Finite Group Databasebeta

← C131×#7710 #45693594

Subgroups — C131×#7710 #45693594

Order 33536.

570 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2850×C131C211yesmaximal, characteristic
2#1797×C131C211yesmaximal, characteristic, complemented
3#1728×C131C211yesmaximal, characteristic, complemented
4#1272×C131C212yesmaximal, complemented
5#1270×C131C212yesmaximal, complemented
6C22×M16×C131—21no—
7C2×#124×C131C411yescharacteristic
8C2×C22⋊Q8×C131C411yescharacteristic
9C2×#121×C131C411yescharacteristic
10C22×C42×C131C2211yescharacteristic
11C2×C4⋊C8×C131—21no—
12C2×C22⋊C8×C131—21no—
13#391×C131C2211yescharacteristic
14#390×C131C2211yescharacteristic
15#388×C131—21no—
16#388×C131—21no—
17#386×C131—21no—
18#386×C131—21no—
19#382×C131C411yescharacteristic
20#336×C131—21no—
21#336×C131C2212yes—
22#336×C131C2212yes—
23C22×Q8×C131C2×C411yescharacteristic
24C22×D4×C131—21no—
25C22×D4×C131C2×C411yescharacteristic
26C23×C4×C131C2×C411yescharacteristic
27C23×C4×C131D411yescharacteristic
28C23×C4×C131D411yescharacteristic
29C2×M16×C131—24no—
30C2×M16×C131—42no—
31C2×M16×C131—42no—
32C22×C8×C131—22no—
33C22×C8×C131—22no—
34#124×C131—42no—
35C22⋊Q8×C131—42no—
36#121×C131—42no—
37C2×C4⋊C4×C131—21no—
38C2×C4⋊C4×C131C2×C411yescharacteristic
39C2×C4⋊C4×C131C2×C411yescharacteristic
40C2×C22⋊C4×C131—21no—
41C2×C22⋊C4×C131—21no—
42C2×C22⋊C4×C131—21no—
43C2×C22⋊C4×C131—21no—
44C2×C22⋊C4×C131—21no—
45C2×C22⋊C4×C131—21no—
46C2×C42×C131—42no—
47C2×C42×C131C2×C411yescharacteristic
48C2×C42×C131D411yescharacteristic
49C2×C42×C131D411yescharacteristic
50C2×C42×C131C2311yescharacteristic
51C4⋊C8×C131—42no—
52C22⋊C8×C131—42no—
53#95×C131—21no—
54#95×C131—21no—
55#95×C131—21no—
56#95×C131—21no—
57C24×C131—21no—
58C24×C131C22⋊C411yescharacteristic
59C2×Q8×C131—22no—
60C2×Q8×C131—41no—
61C2×Q8×C131—41no—
62C2×D4×C131—22no—
63C2×D4×C131—41no—
64C2×D4×C131—41no—
65C2×D4×C131—42no—
66C2×D4×C131—42no—
67C2×D4×C131—42no—
68C22×C4×C131—22no—
69C22×C4×C131—22no—
70C22×C4×C131—21no—
71C22×C4×C131—21no—
72C22×C4×C131—22no—
73C22×C4×C131—22no—
74C22×C4×C131—21no—
75C22×C4×C131—21no—
76C22×C4×C131—21no—
77C22×C4×C131—21no—
78C22×C4×C131—21no—
79C22×C4×C131—41no—
80C22×C4×C131—41no—
81C22×C4×C131—41no—
82C22×C4×C131C22⋊C411yescharacteristic
83C22×C4×C131C22⋊C411yescharacteristic
84C22×C4×C131C22⋊C411yescharacteristic
85C22×C4×C131C22×C411yescharacteristic
86C22×C4×C131C2×D411yescharacteristic
87C22×C4×C131C2×D411yescharacteristic
88M16×C131—48no—
89C2×C8×C131—24no—
90C2×C8×C131—42no—
91C2×C8×C131—42no—
92C2×C8×C131—42no—
93C2×C8×C131—42no—
94C2×C8×C131—42no—
95C4⋊C4×C131—41no—
96C4⋊C4×C131—41no—
97C4⋊C4×C131—42no—
98C22⋊C4×C131—42no—
99C22⋊C4×C131—42no—
100C22⋊C4×C131—42no—
101C22⋊C4×C131—42no—
102C22⋊C4×C131—41no—
103C22⋊C4×C131—41no—
104C22⋊C4×C131—41no—
105C22⋊C4×C131—41no—
106C42×C131—22no—
107C42×C131—22no—
108C42×C131—41no—
109C42×C131—41no—
110C23×C131—21no—
111C23×C131—21no—
112C23×C131—21no—
113C23×C131—21no—
114C23×C131—21no—
115C23×C131—21no—
116C23×C131—41no—
117C23×C131—41no—
118C23×C131—41no—
119C23×C131—41no—
120C23×C131—41no—
121C23×C131—41no—
122C23×C131—41no—
123C23×C131#10412yes—
124C23×C131C2×C22⋊C411yescharacteristic
125Q8×C131—82no—
126D4×C131—82no—
127D4×C131—84no—
128C2×C4×C131—24no—
129C2×C4×C131—24no—
130C2×C4×C131—21no—
131C2×C4×C131—21no—
132C2×C4×C131—21no—
133C2×C4×C131—21no—
134C2×C4×C131—21no—
135C2×C4×C131—21no—
136C2×C4×C131—21no—
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—44no—
144C2×C4×C131—42no—
145C2×C4×C131—42no—
146C2×C4×C131—41no—
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×C131—41no—
154C2×C4×C131—41no—
155C2×C4×C131#9912yes—
156C2×C4×C131#10012yes—
157C2×C4×C131#13112yes—
158C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C131#13711yescharacteristic
161C2×C4×C131#13711yescharacteristic
162C8×C131—44no—
163C8×C131—82no—
164C22×C131—22no—
165C22×C131—22no—
166C22×C131—22no—
167C22×C131—41no—
168C22×C131—41no—
169C22×C131—41no—
170C22×C131—41no—
171C22×C131—81no—
172C22×C131—81no—
173C22×C131—81no—
174C22×C131—81no—
175C22×C131—81no—
176C22×C131—81no—
177C22×C131—81no—
178C22×C131#40811yescharacteristic
179C22×C131C2×#9911yescharacteristic
180C22×C131C2×#10011yescharacteristic
181C22×C131#41711yescharacteristic
182C22×C131#41711yescharacteristic
183C22×C131C2×#10411yescharacteristic
184C22×C131#42111yescharacteristic
185C4×C131—22no—
186C4×C131—22no—
187C4×C131—21no—
