Finite Group Databasebeta

← C22×#353×C131 #45719236

Subgroups — C22×#353×C131 #45719236

Order 33536.

2062 conjugacy classes of subgroups; only the 382 normal subgroups are shown.

normal subgroups only

This group has 2062 conjugacy classes of subgroups — too many to draw. Only its 382 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
1C22×#127×C131C211yesmaximal, characteristic
2C22×#99×C131C212yesmaximal, complemented
3C2×#353×C131C2112yesmaximal, direct product factor
4C23×D4×C131—22no—
5C23×D4×C131C411yescharacteristic, complemented
6C23×D4×C131C2211yescharacteristic
7C2×#127×C131—26no—
8C2×#127×C131C416yescomplemented
9C2×#127×C131C2216yes—
10C22×C22⋊C4×C131—22no—
11C22×C42×C131C411yescharacteristic, complemented
12C2×#99×C131—26no—
13C2×#99×C131C22112yescomplemented
14#353×C131C22116yesdirect product factor
15C25×C131—21no—
16C25×C131D412yes—
17C22×D4×C131—212no—
18C22×D4×C131—212no—
19C22×D4×C131—23no—
20C22×D4×C131—43no—
21C22×D4×C131—41no—
22C22×D4×C131—416no—
23C22×D4×C131—43no—
24C22×D4×C131—41no—
25C22×D4×C131C2×C413yes—
26C22×D4×C131C2×C416yescomplemented
27C22×D4×C131D416yes—
28C22×D4×C131C2313yes—
29C23×C4×C131—21no—
30C23×C4×C131—42no—
31C23×C4×C131C2×C411yescharacteristic
32#127×C131—212no—
33#127×C131—212no—
34#127×C131C2×C4112yescomplemented
35#127×C131C2314yes—
36C2×C22⋊C4×C131—212no—
37C2×C22⋊C4×C131—46no—
38C2×C42×C131—23no—
39C2×C42×C131C2×C416yescomplemented
40#99×C131—212no—
41#99×C131C2318yescomplemented
42C24×C131—22no—
43C24×C131—26no—
44C24×C131—26no—
45C24×C131—48no—
46C24×C131—48no—
47C24×C131—43no—
48C24×C131—41no—
49C24×C131C22⋊C416yes—
50C24×C131C22⋊C411yescharacteristic
51C24×C131C2×D416yes—
52C2×D4×C131—224no—
53C2×D4×C131—28no—
54C2×D4×C131—26no—
55C2×D4×C131—43no—
56C2×D4×C131—43no—
57C2×D4×C131—46no—
58C2×D4×C131—46no—
59C2×D4×C131—43no—
60C2×D4×C131—43no—
61C2×D4×C131—46no—
62C2×D4×C131—46no—
63C2×D4×C131—448no—
64C2×D4×C131—448no—
65C2×D4×C131—46no—
66C2×D4×C131—46no—
67C2×D4×C131C22⋊C416yes—
68C2×D4×C131C22×C413yes—
69C2×D4×C131C22×C414yescomplemented
70C2×D4×C131C2×D416yes—
71C2×D4×C131C2411yescharacteristic
72C22×C4×C131—28no—
73C22×C4×C131—23no—
74C22×C4×C131—21no—
75C22×C4×C131—26no—
76C22×C4×C131—412no—
77C22×C4×C131—88no—
78C22×C4×C131C22⋊C413yes—
79C22×C4×C131C22×C413yes—
80C22⋊C4×C131—28no—
81C22⋊C4×C131—412no—
82C42×C131—26no—
83C42×C131C22×C414yescomplemented
84C23×C131—24no—
85C23×C131—26no—
86C23×C131—26no—
87C23×C131—26no—
88C23×C131—26no—
89C23×C131—24no—
90C23×C131—412no—
91C23×C131—412no—
92C23×C131—424no—
93C23×C131—48no—
94C23×C131—46no—
95C23×C131—46no—
96C23×C131—812no—
97C23×C131—812no—
98C23×C131—84no—
99C23×C131#9913yes—
100C23×C131#9911yescharacteristic
101C23×C131C2×C22⋊C413yes—
