Finite Group Databasebeta

← C131×#32899 #45718783

Subgroups — C131×#32899 #45718783

Order 33536.

3866 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 3866 conjugacy classes of subgroups — too many to draw. Only its 366 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#585×C131C211yesmaximal, characteristic, complemented
2C2×B(4,𝔽2)×C131C214yesmaximal, complemented
3#2404×C131C213yesmaximal, complemented
4#1790×C131C214yesmaximal, complemented
5#1782×C131C213yesmaximal, complemented
6#585×C131—216no—
7C2×2−1+4×C131—23no—
8C2×H(5,𝔽2)×C131—23no—
9C2×H(5,𝔽2)×C131C2214yes—
10C22×#41×C131—26no—
11C22×#41×C131C2213yes—
12C2×#120×C131C2216yescomplemented
13C22×C22⋊C4×C131C2211yescharacteristic, complemented
14B(4,𝔽2)×C131—216no—
15C2×#99×C131C22112yescomplemented
16#393×C131—23no—
17#392×C131—23no—
18#386×C131—26no—
19#386×C131C2216yescomplemented
20#381×C131C2213yescomplemented
21C25×C131C2311yescharacteristic
222−1+4×C131—248no—
23H(5,𝔽2)×C131—248no—
24H(5,𝔽2)×C131—224no—
25H(5,𝔽2)×C131D4116yescomplemented
26C2×#41×C131—24no—
27C2×#41×C131—212no—
28C2×#41×C131—248no—
29C2×#41×C131—248no—
30C2×#41×C131—224no—
31C2×#41×C131—26no—
32C2×#41×C131—212no—
33C2×#41×C131—26no—
34C22×Q8×C131—26no—
35C22×Q8×C131D413yescomplemented
36C22×D4×C131—26no—
37C22×D4×C131—212no—
38C22×D4×C131—26no—
39C22×D4×C131D413yescomplemented
40C22×D4×C131C2316yes—
41C23×C4×C131—24no—
42C23×C4×C131D416yescomplemented
43C23×C4×C131C2311yescharacteristic
44C23×C4×C131C2311yescharacteristic
45#120×C131—224no—
46C2×C22⋊C4×C131—23no—
47C2×C22⋊C4×C131—26no—
48C2×C22⋊C4×C131—23no—
49C2×C22⋊C4×C131—26no—
50C2×C22⋊C4×C131C2316yes—
51#99×C131—224no—
52#95×C131—23no—
53#95×C131—26no—
54#95×C131—23no—
55C24×C131—24no—
56C24×C131—23no—
57C24×C131—24no—
58C24×C131—42no—
59C24×C131—81no—
60C24×C131C2×D416yes—
61C24×C131C2411yescharacteristic
62#41×C131—232no—
63#41×C131—248no—
64#41×C131—296no—
65#41×C131—248no—
66#41×C131—248no—
67#41×C131—248no—
68C2×Q8×C131—24no—
69C2×Q8×C131—248no—
70C2×Q8×C131—26no—
71C2×Q8×C131—212no—
72C2×D4×C131—212no—
73C2×D4×C131—248no—
74C2×D4×C131—248no—
75C2×D4×C131—248no—
76C2×D4×C131—212no—
77C2×D4×C131—212no—
78C2×D4×C131—212no—
79C2×D4×C131—26no—
80C2×D4×C131—412no—
81C2×D4×C131—412no—
82C2×D4×C131—86no—
83C2×D4×C131C2×D4124yes—
84C22×C4×C131—212no—
85C22×C4×C131—232no—
86C22×C4×C131—212no—
87C22×C4×C131—24no—
88C22×C4×C131—26no—
89C22×C4×C131—26no—
90C22×C4×C131—212no—
91C22×C4×C131—26no—
92C22×C4×C131—23no—
93C22×C4×C131—81no—
94C22×C4×C131C2×D413yes—
95C22×C4×C131C2×D416yes—
96C22×C4×C131C2×D413yes—
97C22⋊C4×C131—212no—
98C22⋊C4×C131—41no—
99C22⋊C4×C131—43no—
100C22⋊C4×C131—412no—
101C22⋊C4×C131—86no—
102C23×C131—216no—
103C23×C131—26no—
104C23×C131—26no—
105C23×C131—26no—
106C23×C131—41no—
107C23×C131—41no—
108C23×C131—46no—
