Finite Group Databasebeta

← C131×#29650 #45715534

Subgroups — C131×#29650 #45715534

Order 33536.

1038 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#544×C131C211yesmaximal, characteristic, complemented
2#3094×C131C212yesmaximal
3#2501×C131C211yesmaximal, characteristic
4#2060×C131C214yesmaximal, complemented
5#2027×C131C214yesmaximal, complemented
6#1826×C131C212yesmaximal, complemented
7#1821×C131C211yesmaximal, characteristic, complemented
8#544×C131—24no—
9#544×C131—22no—
10#544×C131C2214yes—
11C2×C4⋊Q8×C131—22no—
12C2×#125×C131—22no—
13C2×#123×C131—22no—
14C2×C22⋊Q8×C131—22no—
15C2×#121×C131C2211yescharacteristic
16C2×#117×C131C2212yes—
17C22×C4⋊C4×C131C2211yescharacteristic
18#482×C131—24no—
19#481×C131—22no—
20#480×C131—22no—
21#428×C131C2214yes—
22#418×C131C2214yes—
23#407×C131C2212yes—
24#399×C131—22no—
25#390×C131C2212yes—
26#384×C131C2212yes—
27C4×C22⋊C4×C131C2211yescharacteristic
28#343×C131C2214yes—
29#339×C131C2218yes—
30C22×Q8×C131—22no—
31C22×D4×C131—21no—
32C22×D4×C131C2311yescharacteristic
33C23×C4×C131D412yes—
34C23×C4×C131C2311yescharacteristic
35C2×M16×C131C2314yes—
36C4⋊Q8×C131—28no—
37C4⋊Q8×C131—28no—
38#125×C131—28no—
39#125×C131—28no—
40#123×C131—48no—
41C22⋊Q8×C131—28no—
42C22⋊Q8×C131—28no—
43#121×C131—22no—
44#121×C131—22no—
45#117×C131—22no—
46#117×C131—22no—
47#117×C131D414yes—
48#117×C131C2314yes—
49C2×C4⋊C4×C131—22no—
50C2×C4⋊C4×C131—24no—
51C2×C4⋊C4×C131—22no—
52C2×C4⋊C4×C131—22no—
53C2×C4⋊C4×C131—24no—
54C2×C4⋊C4×C131D412yes—
55C2×C4⋊C4×C131D412yes—
56C2×C4⋊C4×C131D412yes—
57C2×C4⋊C4×C131C2311yescharacteristic
58C2×C4⋊C4×C131C2312yes—
59C2×C22⋊C4×C131—22no—
60C2×C22⋊C4×C131—21no—
61C2×C22⋊C4×C131—24no—
62C2×C22⋊C4×C131—21no—
63C2×C42×C131—22no—
64C2×C42×C131C2312yes—
65#107×C131—24no—
66#106×C131—24no—
67#102×C131—24no—
68#102×C131—24no—
69C22⋊C8×C131—22no—
70C22⋊C8×C131—22no—
71#95×C131—21no—
72C24×C131—21no—
73C24×C131C2×D411yescharacteristic
74C2×Q8×C131—28no—
75C2×Q8×C131—84no—
76C2×D4×C131—22no—
77C2×D4×C131—24no—
78C2×D4×C131—44no—
79C2×D4×C131—41no—
80C2×D4×C131—41no—
81C22×C4×C131—24no—
82C22×C4×C131—22no—
83C22×C4×C131—22no—
84C22×C4×C131—22no—
85C22×C4×C131—22no—
86C22×C4×C131—22no—
87C22×C4×C131—21no—
88C22×C4×C131—44no—
89C22×C4×C131C2×D411yescharacteristic
90C22×C4×C131C2×D412yes—
91C22×C4×C131C2×D412yes—
92C22×C4×C131C2×D414yes—
93C22×C4×C131C2411yescharacteristic
94M16×C131—28no—
95C2×C8×C131—24no—
96C4⋊C4×C131—28no—
97C4⋊C4×C131—216no—
98C4⋊C4×C131—24no—
99C4⋊C4×C131—22no—
100C4⋊C4×C131—22no—
101C4⋊C4×C131—24no—
102C4⋊C4×C131—22no—
103C4⋊C4×C131—48no—
104C4⋊C4×C131C2×D414yes—
105C4⋊C4×C131C2×D414yes—
106C22⋊C4×C131—24no—
107C22⋊C4×C131—24no—
