22⋊C411yescharacteristic
114C22⋊C4×C131—21no—
115C22⋊C4×C131—21no—
116C22⋊C4×C131—21no—
117C22⋊C4×C131—41no—
118C42×C131—21no—
119C42×C131—21no—
120C42×C131—21no—
121C42×C131—41no—
122C42×C131C22×C411yescharacteristic
123C42×C131C2×D411yescharacteristic
124C42×C131C2×D411yescharacteristic
125C42×C131C2×D411yescharacteristic
126C23×C131—21no—
127C23×C131#12311yescharacteristic
128Q8×C131—21no—
129Q8×C131—21no—
130Q8×C131—41no—
131Q8×C131—41no—
132Q8×C131—41no—
133Q8×C131—41no—
134D4×C131—21no—
135D4×C131—21no—
136D4×C131—42no—
137C2×C4×C131—21no—
138C2×C4×C131—21no—
139C2×C4×C131—21no—
140C2×C4×C131—21no—
141C2×C4×C131—21no—
142C2×C4×C131—21no—
143C2×C4×C131—21no—
144C2×C4×C131—21no—
145C2×C4×C131—21no—
146C2×C4×C131—42no—
147C2×C4×C131—41no—
148C2×C4×C131—41no—
149C2×C4×C131—41no—
150C2×C4×C131—41no—
151C2×C4×C131—41no—
152C2×C4×C131—41no—
153C2×C4×C131C2×C22⋊C411yescharacteristic
154C2×C4×C131C4×D411yescharacteristic
155C2×C4×C131C4×D411yescharacteristic
156C2×C4×C131#12011yescharacteristic
157C2×C4×C131#12111yescharacteristic
158C2×C4×C131#12111yescharacteristic
159C8×C131—42no—
160C8×C131—42no—
161C8×C131—42no—
162C8×C131—41no—
163C8×C131—41no—
164C8×C131—81no—
165C22×C131—21no—
166C22×C131—21no—
167C22×C131—21no—
168C22×C131—41no—
169C22×C131—41no—
170C22×C131—41no—
171C22×C131#38611yescharacteristic
172C4×C131—21no—
173C4×C131—21no—
174C4×C131—21no—
175C4×C131—41no—
176C4×C131—41no—
177C4×C131—41no—
178C4×C131—81no—
179C4×C131—81no—
180C4×C131#42111yescharacteristic
181C4×C131#42111yescharacteristic
182C4×C131#44311yescharacteristic
183C4×C131#44411yescharacteristic
184C4×C131#47111yescharacteristic
185C4×C131#47311yescharacteristic
186C2×C131—41no—
187C2×C131—81no—
188C2×C131#187611yescharacteristic
189C2×C131#189711yescharacteristic
190C2×C131#190811yescharacteristic
191#9214C13111yesmaximal, characteristic, direct product factor, Sylow
192C131#921411yescharacteristic, direct product factor, Sylow
193#3107C2×C13111yescharacteristic
194#2922C2×C13111yescharacteristic
195#1526C2×C13111yescharacteristic, complemented
196#1493C2×C13111yescharacteristic, complemented
197#1489C2×C13111yescharacteristic
198#1299C2×C13111yescharacteristic, complemented
199#1278C2×C13111yescharacteristic, complemented
200#533C22×C13111yescharacteristic
201C4×#41C22×C13111yescharacteristic
202#485—21no—
203#475C4×C13111yescharacteristic
204#474C4×C13111yescharacteristic
205#462C4×C13111yescharacteristic
206#461C4×C13111yescharacteristic
207#452—21no—
208C4×Q16—21no—
209C4×SD16—21no—
210#433—22no—
211#431—22no—
212#431C22×C13111yescharacteristic
213#424—21no—
214#423C22×C13111yescharacteristic
215#408—21no—
216C4×M16C22×C13111yescharacteristic
217C4×M16C22×C13111yescharacteristic
218C2×C4×C8C22×C13111yescharacteristic
219#330—22no—
220Q8⋊C8—21no—
221Q8⋊C8—22no—
222D4⋊C8—21no—
223C2×#41D4×C13111yescharacteristic
224C2×Q16—21no—
225C2×SD16—21no—
226C2×M16—21no—
227C2×M16—21no—
228C2×M16—21no—
229C22×C8—21no—
230C4⋊Q8C2×C4×C13111yescharacteristic
231C4⋊Q8C2×C4×C13111yescharacteristic