188C4×C131—22no—
189C4×C131—21no—
190C4×C131—21no—
191C4×C131—21no—
192C4×C131—41no—
193C4×C131—81no—
194C4×C131—81no—
195C4×C131—81no—
196C2×C131—42no—
197C2×C131—161no—
198C2×C131#147111yescharacteristic
199C2×C131#148311yescharacteristic
200C2×C131#149511yescharacteristic
201C2×C131#150411yescharacteristic
202C2×C131#151311yescharacteristic
203C2×C131#152711yescharacteristic
204C2×C131#156011yescharacteristic
205#7710C13111yesmaximal, characteristic, direct product factor, Sylow
206C131#771011yescharacteristic, direct product factor, Sylow
207#2850C2×C13111yescharacteristic
208#1797C2×C13111yescharacteristic, complemented
209#1728C2×C13111yescharacteristic, complemented
210#1272C2×C13112yescomplemented
211#1270C2×C13112yescomplemented
212C22×M16—21no—
213C2×#124C4×C13111yescharacteristic
214C2×C22⋊Q8C4×C13111yescharacteristic
215C2×#121C4×C13111yescharacteristic
216C22×C42C22×C13111yescharacteristic
217C2×C4⋊C8—21no—
218C2×C22⋊C8—21no—
219#391C22×C13111yescharacteristic
220#390C22×C13111yescharacteristic
221#388—21no—
222#388—21no—
223#386—21no—
224#386—21no—
225#382C4×C13111yescharacteristic
226#336—21no—
227#336C22×C13112yes—
228#336C22×C13112yes—
229C22×Q8C2×C4×C13111yescharacteristic
230C22×D4—21no—
231C22×D4C2×C4×C13111yescharacteristic
232C23×C4C2×C4×C13111yescharacteristic
233C23×C4D4×C13111yescharacteristic
234C23×C4D4×C13111yescharacteristic
235C2×M16—24no—
236C2×M16—42no—
237C2×M16—42no—
238C22×C8—22no—
239C22×C8—22no—
240#124—42no—
241C22⋊Q8—42no—
242#121—42no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4C2×C4×C13111yescharacteristic
245C2×C4⋊C4C2×C4×C13111yescharacteristic
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C42—42no—
253C2×C42C2×C4×C13111yescharacteristic
254C2×C42D4×C13111yescharacteristic
255C2×C42D4×C13111yescharacteristic
256C2×C42C23×C13111yescharacteristic
257C4⋊C8—42no—
258C22⋊C8—42no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263C24—21no—
264C24C22⋊C4×C13111yescharacteristic
265C2×Q8—22no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×D4—22no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—42no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4C22⋊C4×C13111yescharacteristic
289C22×C4C22⋊C4×C13111yescharacteristic
290C22×C4C22⋊C4×C13111yescharacteristic
291C22×C4C22×C4×C13111yescharacteristic
292C22×C4C2×D4×C13111yescharacteristic
293C22×C4C2×D4×C13111yescharacteristic
294M16—48no—
295C2×C8—24no—
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—42no—
300C2×C8—42no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C22⋊C4—42no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C42—22no—
313C42—22no—
314C42—41no—
315C42—41no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23#104×C13112yes—
330C23C2×C22⋊C4×C13111yescharacteristic
331Q8—82no—
332D4—82no—
333D4—84no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4#99×C13112yes—
362C2×C4#100×C13112yes—
363C2×C4#131×C13112yes—
364C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
365C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
366C2×C4#137×C13111yescharacteristic
367C2×C4#137×C13111yescharacteristic
368C8—44no—
369C8—82no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22#408×C13111yescharacteristic
385C22C2×#99×C13111yescharacteristic
386C22C2×#100×C13111yescharacteristic
387C22#417×C13111yescharacteristic
388C22#417×C13111yescharacteristic
389C22C2×#104×C13111yescharacteristic
390C22#421×C13111yescharacteristic
391C4—22no—
392C4—22no—
393C4—21no—
394C4—22no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—41no—
399C4—81no—
400C4—81no—
401C4—81no—
402C2—42no—
403C2—161no—
404C2#1471×C13111yescharacteristic
405C2#1483×C13111yescharacteristic
406C2#1495×C13111yescharacteristic
407C2#1504×C13111yescharacteristic
408C2#1513×C13111yescharacteristic
409C2#1527×C13111yescharacteristic
410C2#1560×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C2×C22⋊C4
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC2×#121×C131C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1797×C131C2semidirect
3. #1728×C131C2semidirect
4. #1272×C131C2semidirect
5. #1270×C131C2semidirect
205. #7710C131direct (N × H)
206. C131#7710direct (N × H)
208. #1797C2×C131semidirect
209. #1728C2×C131semidirect
210. #1272C2×C131semidirect
211. #1270C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2850×C1312
#1797×C1312
#1728×C1312
#1272×C1312
#1270×C1312
#7710131