Finite Group Databasebeta

← C131×#8219 #45694103

Subgroups — C131×#8219 #45694103

Order 33536.

720 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊Q8×C131C211yesmaximal, characteristic
2#1749×C131C211yesmaximal, characteristic
3C2×#328×C131C212yesmaximal
4C4×#95×C131C211yesmaximal, characteristic
5#1294×C131C212yesmaximal
6C2×C22⋊Q8×C131C2211yescharacteristic
7C2×C4×Q8×C131C411yescharacteristic, complemented
8C22×C42×C131—21no—
9C22×C42×C131C2211yescharacteristic
10C2×C22⋊C8×C131C2212yes—
11C2×#97×C131—21no—
12#391×C131C411yescharacteristic, complemented
13#389×C131C411yescharacteristic, complemented
14#387×C131—21no—
15#385×C131—21no—
16#380×C131C2211yescharacteristic
17C4×C4⋊C4×C131—21no—
18C4×C4⋊C4×C131C411yescharacteristic, complemented
19C4×C22⋊C4×C131—21no—
20C2×#95×C131—21no—
21C2×#95×C131C2212yes—
22#336×C131—21no—
23#328×C131C418yescomplemented
24C22×Q8×C131C2×C411yescharacteristic
25C23×C4×C131—22no—
26C23×C4×C131D411yescharacteristic
27C23×C4×C131D411yescharacteristic
28C23×C4×C131C2311yescharacteristic
29C22×C8×C131—22no—
30C22⋊Q8×C131—22no—
31C22⋊Q8×C131C2×C414yes—
32C4×Q8×C131—42no—
33C2×C4⋊C4×C131—21no—
34C2×C4⋊C4×C131—21no—
35C2×C4⋊C4×C131—21no—
36C2×C4⋊C4×C131C2×C411yescharacteristic
37C2×C4⋊C4×C131C2×C411yescharacteristic
38C2×C4⋊C4×C131C2×C411yescharacteristic
39C2×C22⋊C4×C131—21no—
40C2×C22⋊C4×C131—21no—
41C2×C42×C131—24no—
42C2×C42×C131—21no—
43C2×C42×C131—21no—
44C2×C42×C131—42no—
45C2×C42×C131—42no—
46C2×C42×C131—42no—
47C2×C42×C131C2×C411yescharacteristic
48C2×C42×C131C2×C411yescharacteristic
49C2×C42×C131D411yescharacteristic
50C2×C42×C131D411yescharacteristic
51C22⋊C8×C131—22no—
52C22⋊C8×C131C2×C414yes—
53#97×C131—42no—
54#95×C131—24no—
55#95×C131—21no—
56#95×C131—21no—
57#95×C131—21no—
58#95×C131—21no—
59#95×C131—21no—
60#95×C131—22no—
61#95×C131C2×C414yes—
62C24×C131C2×D411yescharacteristic
63C2×Q8×C131—21no—
64C2×Q8×C131—41no—
65C2×Q8×C131—41no—
66C2×Q8×C131C4212yescomplemented
67C22×C4×C131—21no—
68C22×C4×C131—21no—
69C22×C4×C131—22no—
70C22×C4×C131—22no—
71C22×C4×C131—24no—
72C22×C4×C131—24no—
73C22×C4×C131—21no—
74C22×C4×C131—21no—
75C22×C4×C131—24no—
76C22×C4×C131—22no—
77C22×C4×C131—22no—
78C22×C4×C131—21no—
79C22×C4×C131—21no—
80C22×C4×C131—41no—
81C22×C4×C131—41no—
82C22×C4×C131—41no—
83C22×C4×C131—42no—
84C22×C4×C131—42no—
85C22×C4×C131—42no—
86C22×C4×C131—42no—
87C22×C4×C131C22⋊C411yescharacteristic
88C22×C4×C131C22⋊C411yescharacteristic
89C22×C4×C131C22⋊C411yescharacteristic
90C22×C4×C131C22⋊C411yescharacteristic
91C22×C4×C131C22×C411yescharacteristic
92C22×C4×C131C22×C412yes—
93C22×C4×C131C2×D411yescharacteristic
94C22×C4×C131#4112yes—
95C2×C8×C131—24no—
96C2×C8×C131—42no—
97C2×C8×C131—42no—
98C4⋊C4×C131—21no—
99C4⋊C4×C131—24no—
100C4⋊C4×C131—41no—
101C4⋊C4×C131—41no—
102C4⋊C4×C131—42no—
103C4⋊C4×C131—42no—
104C4⋊C4×C131C4212yescomplemented
105C22⋊C4×C131—24no—
106C22⋊C4×C131—41no—
107C22⋊C4×C131—41no—
108C42×C131—22no—
109C42×C131—22no—
110C42×C131—41no—
111C42×C131—41no—
112C42×C131—48no—
113C42×C131—42no—
114C42×C131—42no—
115C23×C131—21no—
116C23×C131—21no—
117C23×C131—21no—
118C23×C131—21no—
119C23×C131C2×C22⋊C411yescharacteristic
120C23×C131C4×D412yes—
121C23×C131AGL(1,ℤ/8)11yescharacteristic
122C23×C131#13711yescharacteristic