232#125—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×Q8C2×C4×C13111yescharacteristic
238C4×Q8D4×C13111yescharacteristic
239C4×D4—21no—
240C4×D4—21no—
241C4×D4C2×C4×C13111yescharacteristic
242C4×D4D4×C13111yescharacteristic
243#117—21no—
244#117—21no—
245#117D4×C13111yescharacteristic
246C2×C42—21no—
247C2×C42C23×C13111yescharacteristic
248#107—21no—
249#106—21no—
250C4⋊C8—24no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8C2×C4×C13111yescharacteristic
254C4⋊C8C2×C4×C13111yescharacteristic
255#103—21no—
256#103—21no—
257#103—21no—
258#102—21no—
259C22⋊C8—24no—
260C22⋊C8—21no—
261#97—21no—
262#97D4×C13112yes—
263C4×C8—21no—
264C4×C8—21no—
265C4×C8—21no—
266C4×C8—21no—
267C4×C8D4×C13112yes—
268#41—41no—
269#41—41no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8C22⋊C4×C13111yescharacteristic
273C2×D4—21no—
274C2×D4C22⋊C4×C13111yescharacteristic
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4C2×D4×C13111yescharacteristic
279C22×C4#41×C13111yescharacteristic
280C22×C4#41×C13111yescharacteristic
281Q16—42no—
282SD16—42no—
283M16—22no—
284M16—41no—
285M16—41no—
286M16—41no—
287M16—81no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4C22⋊C4×C13111yescharacteristic
305C4⋊C4C22⋊C4×C13111yescharacteristic
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—41no—
310C42—21no—
311C42—21no—
312C42—21no—
313C42—41no—
314C42C22×C4×C13111yescharacteristic
315C42C2×D4×C13111yescharacteristic
316C42C2×D4×C13111yescharacteristic
317C42C2×D4×C13111yescharacteristic
318C23—21no—
319C23#123×C13111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—41no—
323Q8—41no—
324Q8—41no—
325Q8—41no—
326D4—21no—
327D4—21no—
328D4—42no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4C2×C22⋊C4×C13111yescharacteristic
346C2×C4C4×D4×C13111yescharacteristic
347C2×C4C4×D4×C13111yescharacteristic
348C2×C4#120×C13111yescharacteristic
349C2×C4#121×C13111yescharacteristic
350C2×C4#121×C13111yescharacteristic
351C8—42no—
352C8—42no—
353C8—42no—
354C8—41no—
355C8—41no—
356C8—81no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22#386×C13111yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—81no—
371C4—81no—
372C4#421×C13111yescharacteristic
373C4#421×C13111yescharacteristic
374C4#443×C13111yescharacteristic
375C4#444×C13111yescharacteristic
376C4#471×C13111yescharacteristic
377C4#473×C13111yescharacteristic
378C2—41no—
379C2—81no—
380C2#1876×C13111yescharacteristic
381C2#1897×C13111yescharacteristic
382C2#1908×C13111yescharacteristic
subgroupG/H
centerC2×C4×C131#121
commutatorC42C22×C4×C131
Frattini, cosocleC2×C42C23×C131
socleC22×C131#386
prime radicalC2×#41×C131D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1526×C131C2semidirect
4. #1493×C131C2semidirect
6. #1299×C131C2semidirect
7. #1278×C131C2semidirect
191. #9214C131direct (N × H)
192. C131#9214direct (N × H)
195. #1526C2×C131semidirect
196. #1493C2×C131semidirect
198. #1299C2×C131semidirect
199. #1278C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3107×C1312
#2922×C1312
#1526×C1312
#1493×C1312
#1489×C1312
#1299×C1312
#1278×C1312
#9214131