Finite Group Databasebeta

← C131×#29627 #45715511

Subgroups — C131×#29627 #45715511

Order 33536.

1326 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊Q8×C131C211yesmaximal, characteristic
2C2×#451×C131C212yesmaximal
3#2855×C131C211yesmaximal, characteristic
4#2043×C131C214yesmaximal, complemented
5#2016×C131C214yesmaximal, complemented
6#1817×C131C211yesmaximal, characteristic
7#1787×C131C212yesmaximal
8C23×Q8×C131C2212yes—
9C22×Q16×C131C2214yes—
10C2×C4⋊Q8×C131—28no—
11C2×C4⋊Q8×C131—22no—
12C2×C4⋊Q8×C131C2214yes—
13C2×C22⋊Q8×C131C2211yescharacteristic
14C22×C4⋊C4×C131—21no—
15C22×C4⋊C4×C131—21no—
16C22×C42×C131C2211yescharacteristic
17#451×C131—28no—
18C2×#103×C131C2214yes—
19C2×#103×C131C2218yes—
20C2×C22⋊C8×C131C2212yes—
21#391×C131C2212yes—
22#389×C131C2212yes—
23#387×C131—22no—
24#385×C131—21no—
25#381×C131—21no—
26#380×C131C2211yescharacteristic
27#336×C131C2214yes—
28C22×Q8×C131—24no—
29C22×Q8×C131—22no—
30C22×Q8×C131—48no—
31C22×Q8×C131D418yes—
32C22×Q8×C131C2311yescharacteristic
33C22×Q8×C131C2314yes—
34C23×C4×C131—22no—
35C23×C4×C131D411yescharacteristic
36C23×C4×C131D411yescharacteristic
37C23×C4×C131C2311yescharacteristic
38C2×Q16×C131—28no—
39C2×Q16×C131—48no—
40C22×C8×C131C2314yes—
41C4⋊Q8×C131—216no—
42C4⋊Q8×C131—216no—
43C22⋊Q8×C131—24no—
44C2×C4⋊C4×C131—28no—
45C2×C4⋊C4×C131—28no—
46C2×C4⋊C4×C131—24no—
47C2×C4⋊C4×C131—24no—
48C2×C4⋊C4×C131—22no—
49C2×C4⋊C4×C131—21no—
50C2×C4⋊C4×C131C2311yescharacteristic
51C2×C4⋊C4×C131C2312yes—
52C2×C22⋊C4×C131—21no—
53C2×C22⋊C4×C131—21no—
54C2×C42×C131—24no—
55C2×C42×C131D412yes—
56C2×C42×C131C2312yes—
57#103×C131—28no—
58#103×C131—48no—
59C22⋊C8×C131—24no—
60#95×C131—22no—
61#95×C131—22no—
62#95×C131—22no—
63#95×C131—21no—
64C24×C131C2×D411yescharacteristic
65C2×Q8×C131—28no—
66C2×Q8×C131—24no—
67C2×Q8×C131—22no—
68C2×Q8×C131—28no—
69C2×Q8×C131—28no—
70C2×Q8×C131—24no—
71C2×Q8×C131—416no—
72C2×Q8×C131—48no—
73C2×Q8×C131—416no—
74C2×Q8×C131C2×D418yes—
75C22×C4×C131—22no—
76C22×C4×C131—22no—
77C22×C4×C131—22no—
78C22×C4×C131—24no—
79C22×C4×C131—24no—
80C22×C4×C131—28no—
81C22×C4×C131—24no—
82C22×C4×C131—22no—
83C22×C4×C131—21no—
84C22×C4×C131—21no—
85C22×C4×C131—48no—
86C22×C4×C131Q1614yescomplemented
87C22×C4×C131C2×D411yescharacteristic
88C22×C4×C131C2×D414yes—
89C22×C4×C131C2×D412yes—
90C22×C4×C131C2×D412yes—
91C22×C4×C131C2411yescharacteristic
92Q16×C131—416no—
93C2×C8×C131—24no—
94C2×C8×C131—28no—
95C4⋊C4×C131—216no—
96C4⋊C4×C131—216no—
97C4⋊C4×C131—22no—
98C4⋊C4×C131—24no—
99C4⋊C4×C131—42no—
100C4⋊C4×C131—44no—
101C22⋊C4×C131—42no—
102C22⋊C4×C131—42no—