123C23×C131#13712yes—
124Q8×C131—42no—
125Q8×C131—42no—
126C2×C4×C131—24no—
127C2×C4×C131—24no—
128C2×C4×C131—21no—
129C2×C4×C131—21no—
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—28no—
139C2×C4×C131—22no—
140C2×C4×C131—22no—
141C2×C4×C131—21no—
142C2×C4×C131—21no—
143C2×C4×C131—21no—
144C2×C4×C131—42no—
145C2×C4×C131—42no—
146C2×C4×C131—44no—
147C2×C4×C131—44no—
148C2×C4×C131—44no—
149C2×C4×C131—44no—
150C2×C4×C131—44no—
151C2×C4×C131—44no—
152C2×C4×C131—41no—
153C2×C4×C131—41no—
154C2×C4×C131—41no—
155C2×C4×C131—41no—
156C2×C4×C131—44no—
157C2×C4×C131—41no—
158C2×C4×C131—41no—
159C2×C4×C131—41no—
160C2×C4×C131—41no—
161C2×C4×C131—41no—
162C2×C4×C131—41no—
163C2×C4×C131#9912yes—
164C2×C4×C131#10412yes—
165C2×C4×C131#10412yes—
166C2×C4×C131C2×C4211yescharacteristic
167C2×C4×C131#11711yescharacteristic
168C2×C4×C131C4×D412yes—
169C8×C131—44no—
170C22×C131—22no—
171C22×C131—22no—
172C22×C131—21no—
173C22×C131—21no—
174C22×C131—22no—
175C22×C131—22no—
176C22×C131—21no—
177C22×C131—21no—
178C22×C131C4×C22⋊C411yescharacteristic
179C22×C131C2×#9911yescharacteristic
180C22×C131#41011yescharacteristic
181C22×C131#41711yescharacteristic
182C22×C131#41911yescharacteristic
183C22×C131C2×#10411yescharacteristic
184C22×C131C2×#10411yescharacteristic
185C22×C131#44012yes—
186C22×C131#44112yes—
187C4×C131—22no—
188C4×C131—21no—
189C4×C131—21no—
190C4×C131—22no—
191C4×C131—22no—
192C4×C131—22no—
193C4×C131—48no—
194C4×C131—42no—
195C4×C131—42no—
196C4×C131—41no—
197C4×C131—81no—
198C4×C131—81no—
199C2×C131—22no—
200C2×C131—22no—
201C2×C131#150411yescharacteristic
202C2×C131#150611yescharacteristic
203C2×C131#150811yescharacteristic
204C2×C131#150911yescharacteristic
205C2×C131C4×#9911yescharacteristic
206C2×C131C4×#10411yescharacteristic
207C2×C131#176311yescharacteristic
208#8219C13111yesmaximal, characteristic, direct product factor, Sylow
209C131#821911yescharacteristic, direct product factor, Sylow
210C4×C22⋊Q8C2×C13111yescharacteristic
211#1749C2×C13111yescharacteristic
212C2×#328C2×C13112yes—
213C4×#95C2×C13111yescharacteristic
214#1294C2×C13112yes—
215C2×C22⋊Q8C22×C13111yescharacteristic
216C2×C4×Q8C4×C13111yescharacteristic, complemented
217C22×C42—21no—
218C22×C42C22×C13111yescharacteristic
219C2×C22⋊C8C22×C13112yes—
220C2×#97—21no—
221#391C4×C13111yescharacteristic, complemented
222#389C4×C13111yescharacteristic, complemented
223#387—21no—
224#385—21no—
225#380C22×C13111yescharacteristic
226C4×C4⋊C4—21no—
227C4×C4⋊C4C4×C13111yescharacteristic, complemented
228C4×C22⋊C4—21no—
229C2×#95—21no—
230C2×#95C22×C13112yes—
231#336—21no—
232#328C4×C13118yescomplemented
233C22×Q8C2×C4×C13111yescharacteristic
234C23×C4—22no—
235C23×C4D4×C13111yescharacteristic
236C23×C4D4×C13111yescharacteristic
237C23×C4C23×C13111yescharacteristic
238C22×C8—22no—
239C22⋊Q8—22no—
240C22⋊Q8C2×C4×C13114yes—
241C4×Q8—42no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4C2×C4×C13111yescharacteristic
246C2×C4⋊C4C2×C4×C13111yescharacteristic
247C2×C4⋊C4C2×C4×C13111yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C42—24no—
251C2×C42—21no—
252C2×C42—21no—
253C2×C42—42no—
254C2×C42—42no—
255C2×C42—42no—
256C2×C42C2×C4×C13111yescharacteristic
257C2×C42C2×C4×C13111yescharacteristic