109C23×C131—46no—
110C23×C131—46no—
111C23×C131—43no—
112C23×C131—46no—
113C23×C131—41no—
114C23×C131—88no—
115C23×C131—84no—
116C23×C131—84no—
117C23×C131#120112yes—
118C23×C131C22×D413yes—
119C23×C131C22×D414yes—
120Q8×C131—216no—
121Q8×C131—224no—
122D4×C131—248no—
123D4×C131—224no—
124D4×C131—248no—
125D4×C131—824no—
126C2×C4×C131—224no—
127C2×C4×C131—248no—
128C2×C4×C131—224no—
129C2×C4×C131—26no—
130C2×C4×C131—26no—
131C2×C4×C131—26no—
132C2×C4×C131—26no—
133C2×C4×C131—46no—
134C2×C4×C131—46no—
135C2×C4×C131—46no—
136C2×C4×C131—46no—
137C2×C4×C131—41no—
138C2×C4×C131#120112yes—
139C2×C4×C131#12011yescharacteristic
140C2×C4×C131#12013yes—
141C22×C131—23no—
142C22×C131—23no—
143C22×C131—212no—
144C22×C131—44no—
145C22×C131—412no—
146C22×C131—412no—
147C22×C131—46no—
148C22×C131—46no—
149C22×C131—42no—
150C22×C131—86no—
151C22×C131—86no—
152C22×C131—816no—
153C22×C131—81no—
154C22×C131—81no—
155C22×C131C2×#12016yes—
156C22×C131C2×#12011yescharacteristic
157C4×C131—21no—
158C4×C131—212no—
159C4×C131—23no—
160C4×C131—86no—
161C4×C131—81no—
162C2×C131—26no—
163C2×C131—412no—
164C2×C131—82no—
165C2×C131#284611yescharacteristic
166C2×C131#302511yescharacteristic
167C2×C131#302711yescharacteristic
168#32899C13111yesmaximal, characteristic, direct product factor, Sylow
169C131#3289911yescharacteristic, direct product factor, Sylow
170C2×#585C2×C13111yescharacteristic, complemented
171C2×B(4,𝔽2)C2×C13114yescomplemented
172#2404C2×C13113yescomplemented
173#1790C2×C13114yescomplemented
174#1782C2×C13113yescomplemented
175#585—216no—
176C2×2−1+4—23no—
177C2×H(5,𝔽2)—23no—
178C2×H(5,𝔽2)C22×C13114yes—
179C22×#41—26no—
180C22×#41C22×C13113yes—
181C2×#120C22×C13116yescomplemented
182C22×C22⋊C4C22×C13111yescharacteristic, complemented
183B(4,𝔽2)—216no—
184C2×#99C22×C131112yescomplemented
185#393—23no—
186#392—23no—
187#386—26no—
188#386C22×C13116yescomplemented
189#381C22×C13113yescomplemented
190C25C23×C13111yescharacteristic
1912−1+4—248no—
192H(5,𝔽2)—248no—
193H(5,𝔽2)—224no—
194H(5,𝔽2)D4×C131116yescomplemented
195C2×#41—24no—
196C2×#41—212no—
197C2×#41—248no—
198C2×#41—248no—
199C2×#41—224no—
200C2×#41—26no—
201C2×#41—212no—
202C2×#41—26no—
203C22×Q8—26no—
204C22×Q8D4×C13113yescomplemented
205C22×D4—26no—
206C22×D4—212no—
207C22×D4—26no—
208C22×D4D4×C13113yescomplemented
209C22×D4C23×C13116yes—
210C23×C4—24no—
211C23×C4D4×C13116yescomplemented
212C23×C4C23×C13111yescharacteristic
213C23×C4C23×C13111yescharacteristic
214#120—224no—
215C2×C22⋊C4—23no—
216C2×C22⋊C4—23no—
217C2×C22⋊C4—26no—
218C2×C22⋊C4—26no—
219C2×C22⋊C4C23×C13116yes—
220#99—224no—
221#95—23no—
222#95—23no—
223#95—26no—
224C24—24no—
225C24—23no—
226C24—24no—
227C24—42no—
228C24—81no—
229C24C2×D4×C13116yes—
230C24C24×C13111yescharacteristic
231#41—232no—
232#41—248no—
233#41—296no—
