Finite Group Databasebeta

← C131×#10426 #45696310

Subgroups — C131×#10426 #45696310

Order 33536.

444 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2820×C131C211yesmaximal, characteristic
2#1992×C131C211yesmaximal, characteristic, complemented
3#1959×C131C211yesmaximal, characteristic
4#1836×C131C211yesmaximal, characteristic, complemented
5C2×#330×C131C211yesmaximal, characteristic, complemented
6C2×#329×C131C211yesmaximal, characteristic
7#1295×C131C211yesmaximal, characteristic, complemented
8C2×#125×C131C2211yescharacteristic
9C2×#124×C131C2211yescharacteristic
10C2×#103×C131—21no—
11C2×#102×C131—21no—
12C2×#97×C131C2211yescharacteristic
13C2×#97×C131C2211yescharacteristic
14C2×#97×C131C2211yescharacteristic
15#399×C131—21no—
16#397×C131—21no—
17#396×C131—21no—
18#396×C131—21no—
19#395×C131—21no—
20#394×C131—21no—
21#384×C131C2211yescharacteristic
22#382×C131C2211yescharacteristic
23#340×C131—21no—
24#340×C131—21no—
25#340×C131—21no—
26#340×C131—21no—
27#330×C131—22no—
28#329×C131—22no—
29C22×Q8×C131D411yescharacteristic
30C22×D4×C131D411yescharacteristic
31C22×C8×C131—21no—
32C22×C8×C131—21no—
33C22×C8×C131—21no—
34#125×C131—21no—
35#125×C131—21no—
36#125×C131—21no—
37#125×C131—21no—
38#124×C131—21no—
39#124×C131—21no—
40#124×C131—21no—
41#124×C131—21no—
42C2×C4⋊C4×C131—21no—
43C2×C4⋊C4×C131—21no—
44C2×C4⋊C4×C131—21no—
45C2×C4⋊C4×C131—21no—
46C2×C4⋊C4×C131—21no—
47C2×C4⋊C4×C131—21no—
48C2×C4⋊C4×C131—21no—
49C2×C4⋊C4×C131D411yescharacteristic
50C2×C4⋊C4×C131D411yescharacteristic
51C2×C4⋊C4×C131D411yescharacteristic
52C2×C4⋊C4×C131D411yescharacteristic
53C2×C22⋊C4×C131—21no—
54C2×C22⋊C4×C131—21no—
55C2×C22⋊C4×C131—21no—
56C2×C22⋊C4×C131—21no—
57C2×C22⋊C4×C131—21no—
58C2×C22⋊C4×C131—21no—
59C2×C42×C131C2311yescharacteristic
60#103×C131—42no—
61#102×C131—42no—
62#97×C131—21no—
63#97×C131—21no—
64#97×C131—21no—
65#97×C131—21no—
66#97×C131—21no—
67#97×C131D412yes—
68#95×C131—21no—
69#95×C131—21no—
70#95×C131—21no—
71#95×C131—21no—
72C24×C131—21no—
73C2×Q8×C131—21no—
74C2×Q8×C131—21no—
75C2×Q8×C131—41no—
76C2×Q8×C131—41no—
77C2×D4×C131—21no—
78C2×D4×C131—21no—
79C2×D4×C131—41no—
80C2×D4×C131—41no—
81C22×C4×C131—21no—
82C22×C4×C131—21no—
83C22×C4×C131—21no—
84C22×C4×C131—21no—
85C22×C4×C131—21no—
86C22×C4×C131—41no—
87C22×C4×C131C2×D411yescharacteristic
88C22×C4×C131C2×D411yescharacteristic
89C22×C4×C131C2×D411yescharacteristic
90C2×C8×C131—22no—
91C2×C8×C131—22no—
92C2×C8×C131—22no—
93C2×C8×C131—41no—
94C2×C8×C131—41no—
95C2×C8×C131—41no—
96C2×C8×C131—41no—
97C2×C8×C131—41no—
98C2×C8×C131—41no—
99C4⋊C4×C131—21no—
100C4⋊C4×C131—21no—
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—42no—
108C4⋊C4×C131—42no—
109C4⋊C4×C131—41no—
110C4⋊C4×C131—41no—
111C4⋊C4×C131—41no—
112C4⋊C4×C131—41no—
113C4⋊C4×C131—81no—
114C4⋊C4×C131—81no—
115C22⋊C4×C131—41no—
116C22⋊C4×C131—41no—
117C22⋊C4×C131—41no—
118C22⋊C4×C131—41no—
119C22⋊C4×C131—81no—
120C22⋊C4×C131—81no—
121C22⋊C4×C131—81no—
122C22⋊C4×C131—81no—
123C42×C131C2×D411yescharacteristic
124C42×C131#4111yescharacteristic
125C42×C131#4111yescharacteristic
126C42×C131#4111yescharacteristic
127C23×C131—41no—
128C23×C131—41no—
129C23×C131—41no—
130C23×C131—41no—
131C23×C131—41no—
132C23×C131—41no—
133C23×C131—41no—
134C23×C131#12011yescharacteristic
135Q8×C131—42no—
136Q8×C131—81no—
137D4×C131—42no—
138D4×C131—81no—
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—41no—
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—41no—
156C2×C4×C131—41no—
157C2×C4×C131—41no—
158C2×C4×C131—41no—
159C2×C4×C131—41no—
160C2×C4×C131—81no—
161C2×C4×C131—81no—
162C2×C4×C131—81no—
163C2×C4×C131#12111yescharacteristic
164C2×C4×C131#12111yescharacteristic
165C2×C4×C131#12111yescharacteristic
166C2×C4×C131#12311yescharacteristic
167C2×C4×C131#12311yescharacteristic
168C2×C4×C131#12411yescharacteristic
169C8×C131—42no—
170C8×C131—42no—
171C8×C131—42no—
172C22×C131—81no—
173C22×C131—81no—
174C22×C131—81no—
175C22×C131—81no—
176C22×C131—81no—
177C22×C131—81no—
178C22×C131—81no—
179C22×C131#39411yescharacteristic
180C22×C131#45311yescharacteristic
181C22×C131#45411yescharacteristic
182C22×C131#45411yescharacteristic
183C22×C131#45511yescharacteristic
184C22×C131#45511yescharacteristic
185C22×C131#45611yescharacteristic
186C4×C131—21no—
187C4×C131—21no—
188C4×C131—21no—
