Finite Group Databasebeta

← C131×#11372 #45697256

Subgroups — C131×#11372 #45697256

Order 33536.

798 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#382×C131C211yesmaximal, characteristic
2C2×#340×C131C212yesmaximal
3C2×#340×C131C212yesmaximal
4C2×#336×C131C211yesmaximal, characteristic
5C4⋊#95×C131C211yesmaximal, characteristic
6C23×C8×C131C2212yes—
7C22×C4⋊C4×C131C2211yescharacteristic
8C22×C4⋊C4×C131C2211yescharacteristic
9C22×C4⋊C4×C131C2212yes—
10C22×C42×C131C2211yescharacteristic
11#382×C131—22no—
12#382×C131C414yescomplemented
13C2×#95×C131—22no—
14C2×#95×C131—22no—
15#340×C131—24no—
16#340×C131—24no—
17#336×C131—22no—
18C23×C4×C131—21no—
19C23×C4×C131—21no—
20C23×C4×C131—22no—
21C23×C4×C131D412yes—
22C23×C4×C131C2311yescharacteristic
23C22×C8×C131—22no—
24C22×C8×C131—22no—
25C22×C8×C131—22no—
26C22×C8×C131—22no—
27C22×C8×C131—22no—
28C22×C8×C131—22no—
29C22×C8×C131D414yes—
30C2×C4⋊C4×C131—22no—
31C2×C4⋊C4×C131—22no—
32C2×C4⋊C4×C131—22no—
33C2×C4⋊C4×C131—22no—
34C2×C4⋊C4×C131—22no—
35C2×C4⋊C4×C131—22no—
36C2×C4⋊C4×C131—22no—
37C2×C4⋊C4×C131—22no—
38C2×C4⋊C4×C131—21no—
39C2×C4⋊C4×C131—21no—
40C2×C4⋊C4×C131—22no—
41C2×C4⋊C4×C131C2×C412yes—
42C2×C4⋊C4×C131C2×C412yes—
43C2×C4⋊C4×C131Q814yes—
44C2×C42×C131—22no—
45C2×C42×C131—22no—
46C2×C42×C131C2×C412yes—
47C2×C42×C131D412yes—
48#95×C131—28no—
49#95×C131—44no—
50C24×C131C2×D411yescharacteristic
51C22×C4×C131—24no—
52C22×C4×C131—24no—
53C22×C4×C131—22no—
54C22×C4×C131—22no—
55C22×C4×C131—22no—
56C22×C4×C131—22no—
57C22×C4×C131—24no—
58C22×C4×C131—42no—
59C22×C4×C131—41no—
60C22×C4×C131—41no—
61C22×C4×C131—41no—
62C22×C4×C131—41no—
63C22×C4×C131—42no—
64C22×C4×C131—44no—
65C22×C4×C131—44no—
66C22×C4×C131—44no—
67C22×C4×C131—42no—
68C22×C4×C131—42no—
69C22×C4×C131C22⋊C414yes—
70C22×C4×C131C22×C411yescharacteristic
71C22×C4×C131C2×D412yes—
72C22×C4×C131C2×D411yescharacteristic
73C22×C4×C131C2×Q812yes—
74C22×C4×C131#4112yes—
75C22×C4×C131#4112yes—
76C22×C4×C131#4112yes—
77C22×C4×C131#4112yes—
78C2×C8×C131—24no—
79C2×C8×C131—24no—
80C2×C8×C131—24no—
81C2×C8×C131—42no—
82C2×C8×C131—42no—
83C2×C8×C131—42no—
84C2×C8×C131—42no—
85C4⋊C4×C131—24no—
86C4⋊C4×C131—24no—
87C4⋊C4×C131—24no—
88C4⋊C4×C131—24no—
89C4⋊C4×C131—42no—
90C4⋊C4×C131—42no—
91C4⋊C4×C131—42no—
92C4⋊C4×C131—42no—
93C42×C131—22no—
94C42×C131—22no—
95C42×C131—24no—
96C23×C131C2×C22⋊C411yescharacteristic
97C23×C131C22⋊Q812yes—
98C23×C131#12312yes—
99C23×C131#12411yescharacteristic
100C23×C131#12711yescharacteristic
101C23×C131#13514yes—
102C23×C131AGL(1,ℤ/8)12yes—
103C23×C131#13712yes—
104C2×C4×C131—24no—
105C2×C4×C131—24no—
106C2×C4×C131—24no—
107C2×C4×C131—44no—
108C2×C4×C131—44no—
109C2×C4×C131—42no—
110C2×C4×C131—42no—
111C2×C4×C131—44no—