103C42×C131—24no—
104C42×C131—24no—
105C23×C131—22no—
106C23×C131—22no—
107C23×C131#12012yes—
108C23×C131C2×Q1612yes—
109C23×C131#13712yes—
110C23×C131C22×D411yescharacteristic
111Q8×C131—28no—
112Q8×C131—28no—
113Q8×C131—416no—
114Q8×C131—48no—
115Q8×C131—44no—
116C2×C4×C131—28no—
117C2×C4×C131—22no—
118C2×C4×C131—22no—
119C2×C4×C131—22no—
120C2×C4×C131—22no—
121C2×C4×C131—22no—
122C2×C4×C131—28no—
123C2×C4×C131—28no—
124C2×C4×C131—28no—
125C2×C4×C131—416no—
126C2×C4×C131—48no—
127C2×C4×C131—41no—
128C2×C4×C131—41no—
129C2×C4×C131—42no—
130C2×C4×C131—42no—
131C2×C4×C131—42no—
132C2×C4×C131—42no—
133C2×C4×C131—42no—
134C2×C4×C131#12012yes—
135C2×C4×C131C2×Q1614yes—
136C2×C4×C131#13714yes—
137C2×C4×C131C22×D412yes—
138C2×C4×C131H(5,𝔽2)14yes—
139C8×C131—44no—
140C22×C131—22no—
141C22×C131—24no—
142C22×C131—24no—
143C22×C131—22no—
144C22×C131#45114yes—
145C22×C131C2×#12011yescharacteristic
146C22×C131#53512yes—
147C22×C131C22×Q1611yescharacteristic
148C22×C131C2×#13712yes—
149C22×C131C2×#13711yescharacteristic
150C4×C131—22no—
151C4×C131—24no—
152C4×C131—24no—
153C4×C131—48no—
154C4×C131—81no—
155C4×C131—82no—
156C4×C131—81no—
157C4×C131#53414yes—
158C2×C131—24no—
159C2×C131#261311yescharacteristic
160C2×C131C2×#45111yescharacteristic
161C2×C131#300411yescharacteristic
162C2×C131#320912yes—
163C2×C131#321812yes—
164#29627C13111yesmaximal, characteristic, direct product factor, Sylow
165C131#2962711yescharacteristic, direct product factor, Sylow
166C22×C4⋊Q8C2×C13111yescharacteristic
167C2×#451C2×C13112yes—
168#2855C2×C13111yescharacteristic
169#2043C2×C13114yescomplemented
170#2016C2×C13114yescomplemented
171#1817C2×C13111yescharacteristic
172#1787C2×C13112yes—
173C23×Q8C22×C13112yes—
174C22×Q16C22×C13114yes—
175C2×C4⋊Q8—28no—
176C2×C4⋊Q8—22no—
177C2×C4⋊Q8C22×C13114yes—
178C2×C22⋊Q8C22×C13111yescharacteristic
179C22×C4⋊C4—21no—
180C22×C4⋊C4—21no—
181C22×C42C22×C13111yescharacteristic
182#451—28no—
183C2×#103C22×C13114yes—
184C2×#103C22×C13118yes—
185C2×C22⋊C8C22×C13112yes—
186#391C22×C13112yes—
187#389C22×C13112yes—
188#387—22no—
189#385—21no—
190#381—21no—
191#380C22×C13111yescharacteristic
192#336C22×C13114yes—
193C22×Q8—24no—
194C22×Q8—22no—
195C22×Q8—48no—
196C22×Q8D4×C13118yes—
197C22×Q8C23×C13111yescharacteristic
198C22×Q8C23×C13114yes—
199C23×C4—22no—
200C23×C4D4×C13111yescharacteristic
201C23×C4D4×C13111yescharacteristic
202C23×C4C23×C13111yescharacteristic
203C2×Q16—28no—
204C2×Q16—48no—
205C22×C8C23×C13114yes—
206C4⋊Q8—216no—
207C4⋊Q8—216no—
208C22⋊Q8—24no—
209C2×C4⋊C4—28no—
210C2×C4⋊C4—28no—
211C2×C4⋊C4—24no—