234#41—248no—
235#41—248no—
236#41—248no—
237C2×Q8—24no—
238C2×Q8—248no—
239C2×Q8—26no—
240C2×Q8—212no—
241C2×D4—212no—
242C2×D4—248no—
243C2×D4—248no—
244C2×D4—248no—
245C2×D4—212no—
246C2×D4—212no—
247C2×D4—212no—
248C2×D4—26no—
249C2×D4—412no—
250C2×D4—412no—
251C2×D4—86no—
252C2×D4C2×D4×C131124yes—
253C22×C4—212no—
254C22×C4—232no—
255C22×C4—212no—
256C22×C4—24no—
257C22×C4—26no—
258C22×C4—26no—
259C22×C4—212no—
260C22×C4—26no—
261C22×C4—23no—
262C22×C4—81no—
263C22×C4C2×D4×C13113yes—
264C22×C4C2×D4×C13116yes—
265C22×C4C2×D4×C13113yes—
266C22⋊C4—212no—
267C22⋊C4—41no—
268C22⋊C4—43no—
269C22⋊C4—412no—
270C22⋊C4—86no—
271C23—216no—
272C23—26no—
273C23—26no—
274C23—26no—
275C23—41no—
276C23—41no—
277C23—46no—
278C23—46no—
279C23—46no—
280C23—43no—
281C23—41no—
282C23—46no—
283C23—88no—
284C23—84no—
285C23—84no—
286C23#120×C131112yes—
287C23C22×D4×C13113yes—
288C23C22×D4×C13114yes—
289Q8—216no—
290Q8—224no—
291D4—248no—
292D4—224no—
293D4—248no—
294D4—824no—
295C2×C4—224no—
296C2×C4—248no—
297C2×C4—224no—
298C2×C4—26no—
299C2×C4—26no—
300C2×C4—26no—
301C2×C4—26no—
302C2×C4—46no—
303C2×C4—46no—
304C2×C4—46no—
305C2×C4—46no—
306C2×C4—41no—
307C2×C4#120×C13111yescharacteristic
308C2×C4#120×C13113yes—
309C2×C4#120×C131112yes—
310C22—23no—
311C22—23no—
312C22—212no—
313C22—44no—
314C22—412no—
315C22—412no—
316C22—46no—
317C22—46no—
318C22—42no—
319C22—86no—
320C22—86no—
321C22—816no—
322C22—81no—
323C22—81no—
324C22C2×#120×C13116yes—
325C22C2×#120×C13111yescharacteristic
326C4—21no—
327C4—212no—
328C4—23no—
329C4—86no—
330C4—81no—
331C2—26no—
332C2—412no—
333C2—82no—
334C2#2846×C13111yescharacteristic
335C2#3025×C13111yescharacteristic
336C2#3027×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC24C24×C131
LCSG ▷ C24 ▷ 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×#585×C131C2semidirect
2. C2×B(4,𝔽2)×C131C2semidirect
3. #2404×C131C2semidirect
4. #1790×C131C2semidirect
5. #1782×C131C2semidirect
12. C2×#120×C131C22semidirect
13. C22×C22⋊C4×C131C22semidirect
15. C2×#99×C131C22semidirect
19. #386×C131C22semidirect
20. #381×C131C22semidirect
25. H(5,𝔽2)×C131D4semidirect
35. C22×Q8×C131D4semidirect
39. C22×D4×C131D4semidirect
42. C23×C4×C131D4semidirect
168. #32899C131direct (N × H)
169. C131#32899direct (N × H)
170. C2×#585C2×C131semidirect
171. C2×B(4,𝔽2)C2×C131semidirect
172. #2404C2×C131semidirect
173. #1790C2×C131semidirect
174. #1782C2×C131semidirect
181. C2×#120C22×C131semidirect
182. C22×C22⋊C4C22×C131semidirect
184. C2×#99C22×C131semidirect
188. #386C22×C131semidirect
189. #381C22×C131semidirect
194. H(5,𝔽2)D4×C131semidirect
204. C22×Q8D4×C131semidirect
208. C22×D4D4×C131semidirect
211. C23×C4D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#585×C1312
C2×B(4,𝔽2)×C1312
#2404×C1312
#1790×C1312
#1782×C1312
#32899131