112C2×C4×C131—44no—
113C2×C4×C131—44no—
114C2×C4×C131—48no—
115C2×C4×C131—84no—
116C2×C4×C131—82no—
117C2×C4×C131—82no—
118C2×C4×C131—82no—
119C2×C4×C131—82no—
120C2×C4×C131—82no—
121C2×C4×C131—81no—
122C2×C4×C131—81no—
123C2×C4×C131#11711yescharacteristic
124C2×C4×C131#11711yescharacteristic
125C2×C4×C131C4×D412yes—
126C2×C4×C131C4×Q812yes—
127C2×C4×C131#12112yes—
128C2×C4×C131C22⋊Q812yes—
129C2×C4×C131C22⋊Q812yes—
130C2×C4×C131#12312yes—
131C2×C4×C131#12312yes—
132C2×C4×C131#12312yes—
133C2×C4×C131#12411yescharacteristic
134C2×C4×C131#12512yes—
135C2×C4×C131#12512yes—
136C2×C4×C131#12612yes—
137C2×C4×C131#12612yes—
138C2×C4×C131C4⋊Q811yescharacteristic
139C8×C131—44no—
140C22×C131#38111yescharacteristic
141C22×C131#39011yescharacteristic
142C22×C131#39111yescharacteristic
143C22×C131#39912yes—
144C22×C131#40012yes—
145C22×C131#41612yes—
146C22×C131#41712yes—
147C22×C131#47814yes—
148C22×C131#47914yes—
149C22×C131#48214yes—
150C22×C131#48514yes—
151C22×C131#48812yes—
152C22×C131#48912yes—
153C22×C131#49512yes—
154C22×C131#49611yescharacteristic
155C22×C131#49711yescharacteristic
156C4×C131—44no—
157C4×C131—84no—
158C4×C131—82no—
159C4×C131—82no—
160C4×C131#38712yes—
161C4×C131#38712yes—
162C4×C131#39712yes—
163C4×C131#39812yes—
164C2×C131#144511yescharacteristic
165C2×C131#182512yes—
166C2×C131#195811yescharacteristic
167C2×C131#195911yescharacteristic
168C2×C131#198912yes—
169C2×C131#209212yes—
170C2×C131#209712yes—
171C2×C131#210114yes—
172#11372C13111yesmaximal, characteristic, direct product factor, Sylow
173C131#1137211yescharacteristic, direct product factor, Sylow
174C2×#382C2×C13111yescharacteristic
175C2×#340C2×C13112yes—
176C2×#340C2×C13112yes—
177C2×#336C2×C13111yescharacteristic
178C4⋊#95C2×C13111yescharacteristic
179C23×C8C22×C13112yes—
180C22×C4⋊C4C22×C13111yescharacteristic
181C22×C4⋊C4C22×C13111yescharacteristic
182C22×C4⋊C4C22×C13112yes—
183C22×C42C22×C13111yescharacteristic
184#382—22no—
185#382C4×C13114yescomplemented
186C2×#95—22no—
187C2×#95—22no—
188#340—24no—
189#340—24no—
190#336—22no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—22no—
194C23×C4D4×C13112yes—
195C23×C4C23×C13111yescharacteristic
196C22×C8—22no—
197C22×C8—22no—
198C22×C8—22no—
199C22×C8—22no—
200C22×C8—22no—
201C22×C8—22no—
202C22×C8D4×C13114yes—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4C2×C4×C13112yes—
215C2×C4⋊C4C2×C4×C13112yes—
216C2×C4⋊C4Q8×C13114yes—
217C2×C42—22no—
218C2×C42—22no—
219C2×C42C2×C4×C13112yes—
220C2×C42D4×C13112yes—
221#95—28no—
222#95—44no—
223C24C2×D4×C13111yescharacteristic
224C22×C4—24no—
225C22×C4—24no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—24no—
231C22×C4—42no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—42no—