102C23×C131C2×C22⋊C416yes—
103C23×C131C22×D412yes—
104D4×C131—46no—
105D4×C131—43no—
106D4×C131—46no—
107D4×C131—41no—
108D4×C131—44no—
109D4×C131—448no—
110D4×C131—416no—
111D4×C131—412no—
112C2×C4×C131—224no—
113C2×C4×C131—24no—
114C2×C4×C131—23no—
115C2×C4×C131—23no—
116C2×C4×C131—23no—
117C2×C4×C131—23no—
118C2×C4×C131—48no—
119C2×C4×C131—824no—
120C2×C4×C131C2×C22⋊C413yes—
121C2×C4×C131C23×C411yescharacteristic
122C22×C131—26no—
123C22×C131—26no—
124C22×C131—22no—
125C22×C131—26no—
126C22×C131—46no—
127C22×C131—42no—
128C22×C131—48no—
129C22×C131—412no—
130C22×C131—412no—
131C22×C131—44no—
132C22×C131—86no—
133C22×C131—86no—
134C22×C131—812no—
135C22×C131—812no—
136C22×C131#35314yesdirect product factor
137C22×C131C2×#9913yes—
138C22×C131C2×#9913yes—
139C22×C131C22×C22⋊C411yescharacteristic
140C4×C131—28no—
141C4×C131—23no—
142C4×C131—21no—
143C4×C131—88no—
144C2×C131—21no—
145C2×C131—23no—
146C2×C131—42no—
147C2×C131—46no—
148C2×C131—84no—
149C2×C131C2×#35316yesdirect product factor
150C2×C131C22×#9911yescharacteristic
151C22×#353C13111yesmaximal, characteristic, direct product factor, Sylow
152C131C22×#35311yescharacteristic, direct product factor, Sylow
153C22×#127C2×C13111yescharacteristic
154C22×#99C2×C13112yescomplemented
155C2×#353C2×C131112yesdirect product factor
156C23×D4—22no—
157C23×D4C4×C13111yescharacteristic, complemented
158C23×D4C22×C13111yescharacteristic
159C2×#127—26no—
160C2×#127C4×C13116yescomplemented
161C2×#127C22×C13116yes—
162C22×C22⋊C4—22no—
163C22×C42C4×C13111yescharacteristic, complemented
164C2×#99—26no—
165C2×#99C22×C131112yescomplemented
166#353C22×C131116yesdirect product factor
167C25—21no—
168C25D4×C13112yes—
169C22×D4—212no—
170C22×D4—212no—
171C22×D4—23no—
172C22×D4—41no—
173C22×D4—43no—
174C22×D4—43no—
175C22×D4—41no—
176C22×D4—416no—
177C22×D4C2×C4×C13113yes—
178C22×D4C2×C4×C13116yescomplemented
179C22×D4D4×C13116yes—
180C22×D4C23×C13113yes—
181C23×C4—21no—
182C23×C4—42no—
183C23×C4C2×C4×C13111yescharacteristic
184#127—212no—
185#127—212no—
186#127C2×C4×C131112yescomplemented
187#127C23×C13114yes—
188C2×C22⋊C4—212no—
189C2×C22⋊C4—46no—
190C2×C42—23no—
191C2×C42C2×C4×C13116yescomplemented
192#99—212no—
193#99C23×C13118yescomplemented
194C24—22no—
195C24—26no—
196C24—26no—
197C24—48no—
198C24—48no—
199C24—43no—
200C24—41no—
201C24C22⋊C4×C13111yescharacteristic
202C24C22⋊C4×C13116yes—
203C24C2×D4×C13116yes—
204C2×D4—224no—
205C2×D4—28no—
206C2×D4—26no—
207C2×D4—43no—
208C2×D4—43no—
209C2×D4—46no—
210C2×D4—46no—
211C2×D4—43no—
212C2×D4—43no—
213C2×D4—46no—
214C2×D4—46no—
215C2×D4—448no—
216C2×D4—448no—
217C2×D4—46no—
218C2×D4—46no—
219C2×D4C22⋊C4×C13116yes—
220C2×D4C22×C4×C13113yes—
221C2×D4C22×C4×C13114yescomplemented
