Finite Group Databasebeta

← C131×#7764 #45693648

Subgroups — C131×#7764 #45693648

Order 33536.

504 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#2683×C131C211yesmaximal, characteristic
2#2057×C131C211yesmaximal, characteristic, complemented
3#2043×C131C211yesmaximal, characteristic, complemented
4#2023×C131C211yesmaximal, characteristic
5#1271×C131C211yesmaximal, characteristic, complemented
6#1271×C131C211yesmaximal, characteristic, complemented
7#1270×C131C211yesmaximal, characteristic
8C2×C4⋊Q8×C131C2211yescharacteristic
9C2×C22⋊Q8×C131—21no—
10C2×C22⋊Q8×C131—21no—
11C2×#107×C131—21no—
12C2×#103×C131—21no—
13C2×#103×C131—21no—
14C2×#102×C131—21no—
15#396×C131—21no—
16#396×C131—21no—
17#395×C131—21no—
18#390×C131C2211yescharacteristic
19#389×C131C2211yescharacteristic
20#389×C131C2211yescharacteristic
21#386×C131—21no—
22#340×C131—21no—
23#340×C131—21no—
24#336×C131C2211yescharacteristic
25#336×C131C2211yescharacteristic
26#336×C131C2211yescharacteristic
27C22×Q8×C131—21no—
28C22×Q8×C131—21no—
29C22×D4×C131D411yescharacteristic
30C23×C4×C131—21no—
31C22×C8×C131—21no—
32C22×C8×C131—21no—
33C22×C8×C131—21no—
34C4⋊Q8×C131—42no—
35C22⋊Q8×C131—42no—
36C22⋊Q8×C131—42no—
37C22⋊Q8×C131—42no—
38C22⋊Q8×C131—42no—
39C2×C4⋊C4×C131—21no—
40C2×C4⋊C4×C131—21no—
41C2×C4⋊C4×C131—21no—
42C2×C4⋊C4×C131—21no—
43C2×C4⋊C4×C131—21no—
44C2×C4⋊C4×C131—21no—
45C2×C4⋊C4×C131D411yescharacteristic
46C2×C4⋊C4×C131D411yescharacteristic
47C2×C4⋊C4×C131D411yescharacteristic
48C2×C4⋊C4×C131D411yescharacteristic
49C2×C4⋊C4×C131D411yescharacteristic
50C2×C22⋊C4×C131—21no—
51C2×C22⋊C4×C131—21no—
52C2×C22⋊C4×C131—21no—
53C2×C22⋊C4×C131—21no—
54C2×C22⋊C4×C131—21no—
55C2×C42×C131C2311yescharacteristic
56#107×C131—42no—
57#103×C131—42no—
58#103×C131—42no—
59#102×C131—42no—
60#95×C131—21no—
61#95×C131—21no—
62#95×C131—21no—
63C24×C131—21no—
64C2×Q8×C131—22no—
65C2×Q8×C131—42no—
66C2×Q8×C131—42no—
67C2×Q8×C131—41no—
68C2×Q8×C131—41no—
69C2×Q8×C131—41no—
70C2×Q8×C131—41no—
71C2×Q8×C131—41no—
72C2×Q8×C131—81no—
73C2×D4×C131—21no—
74C2×D4×C131—41no—
75C2×D4×C131—41no—
76C2×D4×C131Q1612yes—
77C22×C4×C131—21no—
78C22×C4×C131—21no—
79C22×C4×C131—21no—
80C22×C4×C131—21no—
81C22×C4×C131—21no—
82C22×C4×C131—42no—
83C22×C4×C131—42no—
84C22×C4×C131—41no—
85C22×C4×C131—81no—
86C22×C4×C131C2×D411yescharacteristic
87C22×C4×C131C2×D411yescharacteristic
88C22×C4×C131C2×D411yescharacteristic
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—41no—
96C2×C8×C131—41no—
97C2×C8×C131—41no—
98C4⋊C4×C131—21no—
99C4⋊C4×C131—21no—
100C4⋊C4×C131—22no—
101C4⋊C4×C131—22no—
102C4⋊C4×C131—41no—
103C4⋊C4×C131—41no—
104C4⋊C4×C131—41no—
105C4⋊C4×C131—42no—
106C4⋊C4×C131—42no—
107C4⋊C4×C131—41no—
108C4⋊C4×C131—41no—
109C4⋊C4×C131—41no—
110C4⋊C4×C131—41no—
111C4⋊C4×C131—41no—
112C4⋊C4×C131—41no—
113C4⋊C4×C131D812yes—
114C4⋊C4×C131SD1612yes—
115C22⋊C4×C131—42no—
116C22⋊C4×C131—42no—
117C22⋊C4×C131—41no—
118C22⋊C4×C131—41no—
119C22⋊C4×C131—41no—
120C22⋊C4×C131—41no—
121C22⋊C4×C131—81no—
122C42×C131—41no—
123C23×C131—22no—
124C23×C131—41no—
125C23×C131—41no—
126C23×C131—41no—
127C23×C131—41no—
128C23×C131—41no—
129C23×C131—41no—
130C23×C131#12011yescharacteristic
131Q8×C131—42no—
132Q8×C131—42no—
133Q8×C131—81no—
134Q8×C131—81no—
135Q8×C131—84no—
136D4×C131—42no—
137D4×C131—81no—
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—22no—
145C2×C4×C131—22no—
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—42no—
160C2×C4×C131—84no—
161C2×C4×C131—81no—
162C2×C4×C131—81no—
163C2×C4×C131C2×D811yescharacteristic
164C2×C4×C131C2×SD1611yescharacteristic
165C2×C4×C131C2×Q1611yescharacteristic
166C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C131#13711yescharacteristic
169C8×C131—42no—
170C8×C131—81no—
171C8×C131—81no—
172C22×C131—42no—
173C22×C131—42no—
174C22×C131—42no—
175C22×C131—81no—
176C22×C131—81no—
177C22×C131—81no—
178C22×C131—81no—
179C22×C131#44711yescharacteristic
180C22×C131#45011yescharacteristic
181C22×C131#45111yescharacteristic
182C22×C131#45411yescharacteristic
183C22×C131#45511yescharacteristic
184C22×C131#45611yescharacteristic
185C22×C131B(4,𝔽2)11yescharacteristic
186C4×C131—21no—
187C4×C131—21no—
188C4×C131—21no—
189C4×C131—21no—
190C4×C131—21no—
191C4×C131—21no—
192C4×C131—42no—
193C4×C131—42no—
194C4×C131—81no—