237C22×C4—44no—
238C22×C4—44no—
239C22×C4—44no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4C22⋊C4×C13114yes—
243C22×C4C22×C4×C13111yescharacteristic
244C22×C4C2×D4×C13112yes—
245C22×C4C2×D4×C13111yescharacteristic
246C22×C4C2×Q8×C13112yes—
247C22×C4#41×C13112yes—
248C22×C4#41×C13112yes—
249C22×C4#41×C13112yes—
250C22×C4#41×C13112yes—
251C2×C8—24no—
252C2×C8—24no—
253C2×C8—24no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C4⋊C4—24no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—24no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C42—22no—
267C42—22no—
268C42—24no—
269C23C2×C22⋊C4×C13111yescharacteristic
270C23C22⋊Q8×C13112yes—
271C23#123×C13112yes—
272C23#124×C13111yescharacteristic
273C23#127×C13111yescharacteristic
274C23#135×C13114yes—
275C23AGL(1,ℤ/8)×C13112yes—
276C23#137×C13112yes—
277C2×C4—24no—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—48no—
288C2×C4—84no—
289C2×C4—82no—
290C2×C4—82no—
291C2×C4—82no—
292C2×C4—82no—
293C2×C4—82no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4#117×C13111yescharacteristic
297C2×C4#117×C13111yescharacteristic
298C2×C4C4×D4×C13112yes—
299C2×C4C4×Q8×C13112yes—
300C2×C4#121×C13112yes—
301C2×C4C22⋊Q8×C13112yes—
302C2×C4C22⋊Q8×C13112yes—
303C2×C4#123×C13112yes—
304C2×C4#123×C13112yes—
305C2×C4#123×C13112yes—
306C2×C4#124×C13111yescharacteristic
307C2×C4#125×C13112yes—
308C2×C4#125×C13112yes—
309C2×C4#126×C13112yes—
310C2×C4#126×C13112yes—
311C2×C4C4⋊Q8×C13111yescharacteristic
312C8—44no—
313C22#381×C13111yescharacteristic
314C22#390×C13111yescharacteristic
315C22#391×C13111yescharacteristic
316C22#399×C13112yes—
317C22#400×C13112yes—
318C22#416×C13112yes—
319C22#417×C13112yes—
320C22#478×C13114yes—
321C22#479×C13114yes—
322C22#482×C13114yes—
323C22#485×C13114yes—
324C22#488×C13112yes—
325C22#489×C13112yes—
326C22#495×C13112yes—
327C22#496×C13111yescharacteristic
328C22#497×C13111yescharacteristic
329C4—44no—
330C4—84no—
331C4—82no—
332C4—82no—
333C4#387×C13112yes—
334C4#387×C13112yes—
335C4#397×C13112yes—
336C4#398×C13112yes—
337C2#1445×C13111yescharacteristic
338C2#1825×C13112yes—
339C2#1958×C13111yescharacteristic
340C2#1959×C13111yescharacteristic
341C2#1989×C13112yes—
342C2#2092×C13112yes—
343C2#2097×C13112yes—
344C2#2101×C13114yes—
subgroupG/H
center, socle, prime radicalC24×C131C2×D4
commutatorC22×C4C22×C4×C131
Frattini, cosocleC23×C4C23×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C131 ◁ C22×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
12. #382×C131C4semidirect
172. #11372C131direct (N × H)
173. C131#11372direct (N × H)
185. #382C4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#382×C1312
C2×#340×C1312
C2×#336×C1312
C4⋊#95×C1312
#11372131