222C2×D4C2×D4×C13116yes—
223C2×D4C24×C13111yescharacteristic
224C22×C4—28no—
225C22×C4—23no—
226C22×C4—21no—
227C22×C4—26no—
228C22×C4—412no—
229C22×C4—88no—
230C22×C4C22⋊C4×C13113yes—
231C22×C4C22×C4×C13113yes—
232C22⋊C4—28no—
233C22⋊C4—412no—
234C42—26no—
235C42C22×C4×C13114yescomplemented
236C23—24no—
237C23—26no—
238C23—26no—
239C23—26no—
240C23—26no—
241C23—24no—
242C23—412no—
243C23—412no—
244C23—424no—
245C23—48no—
246C23—46no—
247C23—46no—
248C23—812no—
249C23—812no—
250C23—84no—
251C23#99×C13113yes—
252C23#99×C13111yescharacteristic
253C23C2×C22⋊C4×C13113yes—
254C23C2×C22⋊C4×C13116yes—
255C23C22×D4×C13112yes—
256D4—46no—
257D4—43no—
258D4—46no—
259D4—41no—
260D4—44no—
261D4—448no—
262D4—416no—
263D4—412no—
264C2×C4—224no—
265C2×C4—23no—
266C2×C4—23no—
267C2×C4—23no—
268C2×C4—23no—
269C2×C4—24no—
270C2×C4—48no—
271C2×C4—824no—
272C2×C4C2×C22⋊C4×C13113yes—
273C2×C4C23×C4×C13111yescharacteristic
274C22—26no—
275C22—26no—
276C22—22no—
277C22—26no—
278C22—46no—
279C22—42no—
280C22—48no—
281C22—412no—
282C22—412no—
283C22—44no—
284C22—86no—
285C22—86no—
286C22—812no—
287C22—812no—
288C22#353×C13114yesdirect product factor
289C22C2×#99×C13113yes—
290C22C2×#99×C13113yes—
291C22C22×C22⋊C4×C13111yescharacteristic
292C4—28no—
293C4—23no—
294C4—21no—
295C4—88no—
296C2—21no—
297C2—23no—
298C2—42no—
299C2—46no—
300C2—84no—
301C2C2×#353×C13116yesdirect product factor
302C2C22×#99×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#99
commutatorC2×C4C23×C4×C131
Frattini, cosocleC2×D4C24×C131
prime radicalC22×#127×C131C2
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C24×C131 ◁ C23×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#99×C131C2semidirect
3. C2×#353×C131C2direct (N × H)
5. C23×D4×C131C4semidirect
8. C2×#127×C131C4semidirect
11. C22×C42×C131C4semidirect
13. C2×#99×C131C22semidirect
14. #353×C131C22direct (N × H)
26. C22×D4×C131C2×C4semidirect
34. #127×C131C2×C4semidirect
39. C2×C42×C131C2×C4semidirect
41. #99×C131C23semidirect
69. C2×D4×C131C22×C4semidirect
83. C42×C131C22×C4semidirect
136. C22×C131#353direct (N × H)
149. C2×C131C2×#353direct (N × H)
151. C22×#353C131direct (N × H)
152. C131C22×#353direct (N × H)
154. C22×#99C2×C131semidirect
155. C2×#353C2×C131direct (N × H)
157. C23×D4C4×C131semidirect
160. C2×#127C4×C131semidirect
163. C22×C42C4×C131semidirect
165. C2×#99C22×C131semidirect
166. #353C22×C131direct (N × H)
178. C22×D4C2×C4×C131semidirect
186. #127C2×C4×C131semidirect
191. C2×C42C2×C4×C131semidirect
193. #99C23×C131semidirect
221. C2×D4C22×C4×C131semidirect
235. C42C22×C4×C131semidirect
288. C22#353×C131direct (N × H)
301. C2C2×#353×C131direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#127×C1312
C22×#99×C1312
C2×#353×C1312
C22×#353131