189C4×C131—21no—
190C4×C131—21no—
191C4×C131—21no—
192C4×C131—81no—
193C4×C131—81no—
194C4×C131—81no—
195C4×C131—81no—
196C4×C131—81no—
197C4×C131—161no—
198C2×C131—161no—
199C2×C131#165711yescharacteristic
200C2×C131#166111yescharacteristic
201C2×C131#166211yescharacteristic
202C2×C131#166411yescharacteristic
203C2×C131#203711yescharacteristic
204C2×C131#203811yescharacteristic
205C2×C131#204011yescharacteristic
206#10426C13111yesmaximal, characteristic, direct product factor, Sylow
207C131#1042611yescharacteristic, direct product factor, Sylow
208#2820C2×C13111yescharacteristic
209#1992C2×C13111yescharacteristic, complemented
210#1959C2×C13111yescharacteristic
211#1836C2×C13111yescharacteristic, complemented
212C2×#330C2×C13111yescharacteristic, complemented
213C2×#329C2×C13111yescharacteristic
214#1295C2×C13111yescharacteristic, complemented
215C2×#125C22×C13111yescharacteristic
216C2×#124C22×C13111yescharacteristic
217C2×#103—21no—
218C2×#102—21no—
219C2×#97C22×C13111yescharacteristic
220C2×#97C22×C13111yescharacteristic
221C2×#97C22×C13111yescharacteristic
222#399—21no—
223#397—21no—
224#396—21no—
225#396—21no—
226#395—21no—
227#394—21no—
228#384C22×C13111yescharacteristic
229#382C22×C13111yescharacteristic
230#340—21no—
231#340—21no—
232#340—21no—
233#340—21no—
234#330—22no—
235#329—22no—
236C22×Q8D4×C13111yescharacteristic
237C22×D4D4×C13111yescharacteristic
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241#125—21no—
242#125—21no—
243#125—21no—
244#125—21no—
245#124—21no—
246#124—21no—
247#124—21no—
248#124—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4D4×C13111yescharacteristic
257C2×C4⋊C4D4×C13111yescharacteristic
258C2×C4⋊C4D4×C13111yescharacteristic
259C2×C4⋊C4D4×C13111yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C42C23×C13111yescharacteristic
267#103—42no—
268#102—42no—
269#97—21no—
270#97—21no—
271#97—21no—
272#97—21no—
273#97—21no—
274#97D4×C13112yes—
275#95—21no—
276#95—21no—
277#95—21no—
278#95—21no—
279C24—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—41no—
287C2×D4—41no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—41no—
294C22×C4C2×D4×C13111yescharacteristic
295C22×C4C2×D4×C13111yescharacteristic
296C22×C4C2×D4×C13111yescharacteristic
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—81no—
321C4⋊C4—81no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—81no—
327C22⋊C4—81no—
328C22⋊C4—81no—
329C22⋊C4—81no—
330C42C2×D4×C13111yescharacteristic
331C42#41×C13111yescharacteristic
332C42#41×C13111yescharacteristic
333C42#41×C13111yescharacteristic
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23#120×C13111yescharacteristic
342Q8—42no—
343Q8—81no—
344D4—42no—
345D4—81no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
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—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4#121×C13111yescharacteristic
371C2×C4#121×C13111yescharacteristic
372C2×C4#121×C13111yescharacteristic
373C2×C4#123×C13111yescharacteristic
374C2×C4#123×C13111yescharacteristic
375C2×C4#124×C13111yescharacteristic
376C8—42no—
377C8—42no—
378C8—42no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22#394×C13111yescharacteristic
387C22#453×C13111yescharacteristic
388C22#454×C13111yescharacteristic
389C22#454×C13111yescharacteristic
390C22#455×C13111yescharacteristic
391C22#455×C13111yescharacteristic
392C22#456×C13111yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—81no—
403C4—81no—
404C4—161no—
405C2—161no—
406C2#1657×C13111yescharacteristic
407C2#1661×C13111yescharacteristic
408C2#1662×C13111yescharacteristic
409C2#1664×C13111yescharacteristic
410C2#2037×C13111yescharacteristic
411C2#2038×C13111yescharacteristic
412C2#2040×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#120
commutator, Frattini, cosocleC2×C42C23×C131
prime radicalC22×D4×C131D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1992×C131C2semidirect
4. #1836×C131C2semidirect
5. C2×#330×C131C2semidirect
7. #1295×C131C2semidirect
206. #10426C131direct (N × H)
207. C131#10426direct (N × H)
209. #1992C2×C131semidirect
211. #1836C2×C131semidirect
212. C2×#330C2×C131semidirect
214. #1295C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2820×C1312
#1992×C1312
#1959×C1312
#1836×C1312
C2×#330×C1312
C2×#329×C1312
#1295×C1312
#10426131