Finite Group Databasebeta

← #16829427

Subgroups — #16829427

Order 3712.

462 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#121×D29C211yesmaximal, characteristic
2C2×#11745254C211yesmaximal, characteristic, complemented
3#14271490C212yesmaximal, complemented
4#14271486C212yesmaximal, complemented
5#14271482C211yesmaximal, characteristic, complemented
6#14271479C211yesmaximal, characteristic, complemented
7#14271476C211yesmaximal, characteristic, complemented
8#14271204C212yesmaximal, complemented
9#14271166C212yesmaximal, complemented
10#14271125C211yesmaximal, characteristic, complemented
11C29×#480C211yesmaximal, characteristic, complemented
12C2×D4×D29—21no—
13C2×D4×D29C2211yescharacteristic
14C22×C4×D29C2211yescharacteristic
15C29×#121C2211yescharacteristic
16C2×C4⋊C4×C29C2211yescharacteristic, complemented
17#11745301—21no—
18#11745300C2211yescharacteristic
19#11745292C2211yescharacteristic
20C2×#90781—21no—
21C2×C4⋊Dic29C2211yescharacteristic, complemented
22C2×C4×Dic29—21no—
23C2×#90772C2212yes—
24#11745257C2211yescharacteristic
25#11745254—21no—
26#11745254—21no—
27#11745254C2212yes—
28#11745254C2212yescomplemented
29C4⋊C4×D29C2211yescharacteristic
30#11745246—21no—
31C22⋊C4×D29—21no—
32C29×#107C2212yescomplemented
33C29×#102C2212yescomplemented
34C29×C22⋊C8C2211yescharacteristic, complemented
35#11745180C2212yescomplemented
36C22⋊#6597C2211yescharacteristic, complemented
37#11745169C2212yescomplemented
38#11745168C2212yescomplemented
39#11745165C2212yescomplemented
40#11745157C2212yescomplemented
41#11745156C2212yescomplemented
42#11745155C2212yescomplemented
43C23×D29—21no—
44C23×D29D411yescharacteristic
45C2×D4×C29—21no—
46C2×D4×C29C2311yescharacteristic
47C22×C4×C29—21no—
48C22×C4×C29C2311yescharacteristic
49C2×C22⋊D29—21no—
50C2×C22⋊D29—21no—
51C2×C22⋊D29—21no—
52C22×Dic29—21no—
53C22×Dic29D411yescharacteristic
54D4×D29—24no—
55D4×D29—44no—
56C2×D116—21no—
57C2×D116C2311yescharacteristic
58C2×C4×D29—24no—
59C2×C4×D29—21no—
60C2×C4×D29D411yescharacteristic
61C2×C4×D29D411yescharacteristic
62C2×C4×D29C2311yescharacteristic
63C2×C4×D29C2311yescharacteristic
64C2×C8×C29C2312yes—
65C4⋊C4×C29—21no—
66C4⋊C4×C29C2312yes—
67C4⋊C4×C29C2311yescharacteristic
68C22⋊C4×C29—21no—
69C22⋊Dic29—21no—
70#90781—22no—
71#90781—22no—
72#90781—21no—
73#90781—21no—
74C4⋊Dic29—21no—
75C4⋊Dic29C2312yes—
76C4⋊Dic29C2311yescharacteristic
77#90779—21no—
78C4×Dic29—22no—
79C4×Dic29—22no—
80C2×#6597C2312yes—
81#90772—24no—
82C23×C29—21no—
83C23×C29C2×D411yescharacteristic
84C22×D29—22no—
85C22×D29—22no—
86C22×D29—21no—
87C22×D29—41no—
88C22×D29—42no—
89C22×D29—42no—
90C22×D29—42no—
91C22×D29C2×D411yescharacteristic
92C22×D29C2×D411yescharacteristic
93D4×C29—22no—
94D4×C29—42no—
95C2×C4×C29—22no—
96C2×C4×C29—22no—
97C2×C4×C29—21no—
98C2×C4×C29—42no—
99C2×C4×C29C2×D411yescharacteristic
100C2×C4×C29C2411yescharacteristic
101C22⋊D29—42no—
102C22⋊D29—42no—
103C22⋊D29—42no—
104C2×Dic29—22no—
105C2×Dic29—22no—
106C2×Dic29—21no—
107C2×Dic29—42no—
108C2×Dic29C2×D411yescharacteristic
109C2×Dic29C2×D411yescharacteristic
110D116—22no—
111D116—42no—
112C4×D29—22no—
113C4×D29—22no—
114C4×D29—22no—
115C4×D29—42no—
116C4×D29#4114yes—
117C8×C29—22no—
118#6597—22no—
119#3094—291nomaximal, Sylow
120C22×C29—21no—
121C22×C29—21no—
122C22×C29—41no—
123C22×C29—41no—
124C22×C29—41no—
125C22×C29AGL(1,ℤ/8)12yes—
126C22×C29C22×D411yescharacteristic
127C2×D29—21no—
128C2×D29—21no—
129C2×D29—21no—
130C2×D29—21no—
131C2×D29—21no—
132C2×D29—44no—
133C2×D29—41no—
134C2×D29—41no—
135C2×D29—41no—
136C2×D29—84no—
137C2×D29#12312yes—
138C4×C29—21no—
139C4×C29—41no—
140C4×C29—42no—
141C4×C29C2×#4112yes—
142Dic29—21no—
143Dic29—41no—
144Dic29—42no—
145Dic29#12312yes—
146C2×#121—291no—
147C2×#117—291no—
148#482—292no—
149#482—292no—
150#481—291no—
151#481—291no—
152#480—291no—
153#480D2911yescharacteristic, complemented
154#428—292no—
155#418—292no—
156#407—291no—