108C22⋊C4×C131—24no—
109C22⋊C4×C131—48no—
110C22⋊C4×C131—42no—
111C42×C131—24no—
112C42×C131—24no—
113C42×C131—24no—
114C23×C131—22no—
115C23×C131—22no—
116C23×C131—41no—
117C23×C131—42no—
118C23×C131—42no—
119C23×C131—41no—
120C23×C131—42no—
121C23×C131#12011yescharacteristic
122C23×C131#12011yescharacteristic
123C23×C131C22×D411yescharacteristic
124Q8×C131—88no—
125D4×C131—44no—
126D4×C131—82no—
127D4×C131—82no—
128C2×C4×C131—22no—
129C2×C4×C131—24no—
130C2×C4×C131—24no—
131C2×C4×C131—24no—
132C2×C4×C131—24no—
133C2×C4×C131—24no—
134C2×C4×C131—24no—
135C2×C4×C131—42no—
136C2×C4×C131—44no—
137C2×C4×C131—42no—
138C2×C4×C131—44no—
139C2×C4×C131—44no—
140C2×C4×C131—44no—
141C2×C4×C131—42no—
142C2×C4×C131—41no—
143C2×C4×C131—82no—
144C2×C4×C131#12012yes—
145C2×C4×C131C22×D412yes—
146C2×C4×C1312−1+414yes—
147C8×C131—44no—
148C22×C131—21no—
149C22×C131—21no—
150C22×C131—21no—
151C22×C131—21no—
152C22×C131—21no—
153C22×C131—21no—
154C22×C131—21no—
155C22×C131—44no—
156C22×C131—84no—
157C22×C131—81no—
158C22×C131—81no—
159C22×C131—81no—
160C22×C131#45312yes—
161C22×C131C2×#12011yescharacteristic
162C22×C131#53612yes—
163C4×C131—22no—
164C4×C131—44no—
165C4×C131—44no—
166C4×C131—44no—
167C4×C131—44no—
168C4×C131—81no—
169C4×C131#53614yes—
170C2×C131—22no—
171C2×C131—22no—
172C2×C131—41no—
173C2×C131—161no—
174C2×C131#261411yescharacteristic
175C2×C131C2×#45311yescharacteristic
176C2×C131#302011yescharacteristic
177#29650C13111yesmaximal, characteristic, direct product factor, Sylow
178C131#2965011yescharacteristic, direct product factor, Sylow
179C2×#544C2×C13111yescharacteristic, complemented
180#3094C2×C13112yes—
181#2501C2×C13111yescharacteristic
182#2060C2×C13114yescomplemented
183#2027C2×C13114yescomplemented
184#1826C2×C13112yescomplemented
185#1821C2×C13111yescharacteristic, complemented
186#544—24no—
187#544—22no—
188#544C22×C13114yes—
189C2×C4⋊Q8—22no—
190C2×#125—22no—
191C2×#123—22no—
192C2×C22⋊Q8—22no—
193C2×#121C22×C13111yescharacteristic
194C2×#117C22×C13112yes—
195C22×C4⋊C4C22×C13111yescharacteristic
196#482—24no—
197#481—22no—
198#480—22no—
199#428C22×C13114yes—
200#418C22×C13114yes—
201#407C22×C13112yes—
202#399—22no—
203#390C22×C13112yes—
204#384C22×C13112yes—
205C4×C22⋊C4C22×C13111yescharacteristic
206#343C22×C13114yes—
207#339C22×C13118yes—
208C22×Q8—22no—
209C22×D4—21no—
210C22×D4C23×C13111yescharacteristic
211C23×C4D4×C13112yes—
212C23×C4C23×C13111yescharacteristic
213C2×M16C23×C13114yes—
214C4⋊Q8—28no—
215C4⋊Q8—28no—
216#125—28no—
217#125—28no—
218#123—48no—
219C22⋊Q8—28no—
220C22⋊Q8—28no—
221#121—22no—
222#121—22no—
223#117—22no—
224#117—22no—
225#117D4×C13114yes—