212C2×C4⋊C4—24no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4C23×C13111yescharacteristic
216C2×C4⋊C4C23×C13112yes—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C42—24no—
220C2×C42D4×C13112yes—
221C2×C42C23×C13112yes—
222#103—28no—
223#103—48no—
224C22⋊C8—24no—
225#95—21no—
226#95—22no—
227#95—22no—
228#95—22no—
229C24C2×D4×C13111yescharacteristic
230C2×Q8—28no—
231C2×Q8—24no—
232C2×Q8—22no—
233C2×Q8—28no—
234C2×Q8—28no—
235C2×Q8—24no—
236C2×Q8—416no—
237C2×Q8—48no—
238C2×Q8—416no—
239C2×Q8C2×D4×C13118yes—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—28no—
246C22×C4—24no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—48no—
251C22×C4Q16×C13114yescomplemented
252C22×C4C2×D4×C13111yescharacteristic
253C22×C4C2×D4×C13114yes—
254C22×C4C2×D4×C13112yes—
255C22×C4C2×D4×C13112yes—
256C22×C4C24×C13111yescharacteristic
257Q16—416no—
258C2×C8—24no—
259C2×C8—28no—
260C4⋊C4—216no—
261C4⋊C4—216no—
262C4⋊C4—22no—
263C4⋊C4—24no—
264C4⋊C4—42no—
265C4⋊C4—44no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C42—24no—
269C42—24no—
270C23—22no—
271C23—22no—
272C23#120×C13112yes—
273C23C2×Q16×C13112yes—
274C23#137×C13112yes—
275C23C22×D4×C13111yescharacteristic
276Q8—28no—
277Q8—28no—
278Q8—416no—
279Q8—48no—
280Q8—44no—
281C2×C4—28no—
282C2×C4—28no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—28no—
289C2×C4—28no—
290C2×C4—416no—
291C2×C4—48no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4#120×C13112yes—
300C2×C4C2×Q16×C13114yes—
301C2×C4#137×C13114yes—
302C2×C4C22×D4×C13112yes—
303C2×C4H(5,𝔽2)×C13114yes—
304C8—44no—
305C22—22no—
306C22—22no—
307C22—24no—
308C22—24no—
309C22#451×C13114yes—
310C22C2×#120×C13111yescharacteristic
311C22#535×C13112yes—
312C22C22×Q16×C13111yescharacteristic
313C22C2×#137×C13111yescharacteristic
314C22C2×#137×C13112yes—
315C4—24no—
316C4—24no—
317C4—22no—
318C4—48no—
319C4—81no—
320C4—81no—
321C4—82no—
322C4#534×C13114yes—
323C2—24no—
324C2#2613×C13111yescharacteristic
325C2C2×#451×C13111yescharacteristic
326C2#3004×C13111yescharacteristic
327C2#3209×C13112yes—
328C2#3218×C13112yes—
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC24×C131C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
4. #2043×C131C2semidirect
5. #2016×C131C2semidirect
86. C22×C4×C131Q16semidirect
164. #29627C131direct (N × H)
165. C131#29627direct (N × H)
169. #2043C2×C131semidirect
170. #2016C2×C131semidirect
251. C22×C4Q16×C131semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊Q8×C1312
C2×#451×C1312
#2855×C1312
#2043×C1312
#2016×C1312
#1817×C1312
#1787×C1312
#29627131