Finite Group Databasebeta

← #16828734

Subgroups — #16828734

Order 3712.

758 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 165 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×#11745304C211yesmaximal, characteristic, complemented
2C2×#11745294C211yesmaximal, characteristic, complemented
3#14271674C211yesmaximal, characteristic, complemented
4#14271325C214yesmaximal, complemented
5#14271308C214yesmaximal, complemented
6#14271172C211yesmaximal, characteristic, complemented
7#14271168C211yesmaximal, characteristic, complemented
8#14271127C211yesmaximal, characteristic, complemented
9C22×#41×C29C211yesmaximal, characteristic, complemented
10C2×#41×C29—24no—
11C2×#41×C29—24no—
12C2×#41×C29—22no—
13C2×#41×C29C2214yes—
14C22×Q8×C29C2211yescharacteristic
15C22×D4×C29—21no—
16C22×D4×C29C2211yescharacteristic
17C23×C4×C29—21no—
18C23×C4×C29C2211yescharacteristic
19C2×#90805C2211yescharacteristic
20#11745315—21no—
21C2×#90785C2212yescomplemented
22#11745304—24no—
23C2×#90784C2212yescomplemented
24C2×#90783C2212yescomplemented
25#11745294—24no—
26C2×#90782C2212yescomplemented
27#11745292C2212yescomplemented
28#11745291—21no—
29C4×C22⋊D29—22no—
30#11745288C2211yescharacteristic
31#11745286C2212yescomplemented
32C2×#90777C2211yescharacteristic
33C2×#90777C2211yescharacteristic
34#11745183C2214yescomplemented
35#11745180C2214yescomplemented
36C22⋊#6597C2214yescomplemented
37C24×C29—21no—
38C24×C29D411yescharacteristic
39#41×C29—216no—
40#41×C29—28no—
41#41×C29—28no—
42C2×Q8×C29—22no—
43C2×Q8×C29—21no—
44C2×Q8×C29D414yescomplemented
45C2×Q8×C29C2312yes—
46C2×D4×C29—28no—
47C2×D4×C29—24no—
48C2×D4×C29—21no—
49C2×D4×C29—22no—
50C2×D4×C29D414yescomplemented
51C2×D4×C29C2312yes—
52C22×C4×C29—28no—
53C22×C4×C29—21no—
54C22×C4×C29—24no—
55C22×C4×C29—22no—
56C22×C4×C29—22no—
57C22×C4×C29D412yes—
58C22×C4×C29D411yescharacteristic
59C22×C4×C29C2312yes—
60C22×C4×C29C2311yescharacteristic
61C2×C22⋊D29—22no—
62C2×C22⋊D29—21no—
63#90805—22no—
64#90805—22no—
65C2×D116C2311yescharacteristic
66C2×C4×D29—21no—
67C2×Dic58C2311yescharacteristic
68C22⋊Dic29—22no—
69C22⋊Dic29—21no—
70#90785—24no—
71#90784—24no—
72#90783—24no—
73#90782—24no—
74#90781—22no—
75C4⋊Dic29C2312yes—
76#90779—22no—
77C4×Dic29—21no—
78#90777—22no—
79#90777—22no—
80C2×#6597C2312yes—
81C2×#6597C2312yes—
82C23×C29—22no—
83C23×C29—24no—
84C23×C29—22no—
85C23×C29—42no—
86C23×C29—44no—
87C23×C29C2×D412yes—
88C23×C29C2×D411yescharacteristic
89C22×D29—21no—
90Q8×C29—24no—
91Q8×C29—22no—
92Q8×C29C2×D414yes—
93D4×C29—216no—
94D4×C29—24no—
95D4×C29—22no—
96D4×C29C2×D414yes—
97C2×C4×C29—216no—
98C2×C4×C29—22no—
99C2×C4×C29—24no—
100C2×C4×C29—22no—
101C2×C4×C29—24no—
102C2×C4×C29—22no—
103C2×C4×C29—22no—
104C2×C4×C29C2×D412yes—
105C2×C4×C29C2×D411yescharacteristic
106C2×C4×C29C2×D412yes—
107C2×C4×C29C2×D412yes—
108C2×C4×C29C2411yescharacteristic
109C22⋊D29—44no—
110C22⋊D29—42no—
111C2×Dic29—22no—
112C2×Dic29—21no—
113D116—21no—
114D116—21no—
115C4×D29—42no—
116Dic58—21no—
117Dic58—21no—
118#6597—22no—
119#6597—22no—
120#3005—291nomaximal, Sylow
121C22×C29—22no—
122C22×C29—22no—
123C22×C29—24no—
124C22×C29—22no—
125C22×C29—22no—
126C22×C29—44no—
127C22×C29—48no—
128C22×C29—44no—
129C22×C29#12012yes—
130C22×C29C22×D411yescharacteristic
131C2×D29—41no—
132C2×D29—42no—
133C4×C29—22no—
134C4×C29—24no—
135C4×C29#12012yes—
136C4×C29C22×D411yescharacteristic
137C4×C29C22×D411yescharacteristic
138Dic29—41no—
139Dic29—42no—
140C22×#41D2911yescharacteristic, complemented
141C2×#137—291no—
142C2×AGL(1,ℤ/8)—291no—
143#525—291no—
144#452—294no—
145#449—294no—