195C4×C131—82no—
196C4×C131—81no—
197C4×C131—81no—
198C2×C131—82no—
199C2×C131#159811yescharacteristic
200C2×C131#160211yescharacteristic
201C2×C131#160411yescharacteristic
202C2×C131#163711yescharacteristic
203C2×C131#163911yescharacteristic
204C2×C131#164911yescharacteristic
205C2×C131#166411yescharacteristic
206#7764C13111yesmaximal, characteristic, direct product factor, Sylow
207C131#776411yescharacteristic, direct product factor, Sylow
208#2683C2×C13111yescharacteristic
209#2057C2×C13111yescharacteristic, complemented
210#2043C2×C13111yescharacteristic, complemented
211#2023C2×C13111yescharacteristic
212#1271C2×C13111yescharacteristic, complemented
213#1271C2×C13111yescharacteristic, complemented
214#1270C2×C13111yescharacteristic
215C2×C4⋊Q8C22×C13111yescharacteristic
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×#107—21no—
219C2×#103—21no—
220C2×#103—21no—
221C2×#102—21no—
222#396—21no—
223#396—21no—
224#395—21no—
225#390C22×C13111yescharacteristic
226#389C22×C13111yescharacteristic
227#389C22×C13111yescharacteristic
228#386—21no—
229#340—21no—
230#340—21no—
231#336C22×C13111yescharacteristic
232#336C22×C13111yescharacteristic
233#336C22×C13111yescharacteristic
234C22×Q8—21no—
235C22×Q8—21no—
236C22×D4D4×C13111yescharacteristic
237C23×C4—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C4⋊Q8—42no—
242C22⋊Q8—42no—
243C22⋊Q8—42no—
244C22⋊Q8—42no—
245C22⋊Q8—42no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4D4×C13111yescharacteristic
253C2×C4⋊C4D4×C13111yescharacteristic
254C2×C4⋊C4D4×C13111yescharacteristic
255C2×C4⋊C4D4×C13111yescharacteristic
256C2×C4⋊C4D4×C13111yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C42C23×C13111yescharacteristic
263#107—42no—
264#103—42no—
265#103—42no—
266#102—42no—
267#95—21no—
268#95—21no—
269#95—21no—
270C24—21no—
271C2×Q8—22no—
272C2×Q8—42no—
273C2×Q8—42no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—81no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4Q16×C13112yes—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—81no—
293C22×C4C2×D4×C13111yescharacteristic
294C22×C4C2×D4×C13111yescharacteristic
295C22×C4C2×D4×C13111yescharacteristic
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4D8×C13112yes—
321C4⋊C4SD16×C13112yes—
322C22⋊C4—42no—
323C22⋊C4—42no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—81no—
329C42—41no—
330C23—22no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23#120×C13111yescharacteristic
338Q8—42no—
339Q8—42no—
340Q8—81no—
341Q8—81no—
342Q8—84no—
343D4—42no—
344D4—81no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
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—42no—
367C2×C4—84no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4C2×D8×C13111yescharacteristic
371C2×C4C2×SD16×C13111yescharacteristic
372C2×C4C2×Q16×C13111yescharacteristic
373C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
374C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
375C2×C4#137×C13111yescharacteristic
376C8—42no—
377C8—81no—
378C8—81no—
379C22—42no—
380C22—42no—
381C22—42no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22#447×C13111yescharacteristic
387C22#450×C13111yescharacteristic
388C22#451×C13111yescharacteristic
389C22#454×C13111yescharacteristic
390C22#455×C13111yescharacteristic
391C22#456×C13111yescharacteristic
392C22B(4,𝔽2)×C13111yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—42no—
400C4—42no—
401C4—81no—
402C4—82no—
403C4—81no—
404C4—81no—
405C2—82no—
406C2#1598×C13111yescharacteristic
407C2#1602×C13111yescharacteristic
408C2#1604×C13111yescharacteristic
409C2#1637×C13111yescharacteristic
410C2#1639×C13111yescharacteristic
411C2#1649×C13111yescharacteristic
412C2#1664×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#120
commutator, Frattini, cosocleC2×C42C23×C131
prime radicalC22×D4×C131D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2057×C131C2semidirect
3. #2043×C131C2semidirect
5. #1271×C131C2semidirect
6. #1271×C131C2semidirect
206. #7764C131direct (N × H)
207. C131#7764direct (N × H)
209. #2057C2×C131semidirect
210. #2043C2×C131semidirect
212. #1271C2×C131semidirect
213. #1271C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2683×C1312
#2057×C1312
#2043×C1312
#2023×C1312
#1271×C1312
#1270×C1312
#7764131