157C2×C29—22no—
158C2×C29—81no—
159C2×C29C2×#12311yescharacteristic
160C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
161C2×C29#57511yescharacteristic
162D29—22no—
163D29—41no—
164D29—81no—
165C22×D4—291no—
166C22×D4—581no—
167C23×C4—291no—
168C2×M16—292no—
169#121—291no—
170#121—291no—
171#121—291no—
172#121—581no—
173#121—581no—
174#121C2×D2911yescharacteristic
175#117—292no—
176#117—292no—
177#117—581no—
178#117—581no—
179C2×C4⋊C4—291no—
180C2×C4⋊C4—291no—
181C2×C4⋊C4C2×D2911yescharacteristic, complemented
182C2×C22⋊C4—581no—
183C2×C22⋊C4—581no—
184C2×C42—581no—
185#107—292no—
186#107C2×D2912yescomplemented
187#106—292no—
188#106—292no—
189#102—292no—
190#102—292no—
191#102—292no—
192#102C2×D2912yescomplemented
193C22⋊C8—291no—
194C22⋊C8—292no—
195C22⋊C8C2×D2911yescharacteristic, complemented
196C29#309411yescharacteristic, complemented, Sylow
197C24—291no—
198C24—581no—
199C2×D4—21no—
200C2×D4—291no—
201C2×D4—581no—
202C2×D4—584no—
203C2×D4—581no—
204C2×D4—581no—
205C2×D4—581no—
206C2×D4—1164no—
207C2×D4C22×D2911yescharacteristic
208C22×C4—21no—
209C22×C4—291no—
210C22×C4—291no—
211C22×C4—291no—
212C22×C4—291no—
213C22×C4—291no—
214C22×C4—584no—
215C22×C4—581no—
216C22×C4—581no—
217C22×C4C22×D2911yescharacteristic
218M16—584no—
219C2×C8—292no—
220C2×C8C22×D2912yes—
221C4⋊C4—21no—
222C4⋊C4—292no—
223C4⋊C4—291no—
224C4⋊C4—581no—
225C4⋊C4—581no—
226C4⋊C4C22×D2912yes—
227C4⋊C4C22×D2911yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—581no—
230C22⋊C4—582no—
231C22⋊C4—582no—
232C22⋊C4—581no—
233C22⋊C4—581no—
234C42—582no—
235C42—582no—
236C23—21no—
237C23—291no—
238C23—291no—
239C23—582no—
240C23—582no—
241C23—581no—
242C23—1161no—
243C23—1162no—
244C23—1162no—
245C23—1162no—
246C23D4×D2911yescharacteristic
247D4—22no—
248D4—42no—
249D4—582no—
250D4—1162no—
251D4—1162no—
252D4—1162no—
253D4—1162no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—291no—
259C2×C4—294no—
260C2×C4—291no—
261C2×C4—582no—
262C2×C4—582no—
263C2×C4—582no—
264C2×C4—582no—
265C2×C4—582no—
266C2×C4—581no—
267C2×C4—1162no—
268C2×C4—1162no—
269C2×C4D4×D2911yescharacteristic
270C2×C4C23×D2911yescharacteristic
271C8—22no—
272C8—582no—
273C22—21no—
274C22—21no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—292no—
279C22—581no—
280C22—581no—
281C22—581no—
282C22—581no—
283C22—581no—
284C22—1164no—
285C22—1161no—
286C22—1161no—
287C22—1161no—
288C22—2324no—
289C22#1174527312yes—
290C22C2×D4×D2911yescharacteristic
291C4—21no—
292C4—42no—
293C4—41no—
294C4—292no—
295C4—581no—
296C4—1161no—
297C4—1162no—
298C4#41×D2912yes—
299C2—22no—
300C2—81no—
301C2—582no—
302C2—1161no—
303C2—2321no—
304C2#123×D2911yescharacteristic
305C2C2×#1174527311yescharacteristic
306C2#1427196211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#480C2
socleC22×C29C22×D4
prime radical#121×D29C2
hypercenter#480D29
hypocenterC29#3094
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#11745254C2semidirect
3. #14271490C2semidirect
4. #14271486C2semidirect
5. #14271482C2semidirect
6. #14271479C2semidirect
7. #14271476C2semidirect
8. #14271204C2semidirect
9. #14271166C2semidirect
10. #14271125C2semidirect
11. C29×#480C2semidirect
16. C2×C4⋊C4×C29C22semidirect
21. C2×C4⋊Dic29C22semidirect
28. #11745254C22semidirect
32. C29×#107C22semidirect
33. C29×#102C22semidirect
34. C29×C22⋊C8C22semidirect
35. #11745180C22semidirect
36. C22⋊#6597C22semidirect
37. #11745169C22semidirect
38. #11745168C22semidirect
39. #11745165C22semidirect
40. #11745157C22semidirect
41. #11745156C22semidirect
42. #11745155C22semidirect
153. #480D29semidirect
181. C2×C4⋊C4C2×D29semidirect
186. #107C2×D29semidirect
192. #102C2×D29semidirect
195. C22⋊C8C2×D29semidirect
196. C29#3094semidirect

Maximal subgroups

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

subgroupindex
#121×D292
C2×#117452542
#142714902
#142714862
#142714822
#142714792
#142714762
#142712042
#142711662
#142711252
C29×#4802
#309429