146#419—291no—
147#418—291no—
148#407—291no—
149C2×C29—22no—
150C2×C29—42no—
151C2×C29—44no—
152C2×C29C2×#12011yescharacteristic
153C2×C29#57512yes—
154D29—81no—
155C2×#41—24no—
156C2×#41—24no—
157C2×#41—22no—
158C2×#41—291no—
159C2×#41C2×D2914yes—
160C22×Q8C2×D2911yescharacteristic
161C22×D4—21no—
162C22×D4C2×D2911yescharacteristic
163C23×C4—21no—
164C23×C4C2×D2911yescharacteristic
165#137—584no—
166AGL(1,ℤ/8)—584no—
167C2×Q16—292no—
168C2×SD16—292no—
169C2×SD16—292no—
170C2×D8—292no—
171C2×M16—291no—
172C2×M16—291no—
173#123—581no—
174C22⋊Q8—292no—
175#121—292no—
176#120—581no—
177C4×D4—582no—
178#117—291no—
179#103—294no—
180#102—294no—
181C22⋊C8—294no—
182C29#300511yescharacteristic, complemented, Sylow
183C24—21no—
184C24C22⋊D2911yescharacteristic
185#41—216no—
186#41—28no—
187#41—28no—
188#41—582no—
189#41—582no—
190C2×Q8—22no—
191C2×Q8—21no—
192C2×Q8—291no—
193C2×Q8C22⋊D2914yescomplemented
194C2×Q8C22×D2912yes—
195C2×D4—28no—
196C2×D4—24no—
197C2×D4—21no—
198C2×D4—22no—
199C2×D4—291no—
200C2×D4—582no—
201C2×D4—581no—
202C2×D4C22⋊D2914yescomplemented
203C2×D4C22×D2912yes—
204C22×C4—28no—
205C22×C4—21no—
206C22×C4—24no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—581no—
210C22×C4C22⋊D2912yes—
211C22×C4C22⋊D2911yescharacteristic
212C22×C4C22×D2912yes—
213C22×C4C22×D2911yescharacteristic
214Q16—584no—
215SD16—584no—
216SD16—584no—
217D8—584no—
218M16—582no—
219M16—582no—
220C2×C8—292no—
221C2×C8—292no—
222C4⋊C4—292no—
223C4⋊C4—582no—
224C22⋊C4—581no—
225C22⋊C4—582no—
226C22⋊C4—582no—
227C42—581no—
228C23—22no—
229C23—24no—
230C23—22no—
231C23—42no—
232C23—44no—
233C23—581no—
234C23C2×C22⋊D2912yes—
235C23C2×C22⋊D2911yescharacteristic
236Q8—24no—
237Q8—22no—
238Q8—581no—
239Q8—581no—
240Q8C2×C22⋊D2914yes—
241D4—216no—
242D4—24no—
243D4—22no—
244D4—581no—
245D4—581no—
246D4—1164no—
247D4—1162no—
248D4C2×C22⋊D2914yes—
249C2×C4—216no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—582no—
257C2×C4—581no—
258C2×C4—1162no—
259C2×C4C2×C22⋊D2912yes—
260C2×C4C2×C22⋊D2911yescharacteristic
261C2×C4C2×C22⋊D2912yes—
262C2×C4C2×C22⋊D2912yes—
263C2×C4C23×D2911yescharacteristic
264C8—582no—
265C8—582no—
266C22—22no—
267C22—22no—
268C22—24no—
269C22—22no—
270C22—22no—
271C22—44no—
272C22—48no—
273C22—44no—
274C22—1161no—
275C22—1162no—
276C22#1174531512yes—
277C22C22×C22⋊D2911yescharacteristic
278C4—22no—
279C4—24no—
280C4—1161no—
281C4—1162no—
282C4#1174531512yes—
283C4C22×C22⋊D2911yescharacteristic
284C4C22×C22⋊D2911yescharacteristic
285C2—22no—
286C2—42no—
287C2—44no—
288C2—2321no—
289C2C2×#1174531511yescharacteristic
290C2#1427196112yes—
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC22×#41×C29C2
socleC22×C29C22×D4
hypercenterC22×#41D29
hypocenterC29#3005
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#11745304C2semidirect
2. C2×#11745294C2semidirect
3. #14271674C2semidirect
4. #14271325C2semidirect
5. #14271308C2semidirect
6. #14271172C2semidirect
7. #14271168C2semidirect
8. #14271127C2semidirect
9. C22×#41×C29C2semidirect
21. C2×#90785C22semidirect
23. C2×#90784C22semidirect
24. C2×#90783C22semidirect
26. C2×#90782C22semidirect
27. #11745292C22semidirect
31. #11745286C22semidirect
34. #11745183C22semidirect
35. #11745180C22semidirect
36. C22⋊#6597C22semidirect
44. C2×Q8×C29D4semidirect
50. C2×D4×C29D4semidirect
140. C22×#41D29semidirect
182. C29#3005semidirect
193. C2×Q8C22⋊D29semidirect
202. C2×D4C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117453042
C2×#117452942
#142716742
#142713252
#142713082
#142711722
#142711682
#142711272
C22×#41×C292
#300529