258C2×C42D4×C13111yescharacteristic
259C2×C42D4×C13111yescharacteristic
260C22⋊C8—22no—
261C22⋊C8C2×C4×C13114yes—
262#97—42no—
263#95—24no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268#95—21no—
269#95—22no—
270#95C2×C4×C13114yes—
271C24C2×D4×C13111yescharacteristic
272C2×Q8—21no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8C42×C13112yescomplemented
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4C22⋊C4×C13111yescharacteristic
297C22×C4C22⋊C4×C13111yescharacteristic
298C22×C4C22⋊C4×C13111yescharacteristic
299C22×C4C22⋊C4×C13111yescharacteristic
300C22×C4C22×C4×C13111yescharacteristic
301C22×C4C22×C4×C13112yes—
302C22×C4C2×D4×C13111yescharacteristic
303C22×C4#41×C13112yes—
304C2×C8—24no—
305C2×C8—42no—
306C2×C8—42no—
307C4⋊C4—21no—
308C4⋊C4—24no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4C42×C13112yescomplemented
314C22⋊C4—24no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C42—22no—
318C42—22no—
319C42—41no—
320C42—41no—
321C42—48no—
322C42—42no—
323C42—42no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23C2×C22⋊C4×C13111yescharacteristic
329C23C4×D4×C13112yes—
330C23AGL(1,ℤ/8)×C13111yescharacteristic
331C23#137×C13111yescharacteristic
332C23#137×C13112yes—
333Q8—42no—
334Q8—42no—
335C2×C4—24no—
336C2×C4—24no—
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—28no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—44no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—44no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4#99×C13112yes—
373C2×C4#104×C13112yes—
374C2×C4#104×C13112yes—
375C2×C4C2×C42×C13111yescharacteristic
376C2×C4#117×C13111yescharacteristic
377C2×C4C4×D4×C13112yes—
378C8—44no—
379C22—22no—
380C22—22no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—22no—
385C22—21no—
386C22—21no—
387C22C4×C22⋊C4×C13111yescharacteristic
388C22C2×#99×C13111yescharacteristic
389C22#410×C13111yescharacteristic
390C22#417×C13111yescharacteristic
391C22#419×C13111yescharacteristic
392C22C2×#104×C13111yescharacteristic
393C22C2×#104×C13111yescharacteristic
394C22#440×C13112yes—
395C22#441×C13112yes—
396C4—22no—
397C4—21no—
398C4—21no—
399C4—22no—
400C4—22no—
401C4—22no—
402C4—48no—
403C4—42no—
404C4—42no—
405C4—41no—
406C4—81no—
407C4—81no—
408C2—22no—
409C2—22no—
410C2#1504×C13111yescharacteristic
411C2#1506×C13111yescharacteristic
412C2#1508×C13111yescharacteristic
413C2#1509×C13111yescharacteristic
414C2C4×#99×C13111yescharacteristic
415C2C4×#104×C13111yescharacteristic
416C2#1763×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C2×C22⋊C4
commutatorC2×C4C2×C42×C131
Frattini, cosocleC23×C4C23×C131
prime radicalC24×C131C2×D4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
7. C2×C4×Q8×C131C4semidirect
12. #391×C131C4semidirect
13. #389×C131C4semidirect
18. C4×C4⋊C4×C131C4semidirect
23. #328×C131C4semidirect
66. C2×Q8×C131C42semidirect
104. C4⋊C4×C131C42semidirect
208. #8219C131direct (N × H)
209. C131#8219direct (N × H)
216. C2×C4×Q8C4×C131semidirect
221. #391C4×C131semidirect
222. #389C4×C131semidirect
227. C4×C4⋊C4C4×C131semidirect
232. #328C4×C131semidirect
275. C2×Q8C42×C131semidirect
313. C4⋊C4C42×C131semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊Q8×C1312
#1749×C1312
C2×#328×C1312
C4×#95×C1312
#1294×C1312
#8219131