226#117C23×C13114yes—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—24no—
232C2×C4⋊C4D4×C13112yes—
233C2×C4⋊C4D4×C13112yes—
234C2×C4⋊C4D4×C13112yes—
235C2×C4⋊C4C23×C13111yescharacteristic
236C2×C4⋊C4C23×C13112yes—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—24no—
241C2×C42—22no—
242C2×C42C23×C13112yes—
243#107—24no—
244#106—24no—
245#102—24no—
246#102—24no—
247C22⋊C8—22no—
248C22⋊C8—22no—
249#95—21no—
250C24—21no—
251C24C2×D4×C13111yescharacteristic
252C2×Q8—28no—
253C2×Q8—84no—
254C2×D4—22no—
255C2×D4—24no—
256C2×D4—44no—
257C2×D4—41no—
258C2×D4—41no—
259C22×C4—24no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—44no—
267C22×C4C2×D4×C13111yescharacteristic
268C22×C4C2×D4×C13112yes—
269C22×C4C2×D4×C13112yes—
270C22×C4C2×D4×C13114yes—
271C22×C4C24×C13111yescharacteristic
272M16—28no—
273C2×C8—24no—
274C4⋊C4—28no—
275C4⋊C4—216no—
276C4⋊C4—24no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—24no—
280C4⋊C4—22no—
281C4⋊C4—48no—
282C4⋊C4C2×D4×C13114yes—
283C4⋊C4C2×D4×C13114yes—
284C22⋊C4—24no—
285C22⋊C4—24no—
286C22⋊C4—24no—
287C22⋊C4—48no—
288C22⋊C4—42no—
289C42—24no—
290C42—24no—
291C42—24no—
292C23—22no—
293C23—22no—
294C23—41no—
295C23—42no—
296C23—42no—
297C23—41no—
298C23—42no—
299C23#120×C13111yescharacteristic
300C23#120×C13111yescharacteristic
301C23C22×D4×C13111yescharacteristic
302Q8—88no—
303D4—44no—
304D4—82no—
305D4—82no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—42no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—42no—
318C2×C4—44no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—82no—
322C2×C4#120×C13112yes—
323C2×C4C22×D4×C13112yes—
324C2×C42−1+4×C13114yes—
325C8—44no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—44no—
334C22—84no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22#453×C13112yes—
339C22C2×#120×C13111yescharacteristic
340C22#536×C13112yes—
341C4—22no—
342C4—44no—
343C4—44no—
344C4—44no—
345C4—44no—
346C4—81no—
347C4#536×C13114yes—
348C2—22no—
349C2—22no—
350C2—41no—
351C2—161no—
352C2#2614×C13111yescharacteristic
353C2C2×#453×C13111yescharacteristic
354C2#3020×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#121×C131C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#544×C131C2semidirect
4. #2060×C131C2semidirect
5. #2027×C131C2semidirect
6. #1826×C131C2semidirect
7. #1821×C131C2semidirect
177. #29650C131direct (N × H)
178. C131#29650direct (N × H)
179. C2×#544C2×C131semidirect
182. #2060C2×C131semidirect
183. #2027C2×C131semidirect
184. #1826C2×C131semidirect
185. #1821C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#544×C1312
#3094×C1312
#2501×C1312
#2060×C1312
#2027×C1312
#1826×C1312
#1821×C1312
#29650131